Subgroups — C₂₃×#61590 #19209216

Order 5888.

2182 conjugacy classes of subgroups.

The subgroup lattice has 1252 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3519	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×#41×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3333	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#3331	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#3329	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#3326	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3325	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#3322	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3278	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3275	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3274	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3274	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3273	C₂	1	2	yes	maximal, complemented
14	C₂₃×#3272	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3212	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#3207	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#3197	C₂	1	2	yes	maximal, complemented
18	C₂₃×#3194	C₂	1	2	yes	maximal, complemented
19	C₂₃×#3106	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂₃×#3006	C₂	1	2	yes	maximal, complemented
22	C₂₃×#3005	C₂	1	2	yes	maximal, complemented
23	C₂₃×#2975	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₂₃	C₂²	1	2	yes	complemented
25	C₂×C₂₃×#137	C₂²	1	2	yes	complemented
26	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
27	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
28	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
29	C₂₃×#555	C₂²	1	1	yes	characteristic
30	C₂₃×#554	C₂²	1	1	yes	characteristic, complemented
31	C₂₃×#553	—	2	1	no	—
32	C₂₃×#553	C₂²	1	2	yes	complemented
33	C₂₃×#550	C₂²	1	1	yes	characteristic
34	C₂₃×#550	C₂²	1	1	yes	characteristic
35	D₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
36	C₂₃×#548	C₂²	1	2	yes	complemented
37	C₂₃×#547	—	2	1	no	—
38	C₂₃×#547	C₂²	1	1	yes	characteristic
39	C₂₃×#546	—	2	2	no	—
40	C₂₃×#546	—	2	2	no	—
41	C₂₃×#546	C₂²	1	2	yes	complemented
42	C₂₃×#546	C₂²	1	2	yes	complemented
43	D₄²×C₂₃	—	2	1	no	—
44	D₄²×C₂₃	—	2	1	no	—
45	D₄²×C₂₃	C₂²	1	1	yes	characteristic, complemented
46	D₄²×C₂₃	C₂²	1	1	yes	characteristic, complemented
47	C₂₃×#540	—	2	1	no	—
48	C₂₃×#538	—	2	2	no	—
49	C₂₃×#532	—	2	1	no	—
50	C₂₃×#532	C₂²	1	1	yes	characteristic, complemented
51	C₂₃×#532	C₂²	1	1	yes	characteristic, complemented
52	C₂₃×#529	C₂²	1	1	yes	characteristic, complemented
53	C₂₃×#525	—	2	2	no	—
54	C₂₃×#525	C₂²	1	2	yes	complemented
55	C₂₃×#525	C₂²	1	2	yes	complemented
56	C₂×C₂₃×#121	C₂²	1	2	yes	complemented
57	C₂₃×#518	—	2	1	no	—
58	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic, complemented
59	C₂×C₄×D₄×C₂₃	—	2	1	no	—
60	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
61	C₂₃×#495	C₂²	1	2	yes	complemented
62	C₂₃×#493	C₂²	1	1	yes	characteristic, complemented
63	C₂₃×#492	C₂²	1	1	yes	characteristic, complemented
64	C₂₃×#488	C₂²	1	2	yes	complemented
65	C₂₃×#487	C₂²	1	1	yes	characteristic, complemented
66	C₂₃×#486	C₂²	1	1	yes	characteristic, complemented
67	C₂₃×#485	C₂²	1	1	yes	characteristic, complemented
68	C₂₃×#485	C₂²	1	2	yes	complemented
69	C₂₃×#483	C₂²	1	2	yes	complemented
70	C₂₃×#482	C₂²	1	1	yes	characteristic, complemented
71	C₂₃×#482	C₂²	1	2	yes	complemented
72	C₂₃×#482	C₂²	1	2	yes	complemented
73	C₂₃×#480	C₂²	1	2	yes	complemented
74	C₂₃×#479	C₂²	1	1	yes	characteristic, complemented
75	C₂₃×#478	C₂²	1	1	yes	characteristic, complemented
76	C₂₃×#477	C₂²	1	1	yes	characteristic, complemented
77	C₂₃×#476	C₂²	1	1	yes	characteristic, complemented
78	C₂₃×#470	C₂²	1	2	yes	complemented
79	C₂₃×#469	C₂²	1	2	yes	complemented
80	C₂₃×#469	C₂²	1	2	yes	complemented
81	C₂₃×#469	C₂²	1	2	yes	complemented
82	C₂₃×#468	C₂²	1	2	yes	complemented
83	C₂₃×#468	C₂²	1	2	yes	complemented
84	C₂₃×#468	C₂²	1	2	yes	complemented
85	C₂₃×#468	C₂²	1	2	yes	complemented
86	C₂₃×#464	C₂²	1	1	yes	characteristic, complemented
87	C₂₃×#463	C₂²	1	2	yes	complemented
88	C₂₃×#463	C₂²	1	2	yes	complemented
89	C₂₃×#463	C₂²	1	1	yes	characteristic, complemented
90	C₂₃×#462	C₂²	1	1	yes	characteristic, complemented
91	C₂₃×#461	C₂²	1	1	yes	characteristic, complemented
92	C₂₃×#460	C₂²	1	1	yes	characteristic, complemented
93	C₂₃×#460	C₂²	1	1	yes	characteristic, complemented
94	C₂₃×#459	C₂²	1	1	yes	characteristic, complemented
95	C₂₃×#459	C₂²	1	1	yes	characteristic, complemented
96	C₂₃×#452	C₂²	1	2	yes	complemented
97	C₂₃×#452	C₂²	1	2	yes	complemented
98	C₂₃×#452	C₂²	1	1	yes	characteristic, complemented
99	C₂₃×#452	C₂²	1	2	yes	complemented
100	C₂₃×#452	C₂²	1	2	yes	complemented
101	C₂₃×#450	C₂²	1	2	yes	complemented
102	C₂₃×#449	C₂²	1	1	yes	characteristic
103	C₂₃×#449	C₂²	1	2	yes	complemented
104	C₂₃×#449	C₂²	1	2	yes	complemented
105	C₂₃×#449	C₂²	1	2	yes	complemented
106	C₂₃×#449	C₂²	1	2	yes	complemented
107	C₂₃×#449	C₂²	1	2	yes	complemented
108	C₂₃×#449	C₂²	1	2	yes	complemented
109	C₂₃×#449	C₂²	1	2	yes	complemented
110	C₂₃×#448	C₂²	1	2	yes	complemented
111	C₂₃×#448	C₂²	1	2	yes	complemented
112	C₂₃×#447	C₂²	1	2	yes	complemented
113	C₂₃×#447	C₂²	1	2	yes	complemented
114	C₂₃×#447	C₂²	1	2	yes	complemented
115	C₄×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
116	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
117	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
118	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
119	C₄×D₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
120	C₄×D₈×C₂₃	C₂²	1	2	yes	complemented
121	C₂₃×#436	C₂²	1	1	yes	characteristic, complemented
122	C₂₃×#436	C₂²	1	2	yes	complemented
123	C₂₃×#436	C₂²	1	1	yes	characteristic, complemented
124	C₂₃×#436	C₂²	1	1	yes	characteristic, complemented
125	C₂₃×#436	C₂²	1	2	yes	complemented
126	C₂₃×#436	C₂²	1	1	yes	characteristic, complemented
127	C₂₃×#431	C₂²	1	1	yes	characteristic, complemented
128	C₂₃×#431	C₂²	1	1	yes	characteristic, complemented
129	C₂₃×#419	C₂²	1	2	yes	complemented
130	C₂₃×#418	C₂²	1	2	yes	complemented
131	C₂₃×#417	C₂²	1	2	yes	complemented
132	C₂₃×#417	C₂²	1	2	yes	complemented
133	C₂₃×#407	C₂²	1	2	yes	complemented
134	C₂₃×#407	C₂²	1	2	yes	complemented
135	C₂×#41×C₂₃	—	2	2	no	—
136	C₂×#41×C₂₃	—	2	2	no	—
137	C₂×#41×C₂₃	—	2	1	no	—
138	C₂×#41×C₂₃	—	4	4	no	—
139	C₂×#41×C₂₃	—	4	4	no	—
140	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
141	C₂×#41×C₂₃	C₂³	1	2	yes	—
142	C₂×#41×C₂₃	C₂³	1	2	yes	—
143	C₂×#41×C₂₃	C₂³	1	2	yes	—
144	C₂×#41×C₂₃	C₂³	1	2	yes	—
145	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
146	C₂²×D₄×C₂₃	—	2	2	no	—
147	C₂²×D₄×C₂₃	—	2	2	no	—
148	C₂²×D₄×C₂₃	—	2	1	no	—
149	C₂²×D₄×C₂₃	—	2	1	no	—
150	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
151	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
152	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
153	C₂³×C₄×C₂₃	—	2	2	no	—
154	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
155	C₂₃×#137	—	4	4	no	—
156	C₂₃×AGL(1,ℤ/8)	—	4	4	no	—
157	C₂₃×AGL(1,ℤ/8)	—	4	4	no	—
158	C₂₃×AGL(1,ℤ/8)	—	4	4	no	—
159	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
160	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
161	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
162	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
163	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
164	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
165	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
166	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
167	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
168	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
169	C₂×D₈×C₂₃	C₂³	1	2	yes	—
170	C₂×D₈×C₂₃	C₂³	1	2	yes	—
171	C₂×D₈×C₂₃	C₂³	1	2	yes	—
172	C₂×D₈×C₂₃	C₂³	1	2	yes	—
173	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
174	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
175	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
176	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
177	C₂₃×C₄⋊Q₈	—	2	1	no	—
178	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
179	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
180	C₂₃×#127	—	2	1	no	—
181	C₂₃×#127	—	2	1	no	—
182	C₂₃×#127	C₂³	1	1	yes	characteristic
183	C₂₃×#127	C₂³	1	1	yes	characteristic
184	C₂₃×#126	—	2	2	no	—
185	C₂₃×#126	—	2	1	no	—
186	C₂₃×#125	—	2	1	no	—
187	C₂₃×#125	C₂³	1	1	yes	characteristic
188	C₂₃×#124	—	2	2	no	—
189	C₂₃×#124	—	2	2	no	—
190	C₂₃×#124	—	2	1	no	—
191	C₂₃×#124	C₂³	1	2	yes	—
192	C₂₃×#124	C₂³	1	1	yes	characteristic
193	C₂₃×#123	—	2	2	no	—
194	C₂₃×#123	—	2	2	no	—
195	C₂₃×#123	—	2	1	no	—
196	C₂₃×#123	—	2	2	no	—
197	C₂₃×#123	—	2	2	no	—
198	C₂₃×#123	—	2	2	no	—
199	C₂₃×#123	—	2	2	no	—
200	C₂₃×C₂²⋊Q₈	—	2	2	no	—
201	C₂₃×C₂²⋊Q₈	—	2	2	no	—
202	C₂₃×C₂²⋊Q₈	—	2	2	no	—
203	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
204	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
205	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
206	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
207	C₂₃×#121	—	2	1	no	—
208	C₂₃×#121	—	2	2	no	—
209	C₂₃×#121	—	2	2	no	—
210	C₂₃×#121	—	2	1	no	—
211	C₂₃×#121	—	2	1	no	—
212	C₂₃×#121	—	2	2	no	—
213	C₂₃×#121	—	2	1	no	—
214	C₂₃×#121	—	2	2	no	—
215	C₂₃×#121	—	2	1	no	—
216	C₂₃×#121	—	2	1	no	—
217	C₂₃×#121	—	2	1	no	—
218	C₂₃×#121	—	2	2	no	—
219	C₂₃×#121	—	2	2	no	—
220	C₂₃×#121	—	2	2	no	—
221	C₂₃×#121	—	2	2	no	—
222	C₂₃×#121	C₂³	1	2	yes	—
223	C₂₃×#121	C₂³	1	2	yes	—
224	C₂₃×#121	C₂³	1	2	yes	—
225	C₂₃×#121	C₂³	1	2	yes	—
226	C₂₃×#121	C₂³	1	2	yes	—
227	C₂₃×#121	C₂³	1	1	yes	characteristic
228	C₂₃×#121	C₂³	1	2	yes	—
229	C₂₃×#120	—	2	2	no	—
230	C₂₃×#120	—	2	2	no	—
231	C₂₃×#120	—	2	2	no	—
232	C₂₃×#120	—	2	2	no	—
233	C₂₃×#120	—	2	2	no	—
234	C₂₃×#120	—	2	2	no	—
235	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
236	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
237	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
238	C₄×D₄×C₂₃	—	2	1	no	—
239	C₄×D₄×C₂₃	—	2	1	no	—
240	C₄×D₄×C₂₃	—	2	1	no	—
241	C₄×D₄×C₂₃	—	2	2	no	—
242	C₄×D₄×C₂₃	—	2	1	no	—
243	C₄×D₄×C₂₃	—	2	2	no	—
244	C₄×D₄×C₂₃	—	2	1	no	—
245	C₄×D₄×C₂₃	—	2	2	no	—
246	C₄×D₄×C₂₃	—	2	2	no	—
247	C₄×D₄×C₂₃	—	2	1	no	—
248	C₄×D₄×C₂₃	—	2	1	no	—
249	C₄×D₄×C₂₃	—	2	2	no	—
250	C₄×D₄×C₂₃	—	2	2	no	—
251	C₄×D₄×C₂₃	—	2	1	no	—
252	C₄×D₄×C₂₃	—	2	1	no	—
253	C₄×D₄×C₂₃	—	2	1	no	—
254	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
255	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
256	C₄×D₄×C₂₃	D₄	1	2	yes	—
257	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
258	C₄×D₄×C₂₃	C₂³	1	2	yes	—
259	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
260	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
261	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
262	C₄×D₄×C₂₃	C₂³	1	2	yes	—
263	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
264	C₂₃×#117	—	2	1	no	—
265	C₂₃×#117	—	2	1	no	—
266	C₂₃×#117	—	2	1	no	—
267	C₂₃×#117	C₂³	1	2	yes	—
268	C₂₃×#117	C₂³	1	1	yes	characteristic
269	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
270	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
271	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
272	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
273	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
274	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
275	C₂×C₂²⋊C₄×C₂₃	D₄	1	2	yes	—
276	C₂×C₄²×C₂₃	—	2	1	no	—
277	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
278	C₂₃×#107	C₂³	1	2	yes	—
279	C₂₃×#107	C₂³	1	1	yes	characteristic
280	C₂₃×#107	C₂³	1	1	yes	characteristic
281	C₂₃×#106	C₂³	1	1	yes	characteristic
282	C₂₃×#106	C₂³	1	1	yes	characteristic
283	C₂₃×#106	C₂³	1	2	yes	—
284	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
285	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
286	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
287	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
288	C₂₃×#103	C₂³	1	1	yes	characteristic
289	C₂₃×#103	C₂³	1	2	yes	—
290	C₂₃×#103	C₂³	1	2	yes	—
291	C₂₃×#103	C₂³	1	2	yes	—
292	C₂₃×#103	C₂³	1	1	yes	characteristic
293	C₂₃×#103	C₂³	1	2	yes	—
294	C₂₃×#103	C₂³	1	2	yes	—
295	C₂₃×#103	C₂³	1	1	yes	characteristic
296	C₂₃×#103	C₂³	1	1	yes	characteristic
297	C₂₃×#102	C₂³	1	1	yes	characteristic
298	C₂₃×#102	C₂³	1	2	yes	—
299	C₂₃×#102	C₂³	1	2	yes	—
300	C₂₃×#102	C₂³	1	2	yes	—
301	C₂₃×#102	C₂³	1	1	yes	characteristic
302	C₂₃×#102	C₂³	1	2	yes	—
303	C₂₃×#102	C₂³	1	2	yes	—
304	C₂₃×#102	C₂³	1	2	yes	—
305	C₂₃×#102	C₂³	1	1	yes	characteristic
306	C₂₃×#102	C₂³	1	1	yes	characteristic
307	C₂₃×#102	C₂³	1	2	yes	—
308	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
309	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
310	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
311	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
312	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
313	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
314	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
315	C₄×C₈×C₂₃	C₂³	1	2	yes	—
316	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
317	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
318	C₂⁴×C₂₃	—	2	2	no	—
319	C₂⁴×C₂₃	—	2	2	no	—
320	C₂⁴×C₂₃	C₂×D₄	1	2	yes	—
321	#41×C₂₃	—	2	2	no	—
322	#41×C₂₃	—	2	2	no	—
323	#41×C₂₃	—	2	4	no	—
324	#41×C₂₃	—	2	4	no	—
325	#41×C₂₃	—	4	2	no	—
326	#41×C₂₃	—	4	2	no	—
327	#41×C₂₃	—	4	2	no	—
328	#41×C₂₃	—	4	2	no	—
329	#41×C₂₃	—	4	8	no	—
330	#41×C₂₃	—	4	2	no	—
331	#41×C₂₃	—	4	2	no	—
332	#41×C₂₃	—	4	8	no	—
333	#41×C₂₃	—	8	2	no	—
334	C₂×Q₈×C₂₃	—	2	2	no	—
335	C₂×Q₈×C₂₃	—	2	1	no	—
336	C₂×Q₈×C₂₃	—	2	4	no	—
337	C₂×Q₈×C₂₃	—	4	2	no	—
338	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
339	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
340	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
341	C₂×D₄×C₂₃	—	2	1	no	—
342	C₂×D₄×C₂₃	—	2	4	no	—
343	C₂×D₄×C₂₃	—	2	2	no	—
344	C₂×D₄×C₂₃	—	2	2	no	—
345	C₂×D₄×C₂₃	—	2	2	no	—
346	C₂×D₄×C₂₃	—	2	1	no	—
347	C₂×D₄×C₂₃	—	2	2	no	—
348	C₂×D₄×C₂₃	—	2	2	no	—
349	C₂×D₄×C₂₃	—	2	2	no	—
350	C₂×D₄×C₂₃	—	2	2	no	—
351	C₂×D₄×C₂₃	—	2	2	no	—
352	C₂×D₄×C₂₃	—	2	2	no	—
353	C₂×D₄×C₂₃	—	2	2	no	—
354	C₂×D₄×C₂₃	—	2	1	no	—
355	C₂×D₄×C₂₃	—	2	1	no	—
356	C₂×D₄×C₂₃	—	2	2	no	—
357	C₂×D₄×C₂₃	—	2	1	no	—
358	C₂×D₄×C₂₃	—	2	1	no	—
359	C₂×D₄×C₂₃	—	2	2	no	—
360	C₂×D₄×C₂₃	—	4	2	no	—
361	C₂×D₄×C₂₃	—	4	2	no	—
362	C₂×D₄×C₂₃	—	4	2	no	—
363	C₂×D₄×C₂₃	—	4	2	no	—
364	C₂×D₄×C₂₃	—	4	4	no	—
365	C₂×D₄×C₂₃	—	4	4	no	—
366	C₂×D₄×C₂₃	—	4	8	no	—
367	C₂×D₄×C₂₃	—	8	4	no	—
368	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
369	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
370	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
371	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
372	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
373	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
374	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
375	C₂²×C₄×C₂₃	—	2	1	no	—
376	C₂²×C₄×C₂₃	—	2	2	no	—
377	C₂²×C₄×C₂₃	—	2	2	no	—
378	C₂²×C₄×C₂₃	—	2	1	no	—
379	C₂²×C₄×C₂₃	—	2	2	no	—
380	C₂²×C₄×C₂₃	—	2	1	no	—
381	C₂²×C₄×C₂₃	—	2	2	no	—
382	C₂²×C₄×C₂₃	—	2	2	no	—
383	C₂²×C₄×C₂₃	—	2	1	no	—
384	C₂²×C₄×C₂₃	—	2	2	no	—
385	C₂²×C₄×C₂₃	—	2	2	no	—
386	C₂²×C₄×C₂₃	—	4	2	no	—
387	C₂²×C₄×C₂₃	—	4	2	no	—
388	C₂²×C₄×C₂₃	—	4	8	no	—
389	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
390	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
391	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
392	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
393	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
394	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
395	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
396	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
397	Q₁₆×C₂₃	—	2	2	no	—
398	Q₁₆×C₂₃	—	4	2	no	—
399	SD₁₆×C₂₃	—	2	2	no	—
400	SD₁₆×C₂₃	—	2	4	no	—
401	SD₁₆×C₂₃	—	2	2	no	—
402	SD₁₆×C₂₃	—	4	2	no	—
403	SD₁₆×C₂₃	—	4	2	no	—
404	SD₁₆×C₂₃	—	4	2	no	—
405	SD₁₆×C₂₃	—	4	2	no	—
406	D₈×C₂₃	—	2	4	no	—
407	D₈×C₂₃	—	2	2	no	—
408	D₈×C₂₃	—	4	2	no	—
409	D₈×C₂₃	—	4	2	no	—
410	D₈×C₂₃	—	4	2	no	—
411	M₁₆×C₂₃	—	4	2	no	—
412	M₁₆×C₂₃	—	4	2	no	—
413	M₁₆×C₂₃	—	4	2	no	—
414	M₁₆×C₂₃	—	4	2	no	—
415	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
416	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
417	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
418	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
419	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
420	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
421	C₄⋊C₄×C₂₃	—	2	1	no	—
422	C₄⋊C₄×C₂₃	—	2	2	no	—
423	C₄⋊C₄×C₂₃	—	2	2	no	—
424	C₄⋊C₄×C₂₃	—	2	1	no	—
425	C₄⋊C₄×C₂₃	—	2	1	no	—
426	C₄⋊C₄×C₂₃	—	2	1	no	—
427	C₄⋊C₄×C₂₃	—	2	1	no	—
428	C₄⋊C₄×C₂₃	—	2	1	no	—
429	C₄⋊C₄×C₂₃	—	2	1	no	—
430	C₄⋊C₄×C₂₃	—	2	1	no	—
431	C₄⋊C₄×C₂₃	—	2	2	no	—
432	C₄⋊C₄×C₂₃	—	2	2	no	—
433	C₄⋊C₄×C₂₃	—	2	1	no	—
434	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
435	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
436	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
437	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
438	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
439	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
440	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
441	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
442	C₂²⋊C₄×C₂₃	—	2	2	no	—
443	C₂²⋊C₄×C₂₃	—	2	2	no	—
444	C₂²⋊C₄×C₂₃	—	2	1	no	—
445	C₂²⋊C₄×C₂₃	—	2	2	no	—
446	C₂²⋊C₄×C₂₃	—	2	1	no	—
447	C₂²⋊C₄×C₂₃	—	2	2	no	—
448	C₂²⋊C₄×C₂₃	—	2	1	no	—
449	C₂²⋊C₄×C₂₃	—	2	1	no	—
450	C₂²⋊C₄×C₂₃	—	2	2	no	—
451	C₂²⋊C₄×C₂₃	—	2	2	no	—
452	C₂²⋊C₄×C₂₃	—	2	2	no	—
453	C₂²⋊C₄×C₂₃	—	2	2	no	—
454	C₂²⋊C₄×C₂₃	—	2	2	no	—
455	C₂²⋊C₄×C₂₃	—	2	1	no	—
456	C₂²⋊C₄×C₂₃	—	2	1	no	—
457	C₂²⋊C₄×C₂₃	—	2	1	no	—
458	C₂²⋊C₄×C₂₃	—	2	2	no	—
459	C₂²⋊C₄×C₂₃	—	2	2	no	—
460	C₂²⋊C₄×C₂₃	—	2	2	no	—
461	C₂²⋊C₄×C₂₃	—	2	1	no	—
462	C₂²⋊C₄×C₂₃	—	2	2	no	—
463	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
464	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
465	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
466	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
467	C₄²×C₂₃	—	2	1	no	—
468	C₄²×C₂₃	—	2	1	no	—
469	C₄²×C₂₃	—	2	1	no	—
470	C₄²×C₂₃	—	2	2	no	—
471	C₄²×C₂₃	—	2	1	no	—
472	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
473	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
474	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
475	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
476	#61590	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
477	C₂³×C₂₃	—	2	1	no	—
478	C₂³×C₂₃	—	2	1	no	—
479	C₂³×C₂₃	—	2	2	no	—
480	C₂³×C₂₃	—	2	2	no	—
481	C₂³×C₂₃	—	4	2	no	—
482	C₂³×C₂₃	—	4	2	no	—
483	C₂³×C₂₃	—	4	2	no	—
484	C₂³×C₂₃	—	4	4	no	—
485	C₂³×C₂₃	—	4	4	no	—
486	C₂³×C₂₃	—	4	4	no	—
487	C₂³×C₂₃	—	8	2	no	—
488	C₂³×C₂₃	—	8	2	no	—
489	C₂³×C₂₃	—	8	2	no	—
490	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
491	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
492	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
493	Q₈×C₂₃	—	2	1	no	—
494	Q₈×C₂₃	—	2	1	no	—
495	Q₈×C₂₃	—	2	2	no	—
496	Q₈×C₂₃	—	2	2	no	—
497	Q₈×C₂₃	—	2	1	no	—
498	Q₈×C₂₃	—	4	4	no	—
499	Q₈×C₂₃	—	8	1	no	—
500	Q₈×C₂₃	H(5,𝔽₂)	1	2	yes	—
501	D₄×C₂₃	—	2	4	no	—
502	D₄×C₂₃	—	2	2	no	—
503	D₄×C₂₃	—	2	2	no	—
504	D₄×C₂₃	—	2	1	no	—
505	D₄×C₂₃	—	2	2	no	—
506	D₄×C₂₃	—	2	1	no	—
507	D₄×C₂₃	—	2	1	no	—
508	D₄×C₂₃	—	2	2	no	—
509	D₄×C₂₃	—	2	2	no	—
510	D₄×C₂₃	—	2	2	no	—
511	D₄×C₂₃	—	4	2	no	—
512	D₄×C₂₃	—	4	4	no	—
513	D₄×C₂₃	—	4	4	no	—
514	D₄×C₂₃	—	4	4	no	—
515	D₄×C₂₃	—	4	4	no	—
516	D₄×C₂₃	—	4	4	no	—
517	D₄×C₂₃	—	4	4	no	—
518	D₄×C₂₃	—	4	2	no	—
519	D₄×C₂₃	—	4	4	no	—
520	D₄×C₂₃	—	4	2	no	—
521	D₄×C₂₃	—	4	2	no	—
522	D₄×C₂₃	—	8	1	no	—
523	D₄×C₂₃	—	8	2	no	—
524	D₄×C₂₃	—	8	1	no	—
525	D₄×C₂₃	—	8	2	no	—
526	D₄×C₂₃	—	8	2	no	—
527	D₄×C₂₃	—	8	2	no	—
528	D₄×C₂₃	—	8	2	no	—
529	D₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
530	C₂×C₄×C₂₃	—	2	4	no	—
531	C₂×C₄×C₂₃	—	2	1	no	—
532	C₂×C₄×C₂₃	—	2	2	no	—
533	C₂×C₄×C₂₃	—	2	2	no	—
534	C₂×C₄×C₂₃	—	2	2	no	—
535	C₂×C₄×C₂₃	—	2	2	no	—
536	C₂×C₄×C₂₃	—	2	2	no	—
537	C₂×C₄×C₂₃	—	2	1	no	—
538	C₂×C₄×C₂₃	—	2	1	no	—
539	C₂×C₄×C₂₃	—	2	1	no	—
540	C₂×C₄×C₂₃	—	2	1	no	—
541	C₂×C₄×C₂₃	—	2	1	no	—
542	C₂×C₄×C₂₃	—	2	1	no	—
543	C₂×C₄×C₂₃	—	2	2	no	—
544	C₂×C₄×C₂₃	—	2	1	no	—
545	C₂×C₄×C₂₃	—	2	2	no	—
546	C₂×C₄×C₂₃	—	4	2	no	—
547	C₂×C₄×C₂₃	—	4	2	no	—
548	C₂×C₄×C₂₃	—	4	2	no	—
549	C₂×C₄×C₂₃	—	4	1	no	—
550	C₂×C₄×C₂₃	—	4	4	no	—
551	C₂×C₄×C₂₃	—	4	4	no	—
552	C₂×C₄×C₂₃	—	4	4	no	—
553	C₂×C₄×C₂₃	—	4	4	no	—
554	C₂×C₄×C₂₃	—	4	2	no	—
555	C₂×C₄×C₂₃	—	4	2	no	—
556	C₂×C₄×C₂₃	—	8	1	no	—
557	C₂×C₄×C₂₃	—	8	2	no	—
558	C₂×C₄×C₂₃	—	8	2	no	—
559	C₂×C₄×C₂₃	—	8	2	no	—
560	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
561	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
562	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
563	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
564	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
565	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
566	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
567	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
568	C₈×C₂₃	—	2	2	no	—
569	C₈×C₂₃	—	2	1	no	—
570	C₈×C₂₃	—	2	1	no	—
571	C₈×C₂₃	—	2	1	no	—
572	C₈×C₂₃	—	2	2	no	—
573	C₈×C₂₃	—	2	1	no	—
574	#3519	C₂×C₂₃	1	1	yes	characteristic, complemented
575	D₄×#41	C₂×C₂₃	1	1	yes	characteristic, complemented
576	#3333	C₂×C₂₃	1	1	yes	characteristic, complemented
577	#3331	C₂×C₂₃	1	1	yes	characteristic, complemented
578	#3329	C₂×C₂₃	1	1	yes	characteristic, complemented
579	#3326	C₂×C₂₃	1	2	yes	complemented
580	#3325	C₂×C₂₃	1	1	yes	characteristic, complemented
581	#3322	C₂×C₂₃	1	2	yes	complemented
582	#3278	C₂×C₂₃	1	1	yes	characteristic, complemented
583	#3275	C₂×C₂₃	1	2	yes	complemented
584	#3274	C₂×C₂₃	1	1	yes	characteristic, complemented
585	#3274	C₂×C₂₃	1	1	yes	characteristic, complemented
586	#3273	C₂×C₂₃	1	2	yes	complemented
587	#3272	C₂×C₂₃	1	1	yes	characteristic, complemented
588	#3212	C₂×C₂₃	1	1	yes	characteristic, complemented
589	#3207	C₂×C₂₃	1	1	yes	characteristic, complemented
590	#3197	C₂×C₂₃	1	2	yes	complemented
591	#3194	C₂×C₂₃	1	2	yes	complemented
592	#3106	C₂×C₂₃	1	1	yes	characteristic, complemented
593	#3102	C₂×C₂₃	1	1	yes	characteristic, complemented
594	#3006	C₂×C₂₃	1	2	yes	complemented
595	#3005	C₂×C₂₃	1	2	yes	complemented
596	#2975	C₂×C₂₃	1	1	yes	characteristic, complemented
597	C₂²×C₂₃	—	2	1	no	—
598	C₂²×C₂₃	—	2	2	no	—
599	C₂²×C₂₃	—	2	2	no	—
600	C₂²×C₂₃	—	2	2	no	—
601	C₂²×C₂₃	—	2	1	no	—
602	C₂²×C₂₃	—	2	2	no	—
603	C₂²×C₂₃	—	2	2	no	—
604	C₂²×C₂₃	—	2	1	no	—
605	C₂²×C₂₃	—	2	2	no	—
606	C₂²×C₂₃	—	2	2	no	—
607	C₂²×C₂₃	—	4	1	no	—
608	C₂²×C₂₃	—	4	1	no	—
609	C₂²×C₂₃	—	4	2	no	—
610	C₂²×C₂₃	—	4	1	no	—
611	C₂²×C₂₃	—	4	2	no	—
612	C₂²×C₂₃	—	4	2	no	—
613	C₂²×C₂₃	—	4	2	no	—
614	C₂²×C₂₃	—	4	1	no	—
615	C₂²×C₂₃	—	4	1	no	—
616	C₂²×C₂₃	—	4	2	no	—
617	C₂²×C₂₃	—	4	2	no	—
618	C₂²×C₂₃	—	8	4	no	—
619	C₂²×C₂₃	—	8	8	no	—
620	C₂²×C₂₃	—	16	4	no	—
621	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
622	C₄×C₂₃	—	2	1	no	—
623	C₄×C₂₃	—	2	1	no	—
624	C₄×C₂₃	—	2	1	no	—
625	C₄×C₂₃	—	2	2	no	—
626	C₄×C₂₃	—	2	2	no	—
627	C₄×C₂₃	—	2	2	no	—
628	C₄×C₂₃	—	2	1	no	—
629	C₄×C₂₃	—	4	1	no	—
630	C₄×C₂₃	—	4	2	no	—
631	C₄×C₂₃	—	4	1	no	—
632	C₄×C₂₃	—	4	2	no	—
633	C₄×C₂₃	—	4	1	no	—
634	C₄×C₂₃	—	4	1	no	—
635	C₄×C₂₃	—	4	1	no	—
636	C₄×C₂₃	#575	1	2	yes	—
637	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
638	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
639	C₂²×#41	C₂²×C₂₃	1	2	yes	complemented
640	C₂×#137	C₂²×C₂₃	1	2	yes	complemented
641	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	2	yes	complemented
642	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	2	yes	complemented
643	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	2	yes	complemented
644	#555	C₂²×C₂₃	1	1	yes	characteristic
645	#554	C₂²×C₂₃	1	1	yes	characteristic, complemented
646	#553	—	2	1	no	—
647	#553	C₂²×C₂₃	1	2	yes	complemented
648	#550	C₂²×C₂₃	1	1	yes	characteristic
649	#550	C₂²×C₂₃	1	1	yes	characteristic
650	D₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
651	#548	C₂²×C₂₃	1	2	yes	complemented
652	#547	—	2	1	no	—
653	#547	C₂²×C₂₃	1	1	yes	characteristic
654	#546	—	2	2	no	—
655	#546	—	2	2	no	—
656	#546	C₂²×C₂₃	1	2	yes	complemented
657	#546	C₂²×C₂₃	1	2	yes	complemented
658	D₄²	—	2	1	no	—
659	D₄²	—	2	1	no	—
660	D₄²	C₂²×C₂₃	1	1	yes	characteristic, complemented
661	D₄²	C₂²×C₂₃	1	1	yes	characteristic, complemented
662	#540	—	2	1	no	—
663	#538	—	2	2	no	—
664	#532	—	2	1	no	—
665	#532	C₂²×C₂₃	1	1	yes	characteristic, complemented
666	#532	C₂²×C₂₃	1	1	yes	characteristic, complemented
667	#529	C₂²×C₂₃	1	1	yes	characteristic, complemented
668	#525	—	2	2	no	—
669	#525	C₂²×C₂₃	1	2	yes	complemented
670	#525	C₂²×C₂₃	1	2	yes	complemented
671	C₂×#121	C₂²×C₂₃	1	2	yes	complemented
672	#518	—	2	1	no	—
673	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic, complemented
674	C₂×C₄×D₄	—	2	1	no	—
675	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
676	#495	C₂²×C₂₃	1	2	yes	complemented
677	#493	C₂²×C₂₃	1	1	yes	characteristic, complemented
678	#492	C₂²×C₂₃	1	1	yes	characteristic, complemented
679	#488	C₂²×C₂₃	1	2	yes	complemented
680	#487	C₂²×C₂₃	1	1	yes	characteristic, complemented
681	#486	C₂²×C₂₃	1	1	yes	characteristic, complemented
682	#485	C₂²×C₂₃	1	2	yes	complemented
683	#485	C₂²×C₂₃	1	1	yes	characteristic, complemented
684	#483	C₂²×C₂₃	1	2	yes	complemented
685	#482	C₂²×C₂₃	1	1	yes	characteristic, complemented
686	#482	C₂²×C₂₃	1	2	yes	complemented
687	#482	C₂²×C₂₃	1	2	yes	complemented
688	#480	C₂²×C₂₃	1	2	yes	complemented
689	#479	C₂²×C₂₃	1	1	yes	characteristic, complemented
690	#478	C₂²×C₂₃	1	1	yes	characteristic, complemented
691	#477	C₂²×C₂₃	1	1	yes	characteristic, complemented
692	#476	C₂²×C₂₃	1	1	yes	characteristic, complemented
693	#470	C₂²×C₂₃	1	2	yes	complemented
694	#469	C₂²×C₂₃	1	2	yes	complemented
695	#469	C₂²×C₂₃	1	2	yes	complemented
696	#469	C₂²×C₂₃	1	2	yes	complemented
697	#468	C₂²×C₂₃	1	2	yes	complemented
698	#468	C₂²×C₂₃	1	2	yes	complemented
699	#468	C₂²×C₂₃	1	2	yes	complemented
700	#468	C₂²×C₂₃	1	2	yes	complemented
701	#464	C₂²×C₂₃	1	1	yes	characteristic, complemented
702	#463	C₂²×C₂₃	1	1	yes	characteristic, complemented
703	#463	C₂²×C₂₃	1	2	yes	complemented
704	#463	C₂²×C₂₃	1	2	yes	complemented
705	#462	C₂²×C₂₃	1	1	yes	characteristic, complemented
706	#461	C₂²×C₂₃	1	1	yes	characteristic, complemented
707	#460	C₂²×C₂₃	1	1	yes	characteristic, complemented
708	#460	C₂²×C₂₃	1	1	yes	characteristic, complemented
709	#459	C₂²×C₂₃	1	1	yes	characteristic, complemented
710	#459	C₂²×C₂₃	1	1	yes	characteristic, complemented
711	#452	C₂²×C₂₃	1	2	yes	complemented
712	#452	C₂²×C₂₃	1	2	yes	complemented
713	#452	C₂²×C₂₃	1	1	yes	characteristic, complemented
714	#452	C₂²×C₂₃	1	2	yes	complemented
715	#452	C₂²×C₂₃	1	2	yes	complemented
716	#450	C₂²×C₂₃	1	2	yes	complemented
717	#449	C₂²×C₂₃	1	1	yes	characteristic
718	#449	C₂²×C₂₃	1	2	yes	complemented
719	#449	C₂²×C₂₃	1	2	yes	complemented
720	#449	C₂²×C₂₃	1	2	yes	complemented
721	#449	C₂²×C₂₃	1	2	yes	complemented
722	#449	C₂²×C₂₃	1	2	yes	complemented
723	#449	C₂²×C₂₃	1	2	yes	complemented
724	#449	C₂²×C₂₃	1	2	yes	complemented
725	#448	C₂²×C₂₃	1	2	yes	complemented
726	#448	C₂²×C₂₃	1	2	yes	complemented
727	#447	C₂²×C₂₃	1	2	yes	complemented
728	#447	C₂²×C₂₃	1	2	yes	complemented
729	#447	C₂²×C₂₃	1	2	yes	complemented
730	C₄×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
731	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
732	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
733	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
734	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
735	C₄×D₈	C₂²×C₂₃	1	2	yes	complemented
736	#436	C₂²×C₂₃	1	1	yes	characteristic, complemented
737	#436	C₂²×C₂₃	1	1	yes	characteristic, complemented
738	#436	C₂²×C₂₃	1	1	yes	characteristic, complemented
739	#436	C₂²×C₂₃	1	2	yes	complemented
740	#436	C₂²×C₂₃	1	2	yes	complemented
741	#436	C₂²×C₂₃	1	1	yes	characteristic, complemented
742	#431	C₂²×C₂₃	1	1	yes	characteristic, complemented
743	#431	C₂²×C₂₃	1	1	yes	characteristic, complemented
744	#419	C₂²×C₂₃	1	2	yes	complemented
745	#418	C₂²×C₂₃	1	2	yes	complemented
746	#417	C₂²×C₂₃	1	2	yes	complemented
747	#417	C₂²×C₂₃	1	2	yes	complemented
748	#407	C₂²×C₂₃	1	2	yes	complemented
749	#407	C₂²×C₂₃	1	2	yes	complemented
750	C₂×C₂₃	—	4	1	no	—
751	C₂×C₂₃	—	4	2	no	—
752	C₂×C₂₃	—	4	2	no	—
753	C₂×C₂₃	—	4	2	no	—
754	C₂×C₂₃	—	8	2	no	—
755	C₂×C₂₃	—	8	2	no	—
756	C₂×C₂₃	—	8	1	no	—
757	C₂×C₂₃	#3484	1	1	yes	characteristic
758	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
759	C₂×C₂₃	#3585	1	1	yes	characteristic
760	C₂×#41	—	2	2	no	—
761	C₂×#41	—	2	2	no	—
762	C₂×#41	—	2	1	no	—
763	C₂×#41	—	4	4	no	—
764	C₂×#41	—	4	4	no	—
765	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
766	C₂×#41	C₂³×C₂₃	1	2	yes	—
767	C₂×#41	C₂³×C₂₃	1	2	yes	—
768	C₂×#41	C₂³×C₂₃	1	2	yes	—
769	C₂×#41	C₂³×C₂₃	1	2	yes	—
770	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
771	C₂²×D₄	—	2	2	no	—
772	C₂²×D₄	—	2	2	no	—
773	C₂²×D₄	—	2	1	no	—
774	C₂²×D₄	—	2	1	no	—
775	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
776	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
777	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
778	C₂³×C₄	—	2	2	no	—
779	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
780	#137	—	4	4	no	—
781	AGL(1,ℤ/8)	—	4	4	no	—
782	AGL(1,ℤ/8)	—	4	4	no	—
783	AGL(1,ℤ/8)	—	4	4	no	—
784	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
785	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
786	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
787	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
788	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
789	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
790	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
791	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
792	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
793	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
794	C₂×D₈	C₂³×C₂₃	1	2	yes	—
795	C₂×D₈	C₂³×C₂₃	1	2	yes	—
796	C₂×D₈	C₂³×C₂₃	1	2	yes	—
797	C₂×D₈	C₂³×C₂₃	1	2	yes	—
798	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
799	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
800	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
801	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
802	C₄⋊Q₈	—	2	1	no	—
803	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
804	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
805	#127	—	2	1	no	—
806	#127	—	2	1	no	—
807	#127	C₂³×C₂₃	1	1	yes	characteristic
808	#127	C₂³×C₂₃	1	1	yes	characteristic
809	#126	—	2	2	no	—
810	#126	—	2	1	no	—
811	#125	—	2	1	no	—
812	#125	C₂³×C₂₃	1	1	yes	characteristic
813	#124	—	2	2	no	—
814	#124	—	2	2	no	—
815	#124	—	2	1	no	—
816	#124	C₂³×C₂₃	1	1	yes	characteristic
817	#124	C₂³×C₂₃	1	2	yes	—
818	#123	—	2	2	no	—
819	#123	—	2	2	no	—
820	#123	—	2	1	no	—
821	#123	—	2	2	no	—
822	#123	—	2	2	no	—
823	#123	—	2	2	no	—
824	#123	—	2	2	no	—
825	C₂²⋊Q₈	—	2	2	no	—
826	C₂²⋊Q₈	—	2	2	no	—
827	C₂²⋊Q₈	—	2	2	no	—
828	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
829	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
830	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
831	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
832	#121	—	2	2	no	—
833	#121	—	2	1	no	—
834	#121	—	2	2	no	—
835	#121	—	2	1	no	—
836	#121	—	2	2	no	—
837	#121	—	2	2	no	—
838	#121	—	2	1	no	—
839	#121	—	2	1	no	—
840	#121	—	2	1	no	—
841	#121	—	2	1	no	—
842	#121	—	2	1	no	—
843	#121	—	2	2	no	—
844	#121	—	2	2	no	—
845	#121	—	2	2	no	—
846	#121	—	2	2	no	—
847	#121	C₂³×C₂₃	1	1	yes	characteristic
848	#121	C₂³×C₂₃	1	2	yes	—
849	#121	C₂³×C₂₃	1	2	yes	—
850	#121	C₂³×C₂₃	1	2	yes	—
851	#121	C₂³×C₂₃	1	2	yes	—
852	#121	C₂³×C₂₃	1	2	yes	—
853	#121	C₂³×C₂₃	1	2	yes	—
854	#120	—	2	2	no	—
855	#120	—	2	2	no	—
856	#120	—	2	2	no	—
857	#120	—	2	2	no	—
858	#120	—	2	2	no	—
859	#120	—	2	2	no	—
860	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
861	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
862	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
863	C₄×D₄	—	2	1	no	—
864	C₄×D₄	—	2	1	no	—
865	C₄×D₄	—	2	2	no	—
866	C₄×D₄	—	2	1	no	—
867	C₄×D₄	—	2	1	no	—
868	C₄×D₄	—	2	2	no	—
869	C₄×D₄	—	2	2	no	—
870	C₄×D₄	—	2	2	no	—
871	C₄×D₄	—	2	1	no	—
872	C₄×D₄	—	2	1	no	—
873	C₄×D₄	—	2	1	no	—
874	C₄×D₄	—	2	2	no	—
875	C₄×D₄	—	2	2	no	—
876	C₄×D₄	—	2	1	no	—
877	C₄×D₄	—	2	1	no	—
878	C₄×D₄	—	2	1	no	—
879	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
880	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
881	C₄×D₄	D₄×C₂₃	1	2	yes	—
882	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
883	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
884	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
885	C₄×D₄	C₂³×C₂₃	1	2	yes	—
886	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
887	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
888	C₄×D₄	C₂³×C₂₃	1	2	yes	—
889	#117	—	2	1	no	—
890	#117	—	2	1	no	—
891	#117	—	2	1	no	—
892	#117	C₂³×C₂₃	1	1	yes	characteristic
893	#117	C₂³×C₂₃	1	2	yes	—
894	C₂×C₄⋊C₄	—	2	1	no	—
895	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
896	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
897	C₂×C₂²⋊C₄	—	2	2	no	—
898	C₂×C₂²⋊C₄	—	2	2	no	—
899	C₂×C₂²⋊C₄	—	2	2	no	—
900	C₂×C₂²⋊C₄	D₄×C₂₃	1	2	yes	—
901	C₂×C₄²	—	2	1	no	—
902	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
903	#107	C₂³×C₂₃	1	2	yes	—
904	#107	C₂³×C₂₃	1	1	yes	characteristic
905	#107	C₂³×C₂₃	1	1	yes	characteristic
906	#106	C₂³×C₂₃	1	1	yes	characteristic
907	#106	C₂³×C₂₃	1	1	yes	characteristic
908	#106	C₂³×C₂₃	1	2	yes	—
909	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
910	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
911	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
912	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
913	#103	C₂³×C₂₃	1	1	yes	characteristic
914	#103	C₂³×C₂₃	1	2	yes	—
915	#103	C₂³×C₂₃	1	2	yes	—
916	#103	C₂³×C₂₃	1	2	yes	—
917	#103	C₂³×C₂₃	1	1	yes	characteristic
918	#103	C₂³×C₂₃	1	2	yes	—
919	#103	C₂³×C₂₃	1	2	yes	—
920	#103	C₂³×C₂₃	1	1	yes	characteristic
921	#103	C₂³×C₂₃	1	1	yes	characteristic
922	#102	C₂³×C₂₃	1	1	yes	characteristic
923	#102	C₂³×C₂₃	1	2	yes	—
924	#102	C₂³×C₂₃	1	2	yes	—
925	#102	C₂³×C₂₃	1	2	yes	—
926	#102	C₂³×C₂₃	1	1	yes	characteristic
927	#102	C₂³×C₂₃	1	2	yes	—
928	#102	C₂³×C₂₃	1	2	yes	—
929	#102	C₂³×C₂₃	1	2	yes	—
930	#102	C₂³×C₂₃	1	1	yes	characteristic
931	#102	C₂³×C₂₃	1	1	yes	characteristic
932	#102	C₂³×C₂₃	1	2	yes	—
933	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
934	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
935	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
936	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
937	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
938	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
939	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
940	C₄×C₈	C₂³×C₂₃	1	2	yes	—
941	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
942	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
943	C₂₃	#61590	1	1	yes	characteristic, direct product factor, Sylow
944	C₂⁴	—	2	2	no	—
945	C₂⁴	—	2	2	no	—
946	C₂⁴	C₂×D₄×C₂₃	1	2	yes	—
947	#41	—	2	2	no	—
948	#41	—	2	2	no	—
949	#41	—	2	4	no	—
950	#41	—	2	4	no	—
951	#41	—	4	2	no	—
952	#41	—	4	2	no	—
953	#41	—	4	2	no	—
954	#41	—	4	2	no	—
955	#41	—	4	8	no	—
956	#41	—	4	2	no	—
957	#41	—	4	2	no	—
958	#41	—	4	8	no	—
959	#41	—	8	2	no	—
960	C₂×Q₈	—	2	2	no	—
961	C₂×Q₈	—	2	1	no	—
962	C₂×Q₈	—	2	4	no	—
963	C₂×Q₈	—	4	2	no	—
964	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
965	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
966	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
967	C₂×D₄	—	2	1	no	—
968	C₂×D₄	—	2	4	no	—
969	C₂×D₄	—	2	2	no	—
970	C₂×D₄	—	2	2	no	—
971	C₂×D₄	—	2	2	no	—
972	C₂×D₄	—	2	1	no	—
973	C₂×D₄	—	2	2	no	—
974	C₂×D₄	—	2	2	no	—
975	C₂×D₄	—	2	2	no	—
976	C₂×D₄	—	2	2	no	—
977	C₂×D₄	—	2	2	no	—
978	C₂×D₄	—	2	2	no	—
979	C₂×D₄	—	2	2	no	—
980	C₂×D₄	—	2	1	no	—
981	C₂×D₄	—	2	1	no	—
982	C₂×D₄	—	2	2	no	—
983	C₂×D₄	—	2	1	no	—
984	C₂×D₄	—	2	1	no	—
985	C₂×D₄	—	2	2	no	—
986	C₂×D₄	—	4	2	no	—
987	C₂×D₄	—	4	2	no	—
988	C₂×D₄	—	4	2	no	—
989	C₂×D₄	—	4	2	no	—
990	C₂×D₄	—	4	8	no	—
991	C₂×D₄	—	4	4	no	—
992	C₂×D₄	—	4	4	no	—
993	C₂×D₄	—	8	4	no	—
994	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
995	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
996	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
997	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
998	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
999	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
1000	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
1001	C₂²×C₄	—	2	1	no	—
1002	C₂²×C₄	—	2	2	no	—
1003	C₂²×C₄	—	2	2	no	—
1004	C₂²×C₄	—	2	1	no	—
1005	C₂²×C₄	—	2	2	no	—
1006	C₂²×C₄	—	2	1	no	—
1007	C₂²×C₄	—	2	2	no	—
1008	C₂²×C₄	—	2	2	no	—
1009	C₂²×C₄	—	2	1	no	—
1010	C₂²×C₄	—	2	2	no	—
1011	C₂²×C₄	—	2	2	no	—
1012	C₂²×C₄	—	4	2	no	—
1013	C₂²×C₄	—	4	2	no	—
1014	C₂²×C₄	—	4	8	no	—
1015	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1016	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1017	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
1018	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
1019	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
1020	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1021	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
1022	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
1023	Q₁₆	—	2	2	no	—
1024	Q₁₆	—	4	2	no	—
1025	SD₁₆	—	2	2	no	—
1026	SD₁₆	—	2	4	no	—
1027	SD₁₆	—	2	2	no	—
1028	SD₁₆	—	4	2	no	—
1029	SD₁₆	—	4	2	no	—
1030	SD₁₆	—	4	2	no	—
1031	SD₁₆	—	4	2	no	—
1032	D₈	—	2	4	no	—
1033	D₈	—	2	2	no	—
1034	D₈	—	4	2	no	—
1035	D₈	—	4	2	no	—
1036	D₈	—	4	2	no	—
1037	M₁₆	—	4	2	no	—
1038	M₁₆	—	4	2	no	—
1039	M₁₆	—	4	2	no	—
1040	M₁₆	—	4	2	no	—
1041	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1042	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1043	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1044	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1045	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1046	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1047	C₄⋊C₄	—	2	1	no	—
1048	C₄⋊C₄	—	2	2	no	—
1049	C₄⋊C₄	—	2	2	no	—
1050	C₄⋊C₄	—	2	1	no	—
1051	C₄⋊C₄	—	2	1	no	—
1052	C₄⋊C₄	—	2	1	no	—
1053	C₄⋊C₄	—	2	1	no	—
1054	C₄⋊C₄	—	2	1	no	—
1055	C₄⋊C₄	—	2	1	no	—
1056	C₄⋊C₄	—	2	1	no	—
1057	C₄⋊C₄	—	2	2	no	—
1058	C₄⋊C₄	—	2	2	no	—
1059	C₄⋊C₄	—	2	1	no	—
1060	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1061	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1062	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1063	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1064	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1065	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1066	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1067	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1068	C₂²⋊C₄	—	2	2	no	—
1069	C₂²⋊C₄	—	2	2	no	—
1070	C₂²⋊C₄	—	2	1	no	—
1071	C₂²⋊C₄	—	2	2	no	—
1072	C₂²⋊C₄	—	2	1	no	—
1073	C₂²⋊C₄	—	2	2	no	—
1074	C₂²⋊C₄	—	2	1	no	—
1075	C₂²⋊C₄	—	2	1	no	—
1076	C₂²⋊C₄	—	2	2	no	—
1077	C₂²⋊C₄	—	2	2	no	—
1078	C₂²⋊C₄	—	2	2	no	—
1079	C₂²⋊C₄	—	2	2	no	—
1080	C₂²⋊C₄	—	2	2	no	—
1081	C₂²⋊C₄	—	2	1	no	—
1082	C₂²⋊C₄	—	2	1	no	—
1083	C₂²⋊C₄	—	2	1	no	—
1084	C₂²⋊C₄	—	2	2	no	—
1085	C₂²⋊C₄	—	2	2	no	—
1086	C₂²⋊C₄	—	2	2	no	—
1087	C₂²⋊C₄	—	2	1	no	—
1088	C₂²⋊C₄	—	2	2	no	—
1089	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1090	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1091	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1092	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1093	C₄²	—	2	1	no	—
1094	C₄²	—	2	1	no	—
1095	C₄²	—	2	1	no	—
1096	C₄²	—	2	2	no	—
1097	C₄²	—	2	1	no	—
1098	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1099	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1100	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1101	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1102	C₂³	—	2	1	no	—
1103	C₂³	—	2	1	no	—
1104	C₂³	—	2	2	no	—
1105	C₂³	—	2	2	no	—
1106	C₂³	—	4	2	no	—
1107	C₂³	—	4	2	no	—
1108	C₂³	—	4	2	no	—
1109	C₂³	—	4	4	no	—
1110	C₂³	—	4	4	no	—
1111	C₂³	—	4	4	no	—
1112	C₂³	—	8	2	no	—
1113	C₂³	—	8	2	no	—
1114	C₂³	—	8	2	no	—
1115	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
1116	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
1117	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1118	Q₈	—	2	1	no	—
1119	Q₈	—	2	1	no	—
1120	Q₈	—	2	2	no	—
1121	Q₈	—	2	2	no	—
1122	Q₈	—	2	1	no	—
1123	Q₈	—	4	4	no	—
1124	Q₈	—	8	1	no	—
1125	Q₈	C₂₃×H(5,𝔽₂)	1	2	yes	—
1126	D₄	—	2	4	no	—
1127	D₄	—	2	2	no	—
1128	D₄	—	2	2	no	—
1129	D₄	—	2	1	no	—
1130	D₄	—	2	2	no	—
1131	D₄	—	2	1	no	—
1132	D₄	—	2	1	no	—
1133	D₄	—	2	2	no	—
1134	D₄	—	2	2	no	—
1135	D₄	—	2	2	no	—
1136	D₄	—	4	2	no	—
1137	D₄	—	4	4	no	—
1138	D₄	—	4	4	no	—
1139	D₄	—	4	4	no	—
1140	D₄	—	4	4	no	—
1141	D₄	—	4	4	no	—
1142	D₄	—	4	4	no	—
1143	D₄	—	4	2	no	—
1144	D₄	—	4	4	no	—
1145	D₄	—	4	2	no	—
1146	D₄	—	4	2	no	—
1147	D₄	—	8	2	no	—
1148	D₄	—	8	1	no	—
1149	D₄	—	8	1	no	—
1150	D₄	—	8	2	no	—
1151	D₄	—	8	2	no	—
1152	D₄	—	8	2	no	—
1153	D₄	—	8	2	no	—
1154	D₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
1155	C₂×C₄	—	2	4	no	—
1156	C₂×C₄	—	2	1	no	—
1157	C₂×C₄	—	2	2	no	—
1158	C₂×C₄	—	2	2	no	—
1159	C₂×C₄	—	2	2	no	—
1160	C₂×C₄	—	2	2	no	—
1161	C₂×C₄	—	2	2	no	—
1162	C₂×C₄	—	2	1	no	—
1163	C₂×C₄	—	2	1	no	—
1164	C₂×C₄	—	2	1	no	—
1165	C₂×C₄	—	2	1	no	—
1166	C₂×C₄	—	2	1	no	—
1167	C₂×C₄	—	2	1	no	—
1168	C₂×C₄	—	2	2	no	—
1169	C₂×C₄	—	2	1	no	—
1170	C₂×C₄	—	2	2	no	—
1171	C₂×C₄	—	4	2	no	—
1172	C₂×C₄	—	4	2	no	—
1173	C₂×C₄	—	4	2	no	—
1174	C₂×C₄	—	4	1	no	—
1175	C₂×C₄	—	4	4	no	—
1176	C₂×C₄	—	4	4	no	—
1177	C₂×C₄	—	4	4	no	—
1178	C₂×C₄	—	4	4	no	—
1179	C₂×C₄	—	4	2	no	—
1180	C₂×C₄	—	4	2	no	—
1181	C₂×C₄	—	8	2	no	—
1182	C₂×C₄	—	8	2	no	—
1183	C₂×C₄	—	8	1	no	—
1184	C₂×C₄	—	8	2	no	—
1185	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1186	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1187	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1188	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1189	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1190	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1191	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1192	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1193	C₈	—	2	2	no	—
1194	C₈	—	2	1	no	—
1195	C₈	—	2	1	no	—
1196	C₈	—	2	1	no	—
1197	C₈	—	2	2	no	—
1198	C₈	—	2	1	no	—
1199	C₂²	—	2	2	no	—
1200	C₂²	—	2	1	no	—
1201	C₂²	—	2	2	no	—
1202	C₂²	—	2	2	no	—
1203	C₂²	—	2	1	no	—
1204	C₂²	—	2	2	no	—
1205	C₂²	—	2	2	no	—
1206	C₂²	—	2	1	no	—
1207	C₂²	—	2	2	no	—
1208	C₂²	—	2	2	no	—
1209	C₂²	—	4	1	no	—
1210	C₂²	—	4	1	no	—
1211	C₂²	—	4	2	no	—
1212	C₂²	—	4	2	no	—
1213	C₂²	—	4	1	no	—
1214	C₂²	—	4	1	no	—
1215	C₂²	—	4	2	no	—
1216	C₂²	—	4	2	no	—
1217	C₂²	—	4	2	no	—
1218	C₂²	—	4	1	no	—
1219	C₂²	—	4	2	no	—
1220	C₂²	—	8	4	no	—
1221	C₂²	—	8	8	no	—
1222	C₂²	—	16	4	no	—
1223	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1224	C₄	—	2	1	no	—
1225	C₄	—	2	2	no	—
1226	C₄	—	2	2	no	—
1227	C₄	—	2	2	no	—
1228	C₄	—	2	1	no	—
1229	C₄	—	2	1	no	—
1230	C₄	—	2	1	no	—
1231	C₄	—	4	2	no	—
1232	C₄	—	4	1	no	—
1233	C₄	—	4	1	no	—
1234	C₄	—	4	1	no	—
1235	C₄	—	4	1	no	—
1236	C₄	—	4	2	no	—
1237	C₄	—	4	1	no	—
1238	C₄	C₂₃×#575	1	2	yes	—
1239	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1240	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1241	C₂	—	4	2	no	—
1242	C₂	—	4	1	no	—
1243	C₂	—	4	2	no	—
1244	C₂	—	4	2	no	—
1245	C₂	—	8	2	no	—
1246	C₂	—	8	1	no	—
1247	C₂	—	8	2	no	—
1248	C₂	C₂₃×#3484	1	1	yes	characteristic
1249	C₂	C₂×C₂₃×#575	1	1	yes	characteristic
1250	C₂	C₂₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂×C₄×D₄×C₂₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂₃×#3519	C₂	semidirect
2. D₄×#41×C₂₃	C₂	semidirect
3. C₂₃×#3333	C₂	semidirect
4. C₂₃×#3331	C₂	semidirect
5. C₂₃×#3329	C₂	semidirect
6. C₂₃×#3326	C₂	semidirect
7. C₂₃×#3325	C₂	semidirect
8. C₂₃×#3322	C₂	semidirect
9. C₂₃×#3278	C₂	semidirect
10. C₂₃×#3275	C₂	semidirect
11. C₂₃×#3274	C₂	semidirect
12. C₂₃×#3274	C₂	semidirect
13. C₂₃×#3273	C₂	semidirect
14. C₂₃×#3272	C₂	semidirect
15. C₂₃×#3212	C₂	semidirect
16. C₂₃×#3207	C₂	semidirect
17. C₂₃×#3197	C₂	semidirect
18. C₂₃×#3194	C₂	semidirect
19. C₂₃×#3106	C₂	semidirect
20. C₂₃×#3102	C₂	semidirect
21. C₂₃×#3006	C₂	semidirect
22. C₂₃×#3005	C₂	semidirect
23. C₂₃×#2975	C₂	semidirect
24. C₂²×#41×C₂₃	C₂²	semidirect
25. C₂×C₂₃×#137	C₂²	semidirect
26. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
27. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
28. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
30. C₂₃×#554	C₂²	semidirect
32. C₂₃×#553	C₂²	semidirect
35. D₄×Q₈×C₂₃	C₂²	semidirect
36. C₂₃×#548	C₂²	semidirect
41. C₂₃×#546	C₂²	semidirect
42. C₂₃×#546	C₂²	semidirect
45. D₄²×C₂₃	C₂²	semidirect
46. D₄²×C₂₃	C₂²	semidirect
50. C₂₃×#532	C₂²	semidirect
51. C₂₃×#532	C₂²	semidirect
52. C₂₃×#529	C₂²	semidirect
54. C₂₃×#525	C₂²	semidirect
55. C₂₃×#525	C₂²	semidirect
56. C₂×C₂₃×#121	C₂²	semidirect
58. C₄×#41×C₂₃	C₂²	semidirect
61. C₂₃×#495	C₂²	semidirect
62. C₂₃×#493	C₂²	semidirect
63. C₂₃×#492	C₂²	semidirect
64. C₂₃×#488	C₂²	semidirect
65. C₂₃×#487	C₂²	semidirect
66. C₂₃×#486	C₂²	semidirect
67. C₂₃×#485	C₂²	semidirect
68. C₂₃×#485	C₂²	semidirect
69. C₂₃×#483	C₂²	semidirect
70. C₂₃×#482	C₂²	semidirect
71. C₂₃×#482	C₂²	semidirect
72. C₂₃×#482	C₂²	semidirect
73. C₂₃×#480	C₂²	semidirect
74. C₂₃×#479	C₂²	semidirect
75. C₂₃×#478	C₂²	semidirect
76. C₂₃×#477	C₂²	semidirect
77. C₂₃×#476	C₂²	semidirect
78. C₂₃×#470	C₂²	semidirect
79. C₂₃×#469	C₂²	semidirect
80. C₂₃×#469	C₂²	semidirect
81. C₂₃×#469	C₂²	semidirect
82. C₂₃×#468	C₂²	semidirect
83. C₂₃×#468	C₂²	semidirect
84. C₂₃×#468	C₂²	semidirect
85. C₂₃×#468	C₂²	semidirect
86. C₂₃×#464	C₂²	semidirect
87. C₂₃×#463	C₂²	semidirect
88. C₂₃×#463	C₂²	semidirect
89. C₂₃×#463	C₂²	semidirect
90. C₂₃×#462	C₂²	semidirect
91. C₂₃×#461	C₂²	semidirect
92. C₂₃×#460	C₂²	semidirect
93. C₂₃×#460	C₂²	semidirect
94. C₂₃×#459	C₂²	semidirect
95. C₂₃×#459	C₂²	semidirect
96. C₂₃×#452	C₂²	semidirect
97. C₂₃×#452	C₂²	semidirect
98. C₂₃×#452	C₂²	semidirect
99. C₂₃×#452	C₂²	semidirect
100. C₂₃×#452	C₂²	semidirect
101. C₂₃×#450	C₂²	semidirect
103. C₂₃×#449	C₂²	semidirect
104. C₂₃×#449	C₂²	semidirect
105. C₂₃×#449	C₂²	semidirect
106. C₂₃×#449	C₂²	semidirect
107. C₂₃×#449	C₂²	semidirect
108. C₂₃×#449	C₂²	semidirect
109. C₂₃×#449	C₂²	semidirect
110. C₂₃×#448	C₂²	semidirect
111. C₂₃×#448	C₂²	semidirect
112. C₂₃×#447	C₂²	semidirect
113. C₂₃×#447	C₂²	semidirect
114. C₂₃×#447	C₂²	semidirect
115. C₄×Q₁₆×C₂₃	C₂²	semidirect
116. C₄×SD₁₆×C₂₃	C₂²	semidirect
117. C₄×SD₁₆×C₂₃	C₂²	semidirect
118. C₄×SD₁₆×C₂₃	C₂²	semidirect
119. C₄×D₈×C₂₃	C₂²	semidirect
120. C₄×D₈×C₂₃	C₂²	semidirect
121. C₂₃×#436	C₂²	semidirect
122. C₂₃×#436	C₂²	semidirect
123. C₂₃×#436	C₂²	semidirect
124. C₂₃×#436	C₂²	semidirect
125. C₂₃×#436	C₂²	semidirect
126. C₂₃×#436	C₂²	semidirect
127. C₂₃×#431	C₂²	semidirect
128. C₂₃×#431	C₂²	semidirect
129. C₂₃×#419	C₂²	semidirect
130. C₂₃×#418	C₂²	semidirect
131. C₂₃×#417	C₂²	semidirect
132. C₂₃×#417	C₂²	semidirect
133. C₂₃×#407	C₂²	semidirect
134. C₂₃×#407	C₂²	semidirect
476. #61590	C₂₃	direct (N × H)
574. #3519	C₂×C₂₃	semidirect
575. D₄×#41	C₂×C₂₃	semidirect
576. #3333	C₂×C₂₃	semidirect
577. #3331	C₂×C₂₃	semidirect
578. #3329	C₂×C₂₃	semidirect
579. #3326	C₂×C₂₃	semidirect
580. #3325	C₂×C₂₃	semidirect
581. #3322	C₂×C₂₃	semidirect
582. #3278	C₂×C₂₃	semidirect
583. #3275	C₂×C₂₃	semidirect
584. #3274	C₂×C₂₃	semidirect
585. #3274	C₂×C₂₃	semidirect
586. #3273	C₂×C₂₃	semidirect
587. #3272	C₂×C₂₃	semidirect
588. #3212	C₂×C₂₃	semidirect
589. #3207	C₂×C₂₃	semidirect
590. #3197	C₂×C₂₃	semidirect
591. #3194	C₂×C₂₃	semidirect
592. #3106	C₂×C₂₃	semidirect
593. #3102	C₂×C₂₃	semidirect
594. #3006	C₂×C₂₃	semidirect
595. #3005	C₂×C₂₃	semidirect
596. #2975	C₂×C₂₃	semidirect
639. C₂²×#41	C₂²×C₂₃	semidirect
640. C₂×#137	C₂²×C₂₃	semidirect
641. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
642. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
643. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
645. #554	C₂²×C₂₃	semidirect
647. #553	C₂²×C₂₃	semidirect
650. D₄×Q₈	C₂²×C₂₃	semidirect
651. #548	C₂²×C₂₃	semidirect
656. #546	C₂²×C₂₃	semidirect
657. #546	C₂²×C₂₃	semidirect
660. D₄²	C₂²×C₂₃	semidirect
661. D₄²	C₂²×C₂₃	semidirect
665. #532	C₂²×C₂₃	semidirect
666. #532	C₂²×C₂₃	semidirect
667. #529	C₂²×C₂₃	semidirect
669. #525	C₂²×C₂₃	semidirect
670. #525	C₂²×C₂₃	semidirect
671. C₂×#121	C₂²×C₂₃	semidirect
673. C₄×#41	C₂²×C₂₃	semidirect
676. #495	C₂²×C₂₃	semidirect
677. #493	C₂²×C₂₃	semidirect
678. #492	C₂²×C₂₃	semidirect
679. #488	C₂²×C₂₃	semidirect
680. #487	C₂²×C₂₃	semidirect
681. #486	C₂²×C₂₃	semidirect
682. #485	C₂²×C₂₃	semidirect
683. #485	C₂²×C₂₃	semidirect
684. #483	C₂²×C₂₃	semidirect
685. #482	C₂²×C₂₃	semidirect
686. #482	C₂²×C₂₃	semidirect
687. #482	C₂²×C₂₃	semidirect
688. #480	C₂²×C₂₃	semidirect
689. #479	C₂²×C₂₃	semidirect
690. #478	C₂²×C₂₃	semidirect
691. #477	C₂²×C₂₃	semidirect
692. #476	C₂²×C₂₃	semidirect
693. #470	C₂²×C₂₃	semidirect
694. #469	C₂²×C₂₃	semidirect
695. #469	C₂²×C₂₃	semidirect
696. #469	C₂²×C₂₃	semidirect
697. #468	C₂²×C₂₃	semidirect
698. #468	C₂²×C₂₃	semidirect
699. #468	C₂²×C₂₃	semidirect
700. #468	C₂²×C₂₃	semidirect
701. #464	C₂²×C₂₃	semidirect
702. #463	C₂²×C₂₃	semidirect
703. #463	C₂²×C₂₃	semidirect
704. #463	C₂²×C₂₃	semidirect
705. #462	C₂²×C₂₃	semidirect
706. #461	C₂²×C₂₃	semidirect
707. #460	C₂²×C₂₃	semidirect
708. #460	C₂²×C₂₃	semidirect
709. #459	C₂²×C₂₃	semidirect
710. #459	C₂²×C₂₃	semidirect
711. #452	C₂²×C₂₃	semidirect
712. #452	C₂²×C₂₃	semidirect
713. #452	C₂²×C₂₃	semidirect
714. #452	C₂²×C₂₃	semidirect
715. #452	C₂²×C₂₃	semidirect
716. #450	C₂²×C₂₃	semidirect
718. #449	C₂²×C₂₃	semidirect
719. #449	C₂²×C₂₃	semidirect
720. #449	C₂²×C₂₃	semidirect
721. #449	C₂²×C₂₃	semidirect
722. #449	C₂²×C₂₃	semidirect
723. #449	C₂²×C₂₃	semidirect
724. #449	C₂²×C₂₃	semidirect
725. #448	C₂²×C₂₃	semidirect
726. #448	C₂²×C₂₃	semidirect
727. #447	C₂²×C₂₃	semidirect
728. #447	C₂²×C₂₃	semidirect
729. #447	C₂²×C₂₃	semidirect
730. C₄×Q₁₆	C₂²×C₂₃	semidirect
731. C₄×SD₁₆	C₂²×C₂₃	semidirect
732. C₄×SD₁₆	C₂²×C₂₃	semidirect
733. C₄×SD₁₆	C₂²×C₂₃	semidirect
734. C₄×D₈	C₂²×C₂₃	semidirect
735. C₄×D₈	C₂²×C₂₃	semidirect
736. #436	C₂²×C₂₃	semidirect
737. #436	C₂²×C₂₃	semidirect
738. #436	C₂²×C₂₃	semidirect
739. #436	C₂²×C₂₃	semidirect
740. #436	C₂²×C₂₃	semidirect
741. #436	C₂²×C₂₃	semidirect
742. #431	C₂²×C₂₃	semidirect
743. #431	C₂²×C₂₃	semidirect
744. #419	C₂²×C₂₃	semidirect
745. #418	C₂²×C₂₃	semidirect
746. #417	C₂²×C₂₃	semidirect
747. #417	C₂²×C₂₃	semidirect
748. #407	C₂²×C₂₃	semidirect
749. #407	C₂²×C₂₃	semidirect
943. C₂₃	#61590	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂₃×#3519	2
D₄×#41×C₂₃	2
C₂₃×#3333	2
C₂₃×#3331	2
C₂₃×#3329	2
C₂₃×#3326	2
C₂₃×#3325	2
C₂₃×#3322	2
C₂₃×#3278	2
C₂₃×#3275	2
C₂₃×#3274	2
C₂₃×#3273	2
C₂₃×#3272	2
C₂₃×#3212	2
C₂₃×#3207	2
C₂₃×#3197	2
C₂₃×#3194	2
C₂₃×#3106	2
C₂₃×#3102	2
C₂₃×#3006	2
C₂₃×#3005	2
C₂₃×#2975	2
#61590	23

Subgroups — C23×#61590 #19209216

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61590 #19209216