Subgroups — C₂₃×#61608 #19209234

Order 5888.

2132 conjugacy classes of subgroups.

The subgroup lattice has 1230 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3506	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×#41×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3328	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#3324	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#3321	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3319	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3304	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#3302	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#3287	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3284	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3278	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3274	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3269	C₂	1	2	yes	maximal, complemented
14	C₂₃×#3267	C₂	1	2	yes	maximal, complemented
15	C₂₃×#3216	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×#3191	C₂	1	2	yes	maximal, complemented
19	C₂₃×#3115	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#3107	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂₃×#3005	C₂	1	2	yes	maximal, complemented
22	C₂₃×#3002	C₂	1	2	yes	maximal, complemented
23	C₂₃×#2974	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₂₃	C₂²	1	2	yes	—
25	C₂×C₂₃×#137	C₂²	1	2	yes	complemented
26	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
27	C₂×C₂₃×#135	C₂²	1	2	yes	complemented
28	C₂×C₂₃×#135	C₂²	1	2	yes	complemented
29	C₂₃×#559	—	2	1	no	—
30	C₂₃×#559	—	2	1	no	—
31	C₂₃×#556	C₂²	1	1	yes	characteristic
32	C₂₃×#556	C₂²	1	1	yes	characteristic, complemented
33	C₂₃×#555	C₂²	1	2	yes	complemented
34	C₂₃×#553	—	2	2	no	—
35	C₂₃×#550	C₂²	1	1	yes	characteristic
36	C₂₃×#550	C₂²	1	1	yes	characteristic
37	C₂₃×#550	C₂²	1	1	yes	characteristic, complemented
38	D₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
39	C₂₃×#548	C₂²	1	2	yes	—
40	C₂₃×#547	—	2	1	no	—
41	C₂₃×#547	C₂²	1	1	yes	characteristic
42	C₂₃×#547	C₂²	1	2	yes	complemented
43	C₂₃×#546	—	2	2	no	—
44	C₂₃×#546	C₂²	1	2	yes	—
45	D₄²×C₂₃	—	2	1	no	—
46	D₄²×C₂₃	C₂²	1	1	yes	characteristic
47	C₂₃×#538	—	2	2	no	—
48	C₂₃×#535	—	2	1	no	—
49	C₂₃×#533	C₂²	1	1	yes	characteristic, complemented
50	C₂₃×#532	—	2	1	no	—
51	C₂₃×#532	C₂²	1	1	yes	characteristic
52	C₂₃×#532	C₂²	1	1	yes	characteristic, complemented
53	C₂₃×#525	—	2	2	no	—
54	C₂₃×#525	C₂²	1	2	yes	—
55	C₂₃×#525	C₂²	1	2	yes	complemented
56	C₂₃×#525	C₂²	1	2	yes	complemented
57	C₂₃×#520	—	2	1	no	—
58	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
59	C₂×C₄×D₄×C₂₃	—	2	1	no	—
60	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
61	C₂₃×#497	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×#489	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×#485	C₂²	1	1	yes	characteristic, complemented
70	C₂₃×#485	C₂²	1	2	yes	complemented
71	C₂₃×#482	C₂²	1	2	yes	complemented
72	C₂₃×#482	C₂²	1	2	yes	complemented
73	C₂₃×#482	C₂²	1	2	yes	complemented
74	C₂₃×#475	C₂²	1	1	yes	characteristic, complemented
75	C₂₃×#475	C₂²	1	1	yes	characteristic, complemented
76	C₂₃×#474	C₂²	1	1	yes	characteristic, complemented
77	C₂₃×#474	C₂²	1	1	yes	characteristic, complemented
78	C₂₃×#470	C₂²	1	2	yes	complemented
79	C₂₃×#469	C₂²	1	2	yes	complemented
80	C₂₃×#468	C₂²	1	2	yes	complemented
81	C₂₃×#468	C₂²	1	2	yes	complemented
82	C₂₃×#467	C₂²	1	2	yes	complemented
83	C₂₃×#466	C₂²	1	2	yes	complemented
84	C₂₃×#465	C₂²	1	2	yes	complemented
85	C₂₃×#465	C₂²	1	2	yes	complemented
86	C₂₃×#463	C₂²	1	2	yes	complemented
87	C₂₃×#463	C₂²	1	2	yes	complemented
88	C₂₃×#462	C₂²	1	1	yes	characteristic, complemented
89	C₂₃×#462	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×#460	C₂²	1	1	yes	characteristic, complemented
95	C₂₃×#459	C₂²	1	1	yes	characteristic, complemented
96	C₂₃×#452	C₂²	1	1	yes	characteristic
97	C₂₃×#452	C₂²	1	1	yes	characteristic
98	C₂₃×#452	C₂²	1	2	yes	complemented
99	C₂₃×#452	C₂²	1	2	yes	complemented
100	C₂₃×#452	C₂²	1	2	yes	complemented
101	C₂₃×#452	C₂²	1	2	yes	complemented
102	C₂₃×#452	C₂²	1	2	yes	complemented
103	C₂₃×#452	C₂²	1	2	yes	complemented
104	C₂₃×#451	C₂²	1	2	yes	complemented
105	C₂₃×#450	C₂²	1	2	yes	complemented
106	C₂₃×#449	C₂²	1	2	yes	—
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×#449	C₂²	1	2	yes	complemented
111	C₂₃×#449	C₂²	1	2	yes	complemented
112	C₂₃×#449	C₂²	1	2	yes	complemented
113	C₂₃×#448	C₂²	1	2	yes	complemented
114	C₂₃×#447	C₂²	1	2	yes	complemented
115	C₂₃×#442	C₂²	1	2	yes	complemented
116	C₂₃×#440	C₂²	1	2	yes	complemented
117	C₄×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
118	C₄×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
119	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
120	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
121	C₂₃×#436	C₂²	1	1	yes	characteristic
122	C₂₃×#436	C₂²	1	1	yes	characteristic
123	C₂₃×#435	C₂²	1	2	yes	complemented
124	C₂₃×#435	C₂²	1	2	yes	complemented
125	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
126	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
127	C₂₃×#432	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×#416	C₂²	1	2	yes	complemented
132	C₂₃×#416	C₂²	1	2	yes	complemented
133	C₂₃×#407	C₂²	1	2	yes	complemented
134	C₂×C₂₃×C₂²⋊C₈	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	C₂×#41×C₂₃	C₂³	1	2	yes	—
146	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
147	C₂²×D₄×C₂₃	—	2	2	no	—
148	C₂²×D₄×C₂₃	—	2	1	no	—
149	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
150	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
151	C₂³×C₄×C₂₃	—	2	2	no	—
152	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
153	C₂₃×#137	—	4	4	no	—
154	C₂₃×AGL(1,ℤ/8)	—	4	4	no	—
155	C₂₃×#135	—	4	4	no	—
156	C₂₃×#135	—	4	4	no	—
157	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
158	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
159	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
160	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
161	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
162	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
163	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
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	2	yes	—
169	C₂×D₈×C₂₃	C₂³	1	2	yes	—
170	C₂×D₈×C₂₃	C₂³	1	2	yes	—
171	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
172	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
173	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
174	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
175	C₂₃×C₄⋊Q₈	—	2	1	no	—
176	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
177	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
183	C₂₃×#127	C₂³	1	1	yes	characteristic
184	C₂₃×#127	C₂³	1	1	yes	characteristic
185	C₂₃×#126	—	2	2	no	—
186	C₂₃×#126	—	2	2	no	—
187	C₂₃×#125	—	2	1	no	—
188	C₂₃×#124	—	2	1	no	—
189	C₂₃×#124	—	2	1	no	—
190	C₂₃×#124	—	2	2	no	—
191	C₂₃×#124	—	2	2	no	—
192	C₂₃×#124	—	2	2	no	—
193	C₂₃×#124	—	2	1	no	—
194	C₂₃×#124	C₂³	1	2	yes	—
195	C₂₃×#123	—	2	2	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×#123	—	2	2	no	—
201	C₂₃×#123	—	2	2	no	—
202	C₂₃×C₂²⋊Q₈	—	2	1	no	—
203	C₂₃×C₂²⋊Q₈	—	2	2	no	—
204	C₂₃×C₂²⋊Q₈	—	2	2	no	—
205	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
206	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
207	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
208	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
209	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
210	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
211	C₂₃×#121	—	2	1	no	—
212	C₂₃×#121	—	2	2	no	—
213	C₂₃×#121	—	2	2	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	1	no	—
219	C₂₃×#121	—	2	2	no	—
220	C₂₃×#121	—	2	2	no	—
221	C₂₃×#121	—	2	2	no	—
222	C₂₃×#121	—	2	2	no	—
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	2	yes	—
228	C₂₃×#120	—	2	2	no	—
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	C₄×Q₈×C₂₃	—	2	1	no	—
234	C₄×Q₈×C₂₃	—	2	1	no	—
235	C₄×Q₈×C₂₃	—	2	1	no	—
236	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
237	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
238	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
239	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₂₃	—	2	1	no	—
241	C₄×D₄×C₂₃	—	2	1	no	—
242	C₄×D₄×C₂₃	—	2	2	no	—
243	C₄×D₄×C₂₃	—	2	2	no	—
244	C₄×D₄×C₂₃	—	2	2	no	—
245	C₄×D₄×C₂₃	—	2	1	no	—
246	C₄×D₄×C₂₃	—	2	2	no	—
247	C₄×D₄×C₂₃	—	2	2	no	—
248	C₄×D₄×C₂₃	—	2	2	no	—
249	C₄×D₄×C₂₃	—	2	1	no	—
250	C₄×D₄×C₂₃	—	2	1	no	—
251	C₄×D₄×C₂₃	—	2	1	no	—
252	C₄×D₄×C₂₃	—	2	2	no	—
253	C₄×D₄×C₂₃	—	2	1	no	—
254	C₄×D₄×C₂₃	—	2	1	no	—
255	C₄×D₄×C₂₃	—	2	1	no	—
256	C₄×D₄×C₂₃	D₄	1	2	yes	—
257	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
258	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
259	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
260	C₄×D₄×C₂₃	C₂³	1	2	yes	—
261	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
262	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
263	C₄×D₄×C₂₃	C₂³	1	2	yes	—
264	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
265	C₂₃×#117	—	2	1	no	—
266	C₂₃×#117	—	2	2	no	—
267	C₂₃×#117	—	2	1	no	—
268	C₂₃×#117	C₂³	1	2	yes	—
269	C₂₃×#117	C₂³	1	2	yes	—
270	C₂₃×#117	C₂³	1	1	yes	characteristic
271	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
272	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
273	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
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	1	yes	characteristic
279	C₂₃×#107	C₂³	1	1	yes	characteristic
280	C₂₃×#107	C₂³	1	2	yes	—
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×#103	C₂³	1	1	yes	characteristic
298	C₂₃×#103	C₂³	1	1	yes	characteristic
299	C₂₃×#102	C₂³	1	1	yes	characteristic
300	C₂₃×#102	C₂³	1	2	yes	—
301	C₂₃×#102	C₂³	1	2	yes	—
302	C₂₃×#102	C₂³	1	2	yes	—
303	C₂₃×#102	C₂³	1	1	yes	characteristic
304	C₂₃×#102	C₂³	1	2	yes	—
305	C₂₃×#102	C₂³	1	2	yes	—
306	C₂₃×#102	C₂³	1	2	yes	—
307	C₂₃×#102	C₂³	1	2	yes	—
308	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
309	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
310	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
311	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
312	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
313	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
314	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
315	C₂₃×#97	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	C₂×D₄	1	2	yes	—
320	#41×C₂₃	—	2	2	no	—
321	#41×C₂₃	—	2	2	no	—
322	#41×C₂₃	—	2	4	no	—
323	#41×C₂₃	—	2	4	no	—
324	#41×C₂₃	—	4	2	no	—
325	#41×C₂₃	—	4	2	no	—
326	#41×C₂₃	—	4	2	no	—
327	#41×C₂₃	—	4	2	no	—
328	#41×C₂₃	—	4	4	no	—
329	#41×C₂₃	—	4	8	no	—
330	#41×C₂₃	—	4	2	no	—
331	#41×C₂₃	—	4	2	no	—
332	#41×C₂₃	—	4	2	no	—
333	#41×C₂₃	—	4	2	no	—
334	#41×C₂₃	—	4	8	no	—
335	C₂×Q₈×C₂₃	—	2	1	no	—
336	C₂×Q₈×C₂₃	—	2	2	no	—
337	C₂×Q₈×C₂₃	—	2	1	no	—
338	C₂×Q₈×C₂₃	—	2	4	no	—
339	C₂×Q₈×C₂₃	—	4	2	no	—
340	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
341	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
342	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
343	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
344	C₂×D₄×C₂₃	—	2	1	no	—
345	C₂×D₄×C₂₃	—	2	4	no	—
346	C₂×D₄×C₂₃	—	2	2	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	2	no	—
355	C₂×D₄×C₂₃	—	2	2	no	—
356	C₂×D₄×C₂₃	—	2	1	no	—
357	C₂×D₄×C₂₃	—	2	1	no	—
358	C₂×D₄×C₂₃	—	2	2	no	—
359	C₂×D₄×C₂₃	—	2	1	no	—
360	C₂×D₄×C₂₃	—	2	1	no	—
361	C₂×D₄×C₂₃	—	4	2	no	—
362	C₂×D₄×C₂₃	—	4	2	no	—
363	C₂×D₄×C₂₃	—	4	4	no	—
364	C₂×D₄×C₂₃	—	4	8	no	—
365	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
366	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
367	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
368	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
369	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
370	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
371	C₂²×C₄×C₂₃	—	2	1	no	—
372	C₂²×C₄×C₂₃	—	2	2	no	—
373	C₂²×C₄×C₂₃	—	2	1	no	—
374	C₂²×C₄×C₂₃	—	2	2	no	—
375	C₂²×C₄×C₂₃	—	2	2	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	2	no	—
381	C₂²×C₄×C₂₃	—	4	2	no	—
382	C₂²×C₄×C₂₃	—	4	2	no	—
383	C₂²×C₄×C₂₃	—	4	8	no	—
384	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
385	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
386	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
387	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
388	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
389	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
390	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
391	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
392	Q₁₆×C₂₃	—	2	2	no	—
393	Q₁₆×C₂₃	—	2	2	no	—
394	Q₁₆×C₂₃	—	4	2	no	—
395	Q₁₆×C₂₃	—	4	2	no	—
396	SD₁₆×C₂₃	—	2	4	no	—
397	SD₁₆×C₂₃	—	2	2	no	—
398	SD₁₆×C₂₃	—	2	2	no	—
399	SD₁₆×C₂₃	—	4	2	no	—
400	SD₁₆×C₂₃	—	4	2	no	—
401	SD₁₆×C₂₃	—	4	2	no	—
402	SD₁₆×C₂₃	—	4	2	no	—
403	D₈×C₂₃	—	2	4	no	—
404	D₈×C₂₃	—	4	2	no	—
405	D₈×C₂₃	—	4	2	no	—
406	M₁₆×C₂₃	—	4	2	no	—
407	M₁₆×C₂₃	—	4	2	no	—
408	C₂×C₈×C₂₃	—	4	2	no	—
409	C₂×C₈×C₂₃	—	4	2	no	—
410	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
411	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
412	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
413	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
414	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
415	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
416	C₄⋊C₄×C₂₃	—	2	1	no	—
417	C₄⋊C₄×C₂₃	—	2	1	no	—
418	C₄⋊C₄×C₂₃	—	2	2	no	—
419	C₄⋊C₄×C₂₃	—	2	2	no	—
420	C₄⋊C₄×C₂₃	—	2	2	no	—
421	C₄⋊C₄×C₂₃	—	2	1	no	—
422	C₄⋊C₄×C₂₃	—	2	1	no	—
423	C₄⋊C₄×C₂₃	—	2	1	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	2	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	1	no	—
432	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
433	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
434	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
435	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
436	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
437	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
438	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
439	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
440	C₂²⋊C₄×C₂₃	—	2	2	no	—
441	C₂²⋊C₄×C₂₃	—	2	1	no	—
442	C₂²⋊C₄×C₂₃	—	2	1	no	—
443	C₂²⋊C₄×C₂₃	—	2	1	no	—
444	C₂²⋊C₄×C₂₃	—	2	2	no	—
445	C₂²⋊C₄×C₂₃	—	2	2	no	—
446	C₂²⋊C₄×C₂₃	—	2	2	no	—
447	C₂²⋊C₄×C₂₃	—	2	2	no	—
448	C₂²⋊C₄×C₂₃	—	2	2	no	—
449	C₂²⋊C₄×C₂₃	—	2	2	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	1	no	—
454	C₂²⋊C₄×C₂₃	—	2	1	no	—
455	C₂²⋊C₄×C₂₃	—	2	2	no	—
456	C₂²⋊C₄×C₂₃	—	2	2	no	—
457	C₂²⋊C₄×C₂₃	—	2	2	no	—
458	C₂²⋊C₄×C₂₃	—	2	2	no	—
459	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
460	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
461	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
462	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
463	C₄²×C₂₃	—	2	1	no	—
464	C₄²×C₂₃	—	2	1	no	—
465	C₄²×C₂₃	—	2	1	no	—
466	C₄²×C₂₃	—	2	2	no	—
467	C₄²×C₂₃	—	2	2	no	—
468	C₄²×C₂₃	—	2	1	no	—
469	C₄²×C₂₃	—	2	1	no	—
470	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
471	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
472	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
473	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
474	#61608	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
475	C₂³×C₂₃	—	2	1	no	—
476	C₂³×C₂₃	—	2	2	no	—
477	C₂³×C₂₃	—	2	2	no	—
478	C₂³×C₂₃	—	4	2	no	—
479	C₂³×C₂₃	—	4	2	no	—
480	C₂³×C₂₃	—	4	2	no	—
481	C₂³×C₂₃	—	4	4	no	—
482	C₂³×C₂₃	—	4	4	no	—
483	C₂³×C₂₃	—	8	2	no	—
484	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
485	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
486	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
487	Q₈×C₂₃	—	2	1	no	—
488	Q₈×C₂₃	—	2	1	no	—
489	Q₈×C₂₃	—	2	1	no	—
490	Q₈×C₂₃	—	2	1	no	—
491	Q₈×C₂₃	—	2	2	no	—
492	Q₈×C₂₃	—	2	2	no	—
493	Q₈×C₂₃	—	2	1	no	—
494	Q₈×C₂₃	—	4	4	no	—
495	Q₈×C₂₃	—	4	2	no	—
496	Q₈×C₂₃	—	8	1	no	—
497	Q₈×C₂₃	H(5,𝔽₂)	1	2	yes	—
498	D₄×C₂₃	—	2	4	no	—
499	D₄×C₂₃	—	2	2	no	—
500	D₄×C₂₃	—	2	2	no	—
501	D₄×C₂₃	—	2	1	no	—
502	D₄×C₂₃	—	2	2	no	—
503	D₄×C₂₃	—	2	2	no	—
504	D₄×C₂₃	—	2	2	no	—
505	D₄×C₂₃	—	2	2	no	—
506	D₄×C₂₃	—	4	2	no	—
507	D₄×C₂₃	—	4	4	no	—
508	D₄×C₂₃	—	4	4	no	—
509	D₄×C₂₃	—	4	4	no	—
510	D₄×C₂₃	—	4	4	no	—
511	D₄×C₂₃	—	4	4	no	—
512	D₄×C₂₃	—	4	4	no	—
513	D₄×C₂₃	—	4	2	no	—
514	D₄×C₂₃	—	4	2	no	—
515	D₄×C₂₃	—	8	1	no	—
516	D₄×C₂₃	—	8	1	no	—
517	D₄×C₂₃	—	8	2	no	—
518	D₄×C₂₃	—	8	2	no	—
519	D₄×C₂₃	—	8	2	no	—
520	D₄×C₂₃	—	8	2	no	—
521	D₄×C₂₃	—	8	2	no	—
522	D₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
523	C₂×C₄×C₂₃	—	2	4	no	—
524	C₂×C₄×C₂₃	—	2	1	no	—
525	C₂×C₄×C₂₃	—	2	2	no	—
526	C₂×C₄×C₂₃	—	2	2	no	—
527	C₂×C₄×C₂₃	—	2	2	no	—
528	C₂×C₄×C₂₃	—	2	2	no	—
529	C₂×C₄×C₂₃	—	2	2	no	—
530	C₂×C₄×C₂₃	—	2	1	no	—
531	C₂×C₄×C₂₃	—	2	1	no	—
532	C₂×C₄×C₂₃	—	2	1	no	—
533	C₂×C₄×C₂₃	—	2	1	no	—
534	C₂×C₄×C₂₃	—	2	1	no	—
535	C₂×C₄×C₂₃	—	2	1	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	2	no	—
540	C₂×C₄×C₂₃	—	4	2	no	—
541	C₂×C₄×C₂₃	—	4	2	no	—
542	C₂×C₄×C₂₃	—	4	2	no	—
543	C₂×C₄×C₂₃	—	4	1	no	—
544	C₂×C₄×C₂₃	—	4	4	no	—
545	C₂×C₄×C₂₃	—	4	4	no	—
546	C₂×C₄×C₂₃	—	4	4	no	—
547	C₂×C₄×C₂₃	—	4	4	no	—
548	C₂×C₄×C₂₃	—	4	4	no	—
549	C₂×C₄×C₂₃	—	4	2	no	—
550	C₂×C₄×C₂₃	—	8	1	no	—
551	C₂×C₄×C₂₃	—	8	2	no	—
552	C₂×C₄×C₂₃	—	8	2	no	—
553	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
554	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
555	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
556	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
557	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
558	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
559	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
560	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
561	C₈×C₂₃	—	2	1	no	—
562	C₈×C₂₃	—	2	1	no	—
563	C₈×C₂₃	—	2	2	no	—
564	C₈×C₂₃	—	2	2	no	—
565	C₈×C₂₃	—	2	1	no	—
566	C₈×C₂₃	—	2	1	no	—
567	#3506	C₂×C₂₃	1	1	yes	characteristic, complemented
568	D₄×#41	C₂×C₂₃	1	1	yes	characteristic, complemented
569	#3328	C₂×C₂₃	1	1	yes	characteristic, complemented
570	#3324	C₂×C₂₃	1	1	yes	characteristic, complemented
571	#3321	C₂×C₂₃	1	2	yes	complemented
572	#3319	C₂×C₂₃	1	2	yes	complemented
573	#3304	C₂×C₂₃	1	1	yes	characteristic, complemented
574	#3302	C₂×C₂₃	1	1	yes	characteristic, complemented
575	#3287	C₂×C₂₃	1	1	yes	characteristic, complemented
576	#3284	C₂×C₂₃	1	1	yes	characteristic, complemented
577	#3278	C₂×C₂₃	1	1	yes	characteristic, complemented
578	#3274	C₂×C₂₃	1	1	yes	characteristic, complemented
579	#3269	C₂×C₂₃	1	2	yes	complemented
580	#3267	C₂×C₂₃	1	2	yes	complemented
581	#3216	C₂×C₂₃	1	1	yes	characteristic, complemented
582	#3207	C₂×C₂₃	1	1	yes	characteristic, complemented
583	#3197	C₂×C₂₃	1	2	yes	complemented
584	#3191	C₂×C₂₃	1	2	yes	complemented
585	#3115	C₂×C₂₃	1	1	yes	characteristic, complemented
586	#3107	C₂×C₂₃	1	1	yes	characteristic, complemented
587	#3005	C₂×C₂₃	1	2	yes	complemented
588	#3002	C₂×C₂₃	1	2	yes	complemented
589	#2974	C₂×C₂₃	1	1	yes	characteristic, complemented
590	C₂²×C₂₃	—	2	1	no	—
591	C₂²×C₂₃	—	2	2	no	—
592	C₂²×C₂₃	—	2	2	no	—
593	C₂²×C₂₃	—	2	2	no	—
594	C₂²×C₂₃	—	2	1	no	—
595	C₂²×C₂₃	—	2	2	no	—
596	C₂²×C₂₃	—	2	2	no	—
597	C₂²×C₂₃	—	2	1	no	—
598	C₂²×C₂₃	—	2	2	no	—
599	C₂²×C₂₃	—	2	2	no	—
600	C₂²×C₂₃	—	4	1	no	—
601	C₂²×C₂₃	—	4	1	no	—
602	C₂²×C₂₃	—	4	2	no	—
603	C₂²×C₂₃	—	4	2	no	—
604	C₂²×C₂₃	—	4	2	no	—
605	C₂²×C₂₃	—	4	2	no	—
606	C₂²×C₂₃	—	4	2	no	—
607	C₂²×C₂₃	—	4	2	no	—
608	C₂²×C₂₃	—	8	4	no	—
609	C₂²×C₂₃	—	8	8	no	—
610	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
611	C₄×C₂₃	—	2	1	no	—
612	C₄×C₂₃	—	2	1	no	—
613	C₄×C₂₃	—	2	1	no	—
614	C₄×C₂₃	—	2	2	no	—
615	C₄×C₂₃	—	2	2	no	—
616	C₄×C₂₃	—	2	2	no	—
617	C₄×C₂₃	—	2	1	no	—
618	C₄×C₂₃	—	4	1	no	—
619	C₄×C₂₃	—	4	1	no	—
620	C₄×C₂₃	—	4	1	no	—
621	C₄×C₂₃	—	4	2	no	—
622	C₄×C₂₃	—	4	1	no	—
623	C₄×C₂₃	—	4	1	no	—
624	C₄×C₂₃	—	4	1	no	—
625	C₄×C₂₃	—	4	2	no	—
626	C₄×C₂₃	#575	1	2	yes	—
627	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
628	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
629	C₂²×#41	C₂²×C₂₃	1	2	yes	—
630	C₂×#137	C₂²×C₂₃	1	2	yes	complemented
631	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	2	yes	complemented
632	C₂×#135	C₂²×C₂₃	1	2	yes	complemented
633	C₂×#135	C₂²×C₂₃	1	2	yes	complemented
634	#559	—	2	1	no	—
635	#559	—	2	1	no	—
636	#556	C₂²×C₂₃	1	1	yes	characteristic
637	#556	C₂²×C₂₃	1	1	yes	characteristic, complemented
638	#555	C₂²×C₂₃	1	2	yes	complemented
639	#553	—	2	2	no	—
640	#550	C₂²×C₂₃	1	1	yes	characteristic
641	#550	C₂²×C₂₃	1	1	yes	characteristic
642	#550	C₂²×C₂₃	1	1	yes	characteristic, complemented
643	D₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
644	#548	C₂²×C₂₃	1	2	yes	—
645	#547	—	2	1	no	—
646	#547	C₂²×C₂₃	1	1	yes	characteristic
647	#547	C₂²×C₂₃	1	2	yes	complemented
648	#546	—	2	2	no	—
649	#546	C₂²×C₂₃	1	2	yes	—
650	D₄²	—	2	1	no	—
651	D₄²	C₂²×C₂₃	1	1	yes	characteristic
652	#538	—	2	2	no	—
653	#535	—	2	1	no	—
654	#533	C₂²×C₂₃	1	1	yes	characteristic, complemented
655	#532	—	2	1	no	—
656	#532	C₂²×C₂₃	1	1	yes	characteristic
657	#532	C₂²×C₂₃	1	1	yes	characteristic, complemented
658	#525	—	2	2	no	—
659	#525	C₂²×C₂₃	1	2	yes	—
660	#525	C₂²×C₂₃	1	2	yes	complemented
661	#525	C₂²×C₂₃	1	2	yes	complemented
662	#520	—	2	1	no	—
663	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
664	C₂×C₄×D₄	—	2	1	no	—
665	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
666	#497	C₂²×C₂₃	1	2	yes	complemented
667	#493	C₂²×C₂₃	1	1	yes	characteristic, complemented
668	#492	C₂²×C₂₃	1	1	yes	characteristic, complemented
669	#489	C₂²×C₂₃	1	2	yes	complemented
670	#487	C₂²×C₂₃	1	1	yes	characteristic, complemented
671	#486	C₂²×C₂₃	1	1	yes	characteristic, complemented
672	#485	C₂²×C₂₃	1	2	yes	complemented
673	#485	C₂²×C₂₃	1	1	yes	characteristic, complemented
674	#485	C₂²×C₂₃	1	1	yes	characteristic, complemented
675	#485	C₂²×C₂₃	1	2	yes	complemented
676	#482	C₂²×C₂₃	1	2	yes	complemented
677	#482	C₂²×C₂₃	1	2	yes	complemented
678	#482	C₂²×C₂₃	1	2	yes	complemented
679	#475	C₂²×C₂₃	1	1	yes	characteristic, complemented
680	#475	C₂²×C₂₃	1	1	yes	characteristic, complemented
681	#474	C₂²×C₂₃	1	1	yes	characteristic, complemented
682	#474	C₂²×C₂₃	1	1	yes	characteristic, complemented
683	#470	C₂²×C₂₃	1	2	yes	complemented
684	#469	C₂²×C₂₃	1	2	yes	complemented
685	#468	C₂²×C₂₃	1	2	yes	complemented
686	#468	C₂²×C₂₃	1	2	yes	complemented
687	#467	C₂²×C₂₃	1	2	yes	complemented
688	#466	C₂²×C₂₃	1	2	yes	complemented
689	#465	C₂²×C₂₃	1	2	yes	complemented
690	#465	C₂²×C₂₃	1	2	yes	complemented
691	#463	C₂²×C₂₃	1	2	yes	complemented
692	#463	C₂²×C₂₃	1	2	yes	complemented
693	#462	C₂²×C₂₃	1	1	yes	characteristic, complemented
694	#462	C₂²×C₂₃	1	1	yes	characteristic, complemented
695	#462	C₂²×C₂₃	1	1	yes	characteristic, complemented
696	#461	C₂²×C₂₃	1	1	yes	characteristic, complemented
697	#460	C₂²×C₂₃	1	1	yes	characteristic, complemented
698	#460	C₂²×C₂₃	1	1	yes	characteristic, complemented
699	#460	C₂²×C₂₃	1	1	yes	characteristic, complemented
700	#459	C₂²×C₂₃	1	1	yes	characteristic, complemented
701	#452	C₂²×C₂₃	1	1	yes	characteristic
702	#452	C₂²×C₂₃	1	1	yes	characteristic
703	#452	C₂²×C₂₃	1	2	yes	complemented
704	#452	C₂²×C₂₃	1	2	yes	complemented
705	#452	C₂²×C₂₃	1	2	yes	complemented
706	#452	C₂²×C₂₃	1	2	yes	complemented
707	#452	C₂²×C₂₃	1	2	yes	complemented
708	#452	C₂²×C₂₃	1	2	yes	complemented
709	#451	C₂²×C₂₃	1	2	yes	complemented
710	#450	C₂²×C₂₃	1	2	yes	complemented
711	#449	C₂²×C₂₃	1	2	yes	—
712	#449	C₂²×C₂₃	1	2	yes	complemented
713	#449	C₂²×C₂₃	1	2	yes	complemented
714	#449	C₂²×C₂₃	1	2	yes	complemented
715	#449	C₂²×C₂₃	1	2	yes	complemented
716	#449	C₂²×C₂₃	1	2	yes	complemented
717	#449	C₂²×C₂₃	1	2	yes	complemented
718	#448	C₂²×C₂₃	1	2	yes	complemented
719	#447	C₂²×C₂₃	1	2	yes	complemented
720	#442	C₂²×C₂₃	1	2	yes	complemented
721	#440	C₂²×C₂₃	1	2	yes	complemented
722	C₄×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
723	C₄×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
724	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
725	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
726	#436	C₂²×C₂₃	1	1	yes	characteristic
727	#436	C₂²×C₂₃	1	1	yes	characteristic
728	#435	C₂²×C₂₃	1	2	yes	complemented
729	#435	C₂²×C₂₃	1	2	yes	complemented
730	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
731	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
732	#432	C₂²×C₂₃	1	1	yes	characteristic, complemented
733	#431	C₂²×C₂₃	1	1	yes	characteristic, complemented
734	#419	C₂²×C₂₃	1	2	yes	complemented
735	#418	C₂²×C₂₃	1	2	yes	complemented
736	#416	C₂²×C₂₃	1	2	yes	complemented
737	#416	C₂²×C₂₃	1	2	yes	complemented
738	#407	C₂²×C₂₃	1	2	yes	complemented
739	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	complemented
740	C₂×C₂₃	—	4	2	no	—
741	C₂×C₂₃	—	4	1	no	—
742	C₂×C₂₃	—	4	2	no	—
743	C₂×C₂₃	—	4	2	no	—
744	C₂×C₂₃	—	8	2	no	—
745	C₂×C₂₃	—	8	2	no	—
746	C₂×C₂₃	#3484	1	1	yes	characteristic
747	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
748	C₂×C₂₃	#3584	1	1	yes	characteristic
749	C₂×#41	—	2	1	no	—
750	C₂×#41	—	2	2	no	—
751	C₂×#41	—	2	2	no	—
752	C₂×#41	—	4	4	no	—
753	C₂×#41	—	4	4	no	—
754	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
755	C₂×#41	C₂³×C₂₃	1	2	yes	—
756	C₂×#41	C₂³×C₂₃	1	2	yes	—
757	C₂×#41	C₂³×C₂₃	1	2	yes	—
758	C₂×#41	C₂³×C₂₃	1	2	yes	—
759	C₂×#41	C₂³×C₂₃	1	2	yes	—
760	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
761	C₂²×D₄	—	2	2	no	—
762	C₂²×D₄	—	2	1	no	—
763	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
764	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
765	C₂³×C₄	—	2	2	no	—
766	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
767	#137	—	4	4	no	—
768	AGL(1,ℤ/8)	—	4	4	no	—
769	#135	—	4	4	no	—
770	#135	—	4	4	no	—
771	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
772	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
773	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
774	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
775	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
776	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
777	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
778	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
779	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
780	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
781	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
782	C₂×D₈	C₂³×C₂₃	1	2	yes	—
783	C₂×D₈	C₂³×C₂₃	1	2	yes	—
784	C₂×D₈	C₂³×C₂₃	1	2	yes	—
785	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
786	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
787	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
788	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
789	C₄⋊Q₈	—	2	1	no	—
790	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
791	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
792	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
793	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
794	#127	—	2	1	no	—
795	#127	—	2	1	no	—
796	#127	—	2	1	no	—
797	#127	C₂³×C₂₃	1	1	yes	characteristic
798	#127	C₂³×C₂₃	1	1	yes	characteristic
799	#126	—	2	2	no	—
800	#126	—	2	2	no	—
801	#125	—	2	1	no	—
802	#124	—	2	1	no	—
803	#124	—	2	1	no	—
804	#124	—	2	2	no	—
805	#124	—	2	2	no	—
806	#124	—	2	2	no	—
807	#124	—	2	1	no	—
808	#124	C₂³×C₂₃	1	2	yes	—
809	#123	—	2	2	no	—
810	#123	—	2	2	no	—
811	#123	—	2	2	no	—
812	#123	—	2	2	no	—
813	#123	—	2	2	no	—
814	#123	—	2	2	no	—
815	#123	—	2	2	no	—
816	C₂²⋊Q₈	—	2	1	no	—
817	C₂²⋊Q₈	—	2	2	no	—
818	C₂²⋊Q₈	—	2	2	no	—
819	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
820	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
821	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
822	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
823	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
824	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
825	#121	—	2	2	no	—
826	#121	—	2	1	no	—
827	#121	—	2	2	no	—
828	#121	—	2	2	no	—
829	#121	—	2	1	no	—
830	#121	—	2	1	no	—
831	#121	—	2	1	no	—
832	#121	—	2	1	no	—
833	#121	—	2	2	no	—
834	#121	—	2	2	no	—
835	#121	—	2	2	no	—
836	#121	—	2	2	no	—
837	#121	C₂³×C₂₃	1	2	yes	—
838	#121	C₂³×C₂₃	1	2	yes	—
839	#121	C₂³×C₂₃	1	2	yes	—
840	#121	C₂³×C₂₃	1	2	yes	—
841	#121	C₂³×C₂₃	1	2	yes	—
842	#120	—	2	2	no	—
843	#120	—	2	2	no	—
844	#120	—	2	2	no	—
845	#120	—	2	2	no	—
846	#120	—	2	2	no	—
847	C₄×Q₈	—	2	1	no	—
848	C₄×Q₈	—	2	1	no	—
849	C₄×Q₈	—	2	1	no	—
850	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
851	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
852	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
853	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
854	C₄×D₄	—	2	1	no	—
855	C₄×D₄	—	2	2	no	—
856	C₄×D₄	—	2	1	no	—
857	C₄×D₄	—	2	1	no	—
858	C₄×D₄	—	2	2	no	—
859	C₄×D₄	—	2	2	no	—
860	C₄×D₄	—	2	2	no	—
861	C₄×D₄	—	2	2	no	—
862	C₄×D₄	—	2	2	no	—
863	C₄×D₄	—	2	1	no	—
864	C₄×D₄	—	2	1	no	—
865	C₄×D₄	—	2	1	no	—
866	C₄×D₄	—	2	2	no	—
867	C₄×D₄	—	2	1	no	—
868	C₄×D₄	—	2	1	no	—
869	C₄×D₄	—	2	1	no	—
870	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
871	C₄×D₄	D₄×C₂₃	1	2	yes	—
872	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
873	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
874	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
875	C₄×D₄	C₂³×C₂₃	1	2	yes	—
876	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
877	C₄×D₄	C₂³×C₂₃	1	2	yes	—
878	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
879	#117	—	2	1	no	—
880	#117	—	2	2	no	—
881	#117	—	2	1	no	—
882	#117	C₂³×C₂₃	1	1	yes	characteristic
883	#117	C₂³×C₂₃	1	2	yes	—
884	#117	C₂³×C₂₃	1	2	yes	—
885	C₂×C₄⋊C₄	—	2	1	no	—
886	C₂×C₄⋊C₄	—	2	2	no	—
887	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
888	C₂×C₂²⋊C₄	—	2	2	no	—
889	C₂×C₂²⋊C₄	D₄×C₂₃	1	2	yes	—
890	C₂×C₄²	—	2	1	no	—
891	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
892	#107	C₂³×C₂₃	1	1	yes	characteristic
893	#107	C₂³×C₂₃	1	1	yes	characteristic
894	#107	C₂³×C₂₃	1	2	yes	—
895	#106	C₂³×C₂₃	1	1	yes	characteristic
896	#106	C₂³×C₂₃	1	1	yes	characteristic
897	#106	C₂³×C₂₃	1	2	yes	—
898	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
899	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
900	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
901	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
902	#103	C₂³×C₂₃	1	1	yes	characteristic
903	#103	C₂³×C₂₃	1	2	yes	—
904	#103	C₂³×C₂₃	1	2	yes	—
905	#103	C₂³×C₂₃	1	2	yes	—
906	#103	C₂³×C₂₃	1	1	yes	characteristic
907	#103	C₂³×C₂₃	1	2	yes	—
908	#103	C₂³×C₂₃	1	2	yes	—
909	#103	C₂³×C₂₃	1	1	yes	characteristic
910	#103	C₂³×C₂₃	1	1	yes	characteristic
911	#103	C₂³×C₂₃	1	1	yes	characteristic
912	#103	C₂³×C₂₃	1	1	yes	characteristic
913	#102	C₂³×C₂₃	1	1	yes	characteristic
914	#102	C₂³×C₂₃	1	2	yes	—
915	#102	C₂³×C₂₃	1	2	yes	—
916	#102	C₂³×C₂₃	1	2	yes	—
917	#102	C₂³×C₂₃	1	1	yes	characteristic
918	#102	C₂³×C₂₃	1	2	yes	—
919	#102	C₂³×C₂₃	1	2	yes	—
920	#102	C₂³×C₂₃	1	2	yes	—
921	#102	C₂³×C₂₃	1	2	yes	—
922	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
923	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
924	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
925	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
926	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
927	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
928	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
929	#97	C₂³×C₂₃	1	2	yes	—
930	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
931	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
932	C₂₃	#61608	1	1	yes	characteristic, direct product factor, Sylow
933	C₂⁴	—	2	2	no	—
934	C₂⁴	C₂×D₄×C₂₃	1	2	yes	—
935	#41	—	2	2	no	—
936	#41	—	2	2	no	—
937	#41	—	2	4	no	—
938	#41	—	2	4	no	—
939	#41	—	4	2	no	—
940	#41	—	4	2	no	—
941	#41	—	4	2	no	—
942	#41	—	4	2	no	—
943	#41	—	4	8	no	—
944	#41	—	4	4	no	—
945	#41	—	4	2	no	—
946	#41	—	4	2	no	—
947	#41	—	4	2	no	—
948	#41	—	4	2	no	—
949	#41	—	4	8	no	—
950	C₂×Q₈	—	2	1	no	—
951	C₂×Q₈	—	2	2	no	—
952	C₂×Q₈	—	2	1	no	—
953	C₂×Q₈	—	2	4	no	—
954	C₂×Q₈	—	4	2	no	—
955	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
956	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
957	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
958	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
959	C₂×D₄	—	2	1	no	—
960	C₂×D₄	—	2	4	no	—
961	C₂×D₄	—	2	2	no	—
962	C₂×D₄	—	2	2	no	—
963	C₂×D₄	—	2	2	no	—
964	C₂×D₄	—	2	2	no	—
965	C₂×D₄	—	2	2	no	—
966	C₂×D₄	—	2	2	no	—
967	C₂×D₄	—	2	2	no	—
968	C₂×D₄	—	2	2	no	—
969	C₂×D₄	—	2	2	no	—
970	C₂×D₄	—	2	2	no	—
971	C₂×D₄	—	2	1	no	—
972	C₂×D₄	—	2	1	no	—
973	C₂×D₄	—	2	2	no	—
974	C₂×D₄	—	2	1	no	—
975	C₂×D₄	—	2	1	no	—
976	C₂×D₄	—	4	2	no	—
977	C₂×D₄	—	4	2	no	—
978	C₂×D₄	—	4	8	no	—
979	C₂×D₄	—	4	4	no	—
980	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
981	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
982	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
983	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
984	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
985	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
986	C₂²×C₄	—	2	1	no	—
987	C₂²×C₄	—	2	2	no	—
988	C₂²×C₄	—	2	1	no	—
989	C₂²×C₄	—	2	2	no	—
990	C₂²×C₄	—	2	2	no	—
991	C₂²×C₄	—	2	2	no	—
992	C₂²×C₄	—	2	2	no	—
993	C₂²×C₄	—	2	1	no	—
994	C₂²×C₄	—	2	2	no	—
995	C₂²×C₄	—	2	2	no	—
996	C₂²×C₄	—	4	2	no	—
997	C₂²×C₄	—	4	2	no	—
998	C₂²×C₄	—	4	8	no	—
999	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1000	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1001	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
1002	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
1003	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
1004	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1005	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
1006	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
1007	Q₁₆	—	2	2	no	—
1008	Q₁₆	—	2	2	no	—
1009	Q₁₆	—	4	2	no	—
1010	Q₁₆	—	4	2	no	—
1011	SD₁₆	—	2	4	no	—
1012	SD₁₆	—	2	2	no	—
1013	SD₁₆	—	2	2	no	—
1014	SD₁₆	—	4	2	no	—
1015	SD₁₆	—	4	2	no	—
1016	SD₁₆	—	4	2	no	—
1017	SD₁₆	—	4	2	no	—
1018	D₈	—	2	4	no	—
1019	D₈	—	4	2	no	—
1020	D₈	—	4	2	no	—
1021	M₁₆	—	4	2	no	—
1022	M₁₆	—	4	2	no	—
1023	C₂×C₈	—	4	2	no	—
1024	C₂×C₈	—	4	2	no	—
1025	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1026	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1027	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1028	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1029	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1030	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1031	C₄⋊C₄	—	2	1	no	—
1032	C₄⋊C₄	—	2	1	no	—
1033	C₄⋊C₄	—	2	2	no	—
1034	C₄⋊C₄	—	2	2	no	—
1035	C₄⋊C₄	—	2	2	no	—
1036	C₄⋊C₄	—	2	1	no	—
1037	C₄⋊C₄	—	2	1	no	—
1038	C₄⋊C₄	—	2	1	no	—
1039	C₄⋊C₄	—	2	1	no	—
1040	C₄⋊C₄	—	2	1	no	—
1041	C₄⋊C₄	—	2	1	no	—
1042	C₄⋊C₄	—	2	2	no	—
1043	C₄⋊C₄	—	2	1	no	—
1044	C₄⋊C₄	—	2	1	no	—
1045	C₄⋊C₄	—	2	1	no	—
1046	C₄⋊C₄	—	2	1	no	—
1047	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1048	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1049	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1050	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1051	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1052	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1053	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1054	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1055	C₂²⋊C₄	—	2	2	no	—
1056	C₂²⋊C₄	—	2	1	no	—
1057	C₂²⋊C₄	—	2	1	no	—
1058	C₂²⋊C₄	—	2	1	no	—
1059	C₂²⋊C₄	—	2	2	no	—
1060	C₂²⋊C₄	—	2	2	no	—
1061	C₂²⋊C₄	—	2	2	no	—
1062	C₂²⋊C₄	—	2	2	no	—
1063	C₂²⋊C₄	—	2	2	no	—
1064	C₂²⋊C₄	—	2	2	no	—
1065	C₂²⋊C₄	—	2	2	no	—
1066	C₂²⋊C₄	—	2	2	no	—
1067	C₂²⋊C₄	—	2	2	no	—
1068	C₂²⋊C₄	—	2	1	no	—
1069	C₂²⋊C₄	—	2	1	no	—
1070	C₂²⋊C₄	—	2	2	no	—
1071	C₂²⋊C₄	—	2	2	no	—
1072	C₂²⋊C₄	—	2	2	no	—
1073	C₂²⋊C₄	—	2	2	no	—
1074	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1075	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1076	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1077	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1078	C₄²	—	2	1	no	—
1079	C₄²	—	2	1	no	—
1080	C₄²	—	2	1	no	—
1081	C₄²	—	2	2	no	—
1082	C₄²	—	2	2	no	—
1083	C₄²	—	2	1	no	—
1084	C₄²	—	2	1	no	—
1085	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1086	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1087	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1088	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1089	C₂³	—	2	1	no	—
1090	C₂³	—	2	2	no	—
1091	C₂³	—	2	2	no	—
1092	C₂³	—	4	2	no	—
1093	C₂³	—	4	2	no	—
1094	C₂³	—	4	2	no	—
1095	C₂³	—	4	4	no	—
1096	C₂³	—	4	4	no	—
1097	C₂³	—	8	2	no	—
1098	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
1099	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
1100	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1101	Q₈	—	2	1	no	—
1102	Q₈	—	2	1	no	—
1103	Q₈	—	2	1	no	—
1104	Q₈	—	2	1	no	—
1105	Q₈	—	2	2	no	—
1106	Q₈	—	2	2	no	—
1107	Q₈	—	2	1	no	—
1108	Q₈	—	4	4	no	—
1109	Q₈	—	4	2	no	—
1110	Q₈	—	8	1	no	—
1111	Q₈	C₂₃×H(5,𝔽₂)	1	2	yes	—
1112	D₄	—	2	4	no	—
1113	D₄	—	2	2	no	—
1114	D₄	—	2	2	no	—
1115	D₄	—	2	1	no	—
1116	D₄	—	2	2	no	—
1117	D₄	—	2	2	no	—
1118	D₄	—	2	2	no	—
1119	D₄	—	2	2	no	—
1120	D₄	—	4	2	no	—
1121	D₄	—	4	4	no	—
1122	D₄	—	4	4	no	—
1123	D₄	—	4	4	no	—
1124	D₄	—	4	4	no	—
1125	D₄	—	4	4	no	—
1126	D₄	—	4	4	no	—
1127	D₄	—	4	2	no	—
1128	D₄	—	4	2	no	—
1129	D₄	—	8	1	no	—
1130	D₄	—	8	1	no	—
1131	D₄	—	8	2	no	—
1132	D₄	—	8	2	no	—
1133	D₄	—	8	2	no	—
1134	D₄	—	8	2	no	—
1135	D₄	—	8	2	no	—
1136	D₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
1137	C₂×C₄	—	2	4	no	—
1138	C₂×C₄	—	2	1	no	—
1139	C₂×C₄	—	2	2	no	—
1140	C₂×C₄	—	2	2	no	—
1141	C₂×C₄	—	2	2	no	—
1142	C₂×C₄	—	2	2	no	—
1143	C₂×C₄	—	2	2	no	—
1144	C₂×C₄	—	2	1	no	—
1145	C₂×C₄	—	2	1	no	—
1146	C₂×C₄	—	2	1	no	—
1147	C₂×C₄	—	2	1	no	—
1148	C₂×C₄	—	2	1	no	—
1149	C₂×C₄	—	2	1	no	—
1150	C₂×C₄	—	2	2	no	—
1151	C₂×C₄	—	2	1	no	—
1152	C₂×C₄	—	2	1	no	—
1153	C₂×C₄	—	2	2	no	—
1154	C₂×C₄	—	4	2	no	—
1155	C₂×C₄	—	4	2	no	—
1156	C₂×C₄	—	4	2	no	—
1157	C₂×C₄	—	4	1	no	—
1158	C₂×C₄	—	4	4	no	—
1159	C₂×C₄	—	4	4	no	—
1160	C₂×C₄	—	4	4	no	—
1161	C₂×C₄	—	4	4	no	—
1162	C₂×C₄	—	4	4	no	—
1163	C₂×C₄	—	4	2	no	—
1164	C₂×C₄	—	8	2	no	—
1165	C₂×C₄	—	8	2	no	—
1166	C₂×C₄	—	8	1	no	—
1167	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1168	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1169	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1170	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1171	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1172	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1173	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1174	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1175	C₈	—	2	1	no	—
1176	C₈	—	2	1	no	—
1177	C₈	—	2	2	no	—
1178	C₈	—	2	2	no	—
1179	C₈	—	2	1	no	—
1180	C₈	—	2	1	no	—
1181	C₂²	—	2	2	no	—
1182	C₂²	—	2	1	no	—
1183	C₂²	—	2	2	no	—
1184	C₂²	—	2	2	no	—
1185	C₂²	—	2	1	no	—
1186	C₂²	—	2	2	no	—
1187	C₂²	—	2	2	no	—
1188	C₂²	—	2	1	no	—
1189	C₂²	—	2	2	no	—
1190	C₂²	—	2	2	no	—
1191	C₂²	—	4	1	no	—
1192	C₂²	—	4	1	no	—
1193	C₂²	—	4	2	no	—
1194	C₂²	—	4	2	no	—
1195	C₂²	—	4	2	no	—
1196	C₂²	—	4	2	no	—
1197	C₂²	—	4	2	no	—
1198	C₂²	—	4	2	no	—
1199	C₂²	—	8	4	no	—
1200	C₂²	—	8	8	no	—
1201	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1202	C₄	—	2	1	no	—
1203	C₄	—	2	2	no	—
1204	C₄	—	2	2	no	—
1205	C₄	—	2	2	no	—
1206	C₄	—	2	1	no	—
1207	C₄	—	2	1	no	—
1208	C₄	—	2	1	no	—
1209	C₄	—	4	2	no	—
1210	C₄	—	4	1	no	—
1211	C₄	—	4	1	no	—
1212	C₄	—	4	1	no	—
1213	C₄	—	4	2	no	—
1214	C₄	—	4	1	no	—
1215	C₄	—	4	1	no	—
1216	C₄	—	4	1	no	—
1217	C₄	C₂₃×#575	1	2	yes	—
1218	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1219	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1220	C₂	—	4	2	no	—
1221	C₂	—	4	1	no	—
1222	C₂	—	4	2	no	—
1223	C₂	—	4	2	no	—
1224	C₂	—	8	2	no	—
1225	C₂	—	8	2	no	—
1226	C₂	C₂₃×#3484	1	1	yes	characteristic
1227	C₂	C₂×C₂₃×#575	1	1	yes	characteristic
1228	C₂	C₂₃×#3584	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×#3506	C₂	semidirect
2. D₄×#41×C₂₃	C₂	semidirect
3. C₂₃×#3328	C₂	semidirect
4. C₂₃×#3324	C₂	semidirect
5. C₂₃×#3321	C₂	semidirect
6. C₂₃×#3319	C₂	semidirect
7. C₂₃×#3304	C₂	semidirect
8. C₂₃×#3302	C₂	semidirect
9. C₂₃×#3287	C₂	semidirect
10. C₂₃×#3284	C₂	semidirect
11. C₂₃×#3278	C₂	semidirect
12. C₂₃×#3274	C₂	semidirect
13. C₂₃×#3269	C₂	semidirect
14. C₂₃×#3267	C₂	semidirect
15. C₂₃×#3216	C₂	semidirect
16. C₂₃×#3207	C₂	semidirect
17. C₂₃×#3197	C₂	semidirect
18. C₂₃×#3191	C₂	semidirect
19. C₂₃×#3115	C₂	semidirect
20. C₂₃×#3107	C₂	semidirect
21. C₂₃×#3005	C₂	semidirect
22. C₂₃×#3002	C₂	semidirect
23. C₂₃×#2974	C₂	semidirect
25. C₂×C₂₃×#137	C₂²	semidirect
26. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
27. C₂×C₂₃×#135	C₂²	semidirect
28. C₂×C₂₃×#135	C₂²	semidirect
32. C₂₃×#556	C₂²	semidirect
33. C₂₃×#555	C₂²	semidirect
37. C₂₃×#550	C₂²	semidirect
42. C₂₃×#547	C₂²	semidirect
49. C₂₃×#533	C₂²	semidirect
52. C₂₃×#532	C₂²	semidirect
55. C₂₃×#525	C₂²	semidirect
56. C₂₃×#525	C₂²	semidirect
61. C₂₃×#497	C₂²	semidirect
62. C₂₃×#493	C₂²	semidirect
63. C₂₃×#492	C₂²	semidirect
64. C₂₃×#489	C₂²	semidirect
65. C₂₃×#487	C₂²	semidirect
66. C₂₃×#486	C₂²	semidirect
67. C₂₃×#485	C₂²	semidirect
68. C₂₃×#485	C₂²	semidirect
69. C₂₃×#485	C₂²	semidirect
70. C₂₃×#485	C₂²	semidirect
71. C₂₃×#482	C₂²	semidirect
72. C₂₃×#482	C₂²	semidirect
73. C₂₃×#482	C₂²	semidirect
74. C₂₃×#475	C₂²	semidirect
75. C₂₃×#475	C₂²	semidirect
76. C₂₃×#474	C₂²	semidirect
77. C₂₃×#474	C₂²	semidirect
78. C₂₃×#470	C₂²	semidirect
79. C₂₃×#469	C₂²	semidirect
80. C₂₃×#468	C₂²	semidirect
81. C₂₃×#468	C₂²	semidirect
82. C₂₃×#467	C₂²	semidirect
83. C₂₃×#466	C₂²	semidirect
84. C₂₃×#465	C₂²	semidirect
85. C₂₃×#465	C₂²	semidirect
86. C₂₃×#463	C₂²	semidirect
87. C₂₃×#463	C₂²	semidirect
88. C₂₃×#462	C₂²	semidirect
89. C₂₃×#462	C₂²	semidirect
90. C₂₃×#462	C₂²	semidirect
91. C₂₃×#461	C₂²	semidirect
92. C₂₃×#460	C₂²	semidirect
93. C₂₃×#460	C₂²	semidirect
94. C₂₃×#460	C₂²	semidirect
95. C₂₃×#459	C₂²	semidirect
98. C₂₃×#452	C₂²	semidirect
99. C₂₃×#452	C₂²	semidirect
100. C₂₃×#452	C₂²	semidirect
101. C₂₃×#452	C₂²	semidirect
102. C₂₃×#452	C₂²	semidirect
103. C₂₃×#452	C₂²	semidirect
104. C₂₃×#451	C₂²	semidirect
105. C₂₃×#450	C₂²	semidirect
107. C₂₃×#449	C₂²	semidirect
108. C₂₃×#449	C₂²	semidirect
109. C₂₃×#449	C₂²	semidirect
110. C₂₃×#449	C₂²	semidirect
111. C₂₃×#449	C₂²	semidirect
112. C₂₃×#449	C₂²	semidirect
113. C₂₃×#448	C₂²	semidirect
114. C₂₃×#447	C₂²	semidirect
115. C₂₃×#442	C₂²	semidirect
116. C₂₃×#440	C₂²	semidirect
117. C₄×Q₁₆×C₂₃	C₂²	semidirect
118. C₄×Q₁₆×C₂₃	C₂²	semidirect
119. C₄×SD₁₆×C₂₃	C₂²	semidirect
120. C₄×SD₁₆×C₂₃	C₂²	semidirect
123. C₂₃×#435	C₂²	semidirect
124. C₂₃×#435	C₂²	semidirect
125. C₈×D₄×C₂₃	C₂²	semidirect
126. C₈×D₄×C₂₃	C₂²	semidirect
127. C₂₃×#432	C₂²	semidirect
128. C₂₃×#431	C₂²	semidirect
129. C₂₃×#419	C₂²	semidirect
130. C₂₃×#418	C₂²	semidirect
131. C₂₃×#416	C₂²	semidirect
132. C₂₃×#416	C₂²	semidirect
133. C₂₃×#407	C₂²	semidirect
134. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
474. #61608	C₂₃	direct (N × H)
567. #3506	C₂×C₂₃	semidirect
568. D₄×#41	C₂×C₂₃	semidirect
569. #3328	C₂×C₂₃	semidirect
570. #3324	C₂×C₂₃	semidirect
571. #3321	C₂×C₂₃	semidirect
572. #3319	C₂×C₂₃	semidirect
573. #3304	C₂×C₂₃	semidirect
574. #3302	C₂×C₂₃	semidirect
575. #3287	C₂×C₂₃	semidirect
576. #3284	C₂×C₂₃	semidirect
577. #3278	C₂×C₂₃	semidirect
578. #3274	C₂×C₂₃	semidirect
579. #3269	C₂×C₂₃	semidirect
580. #3267	C₂×C₂₃	semidirect
581. #3216	C₂×C₂₃	semidirect
582. #3207	C₂×C₂₃	semidirect
583. #3197	C₂×C₂₃	semidirect
584. #3191	C₂×C₂₃	semidirect
585. #3115	C₂×C₂₃	semidirect
586. #3107	C₂×C₂₃	semidirect
587. #3005	C₂×C₂₃	semidirect
588. #3002	C₂×C₂₃	semidirect
589. #2974	C₂×C₂₃	semidirect
630. C₂×#137	C₂²×C₂₃	semidirect
631. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
632. C₂×#135	C₂²×C₂₃	semidirect
633. C₂×#135	C₂²×C₂₃	semidirect
637. #556	C₂²×C₂₃	semidirect
638. #555	C₂²×C₂₃	semidirect
642. #550	C₂²×C₂₃	semidirect
647. #547	C₂²×C₂₃	semidirect
654. #533	C₂²×C₂₃	semidirect
657. #532	C₂²×C₂₃	semidirect
660. #525	C₂²×C₂₃	semidirect
661. #525	C₂²×C₂₃	semidirect
666. #497	C₂²×C₂₃	semidirect
667. #493	C₂²×C₂₃	semidirect
668. #492	C₂²×C₂₃	semidirect
669. #489	C₂²×C₂₃	semidirect
670. #487	C₂²×C₂₃	semidirect
671. #486	C₂²×C₂₃	semidirect
672. #485	C₂²×C₂₃	semidirect
673. #485	C₂²×C₂₃	semidirect
674. #485	C₂²×C₂₃	semidirect
675. #485	C₂²×C₂₃	semidirect
676. #482	C₂²×C₂₃	semidirect
677. #482	C₂²×C₂₃	semidirect
678. #482	C₂²×C₂₃	semidirect
679. #475	C₂²×C₂₃	semidirect
680. #475	C₂²×C₂₃	semidirect
681. #474	C₂²×C₂₃	semidirect
682. #474	C₂²×C₂₃	semidirect
683. #470	C₂²×C₂₃	semidirect
684. #469	C₂²×C₂₃	semidirect
685. #468	C₂²×C₂₃	semidirect
686. #468	C₂²×C₂₃	semidirect
687. #467	C₂²×C₂₃	semidirect
688. #466	C₂²×C₂₃	semidirect
689. #465	C₂²×C₂₃	semidirect
690. #465	C₂²×C₂₃	semidirect
691. #463	C₂²×C₂₃	semidirect
692. #463	C₂²×C₂₃	semidirect
693. #462	C₂²×C₂₃	semidirect
694. #462	C₂²×C₂₃	semidirect
695. #462	C₂²×C₂₃	semidirect
696. #461	C₂²×C₂₃	semidirect
697. #460	C₂²×C₂₃	semidirect
698. #460	C₂²×C₂₃	semidirect
699. #460	C₂²×C₂₃	semidirect
700. #459	C₂²×C₂₃	semidirect
703. #452	C₂²×C₂₃	semidirect
704. #452	C₂²×C₂₃	semidirect
705. #452	C₂²×C₂₃	semidirect
706. #452	C₂²×C₂₃	semidirect
707. #452	C₂²×C₂₃	semidirect
708. #452	C₂²×C₂₃	semidirect
709. #451	C₂²×C₂₃	semidirect
710. #450	C₂²×C₂₃	semidirect
712. #449	C₂²×C₂₃	semidirect
713. #449	C₂²×C₂₃	semidirect
714. #449	C₂²×C₂₃	semidirect
715. #449	C₂²×C₂₃	semidirect
716. #449	C₂²×C₂₃	semidirect
717. #449	C₂²×C₂₃	semidirect
718. #448	C₂²×C₂₃	semidirect
719. #447	C₂²×C₂₃	semidirect
720. #442	C₂²×C₂₃	semidirect
721. #440	C₂²×C₂₃	semidirect
722. C₄×Q₁₆	C₂²×C₂₃	semidirect
723. C₄×Q₁₆	C₂²×C₂₃	semidirect
724. C₄×SD₁₆	C₂²×C₂₃	semidirect
725. C₄×SD₁₆	C₂²×C₂₃	semidirect
728. #435	C₂²×C₂₃	semidirect
729. #435	C₂²×C₂₃	semidirect
730. C₈×D₄	C₂²×C₂₃	semidirect
731. C₈×D₄	C₂²×C₂₃	semidirect
732. #432	C₂²×C₂₃	semidirect
733. #431	C₂²×C₂₃	semidirect
734. #419	C₂²×C₂₃	semidirect
735. #418	C₂²×C₂₃	semidirect
736. #416	C₂²×C₂₃	semidirect
737. #416	C₂²×C₂₃	semidirect
738. #407	C₂²×C₂₃	semidirect
739. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
932. C₂₃	#61608	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×#3506	2
D₄×#41×C₂₃	2
C₂₃×#3328	2
C₂₃×#3324	2
C₂₃×#3321	2
C₂₃×#3319	2
C₂₃×#3304	2
C₂₃×#3302	2
C₂₃×#3287	2
C₂₃×#3284	2
C₂₃×#3278	2
C₂₃×#3274	2
C₂₃×#3269	2
C₂₃×#3267	2
C₂₃×#3216	2
C₂₃×#3207	2
C₂₃×#3197	2
C₂₃×#3191	2
C₂₃×#3115	2
C₂₃×#3107	2
C₂₃×#3005	2
C₂₃×#3002	2
C₂₃×#2974	2
#61608	23

Subgroups — C23×#61608 #19209234

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61608 #19209234