Subgroups — C₂₃×#61187 #19208813

Order 5888.

2116 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×#3494	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3485	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3330	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3322	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3319	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3307	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3307	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3306	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3303	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3297	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3137	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3097	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3091	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3081	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3057	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#3055	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#3042	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#3008	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₂₃×#449	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#2948	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂₃×#2933	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂₃×#2897	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂₃×#2896	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₂₃×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
25	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
26	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
27	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
28	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
29	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic
30	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
31	C₂₃×#555	C₂²	1	2	yes	complemented
32	C₂₃×#553	C₂²	1	2	yes	complemented
33	C₂₃×#553	C₂²	1	2	yes	complemented
34	C₂₃×#551	—	2	2	no	—
35	C₂₃×#547	—	2	1	no	—
36	C₂₃×#547	—	2	1	no	—
37	C₂₃×#547	C₂²	1	2	yes	complemented
38	C₂₃×#547	C₂²	1	2	yes	complemented
39	C₂₃×#547	C₂²	1	2	yes	complemented
40	C₂₃×#546	—	2	1	no	—
41	C₂₃×#546	—	2	1	no	—
42	C₂₃×#546	—	2	2	no	—
43	C₂₃×#546	C₂²	1	2	yes	complemented
44	C₂₃×#546	C₂²	1	2	yes	complemented
45	C₂₃×#544	C₂²	1	1	yes	characteristic, complemented
46	C₂₃×#542	—	2	1	no	—
47	C₂₃×#540	—	2	1	no	—
48	C₂₃×#536	C₂²	1	1	yes	characteristic
49	C₂₃×#536	C₂²	1	1	yes	characteristic
50	C₂₃×#535	C₂²	1	1	yes	characteristic
51	C₂₃×#534	—	2	2	no	—
52	C₂₃×#532	—	2	1	no	—
53	C₂₃×#529	—	2	1	no	—
54	C₂₃×#525	C₂²	1	1	yes	characteristic
55	C₂₃×#525	C₂²	1	1	yes	characteristic
56	C₂×C₂₃×#123	—	2	2	no	—
57	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic, complemented
58	C₂₃×#520	C₂²	1	1	yes	characteristic
59	C₂₃×#518	C₂²	1	1	yes	characteristic
60	C₂₃×#518	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic, complemented
62	C₂₃×#491	C₂²	1	2	yes	complemented
63	C₂₃×#489	C₂²	1	2	yes	complemented
64	C₂₃×#488	C₂²	1	2	yes	complemented
65	C₂₃×#487	C₂²	1	2	yes	complemented
66	C₂₃×#485	C₂²	1	1	yes	characteristic, complemented
67	C₂₃×#485	C₂²	1	2	yes	complemented
68	C₂₃×#485	C₂²	1	1	yes	characteristic, complemented
69	C₂₃×#485	C₂²	1	2	yes	complemented
70	C₂₃×#484	C₂²	1	2	yes	complemented
71	C₂₃×#484	C₂²	1	1	yes	characteristic, complemented
72	C₂₃×#483	C₂²	1	2	yes	complemented
73	C₂₃×#483	C₂²	1	1	yes	characteristic, complemented
74	C₂₃×#482	C₂²	1	1	yes	characteristic, complemented
75	C₂₃×#482	C₂²	1	1	yes	characteristic, complemented
76	C₂₃×#481	C₂²	1	1	yes	characteristic, complemented
77	C₂₃×#480	C₂²	1	1	yes	characteristic, complemented
78	C₂₃×#478	C₂²	1	2	yes	complemented
79	C₂₃×#478	C₂²	1	2	yes	complemented
80	C₂₃×#476	C₂²	1	2	yes	complemented
81	C₂₃×#474	C₂²	1	2	yes	complemented
82	C₂₃×#469	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×#466	C₂²	1	2	yes	complemented
87	C₂₃×#465	C₂²	1	2	yes	complemented
88	C₂₃×#465	C₂²	1	2	yes	complemented
89	C₂₃×#465	C₂²	1	2	yes	complemented
90	C₂₃×#463	C₂²	1	2	yes	complemented
91	C₂₃×#463	C₂²	1	2	yes	complemented
92	C₂₃×#461	C₂²	1	2	yes	complemented
93	C₂₃×#461	C₂²	1	2	yes	complemented
94	C₂₃×#449	C₂²	1	2	yes	complemented
95	C₂₃×#449	C₂²	1	2	yes	complemented
96	C₂₃×#449	C₂²	1	2	yes	complemented
97	C₂₃×#449	C₂²	1	2	yes	complemented
98	C₂₃×#449	C₂²	1	2	yes	complemented
99	C₂₃×#449	C₂²	1	2	yes	complemented
100	C₂₃×#447	C₂²	1	2	yes	complemented
101	C₂₃×#447	C₂²	1	2	yes	complemented
102	C₂₃×#442	C₂²	1	2	yes	complemented
103	C₂₃×#442	C₂²	1	2	yes	complemented
104	C₄×D₈×C₂₃	C₂²	1	2	yes	complemented
105	C₄×D₈×C₂₃	C₂²	1	2	yes	complemented
106	C₂₃×#436	C₂²	1	2	yes	complemented
107	C₂₃×#435	C₂²	1	2	yes	complemented
108	C₂₃×#435	C₂²	1	2	yes	complemented
109	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
110	C₂₃×#428	C₂²	1	1	yes	characteristic, complemented
111	C₂₃×#427	C₂²	1	1	yes	characteristic, complemented
112	C₂₃×#427	C₂²	1	1	yes	characteristic, complemented
113	C₂₃×#424	C₂²	1	1	yes	characteristic, complemented
114	C₂₃×#419	C₂²	1	1	yes	characteristic, complemented
115	C₂₃×#419	C₂²	1	1	yes	characteristic, complemented
116	C₂₃×#418	C₂²	1	1	yes	characteristic
117	C₂₃×#418	C₂²	1	1	yes	characteristic
118	C₂₃×#418	C₂²	1	1	yes	characteristic, complemented
119	C₂₃×#418	C₂²	1	2	yes	complemented
120	C₂₃×#417	C₂²	1	1	yes	characteristic
121	C₂₃×#417	C₂²	1	2	yes	complemented
122	C₂₃×#417	C₂²	1	2	yes	complemented
123	C₂₃×#417	C₂²	1	2	yes	complemented
124	C₂₃×#416	C₂²	1	1	yes	characteristic
125	C₂₃×#416	C₂²	1	1	yes	characteristic
126	C₂₃×#416	C₂²	1	2	yes	complemented
127	C₂₃×#416	C₂²	1	2	yes	complemented
128	C₂₃×#416	C₂²	1	2	yes	complemented
129	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic, complemented
130	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
131	C₂×C₂₃×#102	C₂²	1	2	yes	complemented
132	C₂₃×#408	C₂²	1	1	yes	characteristic
133	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
134	C₂₃×#405	C₂²	1	1	yes	characteristic, complemented
135	C₂₃×H(5,𝔽₂)	—	2	4	no	—
136	C₂₃×H(5,𝔽₂)	—	4	2	no	—
137	C₂×#41×C₂₃	—	2	1	no	—
138	C₂×#41×C₂₃	—	2	2	no	—
139	C₂×#41×C₂₃	—	2	1	no	—
140	C₂×#41×C₂₃	—	2	1	no	—
141	C₂×#41×C₂₃	—	2	4	no	—
142	C₂×#41×C₂₃	—	4	2	no	—
143	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
144	C₂×#41×C₂₃	C₂³	1	2	yes	—
145	C₂×#41×C₂₃	C₂³	1	2	yes	—
146	C₂×#41×C₂₃	C₂³	1	2	yes	—
147	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
148	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
149	C₂²×D₄×C₂₃	—	2	1	no	—
150	C₂²×D₄×C₂₃	—	2	1	no	—
151	C₂²×D₄×C₂₃	—	2	2	no	—
152	C₂²×D₄×C₂₃	—	2	1	no	—
153	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
154	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
155	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
156	C₂³×C₄×C₂₃	—	2	1	no	—
157	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
158	C₂₃×AGL(1,ℤ/8)	—	4	2	no	—
159	C₂×SD₁₆×C₂₃	—	4	2	no	—
160	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
161	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
162	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
163	C₂×D₈×C₂₃	—	2	4	no	—
164	C₂×D₈×C₂₃	C₂³	1	2	yes	—
165	C₂×D₈×C₂₃	C₂³	1	2	yes	—
166	C₂×D₈×C₂₃	C₂³	1	2	yes	—
167	C₂₃×#131	—	4	2	no	—
168	C₂×M₁₆×C₂₃	—	4	2	no	—
169	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
170	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
171	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
172	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
173	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
174	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
175	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
176	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
177	C₂₃×C₄⋊Q₈	—	2	1	no	—
178	C₂₃×C₄⋊Q₈	—	2	1	no	—
179	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
180	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
181	C₂₃×#127	—	2	1	no	—
182	C₂₃×#126	—	2	2	no	—
183	C₂₃×#126	—	2	2	no	—
184	C₂₃×#125	—	2	1	no	—
185	C₂₃×#125	C₂³	1	2	yes	—
186	C₂₃×#124	—	2	1	no	—
187	C₂₃×#124	—	2	1	no	—
188	C₂₃×#124	—	2	2	no	—
189	C₂₃×#124	—	2	2	no	—
190	C₂₃×#124	C₂³	1	2	yes	—
191	C₂₃×#123	—	2	2	no	—
192	C₂₃×#123	—	2	1	no	—
193	C₂₃×#123	—	2	2	no	—
194	C₂₃×#123	—	2	2	no	—
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×#123	—	2	2	no	—
203	C₂₃×#123	—	2	2	no	—
204	C₂₃×#123	D₄	1	2	yes	—
205	C₂₃×C₂²⋊Q₈	—	2	1	no	—
206	C₂₃×C₂²⋊Q₈	—	2	1	no	—
207	C₂₃×C₂²⋊Q₈	—	2	2	no	—
208	C₂₃×C₂²⋊Q₈	—	2	2	no	—
209	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
210	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
211	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
212	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
213	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
214	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
215	C₂₃×#121	—	2	2	no	—
216	C₂₃×#121	—	2	2	no	—
217	C₂₃×#121	—	2	2	no	—
218	C₂₃×#121	—	2	2	no	—
219	C₂₃×#121	—	2	2	no	—
220	C₂₃×#121	—	2	1	no	—
221	C₂₃×#121	—	2	1	no	—
222	C₂₃×#121	—	2	2	no	—
223	C₂₃×#121	—	2	2	no	—
224	C₂₃×#121	D₄	1	1	yes	characteristic
225	C₂₃×#121	D₄	1	1	yes	characteristic
226	C₂₃×#121	C₂³	1	2	yes	—
227	C₂₃×#121	C₂³	1	2	yes	—
228	C₂₃×#121	C₂³	1	2	yes	—
229	C₂₃×#121	C₂³	1	2	yes	—
230	C₂₃×#121	C₂³	1	1	yes	characteristic
231	C₂₃×#121	C₂³	1	1	yes	characteristic
232	C₂₃×#120	—	2	1	no	—
233	C₂₃×#120	—	2	2	no	—
234	C₂₃×#120	—	2	2	no	—
235	C₂₃×#120	—	2	2	no	—
236	C₂₃×#120	D₄	1	2	yes	—
237	C₄×Q₈×C₂₃	—	2	1	no	—
238	C₄×D₄×C₂₃	—	2	2	no	—
239	C₄×D₄×C₂₃	—	2	1	no	—
240	C₄×D₄×C₂₃	—	2	1	no	—
241	C₄×D₄×C₂₃	—	2	1	no	—
242	C₄×D₄×C₂₃	—	2	1	no	—
243	C₄×D₄×C₂₃	—	2	1	no	—
244	C₄×D₄×C₂₃	—	2	1	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	C₂³	1	2	yes	—
249	C₄×D₄×C₂₃	C₂³	1	2	yes	—
250	C₄×D₄×C₂₃	C₂³	1	2	yes	—
251	C₄×D₄×C₂₃	C₂³	1	2	yes	—
252	C₄×D₄×C₂₃	C₂³	1	2	yes	—
253	C₄×D₄×C₂₃	C₂³	1	2	yes	—
254	C₂₃×#117	—	2	1	no	—
255	C₂₃×#117	—	2	1	no	—
256	C₂₃×#117	—	2	2	no	—
257	C₂₃×#117	C₂³	1	1	yes	characteristic
258	C₂₃×#117	C₂³	1	2	yes	—
259	C₂₃×#117	C₂³	1	1	yes	characteristic
260	C₂₃×#117	C₂³	1	1	yes	characteristic
261	C₂₃×#117	C₂³	1	1	yes	characteristic
262	C₂₃×#117	C₂³	1	1	yes	characteristic
263	C₂₃×#117	C₂³	1	1	yes	characteristic
264	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
265	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
266	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
267	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
268	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
269	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
270	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
271	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
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	—	2	2	no	—
276	C₂×C₄²×C₂₃	—	2	1	no	—
277	C₂₃×#107	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	1	yes	characteristic
281	C₂₃×#107	C₂³	1	2	yes	—
282	C₂₃×#106	C₂³	1	1	yes	characteristic
283	C₂₃×#106	C₂³	1	1	yes	characteristic
284	C₂₃×#106	C₂³	1	1	yes	characteristic
285	C₂₃×#106	C₂³	1	1	yes	characteristic
286	C₂₃×#106	C₂³	1	2	yes	—
287	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
288	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
289	C₂₃×#103	C₂³	1	2	yes	—
290	C₂₃×#103	C₂³	1	2	yes	—
291	C₂₃×#103	C₂³	1	1	yes	characteristic
292	C₂₃×#103	C₂³	1	1	yes	characteristic
293	C₂₃×#103	C₂³	1	1	yes	characteristic
294	C₂₃×#103	C₂³	1	1	yes	characteristic
295	C₂₃×#103	C₂³	1	2	yes	—
296	C₂₃×#103	C₂³	1	2	yes	—
297	C₂₃×#103	C₂³	1	2	yes	—
298	C₂₃×#103	C₂³	1	2	yes	—
299	C₂₃×#103	C₂³	1	2	yes	—
300	C₂₃×#102	C₂³	1	2	yes	—
301	C₂₃×#102	C₂³	1	2	yes	—
302	C₂₃×#102	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
308	C₂₃×#102	C₂³	1	2	yes	—
309	C₂₃×#102	C₂³	1	2	yes	—
310	C₂₃×#102	C₂³	1	2	yes	—
311	C₂₃×#102	C₂³	1	2	yes	—
312	C₂₃×#102	C₂³	1	2	yes	—
313	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
314	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
315	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
316	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
317	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
318	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
319	C₂₃×#97	C₂³	1	2	yes	—
320	C₄×C₈×C₂₃	C₂³	1	2	yes	—
321	C₂⁴×C₂₃	—	2	1	no	—
322	C₂⁴×C₂₃	—	2	1	no	—
323	C₂⁴×C₂₃	—	2	2	no	—
324	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
325	#41×C₂₃	—	2	2	no	—
326	#41×C₂₃	—	2	2	no	—
327	#41×C₂₃	—	2	4	no	—
328	#41×C₂₃	—	2	4	no	—
329	#41×C₂₃	—	2	4	no	—
330	#41×C₂₃	—	2	2	no	—
331	#41×C₂₃	—	2	2	no	—
332	#41×C₂₃	—	4	2	no	—
333	#41×C₂₃	—	4	2	no	—
334	#41×C₂₃	—	4	2	no	—
335	#41×C₂₃	—	4	4	no	—
336	#41×C₂₃	—	4	4	no	—
337	#41×C₂₃	—	4	4	no	—
338	#41×C₂₃	—	8	4	no	—
339	C₂×Q₈×C₂₃	—	2	1	no	—
340	C₂×Q₈×C₂₃	—	2	2	no	—
341	C₂×Q₈×C₂₃	—	2	2	no	—
342	C₂×Q₈×C₂₃	—	2	2	no	—
343	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
344	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
345	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
346	C₂×D₄×C₂₃	—	2	4	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	1	no	—
351	C₂×D₄×C₂₃	—	2	2	no	—
352	C₂×D₄×C₂₃	—	2	1	no	—
353	C₂×D₄×C₂₃	—	2	1	no	—
354	C₂×D₄×C₂₃	—	2	2	no	—
355	C₂×D₄×C₂₃	—	2	2	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	—	2	2	no	—
361	C₂×D₄×C₂₃	—	2	2	no	—
362	C₂×D₄×C₂₃	—	2	2	no	—
363	C₂×D₄×C₂₃	—	4	2	no	—
364	C₂×D₄×C₂₃	—	4	4	no	—
365	C₂×D₄×C₂₃	—	4	8	no	—
366	C₂×D₄×C₂₃	—	4	4	no	—
367	C₂×D₄×C₂₃	—	8	2	no	—
368	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
369	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
370	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
371	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
372	C₂×D₄×C₂₃	#41	1	4	yes	complemented
373	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
374	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
375	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
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	1	no	—
380	C₂²×C₄×C₂₃	—	2	1	no	—
381	C₂²×C₄×C₂₃	—	2	1	no	—
382	C₂²×C₄×C₂₃	—	2	2	no	—
383	C₂²×C₄×C₂₃	—	2	2	no	—
384	C₂²×C₄×C₂₃	—	2	2	no	—
385	C₂²×C₄×C₂₃	—	2	2	no	—
386	C₂²×C₄×C₂₃	—	2	1	no	—
387	C₂²×C₄×C₂₃	—	2	2	no	—
388	C₂²×C₄×C₂₃	—	2	2	no	—
389	C₂²×C₄×C₂₃	—	2	2	no	—
390	C₂²×C₄×C₂₃	—	2	2	no	—
391	C₂²×C₄×C₂₃	—	4	4	no	—
392	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
393	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
394	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
395	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
396	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
397	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
398	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
399	SD₁₆×C₂₃	—	4	2	no	—
400	SD₁₆×C₂₃	—	4	2	no	—
401	SD₁₆×C₂₃	—	4	2	no	—
402	D₈×C₂₃	—	2	4	no	—
403	D₈×C₂₃	—	2	4	no	—
404	D₈×C₂₃	—	4	2	no	—
405	M₁₆×C₂₃	—	2	2	no	—
406	M₁₆×C₂₃	—	2	2	no	—
407	M₁₆×C₂₃	—	4	2	no	—
408	M₁₆×C₂₃	—	4	2	no	—
409	C₂×C₈×C₂₃	—	2	2	no	—
410	C₂×C₈×C₂₃	—	2	2	no	—
411	C₂×C₈×C₂₃	—	4	2	no	—
412	C₂×C₈×C₂₃	—	4	2	no	—
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	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
417	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
418	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
419	C₄⋊C₄×C₂₃	—	2	1	no	—
420	C₄⋊C₄×C₂₃	—	2	1	no	—
421	C₄⋊C₄×C₂₃	—	2	2	no	—
422	C₄⋊C₄×C₂₃	—	2	2	no	—
423	C₄⋊C₄×C₂₃	—	2	2	no	—
424	C₄⋊C₄×C₂₃	—	2	2	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	2	no	—
429	C₄⋊C₄×C₂₃	—	2	2	no	—
430	C₄⋊C₄×C₂₃	—	2	2	no	—
431	C₄⋊C₄×C₂₃	—	2	2	no	—
432	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
433	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
434	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
435	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
436	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
437	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
438	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
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	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
443	C₂²⋊C₄×C₂₃	—	2	1	no	—
444	C₂²⋊C₄×C₂₃	—	2	1	no	—
445	C₂²⋊C₄×C₂₃	—	2	1	no	—
446	C₂²⋊C₄×C₂₃	—	2	1	no	—
447	C₂²⋊C₄×C₂₃	—	2	1	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	1	no	—
452	C₂²⋊C₄×C₂₃	—	2	1	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	—	2	2	no	—
460	C₂²⋊C₄×C₂₃	—	2	2	no	—
461	C₂²⋊C₄×C₂₃	—	2	2	no	—
462	C₂²⋊C₄×C₂₃	—	2	2	no	—
463	C₂²⋊C₄×C₂₃	—	2	2	no	—
464	C₂²⋊C₄×C₂₃	—	2	2	no	—
465	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
466	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
467	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
468	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
469	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
470	C₄²×C₂₃	—	2	1	no	—
471	C₄²×C₂₃	—	2	1	no	—
472	C₄²×C₂₃	—	2	1	no	—
473	C₄²×C₂₃	—	2	1	no	—
474	C₄²×C₂₃	—	2	2	no	—
475	C₄²×C₂₃	—	2	1	no	—
476	C₄²×C₂₃	C₂⁴	1	2	yes	—
477	#61187	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
478	C₂³×C₂₃	—	2	2	no	—
479	C₂³×C₂₃	—	2	2	no	—
480	C₂³×C₂₃	—	2	4	no	—
481	C₂³×C₂₃	—	2	2	no	—
482	C₂³×C₂₃	—	2	1	no	—
483	C₂³×C₂₃	—	4	1	no	—
484	C₂³×C₂₃	—	4	1	no	—
485	C₂³×C₂₃	—	4	4	no	—
486	C₂³×C₂₃	—	4	2	no	—
487	C₂³×C₂₃	—	8	1	no	—
488	C₂³×C₂₃	—	8	1	no	—
489	C₂³×C₂₃	—	8	1	no	—
490	C₂³×C₂₃	—	8	1	no	—
491	C₂³×C₂₃	—	8	2	no	—
492	C₂³×C₂₃	—	8	2	no	—
493	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
494	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
495	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
496	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
497	Q₈×C₂₃	—	2	2	no	—
498	Q₈×C₂₃	—	2	2	no	—
499	Q₈×C₂₃	—	2	1	no	—
500	Q₈×C₂₃	—	2	2	no	—
501	Q₈×C₂₃	—	2	1	no	—
502	Q₈×C₂₃	—	4	2	no	—
503	Q₈×C₂₃	—	8	2	no	—
504	D₄×C₂₃	—	2	4	no	—
505	D₄×C₂₃	—	2	4	no	—
506	D₄×C₂₃	—	2	2	no	—
507	D₄×C₂₃	—	2	2	no	—
508	D₄×C₂₃	—	2	1	no	—
509	D₄×C₂₃	—	2	2	no	—
510	D₄×C₂₃	—	2	1	no	—
511	D₄×C₂₃	—	2	2	no	—
512	D₄×C₂₃	—	4	2	no	—
513	D₄×C₂₃	—	4	2	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	4	no	—
519	D₄×C₂₃	—	4	2	no	—
520	D₄×C₂₃	—	4	2	no	—
521	D₄×C₂₃	—	8	1	no	—
522	D₄×C₂₃	—	8	2	no	—
523	D₄×C₂₃	—	8	1	no	—
524	D₄×C₂₃	—	8	2	no	—
525	D₄×C₂₃	—	8	2	no	—
526	D₄×C₂₃	C₂×#41	1	4	yes	—
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	2	no	—
533	C₂×C₄×C₂₃	—	2	1	no	—
534	C₂×C₄×C₂₃	—	2	2	no	—
535	C₂×C₄×C₂₃	—	2	1	no	—
536	C₂×C₄×C₂₃	—	2	1	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	2	no	—
543	C₂×C₄×C₂₃	—	2	2	no	—
544	C₂×C₄×C₂₃	—	2	1	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	2	no	—
549	C₂×C₄×C₂₃	—	4	2	no	—
550	C₂×C₄×C₂₃	—	4	2	no	—
551	C₂×C₄×C₂₃	—	8	2	no	—
552	C₂×C₄×C₂₃	—	8	2	no	—
553	C₂×C₄×C₂₃	—	8	2	no	—
554	C₂×C₄×C₂₃	—	8	2	no	—
555	C₂×C₄×C₂₃	—	8	1	no	—
556	C₂×C₄×C₂₃	—	8	1	no	—
557	C₂×C₄×C₂₃	—	8	2	no	—
558	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
559	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
560	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
561	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
562	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
563	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
564	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
565	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
566	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
567	C₈×C₂₃	—	2	1	no	—
568	C₈×C₂₃	—	2	1	no	—
569	C₈×C₂₃	—	2	1	no	—
570	C₈×C₂₃	—	2	1	no	—
571	C₈×C₂₃	—	2	2	no	—
572	C₈×C₂₃	—	2	2	no	—
573	#3494	C₂×C₂₃	1	1	yes	characteristic, complemented
574	#3485	C₂×C₂₃	1	1	yes	characteristic, complemented
575	#3330	C₂×C₂₃	1	2	yes	complemented
576	#3322	C₂×C₂₃	1	2	yes	complemented
577	#3319	C₂×C₂₃	1	2	yes	complemented
578	#3307	C₂×C₂₃	1	2	yes	complemented
579	#3307	C₂×C₂₃	1	2	yes	complemented
580	#3306	C₂×C₂₃	1	2	yes	complemented
581	#3303	C₂×C₂₃	1	2	yes	complemented
582	#3297	C₂×C₂₃	1	2	yes	complemented
583	#3137	C₂×C₂₃	1	1	yes	characteristic, complemented
584	#3097	C₂×C₂₃	1	1	yes	characteristic, complemented
585	#3091	C₂×C₂₃	1	1	yes	characteristic, complemented
586	#3081	C₂×C₂₃	1	1	yes	characteristic, complemented
587	#3057	C₂×C₂₃	1	1	yes	characteristic, complemented
588	#3055	C₂×C₂₃	1	1	yes	characteristic, complemented
589	#3042	C₂×C₂₃	1	1	yes	characteristic, complemented
590	#3008	C₂×C₂₃	1	1	yes	characteristic, complemented
591	C₂×#449	C₂×C₂₃	1	1	yes	characteristic, complemented
592	#2948	C₂×C₂₃	1	1	yes	characteristic, complemented
593	#2933	C₂×C₂₃	1	1	yes	characteristic, complemented
594	#2897	C₂×C₂₃	1	1	yes	characteristic, complemented
595	#2896	C₂×C₂₃	1	1	yes	characteristic, complemented
596	C₂²×C₂₃	—	2	1	no	—
597	C₂²×C₂₃	—	2	1	no	—
598	C₂²×C₂₃	—	2	1	no	—
599	C₂²×C₂₃	—	2	1	no	—
600	C₂²×C₂₃	—	2	2	no	—
601	C₂²×C₂₃	—	2	1	no	—
602	C₂²×C₂₃	—	2	2	no	—
603	C₂²×C₂₃	—	2	1	no	—
604	C₂²×C₂₃	—	2	1	no	—
605	C₂²×C₂₃	—	2	1	no	—
606	C₂²×C₂₃	—	2	2	no	—
607	C₂²×C₂₃	—	2	4	no	—
608	C₂²×C₂₃	—	4	2	no	—
609	C₂²×C₂₃	—	4	2	no	—
610	C₂²×C₂₃	—	4	2	no	—
611	C₂²×C₂₃	—	4	1	no	—
612	C₂²×C₂₃	—	4	2	no	—
613	C₂²×C₂₃	—	4	1	no	—
614	C₂²×C₂₃	—	4	1	no	—
615	C₂²×C₂₃	—	4	2	no	—
616	C₂²×C₂₃	—	8	2	no	—
617	C₂²×C₂₃	—	8	4	no	—
618	C₂²×C₂₃	—	16	2	no	—
619	C₂²×C₂₃	—	16	4	no	—
620	C₂²×C₂₃	#546	1	2	yes	—
621	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
622	C₄×C₂₃	—	2	2	no	—
623	C₄×C₂₃	—	2	2	no	—
624	C₄×C₂₃	—	2	1	no	—
625	C₄×C₂₃	—	2	1	no	—
626	C₄×C₂₃	—	2	2	no	—
627	C₄×C₂₃	—	4	1	no	—
628	C₄×C₂₃	—	4	1	no	—
629	C₄×C₂₃	—	4	1	no	—
630	C₄×C₂₃	—	4	1	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	2	no	—
636	C₄×C₂₃	#546	1	2	yes	—
637	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
638	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
639	C₂×H(5,𝔽₂)	C₂²×C₂₃	1	1	yes	characteristic
640	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
641	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	1	yes	characteristic
642	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
643	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
644	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic
645	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
646	#555	C₂²×C₂₃	1	2	yes	complemented
647	#553	C₂²×C₂₃	1	2	yes	complemented
648	#553	C₂²×C₂₃	1	2	yes	complemented
649	#551	—	2	2	no	—
650	#547	—	2	1	no	—
651	#547	—	2	1	no	—
652	#547	C₂²×C₂₃	1	2	yes	complemented
653	#547	C₂²×C₂₃	1	2	yes	complemented
654	#547	C₂²×C₂₃	1	2	yes	complemented
655	#546	—	2	1	no	—
656	#546	—	2	1	no	—
657	#546	—	2	2	no	—
658	#546	C₂²×C₂₃	1	2	yes	complemented
659	#546	C₂²×C₂₃	1	2	yes	complemented
660	#544	C₂²×C₂₃	1	1	yes	characteristic, complemented
661	#542	—	2	1	no	—
662	#540	—	2	1	no	—
663	#536	C₂²×C₂₃	1	1	yes	characteristic
664	#536	C₂²×C₂₃	1	1	yes	characteristic
665	#535	C₂²×C₂₃	1	1	yes	characteristic
666	#534	—	2	2	no	—
667	#532	—	2	1	no	—
668	#529	—	2	1	no	—
669	#525	C₂²×C₂₃	1	1	yes	characteristic
670	#525	C₂²×C₂₃	1	1	yes	characteristic
671	C₂×#123	—	2	2	no	—
672	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic, complemented
673	#520	C₂²×C₂₃	1	1	yes	characteristic
674	#518	C₂²×C₂₃	1	1	yes	characteristic
675	#518	C₂²×C₂₃	1	1	yes	characteristic, complemented
676	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic, complemented
677	#491	C₂²×C₂₃	1	2	yes	complemented
678	#489	C₂²×C₂₃	1	2	yes	complemented
679	#488	C₂²×C₂₃	1	2	yes	complemented
680	#487	C₂²×C₂₃	1	2	yes	complemented
681	#485	C₂²×C₂₃	1	1	yes	characteristic, complemented
682	#485	C₂²×C₂₃	1	1	yes	characteristic, complemented
683	#485	C₂²×C₂₃	1	2	yes	complemented
684	#485	C₂²×C₂₃	1	2	yes	complemented
685	#484	C₂²×C₂₃	1	1	yes	characteristic, complemented
686	#484	C₂²×C₂₃	1	2	yes	complemented
687	#483	C₂²×C₂₃	1	1	yes	characteristic, complemented
688	#483	C₂²×C₂₃	1	2	yes	complemented
689	#482	C₂²×C₂₃	1	1	yes	characteristic, complemented
690	#482	C₂²×C₂₃	1	1	yes	characteristic, complemented
691	#481	C₂²×C₂₃	1	1	yes	characteristic, complemented
692	#480	C₂²×C₂₃	1	1	yes	characteristic, complemented
693	#478	C₂²×C₂₃	1	2	yes	complemented
694	#478	C₂²×C₂₃	1	2	yes	complemented
695	#476	C₂²×C₂₃	1	2	yes	complemented
696	#474	C₂²×C₂₃	1	2	yes	complemented
697	#469	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	#466	C₂²×C₂₃	1	2	yes	complemented
702	#465	C₂²×C₂₃	1	2	yes	complemented
703	#465	C₂²×C₂₃	1	2	yes	complemented
704	#465	C₂²×C₂₃	1	2	yes	complemented
705	#463	C₂²×C₂₃	1	2	yes	complemented
706	#463	C₂²×C₂₃	1	2	yes	complemented
707	#461	C₂²×C₂₃	1	2	yes	complemented
708	#461	C₂²×C₂₃	1	2	yes	complemented
709	#449	C₂²×C₂₃	1	2	yes	complemented
710	#449	C₂²×C₂₃	1	2	yes	complemented
711	#449	C₂²×C₂₃	1	2	yes	complemented
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	#447	C₂²×C₂₃	1	2	yes	complemented
716	#447	C₂²×C₂₃	1	2	yes	complemented
717	#442	C₂²×C₂₃	1	2	yes	complemented
718	#442	C₂²×C₂₃	1	2	yes	complemented
719	C₄×D₈	C₂²×C₂₃	1	2	yes	complemented
720	C₄×D₈	C₂²×C₂₃	1	2	yes	complemented
721	#436	C₂²×C₂₃	1	2	yes	complemented
722	#435	C₂²×C₂₃	1	2	yes	complemented
723	#435	C₂²×C₂₃	1	2	yes	complemented
724	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
725	#428	C₂²×C₂₃	1	1	yes	characteristic, complemented
726	#427	C₂²×C₂₃	1	1	yes	characteristic, complemented
727	#427	C₂²×C₂₃	1	1	yes	characteristic, complemented
728	#424	C₂²×C₂₃	1	1	yes	characteristic, complemented
729	#419	C₂²×C₂₃	1	1	yes	characteristic, complemented
730	#419	C₂²×C₂₃	1	1	yes	characteristic, complemented
731	#418	C₂²×C₂₃	1	1	yes	characteristic
732	#418	C₂²×C₂₃	1	1	yes	characteristic
733	#418	C₂²×C₂₃	1	2	yes	complemented
734	#418	C₂²×C₂₃	1	1	yes	characteristic, complemented
735	#417	C₂²×C₂₃	1	1	yes	characteristic
736	#417	C₂²×C₂₃	1	2	yes	complemented
737	#417	C₂²×C₂₃	1	2	yes	complemented
738	#417	C₂²×C₂₃	1	2	yes	complemented
739	#416	C₂²×C₂₃	1	1	yes	characteristic
740	#416	C₂²×C₂₃	1	1	yes	characteristic
741	#416	C₂²×C₂₃	1	2	yes	complemented
742	#416	C₂²×C₂₃	1	2	yes	complemented
743	#416	C₂²×C₂₃	1	2	yes	complemented
744	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic, complemented
745	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
746	C₂×#102	C₂²×C₂₃	1	2	yes	complemented
747	#408	C₂²×C₂₃	1	1	yes	characteristic
748	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
749	#405	C₂²×C₂₃	1	1	yes	characteristic, complemented
750	C₂×C₂₃	—	2	2	no	—
751	C₂×C₂₃	—	4	1	no	—
752	C₂×C₂₃	—	4	1	no	—
753	C₂×C₂₃	—	4	2	no	—
754	C₂×C₂₃	—	4	4	no	—
755	C₂×C₂₃	—	8	2	no	—
756	C₂×C₂₃	—	8	1	no	—
757	C₂×C₂₃	C₂×#546	1	1	yes	characteristic
758	C₂×C₂₃	#3584	1	1	yes	characteristic
759	C₂×C₂₃	#3585	1	1	yes	characteristic
760	H(5,𝔽₂)	—	2	4	no	—
761	H(5,𝔽₂)	—	4	2	no	—
762	C₂×#41	—	2	1	no	—
763	C₂×#41	—	2	2	no	—
764	C₂×#41	—	2	1	no	—
765	C₂×#41	—	2	1	no	—
766	C₂×#41	—	2	4	no	—
767	C₂×#41	—	4	2	no	—
768	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
769	C₂×#41	C₂³×C₂₃	1	2	yes	—
770	C₂×#41	C₂³×C₂₃	1	2	yes	—
771	C₂×#41	C₂³×C₂₃	1	2	yes	—
772	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
773	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
774	C₂²×D₄	—	2	1	no	—
775	C₂²×D₄	—	2	1	no	—
776	C₂²×D₄	—	2	2	no	—
777	C₂²×D₄	—	2	1	no	—
778	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
779	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
780	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
781	C₂³×C₄	—	2	1	no	—
782	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
783	AGL(1,ℤ/8)	—	4	2	no	—
784	C₂×SD₁₆	—	4	2	no	—
785	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
786	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
787	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
788	C₂×D₈	—	2	4	no	—
789	C₂×D₈	C₂³×C₂₃	1	2	yes	—
790	C₂×D₈	C₂³×C₂₃	1	2	yes	—
791	C₂×D₈	C₂³×C₂₃	1	2	yes	—
792	#131	—	4	2	no	—
793	C₂×M₁₆	—	4	2	no	—
794	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
795	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
796	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
797	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
798	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
799	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
800	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
801	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
802	C₄⋊Q₈	—	2	1	no	—
803	C₄⋊Q₈	—	2	1	no	—
804	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
805	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
806	#127	—	2	1	no	—
807	#126	—	2	2	no	—
808	#126	—	2	2	no	—
809	#125	—	2	1	no	—
810	#125	C₂³×C₂₃	1	2	yes	—
811	#124	—	2	1	no	—
812	#124	—	2	1	no	—
813	#124	—	2	2	no	—
814	#124	—	2	2	no	—
815	#124	C₂³×C₂₃	1	2	yes	—
816	#123	—	2	2	no	—
817	#123	—	2	1	no	—
818	#123	—	2	2	no	—
819	#123	—	2	2	no	—
820	#123	—	2	2	no	—
821	#123	—	2	2	no	—
822	#123	—	2	2	no	—
823	#123	—	2	2	no	—
824	#123	—	2	2	no	—
825	#123	—	2	2	no	—
826	#123	—	2	2	no	—
827	#123	—	2	2	no	—
828	#123	—	2	2	no	—
829	#123	D₄×C₂₃	1	2	yes	—
830	C₂²⋊Q₈	—	2	1	no	—
831	C₂²⋊Q₈	—	2	1	no	—
832	C₂²⋊Q₈	—	2	2	no	—
833	C₂²⋊Q₈	—	2	2	no	—
834	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
835	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
836	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
837	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
838	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
839	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
840	#121	—	2	2	no	—
841	#121	—	2	2	no	—
842	#121	—	2	2	no	—
843	#121	—	2	2	no	—
844	#121	—	2	2	no	—
845	#121	—	2	1	no	—
846	#121	—	2	1	no	—
847	#121	—	2	2	no	—
848	#121	—	2	2	no	—
849	#121	D₄×C₂₃	1	1	yes	characteristic
850	#121	D₄×C₂₃	1	1	yes	characteristic
851	#121	C₂³×C₂₃	1	2	yes	—
852	#121	C₂³×C₂₃	1	2	yes	—
853	#121	C₂³×C₂₃	1	1	yes	characteristic
854	#121	C₂³×C₂₃	1	1	yes	characteristic
855	#121	C₂³×C₂₃	1	2	yes	—
856	#121	C₂³×C₂₃	1	2	yes	—
857	#120	—	2	1	no	—
858	#120	—	2	2	no	—
859	#120	—	2	2	no	—
860	#120	—	2	2	no	—
861	#120	D₄×C₂₃	1	2	yes	—
862	C₄×Q₈	—	2	1	no	—
863	C₄×D₄	—	2	1	no	—
864	C₄×D₄	—	2	2	no	—
865	C₄×D₄	—	2	1	no	—
866	C₄×D₄	—	2	1	no	—
867	C₄×D₄	—	2	1	no	—
868	C₄×D₄	—	2	1	no	—
869	C₄×D₄	—	2	1	no	—
870	C₄×D₄	—	2	1	no	—
871	C₄×D₄	—	2	2	no	—
872	C₄×D₄	—	2	2	no	—
873	C₄×D₄	C₂³×C₂₃	1	2	yes	—
874	C₄×D₄	C₂³×C₂₃	1	2	yes	—
875	C₄×D₄	C₂³×C₂₃	1	2	yes	—
876	C₄×D₄	C₂³×C₂₃	1	2	yes	—
877	C₄×D₄	C₂³×C₂₃	1	2	yes	—
878	C₄×D₄	C₂³×C₂₃	1	2	yes	—
879	#117	—	2	1	no	—
880	#117	—	2	1	no	—
881	#117	—	2	2	no	—
882	#117	C₂³×C₂₃	1	1	yes	characteristic
883	#117	C₂³×C₂₃	1	1	yes	characteristic
884	#117	C₂³×C₂₃	1	1	yes	characteristic
885	#117	C₂³×C₂₃	1	1	yes	characteristic
886	#117	C₂³×C₂₃	1	1	yes	characteristic
887	#117	C₂³×C₂₃	1	2	yes	—
888	#117	C₂³×C₂₃	1	1	yes	characteristic
889	C₂×C₄⋊C₄	—	2	2	no	—
890	C₂×C₄⋊C₄	—	2	2	no	—
891	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
892	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
893	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
894	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
895	C₂×C₂²⋊C₄	—	2	1	no	—
896	C₂×C₂²⋊C₄	—	2	1	no	—
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	—	2	2	no	—
901	C₂×C₄²	—	2	1	no	—
902	#107	C₂³×C₂₃	1	1	yes	characteristic
903	#107	C₂³×C₂₃	1	1	yes	characteristic
904	#107	C₂³×C₂₃	1	1	yes	characteristic
905	#107	C₂³×C₂₃	1	1	yes	characteristic
906	#107	C₂³×C₂₃	1	2	yes	—
907	#106	C₂³×C₂₃	1	1	yes	characteristic
908	#106	C₂³×C₂₃	1	1	yes	characteristic
909	#106	C₂³×C₂₃	1	1	yes	characteristic
910	#106	C₂³×C₂₃	1	1	yes	characteristic
911	#106	C₂³×C₂₃	1	2	yes	—
912	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
913	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
914	#103	C₂³×C₂₃	1	2	yes	—
915	#103	C₂³×C₂₃	1	2	yes	—
916	#103	C₂³×C₂₃	1	1	yes	characteristic
917	#103	C₂³×C₂₃	1	1	yes	characteristic
918	#103	C₂³×C₂₃	1	1	yes	characteristic
919	#103	C₂³×C₂₃	1	1	yes	characteristic
920	#103	C₂³×C₂₃	1	2	yes	—
921	#103	C₂³×C₂₃	1	2	yes	—
922	#103	C₂³×C₂₃	1	2	yes	—
923	#103	C₂³×C₂₃	1	2	yes	—
924	#103	C₂³×C₂₃	1	2	yes	—
925	#102	C₂³×C₂₃	1	2	yes	—
926	#102	C₂³×C₂₃	1	2	yes	—
927	#102	C₂³×C₂₃	1	1	yes	characteristic
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	1	yes	characteristic
933	#102	C₂³×C₂₃	1	2	yes	—
934	#102	C₂³×C₂₃	1	2	yes	—
935	#102	C₂³×C₂₃	1	2	yes	—
936	#102	C₂³×C₂₃	1	2	yes	—
937	#102	C₂³×C₂₃	1	2	yes	—
938	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
939	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
940	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
941	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
942	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
943	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
944	#97	C₂³×C₂₃	1	2	yes	—
945	C₄×C₈	C₂³×C₂₃	1	2	yes	—
946	C₂₃	#61187	1	1	yes	characteristic, direct product factor, Sylow
947	C₂⁴	—	2	1	no	—
948	C₂⁴	—	2	1	no	—
949	C₂⁴	—	2	2	no	—
950	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
951	#41	—	2	2	no	—
952	#41	—	2	2	no	—
953	#41	—	2	4	no	—
954	#41	—	2	4	no	—
955	#41	—	2	4	no	—
956	#41	—	2	2	no	—
957	#41	—	2	2	no	—
958	#41	—	4	2	no	—
959	#41	—	4	2	no	—
960	#41	—	4	2	no	—
961	#41	—	4	4	no	—
962	#41	—	4	4	no	—
963	#41	—	4	4	no	—
964	#41	—	8	4	no	—
965	C₂×Q₈	—	2	1	no	—
966	C₂×Q₈	—	2	2	no	—
967	C₂×Q₈	—	2	2	no	—
968	C₂×Q₈	—	2	2	no	—
969	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
970	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
971	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
972	C₂×D₄	—	2	4	no	—
973	C₂×D₄	—	2	2	no	—
974	C₂×D₄	—	2	2	no	—
975	C₂×D₄	—	2	2	no	—
976	C₂×D₄	—	2	1	no	—
977	C₂×D₄	—	2	2	no	—
978	C₂×D₄	—	2	1	no	—
979	C₂×D₄	—	2	1	no	—
980	C₂×D₄	—	2	2	no	—
981	C₂×D₄	—	2	2	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	—	2	2	no	—
987	C₂×D₄	—	2	2	no	—
988	C₂×D₄	—	2	2	no	—
989	C₂×D₄	—	4	2	no	—
990	C₂×D₄	—	4	4	no	—
991	C₂×D₄	—	4	8	no	—
992	C₂×D₄	—	4	4	no	—
993	C₂×D₄	—	8	2	no	—
994	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
995	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
996	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
997	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
998	C₂×D₄	#41×C₂₃	1	4	yes	complemented
999	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
1000	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
1001	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
1002	C₂²×C₄	—	2	2	no	—
1003	C₂²×C₄	—	2	2	no	—
1004	C₂²×C₄	—	2	1	no	—
1005	C₂²×C₄	—	2	1	no	—
1006	C₂²×C₄	—	2	1	no	—
1007	C₂²×C₄	—	2	1	no	—
1008	C₂²×C₄	—	2	2	no	—
1009	C₂²×C₄	—	2	2	no	—
1010	C₂²×C₄	—	2	2	no	—
1011	C₂²×C₄	—	2	2	no	—
1012	C₂²×C₄	—	2	1	no	—
1013	C₂²×C₄	—	2	2	no	—
1014	C₂²×C₄	—	2	2	no	—
1015	C₂²×C₄	—	2	2	no	—
1016	C₂²×C₄	—	2	2	no	—
1017	C₂²×C₄	—	4	4	no	—
1018	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1019	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1020	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1021	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1022	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
1023	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1024	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1025	SD₁₆	—	4	2	no	—
1026	SD₁₆	—	4	2	no	—
1027	SD₁₆	—	4	2	no	—
1028	D₈	—	2	4	no	—
1029	D₈	—	2	4	no	—
1030	D₈	—	4	2	no	—
1031	M₁₆	—	2	2	no	—
1032	M₁₆	—	2	2	no	—
1033	M₁₆	—	4	2	no	—
1034	M₁₆	—	4	2	no	—
1035	C₂×C₈	—	2	2	no	—
1036	C₂×C₈	—	2	2	no	—
1037	C₂×C₈	—	4	2	no	—
1038	C₂×C₈	—	4	2	no	—
1039	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1040	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1041	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1042	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1043	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1044	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1045	C₄⋊C₄	—	2	1	no	—
1046	C₄⋊C₄	—	2	1	no	—
1047	C₄⋊C₄	—	2	2	no	—
1048	C₄⋊C₄	—	2	2	no	—
1049	C₄⋊C₄	—	2	2	no	—
1050	C₄⋊C₄	—	2	2	no	—
1051	C₄⋊C₄	—	2	1	no	—
1052	C₄⋊C₄	—	2	1	no	—
1053	C₄⋊C₄	—	2	1	no	—
1054	C₄⋊C₄	—	2	2	no	—
1055	C₄⋊C₄	—	2	2	no	—
1056	C₄⋊C₄	—	2	2	no	—
1057	C₄⋊C₄	—	2	2	no	—
1058	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1059	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1060	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1061	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1062	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1063	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1064	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
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	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1069	C₂²⋊C₄	—	2	1	no	—
1070	C₂²⋊C₄	—	2	1	no	—
1071	C₂²⋊C₄	—	2	1	no	—
1072	C₂²⋊C₄	—	2	1	no	—
1073	C₂²⋊C₄	—	2	1	no	—
1074	C₂²⋊C₄	—	2	2	no	—
1075	C₂²⋊C₄	—	2	2	no	—
1076	C₂²⋊C₄	—	2	2	no	—
1077	C₂²⋊C₄	—	2	1	no	—
1078	C₂²⋊C₄	—	2	1	no	—
1079	C₂²⋊C₄	—	2	1	no	—
1080	C₂²⋊C₄	—	2	1	no	—
1081	C₂²⋊C₄	—	2	2	no	—
1082	C₂²⋊C₄	—	2	2	no	—
1083	C₂²⋊C₄	—	2	2	no	—
1084	C₂²⋊C₄	—	2	2	no	—
1085	C₂²⋊C₄	—	2	2	no	—
1086	C₂²⋊C₄	—	2	2	no	—
1087	C₂²⋊C₄	—	2	2	no	—
1088	C₂²⋊C₄	—	2	2	no	—
1089	C₂²⋊C₄	—	2	2	no	—
1090	C₂²⋊C₄	—	2	2	no	—
1091	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1092	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1093	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1094	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1095	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1096	C₄²	—	2	1	no	—
1097	C₄²	—	2	1	no	—
1098	C₄²	—	2	1	no	—
1099	C₄²	—	2	1	no	—
1100	C₄²	—	2	2	no	—
1101	C₄²	—	2	1	no	—
1102	C₄²	C₂⁴×C₂₃	1	2	yes	—
1103	C₂³	—	2	2	no	—
1104	C₂³	—	2	2	no	—
1105	C₂³	—	2	4	no	—
1106	C₂³	—	2	2	no	—
1107	C₂³	—	2	1	no	—
1108	C₂³	—	4	1	no	—
1109	C₂³	—	4	1	no	—
1110	C₂³	—	4	4	no	—
1111	C₂³	—	4	2	no	—
1112	C₂³	—	8	1	no	—
1113	C₂³	—	8	1	no	—
1114	C₂³	—	8	1	no	—
1115	C₂³	—	8	1	no	—
1116	C₂³	—	8	2	no	—
1117	C₂³	—	8	2	no	—
1118	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
1119	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1120	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1121	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1122	Q₈	—	2	2	no	—
1123	Q₈	—	2	2	no	—
1124	Q₈	—	2	1	no	—
1125	Q₈	—	2	2	no	—
1126	Q₈	—	2	1	no	—
1127	Q₈	—	4	2	no	—
1128	Q₈	—	8	2	no	—
1129	D₄	—	2	4	no	—
1130	D₄	—	2	2	no	—
1131	D₄	—	2	1	no	—
1132	D₄	—	2	2	no	—
1133	D₄	—	2	1	no	—
1134	D₄	—	2	2	no	—
1135	D₄	—	2	4	no	—
1136	D₄	—	2	2	no	—
1137	D₄	—	4	2	no	—
1138	D₄	—	4	2	no	—
1139	D₄	—	4	4	no	—
1140	D₄	—	4	4	no	—
1141	D₄	—	4	4	no	—
1142	D₄	—	4	4	no	—
1143	D₄	—	4	4	no	—
1144	D₄	—	4	2	no	—
1145	D₄	—	4	2	no	—
1146	D₄	—	8	2	no	—
1147	D₄	—	8	2	no	—
1148	D₄	—	8	1	no	—
1149	D₄	—	8	2	no	—
1150	D₄	—	8	1	no	—
1151	D₄	C₂×#41×C₂₃	1	4	yes	—
1152	C₂×C₄	—	2	2	no	—
1153	C₂×C₄	—	2	1	no	—
1154	C₂×C₄	—	2	1	no	—
1155	C₂×C₄	—	2	2	no	—
1156	C₂×C₄	—	2	1	no	—
1157	C₂×C₄	—	2	2	no	—
1158	C₂×C₄	—	2	1	no	—
1159	C₂×C₄	—	2	2	no	—
1160	C₂×C₄	—	2	2	no	—
1161	C₂×C₄	—	2	1	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	2	no	—
1168	C₂×C₄	—	2	2	no	—
1169	C₂×C₄	—	2	1	no	—
1170	C₂×C₄	—	4	4	no	—
1171	C₂×C₄	—	4	4	no	—
1172	C₂×C₄	—	4	4	no	—
1173	C₂×C₄	—	4	2	no	—
1174	C₂×C₄	—	4	2	no	—
1175	C₂×C₄	—	4	2	no	—
1176	C₂×C₄	—	8	2	no	—
1177	C₂×C₄	—	8	2	no	—
1178	C₂×C₄	—	8	2	no	—
1179	C₂×C₄	—	8	2	no	—
1180	C₂×C₄	—	8	1	no	—
1181	C₂×C₄	—	8	2	no	—
1182	C₂×C₄	—	8	1	no	—
1183	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1184	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1185	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1186	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1187	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1188	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1189	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
1190	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
1191	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1192	C₈	—	2	1	no	—
1193	C₈	—	2	1	no	—
1194	C₈	—	2	1	no	—
1195	C₈	—	2	1	no	—
1196	C₈	—	2	2	no	—
1197	C₈	—	2	2	no	—
1198	C₂²	—	2	1	no	—
1199	C₂²	—	2	1	no	—
1200	C₂²	—	2	1	no	—
1201	C₂²	—	2	1	no	—
1202	C₂²	—	2	2	no	—
1203	C₂²	—	2	4	no	—
1204	C₂²	—	2	1	no	—
1205	C₂²	—	2	1	no	—
1206	C₂²	—	2	2	no	—
1207	C₂²	—	2	1	no	—
1208	C₂²	—	2	2	no	—
1209	C₂²	—	2	1	no	—
1210	C₂²	—	4	2	no	—
1211	C₂²	—	4	2	no	—
1212	C₂²	—	4	1	no	—
1213	C₂²	—	4	2	no	—
1214	C₂²	—	4	2	no	—
1215	C₂²	—	4	1	no	—
1216	C₂²	—	4	2	no	—
1217	C₂²	—	4	1	no	—
1218	C₂²	—	8	2	no	—
1219	C₂²	—	8	4	no	—
1220	C₂²	—	16	2	no	—
1221	C₂²	—	16	4	no	—
1222	C₂²	C₂₃×#546	1	2	yes	—
1223	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1224	C₄	—	2	1	no	—
1225	C₄	—	2	1	no	—
1226	C₄	—	2	2	no	—
1227	C₄	—	2	2	no	—
1228	C₄	—	2	2	no	—
1229	C₄	—	4	1	no	—
1230	C₄	—	4	2	no	—
1231	C₄	—	4	1	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×#546	1	2	yes	—
1239	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
1240	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1241	C₂	—	2	2	no	—
1242	C₂	—	4	1	no	—
1243	C₂	—	4	1	no	—
1244	C₂	—	4	2	no	—
1245	C₂	—	4	4	no	—
1246	C₂	—	8	1	no	—
1247	C₂	—	8	2	no	—
1248	C₂	C₂×C₂₃×#546	1	1	yes	characteristic
1249	C₂	C₂₃×#3584	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 ◁ C₂₃×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3494	C₂	semidirect
2. C₂₃×#3485	C₂	semidirect
3. C₂₃×#3330	C₂	semidirect
4. C₂₃×#3322	C₂	semidirect
5. C₂₃×#3319	C₂	semidirect
6. C₂₃×#3307	C₂	semidirect
7. C₂₃×#3307	C₂	semidirect
8. C₂₃×#3306	C₂	semidirect
9. C₂₃×#3303	C₂	semidirect
10. C₂₃×#3297	C₂	semidirect
11. C₂₃×#3137	C₂	semidirect
12. C₂₃×#3097	C₂	semidirect
13. C₂₃×#3091	C₂	semidirect
14. C₂₃×#3081	C₂	semidirect
15. C₂₃×#3057	C₂	semidirect
16. C₂₃×#3055	C₂	semidirect
17. C₂₃×#3042	C₂	semidirect
18. C₂₃×#3008	C₂	semidirect
19. C₂×C₂₃×#449	C₂	semidirect
20. C₂₃×#2948	C₂	semidirect
21. C₂₃×#2933	C₂	semidirect
22. C₂₃×#2897	C₂	semidirect
23. C₂₃×#2896	C₂	semidirect
27. C₂²×SD₁₆×C₂₃	C₂²	semidirect
30. C₂²×M₁₆×C₂₃	C₂²	semidirect
31. C₂₃×#555	C₂²	semidirect
32. C₂₃×#553	C₂²	semidirect
33. C₂₃×#553	C₂²	semidirect
37. C₂₃×#547	C₂²	semidirect
38. C₂₃×#547	C₂²	semidirect
39. C₂₃×#547	C₂²	semidirect
43. C₂₃×#546	C₂²	semidirect
44. C₂₃×#546	C₂²	semidirect
45. C₂₃×#544	C₂²	semidirect
57. C₂×C₂₃×#121	C₂²	semidirect
60. C₂₃×#518	C₂²	semidirect
61. C₂×C₂₃×#117	C₂²	semidirect
62. C₂₃×#491	C₂²	semidirect
63. C₂₃×#489	C₂²	semidirect
64. C₂₃×#488	C₂²	semidirect
65. C₂₃×#487	C₂²	semidirect
66. C₂₃×#485	C₂²	semidirect
67. C₂₃×#485	C₂²	semidirect
68. C₂₃×#485	C₂²	semidirect
69. C₂₃×#485	C₂²	semidirect
70. C₂₃×#484	C₂²	semidirect
71. C₂₃×#484	C₂²	semidirect
72. C₂₃×#483	C₂²	semidirect
73. C₂₃×#483	C₂²	semidirect
74. C₂₃×#482	C₂²	semidirect
75. C₂₃×#482	C₂²	semidirect
76. C₂₃×#481	C₂²	semidirect
77. C₂₃×#480	C₂²	semidirect
78. C₂₃×#478	C₂²	semidirect
79. C₂₃×#478	C₂²	semidirect
80. C₂₃×#476	C₂²	semidirect
81. C₂₃×#474	C₂²	semidirect
82. C₂₃×#469	C₂²	semidirect
83. C₂₃×#468	C₂²	semidirect
84. C₂₃×#468	C₂²	semidirect
85. C₂₃×#468	C₂²	semidirect
86. C₂₃×#466	C₂²	semidirect
87. C₂₃×#465	C₂²	semidirect
88. C₂₃×#465	C₂²	semidirect
89. C₂₃×#465	C₂²	semidirect
90. C₂₃×#463	C₂²	semidirect
91. C₂₃×#463	C₂²	semidirect
92. C₂₃×#461	C₂²	semidirect
93. C₂₃×#461	C₂²	semidirect
94. C₂₃×#449	C₂²	semidirect
95. C₂₃×#449	C₂²	semidirect
96. C₂₃×#449	C₂²	semidirect
97. C₂₃×#449	C₂²	semidirect
98. C₂₃×#449	C₂²	semidirect
99. C₂₃×#449	C₂²	semidirect
100. C₂₃×#447	C₂²	semidirect
101. C₂₃×#447	C₂²	semidirect
102. C₂₃×#442	C₂²	semidirect
103. C₂₃×#442	C₂²	semidirect
104. C₄×D₈×C₂₃	C₂²	semidirect
105. C₄×D₈×C₂₃	C₂²	semidirect
106. C₂₃×#436	C₂²	semidirect
107. C₂₃×#435	C₂²	semidirect
108. C₂₃×#435	C₂²	semidirect
109. C₈×D₄×C₂₃	C₂²	semidirect
110. C₂₃×#428	C₂²	semidirect
111. C₂₃×#427	C₂²	semidirect
112. C₂₃×#427	C₂²	semidirect
113. C₂₃×#424	C₂²	semidirect
114. C₂₃×#419	C₂²	semidirect
115. C₂₃×#419	C₂²	semidirect
118. C₂₃×#418	C₂²	semidirect
119. C₂₃×#418	C₂²	semidirect
121. C₂₃×#417	C₂²	semidirect
122. C₂₃×#417	C₂²	semidirect
123. C₂₃×#417	C₂²	semidirect
126. C₂₃×#416	C₂²	semidirect
127. C₂₃×#416	C₂²	semidirect
128. C₂₃×#416	C₂²	semidirect
129. C₂×C₂₃×#103	C₂²	semidirect
131. C₂×C₂₃×#102	C₂²	semidirect
133. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
134. C₂₃×#405	C₂²	semidirect
372. C₂×D₄×C₂₃	#41	semidirect
477. #61187	C₂₃	direct (N × H)
573. #3494	C₂×C₂₃	semidirect
574. #3485	C₂×C₂₃	semidirect
575. #3330	C₂×C₂₃	semidirect
576. #3322	C₂×C₂₃	semidirect
577. #3319	C₂×C₂₃	semidirect
578. #3307	C₂×C₂₃	semidirect
579. #3307	C₂×C₂₃	semidirect
580. #3306	C₂×C₂₃	semidirect
581. #3303	C₂×C₂₃	semidirect
582. #3297	C₂×C₂₃	semidirect
583. #3137	C₂×C₂₃	semidirect
584. #3097	C₂×C₂₃	semidirect
585. #3091	C₂×C₂₃	semidirect
586. #3081	C₂×C₂₃	semidirect
587. #3057	C₂×C₂₃	semidirect
588. #3055	C₂×C₂₃	semidirect
589. #3042	C₂×C₂₃	semidirect
590. #3008	C₂×C₂₃	semidirect
591. C₂×#449	C₂×C₂₃	semidirect
592. #2948	C₂×C₂₃	semidirect
593. #2933	C₂×C₂₃	semidirect
594. #2897	C₂×C₂₃	semidirect
595. #2896	C₂×C₂₃	semidirect
642. C₂²×SD₁₆	C₂²×C₂₃	semidirect
645. C₂²×M₁₆	C₂²×C₂₃	semidirect
646. #555	C₂²×C₂₃	semidirect
647. #553	C₂²×C₂₃	semidirect
648. #553	C₂²×C₂₃	semidirect
652. #547	C₂²×C₂₃	semidirect
653. #547	C₂²×C₂₃	semidirect
654. #547	C₂²×C₂₃	semidirect
658. #546	C₂²×C₂₃	semidirect
659. #546	C₂²×C₂₃	semidirect
660. #544	C₂²×C₂₃	semidirect
672. C₂×#121	C₂²×C₂₃	semidirect
675. #518	C₂²×C₂₃	semidirect
676. C₂×#117	C₂²×C₂₃	semidirect
677. #491	C₂²×C₂₃	semidirect
678. #489	C₂²×C₂₃	semidirect
679. #488	C₂²×C₂₃	semidirect
680. #487	C₂²×C₂₃	semidirect
681. #485	C₂²×C₂₃	semidirect
682. #485	C₂²×C₂₃	semidirect
683. #485	C₂²×C₂₃	semidirect
684. #485	C₂²×C₂₃	semidirect
685. #484	C₂²×C₂₃	semidirect
686. #484	C₂²×C₂₃	semidirect
687. #483	C₂²×C₂₃	semidirect
688. #483	C₂²×C₂₃	semidirect
689. #482	C₂²×C₂₃	semidirect
690. #482	C₂²×C₂₃	semidirect
691. #481	C₂²×C₂₃	semidirect
692. #480	C₂²×C₂₃	semidirect
693. #478	C₂²×C₂₃	semidirect
694. #478	C₂²×C₂₃	semidirect
695. #476	C₂²×C₂₃	semidirect
696. #474	C₂²×C₂₃	semidirect
697. #469	C₂²×C₂₃	semidirect
698. #468	C₂²×C₂₃	semidirect
699. #468	C₂²×C₂₃	semidirect
700. #468	C₂²×C₂₃	semidirect
701. #466	C₂²×C₂₃	semidirect
702. #465	C₂²×C₂₃	semidirect
703. #465	C₂²×C₂₃	semidirect
704. #465	C₂²×C₂₃	semidirect
705. #463	C₂²×C₂₃	semidirect
706. #463	C₂²×C₂₃	semidirect
707. #461	C₂²×C₂₃	semidirect
708. #461	C₂²×C₂₃	semidirect
709. #449	C₂²×C₂₃	semidirect
710. #449	C₂²×C₂₃	semidirect
711. #449	C₂²×C₂₃	semidirect
712. #449	C₂²×C₂₃	semidirect
713. #449	C₂²×C₂₃	semidirect
714. #449	C₂²×C₂₃	semidirect
715. #447	C₂²×C₂₃	semidirect
716. #447	C₂²×C₂₃	semidirect
717. #442	C₂²×C₂₃	semidirect
718. #442	C₂²×C₂₃	semidirect
719. C₄×D₈	C₂²×C₂₃	semidirect
720. C₄×D₈	C₂²×C₂₃	semidirect
721. #436	C₂²×C₂₃	semidirect
722. #435	C₂²×C₂₃	semidirect
723. #435	C₂²×C₂₃	semidirect
724. C₈×D₄	C₂²×C₂₃	semidirect
725. #428	C₂²×C₂₃	semidirect
726. #427	C₂²×C₂₃	semidirect
727. #427	C₂²×C₂₃	semidirect
728. #424	C₂²×C₂₃	semidirect
729. #419	C₂²×C₂₃	semidirect
730. #419	C₂²×C₂₃	semidirect
733. #418	C₂²×C₂₃	semidirect
734. #418	C₂²×C₂₃	semidirect
736. #417	C₂²×C₂₃	semidirect
737. #417	C₂²×C₂₃	semidirect
738. #417	C₂²×C₂₃	semidirect
741. #416	C₂²×C₂₃	semidirect
742. #416	C₂²×C₂₃	semidirect
743. #416	C₂²×C₂₃	semidirect
744. C₂×#103	C₂²×C₂₃	semidirect
746. C₂×#102	C₂²×C₂₃	semidirect
748. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
749. #405	C₂²×C₂₃	semidirect
946. C₂₃	#61187	direct (N × H)
998. C₂×D₄	#41×C₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₂₃×#3494	2
C₂₃×#3485	2
C₂₃×#3330	2
C₂₃×#3322	2
C₂₃×#3319	2
C₂₃×#3307	2
C₂₃×#3306	2
C₂₃×#3303	2
C₂₃×#3297	2
C₂₃×#3137	2
C₂₃×#3097	2
C₂₃×#3091	2
C₂₃×#3081	2
C₂₃×#3057	2
C₂₃×#3055	2
C₂₃×#3042	2
C₂₃×#3008	2
C₂×C₂₃×#449	2
C₂₃×#2948	2
C₂₃×#2933	2
C₂₃×#2897	2
C₂₃×#2896	2
#61187	23

Subgroups — C23×#61187 #19208813

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61187 #19208813