Subgroups — C₂₃×#61621 #19209247

Order 5888.

2156 conjugacy classes of subgroups.

The subgroup lattice has 1226 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3537	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3489	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3326	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3320	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3307	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3297	C₂	1	2	yes	maximal, complemented
7	D₄×SD₁₆×C₂₃	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3272	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3265	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3264	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3221	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3198	C₂	1	2	yes	maximal, complemented
13	C₂₃×#3193	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3187	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3119	C₂	1	2	yes	maximal, complemented
16	C₂₃×#3010	C₂	1	2	yes	maximal, complemented
17	C₂₃×#3006	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₂₃×#449	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#2976	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₂₃×2₋¹⁺⁴	C₂²	1	1	yes	characteristic, complemented
21	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
25	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
26	C₂²×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
27	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
28	C₂₃×#560	—	2	2	no	—
29	C₂₃×#553	C₂²	1	2	yes	—
30	C₂₃×#553	C₂²	1	2	yes	complemented
31	D₄×Q₈×C₂₃	C₂²	1	2	yes	complemented
32	C₂₃×#548	C₂²	1	2	yes	complemented
33	C₂₃×#547	—	2	2	no	—
34	C₂₃×#547	C₂²	1	2	yes	complemented
35	C₂₃×#546	—	2	2	no	—
36	C₂₃×#546	C₂²	1	2	yes	complemented
37	D₄²×C₂₃	—	2	2	no	—
38	D₄²×C₂₃	C₂²	1	2	yes	—
39	D₄²×C₂₃	C₂²	1	2	yes	complemented
40	C₂₃×#540	C₂²	1	2	yes	complemented
41	C₂₃×#538	—	2	1	no	—
42	C₂₃×#538	—	2	1	no	—
43	C₂₃×#537	—	2	1	no	—
44	C₂₃×#537	C₂²	1	1	yes	characteristic, complemented
45	C₂₃×#536	—	2	1	no	—
46	C₂₃×#536	C₂²	1	1	yes	characteristic, complemented
47	C₂₃×#535	C₂²	1	2	yes	complemented
48	C₂₃×#534	—	2	1	no	—
49	C₂₃×#534	—	2	1	no	—
50	C₂₃×#525	—	2	1	no	—
51	C₂₃×#525	C₂²	1	1	yes	characteristic
52	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
53	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
54	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
55	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
56	C₂₃×#520	C₂²	1	1	yes	characteristic, complemented
57	C₂₃×#496	C₂²	1	2	yes	complemented
58	C₂₃×#492	C₂²	1	2	yes	complemented
59	C₂₃×#491	C₂²	1	2	yes	complemented
60	C₂₃×#488	C₂²	1	2	yes	complemented
61	C₂₃×#485	C₂²	1	2	yes	complemented
62	C₂₃×#484	C₂²	1	2	yes	complemented
63	C₂₃×#483	C₂²	1	2	yes	complemented
64	C₂₃×#482	C₂²	1	2	yes	complemented
65	C₂₃×#481	C₂²	1	2	yes	complemented
66	C₂₃×#480	C₂²	1	2	yes	complemented
67	C₂₃×#479	C₂²	1	2	yes	complemented
68	C₂₃×#478	C₂²	1	2	yes	complemented
69	C₂₃×#469	C₂²	1	2	yes	complemented
70	C₂₃×#468	C₂²	1	2	yes	complemented
71	C₂₃×#468	C₂²	1	2	yes	complemented
72	C₂₃×#468	C₂²	1	2	yes	complemented
73	C₂₃×#466	C₂²	1	2	yes	complemented
74	C₂₃×#465	C₂²	1	2	yes	complemented
75	C₂₃×#465	C₂²	1	2	yes	complemented
76	C₂₃×#465	C₂²	1	2	yes	complemented
77	C₂₃×#463	C₂²	1	2	yes	complemented
78	C₂₃×#463	C₂²	1	2	yes	complemented
79	C₂₃×#461	C₂²	1	2	yes	complemented
80	C₂₃×#461	C₂²	1	2	yes	complemented
81	C₂₃×#460	C₂²	1	2	yes	complemented
82	C₂₃×#459	C₂²	1	2	yes	complemented
83	C₂₃×#450	C₂²	1	2	yes	complemented
84	C₂₃×#450	C₂²	1	2	yes	complemented
85	C₂₃×#450	C₂²	1	2	yes	complemented
86	C₂₃×#449	C₂²	1	2	yes	complemented
87	C₂₃×#449	C₂²	1	2	yes	complemented
88	C₂₃×#449	C₂²	1	2	yes	complemented
89	C₂₃×#449	C₂²	1	2	yes	complemented
90	C₂₃×#449	C₂²	1	2	yes	complemented
91	C₂₃×#449	C₂²	1	2	yes	complemented
92	C₂₃×#449	C₂²	1	2	yes	complemented
93	C₂₃×#449	C₂²	1	2	yes	complemented
94	C₂₃×#448	C₂²	1	2	yes	complemented
95	C₂₃×#448	C₂²	1	2	yes	complemented
96	C₂₃×#448	C₂²	1	2	yes	complemented
97	C₂₃×#448	C₂²	1	2	yes	complemented
98	C₂₃×#448	C₂²	1	2	yes	complemented
99	C₂₃×#447	C₂²	1	2	yes	complemented
100	C₂₃×#447	C₂²	1	2	yes	complemented
101	C₂₃×#442	C₂²	1	2	yes	complemented
102	C₂₃×#440	C₂²	1	2	yes	complemented
103	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
104	C₄×D₈×C₂₃	C₂²	1	2	yes	complemented
105	C₂₃×#436	C₂²	1	2	yes	complemented
106	C₂₃×#435	C₂²	1	2	yes	complemented
107	C₂₃×#435	C₂²	1	2	yes	complemented
108	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
109	C₂₃×#433	C₂²	1	2	yes	complemented
110	C₂₃×#419	C₂²	1	2	yes	complemented
111	C₂₃×#417	C₂²	1	1	yes	characteristic, complemented
112	C₂₃×#417	C₂²	1	1	yes	characteristic, complemented
113	C₂₃×#416	C₂²	1	2	yes	complemented
114	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic, complemented
115	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic, complemented
116	C₂₃×#408	C₂²	1	2	yes	complemented
117	C₂₃×#407	C₂²	1	1	yes	characteristic, complemented
118	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
119	C₂₃×2₋¹⁺⁴	—	4	2	no	—
120	C₂₃×2₋¹⁺⁴	—	4	2	no	—
121	C₂×#41×C₂₃	—	2	2	no	—
122	C₂×#41×C₂₃	—	2	1	no	—
123	C₂×#41×C₂₃	—	2	1	no	—
124	C₂×#41×C₂₃	—	2	1	no	—
125	C₂×#41×C₂₃	—	4	2	no	—
126	C₂×#41×C₂₃	—	4	2	no	—
127	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
128	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
129	C₂×#41×C₂₃	C₂³	1	2	yes	—
130	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
131	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
132	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
133	C₂²×Q₈×C₂₃	—	2	1	no	—
134	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
135	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
136	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
137	C₂²×D₄×C₂₃	—	2	1	no	—
138	C₂²×D₄×C₂₃	—	2	1	no	—
139	C₂²×D₄×C₂₃	—	2	1	no	—
140	C₂²×D₄×C₂₃	—	2	2	no	—
141	C₂²×D₄×C₂₃	—	2	2	no	—
142	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
143	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
144	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
145	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
146	C₂³×C₄×C₂₃	—	2	1	no	—
147	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
148	C₂₃×AGL(1,ℤ/8)	—	4	4	no	—
149	C₂₃×AGL(1,ℤ/8)	—	4	2	no	—
150	C₂₃×AGL(1,ℤ/8)	—	4	2	no	—
151	C₂×SD₁₆×C₂₃	—	4	2	no	—
152	C₂×SD₁₆×C₂₃	—	4	4	no	—
153	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
155	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
156	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
157	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
158	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
159	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
160	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
161	C₂×D₈×C₂₃	—	4	2	no	—
162	C₂×D₈×C₂₃	C₂³	1	2	yes	—
163	C₂×D₈×C₂₃	C₂³	1	2	yes	—
164	C₂×D₈×C₂₃	C₂³	1	2	yes	—
165	C₂×D₈×C₂₃	C₂³	1	2	yes	—
166	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
167	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
168	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
169	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
170	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
171	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
172	C₂₃×C₄⋊Q₈	—	2	2	no	—
173	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
174	C₂₃×#127	—	2	2	no	—
175	C₂₃×#127	C₂³	1	2	yes	—
176	C₂₃×#126	—	2	2	no	—
177	C₂₃×#126	—	2	2	no	—
178	C₂₃×#125	C₂³	1	2	yes	—
179	C₂₃×#124	—	2	2	no	—
180	C₂₃×#124	—	2	2	no	—
181	C₂₃×#124	C₂³	1	2	yes	—
182	C₂₃×#123	—	2	2	no	—
183	C₂₃×#123	—	2	2	no	—
184	C₂₃×#123	—	2	2	no	—
185	C₂₃×#123	—	2	2	no	—
186	C₂₃×#123	—	2	2	no	—
187	C₂₃×#123	—	2	2	no	—
188	C₂₃×#123	—	2	2	no	—
189	C₂₃×#123	—	2	2	no	—
190	C₂₃×#123	D₄	1	2	yes	—
191	C₂₃×C₂²⋊Q₈	—	2	1	no	—
192	C₂₃×C₂²⋊Q₈	—	2	1	no	—
193	C₂₃×C₂²⋊Q₈	—	2	1	no	—
194	C₂₃×C₂²⋊Q₈	—	2	2	no	—
195	C₂₃×C₂²⋊Q₈	—	2	1	no	—
196	C₂₃×C₂²⋊Q₈	—	2	1	no	—
197	C₂₃×C₂²⋊Q₈	—	2	2	no	—
198	C₂₃×C₂²⋊Q₈	—	2	2	no	—
199	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
200	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
201	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
202	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
203	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
204	C₂₃×#121	—	2	2	no	—
205	C₂₃×#121	—	2	2	no	—
206	C₂₃×#121	—	2	2	no	—
207	C₂₃×#121	—	2	2	no	—
208	C₂₃×#121	—	2	2	no	—
209	C₂₃×#121	—	2	1	no	—
210	C₂₃×#121	—	2	1	no	—
211	C₂₃×#121	—	2	1	no	—
212	C₂₃×#121	—	2	1	no	—
213	C₂₃×#121	—	2	1	no	—
214	C₂₃×#121	—	2	2	no	—
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	D₄	1	1	yes	characteristic
220	C₂₃×#121	D₄	1	1	yes	characteristic
221	C₂₃×#121	C₂³	1	2	yes	—
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	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	C₂₃×#120	—	2	2	no	—
234	C₂₃×#120	—	2	2	no	—
235	C₂₃×#120	D₄	1	2	yes	—
236	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
237	C₄×D₄×C₂₃	—	2	2	no	—
238	C₄×D₄×C₂₃	—	2	2	no	—
239	C₄×D₄×C₂₃	—	2	2	no	—
240	C₄×D₄×C₂₃	—	2	2	no	—
241	C₄×D₄×C₂₃	—	2	2	no	—
242	C₄×D₄×C₂₃	C₂³	1	2	yes	—
243	C₄×D₄×C₂₃	C₂³	1	2	yes	—
244	C₄×D₄×C₂₃	C₂³	1	2	yes	—
245	C₄×D₄×C₂₃	C₂³	1	2	yes	—
246	C₄×D₄×C₂₃	C₂³	1	2	yes	—
247	C₂₃×#117	—	2	1	no	—
248	C₂₃×#117	C₂³	1	2	yes	—
249	C₂₃×#117	C₂³	1	1	yes	characteristic
250	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
251	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
252	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
253	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
254	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
255	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
256	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
257	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
258	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
259	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
260	C₂₃×#107	C₂³	1	2	yes	—
261	C₂₃×#107	C₂³	1	2	yes	—
262	C₂₃×#106	C₂³	1	2	yes	—
263	C₂₃×#106	C₂³	1	2	yes	—
264	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
265	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
266	C₂₃×#103	C₂³	1	2	yes	—
267	C₂₃×#103	C₂³	1	2	yes	—
268	C₂₃×#103	C₂³	1	2	yes	—
269	C₂₃×#103	C₂³	1	2	yes	—
270	C₂₃×#103	C₂³	1	2	yes	—
271	C₂₃×#103	C₂³	1	2	yes	—
272	C₂₃×#103	C₂³	1	2	yes	—
273	C₂₃×#103	C₂³	1	2	yes	—
274	C₂₃×#102	C₂³	1	2	yes	—
275	C₂₃×#102	C₂³	1	2	yes	—
276	C₂₃×#102	C₂³	1	2	yes	—
277	C₂₃×#102	C₂³	1	2	yes	—
278	C₂₃×#102	C₂³	1	2	yes	—
279	C₂₃×#102	C₂³	1	2	yes	—
280	C₂₃×#102	C₂³	1	2	yes	—
281	C₂₃×#102	C₂³	1	2	yes	—
282	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
283	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
284	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
285	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
286	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
287	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
288	C₂₃×#97	C₂³	1	2	yes	—
289	C₄×C₈×C₂₃	C₂³	1	2	yes	—
290	C₂⁴×C₂₃	—	2	1	no	—
291	C₂⁴×C₂₃	—	2	1	no	—
292	C₂⁴×C₂₃	—	2	1	no	—
293	C₂⁴×C₂₃	—	2	2	no	—
294	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
295	#41×C₂₃	—	2	2	no	—
296	#41×C₂₃	—	2	2	no	—
297	#41×C₂₃	—	2	2	no	—
298	#41×C₂₃	—	2	2	no	—
299	#41×C₂₃	—	2	4	no	—
300	#41×C₂₃	—	4	1	no	—
301	#41×C₂₃	—	4	1	no	—
302	#41×C₂₃	—	4	1	no	—
303	#41×C₂₃	—	4	1	no	—
304	#41×C₂₃	—	4	1	no	—
305	#41×C₂₃	—	4	1	no	—
306	#41×C₂₃	—	4	2	no	—
307	#41×C₂₃	—	4	4	no	—
308	#41×C₂₃	—	4	4	no	—
309	#41×C₂₃	—	4	4	no	—
310	#41×C₂₃	—	4	8	no	—
311	C₂×Q₈×C₂₃	—	2	1	no	—
312	C₂×Q₈×C₂₃	—	2	2	no	—
313	C₂×Q₈×C₂₃	—	2	1	no	—
314	C₂×Q₈×C₂₃	—	2	2	no	—
315	C₂×Q₈×C₂₃	—	2	4	no	—
316	C₂×Q₈×C₂₃	—	4	1	no	—
317	C₂×Q₈×C₂₃	—	4	2	no	—
318	C₂×Q₈×C₂₃	—	4	1	no	—
319	C₂×Q₈×C₂₃	—	4	1	no	—
320	C₂×Q₈×C₂₃	—	4	4	no	—
321	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
322	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
323	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
324	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
325	C₂×D₄×C₂₃	—	2	1	no	—
326	C₂×D₄×C₂₃	—	2	2	no	—
327	C₂×D₄×C₂₃	—	2	2	no	—
328	C₂×D₄×C₂₃	—	2	2	no	—
329	C₂×D₄×C₂₃	—	2	2	no	—
330	C₂×D₄×C₂₃	—	2	1	no	—
331	C₂×D₄×C₂₃	—	2	1	no	—
332	C₂×D₄×C₂₃	—	2	1	no	—
333	C₂×D₄×C₂₃	—	2	2	no	—
334	C₂×D₄×C₂₃	—	2	2	no	—
335	C₂×D₄×C₂₃	—	2	2	no	—
336	C₂×D₄×C₂₃	—	2	2	no	—
337	C₂×D₄×C₂₃	—	2	2	no	—
338	C₂×D₄×C₂₃	—	2	1	no	—
339	C₂×D₄×C₂₃	—	2	1	no	—
340	C₂×D₄×C₂₃	—	2	1	no	—
341	C₂×D₄×C₂₃	—	2	2	no	—
342	C₂×D₄×C₂₃	—	2	2	no	—
343	C₂×D₄×C₂₃	—	2	2	no	—
344	C₂×D₄×C₂₃	—	4	1	no	—
345	C₂×D₄×C₂₃	—	4	1	no	—
346	C₂×D₄×C₂₃	—	4	1	no	—
347	C₂×D₄×C₂₃	—	4	2	no	—
348	C₂×D₄×C₂₃	—	4	1	no	—
349	C₂×D₄×C₂₃	—	4	1	no	—
350	C₂×D₄×C₂₃	—	4	2	no	—
351	C₂×D₄×C₂₃	—	4	4	no	—
352	C₂×D₄×C₂₃	—	8	4	no	—
353	C₂×D₄×C₂₃	—	8	2	no	—
354	C₂×D₄×C₂₃	—	8	4	no	—
355	C₂×D₄×C₂₃	—	8	2	no	—
356	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
357	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
358	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
359	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
360	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
361	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
362	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
363	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
364	C₂²×C₄×C₂₃	—	2	1	no	—
365	C₂²×C₄×C₂₃	—	2	1	no	—
366	C₂²×C₄×C₂₃	—	2	2	no	—
367	C₂²×C₄×C₂₃	—	2	1	no	—
368	C₂²×C₄×C₂₃	—	2	1	no	—
369	C₂²×C₄×C₂₃	—	2	1	no	—
370	C₂²×C₄×C₂₃	—	2	1	no	—
371	C₂²×C₄×C₂₃	—	2	2	no	—
372	C₂²×C₄×C₂₃	—	2	1	no	—
373	C₂²×C₄×C₂₃	—	2	1	no	—
374	C₂²×C₄×C₂₃	—	2	1	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	—	4	1	no	—
379	C₂²×C₄×C₂₃	—	4	1	no	—
380	C₂²×C₄×C₂₃	—	4	4	no	—
381	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
382	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
383	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
384	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
385	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
386	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
387	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
388	SD₁₆×C₂₃	—	2	4	no	—
389	SD₁₆×C₂₃	—	2	4	no	—
390	SD₁₆×C₂₃	—	4	2	no	—
391	SD₁₆×C₂₃	—	4	2	no	—
392	SD₁₆×C₂₃	—	4	2	no	—
393	SD₁₆×C₂₃	—	4	2	no	—
394	SD₁₆×C₂₃	—	4	2	no	—
395	SD₁₆×C₂₃	—	4	2	no	—
396	D₈×C₂₃	—	2	4	no	—
397	D₈×C₂₃	—	2	4	no	—
398	D₈×C₂₃	—	4	2	no	—
399	D₈×C₂₃	—	4	2	no	—
400	M₁₆×C₂₃	—	4	2	no	—
401	M₁₆×C₂₃	—	4	1	no	—
402	M₁₆×C₂₃	—	4	1	no	—
403	C₂×C₈×C₂₃	—	4	1	no	—
404	C₂×C₈×C₂₃	—	4	1	no	—
405	C₂×C₈×C₂₃	—	4	2	no	—
406	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
407	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
408	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
409	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
410	C₄⋊C₄×C₂₃	—	2	2	no	—
411	C₄⋊C₄×C₂₃	—	2	1	no	—
412	C₄⋊C₄×C₂₃	—	2	2	no	—
413	C₄⋊C₄×C₂₃	—	2	2	no	—
414	C₄⋊C₄×C₂₃	—	2	2	no	—
415	C₄⋊C₄×C₂₃	—	2	2	no	—
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	C₂×D₄	1	1	yes	characteristic
422	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
423	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
424	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
425	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
426	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
427	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
428	C₂²⋊C₄×C₂₃	—	2	2	no	—
429	C₂²⋊C₄×C₂₃	—	2	2	no	—
430	C₂²⋊C₄×C₂₃	—	2	2	no	—
431	C₂²⋊C₄×C₂₃	—	2	2	no	—
432	C₂²⋊C₄×C₂₃	—	2	2	no	—
433	C₂²⋊C₄×C₂₃	—	2	2	no	—
434	C₂²⋊C₄×C₂₃	—	2	2	no	—
435	C₂²⋊C₄×C₂₃	—	2	2	no	—
436	C₂²⋊C₄×C₂₃	—	2	2	no	—
437	C₂²⋊C₄×C₂₃	—	2	2	no	—
438	C₂²⋊C₄×C₂₃	—	2	2	no	—
439	C₂²⋊C₄×C₂₃	—	2	2	no	—
440	C₂²⋊C₄×C₂₃	—	2	2	no	—
441	C₂²⋊C₄×C₂₃	—	2	2	no	—
442	C₂²⋊C₄×C₂₃	—	2	2	no	—
443	C₂²⋊C₄×C₂₃	—	2	2	no	—
444	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
445	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
446	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
447	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
448	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
449	C₄²×C₂₃	—	2	2	no	—
450	C₄²×C₂₃	—	2	2	no	—
451	C₄²×C₂₃	C₂⁴	1	2	yes	—
452	#61621	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
453	C₂³×C₂₃	—	2	1	no	—
454	C₂³×C₂₃	—	2	2	no	—
455	C₂³×C₂₃	—	2	1	no	—
456	C₂³×C₂₃	—	2	2	no	—
457	C₂³×C₂₃	—	2	2	no	—
458	C₂³×C₂₃	—	4	1	no	—
459	C₂³×C₂₃	—	4	1	no	—
460	C₂³×C₂₃	—	4	2	no	—
461	C₂³×C₂₃	—	4	2	no	—
462	C₂³×C₂₃	—	4	2	no	—
463	C₂³×C₂₃	—	4	2	no	—
464	C₂³×C₂₃	—	8	1	no	—
465	C₂³×C₂₃	—	8	1	no	—
466	C₂³×C₂₃	—	8	2	no	—
467	C₂³×C₂₃	—	8	1	no	—
468	C₂³×C₂₃	—	8	1	no	—
469	C₂³×C₂₃	—	8	2	no	—
470	C₂³×C₂₃	—	8	1	no	—
471	C₂³×C₂₃	—	8	2	no	—
472	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
473	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
474	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
475	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
476	Q₈×C₂₃	—	2	1	no	—
477	Q₈×C₂₃	—	2	2	no	—
478	Q₈×C₂₃	—	2	1	no	—
479	Q₈×C₂₃	—	2	2	no	—
480	Q₈×C₂₃	—	2	1	no	—
481	Q₈×C₂₃	—	4	1	no	—
482	Q₈×C₂₃	—	4	4	no	—
483	Q₈×C₂₃	—	4	2	no	—
484	Q₈×C₂₃	—	4	2	no	—
485	Q₈×C₂₃	H(5,𝔽₂)	1	2	yes	—
486	D₄×C₂₃	—	2	4	no	—
487	D₄×C₂₃	—	2	4	no	—
488	D₄×C₂₃	—	2	1	no	—
489	D₄×C₂₃	—	2	2	no	—
490	D₄×C₂₃	—	2	2	no	—
491	D₄×C₂₃	—	2	1	no	—
492	D₄×C₂₃	—	2	1	no	—
493	D₄×C₂₃	—	2	2	no	—
494	D₄×C₂₃	—	2	2	no	—
495	D₄×C₂₃	—	4	2	no	—
496	D₄×C₂₃	—	4	1	no	—
497	D₄×C₂₃	—	4	2	no	—
498	D₄×C₂₃	—	4	2	no	—
499	D₄×C₂₃	—	4	2	no	—
500	D₄×C₂₃	—	4	2	no	—
501	D₄×C₂₃	—	4	4	no	—
502	D₄×C₂₃	—	4	2	no	—
503	D₄×C₂₃	—	4	4	no	—
504	D₄×C₂₃	—	4	4	no	—
505	D₄×C₂₃	—	8	1	no	—
506	D₄×C₂₃	—	8	1	no	—
507	D₄×C₂₃	—	8	2	no	—
508	D₄×C₂₃	—	8	2	no	—
509	D₄×C₂₃	—	8	2	no	—
510	D₄×C₂₃	—	8	2	no	—
511	D₄×C₂₃	—	8	2	no	—
512	D₄×C₂₃	—	8	2	no	—
513	D₄×C₂₃	—	8	2	no	—
514	D₄×C₂₃	—	8	2	no	—
515	D₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
516	C₂×C₄×C₂₃	—	2	4	no	—
517	C₂×C₄×C₂₃	—	2	1	no	—
518	C₂×C₄×C₂₃	—	2	1	no	—
519	C₂×C₄×C₂₃	—	2	1	no	—
520	C₂×C₄×C₂₃	—	2	2	no	—
521	C₂×C₄×C₂₃	—	2	1	no	—
522	C₂×C₄×C₂₃	—	2	1	no	—
523	C₂×C₄×C₂₃	—	2	2	no	—
524	C₂×C₄×C₂₃	—	2	1	no	—
525	C₂×C₄×C₂₃	—	2	1	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	—	4	1	no	—
532	C₂×C₄×C₂₃	—	4	1	no	—
533	C₂×C₄×C₂₃	—	4	1	no	—
534	C₂×C₄×C₂₃	—	4	2	no	—
535	C₂×C₄×C₂₃	—	4	2	no	—
536	C₂×C₄×C₂₃	—	4	2	no	—
537	C₂×C₄×C₂₃	—	4	4	no	—
538	C₂×C₄×C₂₃	—	4	4	no	—
539	C₂×C₄×C₂₃	—	4	2	no	—
540	C₂×C₄×C₂₃	—	4	2	no	—
541	C₂×C₄×C₂₃	—	8	2	no	—
542	C₂×C₄×C₂₃	—	8	2	no	—
543	C₂×C₄×C₂₃	—	8	2	no	—
544	C₂×C₄×C₂₃	—	8	1	no	—
545	C₂×C₄×C₂₃	—	8	1	no	—
546	C₂×C₄×C₂₃	—	8	1	no	—
547	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
548	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
549	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
550	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
551	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
552	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
553	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
554	C₈×C₂₃	—	2	2	no	—
555	C₈×C₂₃	—	2	2	no	—
556	C₈×C₂₃	—	2	2	no	—
557	C₈×C₂₃	—	2	2	no	—
558	#3537	C₂×C₂₃	1	1	yes	characteristic, complemented
559	#3489	C₂×C₂₃	1	1	yes	characteristic, complemented
560	#3326	C₂×C₂₃	1	2	yes	complemented
561	#3320	C₂×C₂₃	1	2	yes	complemented
562	#3307	C₂×C₂₃	1	2	yes	complemented
563	#3297	C₂×C₂₃	1	2	yes	complemented
564	D₄×SD₁₆	C₂×C₂₃	1	2	yes	complemented
565	#3272	C₂×C₂₃	1	2	yes	complemented
566	#3265	C₂×C₂₃	1	2	yes	complemented
567	#3264	C₂×C₂₃	1	2	yes	complemented
568	#3221	C₂×C₂₃	1	2	yes	complemented
569	#3198	C₂×C₂₃	1	2	yes	complemented
570	#3193	C₂×C₂₃	1	1	yes	characteristic, complemented
571	#3187	C₂×C₂₃	1	1	yes	characteristic, complemented
572	#3119	C₂×C₂₃	1	2	yes	complemented
573	#3010	C₂×C₂₃	1	2	yes	complemented
574	#3006	C₂×C₂₃	1	1	yes	characteristic, complemented
575	C₂×#449	C₂×C₂₃	1	1	yes	characteristic, complemented
576	#2976	C₂×C₂₃	1	1	yes	characteristic, complemented
577	C₂²×C₂₃	—	2	1	no	—
578	C₂²×C₂₃	—	2	1	no	—
579	C₂²×C₂₃	—	2	1	no	—
580	C₂²×C₂₃	—	2	1	no	—
581	C₂²×C₂₃	—	2	2	no	—
582	C₂²×C₂₃	—	2	1	no	—
583	C₂²×C₂₃	—	2	2	no	—
584	C₂²×C₂₃	—	2	2	no	—
585	C₂²×C₂₃	—	2	1	no	—
586	C₂²×C₂₃	—	2	1	no	—
587	C₂²×C₂₃	—	2	2	no	—
588	C₂²×C₂₃	—	2	1	no	—
589	C₂²×C₂₃	—	4	1	no	—
590	C₂²×C₂₃	—	4	1	no	—
591	C₂²×C₂₃	—	4	2	no	—
592	C₂²×C₂₃	—	4	2	no	—
593	C₂²×C₂₃	—	4	1	no	—
594	C₂²×C₂₃	—	4	1	no	—
595	C₂²×C₂₃	—	4	2	no	—
596	C₂²×C₂₃	—	4	2	no	—
597	C₂²×C₂₃	—	4	2	no	—
598	C₂²×C₂₃	—	4	2	no	—
599	C₂²×C₂₃	—	4	1	no	—
600	C₂²×C₂₃	—	8	2	no	—
601	C₂²×C₂₃	—	8	4	no	—
602	C₂²×C₂₃	—	16	2	no	—
603	C₂²×C₂₃	—	16	2	no	—
604	C₂²×C₂₃	—	16	4	no	—
605	C₂²×C₂₃	#577	1	2	yes	—
606	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
607	C₄×C₂₃	—	2	2	no	—
608	C₄×C₂₃	—	2	1	no	—
609	C₄×C₂₃	—	2	2	no	—
610	C₄×C₂₃	—	2	1	no	—
611	C₄×C₂₃	—	2	1	no	—
612	C₄×C₂₃	—	2	2	no	—
613	C₄×C₂₃	—	2	2	no	—
614	C₄×C₂₃	—	4	2	no	—
615	C₄×C₂₃	—	4	2	no	—
616	C₄×C₂₃	—	4	1	no	—
617	C₄×C₂₃	—	4	2	no	—
618	C₄×C₂₃	—	4	2	no	—
619	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
620	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
621	C₂×2₋¹⁺⁴	C₂²×C₂₃	1	1	yes	characteristic, complemented
622	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic, complemented
623	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	1	yes	characteristic, complemented
624	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	1	yes	characteristic, complemented
625	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	2	yes	complemented
626	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
627	C₂²×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
628	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
629	#560	—	2	2	no	—
630	#553	C₂²×C₂₃	1	2	yes	—
631	#553	C₂²×C₂₃	1	2	yes	complemented
632	D₄×Q₈	C₂²×C₂₃	1	2	yes	complemented
633	#548	C₂²×C₂₃	1	2	yes	complemented
634	#547	—	2	2	no	—
635	#547	C₂²×C₂₃	1	2	yes	complemented
636	#546	—	2	2	no	—
637	#546	C₂²×C₂₃	1	2	yes	complemented
638	D₄²	—	2	2	no	—
639	D₄²	C₂²×C₂₃	1	2	yes	—
640	D₄²	C₂²×C₂₃	1	2	yes	complemented
641	#540	C₂²×C₂₃	1	2	yes	complemented
642	#538	—	2	1	no	—
643	#538	—	2	1	no	—
644	#537	—	2	1	no	—
645	#537	C₂²×C₂₃	1	1	yes	characteristic, complemented
646	#536	—	2	1	no	—
647	#536	C₂²×C₂₃	1	1	yes	characteristic, complemented
648	#535	C₂²×C₂₃	1	2	yes	complemented
649	#534	—	2	1	no	—
650	#534	—	2	1	no	—
651	#525	—	2	1	no	—
652	#525	C₂²×C₂₃	1	1	yes	characteristic
653	C₂×C₂²⋊Q₈	—	2	1	no	—
654	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
655	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
656	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
657	#520	C₂²×C₂₃	1	1	yes	characteristic, complemented
658	#496	C₂²×C₂₃	1	2	yes	complemented
659	#492	C₂²×C₂₃	1	2	yes	complemented
660	#491	C₂²×C₂₃	1	2	yes	complemented
661	#488	C₂²×C₂₃	1	2	yes	complemented
662	#485	C₂²×C₂₃	1	2	yes	complemented
663	#484	C₂²×C₂₃	1	2	yes	complemented
664	#483	C₂²×C₂₃	1	2	yes	complemented
665	#482	C₂²×C₂₃	1	2	yes	complemented
666	#481	C₂²×C₂₃	1	2	yes	complemented
667	#480	C₂²×C₂₃	1	2	yes	complemented
668	#479	C₂²×C₂₃	1	2	yes	complemented
669	#478	C₂²×C₂₃	1	2	yes	complemented
670	#469	C₂²×C₂₃	1	2	yes	complemented
671	#468	C₂²×C₂₃	1	2	yes	complemented
672	#468	C₂²×C₂₃	1	2	yes	complemented
673	#468	C₂²×C₂₃	1	2	yes	complemented
674	#466	C₂²×C₂₃	1	2	yes	complemented
675	#465	C₂²×C₂₃	1	2	yes	complemented
676	#465	C₂²×C₂₃	1	2	yes	complemented
677	#465	C₂²×C₂₃	1	2	yes	complemented
678	#463	C₂²×C₂₃	1	2	yes	complemented
679	#463	C₂²×C₂₃	1	2	yes	complemented
680	#461	C₂²×C₂₃	1	2	yes	complemented
681	#461	C₂²×C₂₃	1	2	yes	complemented
682	#460	C₂²×C₂₃	1	2	yes	complemented
683	#459	C₂²×C₂₃	1	2	yes	complemented
684	#450	C₂²×C₂₃	1	2	yes	complemented
685	#450	C₂²×C₂₃	1	2	yes	complemented
686	#450	C₂²×C₂₃	1	2	yes	complemented
687	#449	C₂²×C₂₃	1	2	yes	complemented
688	#449	C₂²×C₂₃	1	2	yes	complemented
689	#449	C₂²×C₂₃	1	2	yes	complemented
690	#449	C₂²×C₂₃	1	2	yes	complemented
691	#449	C₂²×C₂₃	1	2	yes	complemented
692	#449	C₂²×C₂₃	1	2	yes	complemented
693	#449	C₂²×C₂₃	1	2	yes	complemented
694	#449	C₂²×C₂₃	1	2	yes	complemented
695	#448	C₂²×C₂₃	1	2	yes	complemented
696	#448	C₂²×C₂₃	1	2	yes	complemented
697	#448	C₂²×C₂₃	1	2	yes	complemented
698	#448	C₂²×C₂₃	1	2	yes	complemented
699	#448	C₂²×C₂₃	1	2	yes	complemented
700	#447	C₂²×C₂₃	1	2	yes	complemented
701	#447	C₂²×C₂₃	1	2	yes	complemented
702	#442	C₂²×C₂₃	1	2	yes	complemented
703	#440	C₂²×C₂₃	1	2	yes	complemented
704	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
705	C₄×D₈	C₂²×C₂₃	1	2	yes	complemented
706	#436	C₂²×C₂₃	1	2	yes	complemented
707	#435	C₂²×C₂₃	1	2	yes	complemented
708	#435	C₂²×C₂₃	1	2	yes	complemented
709	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
710	#433	C₂²×C₂₃	1	2	yes	complemented
711	#419	C₂²×C₂₃	1	2	yes	complemented
712	#417	C₂²×C₂₃	1	1	yes	characteristic, complemented
713	#417	C₂²×C₂₃	1	1	yes	characteristic, complemented
714	#416	C₂²×C₂₃	1	2	yes	complemented
715	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic, complemented
716	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic, complemented
717	#408	C₂²×C₂₃	1	2	yes	complemented
718	#407	C₂²×C₂₃	1	1	yes	characteristic, complemented
719	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
720	C₂×C₂₃	—	2	2	no	—
721	C₂×C₂₃	—	4	1	no	—
722	C₂×C₂₃	—	4	1	no	—
723	C₂×C₂₃	—	4	2	no	—
724	C₂×C₂₃	—	4	2	no	—
725	C₂×C₂₃	—	8	1	no	—
726	C₂×C₂₃	—	8	2	no	—
727	C₂×C₂₃	—	8	2	no	—
728	C₂×C₂₃	#3484	1	1	yes	characteristic
729	C₂×C₂₃	C₂×#577	1	1	yes	characteristic
730	C₂×C₂₃	#3585	1	1	yes	characteristic
731	2₋¹⁺⁴	—	4	2	no	—
732	2₋¹⁺⁴	—	4	2	no	—
733	C₂×#41	—	2	1	no	—
734	C₂×#41	—	2	2	no	—
735	C₂×#41	—	2	1	no	—
736	C₂×#41	—	2	1	no	—
737	C₂×#41	—	4	2	no	—
738	C₂×#41	—	4	2	no	—
739	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
740	C₂×#41	C₂³×C₂₃	1	2	yes	—
741	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
742	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
743	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
744	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
745	C₂²×Q₈	—	2	1	no	—
746	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
747	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
748	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
749	C₂²×D₄	—	2	1	no	—
750	C₂²×D₄	—	2	1	no	—
751	C₂²×D₄	—	2	1	no	—
752	C₂²×D₄	—	2	2	no	—
753	C₂²×D₄	—	2	2	no	—
754	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
755	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
756	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
757	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
758	C₂³×C₄	—	2	1	no	—
759	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
760	AGL(1,ℤ/8)	—	4	4	no	—
761	AGL(1,ℤ/8)	—	4	2	no	—
762	AGL(1,ℤ/8)	—	4	2	no	—
763	C₂×SD₁₆	—	4	2	no	—
764	C₂×SD₁₆	—	4	4	no	—
765	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
766	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
767	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
768	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
769	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
770	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
771	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
772	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
773	C₂×D₈	—	4	2	no	—
774	C₂×D₈	C₂³×C₂₃	1	2	yes	—
775	C₂×D₈	C₂³×C₂₃	1	2	yes	—
776	C₂×D₈	C₂³×C₂₃	1	2	yes	—
777	C₂×D₈	C₂³×C₂₃	1	2	yes	—
778	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
779	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
780	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
781	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
782	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
783	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
784	C₄⋊Q₈	—	2	2	no	—
785	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
786	#127	—	2	2	no	—
787	#127	C₂³×C₂₃	1	2	yes	—
788	#126	—	2	2	no	—
789	#126	—	2	2	no	—
790	#125	C₂³×C₂₃	1	2	yes	—
791	#124	—	2	2	no	—
792	#124	—	2	2	no	—
793	#124	C₂³×C₂₃	1	2	yes	—
794	#123	—	2	2	no	—
795	#123	—	2	2	no	—
796	#123	—	2	2	no	—
797	#123	—	2	2	no	—
798	#123	—	2	2	no	—
799	#123	—	2	2	no	—
800	#123	—	2	2	no	—
801	#123	—	2	2	no	—
802	#123	D₄×C₂₃	1	2	yes	—
803	C₂²⋊Q₈	—	2	1	no	—
804	C₂²⋊Q₈	—	2	1	no	—
805	C₂²⋊Q₈	—	2	1	no	—
806	C₂²⋊Q₈	—	2	1	no	—
807	C₂²⋊Q₈	—	2	2	no	—
808	C₂²⋊Q₈	—	2	1	no	—
809	C₂²⋊Q₈	—	2	2	no	—
810	C₂²⋊Q₈	—	2	2	no	—
811	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
812	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
813	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
814	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
815	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
816	#121	—	2	1	no	—
817	#121	—	2	2	no	—
818	#121	—	2	2	no	—
819	#121	—	2	2	no	—
820	#121	—	2	2	no	—
821	#121	—	2	2	no	—
822	#121	—	2	1	no	—
823	#121	—	2	1	no	—
824	#121	—	2	1	no	—
825	#121	—	2	1	no	—
826	#121	—	2	2	no	—
827	#121	—	2	2	no	—
828	#121	—	2	2	no	—
829	#121	—	2	2	no	—
830	#121	—	2	2	no	—
831	#121	D₄×C₂₃	1	1	yes	characteristic
832	#121	D₄×C₂₃	1	1	yes	characteristic
833	#121	C₂³×C₂₃	1	2	yes	—
834	#121	C₂³×C₂₃	1	2	yes	—
835	#121	C₂³×C₂₃	1	2	yes	—
836	#121	C₂³×C₂₃	1	2	yes	—
837	#121	C₂³×C₂₃	1	2	yes	—
838	#121	C₂³×C₂₃	1	2	yes	—
839	#121	C₂³×C₂₃	1	2	yes	—
840	#120	—	2	2	no	—
841	#120	—	2	2	no	—
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	#120	D₄×C₂₃	1	2	yes	—
848	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
849	C₄×D₄	—	2	2	no	—
850	C₄×D₄	—	2	2	no	—
851	C₄×D₄	—	2	2	no	—
852	C₄×D₄	—	2	2	no	—
853	C₄×D₄	—	2	2	no	—
854	C₄×D₄	C₂³×C₂₃	1	2	yes	—
855	C₄×D₄	C₂³×C₂₃	1	2	yes	—
856	C₄×D₄	C₂³×C₂₃	1	2	yes	—
857	C₄×D₄	C₂³×C₂₃	1	2	yes	—
858	C₄×D₄	C₂³×C₂₃	1	2	yes	—
859	#117	—	2	1	no	—
860	#117	C₂³×C₂₃	1	2	yes	—
861	#117	C₂³×C₂₃	1	1	yes	characteristic
862	C₂×C₄⋊C₄	—	2	1	no	—
863	C₂×C₄⋊C₄	—	2	1	no	—
864	C₂×C₄⋊C₄	—	2	2	no	—
865	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
866	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
867	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
868	C₂×C₂²⋊C₄	—	2	1	no	—
869	C₂×C₂²⋊C₄	—	2	1	no	—
870	C₂×C₂²⋊C₄	—	2	1	no	—
871	C₂×C₂²⋊C₄	—	2	2	no	—
872	#107	C₂³×C₂₃	1	2	yes	—
873	#107	C₂³×C₂₃	1	2	yes	—
874	#106	C₂³×C₂₃	1	2	yes	—
875	#106	C₂³×C₂₃	1	2	yes	—
876	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
877	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
878	#103	C₂³×C₂₃	1	2	yes	—
879	#103	C₂³×C₂₃	1	2	yes	—
880	#103	C₂³×C₂₃	1	2	yes	—
881	#103	C₂³×C₂₃	1	2	yes	—
882	#103	C₂³×C₂₃	1	2	yes	—
883	#103	C₂³×C₂₃	1	2	yes	—
884	#103	C₂³×C₂₃	1	2	yes	—
885	#103	C₂³×C₂₃	1	2	yes	—
886	#102	C₂³×C₂₃	1	2	yes	—
887	#102	C₂³×C₂₃	1	2	yes	—
888	#102	C₂³×C₂₃	1	2	yes	—
889	#102	C₂³×C₂₃	1	2	yes	—
890	#102	C₂³×C₂₃	1	2	yes	—
891	#102	C₂³×C₂₃	1	2	yes	—
892	#102	C₂³×C₂₃	1	2	yes	—
893	#102	C₂³×C₂₃	1	2	yes	—
894	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
895	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
896	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
897	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
898	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
899	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
900	#97	C₂³×C₂₃	1	2	yes	—
901	C₄×C₈	C₂³×C₂₃	1	2	yes	—
902	C₂₃	#61621	1	1	yes	characteristic, direct product factor, Sylow
903	C₂⁴	—	2	1	no	—
904	C₂⁴	—	2	1	no	—
905	C₂⁴	—	2	1	no	—
906	C₂⁴	—	2	2	no	—
907	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
908	#41	—	2	2	no	—
909	#41	—	2	2	no	—
910	#41	—	2	2	no	—
911	#41	—	2	2	no	—
912	#41	—	2	4	no	—
913	#41	—	4	1	no	—
914	#41	—	4	1	no	—
915	#41	—	4	1	no	—
916	#41	—	4	1	no	—
917	#41	—	4	1	no	—
918	#41	—	4	1	no	—
919	#41	—	4	2	no	—
920	#41	—	4	4	no	—
921	#41	—	4	4	no	—
922	#41	—	4	4	no	—
923	#41	—	4	8	no	—
924	C₂×Q₈	—	2	1	no	—
925	C₂×Q₈	—	2	2	no	—
926	C₂×Q₈	—	2	1	no	—
927	C₂×Q₈	—	2	2	no	—
928	C₂×Q₈	—	2	4	no	—
929	C₂×Q₈	—	4	1	no	—
930	C₂×Q₈	—	4	2	no	—
931	C₂×Q₈	—	4	1	no	—
932	C₂×Q₈	—	4	1	no	—
933	C₂×Q₈	—	4	4	no	—
934	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
935	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
936	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
937	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
938	C₂×D₄	—	2	1	no	—
939	C₂×D₄	—	2	2	no	—
940	C₂×D₄	—	2	2	no	—
941	C₂×D₄	—	2	2	no	—
942	C₂×D₄	—	2	2	no	—
943	C₂×D₄	—	2	1	no	—
944	C₂×D₄	—	2	1	no	—
945	C₂×D₄	—	2	1	no	—
946	C₂×D₄	—	2	2	no	—
947	C₂×D₄	—	2	2	no	—
948	C₂×D₄	—	2	2	no	—
949	C₂×D₄	—	2	2	no	—
950	C₂×D₄	—	2	2	no	—
951	C₂×D₄	—	2	1	no	—
952	C₂×D₄	—	2	1	no	—
953	C₂×D₄	—	2	1	no	—
954	C₂×D₄	—	2	2	no	—
955	C₂×D₄	—	2	2	no	—
956	C₂×D₄	—	2	2	no	—
957	C₂×D₄	—	4	1	no	—
958	C₂×D₄	—	4	1	no	—
959	C₂×D₄	—	4	1	no	—
960	C₂×D₄	—	4	2	no	—
961	C₂×D₄	—	4	1	no	—
962	C₂×D₄	—	4	1	no	—
963	C₂×D₄	—	4	2	no	—
964	C₂×D₄	—	4	4	no	—
965	C₂×D₄	—	8	4	no	—
966	C₂×D₄	—	8	2	no	—
967	C₂×D₄	—	8	4	no	—
968	C₂×D₄	—	8	2	no	—
969	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
970	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
971	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
972	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
973	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
974	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
975	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
976	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
977	C₂²×C₄	—	2	1	no	—
978	C₂²×C₄	—	2	1	no	—
979	C₂²×C₄	—	2	2	no	—
980	C₂²×C₄	—	2	1	no	—
981	C₂²×C₄	—	2	1	no	—
982	C₂²×C₄	—	2	1	no	—
983	C₂²×C₄	—	2	1	no	—
984	C₂²×C₄	—	2	2	no	—
985	C₂²×C₄	—	2	1	no	—
986	C₂²×C₄	—	2	1	no	—
987	C₂²×C₄	—	2	1	no	—
988	C₂²×C₄	—	2	2	no	—
989	C₂²×C₄	—	2	2	no	—
990	C₂²×C₄	—	2	2	no	—
991	C₂²×C₄	—	4	1	no	—
992	C₂²×C₄	—	4	1	no	—
993	C₂²×C₄	—	4	4	no	—
994	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
995	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
996	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
997	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
998	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
999	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1000	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
1001	SD₁₆	—	2	4	no	—
1002	SD₁₆	—	2	4	no	—
1003	SD₁₆	—	4	2	no	—
1004	SD₁₆	—	4	2	no	—
1005	SD₁₆	—	4	2	no	—
1006	SD₁₆	—	4	2	no	—
1007	SD₁₆	—	4	2	no	—
1008	SD₁₆	—	4	2	no	—
1009	D₈	—	2	4	no	—
1010	D₈	—	2	4	no	—
1011	D₈	—	4	2	no	—
1012	D₈	—	4	2	no	—
1013	M₁₆	—	4	2	no	—
1014	M₁₆	—	4	1	no	—
1015	M₁₆	—	4	1	no	—
1016	C₂×C₈	—	4	1	no	—
1017	C₂×C₈	—	4	1	no	—
1018	C₂×C₈	—	4	2	no	—
1019	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1020	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1021	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1022	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1023	C₄⋊C₄	—	2	2	no	—
1024	C₄⋊C₄	—	2	1	no	—
1025	C₄⋊C₄	—	2	2	no	—
1026	C₄⋊C₄	—	2	2	no	—
1027	C₄⋊C₄	—	2	2	no	—
1028	C₄⋊C₄	—	2	2	no	—
1029	C₄⋊C₄	—	2	1	no	—
1030	C₄⋊C₄	—	2	1	no	—
1031	C₄⋊C₄	—	2	2	no	—
1032	C₄⋊C₄	—	2	2	no	—
1033	C₄⋊C₄	—	2	2	no	—
1034	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1035	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1036	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1037	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1038	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1039	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1040	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1041	C₂²⋊C₄	—	2	2	no	—
1042	C₂²⋊C₄	—	2	2	no	—
1043	C₂²⋊C₄	—	2	2	no	—
1044	C₂²⋊C₄	—	2	2	no	—
1045	C₂²⋊C₄	—	2	2	no	—
1046	C₂²⋊C₄	—	2	2	no	—
1047	C₂²⋊C₄	—	2	2	no	—
1048	C₂²⋊C₄	—	2	2	no	—
1049	C₂²⋊C₄	—	2	2	no	—
1050	C₂²⋊C₄	—	2	2	no	—
1051	C₂²⋊C₄	—	2	2	no	—
1052	C₂²⋊C₄	—	2	2	no	—
1053	C₂²⋊C₄	—	2	2	no	—
1054	C₂²⋊C₄	—	2	2	no	—
1055	C₂²⋊C₄	—	2	2	no	—
1056	C₂²⋊C₄	—	2	2	no	—
1057	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1058	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1059	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1060	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1061	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1062	C₄²	—	2	2	no	—
1063	C₄²	—	2	2	no	—
1064	C₄²	C₂⁴×C₂₃	1	2	yes	—
1065	C₂³	—	2	1	no	—
1066	C₂³	—	2	2	no	—
1067	C₂³	—	2	1	no	—
1068	C₂³	—	2	2	no	—
1069	C₂³	—	2	2	no	—
1070	C₂³	—	4	1	no	—
1071	C₂³	—	4	1	no	—
1072	C₂³	—	4	2	no	—
1073	C₂³	—	4	2	no	—
1074	C₂³	—	4	2	no	—
1075	C₂³	—	4	2	no	—
1076	C₂³	—	8	1	no	—
1077	C₂³	—	8	1	no	—
1078	C₂³	—	8	2	no	—
1079	C₂³	—	8	1	no	—
1080	C₂³	—	8	1	no	—
1081	C₂³	—	8	1	no	—
1082	C₂³	—	8	2	no	—
1083	C₂³	—	8	2	no	—
1084	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1085	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
1086	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1087	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1088	Q₈	—	2	1	no	—
1089	Q₈	—	2	2	no	—
1090	Q₈	—	2	1	no	—
1091	Q₈	—	2	2	no	—
1092	Q₈	—	2	1	no	—
1093	Q₈	—	4	1	no	—
1094	Q₈	—	4	4	no	—
1095	Q₈	—	4	2	no	—
1096	Q₈	—	4	2	no	—
1097	Q₈	C₂₃×H(5,𝔽₂)	1	2	yes	—
1098	D₄	—	2	4	no	—
1099	D₄	—	2	4	no	—
1100	D₄	—	2	1	no	—
1101	D₄	—	2	2	no	—
1102	D₄	—	2	2	no	—
1103	D₄	—	2	1	no	—
1104	D₄	—	2	1	no	—
1105	D₄	—	2	2	no	—
1106	D₄	—	2	2	no	—
1107	D₄	—	4	2	no	—
1108	D₄	—	4	1	no	—
1109	D₄	—	4	2	no	—
1110	D₄	—	4	2	no	—
1111	D₄	—	4	2	no	—
1112	D₄	—	4	2	no	—
1113	D₄	—	4	4	no	—
1114	D₄	—	4	2	no	—
1115	D₄	—	4	4	no	—
1116	D₄	—	4	4	no	—
1117	D₄	—	8	1	no	—
1118	D₄	—	8	1	no	—
1119	D₄	—	8	2	no	—
1120	D₄	—	8	2	no	—
1121	D₄	—	8	2	no	—
1122	D₄	—	8	2	no	—
1123	D₄	—	8	2	no	—
1124	D₄	—	8	2	no	—
1125	D₄	—	8	2	no	—
1126	D₄	—	8	2	no	—
1127	D₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
1128	C₂×C₄	—	2	4	no	—
1129	C₂×C₄	—	2	1	no	—
1130	C₂×C₄	—	2	1	no	—
1131	C₂×C₄	—	2	1	no	—
1132	C₂×C₄	—	2	2	no	—
1133	C₂×C₄	—	2	1	no	—
1134	C₂×C₄	—	2	1	no	—
1135	C₂×C₄	—	2	2	no	—
1136	C₂×C₄	—	2	1	no	—
1137	C₂×C₄	—	2	1	no	—
1138	C₂×C₄	—	2	2	no	—
1139	C₂×C₄	—	2	2	no	—
1140	C₂×C₄	—	2	2	no	—
1141	C₂×C₄	—	2	2	no	—
1142	C₂×C₄	—	2	1	no	—
1143	C₂×C₄	—	4	1	no	—
1144	C₂×C₄	—	4	1	no	—
1145	C₂×C₄	—	4	1	no	—
1146	C₂×C₄	—	4	2	no	—
1147	C₂×C₄	—	4	2	no	—
1148	C₂×C₄	—	4	2	no	—
1149	C₂×C₄	—	4	4	no	—
1150	C₂×C₄	—	4	4	no	—
1151	C₂×C₄	—	4	2	no	—
1152	C₂×C₄	—	4	2	no	—
1153	C₂×C₄	—	8	2	no	—
1154	C₂×C₄	—	8	2	no	—
1155	C₂×C₄	—	8	2	no	—
1156	C₂×C₄	—	8	1	no	—
1157	C₂×C₄	—	8	1	no	—
1158	C₂×C₄	—	8	1	no	—
1159	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1160	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1161	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1162	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1163	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1164	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1165	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1166	C₈	—	2	2	no	—
1167	C₈	—	2	2	no	—
1168	C₈	—	2	2	no	—
1169	C₈	—	2	2	no	—
1170	C₂²	—	2	1	no	—
1171	C₂²	—	2	1	no	—
1172	C₂²	—	2	1	no	—
1173	C₂²	—	2	2	no	—
1174	C₂²	—	2	2	no	—
1175	C₂²	—	2	1	no	—
1176	C₂²	—	2	1	no	—
1177	C₂²	—	2	2	no	—
1178	C₂²	—	2	1	no	—
1179	C₂²	—	2	1	no	—
1180	C₂²	—	2	1	no	—
1181	C₂²	—	2	2	no	—
1182	C₂²	—	4	1	no	—
1183	C₂²	—	4	1	no	—
1184	C₂²	—	4	1	no	—
1185	C₂²	—	4	2	no	—
1186	C₂²	—	4	2	no	—
1187	C₂²	—	4	2	no	—
1188	C₂²	—	4	2	no	—
1189	C₂²	—	4	1	no	—
1190	C₂²	—	4	2	no	—
1191	C₂²	—	4	2	no	—
1192	C₂²	—	4	1	no	—
1193	C₂²	—	8	2	no	—
1194	C₂²	—	8	4	no	—
1195	C₂²	—	16	2	no	—
1196	C₂²	—	16	2	no	—
1197	C₂²	—	16	4	no	—
1198	C₂²	C₂₃×#577	1	2	yes	—
1199	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1200	C₄	—	2	1	no	—
1201	C₄	—	2	2	no	—
1202	C₄	—	2	1	no	—
1203	C₄	—	2	1	no	—
1204	C₄	—	2	2	no	—
1205	C₄	—	2	2	no	—
1206	C₄	—	2	2	no	—
1207	C₄	—	4	1	no	—
1208	C₄	—	4	2	no	—
1209	C₄	—	4	2	no	—
1210	C₄	—	4	2	no	—
1211	C₄	—	4	2	no	—
1212	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1213	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1214	C₂	—	2	2	no	—
1215	C₂	—	4	1	no	—
1216	C₂	—	4	1	no	—
1217	C₂	—	4	2	no	—
1218	C₂	—	4	2	no	—
1219	C₂	—	8	1	no	—
1220	C₂	—	8	2	no	—
1221	C₂	—	8	2	no	—
1222	C₂	C₂₃×#3484	1	1	yes	characteristic
1223	C₂	C₂×C₂₃×#577	1	1	yes	characteristic
1224	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×#3537	C₂	semidirect
2. C₂₃×#3489	C₂	semidirect
3. C₂₃×#3326	C₂	semidirect
4. C₂₃×#3320	C₂	semidirect
5. C₂₃×#3307	C₂	semidirect
6. C₂₃×#3297	C₂	semidirect
7. D₄×SD₁₆×C₂₃	C₂	semidirect
8. C₂₃×#3272	C₂	semidirect
9. C₂₃×#3265	C₂	semidirect
10. C₂₃×#3264	C₂	semidirect
11. C₂₃×#3221	C₂	semidirect
12. C₂₃×#3198	C₂	semidirect
13. C₂₃×#3193	C₂	semidirect
14. C₂₃×#3187	C₂	semidirect
15. C₂₃×#3119	C₂	semidirect
16. C₂₃×#3010	C₂	semidirect
17. C₂₃×#3006	C₂	semidirect
18. C₂×C₂₃×#449	C₂	semidirect
19. C₂₃×#2976	C₂	semidirect
20. C₂×C₂₃×2₋¹⁺⁴	C₂²	semidirect
21. C₂²×#41×C₂₃	C₂²	semidirect
22. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
23. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
24. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
25. C₂²×SD₁₆×C₂₃	C₂²	semidirect
26. C₂²×SD₁₆×C₂₃	C₂²	semidirect
27. C₂²×D₈×C₂₃	C₂²	semidirect
30. C₂₃×#553	C₂²	semidirect
31. D₄×Q₈×C₂₃	C₂²	semidirect
32. C₂₃×#548	C₂²	semidirect
34. C₂₃×#547	C₂²	semidirect
36. C₂₃×#546	C₂²	semidirect
39. D₄²×C₂₃	C₂²	semidirect
40. C₂₃×#540	C₂²	semidirect
44. C₂₃×#537	C₂²	semidirect
46. C₂₃×#536	C₂²	semidirect
47. C₂₃×#535	C₂²	semidirect
53. C₂×C₂₃×C₂²⋊Q₈	C₂²	semidirect
56. C₂₃×#520	C₂²	semidirect
57. C₂₃×#496	C₂²	semidirect
58. C₂₃×#492	C₂²	semidirect
59. C₂₃×#491	C₂²	semidirect
60. C₂₃×#488	C₂²	semidirect
61. C₂₃×#485	C₂²	semidirect
62. C₂₃×#484	C₂²	semidirect
63. C₂₃×#483	C₂²	semidirect
64. C₂₃×#482	C₂²	semidirect
65. C₂₃×#481	C₂²	semidirect
66. C₂₃×#480	C₂²	semidirect
67. C₂₃×#479	C₂²	semidirect
68. C₂₃×#478	C₂²	semidirect
69. C₂₃×#469	C₂²	semidirect
70. C₂₃×#468	C₂²	semidirect
71. C₂₃×#468	C₂²	semidirect
72. C₂₃×#468	C₂²	semidirect
73. C₂₃×#466	C₂²	semidirect
74. C₂₃×#465	C₂²	semidirect
75. C₂₃×#465	C₂²	semidirect
76. C₂₃×#465	C₂²	semidirect
77. C₂₃×#463	C₂²	semidirect
78. C₂₃×#463	C₂²	semidirect
79. C₂₃×#461	C₂²	semidirect
80. C₂₃×#461	C₂²	semidirect
81. C₂₃×#460	C₂²	semidirect
82. C₂₃×#459	C₂²	semidirect
83. C₂₃×#450	C₂²	semidirect
84. C₂₃×#450	C₂²	semidirect
85. C₂₃×#450	C₂²	semidirect
86. C₂₃×#449	C₂²	semidirect
87. C₂₃×#449	C₂²	semidirect
88. C₂₃×#449	C₂²	semidirect
89. C₂₃×#449	C₂²	semidirect
90. C₂₃×#449	C₂²	semidirect
91. C₂₃×#449	C₂²	semidirect
92. C₂₃×#449	C₂²	semidirect
93. C₂₃×#449	C₂²	semidirect
94. C₂₃×#448	C₂²	semidirect
95. C₂₃×#448	C₂²	semidirect
96. C₂₃×#448	C₂²	semidirect
97. C₂₃×#448	C₂²	semidirect
98. C₂₃×#448	C₂²	semidirect
99. C₂₃×#447	C₂²	semidirect
100. C₂₃×#447	C₂²	semidirect
101. C₂₃×#442	C₂²	semidirect
102. C₂₃×#440	C₂²	semidirect
103. C₄×SD₁₆×C₂₃	C₂²	semidirect
104. C₄×D₈×C₂₃	C₂²	semidirect
105. C₂₃×#436	C₂²	semidirect
106. C₂₃×#435	C₂²	semidirect
107. C₂₃×#435	C₂²	semidirect
108. C₈×D₄×C₂₃	C₂²	semidirect
109. C₂₃×#433	C₂²	semidirect
110. C₂₃×#419	C₂²	semidirect
111. C₂₃×#417	C₂²	semidirect
112. C₂₃×#417	C₂²	semidirect
113. C₂₃×#416	C₂²	semidirect
114. C₂×C₂₃×#103	C₂²	semidirect
115. C₂×C₂₃×#102	C₂²	semidirect
116. C₂₃×#408	C₂²	semidirect
117. C₂₃×#407	C₂²	semidirect
118. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
452. #61621	C₂₃	direct (N × H)
558. #3537	C₂×C₂₃	semidirect
559. #3489	C₂×C₂₃	semidirect
560. #3326	C₂×C₂₃	semidirect
561. #3320	C₂×C₂₃	semidirect
562. #3307	C₂×C₂₃	semidirect
563. #3297	C₂×C₂₃	semidirect
564. D₄×SD₁₆	C₂×C₂₃	semidirect
565. #3272	C₂×C₂₃	semidirect
566. #3265	C₂×C₂₃	semidirect
567. #3264	C₂×C₂₃	semidirect
568. #3221	C₂×C₂₃	semidirect
569. #3198	C₂×C₂₃	semidirect
570. #3193	C₂×C₂₃	semidirect
571. #3187	C₂×C₂₃	semidirect
572. #3119	C₂×C₂₃	semidirect
573. #3010	C₂×C₂₃	semidirect
574. #3006	C₂×C₂₃	semidirect
575. C₂×#449	C₂×C₂₃	semidirect
576. #2976	C₂×C₂₃	semidirect
621. C₂×2₋¹⁺⁴	C₂²×C₂₃	semidirect
622. C₂²×#41	C₂²×C₂₃	semidirect
623. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
624. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
625. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
626. C₂²×SD₁₆	C₂²×C₂₃	semidirect
627. C₂²×SD₁₆	C₂²×C₂₃	semidirect
628. C₂²×D₈	C₂²×C₂₃	semidirect
631. #553	C₂²×C₂₃	semidirect
632. D₄×Q₈	C₂²×C₂₃	semidirect
633. #548	C₂²×C₂₃	semidirect
635. #547	C₂²×C₂₃	semidirect
637. #546	C₂²×C₂₃	semidirect
640. D₄²	C₂²×C₂₃	semidirect
641. #540	C₂²×C₂₃	semidirect
645. #537	C₂²×C₂₃	semidirect
647. #536	C₂²×C₂₃	semidirect
648. #535	C₂²×C₂₃	semidirect
654. C₂×C₂²⋊Q₈	C₂²×C₂₃	semidirect
657. #520	C₂²×C₂₃	semidirect
658. #496	C₂²×C₂₃	semidirect
659. #492	C₂²×C₂₃	semidirect
660. #491	C₂²×C₂₃	semidirect
661. #488	C₂²×C₂₃	semidirect
662. #485	C₂²×C₂₃	semidirect
663. #484	C₂²×C₂₃	semidirect
664. #483	C₂²×C₂₃	semidirect
665. #482	C₂²×C₂₃	semidirect
666. #481	C₂²×C₂₃	semidirect
667. #480	C₂²×C₂₃	semidirect
668. #479	C₂²×C₂₃	semidirect
669. #478	C₂²×C₂₃	semidirect
670. #469	C₂²×C₂₃	semidirect
671. #468	C₂²×C₂₃	semidirect
672. #468	C₂²×C₂₃	semidirect
673. #468	C₂²×C₂₃	semidirect
674. #466	C₂²×C₂₃	semidirect
675. #465	C₂²×C₂₃	semidirect
676. #465	C₂²×C₂₃	semidirect
677. #465	C₂²×C₂₃	semidirect
678. #463	C₂²×C₂₃	semidirect
679. #463	C₂²×C₂₃	semidirect
680. #461	C₂²×C₂₃	semidirect
681. #461	C₂²×C₂₃	semidirect
682. #460	C₂²×C₂₃	semidirect
683. #459	C₂²×C₂₃	semidirect
684. #450	C₂²×C₂₃	semidirect
685. #450	C₂²×C₂₃	semidirect
686. #450	C₂²×C₂₃	semidirect
687. #449	C₂²×C₂₃	semidirect
688. #449	C₂²×C₂₃	semidirect
689. #449	C₂²×C₂₃	semidirect
690. #449	C₂²×C₂₃	semidirect
691. #449	C₂²×C₂₃	semidirect
692. #449	C₂²×C₂₃	semidirect
693. #449	C₂²×C₂₃	semidirect
694. #449	C₂²×C₂₃	semidirect
695. #448	C₂²×C₂₃	semidirect
696. #448	C₂²×C₂₃	semidirect
697. #448	C₂²×C₂₃	semidirect
698. #448	C₂²×C₂₃	semidirect
699. #448	C₂²×C₂₃	semidirect
700. #447	C₂²×C₂₃	semidirect
701. #447	C₂²×C₂₃	semidirect
702. #442	C₂²×C₂₃	semidirect
703. #440	C₂²×C₂₃	semidirect
704. C₄×SD₁₆	C₂²×C₂₃	semidirect
705. C₄×D₈	C₂²×C₂₃	semidirect
706. #436	C₂²×C₂₃	semidirect
707. #435	C₂²×C₂₃	semidirect
708. #435	C₂²×C₂₃	semidirect
709. C₈×D₄	C₂²×C₂₃	semidirect
710. #433	C₂²×C₂₃	semidirect
711. #419	C₂²×C₂₃	semidirect
712. #417	C₂²×C₂₃	semidirect
713. #417	C₂²×C₂₃	semidirect
714. #416	C₂²×C₂₃	semidirect
715. C₂×#103	C₂²×C₂₃	semidirect
716. C₂×#102	C₂²×C₂₃	semidirect
717. #408	C₂²×C₂₃	semidirect
718. #407	C₂²×C₂₃	semidirect
719. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
902. C₂₃	#61621	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×#3537	2
C₂₃×#3489	2
C₂₃×#3326	2
C₂₃×#3320	2
C₂₃×#3307	2
C₂₃×#3297	2
D₄×SD₁₆×C₂₃	2
C₂₃×#3272	2
C₂₃×#3265	2
C₂₃×#3264	2
C₂₃×#3221	2
C₂₃×#3198	2
C₂₃×#3193	2
C₂₃×#3187	2
C₂₃×#3119	2
C₂₃×#3010	2
C₂₃×#3006	2
C₂×C₂₃×#449	2
C₂₃×#2976	2
#61621	23

Subgroups — C23×#61621 #19209247

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61621 #19209247