Subgroups — C₂₃×#61577 #19209203

Order 5888.

2178 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3505	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#550	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3317	C₂	1	4	yes	maximal, complemented
4	C₂₃×#3309	C₂	1	4	yes	maximal, complemented
5	C₂₃×#3271	C₂	1	4	yes	maximal, complemented
6	C₂₃×#3268	C₂	1	4	yes	maximal, complemented
7	C₂₃×#3217	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3193	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#3192	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3188	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3117	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3007	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3006	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3002	C₂	1	2	yes	maximal, complemented
15	C₂₃×#2973	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
17	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic, complemented
18	C₂×C₂₃×#137	C₂²	1	2	yes	complemented
19	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
20	C₂×C₂₃×#135	C₂²	1	4	yes	complemented
21	C₂₃×#553	—	2	2	no	—
22	C₂₃×#553	C₂²	1	2	yes	complemented
23	C₂₃×#552	C₂²	1	2	yes	complemented
24	C₂₃×#551	—	2	2	no	—
25	C₂₃×#550	—	2	2	no	—
26	C₂₃×#550	—	2	2	no	—
27	C₂₃×#550	C₂²	1	4	yes	—
28	C₂₃×#550	C₂²	1	4	yes	complemented
29	C₂₃×#548	C₂²	1	2	yes	complemented
30	C₂₃×#546	C₂²	1	2	yes	complemented
31	C₂₃×#539	—	2	1	no	—
32	C₂₃×#538	—	2	1	no	—
33	C₂₃×#534	—	2	1	no	—
34	C₂×C₂₃×#127	—	2	1	no	—
35	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic, complemented
36	C₂₃×#529	C₂²	1	2	yes	—
37	C₂₃×#525	C₂²	1	2	yes	—
38	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
39	C₂×C₂₃×#121	—	2	1	no	—
40	C₂×C₂₃×#121	—	2	1	no	—
41	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
42	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
43	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic, complemented
44	C₂₃×#518	—	2	1	no	—
45	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₄×D₄×C₂₃	—	2	1	no	—
47	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
48	C₂₃×#496	C₂²	1	4	yes	complemented
49	C₂₃×#490	C₂²	1	4	yes	complemented
50	C₂₃×#484	C₂²	1	2	yes	complemented
51	C₂₃×#482	C₂²	1	4	yes	complemented
52	C₂₃×#481	C₂²	1	2	yes	—
53	C₂₃×#481	C₂²	1	2	yes	complemented
54	C₂₃×#480	C₂²	1	2	yes	complemented
55	C₂₃×#479	C₂²	1	4	yes	complemented
56	C₂₃×#469	C₂²	1	4	yes	complemented
57	C₂₃×#468	C₂²	1	4	yes	complemented
58	C₂₃×#466	C₂²	1	4	yes	complemented
59	C₂₃×#465	C₂²	1	4	yes	complemented
60	C₂₃×#464	C₂²	1	4	yes	complemented
61	C₂₃×#460	C₂²	1	4	yes	complemented
62	C₂₃×#459	C₂²	1	4	yes	complemented
63	C₂₃×#452	C₂²	1	4	yes	complemented
64	C₂₃×#452	C₂²	1	4	yes	complemented
65	C₂₃×#451	C₂²	1	2	yes	complemented
66	C₂₃×#450	C₂²	1	2	yes	complemented
67	C₂₃×#450	C₂²	1	2	yes	complemented
68	C₂₃×#449	C₂²	1	4	yes	complemented
69	C₂₃×#449	C₂²	1	4	yes	complemented
70	C₂₃×#449	C₂²	1	4	yes	complemented
71	C₂₃×#448	C₂²	1	2	yes	—
72	C₂₃×#448	C₂²	1	2	yes	complemented
73	C₂₃×#447	C₂²	1	2	yes	—
74	C₂₃×#447	C₂²	1	2	yes	—
75	C₂₃×#447	C₂²	1	2	yes	complemented
76	C₂₃×#441	C₂²	1	4	yes	complemented
77	C₂₃×#440	C₂²	1	4	yes	complemented
78	C₂₃×#435	C₂²	1	4	yes	complemented
79	C₂₃×#435	C₂²	1	4	yes	complemented
80	C₂₃×#432	C₂²	1	2	yes	complemented
81	C₂₃×#417	C₂²	1	2	yes	complemented
82	C₂₃×#417	C₂²	1	2	yes	complemented
83	C₂₃×#416	C₂²	1	4	yes	complemented
84	C₂₃×#407	C₂²	1	1	yes	characteristic
85	C₂₃×#407	C₂²	1	1	yes	characteristic
86	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	complemented
87	C₂×#41×C₂₃	—	2	1	no	—
88	C₂×#41×C₂₃	—	2	1	no	—
89	C₂×#41×C₂₃	—	2	2	no	—
90	C₂×#41×C₂₃	—	4	4	no	—
91	C₂×#41×C₂₃	—	4	4	no	—
92	C₂×#41×C₂₃	C₂³	1	2	yes	—
93	C₂×#41×C₂₃	C₂³	1	4	yes	—
94	C₂×#41×C₂₃	C₂³	1	2	yes	—
95	C₂×#41×C₂₃	C₂³	1	2	yes	—
96	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
97	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
98	C₂²×D₄×C₂₃	—	2	1	no	—
99	C₂²×D₄×C₂₃	—	2	1	no	—
100	C₂²×D₄×C₂₃	—	2	1	no	—
101	C₂²×D₄×C₂₃	—	2	1	no	—
102	C₂²×D₄×C₂₃	—	2	1	no	—
103	C₂²×D₄×C₂₃	—	2	1	no	—
104	C₂²×D₄×C₂₃	—	2	1	no	—
105	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
106	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
107	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
108	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
109	C₂³×C₄×C₂₃	—	2	1	no	—
110	C₂³×C₄×C₂₃	—	2	1	no	—
111	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
113	C₂₃×#137	—	4	4	no	—
114	C₂₃×AGL(1,ℤ/8)	—	4	4	no	—
115	C₂₃×#135	—	4	8	no	—
116	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
117	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
118	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
119	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
120	C₂×D₈×C₂₃	C₂³	1	4	yes	—
121	C₂×D₈×C₂₃	C₂³	1	4	yes	—
122	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
123	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
124	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
125	C₂₃×#127	—	2	4	no	—
126	C₂₃×#127	—	2	4	no	—
127	C₂₃×#127	—	2	2	no	—
128	C₂₃×#127	C₂³	1	4	yes	—
129	C₂₃×#126	—	2	2	no	—
130	C₂₃×#126	—	2	2	no	—
131	C₂₃×#126	—	2	2	no	—
132	C₂₃×#125	—	2	2	no	—
133	C₂₃×#125	C₂³	1	2	yes	—
134	C₂₃×#124	—	2	2	no	—
135	C₂₃×#124	C₂³	1	2	yes	—
136	C₂₃×#123	—	2	2	no	—
137	C₂₃×#123	—	2	2	no	—
138	C₂₃×#123	—	2	2	no	—
139	C₂₃×#123	—	2	2	no	—
140	C₂₃×#123	—	2	2	no	—
141	C₂₃×C₂²⋊Q₈	—	2	1	no	—
142	C₂₃×C₂²⋊Q₈	—	2	1	no	—
143	C₂₃×C₂²⋊Q₈	—	2	2	no	—
144	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
145	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
146	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
147	C₂₃×#121	—	2	2	no	—
148	C₂₃×#121	—	2	2	no	—
149	C₂₃×#121	—	2	1	no	—
150	C₂₃×#121	—	2	1	no	—
151	C₂₃×#121	—	2	2	no	—
152	C₂₃×#121	—	2	1	no	—
153	C₂₃×#121	—	2	1	no	—
154	C₂₃×#121	—	2	4	no	—
155	C₂₃×#121	—	2	4	no	—
156	C₂₃×#121	—	2	4	no	—
157	C₂₃×#121	—	2	4	no	—
158	C₂₃×#121	—	2	2	no	—
159	C₂₃×#121	C₂³	1	2	yes	—
160	C₂₃×#121	C₂³	1	2	yes	—
161	C₂₃×#121	C₂³	1	4	yes	—
162	C₂₃×#121	C₂³	1	2	yes	—
163	C₂₃×#121	C₂³	1	2	yes	—
164	C₂₃×#121	C₂³	1	2	yes	—
165	C₂₃×#120	—	2	2	no	—
166	C₂₃×#120	—	2	2	no	—
167	C₄×Q₈×C₂₃	—	2	2	no	—
168	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
169	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
170	C₄×D₄×C₂₃	—	2	2	no	—
171	C₄×D₄×C₂₃	—	2	2	no	—
172	C₄×D₄×C₂₃	—	2	2	no	—
173	C₄×D₄×C₂₃	—	2	4	no	—
174	C₄×D₄×C₂₃	—	2	4	no	—
175	C₄×D₄×C₂₃	—	2	2	no	—
176	C₄×D₄×C₂₃	—	2	2	no	—
177	C₄×D₄×C₂₃	D₄	1	2	yes	—
178	C₄×D₄×C₂₃	D₄	1	2	yes	—
179	C₄×D₄×C₂₃	C₂³	1	2	yes	—
180	C₄×D₄×C₂₃	C₂³	1	2	yes	—
181	C₄×D₄×C₂₃	C₂³	1	2	yes	—
182	C₂₃×#117	—	2	2	no	—
183	C₂₃×#117	—	2	2	no	—
184	C₂₃×#117	C₂³	1	2	yes	—
185	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
186	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
187	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
188	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
189	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
190	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
191	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
192	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
193	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
194	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
195	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
196	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
197	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
198	C₂×C₄²×C₂₃	—	2	1	no	—
199	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
200	C₂₃×#107	C₂³	1	4	yes	—
201	C₂₃×#106	C₂³	1	4	yes	—
202	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
203	C₂₃×#103	C₂³	1	4	yes	—
204	C₂₃×#103	C₂³	1	4	yes	—
205	C₂₃×#103	C₂³	1	4	yes	—
206	C₂₃×#102	C₂³	1	4	yes	—
207	C₂₃×#102	C₂³	1	4	yes	—
208	C₂₃×#102	C₂³	1	4	yes	—
209	C₂₃×#102	C₂³	1	4	yes	—
210	C₂₃×#102	C₂³	1	4	yes	—
211	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
212	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
213	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
214	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
215	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
216	C₂₃×#97	C₂³	1	4	yes	—
217	C₂⁴×C₂₃	—	2	1	no	—
218	C₂⁴×C₂₃	—	2	1	no	—
219	C₂⁴×C₂₃	—	2	1	no	—
220	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
221	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
222	#41×C₂₃	—	2	8	no	—
223	#41×C₂₃	—	2	4	no	—
224	#41×C₂₃	—	2	4	no	—
225	#41×C₂₃	—	4	4	no	—
226	#41×C₂₃	—	4	2	no	—
227	#41×C₂₃	—	4	2	no	—
228	#41×C₂₃	—	4	4	no	—
229	#41×C₂₃	—	4	4	no	—
230	#41×C₂₃	—	4	4	no	—
231	#41×C₂₃	—	4	8	no	—
232	C₂×Q₈×C₂₃	—	2	4	no	—
233	C₂×Q₈×C₂₃	—	2	1	no	—
234	C₂×Q₈×C₂₃	—	2	1	no	—
235	C₂×Q₈×C₂₃	—	4	2	no	—
236	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
237	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
238	C₂×D₄×C₂₃	—	2	2	no	—
239	C₂×D₄×C₂₃	—	2	2	no	—
240	C₂×D₄×C₂₃	—	2	2	no	—
241	C₂×D₄×C₂₃	—	2	4	no	—
242	C₂×D₄×C₂₃	—	2	2	no	—
243	C₂×D₄×C₂₃	—	2	2	no	—
244	C₂×D₄×C₂₃	—	2	2	no	—
245	C₂×D₄×C₂₃	—	2	2	no	—
246	C₂×D₄×C₂₃	—	2	4	no	—
247	C₂×D₄×C₂₃	—	2	2	no	—
248	C₂×D₄×C₂₃	—	2	4	no	—
249	C₂×D₄×C₂₃	—	2	1	no	—
250	C₂×D₄×C₂₃	—	2	1	no	—
251	C₂×D₄×C₂₃	—	2	1	no	—
252	C₂×D₄×C₂₃	—	2	4	no	—
253	C₂×D₄×C₂₃	—	4	2	no	—
254	C₂×D₄×C₂₃	—	4	2	no	—
255	C₂×D₄×C₂₃	—	4	2	no	—
256	C₂×D₄×C₂₃	—	4	2	no	—
257	C₂×D₄×C₂₃	—	4	4	no	—
258	C₂×D₄×C₂₃	—	4	4	no	—
259	C₂×D₄×C₂₃	—	4	4	no	—
260	C₂×D₄×C₂₃	—	4	4	no	—
261	C₂×D₄×C₂₃	—	8	2	no	—
262	C₂×D₄×C₂₃	—	8	2	no	—
263	C₂×D₄×C₂₃	—	8	2	no	—
264	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
265	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
266	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
267	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
268	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
269	C₂²×C₄×C₂₃	—	2	1	no	—
270	C₂²×C₄×C₂₃	—	2	1	no	—
271	C₂²×C₄×C₂₃	—	2	1	no	—
272	C₂²×C₄×C₂₃	—	2	1	no	—
273	C₂²×C₄×C₂₃	—	2	1	no	—
274	C₂²×C₄×C₂₃	—	2	4	no	—
275	C₂²×C₄×C₂₃	—	2	2	no	—
276	C₂²×C₄×C₂₃	—	2	2	no	—
277	C₂²×C₄×C₂₃	—	2	2	no	—
278	C₂²×C₄×C₂₃	—	2	2	no	—
279	C₂²×C₄×C₂₃	—	4	2	no	—
280	C₂²×C₄×C₂₃	—	4	2	no	—
281	C₂²×C₄×C₂₃	—	4	4	no	—
282	C₂²×C₄×C₂₃	—	4	4	no	—
283	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
284	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
285	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
286	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
287	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
288	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
289	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
290	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
292	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
293	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
294	Q₁₆×C₂₃	—	2	8	no	—
295	SD₁₆×C₂₃	—	2	8	no	—
296	SD₁₆×C₂₃	—	4	4	no	—
297	SD₁₆×C₂₃	—	4	4	no	—
298	D₈×C₂₃	—	4	4	no	—
299	D₈×C₂₃	—	4	4	no	—
300	M₁₆×C₂₃	—	4	2	no	—
301	M₁₆×C₂₃	—	4	2	no	—
302	C₂×C₈×C₂₃	—	4	4	no	—
303	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
304	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
305	C₄⋊C₄×C₂₃	—	2	2	no	—
306	C₄⋊C₄×C₂₃	—	2	4	no	—
307	C₄⋊C₄×C₂₃	—	2	2	no	—
308	C₄⋊C₄×C₂₃	—	2	1	no	—
309	C₄⋊C₄×C₂₃	—	2	1	no	—
310	C₄⋊C₄×C₂₃	—	2	1	no	—
311	C₄⋊C₄×C₂₃	—	2	2	no	—
312	C₄⋊C₄×C₂₃	—	2	2	no	—
313	C₄⋊C₄×C₂₃	—	2	2	no	—
314	C₄⋊C₄×C₂₃	—	2	2	no	—
315	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
316	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
317	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
318	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
319	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
320	C₂²⋊C₄×C₂₃	—	2	2	no	—
321	C₂²⋊C₄×C₂₃	—	2	2	no	—
322	C₂²⋊C₄×C₂₃	—	2	2	no	—
323	C₂²⋊C₄×C₂₃	—	2	2	no	—
324	C₂²⋊C₄×C₂₃	—	2	2	no	—
325	C₂²⋊C₄×C₂₃	—	2	4	no	—
326	C₂²⋊C₄×C₂₃	—	2	2	no	—
327	C₂²⋊C₄×C₂₃	—	2	2	no	—
328	C₂²⋊C₄×C₂₃	—	2	2	no	—
329	C₂²⋊C₄×C₂₃	—	2	2	no	—
330	C₂²⋊C₄×C₂₃	—	2	2	no	—
331	C₂²⋊C₄×C₂₃	—	2	2	no	—
332	C₂²⋊C₄×C₂₃	—	2	2	no	—
333	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
334	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
335	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
336	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
337	C₄²×C₂₃	—	2	4	no	—
338	C₄²×C₂₃	—	2	2	no	—
339	C₄²×C₂₃	—	2	2	no	—
340	C₄²×C₂₃	C₂×D₄	1	2	yes	—
341	C₄²×C₂₃	C₂⁴	1	2	yes	—
342	#61577	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
343	C₂³×C₂₃	—	2	2	no	—
344	C₂³×C₂₃	—	2	2	no	—
345	C₂³×C₂₃	—	2	2	no	—
346	C₂³×C₂₃	—	2	2	no	—
347	C₂³×C₂₃	—	2	2	no	—
348	C₂³×C₂₃	—	4	1	no	—
349	C₂³×C₂₃	—	4	1	no	—
350	C₂³×C₂₃	—	4	1	no	—
351	C₂³×C₂₃	—	4	1	no	—
352	C₂³×C₂₃	—	4	2	no	—
353	C₂³×C₂₃	—	4	2	no	—
354	C₂³×C₂₃	—	4	2	no	—
355	C₂³×C₂₃	—	4	2	no	—
356	C₂³×C₂₃	—	4	2	no	—
357	C₂³×C₂₃	—	4	2	no	—
358	C₂³×C₂₃	—	4	2	no	—
359	C₂³×C₂₃	—	8	1	no	—
360	C₂³×C₂₃	—	8	1	no	—
361	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
362	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
363	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
364	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
365	Q₈×C₂₃	—	2	4	no	—
366	Q₈×C₂₃	—	2	2	no	—
367	Q₈×C₂₃	—	2	4	no	—
368	Q₈×C₂₃	—	8	1	no	—
369	Q₈×C₂₃	H(5,𝔽₂)	1	4	yes	—
370	D₄×C₂₃	—	2	4	no	—
371	D₄×C₂₃	—	2	2	no	—
372	D₄×C₂₃	—	2	4	no	—
373	D₄×C₂₃	—	2	2	no	—
374	D₄×C₂₃	—	4	2	no	—
375	D₄×C₂₃	—	4	2	no	—
376	D₄×C₂₃	—	4	4	no	—
377	D₄×C₂₃	—	4	8	no	—
378	D₄×C₂₃	—	4	4	no	—
379	D₄×C₂₃	—	4	8	no	—
380	D₄×C₂₃	—	4	2	no	—
381	D₄×C₂₃	—	4	2	no	—
382	D₄×C₂₃	—	4	4	no	—
383	D₄×C₂₃	—	4	4	no	—
384	D₄×C₂₃	—	8	1	no	—
385	D₄×C₂₃	—	8	4	no	—
386	D₄×C₂₃	—	8	2	no	—
387	D₄×C₂₃	—	8	2	no	—
388	D₄×C₂₃	—	8	4	no	—
389	D₄×C₂₃	—	8	2	no	—
390	D₄×C₂₃	—	8	2	no	—
391	C₂×C₄×C₂₃	—	2	4	no	—
392	C₂×C₄×C₂₃	—	2	2	no	—
393	C₂×C₄×C₂₃	—	2	2	no	—
394	C₂×C₄×C₂₃	—	2	4	no	—
395	C₂×C₄×C₂₃	—	2	2	no	—
396	C₂×C₄×C₂₃	—	2	2	no	—
397	C₂×C₄×C₂₃	—	2	2	no	—
398	C₂×C₄×C₂₃	—	2	2	no	—
399	C₂×C₄×C₂₃	—	2	2	no	—
400	C₂×C₄×C₂₃	—	2	2	no	—
401	C₂×C₄×C₂₃	—	2	2	no	—
402	C₂×C₄×C₂₃	—	4	1	no	—
403	C₂×C₄×C₂₃	—	4	1	no	—
404	C₂×C₄×C₂₃	—	4	2	no	—
405	C₂×C₄×C₂₃	—	4	1	no	—
406	C₂×C₄×C₂₃	—	4	1	no	—
407	C₂×C₄×C₂₃	—	4	1	no	—
408	C₂×C₄×C₂₃	—	4	8	no	—
409	C₂×C₄×C₂₃	—	4	4	no	—
410	C₂×C₄×C₂₃	—	4	4	no	—
411	C₂×C₄×C₂₃	—	4	2	no	—
412	C₂×C₄×C₂₃	—	4	2	no	—
413	C₂×C₄×C₂₃	—	8	2	no	—
414	C₂×C₄×C₂₃	—	8	2	no	—
415	C₂×C₄×C₂₃	—	8	1	no	—
416	C₂×C₄×C₂₃	—	8	1	no	—
417	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
418	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
419	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
420	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
421	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
422	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
423	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
424	C₈×C₂₃	—	2	4	no	—
425	C₈×C₂₃	—	2	4	no	—
426	#3505	C₂×C₂₃	1	1	yes	characteristic, complemented
427	C₂×#550	C₂×C₂₃	1	1	yes	characteristic, complemented
428	#3317	C₂×C₂₃	1	4	yes	complemented
429	#3309	C₂×C₂₃	1	4	yes	complemented
430	#3271	C₂×C₂₃	1	4	yes	complemented
431	#3268	C₂×C₂₃	1	4	yes	complemented
432	#3217	C₂×C₂₃	1	2	yes	complemented
433	#3193	C₂×C₂₃	1	1	yes	characteristic, complemented
434	#3192	C₂×C₂₃	1	1	yes	characteristic, complemented
435	#3188	C₂×C₂₃	1	2	yes	complemented
436	#3117	C₂×C₂₃	1	2	yes	complemented
437	#3007	C₂×C₂₃	1	1	yes	characteristic, complemented
438	#3006	C₂×C₂₃	1	1	yes	characteristic, complemented
439	#3002	C₂×C₂₃	1	2	yes	complemented
440	#2973	C₂×C₂₃	1	1	yes	characteristic, complemented
441	C₂²×C₂₃	—	2	1	no	—
442	C₂²×C₂₃	—	2	1	no	—
443	C₂²×C₂₃	—	2	1	no	—
444	C₂²×C₂₃	—	2	2	no	—
445	C₂²×C₂₃	—	2	1	no	—
446	C₂²×C₂₃	—	2	1	no	—
447	C₂²×C₂₃	—	2	2	no	—
448	C₂²×C₂₃	—	2	1	no	—
449	C₂²×C₂₃	—	2	1	no	—
450	C₂²×C₂₃	—	2	1	no	—
451	C₂²×C₂₃	—	2	2	no	—
452	C₂²×C₂₃	—	4	2	no	—
453	C₂²×C₂₃	—	4	2	no	—
454	C₂²×C₂₃	—	4	2	no	—
455	C₂²×C₂₃	—	4	2	no	—
456	C₂²×C₂₃	—	4	2	no	—
457	C₂²×C₂₃	—	4	2	no	—
458	C₂²×C₂₃	—	4	2	no	—
459	C₂²×C₂₃	—	4	2	no	—
460	C₂²×C₂₃	—	4	2	no	—
461	C₂²×C₂₃	—	8	2	no	—
462	C₂²×C₂₃	—	8	2	no	—
463	C₂²×C₂₃	—	8	4	no	—
464	C₂²×C₂₃	—	8	4	no	—
465	C₂²×C₂₃	—	16	2	no	—
466	C₂²×C₂₃	#575	1	2	yes	—
467	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
468	C₄×C₂₃	—	2	2	no	—
469	C₄×C₂₃	—	2	4	no	—
470	C₄×C₂₃	—	2	2	no	—
471	C₄×C₂₃	—	2	1	no	—
472	C₄×C₂₃	—	2	1	no	—
473	C₄×C₂₃	—	2	1	no	—
474	C₄×C₂₃	—	2	2	no	—
475	C₄×C₂₃	—	4	2	no	—
476	C₄×C₂₃	—	4	2	no	—
477	C₄×C₂₃	—	4	2	no	—
478	C₄×C₂₃	—	4	2	no	—
479	C₄×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
480	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
481	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic, complemented
482	C₂×#137	C₂²×C₂₃	1	2	yes	complemented
483	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	2	yes	complemented
484	C₂×#135	C₂²×C₂₃	1	4	yes	complemented
485	#553	—	2	2	no	—
486	#553	C₂²×C₂₃	1	2	yes	complemented
487	#552	C₂²×C₂₃	1	2	yes	complemented
488	#551	—	2	2	no	—
489	#550	—	2	2	no	—
490	#550	—	2	2	no	—
491	#550	C₂²×C₂₃	1	4	yes	—
492	#550	C₂²×C₂₃	1	4	yes	complemented
493	#548	C₂²×C₂₃	1	2	yes	complemented
494	#546	C₂²×C₂₃	1	2	yes	complemented
495	#539	—	2	1	no	—
496	#538	—	2	1	no	—
497	#534	—	2	1	no	—
498	C₂×#127	—	2	1	no	—
499	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic, complemented
500	#529	C₂²×C₂₃	1	2	yes	—
501	#525	C₂²×C₂₃	1	2	yes	—
502	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
503	C₂×#121	—	2	1	no	—
504	C₂×#121	—	2	1	no	—
505	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
506	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
507	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic, complemented
508	#518	—	2	1	no	—
509	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
510	C₂×C₄×D₄	—	2	1	no	—
511	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
512	#496	C₂²×C₂₃	1	4	yes	complemented
513	#490	C₂²×C₂₃	1	4	yes	complemented
514	#484	C₂²×C₂₃	1	2	yes	complemented
515	#482	C₂²×C₂₃	1	4	yes	complemented
516	#481	C₂²×C₂₃	1	2	yes	—
517	#481	C₂²×C₂₃	1	2	yes	complemented
518	#480	C₂²×C₂₃	1	2	yes	complemented
519	#479	C₂²×C₂₃	1	4	yes	complemented
520	#469	C₂²×C₂₃	1	4	yes	complemented
521	#468	C₂²×C₂₃	1	4	yes	complemented
522	#466	C₂²×C₂₃	1	4	yes	complemented
523	#465	C₂²×C₂₃	1	4	yes	complemented
524	#464	C₂²×C₂₃	1	4	yes	complemented
525	#460	C₂²×C₂₃	1	4	yes	complemented
526	#459	C₂²×C₂₃	1	4	yes	complemented
527	#452	C₂²×C₂₃	1	4	yes	complemented
528	#452	C₂²×C₂₃	1	4	yes	complemented
529	#451	C₂²×C₂₃	1	2	yes	complemented
530	#450	C₂²×C₂₃	1	2	yes	complemented
531	#450	C₂²×C₂₃	1	2	yes	complemented
532	#449	C₂²×C₂₃	1	4	yes	complemented
533	#449	C₂²×C₂₃	1	4	yes	complemented
534	#449	C₂²×C₂₃	1	4	yes	complemented
535	#448	C₂²×C₂₃	1	2	yes	—
536	#448	C₂²×C₂₃	1	2	yes	complemented
537	#447	C₂²×C₂₃	1	2	yes	—
538	#447	C₂²×C₂₃	1	2	yes	—
539	#447	C₂²×C₂₃	1	2	yes	complemented
540	#441	C₂²×C₂₃	1	4	yes	complemented
541	#440	C₂²×C₂₃	1	4	yes	complemented
542	#435	C₂²×C₂₃	1	4	yes	complemented
543	#435	C₂²×C₂₃	1	4	yes	complemented
544	#432	C₂²×C₂₃	1	2	yes	complemented
545	#417	C₂²×C₂₃	1	2	yes	complemented
546	#417	C₂²×C₂₃	1	2	yes	complemented
547	#416	C₂²×C₂₃	1	4	yes	complemented
548	#407	C₂²×C₂₃	1	1	yes	characteristic
549	#407	C₂²×C₂₃	1	1	yes	characteristic
550	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	complemented
551	C₂×C₂₃	—	2	2	no	—
552	C₂×C₂₃	—	4	1	no	—
553	C₂×C₂₃	—	4	2	no	—
554	C₂×C₂₃	—	4	1	no	—
555	C₂×C₂₃	—	8	2	no	—
556	C₂×C₂₃	—	8	2	no	—
557	C₂×C₂₃	—	8	2	no	—
558	C₂×C₂₃	#3484	1	1	yes	characteristic
559	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
560	C₂×C₂₃	#3585	1	1	yes	characteristic
561	C₂×#41	—	2	1	no	—
562	C₂×#41	—	2	1	no	—
563	C₂×#41	—	2	2	no	—
564	C₂×#41	—	4	4	no	—
565	C₂×#41	—	4	4	no	—
566	C₂×#41	C₂³×C₂₃	1	2	yes	—
567	C₂×#41	C₂³×C₂₃	1	4	yes	—
568	C₂×#41	C₂³×C₂₃	1	2	yes	—
569	C₂×#41	C₂³×C₂₃	1	2	yes	—
570	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
571	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
572	C₂²×D₄	—	2	1	no	—
573	C₂²×D₄	—	2	1	no	—
574	C₂²×D₄	—	2	1	no	—
575	C₂²×D₄	—	2	1	no	—
576	C₂²×D₄	—	2	1	no	—
577	C₂²×D₄	—	2	1	no	—
578	C₂²×D₄	—	2	1	no	—
579	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
580	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
581	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
582	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
583	C₂³×C₄	—	2	1	no	—
584	C₂³×C₄	—	2	1	no	—
585	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
586	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
587	#137	—	4	4	no	—
588	AGL(1,ℤ/8)	—	4	4	no	—
589	#135	—	4	8	no	—
590	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
591	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
592	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
593	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
594	C₂×D₈	C₂³×C₂₃	1	4	yes	—
595	C₂×D₈	C₂³×C₂₃	1	4	yes	—
596	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
597	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
598	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
599	#127	—	2	4	no	—
600	#127	—	2	4	no	—
601	#127	—	2	2	no	—
602	#127	C₂³×C₂₃	1	4	yes	—
603	#126	—	2	2	no	—
604	#126	—	2	2	no	—
605	#126	—	2	2	no	—
606	#125	—	2	2	no	—
607	#125	C₂³×C₂₃	1	2	yes	—
608	#124	—	2	2	no	—
609	#124	C₂³×C₂₃	1	2	yes	—
610	#123	—	2	2	no	—
611	#123	—	2	2	no	—
612	#123	—	2	2	no	—
613	#123	—	2	2	no	—
614	#123	—	2	2	no	—
615	C₂²⋊Q₈	—	2	1	no	—
616	C₂²⋊Q₈	—	2	1	no	—
617	C₂²⋊Q₈	—	2	2	no	—
618	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
619	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
620	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
621	#121	—	2	2	no	—
622	#121	—	2	2	no	—
623	#121	—	2	1	no	—
624	#121	—	2	1	no	—
625	#121	—	2	1	no	—
626	#121	—	2	1	no	—
627	#121	—	2	2	no	—
628	#121	—	2	4	no	—
629	#121	—	2	4	no	—
630	#121	—	2	4	no	—
631	#121	—	2	4	no	—
632	#121	—	2	2	no	—
633	#121	C₂³×C₂₃	1	2	yes	—
634	#121	C₂³×C₂₃	1	2	yes	—
635	#121	C₂³×C₂₃	1	2	yes	—
636	#121	C₂³×C₂₃	1	2	yes	—
637	#121	C₂³×C₂₃	1	4	yes	—
638	#121	C₂³×C₂₃	1	2	yes	—
639	#120	—	2	2	no	—
640	#120	—	2	2	no	—
641	C₄×Q₈	—	2	2	no	—
642	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
643	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
644	C₄×D₄	—	2	2	no	—
645	C₄×D₄	—	2	2	no	—
646	C₄×D₄	—	2	2	no	—
647	C₄×D₄	—	2	4	no	—
648	C₄×D₄	—	2	4	no	—
649	C₄×D₄	—	2	2	no	—
650	C₄×D₄	—	2	2	no	—
651	C₄×D₄	D₄×C₂₃	1	2	yes	—
652	C₄×D₄	D₄×C₂₃	1	2	yes	—
653	C₄×D₄	C₂³×C₂₃	1	2	yes	—
654	C₄×D₄	C₂³×C₂₃	1	2	yes	—
655	C₄×D₄	C₂³×C₂₃	1	2	yes	—
656	#117	—	2	2	no	—
657	#117	—	2	2	no	—
658	#117	C₂³×C₂₃	1	2	yes	—
659	C₂×C₄⋊C₄	—	2	1	no	—
660	C₂×C₄⋊C₄	—	2	1	no	—
661	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
662	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
663	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
664	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
665	C₂×C₂²⋊C₄	—	2	1	no	—
666	C₂×C₂²⋊C₄	—	2	1	no	—
667	C₂×C₂²⋊C₄	—	2	1	no	—
668	C₂×C₂²⋊C₄	—	2	1	no	—
669	C₂×C₂²⋊C₄	—	2	2	no	—
670	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
671	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
672	C₂×C₄²	—	2	1	no	—
673	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
674	#107	C₂³×C₂₃	1	4	yes	—
675	#106	C₂³×C₂₃	1	4	yes	—
676	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
677	#103	C₂³×C₂₃	1	4	yes	—
678	#103	C₂³×C₂₃	1	4	yes	—
679	#103	C₂³×C₂₃	1	4	yes	—
680	#102	C₂³×C₂₃	1	4	yes	—
681	#102	C₂³×C₂₃	1	4	yes	—
682	#102	C₂³×C₂₃	1	4	yes	—
683	#102	C₂³×C₂₃	1	4	yes	—
684	#102	C₂³×C₂₃	1	4	yes	—
685	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
686	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
687	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
688	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
689	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
690	#97	C₂³×C₂₃	1	4	yes	—
691	C₂₃	#61577	1	1	yes	characteristic, direct product factor, Sylow
692	C₂⁴	—	2	1	no	—
693	C₂⁴	—	2	1	no	—
694	C₂⁴	—	2	1	no	—
695	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
696	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
697	#41	—	2	8	no	—
698	#41	—	2	4	no	—
699	#41	—	2	4	no	—
700	#41	—	4	4	no	—
701	#41	—	4	2	no	—
702	#41	—	4	2	no	—
703	#41	—	4	4	no	—
704	#41	—	4	4	no	—
705	#41	—	4	4	no	—
706	#41	—	4	8	no	—
707	C₂×Q₈	—	2	4	no	—
708	C₂×Q₈	—	2	1	no	—
709	C₂×Q₈	—	2	1	no	—
710	C₂×Q₈	—	4	2	no	—
711	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
712	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
713	C₂×D₄	—	2	2	no	—
714	C₂×D₄	—	2	2	no	—
715	C₂×D₄	—	2	2	no	—
716	C₂×D₄	—	2	4	no	—
717	C₂×D₄	—	2	2	no	—
718	C₂×D₄	—	2	2	no	—
719	C₂×D₄	—	2	2	no	—
720	C₂×D₄	—	2	2	no	—
721	C₂×D₄	—	2	4	no	—
722	C₂×D₄	—	2	2	no	—
723	C₂×D₄	—	2	4	no	—
724	C₂×D₄	—	2	1	no	—
725	C₂×D₄	—	2	1	no	—
726	C₂×D₄	—	2	1	no	—
727	C₂×D₄	—	2	4	no	—
728	C₂×D₄	—	4	2	no	—
729	C₂×D₄	—	4	2	no	—
730	C₂×D₄	—	4	2	no	—
731	C₂×D₄	—	4	2	no	—
732	C₂×D₄	—	4	4	no	—
733	C₂×D₄	—	4	4	no	—
734	C₂×D₄	—	4	4	no	—
735	C₂×D₄	—	4	4	no	—
736	C₂×D₄	—	8	2	no	—
737	C₂×D₄	—	8	2	no	—
738	C₂×D₄	—	8	2	no	—
739	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
740	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
741	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
742	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
743	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
744	C₂²×C₄	—	2	1	no	—
745	C₂²×C₄	—	2	1	no	—
746	C₂²×C₄	—	2	1	no	—
747	C₂²×C₄	—	2	1	no	—
748	C₂²×C₄	—	2	1	no	—
749	C₂²×C₄	—	2	4	no	—
750	C₂²×C₄	—	2	2	no	—
751	C₂²×C₄	—	2	2	no	—
752	C₂²×C₄	—	2	2	no	—
753	C₂²×C₄	—	2	2	no	—
754	C₂²×C₄	—	4	2	no	—
755	C₂²×C₄	—	4	2	no	—
756	C₂²×C₄	—	4	4	no	—
757	C₂²×C₄	—	4	4	no	—
758	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
759	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
760	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
761	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
762	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
763	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
764	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
765	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
766	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
767	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
768	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
769	Q₁₆	—	2	8	no	—
770	SD₁₆	—	2	8	no	—
771	SD₁₆	—	4	4	no	—
772	SD₁₆	—	4	4	no	—
773	D₈	—	4	4	no	—
774	D₈	—	4	4	no	—
775	M₁₆	—	4	2	no	—
776	M₁₆	—	4	2	no	—
777	C₂×C₈	—	4	4	no	—
778	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
779	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
780	C₄⋊C₄	—	2	2	no	—
781	C₄⋊C₄	—	2	4	no	—
782	C₄⋊C₄	—	2	2	no	—
783	C₄⋊C₄	—	2	1	no	—
784	C₄⋊C₄	—	2	1	no	—
785	C₄⋊C₄	—	2	1	no	—
786	C₄⋊C₄	—	2	2	no	—
787	C₄⋊C₄	—	2	2	no	—
788	C₄⋊C₄	—	2	2	no	—
789	C₄⋊C₄	—	2	2	no	—
790	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
791	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
792	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
793	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
794	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
795	C₂²⋊C₄	—	2	2	no	—
796	C₂²⋊C₄	—	2	2	no	—
797	C₂²⋊C₄	—	2	2	no	—
798	C₂²⋊C₄	—	2	2	no	—
799	C₂²⋊C₄	—	2	2	no	—
800	C₂²⋊C₄	—	2	4	no	—
801	C₂²⋊C₄	—	2	2	no	—
802	C₂²⋊C₄	—	2	2	no	—
803	C₂²⋊C₄	—	2	2	no	—
804	C₂²⋊C₄	—	2	2	no	—
805	C₂²⋊C₄	—	2	2	no	—
806	C₂²⋊C₄	—	2	2	no	—
807	C₂²⋊C₄	—	2	2	no	—
808	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
809	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
810	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
811	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
812	C₄²	—	2	4	no	—
813	C₄²	—	2	2	no	—
814	C₄²	—	2	2	no	—
815	C₄²	C₂×D₄×C₂₃	1	2	yes	—
816	C₄²	C₂⁴×C₂₃	1	2	yes	—
817	C₂³	—	2	2	no	—
818	C₂³	—	2	2	no	—
819	C₂³	—	2	2	no	—
820	C₂³	—	2	2	no	—
821	C₂³	—	2	2	no	—
822	C₂³	—	4	1	no	—
823	C₂³	—	4	1	no	—
824	C₂³	—	4	1	no	—
825	C₂³	—	4	1	no	—
826	C₂³	—	4	2	no	—
827	C₂³	—	4	2	no	—
828	C₂³	—	4	2	no	—
829	C₂³	—	4	2	no	—
830	C₂³	—	4	2	no	—
831	C₂³	—	4	2	no	—
832	C₂³	—	4	2	no	—
833	C₂³	—	8	1	no	—
834	C₂³	—	8	1	no	—
835	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
836	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
837	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
838	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
839	Q₈	—	2	4	no	—
840	Q₈	—	2	2	no	—
841	Q₈	—	2	4	no	—
842	Q₈	—	8	1	no	—
843	Q₈	C₂₃×H(5,𝔽₂)	1	4	yes	—
844	D₄	—	2	4	no	—
845	D₄	—	2	2	no	—
846	D₄	—	2	4	no	—
847	D₄	—	2	2	no	—
848	D₄	—	4	2	no	—
849	D₄	—	4	2	no	—
850	D₄	—	4	4	no	—
851	D₄	—	4	8	no	—
852	D₄	—	4	4	no	—
853	D₄	—	4	2	no	—
854	D₄	—	4	2	no	—
855	D₄	—	4	8	no	—
856	D₄	—	4	4	no	—
857	D₄	—	4	4	no	—
858	D₄	—	8	1	no	—
859	D₄	—	8	4	no	—
860	D₄	—	8	2	no	—
861	D₄	—	8	4	no	—
862	D₄	—	8	2	no	—
863	D₄	—	8	2	no	—
864	D₄	—	8	2	no	—
865	C₂×C₄	—	2	4	no	—
866	C₂×C₄	—	2	2	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	4	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	4	1	no	—
877	C₂×C₄	—	4	1	no	—
878	C₂×C₄	—	4	2	no	—
879	C₂×C₄	—	4	1	no	—
880	C₂×C₄	—	4	1	no	—
881	C₂×C₄	—	4	1	no	—
882	C₂×C₄	—	4	8	no	—
883	C₂×C₄	—	4	4	no	—
884	C₂×C₄	—	4	4	no	—
885	C₂×C₄	—	4	2	no	—
886	C₂×C₄	—	4	2	no	—
887	C₂×C₄	—	8	2	no	—
888	C₂×C₄	—	8	2	no	—
889	C₂×C₄	—	8	1	no	—
890	C₂×C₄	—	8	1	no	—
891	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
892	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
893	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
894	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
895	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
896	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
897	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
898	C₈	—	2	4	no	—
899	C₈	—	2	4	no	—
900	C₂²	—	2	1	no	—
901	C₂²	—	2	1	no	—
902	C₂²	—	2	1	no	—
903	C₂²	—	2	2	no	—
904	C₂²	—	2	1	no	—
905	C₂²	—	2	1	no	—
906	C₂²	—	2	1	no	—
907	C₂²	—	2	2	no	—
908	C₂²	—	2	1	no	—
909	C₂²	—	2	2	no	—
910	C₂²	—	2	1	no	—
911	C₂²	—	4	2	no	—
912	C₂²	—	4	2	no	—
913	C₂²	—	4	2	no	—
914	C₂²	—	4	2	no	—
915	C₂²	—	4	2	no	—
916	C₂²	—	4	2	no	—
917	C₂²	—	4	2	no	—
918	C₂²	—	4	2	no	—
919	C₂²	—	4	2	no	—
920	C₂²	—	8	2	no	—
921	C₂²	—	8	2	no	—
922	C₂²	—	8	4	no	—
923	C₂²	—	8	4	no	—
924	C₂²	—	16	2	no	—
925	C₂²	C₂₃×#575	1	2	yes	—
926	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
927	C₄	—	2	4	no	—
928	C₄	—	2	2	no	—
929	C₄	—	2	1	no	—
930	C₄	—	2	1	no	—
931	C₄	—	2	1	no	—
932	C₄	—	2	2	no	—
933	C₄	—	2	2	no	—
934	C₄	—	4	2	no	—
935	C₄	—	4	2	no	—
936	C₄	—	4	2	no	—
937	C₄	—	4	2	no	—
938	C₄	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
939	C₂	—	2	2	no	—
940	C₂	—	4	1	no	—
941	C₂	—	4	1	no	—
942	C₂	—	4	2	no	—
943	C₂	—	8	2	no	—
944	C₂	—	8	2	no	—
945	C₂	—	8	2	no	—
946	C₂	C₂₃×#3484	1	1	yes	characteristic
947	C₂	C₂×C₂₃×#575	1	1	yes	characteristic
948	C₂	C₂₃×#3585	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3505	C₂	semidirect
2. C₂×C₂₃×#550	C₂	semidirect
3. C₂₃×#3317	C₂	semidirect
4. C₂₃×#3309	C₂	semidirect
5. C₂₃×#3271	C₂	semidirect
6. C₂₃×#3268	C₂	semidirect
7. C₂₃×#3217	C₂	semidirect
8. C₂₃×#3193	C₂	semidirect
9. C₂₃×#3192	C₂	semidirect
10. C₂₃×#3188	C₂	semidirect
11. C₂₃×#3117	C₂	semidirect
12. C₂₃×#3007	C₂	semidirect
13. C₂₃×#3006	C₂	semidirect
14. C₂₃×#3002	C₂	semidirect
15. C₂₃×#2973	C₂	semidirect
17. C₂²×#41×C₂₃	C₂²	semidirect
18. C₂×C₂₃×#137	C₂²	semidirect
19. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
20. C₂×C₂₃×#135	C₂²	semidirect
22. C₂₃×#553	C₂²	semidirect
23. C₂₃×#552	C₂²	semidirect
28. C₂₃×#550	C₂²	semidirect
29. C₂₃×#548	C₂²	semidirect
30. C₂₃×#546	C₂²	semidirect
35. C₂×C₂₃×#127	C₂²	semidirect
43. C₂×C₂₃×#121	C₂²	semidirect
45. C₂×C₄×Q₈×C₂₃	C₂²	semidirect
48. C₂₃×#496	C₂²	semidirect
49. C₂₃×#490	C₂²	semidirect
50. C₂₃×#484	C₂²	semidirect
51. C₂₃×#482	C₂²	semidirect
53. C₂₃×#481	C₂²	semidirect
54. C₂₃×#480	C₂²	semidirect
55. C₂₃×#479	C₂²	semidirect
56. C₂₃×#469	C₂²	semidirect
57. C₂₃×#468	C₂²	semidirect
58. C₂₃×#466	C₂²	semidirect
59. C₂₃×#465	C₂²	semidirect
60. C₂₃×#464	C₂²	semidirect
61. C₂₃×#460	C₂²	semidirect
62. C₂₃×#459	C₂²	semidirect
63. C₂₃×#452	C₂²	semidirect
64. C₂₃×#452	C₂²	semidirect
65. C₂₃×#451	C₂²	semidirect
66. C₂₃×#450	C₂²	semidirect
67. C₂₃×#450	C₂²	semidirect
68. C₂₃×#449	C₂²	semidirect
69. C₂₃×#449	C₂²	semidirect
70. C₂₃×#449	C₂²	semidirect
72. C₂₃×#448	C₂²	semidirect
75. C₂₃×#447	C₂²	semidirect
76. C₂₃×#441	C₂²	semidirect
77. C₂₃×#440	C₂²	semidirect
78. C₂₃×#435	C₂²	semidirect
79. C₂₃×#435	C₂²	semidirect
80. C₂₃×#432	C₂²	semidirect
81. C₂₃×#417	C₂²	semidirect
82. C₂₃×#417	C₂²	semidirect
83. C₂₃×#416	C₂²	semidirect
86. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
342. #61577	C₂₃	direct (N × H)
426. #3505	C₂×C₂₃	semidirect
427. C₂×#550	C₂×C₂₃	semidirect
428. #3317	C₂×C₂₃	semidirect
429. #3309	C₂×C₂₃	semidirect
430. #3271	C₂×C₂₃	semidirect
431. #3268	C₂×C₂₃	semidirect
432. #3217	C₂×C₂₃	semidirect
433. #3193	C₂×C₂₃	semidirect
434. #3192	C₂×C₂₃	semidirect
435. #3188	C₂×C₂₃	semidirect
436. #3117	C₂×C₂₃	semidirect
437. #3007	C₂×C₂₃	semidirect
438. #3006	C₂×C₂₃	semidirect
439. #3002	C₂×C₂₃	semidirect
440. #2973	C₂×C₂₃	semidirect
481. C₂²×#41	C₂²×C₂₃	semidirect
482. C₂×#137	C₂²×C₂₃	semidirect
483. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
484. C₂×#135	C₂²×C₂₃	semidirect
486. #553	C₂²×C₂₃	semidirect
487. #552	C₂²×C₂₃	semidirect
492. #550	C₂²×C₂₃	semidirect
493. #548	C₂²×C₂₃	semidirect
494. #546	C₂²×C₂₃	semidirect
499. C₂×#127	C₂²×C₂₃	semidirect
507. C₂×#121	C₂²×C₂₃	semidirect
509. C₂×C₄×Q₈	C₂²×C₂₃	semidirect
512. #496	C₂²×C₂₃	semidirect
513. #490	C₂²×C₂₃	semidirect
514. #484	C₂²×C₂₃	semidirect
515. #482	C₂²×C₂₃	semidirect
517. #481	C₂²×C₂₃	semidirect
518. #480	C₂²×C₂₃	semidirect
519. #479	C₂²×C₂₃	semidirect
520. #469	C₂²×C₂₃	semidirect
521. #468	C₂²×C₂₃	semidirect
522. #466	C₂²×C₂₃	semidirect
523. #465	C₂²×C₂₃	semidirect
524. #464	C₂²×C₂₃	semidirect
525. #460	C₂²×C₂₃	semidirect
526. #459	C₂²×C₂₃	semidirect
527. #452	C₂²×C₂₃	semidirect
528. #452	C₂²×C₂₃	semidirect
529. #451	C₂²×C₂₃	semidirect
530. #450	C₂²×C₂₃	semidirect
531. #450	C₂²×C₂₃	semidirect
532. #449	C₂²×C₂₃	semidirect
533. #449	C₂²×C₂₃	semidirect
534. #449	C₂²×C₂₃	semidirect
536. #448	C₂²×C₂₃	semidirect
539. #447	C₂²×C₂₃	semidirect
540. #441	C₂²×C₂₃	semidirect
541. #440	C₂²×C₂₃	semidirect
542. #435	C₂²×C₂₃	semidirect
543. #435	C₂²×C₂₃	semidirect
544. #432	C₂²×C₂₃	semidirect
545. #417	C₂²×C₂₃	semidirect
546. #417	C₂²×C₂₃	semidirect
547. #416	C₂²×C₂₃	semidirect
550. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
691. C₂₃	#61577	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×#3505	2
C₂×C₂₃×#550	2
C₂₃×#3317	2
C₂₃×#3309	2
C₂₃×#3271	2
C₂₃×#3268	2
C₂₃×#3217	2
C₂₃×#3193	2
C₂₃×#3192	2
C₂₃×#3188	2
C₂₃×#3117	2
C₂₃×#3007	2
C₂₃×#3006	2
C₂₃×#3002	2
C₂₃×#2973	2
#61577	23

Subgroups — C23×#61577 #19209203

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61577 #19209203