Subgroups — C₂₃×#61203 #19208829

Order 5888.

2068 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3497	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3333	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3329	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3313	C₂	1	4	yes	maximal, complemented
6	C₂₃×#3308	C₂	1	4	yes	maximal, complemented
7	C₂₃×#3305	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3299	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3141	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3098	C₂	1	2	yes	maximal, complemented
11	C₂×C₂₃×#477	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3061	C₂	1	2	yes	maximal, complemented
13	C₂₃×#3035	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3013	C₂	1	2	yes	maximal, complemented
15	C₄×C₂₃×#137	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#2935	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#2898	C₂	1	2	yes	maximal, complemented
18	C₂×C₂₃×2₋¹⁺⁴	C₂²	1	2	yes	—
19	C₂×C₂₃×#137	C₂²	1	1	yes	characteristic
20	C₂×C₂₃×#135	C₂²	1	2	yes	—
21	C₂×C₂₃×#131	C₂²	1	2	yes	—
22	C₂₃×#556	C₂²	1	2	yes	—
23	C₂₃×#555	C₂²	1	2	yes	—
24	C₂₃×#554	C₂²	1	2	yes	—
25	C₂₃×#553	—	2	2	no	—
26	C₂₃×#550	—	2	1	no	—
27	C₂₃×#550	C₂²	1	2	yes	—
28	D₄×Q₈×C₂₃	—	2	1	no	—
29	D₄×Q₈×C₂₃	C₂²	1	2	yes	—
30	C₂₃×#548	—	2	2	no	—
31	C₂₃×#548	—	2	2	no	—
32	C₂₃×#548	C₂²	1	4	yes	—
33	C₂₃×#547	C₂²	1	2	yes	—
34	C₂₃×#542	—	2	2	no	—
35	C₂₃×#537	—	2	2	no	—
36	C₂₃×#537	C₂²	1	2	yes	—
37	C₂₃×#537	C₂²	1	2	yes	—
38	C₂₃×#533	—	2	1	no	—
39	C₂₃×#532	—	2	1	no	—
40	C₂₃×#532	—	2	2	no	—
41	C₂₃×#532	C₂²	1	1	yes	characteristic
42	C₂₃×#532	C₂²	1	1	yes	characteristic
43	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
44	C₂₃×#520	C₂²	1	2	yes	—
45	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
46	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
47	C₂₃×#489	C₂²	1	4	yes	—
48	C₂₃×#487	C₂²	1	2	yes	—
49	C₂₃×#486	C₂²	1	2	yes	—
50	C₂₃×#485	C₂²	1	4	yes	—
51	C₂₃×#484	C₂²	1	4	yes	—
52	C₂₃×#482	C₂²	1	4	yes	—
53	C₂₃×#480	C₂²	1	4	yes	—
54	C₂₃×#477	C₂²	1	2	yes	—
55	C₂₃×#477	C₂²	1	4	yes	—
56	C₂₃×#477	C₂²	1	2	yes	—
57	C₂₃×#468	C₂²	1	4	yes	—
58	C₂₃×#468	C₂²	1	4	yes	—
59	C₂₃×#467	C₂²	1	4	yes	—
60	C₂₃×#466	C₂²	1	4	yes	—
61	C₂₃×#464	C₂²	1	2	yes	—
62	C₂₃×#463	C₂²	1	2	yes	—
63	C₂₃×#462	C₂²	1	1	yes	characteristic
64	C₂₃×#461	C₂²	1	1	yes	characteristic
65	C₂₃×#460	C₂²	1	1	yes	characteristic
66	C₂₃×#459	C₂²	1	1	yes	characteristic
67	C₂₃×#452	C₂²	1	4	yes	—
68	C₂₃×#451	C₂²	1	4	yes	—
69	C₂₃×#449	C₂²	1	4	yes	—
70	C₂₃×#448	C₂²	1	4	yes	—
71	C₂₃×#441	C₂²	1	2	yes	—
72	C₂₃×#440	C₂²	1	2	yes	—
73	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	—
74	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
75	C₂₃×#436	C₂²	1	2	yes	—
76	C₂₃×#435	C₂²	1	4	yes	—
77	C₈×D₄×C₂₃	C₂²	1	2	yes	—
78	C₂₃×#428	C₂²	1	1	yes	characteristic
79	C₂×C₂₃×#107	C₂²	1	2	yes	—
80	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
81	C₂₃×#419	C₂²	1	1	yes	characteristic
82	C₂₃×#419	C₂²	1	4	yes	—
83	C₂₃×#417	C₂²	1	1	yes	characteristic
84	C₂₃×#417	C₂²	1	2	yes	—
85	C₂₃×#417	C₂²	1	4	yes	—
86	C₂₃×#417	C₂²	1	2	yes	—
87	C₂₃×#416	C₂²	1	2	yes	—
88	C₂₃×#416	C₂²	1	4	yes	—
89	C₂×C₂₃×#103	C₂²	1	2	yes	—
90	C₂×C₂₃×#103	C₂²	1	4	yes	—
91	C₂₃×#408	C₂²	1	2	yes	—
92	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
93	C₂₃×2₋¹⁺⁴	—	2	8	no	—
94	C₂₃×2₋¹⁺⁴	—	4	4	no	—
95	C₂×#41×C₂₃	—	2	2	no	—
96	C₂×#41×C₂₃	—	2	4	no	—
97	C₂×#41×C₂₃	—	2	2	no	—
98	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
99	C₂×#41×C₂₃	C₂³	1	2	yes	—
100	C₂×#41×C₂₃	C₂³	1	4	yes	—
101	C₂×#41×C₂₃	C₂³	1	2	yes	—
102	C₂²×Q₈×C₂₃	—	2	2	no	—
103	C₂²×Q₈×C₂₃	—	2	1	no	—
104	C₂²×Q₈×C₂₃	C₂³	1	4	yes	—
105	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
106	C₂₃×#137	—	2	4	no	—
107	C₂₃×#135	—	4	4	no	—
108	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
109	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
110	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
111	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
112	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
113	C₂×D₈×C₂₃	C₂³	1	2	yes	—
114	C₂₃×#131	—	4	4	no	—
115	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
116	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
117	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
118	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
119	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
120	C₂₃×C₄⋊Q₈	—	2	2	no	—
121	C₂₃×C₄⋊Q₈	—	2	1	no	—
122	C₂₃×C₄⋊Q₈	—	2	1	no	—
123	C₂₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
124	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
125	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
126	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
127	C₂₃×#127	—	2	2	no	—
128	C₂₃×#127	D₄	1	1	yes	characteristic
129	C₂₃×#127	C₂³	1	1	yes	characteristic
130	C₂₃×#126	—	2	4	no	—
131	C₂₃×#125	—	2	2	no	—
132	C₂₃×#124	—	2	2	no	—
133	C₂₃×#124	—	2	4	no	—
134	C₂₃×#124	—	2	4	no	—
135	C₂₃×#124	D₄	1	2	yes	—
136	C₂₃×#124	C₂³	1	2	yes	—
137	C₂₃×#123	—	2	4	no	—
138	C₂₃×C₂²⋊Q₈	—	2	2	no	—
139	C₂₃×C₂²⋊Q₈	—	2	2	no	—
140	C₂₃×C₂²⋊Q₈	—	2	2	no	—
141	C₂₃×C₂²⋊Q₈	—	2	4	no	—
142	C₂₃×C₂²⋊Q₈	—	2	4	no	—
143	C₂₃×C₂²⋊Q₈	—	2	4	no	—
144	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
145	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
146	C₂₃×#121	—	2	2	no	—
147	C₂₃×#121	—	2	4	no	—
148	C₂₃×#121	—	2	4	no	—
149	C₂₃×#121	—	2	2	no	—
150	C₂₃×#121	—	2	4	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	D₄	1	2	yes	—
156	C₂₃×#121	D₄	1	2	yes	—
157	C₂₃×#121	C₂³	1	4	yes	—
158	C₂₃×#121	C₂³	1	4	yes	—
159	C₄×Q₈×C₂₃	—	2	2	no	—
160	C₄×Q₈×C₂₃	—	2	2	no	—
161	C₄×Q₈×C₂₃	—	2	1	no	—
162	C₄×Q₈×C₂₃	—	2	1	no	—
163	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
164	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
165	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
166	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
167	C₄×D₄×C₂₃	—	2	4	no	—
168	C₄×D₄×C₂₃	—	2	2	no	—
169	C₄×D₄×C₂₃	—	2	2	no	—
170	C₄×D₄×C₂₃	—	2	2	no	—
171	C₄×D₄×C₂₃	—	2	1	no	—
172	C₄×D₄×C₂₃	—	2	1	no	—
173	C₄×D₄×C₂₃	—	2	2	no	—
174	C₄×D₄×C₂₃	—	2	4	no	—
175	C₄×D₄×C₂₃	—	2	1	no	—
176	C₄×D₄×C₂₃	—	2	1	no	—
177	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
178	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
179	C₄×D₄×C₂₃	C₂³	1	2	yes	—
180	C₄×D₄×C₂₃	C₂³	1	2	yes	—
181	C₂₃×#117	—	2	2	no	—
182	C₂₃×#117	—	2	1	no	—
183	C₂₃×#117	C₂³	1	4	yes	—
184	C₂₃×#117	C₂³	1	1	yes	characteristic
185	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
186	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
187	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
188	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
189	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₂₃	—	2	1	no	—
191	C₂×C₄²×C₂₃	—	2	1	no	—
192	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
193	C₂₃×#107	C₂³	1	4	yes	—
194	C₂₃×#107	C₂³	1	4	yes	—
195	C₂₃×#107	C₂³	1	2	yes	—
196	C₂₃×#106	C₂³	1	2	yes	—
197	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
198	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
199	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
200	C₂₃×#103	C₂³	1	4	yes	—
201	C₂₃×#103	C₂³	1	2	yes	—
202	C₂₃×#103	C₂³	1	2	yes	—
203	C₂₃×#103	C₂³	1	4	yes	—
204	C₂₃×#103	C₂³	1	4	yes	—
205	C₂₃×#103	C₂³	1	2	yes	—
206	C₂₃×#103	C₂³	1	2	yes	—
207	C₂₃×#103	C₂³	1	2	yes	—
208	C₂₃×#103	C₂³	1	4	yes	—
209	C₂₃×#102	C₂³	1	2	yes	—
210	C₂₃×#102	C₂³	1	2	yes	—
211	C₂₃×#102	C₂³	1	4	yes	—
212	C₂₃×#102	C₂³	1	2	yes	—
213	C₂₃×#102	C₂³	1	4	yes	—
214	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
215	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
216	C₂₃×#97	C₂³	1	2	yes	—
217	C₄×C₈×C₂₃	C₂³	1	2	yes	—
218	#41×C₂₃	—	2	4	no	—
219	#41×C₂₃	—	2	4	no	—
220	#41×C₂₃	—	2	8	no	—
221	#41×C₂₃	—	2	2	no	—
222	#41×C₂₃	—	2	4	no	—
223	#41×C₂₃	—	2	2	no	—
224	#41×C₂₃	—	2	4	no	—
225	#41×C₂₃	—	4	4	no	—
226	#41×C₂₃	—	4	16	no	—
227	#41×C₂₃	—	4	8	no	—
228	#41×C₂₃	—	8	4	no	—
229	C₂×Q₈×C₂₃	—	2	1	no	—
230	C₂×Q₈×C₂₃	—	2	2	no	—
231	C₂×Q₈×C₂₃	—	2	4	no	—
232	C₂×Q₈×C₂₃	—	2	2	no	—
233	C₂×Q₈×C₂₃	—	2	2	no	—
234	C₂×Q₈×C₂₃	—	2	8	no	—
235	C₂×Q₈×C₂₃	—	4	4	no	—
236	C₂×Q₈×C₂₃	—	4	8	no	—
237	C₂×Q₈×C₂₃	—	8	2	no	—
238	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
239	C₂×Q₈×C₂₃	#41	1	4	yes	complemented
240	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
241	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
242	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
243	C₂×D₄×C₂₃	—	2	1	no	—
244	C₂×D₄×C₂₃	—	2	2	no	—
245	C₂×D₄×C₂₃	—	2	4	no	—
246	C₂×D₄×C₂₃	—	2	4	no	—
247	C₂×D₄×C₂₃	—	2	4	no	—
248	C₂×D₄×C₂₃	—	2	1	no	—
249	C₂×D₄×C₂₃	—	2	1	no	—
250	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
251	C₂×D₄×C₂₃	C₂×D₄	1	4	yes	—
252	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
253	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
254	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
255	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₂₃	—	2	1	no	—
257	C₂²×C₄×C₂₃	—	2	4	no	—
258	C₂²×C₄×C₂₃	—	2	1	no	—
259	C₂²×C₄×C₂₃	—	2	2	no	—
260	C₂²×C₄×C₂₃	—	2	4	no	—
261	C₂²×C₄×C₂₃	—	2	1	no	—
262	C₂²×C₄×C₂₃	—	2	1	no	—
263	C₂²×C₄×C₂₃	—	2	1	no	—
264	C₂²×C₄×C₂₃	—	2	4	no	—
265	C₂²×C₄×C₂₃	—	2	2	no	—
266	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
267	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
268	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
269	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
270	Q₁₆×C₂₃	—	2	4	no	—
271	Q₁₆×C₂₃	—	4	2	no	—
272	SD₁₆×C₂₃	—	2	4	no	—
273	SD₁₆×C₂₃	—	4	2	no	—
274	SD₁₆×C₂₃	—	4	2	no	—
275	D₈×C₂₃	—	4	2	no	—
276	M₁₆×C₂₃	—	2	2	no	—
277	M₁₆×C₂₃	—	2	2	no	—
278	M₁₆×C₂₃	—	4	4	no	—
279	C₂×C₈×C₂₃	—	2	4	no	—
280	C₂×C₈×C₂₃	—	4	4	no	—
281	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
282	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
283	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
284	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
285	C₄⋊C₄×C₂₃	—	2	2	no	—
286	C₄⋊C₄×C₂₃	—	2	2	no	—
287	C₄⋊C₄×C₂₃	—	2	2	no	—
288	C₄⋊C₄×C₂₃	—	2	2	no	—
289	C₄⋊C₄×C₂₃	—	2	2	no	—
290	C₄⋊C₄×C₂₃	—	2	4	no	—
291	C₄⋊C₄×C₂₃	—	2	1	no	—
292	C₄⋊C₄×C₂₃	—	2	1	no	—
293	C₄⋊C₄×C₂₃	—	2	1	no	—
294	C₄⋊C₄×C₂₃	—	2	1	no	—
295	C₄⋊C₄×C₂₃	—	2	1	no	—
296	C₄⋊C₄×C₂₃	—	2	4	no	—
297	C₄⋊C₄×C₂₃	—	2	4	no	—
298	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
299	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
300	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
301	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
302	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
303	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
304	C₂²⋊C₄×C₂₃	—	2	1	no	—
305	C₂²⋊C₄×C₂₃	—	2	4	no	—
306	C₂²⋊C₄×C₂₃	—	2	4	no	—
307	C₂²⋊C₄×C₂₃	—	2	4	no	—
308	C₂²⋊C₄×C₂₃	—	2	1	no	—
309	C₂²⋊C₄×C₂₃	—	2	1	no	—
310	C₂²⋊C₄×C₂₃	—	2	4	no	—
311	C₂²⋊C₄×C₂₃	—	2	2	no	—
312	C₂²⋊C₄×C₂₃	—	2	2	no	—
313	C₂²⋊C₄×C₂₃	—	2	4	no	—
314	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
315	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
316	C₄²×C₂₃	—	2	1	no	—
317	C₄²×C₂₃	—	2	1	no	—
318	C₄²×C₂₃	—	2	2	no	—
319	C₄²×C₂₃	—	2	2	no	—
320	C₄²×C₂₃	—	2	1	no	—
321	C₄²×C₂₃	—	2	4	no	—
322	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
323	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
324	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
325	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
326	#61203	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
327	C₂³×C₂₃	—	2	1	no	—
328	C₂³×C₂₃	—	2	2	no	—
329	C₂³×C₂₃	C₂²×D₄	1	4	yes	—
330	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
331	Q₈×C₂₃	—	2	4	no	—
332	Q₈×C₂₃	—	2	4	no	—
333	Q₈×C₂₃	—	2	2	no	—
334	Q₈×C₂₃	—	2	1	no	—
335	Q₈×C₂₃	—	2	2	no	—
336	Q₈×C₂₃	—	2	1	no	—
337	Q₈×C₂₃	—	2	2	no	—
338	Q₈×C₂₃	—	4	8	no	—
339	Q₈×C₂₃	—	4	4	no	—
340	Q₈×C₂₃	—	8	2	no	—
341	Q₈×C₂₃	C₂×#41	1	4	yes	—
342	D₄×C₂₃	—	2	8	no	—
343	D₄×C₂₃	—	2	4	no	—
344	D₄×C₂₃	—	2	4	no	—
345	D₄×C₂₃	—	2	1	no	—
346	D₄×C₂₃	—	2	2	no	—
347	D₄×C₂₃	—	2	1	no	—
348	D₄×C₂₃	—	2	2	no	—
349	D₄×C₂₃	—	4	2	no	—
350	D₄×C₂₃	—	4	8	no	—
351	D₄×C₂₃	—	4	2	no	—
352	D₄×C₂₃	—	4	4	no	—
353	D₄×C₂₃	—	4	2	no	—
354	D₄×C₂₃	—	8	1	no	—
355	D₄×C₂₃	—	8	4	no	—
356	D₄×C₂₃	—	8	4	no	—
357	C₂×C₄×C₂₃	—	2	4	no	—
358	C₂×C₄×C₂₃	—	2	2	no	—
359	C₂×C₄×C₂₃	—	2	2	no	—
360	C₂×C₄×C₂₃	—	2	4	no	—
361	C₂×C₄×C₂₃	—	2	4	no	—
362	C₂×C₄×C₂₃	—	2	1	no	—
363	C₂×C₄×C₂₃	—	2	1	no	—
364	C₂×C₄×C₂₃	—	2	2	no	—
365	C₂×C₄×C₂₃	—	2	1	no	—
366	C₂×C₄×C₂₃	—	2	4	no	—
367	C₂×C₄×C₂₃	—	2	2	no	—
368	C₂×C₄×C₂₃	—	4	1	no	—
369	C₂×C₄×C₂₃	—	4	8	no	—
370	C₂×C₄×C₂₃	—	4	8	no	—
371	C₂×C₄×C₂₃	—	4	2	no	—
372	C₂×C₄×C₂₃	—	4	4	no	—
373	C₂×C₄×C₂₃	—	4	2	no	—
374	C₂×C₄×C₂₃	—	4	2	no	—
375	C₂×C₄×C₂₃	—	8	1	no	—
376	C₂×C₄×C₂₃	—	8	2	no	—
377	C₂×C₄×C₂₃	—	8	4	no	—
378	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
379	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
380	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
381	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
382	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
383	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
384	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
385	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
386	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
387	C₈×C₂₃	—	2	2	no	—
388	C₈×C₂₃	—	2	2	no	—
389	C₈×C₂₃	—	2	2	no	—
390	C₈×C₂₃	—	2	2	no	—
391	#3511	C₂×C₂₃	1	1	yes	characteristic, complemented
392	#3497	C₂×C₂₃	1	1	yes	characteristic, complemented
393	#3333	C₂×C₂₃	1	2	yes	complemented
394	#3329	C₂×C₂₃	1	2	yes	complemented
395	#3313	C₂×C₂₃	1	4	yes	complemented
396	#3308	C₂×C₂₃	1	4	yes	complemented
397	#3305	C₂×C₂₃	1	2	yes	complemented
398	#3299	C₂×C₂₃	1	2	yes	complemented
399	#3141	C₂×C₂₃	1	1	yes	characteristic, complemented
400	#3098	C₂×C₂₃	1	2	yes	complemented
401	C₂×#477	C₂×C₂₃	1	1	yes	characteristic, complemented
402	#3061	C₂×C₂₃	1	2	yes	complemented
403	#3035	C₂×C₂₃	1	1	yes	characteristic, complemented
404	#3013	C₂×C₂₃	1	2	yes	complemented
405	C₄×#137	C₂×C₂₃	1	1	yes	characteristic, complemented
406	#2935	C₂×C₂₃	1	1	yes	characteristic, complemented
407	#2898	C₂×C₂₃	1	2	yes	complemented
408	C₂²×C₂₃	—	2	1	no	—
409	C₂²×C₂₃	—	2	1	no	—
410	C₂²×C₂₃	—	2	4	no	—
411	C₂²×C₂₃	—	2	4	no	—
412	C₂²×C₂₃	—	2	4	no	—
413	C₂²×C₂₃	—	4	1	no	—
414	C₂²×C₂₃	—	4	2	no	—
415	C₂²×C₂₃	—	4	2	no	—
416	C₂²×C₂₃	—	4	1	no	—
417	C₂²×C₂₃	—	4	1	no	—
418	C₂²×C₂₃	—	4	2	no	—
419	C₂²×C₂₃	#546	1	2	yes	—
420	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
421	C₄×C₂₃	—	2	1	no	—
422	C₄×C₂₃	—	2	1	no	—
423	C₄×C₂₃	—	2	4	no	—
424	C₄×C₂₃	—	2	4	no	—
425	C₄×C₂₃	—	2	1	no	—
426	C₄×C₂₃	—	4	1	no	—
427	C₄×C₂₃	—	4	4	no	—
428	C₄×C₂₃	—	4	2	no	—
429	C₄×C₂₃	—	4	2	no	—
430	C₄×C₂₃	—	4	1	no	—
431	C₄×C₂₃	—	4	1	no	—
432	C₄×C₂₃	#546	1	2	yes	—
433	C₄×C₂₃	#578	1	2	yes	—
434	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
435	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
436	C₂×2₋¹⁺⁴	C₂²×C₂₃	1	2	yes	—
437	C₂×#137	C₂²×C₂₃	1	1	yes	characteristic
438	C₂×#135	C₂²×C₂₃	1	2	yes	—
439	C₂×#131	C₂²×C₂₃	1	2	yes	—
440	#556	C₂²×C₂₃	1	2	yes	—
441	#555	C₂²×C₂₃	1	2	yes	—
442	#554	C₂²×C₂₃	1	2	yes	—
443	#553	—	2	2	no	—
444	#550	—	2	1	no	—
445	#550	C₂²×C₂₃	1	2	yes	—
446	D₄×Q₈	—	2	1	no	—
447	D₄×Q₈	C₂²×C₂₃	1	2	yes	—
448	#548	—	2	2	no	—
449	#548	—	2	2	no	—
450	#548	C₂²×C₂₃	1	4	yes	—
451	#547	C₂²×C₂₃	1	2	yes	—
452	#542	—	2	2	no	—
453	#537	—	2	2	no	—
454	#537	C₂²×C₂₃	1	2	yes	—
455	#537	C₂²×C₂₃	1	2	yes	—
456	#533	—	2	1	no	—
457	#532	—	2	1	no	—
458	#532	—	2	2	no	—
459	#532	C₂²×C₂₃	1	1	yes	characteristic
460	#532	C₂²×C₂₃	1	1	yes	characteristic
461	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
462	#520	C₂²×C₂₃	1	2	yes	—
463	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
464	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
465	#489	C₂²×C₂₃	1	4	yes	—
466	#487	C₂²×C₂₃	1	2	yes	—
467	#486	C₂²×C₂₃	1	2	yes	—
468	#485	C₂²×C₂₃	1	4	yes	—
469	#484	C₂²×C₂₃	1	4	yes	—
470	#482	C₂²×C₂₃	1	4	yes	—
471	#480	C₂²×C₂₃	1	4	yes	—
472	#477	C₂²×C₂₃	1	2	yes	—
473	#477	C₂²×C₂₃	1	2	yes	—
474	#477	C₂²×C₂₃	1	4	yes	—
475	#468	C₂²×C₂₃	1	4	yes	—
476	#468	C₂²×C₂₃	1	4	yes	—
477	#467	C₂²×C₂₃	1	4	yes	—
478	#466	C₂²×C₂₃	1	4	yes	—
479	#464	C₂²×C₂₃	1	2	yes	—
480	#463	C₂²×C₂₃	1	2	yes	—
481	#462	C₂²×C₂₃	1	1	yes	characteristic
482	#461	C₂²×C₂₃	1	1	yes	characteristic
483	#460	C₂²×C₂₃	1	1	yes	characteristic
484	#459	C₂²×C₂₃	1	1	yes	characteristic
485	#452	C₂²×C₂₃	1	4	yes	—
486	#451	C₂²×C₂₃	1	4	yes	—
487	#449	C₂²×C₂₃	1	4	yes	—
488	#448	C₂²×C₂₃	1	4	yes	—
489	#441	C₂²×C₂₃	1	2	yes	—
490	#440	C₂²×C₂₃	1	2	yes	—
491	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	—
492	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
493	#436	C₂²×C₂₃	1	2	yes	—
494	#435	C₂²×C₂₃	1	4	yes	—
495	C₈×D₄	C₂²×C₂₃	1	2	yes	—
496	#428	C₂²×C₂₃	1	1	yes	characteristic
497	C₂×#107	C₂²×C₂₃	1	2	yes	—
498	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
499	#419	C₂²×C₂₃	1	4	yes	—
500	#419	C₂²×C₂₃	1	1	yes	characteristic
501	#417	C₂²×C₂₃	1	4	yes	—
502	#417	C₂²×C₂₃	1	2	yes	—
503	#417	C₂²×C₂₃	1	2	yes	—
504	#417	C₂²×C₂₃	1	1	yes	characteristic
505	#416	C₂²×C₂₃	1	2	yes	—
506	#416	C₂²×C₂₃	1	4	yes	—
507	C₂×#103	C₂²×C₂₃	1	2	yes	—
508	C₂×#103	C₂²×C₂₃	1	4	yes	—
509	#408	C₂²×C₂₃	1	2	yes	—
510	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
511	C₂×C₂₃	—	2	2	no	—
512	C₂×C₂₃	—	4	4	no	—
513	C₂×C₂₃	—	8	1	no	—
514	C₂×C₂₃	—	8	2	no	—
515	C₂×C₂₃	C₂×#546	1	1	yes	characteristic
516	C₂×C₂₃	C₂×#578	1	1	yes	characteristic
517	C₂×C₂₃	#3585	1	1	yes	characteristic
518	2₋¹⁺⁴	—	2	8	no	—
519	2₋¹⁺⁴	—	4	4	no	—
520	C₂×#41	—	2	4	no	—
521	C₂×#41	—	2	2	no	—
522	C₂×#41	—	2	2	no	—
523	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
524	C₂×#41	C₂³×C₂₃	1	2	yes	—
525	C₂×#41	C₂³×C₂₃	1	4	yes	—
526	C₂×#41	C₂³×C₂₃	1	2	yes	—
527	C₂²×Q₈	—	2	2	no	—
528	C₂²×Q₈	—	2	1	no	—
529	C₂²×Q₈	C₂³×C₂₃	1	4	yes	—
530	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
531	#137	—	2	4	no	—
532	#135	—	4	4	no	—
533	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
534	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
535	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
536	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
537	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
538	C₂×D₈	C₂³×C₂₃	1	2	yes	—
539	#131	—	4	4	no	—
540	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
541	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
542	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
543	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
544	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
545	C₄⋊Q₈	—	2	2	no	—
546	C₄⋊Q₈	—	2	1	no	—
547	C₄⋊Q₈	—	2	1	no	—
548	C₄⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
549	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
550	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
551	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
552	#127	—	2	2	no	—
553	#127	D₄×C₂₃	1	1	yes	characteristic
554	#127	C₂³×C₂₃	1	1	yes	characteristic
555	#126	—	2	4	no	—
556	#125	—	2	2	no	—
557	#124	—	2	2	no	—
558	#124	—	2	4	no	—
559	#124	—	2	4	no	—
560	#124	D₄×C₂₃	1	2	yes	—
561	#124	C₂³×C₂₃	1	2	yes	—
562	#123	—	2	4	no	—
563	C₂²⋊Q₈	—	2	2	no	—
564	C₂²⋊Q₈	—	2	2	no	—
565	C₂²⋊Q₈	—	2	2	no	—
566	C₂²⋊Q₈	—	2	4	no	—
567	C₂²⋊Q₈	—	2	4	no	—
568	C₂²⋊Q₈	—	2	4	no	—
569	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
570	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
571	#121	—	2	4	no	—
572	#121	—	2	2	no	—
573	#121	—	2	2	no	—
574	#121	—	2	4	no	—
575	#121	—	2	2	no	—
576	#121	—	2	4	no	—
577	#121	—	2	1	no	—
578	#121	—	2	1	no	—
579	#121	—	2	4	no	—
580	#121	D₄×C₂₃	1	2	yes	—
581	#121	D₄×C₂₃	1	2	yes	—
582	#121	C₂³×C₂₃	1	4	yes	—
583	#121	C₂³×C₂₃	1	4	yes	—
584	C₄×Q₈	—	2	2	no	—
585	C₄×Q₈	—	2	2	no	—
586	C₄×Q₈	—	2	1	no	—
587	C₄×Q₈	—	2	1	no	—
588	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
589	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
590	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
591	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
592	C₄×D₄	—	2	2	no	—
593	C₄×D₄	—	2	4	no	—
594	C₄×D₄	—	2	2	no	—
595	C₄×D₄	—	2	2	no	—
596	C₄×D₄	—	2	1	no	—
597	C₄×D₄	—	2	1	no	—
598	C₄×D₄	—	2	2	no	—
599	C₄×D₄	—	2	4	no	—
600	C₄×D₄	—	2	1	no	—
601	C₄×D₄	—	2	1	no	—
602	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
603	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
604	C₄×D₄	C₂³×C₂₃	1	2	yes	—
605	C₄×D₄	C₂³×C₂₃	1	2	yes	—
606	#117	—	2	2	no	—
607	#117	—	2	1	no	—
608	#117	C₂³×C₂₃	1	1	yes	characteristic
609	#117	C₂³×C₂₃	1	4	yes	—
610	C₂×C₄⋊C₄	—	2	1	no	—
611	C₂×C₄⋊C₄	—	2	1	no	—
612	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
613	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
614	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
615	C₂×C₄²	—	2	1	no	—
616	C₂×C₄²	—	2	1	no	—
617	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
618	#107	C₂³×C₂₃	1	4	yes	—
619	#107	C₂³×C₂₃	1	4	yes	—
620	#107	C₂³×C₂₃	1	2	yes	—
621	#106	C₂³×C₂₃	1	2	yes	—
622	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
623	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
624	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
625	#103	C₂³×C₂₃	1	4	yes	—
626	#103	C₂³×C₂₃	1	2	yes	—
627	#103	C₂³×C₂₃	1	2	yes	—
628	#103	C₂³×C₂₃	1	4	yes	—
629	#103	C₂³×C₂₃	1	4	yes	—
630	#103	C₂³×C₂₃	1	2	yes	—
631	#103	C₂³×C₂₃	1	2	yes	—
632	#103	C₂³×C₂₃	1	2	yes	—
633	#103	C₂³×C₂₃	1	4	yes	—
634	#102	C₂³×C₂₃	1	2	yes	—
635	#102	C₂³×C₂₃	1	2	yes	—
636	#102	C₂³×C₂₃	1	4	yes	—
637	#102	C₂³×C₂₃	1	2	yes	—
638	#102	C₂³×C₂₃	1	4	yes	—
639	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
640	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
641	#97	C₂³×C₂₃	1	2	yes	—
642	C₄×C₈	C₂³×C₂₃	1	2	yes	—
643	C₂₃	#61203	1	1	yes	characteristic, direct product factor, Sylow
644	#41	—	2	4	no	—
645	#41	—	2	4	no	—
646	#41	—	2	8	no	—
647	#41	—	2	2	no	—
648	#41	—	2	4	no	—
649	#41	—	2	2	no	—
650	#41	—	2	4	no	—
651	#41	—	4	4	no	—
652	#41	—	4	16	no	—
653	#41	—	4	8	no	—
654	#41	—	8	4	no	—
655	C₂×Q₈	—	2	1	no	—
656	C₂×Q₈	—	2	2	no	—
657	C₂×Q₈	—	2	4	no	—
658	C₂×Q₈	—	2	2	no	—
659	C₂×Q₈	—	2	2	no	—
660	C₂×Q₈	—	2	8	no	—
661	C₂×Q₈	—	4	4	no	—
662	C₂×Q₈	—	4	8	no	—
663	C₂×Q₈	—	8	2	no	—
664	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
665	C₂×Q₈	#41×C₂₃	1	4	yes	complemented
666	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
667	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
668	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
669	C₂×D₄	—	2	1	no	—
670	C₂×D₄	—	2	2	no	—
671	C₂×D₄	—	2	4	no	—
672	C₂×D₄	—	2	4	no	—
673	C₂×D₄	—	2	4	no	—
674	C₂×D₄	—	2	1	no	—
675	C₂×D₄	—	2	1	no	—
676	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
677	C₂×D₄	C₂×D₄×C₂₃	1	4	yes	—
678	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
679	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
680	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
681	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
682	C₂²×C₄	—	2	1	no	—
683	C₂²×C₄	—	2	4	no	—
684	C₂²×C₄	—	2	1	no	—
685	C₂²×C₄	—	2	2	no	—
686	C₂²×C₄	—	2	4	no	—
687	C₂²×C₄	—	2	1	no	—
688	C₂²×C₄	—	2	1	no	—
689	C₂²×C₄	—	2	1	no	—
690	C₂²×C₄	—	2	4	no	—
691	C₂²×C₄	—	2	2	no	—
692	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
693	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
694	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
695	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
696	Q₁₆	—	2	4	no	—
697	Q₁₆	—	4	2	no	—
698	SD₁₆	—	2	4	no	—
699	SD₁₆	—	4	2	no	—
700	SD₁₆	—	4	2	no	—
701	D₈	—	4	2	no	—
702	M₁₆	—	2	2	no	—
703	M₁₆	—	2	2	no	—
704	M₁₆	—	4	4	no	—
705	C₂×C₈	—	2	4	no	—
706	C₂×C₈	—	4	4	no	—
707	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
708	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
709	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
710	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
711	C₄⋊C₄	—	2	2	no	—
712	C₄⋊C₄	—	2	2	no	—
713	C₄⋊C₄	—	2	2	no	—
714	C₄⋊C₄	—	2	2	no	—
715	C₄⋊C₄	—	2	2	no	—
716	C₄⋊C₄	—	2	4	no	—
717	C₄⋊C₄	—	2	1	no	—
718	C₄⋊C₄	—	2	1	no	—
719	C₄⋊C₄	—	2	1	no	—
720	C₄⋊C₄	—	2	1	no	—
721	C₄⋊C₄	—	2	1	no	—
722	C₄⋊C₄	—	2	4	no	—
723	C₄⋊C₄	—	2	4	no	—
724	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
725	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
726	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
727	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
728	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
729	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
730	C₂²⋊C₄	—	2	1	no	—
731	C₂²⋊C₄	—	2	4	no	—
732	C₂²⋊C₄	—	2	4	no	—
733	C₂²⋊C₄	—	2	4	no	—
734	C₂²⋊C₄	—	2	1	no	—
735	C₂²⋊C₄	—	2	1	no	—
736	C₂²⋊C₄	—	2	4	no	—
737	C₂²⋊C₄	—	2	2	no	—
738	C₂²⋊C₄	—	2	2	no	—
739	C₂²⋊C₄	—	2	4	no	—
740	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
741	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
742	C₄²	—	2	1	no	—
743	C₄²	—	2	1	no	—
744	C₄²	—	2	2	no	—
745	C₄²	—	2	2	no	—
746	C₄²	—	2	1	no	—
747	C₄²	—	2	4	no	—
748	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
749	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
750	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
751	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
752	C₂³	—	2	1	no	—
753	C₂³	—	2	2	no	—
754	C₂³	C₂²×D₄×C₂₃	1	4	yes	—
755	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
756	Q₈	—	2	2	no	—
757	Q₈	—	2	4	no	—
758	Q₈	—	2	4	no	—
759	Q₈	—	2	1	no	—
760	Q₈	—	2	2	no	—
761	Q₈	—	2	1	no	—
762	Q₈	—	2	2	no	—
763	Q₈	—	4	8	no	—
764	Q₈	—	4	4	no	—
765	Q₈	—	8	2	no	—
766	Q₈	C₂×#41×C₂₃	1	4	yes	—
767	D₄	—	2	8	no	—
768	D₄	—	2	4	no	—
769	D₄	—	2	1	no	—
770	D₄	—	2	2	no	—
771	D₄	—	2	1	no	—
772	D₄	—	2	2	no	—
773	D₄	—	2	4	no	—
774	D₄	—	4	2	no	—
775	D₄	—	4	8	no	—
776	D₄	—	4	4	no	—
777	D₄	—	4	2	no	—
778	D₄	—	4	2	no	—
779	D₄	—	8	1	no	—
780	D₄	—	8	4	no	—
781	D₄	—	8	4	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	4	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	4	no	—
786	C₂×C₄	—	2	4	no	—
787	C₂×C₄	—	2	1	no	—
788	C₂×C₄	—	2	1	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	1	no	—
791	C₂×C₄	—	2	4	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	4	1	no	—
794	C₂×C₄	—	4	8	no	—
795	C₂×C₄	—	4	8	no	—
796	C₂×C₄	—	4	2	no	—
797	C₂×C₄	—	4	2	no	—
798	C₂×C₄	—	4	4	no	—
799	C₂×C₄	—	4	2	no	—
800	C₂×C₄	—	8	2	no	—
801	C₂×C₄	—	8	4	no	—
802	C₂×C₄	—	8	1	no	—
803	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
804	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
805	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
806	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
807	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
808	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
809	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
810	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
811	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
812	C₈	—	2	2	no	—
813	C₈	—	2	2	no	—
814	C₈	—	2	2	no	—
815	C₈	—	2	2	no	—
816	C₂²	—	2	1	no	—
817	C₂²	—	2	1	no	—
818	C₂²	—	2	4	no	—
819	C₂²	—	2	4	no	—
820	C₂²	—	2	4	no	—
821	C₂²	—	4	2	no	—
822	C₂²	—	4	1	no	—
823	C₂²	—	4	1	no	—
824	C₂²	—	4	2	no	—
825	C₂²	—	4	1	no	—
826	C₂²	—	4	2	no	—
827	C₂²	C₂₃×#546	1	2	yes	—
828	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
829	C₄	—	2	4	no	—
830	C₄	—	2	4	no	—
831	C₄	—	2	1	no	—
832	C₄	—	2	1	no	—
833	C₄	—	2	1	no	—
834	C₄	—	4	2	no	—
835	C₄	—	4	1	no	—
836	C₄	—	4	1	no	—
837	C₄	—	4	1	no	—
838	C₄	—	4	4	no	—
839	C₄	—	4	2	no	—
840	C₄	C₂₃×#546	1	2	yes	—
841	C₄	C₂₃×#578	1	2	yes	—
842	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
843	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
844	C₂	—	2	2	no	—
845	C₂	—	4	4	no	—
846	C₂	—	8	2	no	—
847	C₂	—	8	1	no	—
848	C₂	C₂×C₂₃×#546	1	1	yes	characteristic
849	C₂	C₂×C₂₃×#578	1	1	yes	characteristic
850	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×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3511	C₂	semidirect
2. C₂₃×#3497	C₂	semidirect
3. C₂₃×#3333	C₂	semidirect
4. C₂₃×#3329	C₂	semidirect
5. C₂₃×#3313	C₂	semidirect
6. C₂₃×#3308	C₂	semidirect
7. C₂₃×#3305	C₂	semidirect
8. C₂₃×#3299	C₂	semidirect
9. C₂₃×#3141	C₂	semidirect
10. C₂₃×#3098	C₂	semidirect
11. C₂×C₂₃×#477	C₂	semidirect
12. C₂₃×#3061	C₂	semidirect
13. C₂₃×#3035	C₂	semidirect
14. C₂₃×#3013	C₂	semidirect
15. C₄×C₂₃×#137	C₂	semidirect
16. C₂₃×#2935	C₂	semidirect
17. C₂₃×#2898	C₂	semidirect
239. C₂×Q₈×C₂₃	#41	semidirect
326. #61203	C₂₃	direct (N × H)
391. #3511	C₂×C₂₃	semidirect
392. #3497	C₂×C₂₃	semidirect
393. #3333	C₂×C₂₃	semidirect
394. #3329	C₂×C₂₃	semidirect
395. #3313	C₂×C₂₃	semidirect
396. #3308	C₂×C₂₃	semidirect
397. #3305	C₂×C₂₃	semidirect
398. #3299	C₂×C₂₃	semidirect
399. #3141	C₂×C₂₃	semidirect
400. #3098	C₂×C₂₃	semidirect
401. C₂×#477	C₂×C₂₃	semidirect
402. #3061	C₂×C₂₃	semidirect
403. #3035	C₂×C₂₃	semidirect
404. #3013	C₂×C₂₃	semidirect
405. C₄×#137	C₂×C₂₃	semidirect
406. #2935	C₂×C₂₃	semidirect
407. #2898	C₂×C₂₃	semidirect
643. C₂₃	#61203	direct (N × H)
665. C₂×Q₈	#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×#3511	2
C₂₃×#3497	2
C₂₃×#3333	2
C₂₃×#3329	2
C₂₃×#3313	2
C₂₃×#3308	2
C₂₃×#3305	2
C₂₃×#3299	2
C₂₃×#3141	2
C₂₃×#3098	2
C₂×C₂₃×#477	2
C₂₃×#3061	2
C₂₃×#3035	2
C₂₃×#3013	2
C₄×C₂₃×#137	2
C₂₃×#2935	2
C₂₃×#2898	2
#61203	23

Subgroups — C23×#61203 #19208829

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61203 #19208829