Subgroups — C₂₃×#61874 #19209500

Order 5888.

1654 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3554	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#3502	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3390	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3388	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3386	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3385	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3375	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3371	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3371	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3368	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3243	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3241	C₂	1	2	yes	maximal, complemented
13	C₂₃×#3240	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3235	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3126	C₂	1	2	yes	maximal, complemented
16	C₂₃×#3121	C₂	1	2	yes	maximal, complemented
17	C₂₃×#3117	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#3112	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#2987	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#562	—	2	2	no	—
21	C₂₃×#559	C₂²	1	1	yes	characteristic
22	C₂₃×#559	C₂²	1	2	yes	—
23	Q₈²×C₂₃	—	2	1	no	—
24	Q₈²×C₂₃	C₂²	1	2	yes	—
25	C₂₃×#557	—	2	1	no	—
26	C₂₃×#557	—	2	2	no	—
27	C₂₃×#557	C₂²	1	2	yes	—
28	C₂₃×#557	C₂²	1	2	yes	—
29	C₂₃×#557	C₂²	1	2	yes	—
30	C₂₃×#557	C₂²	1	1	yes	characteristic
31	C₂₃×#554	C₂²	1	2	yes	—
32	C₂₃×#550	C₂²	1	1	yes	characteristic
33	D₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
34	C₂₃×#548	—	2	1	no	—
35	C₂₃×#547	—	2	1	no	—
36	C₂₃×#544	—	2	1	no	—
37	C₂₃×#544	—	2	1	no	—
38	C₂₃×#544	C₂²	1	2	yes	—
39	C₂₃×#542	—	2	1	no	—
40	C₂₃×#542	C₂²	1	2	yes	—
41	C₂₃×#540	C₂²	1	2	yes	—
42	C₂₃×#539	—	2	2	no	—
43	C₂₃×#536	—	2	1	no	—
44	C₂₃×#533	—	2	2	no	—
45	C₂₃×#533	C₂²	1	1	yes	characteristic
46	C₂₃×#533	C₂²	1	1	yes	characteristic
47	C₂₃×#532	C₂²	1	1	yes	characteristic
48	C₂₃×#529	C₂²	1	1	yes	characteristic
49	C₂₃×#519	C₂²	1	2	yes	—
50	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
51	C₂₃×#501	C₂²	1	2	yes	—
52	C₂₃×#501	C₂²	1	1	yes	characteristic
53	C₂₃×#501	C₂²	1	1	yes	characteristic
54	C₂₃×#501	C₂²	1	2	yes	—
55	C₂₃×#501	C₂²	1	2	yes	—
56	C₂₃×#500	C₂²	1	2	yes	—
57	C₂₃×#499	C₂²	1	2	yes	—
58	C₂₃×#490	C₂²	1	2	yes	—
59	C₂₃×#490	C₂²	1	2	yes	—
60	C₂₃×#489	C₂²	1	1	yes	characteristic
61	C₂₃×#489	C₂²	1	1	yes	characteristic
62	C₂₃×#489	C₂²	1	2	yes	—
63	C₂₃×#488	C₂²	1	2	yes	—
64	C₂₃×#486	C₂²	1	2	yes	—
65	C₂₃×#485	C₂²	1	2	yes	—
66	C₂₃×#484	C₂²	1	1	yes	characteristic
67	C₂₃×#482	C₂²	1	2	yes	—
68	C₂₃×#482	C₂²	1	2	yes	—
69	C₂₃×#482	C₂²	1	2	yes	—
70	C₂₃×#481	C₂²	1	1	yes	characteristic
71	C₂₃×#480	C₂²	1	2	yes	—
72	C₂₃×#479	C₂²	1	2	yes	—
73	C₂₃×#479	C₂²	1	2	yes	—
74	C₂₃×#479	C₂²	1	2	yes	—
75	C₂₃×#479	C₂²	1	2	yes	—
76	C₂₃×#479	C₂²	1	2	yes	—
77	C₂₃×#478	C₂²	1	2	yes	—
78	C₂₃×#478	C₂²	1	2	yes	—
79	C₂₃×#478	C₂²	1	2	yes	—
80	C₂₃×#478	C₂²	1	2	yes	—
81	C₂₃×#477	C₂²	1	2	yes	—
82	C₂₃×#477	C₂²	1	2	yes	—
83	C₂₃×#477	C₂²	1	2	yes	—
84	C₂₃×#476	C₂²	1	2	yes	—
85	C₂₃×#476	C₂²	1	2	yes	—
86	C₂₃×#475	C₂²	1	2	yes	—
87	C₂₃×#474	C₂²	1	2	yes	—
88	C₂₃×#474	C₂²	1	2	yes	—
89	C₂₃×#474	C₂²	1	2	yes	—
90	C₂₃×#464	C₂²	1	2	yes	—
91	C₂₃×#464	C₂²	1	2	yes	—
92	C₂₃×#464	C₂²	1	2	yes	—
93	C₂₃×#460	C₂²	1	2	yes	—
94	C₂₃×#460	C₂²	1	2	yes	—
95	C₂₃×#460	C₂²	1	2	yes	—
96	C₂₃×#451	C₂²	1	1	yes	characteristic
97	C₂₃×#448	C₂²	1	2	yes	—
98	C₂₃×#448	C₂²	1	1	yes	characteristic
99	C₂₃×#446	C₂²	1	2	yes	—
100	C₂₃×#446	C₂²	1	2	yes	—
101	C₂₃×#446	C₂²	1	2	yes	—
102	C₂₃×#446	C₂²	1	2	yes	—
103	C₂₃×#441	C₂²	1	2	yes	—
104	C₂₃×#441	C₂²	1	2	yes	—
105	C₂₃×#440	C₂²	1	2	yes	—
106	C₂₃×#440	C₂²	1	2	yes	—
107	C₂₃×#440	C₂²	1	2	yes	—
108	C₂₃×#440	C₂²	1	2	yes	—
109	C₂₃×#440	C₂²	1	2	yes	—
110	C₂₃×#440	C₂²	1	2	yes	—
111	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	—
112	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
113	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
114	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
115	C₂₃×#433	C₂²	1	2	yes	—
116	C₂₃×#433	C₂²	1	2	yes	—
117	C₂₃×#432	C₂²	1	1	yes	characteristic
118	C₂₃×#432	C₂²	1	1	yes	characteristic
119	C₂×#41×C₂₃	—	2	1	no	—
120	C₂×#41×C₂₃	—	2	1	no	—
121	C₂²×Q₈×C₂₃	—	2	1	no	—
122	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
123	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
124	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
125	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
126	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
127	C₂₃×C₄⋊Q₈	—	2	1	no	—
128	C₂₃×C₄⋊Q₈	—	2	2	no	—
129	C₂₃×C₄⋊Q₈	—	2	2	no	—
130	C₂₃×C₄⋊Q₈	—	2	2	no	—
131	C₂₃×C₄⋊Q₈	—	2	2	no	—
132	C₂₃×C₄⋊Q₈	—	2	2	no	—
133	C₂₃×C₄⋊Q₈	—	2	2	no	—
134	C₂₃×C₄⋊Q₈	—	2	2	no	—
135	C₂₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
136	C₂₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
137	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
138	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
139	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
140	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
141	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
142	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
143	C₂₃×#127	C₂³	1	2	yes	—
144	C₂₃×#127	C₂³	1	1	yes	characteristic
145	C₂₃×#126	—	2	2	no	—
146	C₂₃×#126	—	2	1	no	—
147	C₂₃×#125	—	2	2	no	—
148	C₂₃×#125	—	2	2	no	—
149	C₂₃×#125	—	2	2	no	—
150	C₂₃×#125	—	2	2	no	—
151	C₂₃×#125	—	2	2	no	—
152	C₂₃×#125	—	2	2	no	—
153	C₂₃×#125	—	2	2	no	—
154	C₂₃×#125	—	2	2	no	—
155	C₂₃×#125	D₄	1	2	yes	—
156	C₂₃×#125	C₂³	1	1	yes	characteristic
157	C₂₃×#125	C₂³	1	2	yes	—
158	C₂₃×#125	C₂³	1	2	yes	—
159	C₂₃×#125	C₂³	1	2	yes	—
160	C₂₃×#125	C₂³	1	2	yes	—
161	C₂₃×#124	—	2	1	no	—
162	C₂₃×#124	—	2	2	no	—
163	C₂₃×#124	—	2	2	no	—
164	C₂₃×#124	—	2	1	no	—
165	C₂₃×#124	C₂³	1	2	yes	—
166	C₂₃×#124	C₂³	1	1	yes	characteristic
167	C₂₃×#123	—	2	1	no	—
168	C₂₃×#123	—	2	2	no	—
169	C₂₃×#123	—	2	2	no	—
170	C₂₃×#123	—	2	2	no	—
171	C₂₃×#123	—	2	2	no	—
172	C₂₃×#123	—	2	2	no	—
173	C₂₃×#123	—	2	2	no	—
174	C₂₃×C₂²⋊Q₈	—	2	2	no	—
175	C₂₃×C₂²⋊Q₈	—	2	1	no	—
176	C₂₃×C₂²⋊Q₈	—	2	1	no	—
177	C₂₃×C₂²⋊Q₈	—	2	1	no	—
178	C₂₃×C₂²⋊Q₈	—	2	2	no	—
179	C₂₃×C₂²⋊Q₈	—	2	2	no	—
180	C₂₃×C₂²⋊Q₈	—	2	2	no	—
181	C₂₃×C₂²⋊Q₈	—	2	2	no	—
182	C₂₃×C₂²⋊Q₈	—	2	2	no	—
183	C₂₃×C₂²⋊Q₈	—	2	2	no	—
184	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
185	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
186	C₂₃×C₂²⋊Q₈	D₄	1	2	yes	—
187	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
188	C₂₃×#121	—	2	1	no	—
189	C₂₃×#121	—	2	1	no	—
190	C₂₃×#121	—	2	2	no	—
191	C₂₃×#121	—	2	2	no	—
192	C₂₃×#121	—	2	2	no	—
193	C₂₃×#121	C₂³	1	2	yes	—
194	C₂₃×#121	C₂³	1	1	yes	characteristic
195	C₄×Q₈×C₂₃	—	2	2	no	—
196	C₄×Q₈×C₂₃	—	2	1	no	—
197	C₄×Q₈×C₂₃	—	2	2	no	—
198	C₄×Q₈×C₂₃	—	2	2	no	—
199	C₄×Q₈×C₂₃	—	2	2	no	—
200	C₄×Q₈×C₂₃	—	2	2	no	—
201	C₄×Q₈×C₂₃	—	2	2	no	—
202	C₄×Q₈×C₂₃	—	2	1	no	—
203	C₄×Q₈×C₂₃	—	2	1	no	—
204	C₄×Q₈×C₂₃	—	2	1	no	—
205	C₄×Q₈×C₂₃	—	2	1	no	—
206	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
207	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
208	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
209	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
210	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
211	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
212	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
213	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
214	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
215	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
216	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
217	C₄×D₄×C₂₃	—	2	1	no	—
218	C₄×D₄×C₂₃	—	2	1	no	—
219	C₄×D₄×C₂₃	—	2	2	no	—
220	C₄×D₄×C₂₃	—	2	1	no	—
221	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
222	C₄×D₄×C₂₃	C₂³	1	2	yes	—
223	C₄×D₄×C₂₃	C₂³	1	2	yes	—
224	C₄×D₄×C₂₃	C₂³	1	2	yes	—
225	C₄×D₄×C₂₃	C₂³	1	2	yes	—
226	C₂₃×#117	—	2	2	no	—
227	C₂₃×#117	—	2	2	no	—
228	C₂₃×#117	—	2	1	no	—
229	C₂₃×#117	C₂³	1	2	yes	—
230	C₂₃×#117	C₂³	1	2	yes	—
231	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
232	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
233	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
234	C₂×C₄²×C₂₃	—	2	1	no	—
235	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
236	C₂₃×#107	C₂³	1	2	yes	—
237	C₂₃×#107	C₂³	1	2	yes	—
238	C₂₃×#107	C₂³	1	2	yes	—
239	C₂₃×#107	C₂³	1	2	yes	—
240	C₂₃×#107	C₂³	1	2	yes	—
241	C₂₃×#107	C₂³	1	2	yes	—
242	C₂₃×#107	C₂³	1	2	yes	—
243	C₂₃×#106	C₂³	1	2	yes	—
244	C₂₃×#106	C₂³	1	2	yes	—
245	C₂₃×#106	C₂³	1	2	yes	—
246	C₂₃×#106	C₂³	1	2	yes	—
247	C₂₃×#106	C₂³	1	2	yes	—
248	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
249	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
250	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
251	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
252	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
253	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
254	C₂₃×#103	C₂³	1	2	yes	—
255	C₂₃×#103	C₂³	1	2	yes	—
256	C₂₃×#103	C₂³	1	2	yes	—
257	C₂₃×#103	C₂³	1	2	yes	—
258	C₂₃×#103	C₂³	1	2	yes	—
259	C₂₃×#103	C₂³	1	2	yes	—
260	C₂₃×#103	C₂³	1	2	yes	—
261	C₂₃×#102	C₂³	1	2	yes	—
262	C₂₃×#102	C₂³	1	2	yes	—
263	C₂₃×#102	C₂³	1	2	yes	—
264	C₂₃×#102	C₂³	1	2	yes	—
265	C₂₃×#102	C₂³	1	2	yes	—
266	C₂₃×#102	C₂³	1	2	yes	—
267	C₂₃×#102	C₂³	1	2	yes	—
268	C₂₃×#102	C₂³	1	2	yes	—
269	C₂₃×#102	C₂³	1	2	yes	—
270	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
271	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
272	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
273	C₂₃×#97	C₂³	1	1	yes	characteristic
274	C₂₃×#97	C₂³	1	1	yes	characteristic
275	C₂₃×#97	C₂³	1	2	yes	—
276	C₂₃×#97	C₂³	1	2	yes	—
277	C₂₃×#97	C₂³	1	2	yes	—
278	C₄×C₈×C₂₃	C₂³	1	2	yes	—
279	C₄×C₈×C₂₃	C₂³	1	2	yes	—
280	#41×C₂₃	—	8	2	no	—
281	#41×C₂₃	—	8	2	no	—
282	C₂×Q₈×C₂₃	—	2	4	no	—
283	C₂×Q₈×C₂₃	—	2	1	no	—
284	C₂×Q₈×C₂₃	—	2	1	no	—
285	C₂×Q₈×C₂₃	—	2	1	no	—
286	C₂×Q₈×C₂₃	—	2	1	no	—
287	C₂×Q₈×C₂₃	—	2	2	no	—
288	C₂×Q₈×C₂₃	—	2	2	no	—
289	C₂×Q₈×C₂₃	—	2	2	no	—
290	C₂×Q₈×C₂₃	—	8	2	no	—
291	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
292	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
293	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
294	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
295	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
296	C₂×D₄×C₂₃	—	2	1	no	—
297	C₂×D₄×C₂₃	—	2	2	no	—
298	C₂×D₄×C₂₃	—	2	1	no	—
299	C₂×D₄×C₂₃	—	2	1	no	—
300	C₂×D₄×C₂₃	—	2	2	no	—
301	C₂×D₄×C₂₃	—	2	2	no	—
302	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
303	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
304	C₂²×C₄×C₂₃	—	2	1	no	—
305	C₂²×C₄×C₂₃	—	2	1	no	—
306	C₂²×C₄×C₂₃	—	2	1	no	—
307	C₂²×C₄×C₂₃	—	2	2	no	—
308	C₂²×C₄×C₂₃	—	2	2	no	—
309	C₂²×C₄×C₂₃	—	2	2	no	—
310	C₂²×C₄×C₂₃	—	2	2	no	—
311	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
312	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
313	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
314	Q₁₆×C₂₃	—	2	4	no	—
315	SD₁₆×C₂₃	—	2	4	no	—
316	SD₁₆×C₂₃	—	2	4	no	—
317	SD₁₆×C₂₃	—	2	4	no	—
318	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
319	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
320	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
321	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
322	C₄⋊C₄×C₂₃	—	2	1	no	—
323	C₄⋊C₄×C₂₃	—	2	2	no	—
324	C₄⋊C₄×C₂₃	—	2	2	no	—
325	C₄⋊C₄×C₂₃	—	2	2	no	—
326	C₄⋊C₄×C₂₃	—	2	2	no	—
327	C₄⋊C₄×C₂₃	—	2	1	no	—
328	C₄⋊C₄×C₂₃	—	2	2	no	—
329	C₄⋊C₄×C₂₃	—	2	2	no	—
330	C₄⋊C₄×C₂₃	—	2	2	no	—
331	C₄⋊C₄×C₂₃	—	2	2	no	—
332	C₄⋊C₄×C₂₃	—	2	1	no	—
333	C₄⋊C₄×C₂₃	—	2	1	no	—
334	C₄⋊C₄×C₂₃	—	2	1	no	—
335	C₄⋊C₄×C₂₃	—	2	2	no	—
336	C₄⋊C₄×C₂₃	—	2	1	no	—
337	C₄⋊C₄×C₂₃	—	2	2	no	—
338	C₄⋊C₄×C₂₃	—	2	1	no	—
339	C₄⋊C₄×C₂₃	—	2	2	no	—
340	C₄⋊C₄×C₂₃	—	2	2	no	—
341	C₄⋊C₄×C₂₃	—	2	2	no	—
342	C₄⋊C₄×C₂₃	—	2	2	no	—
343	C₄⋊C₄×C₂₃	—	2	2	no	—
344	C₄⋊C₄×C₂₃	—	2	2	no	—
345	C₄⋊C₄×C₂₃	—	2	2	no	—
346	C₄⋊C₄×C₂₃	—	2	2	no	—
347	C₄⋊C₄×C₂₃	—	2	1	no	—
348	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
349	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
350	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
351	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
352	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
353	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
354	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
355	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
356	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
357	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
358	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
359	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
360	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
361	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
362	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
363	C₂²⋊C₄×C₂₃	—	2	2	no	—
364	C₂²⋊C₄×C₂₃	—	2	1	no	—
365	C₂²⋊C₄×C₂₃	—	2	1	no	—
366	C₂²⋊C₄×C₂₃	—	2	1	no	—
367	C₂²⋊C₄×C₂₃	—	2	1	no	—
368	C₂²⋊C₄×C₂₃	—	2	2	no	—
369	C₂²⋊C₄×C₂₃	—	2	2	no	—
370	C₂²⋊C₄×C₂₃	—	2	2	no	—
371	C₂²⋊C₄×C₂₃	—	2	1	no	—
372	C₂²⋊C₄×C₂₃	—	2	2	no	—
373	C₂²⋊C₄×C₂₃	—	2	2	no	—
374	C₂²⋊C₄×C₂₃	—	2	2	no	—
375	C₂²⋊C₄×C₂₃	—	2	2	no	—
376	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
377	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
378	C₄²×C₂₃	—	2	2	no	—
379	C₄²×C₂₃	—	2	2	no	—
380	C₄²×C₂₃	—	2	1	no	—
381	C₄²×C₂₃	—	2	2	no	—
382	C₄²×C₂₃	—	2	2	no	—
383	C₄²×C₂₃	—	2	2	no	—
384	C₄²×C₂₃	—	2	2	no	—
385	C₄²×C₂₃	—	2	2	no	—
386	C₄²×C₂₃	—	2	2	no	—
387	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
388	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
389	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
390	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
391	C₄²×C₂₃	C₂⁴	1	2	yes	—
392	C₄²×C₂₃	C₂⁴	1	2	yes	—
393	#61874	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
394	C₂³×C₂₃	—	2	1	no	—
395	C₂³×C₂₃	—	2	2	no	—
396	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
397	Q₈×C₂₃	—	2	4	no	—
398	Q₈×C₂₃	—	2	2	no	—
399	Q₈×C₂₃	—	2	2	no	—
400	Q₈×C₂₃	—	4	1	no	—
401	Q₈×C₂₃	—	4	2	no	—
402	Q₈×C₂₃	—	4	1	no	—
403	Q₈×C₂₃	—	4	2	no	—
404	Q₈×C₂₃	—	4	2	no	—
405	Q₈×C₂₃	—	8	1	no	—
406	Q₈×C₂₃	—	8	2	no	—
407	Q₈×C₂₃	—	8	2	no	—
408	Q₈×C₂₃	—	8	2	no	—
409	Q₈×C₂₃	2₋¹⁺⁴	1	4	yes	—
410	D₄×C₂₃	—	2	2	no	—
411	D₄×C₂₃	—	2	2	no	—
412	D₄×C₂₃	—	2	2	no	—
413	D₄×C₂₃	—	4	2	no	—
414	D₄×C₂₃	—	8	1	no	—
415	D₄×C₂₃	—	8	2	no	—
416	D₄×C₂₃	—	8	2	no	—
417	D₄×C₂₃	—	8	1	no	—
418	D₄×C₂₃	—	8	2	no	—
419	C₂×C₄×C₂₃	—	2	4	no	—
420	C₂×C₄×C₂₃	—	2	2	no	—
421	C₂×C₄×C₂₃	—	2	2	no	—
422	C₂×C₄×C₂₃	—	2	1	no	—
423	C₂×C₄×C₂₃	—	2	2	no	—
424	C₂×C₄×C₂₃	—	2	2	no	—
425	C₂×C₄×C₂₃	—	2	2	no	—
426	C₂×C₄×C₂₃	—	2	1	no	—
427	C₂×C₄×C₂₃	—	2	2	no	—
428	C₂×C₄×C₂₃	—	2	1	no	—
429	C₂×C₄×C₂₃	—	4	1	no	—
430	C₂×C₄×C₂₃	—	4	1	no	—
431	C₂×C₄×C₂₃	—	4	2	no	—
432	C₂×C₄×C₂₃	—	8	2	no	—
433	C₂×C₄×C₂₃	—	8	2	no	—
434	C₂×C₄×C₂₃	—	8	2	no	—
435	C₂×C₄×C₂₃	—	8	2	no	—
436	C₂×C₄×C₂₃	—	8	1	no	—
437	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
438	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
439	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
440	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
441	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
442	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
443	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
444	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
445	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
446	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
447	C₈×C₂₃	—	2	2	no	—
448	C₈×C₂₃	—	2	2	no	—
449	C₈×C₂₃	—	2	2	no	—
450	C₈×C₂₃	—	2	2	no	—
451	#3554	C₂×C₂₃	1	1	yes	characteristic
452	#3502	C₂×C₂₃	1	1	yes	characteristic, complemented
453	#3390	C₂×C₂₃	1	2	yes	complemented
454	#3388	C₂×C₂₃	1	2	yes	complemented
455	#3386	C₂×C₂₃	1	2	yes	complemented
456	#3385	C₂×C₂₃	1	2	yes	complemented
457	#3375	C₂×C₂₃	1	2	yes	complemented
458	#3371	C₂×C₂₃	1	2	yes	complemented
459	#3371	C₂×C₂₃	1	2	yes	complemented
460	#3368	C₂×C₂₃	1	2	yes	complemented
461	#3243	C₂×C₂₃	1	2	yes	complemented
462	#3241	C₂×C₂₃	1	2	yes	complemented
463	#3240	C₂×C₂₃	1	1	yes	characteristic, complemented
464	#3235	C₂×C₂₃	1	1	yes	characteristic, complemented
465	#3126	C₂×C₂₃	1	2	yes	complemented
466	#3121	C₂×C₂₃	1	2	yes	complemented
467	#3117	C₂×C₂₃	1	1	yes	characteristic, complemented
468	#3112	C₂×C₂₃	1	1	yes	characteristic, complemented
469	#2987	C₂×C₂₃	1	1	yes	characteristic, complemented
470	C₂²×C₂₃	—	2	1	no	—
471	C₂²×C₂₃	—	2	1	no	—
472	C₂²×C₂₃	—	2	1	no	—
473	C₂²×C₂₃	—	4	1	no	—
474	C₂²×C₂₃	—	4	2	no	—
475	C₂²×C₂₃	—	4	2	no	—
476	C₂²×C₂₃	—	4	1	no	—
477	C₂²×C₂₃	—	4	1	no	—
478	C₂²×C₂₃	—	4	2	no	—
479	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
480	C₄×C₂₃	—	2	1	no	—
481	C₄×C₂₃	—	2	1	no	—
482	C₄×C₂₃	—	2	2	no	—
483	C₄×C₂₃	—	2	2	no	—
484	C₄×C₂₃	—	2	1	no	—
485	C₄×C₂₃	—	2	1	no	—
486	C₄×C₂₃	—	2	2	no	—
487	C₄×C₂₃	—	2	2	no	—
488	C₄×C₂₃	—	2	4	no	—
489	C₄×C₂₃	—	2	1	no	—
490	C₄×C₂₃	—	4	1	no	—
491	C₄×C₂₃	—	4	2	no	—
492	C₄×C₂₃	—	4	2	no	—
493	C₄×C₂₃	—	4	2	no	—
494	C₄×C₂₃	—	4	1	no	—
495	C₄×C₂₃	—	4	2	no	—
496	C₄×C₂₃	—	4	1	no	—
497	C₄×C₂₃	C₂×2₋¹⁺⁴	1	2	yes	—
498	#562	—	2	2	no	—
499	#559	C₂²×C₂₃	1	1	yes	characteristic
500	#559	C₂²×C₂₃	1	2	yes	—
501	Q₈²	—	2	1	no	—
502	Q₈²	C₂²×C₂₃	1	2	yes	—
503	#557	—	2	1	no	—
504	#557	—	2	2	no	—
505	#557	C₂²×C₂₃	1	2	yes	—
506	#557	C₂²×C₂₃	1	2	yes	—
507	#557	C₂²×C₂₃	1	2	yes	—
508	#557	C₂²×C₂₃	1	1	yes	characteristic
509	#554	C₂²×C₂₃	1	2	yes	—
510	#550	C₂²×C₂₃	1	1	yes	characteristic
511	D₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
512	#548	—	2	1	no	—
513	#547	—	2	1	no	—
514	#544	—	2	1	no	—
515	#544	—	2	1	no	—
516	#544	C₂²×C₂₃	1	2	yes	—
517	#542	—	2	1	no	—
518	#542	C₂²×C₂₃	1	2	yes	—
519	#540	C₂²×C₂₃	1	2	yes	—
520	#539	—	2	2	no	—
521	#536	—	2	1	no	—
522	#533	—	2	2	no	—
523	#533	C₂²×C₂₃	1	1	yes	characteristic
524	#533	C₂²×C₂₃	1	1	yes	characteristic
525	#532	C₂²×C₂₃	1	1	yes	characteristic
526	#529	C₂²×C₂₃	1	1	yes	characteristic
527	#519	C₂²×C₂₃	1	2	yes	—
528	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
529	#501	C₂²×C₂₃	1	1	yes	characteristic
530	#501	C₂²×C₂₃	1	2	yes	—
531	#501	C₂²×C₂₃	1	2	yes	—
532	#501	C₂²×C₂₃	1	2	yes	—
533	#501	C₂²×C₂₃	1	1	yes	characteristic
534	#500	C₂²×C₂₃	1	2	yes	—
535	#499	C₂²×C₂₃	1	2	yes	—
536	#490	C₂²×C₂₃	1	2	yes	—
537	#490	C₂²×C₂₃	1	2	yes	—
538	#489	C₂²×C₂₃	1	1	yes	characteristic
539	#489	C₂²×C₂₃	1	2	yes	—
540	#489	C₂²×C₂₃	1	1	yes	characteristic
541	#488	C₂²×C₂₃	1	2	yes	—
542	#486	C₂²×C₂₃	1	2	yes	—
543	#485	C₂²×C₂₃	1	2	yes	—
544	#484	C₂²×C₂₃	1	1	yes	characteristic
545	#482	C₂²×C₂₃	1	2	yes	—
546	#482	C₂²×C₂₃	1	2	yes	—
547	#482	C₂²×C₂₃	1	2	yes	—
548	#481	C₂²×C₂₃	1	1	yes	characteristic
549	#480	C₂²×C₂₃	1	2	yes	—
550	#479	C₂²×C₂₃	1	2	yes	—
551	#479	C₂²×C₂₃	1	2	yes	—
552	#479	C₂²×C₂₃	1	2	yes	—
553	#479	C₂²×C₂₃	1	2	yes	—
554	#479	C₂²×C₂₃	1	2	yes	—
555	#478	C₂²×C₂₃	1	2	yes	—
556	#478	C₂²×C₂₃	1	2	yes	—
557	#478	C₂²×C₂₃	1	2	yes	—
558	#478	C₂²×C₂₃	1	2	yes	—
559	#477	C₂²×C₂₃	1	2	yes	—
560	#477	C₂²×C₂₃	1	2	yes	—
561	#477	C₂²×C₂₃	1	2	yes	—
562	#476	C₂²×C₂₃	1	2	yes	—
563	#476	C₂²×C₂₃	1	2	yes	—
564	#475	C₂²×C₂₃	1	2	yes	—
565	#474	C₂²×C₂₃	1	2	yes	—
566	#474	C₂²×C₂₃	1	2	yes	—
567	#474	C₂²×C₂₃	1	2	yes	—
568	#464	C₂²×C₂₃	1	2	yes	—
569	#464	C₂²×C₂₃	1	2	yes	—
570	#464	C₂²×C₂₃	1	2	yes	—
571	#460	C₂²×C₂₃	1	2	yes	—
572	#460	C₂²×C₂₃	1	2	yes	—
573	#460	C₂²×C₂₃	1	2	yes	—
574	#451	C₂²×C₂₃	1	1	yes	characteristic
575	#448	C₂²×C₂₃	1	2	yes	—
576	#448	C₂²×C₂₃	1	1	yes	characteristic
577	#446	C₂²×C₂₃	1	2	yes	—
578	#446	C₂²×C₂₃	1	2	yes	—
579	#446	C₂²×C₂₃	1	2	yes	—
580	#446	C₂²×C₂₃	1	2	yes	—
581	#441	C₂²×C₂₃	1	2	yes	—
582	#441	C₂²×C₂₃	1	2	yes	—
583	#440	C₂²×C₂₃	1	2	yes	—
584	#440	C₂²×C₂₃	1	2	yes	—
585	#440	C₂²×C₂₃	1	2	yes	—
586	#440	C₂²×C₂₃	1	2	yes	—
587	#440	C₂²×C₂₃	1	2	yes	—
588	#440	C₂²×C₂₃	1	2	yes	—
589	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	—
590	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
591	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
592	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
593	#433	C₂²×C₂₃	1	2	yes	—
594	#433	C₂²×C₂₃	1	2	yes	—
595	#432	C₂²×C₂₃	1	1	yes	characteristic
596	#432	C₂²×C₂₃	1	1	yes	characteristic
597	C₂×C₂₃	—	4	1	no	—
598	C₂×C₂₃	—	8	1	no	—
599	C₂×C₂₃	—	8	2	no	—
600	C₂×C₂₃	#3486	1	1	yes	characteristic
601	C₂×C₂₃	#3585	1	1	yes	characteristic
602	C₂×C₂₃	#3586	1	1	yes	characteristic
603	C₂×#41	—	2	1	no	—
604	C₂×#41	—	2	1	no	—
605	C₂²×Q₈	—	2	1	no	—
606	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
607	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
608	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
609	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
610	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
611	C₄⋊Q₈	—	2	2	no	—
612	C₄⋊Q₈	—	2	1	no	—
613	C₄⋊Q₈	—	2	2	no	—
614	C₄⋊Q₈	—	2	2	no	—
615	C₄⋊Q₈	—	2	2	no	—
616	C₄⋊Q₈	—	2	2	no	—
617	C₄⋊Q₈	—	2	2	no	—
618	C₄⋊Q₈	—	2	2	no	—
619	C₄⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
620	C₄⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
621	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
622	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
623	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
624	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
625	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
626	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
627	#127	C₂³×C₂₃	1	1	yes	characteristic
628	#127	C₂³×C₂₃	1	2	yes	—
629	#126	—	2	2	no	—
630	#126	—	2	1	no	—
631	#125	—	2	2	no	—
632	#125	—	2	2	no	—
633	#125	—	2	2	no	—
634	#125	—	2	2	no	—
635	#125	—	2	2	no	—
636	#125	—	2	2	no	—
637	#125	—	2	2	no	—
638	#125	—	2	2	no	—
639	#125	D₄×C₂₃	1	2	yes	—
640	#125	C₂³×C₂₃	1	1	yes	characteristic
641	#125	C₂³×C₂₃	1	2	yes	—
642	#125	C₂³×C₂₃	1	2	yes	—
643	#125	C₂³×C₂₃	1	2	yes	—
644	#125	C₂³×C₂₃	1	2	yes	—
645	#124	—	2	1	no	—
646	#124	—	2	2	no	—
647	#124	—	2	2	no	—
648	#124	—	2	1	no	—
649	#124	C₂³×C₂₃	1	1	yes	characteristic
650	#124	C₂³×C₂₃	1	2	yes	—
651	#123	—	2	1	no	—
652	#123	—	2	2	no	—
653	#123	—	2	2	no	—
654	#123	—	2	2	no	—
655	#123	—	2	2	no	—
656	#123	—	2	2	no	—
657	#123	—	2	2	no	—
658	C₂²⋊Q₈	—	2	2	no	—
659	C₂²⋊Q₈	—	2	1	no	—
660	C₂²⋊Q₈	—	2	1	no	—
661	C₂²⋊Q₈	—	2	2	no	—
662	C₂²⋊Q₈	—	2	2	no	—
663	C₂²⋊Q₈	—	2	2	no	—
664	C₂²⋊Q₈	—	2	2	no	—
665	C₂²⋊Q₈	—	2	1	no	—
666	C₂²⋊Q₈	—	2	2	no	—
667	C₂²⋊Q₈	—	2	2	no	—
668	C₂²⋊Q₈	D₄×C₂₃	1	2	yes	—
669	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
670	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
671	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
672	#121	—	2	1	no	—
673	#121	—	2	2	no	—
674	#121	—	2	1	no	—
675	#121	—	2	2	no	—
676	#121	—	2	2	no	—
677	#121	C₂³×C₂₃	1	1	yes	characteristic
678	#121	C₂³×C₂₃	1	2	yes	—
679	C₄×Q₈	—	2	2	no	—
680	C₄×Q₈	—	2	2	no	—
681	C₄×Q₈	—	2	2	no	—
682	C₄×Q₈	—	2	2	no	—
683	C₄×Q₈	—	2	2	no	—
684	C₄×Q₈	—	2	2	no	—
685	C₄×Q₈	—	2	1	no	—
686	C₄×Q₈	—	2	1	no	—
687	C₄×Q₈	—	2	1	no	—
688	C₄×Q₈	—	2	1	no	—
689	C₄×Q₈	—	2	1	no	—
690	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
691	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
692	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
693	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
694	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
695	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
696	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
697	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
698	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
699	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
700	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
701	C₄×D₄	—	2	1	no	—
702	C₄×D₄	—	2	2	no	—
703	C₄×D₄	—	2	1	no	—
704	C₄×D₄	—	2	1	no	—
705	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
706	C₄×D₄	C₂³×C₂₃	1	2	yes	—
707	C₄×D₄	C₂³×C₂₃	1	2	yes	—
708	C₄×D₄	C₂³×C₂₃	1	2	yes	—
709	C₄×D₄	C₂³×C₂₃	1	2	yes	—
710	#117	—	2	2	no	—
711	#117	—	2	2	no	—
712	#117	—	2	1	no	—
713	#117	C₂³×C₂₃	1	2	yes	—
714	#117	C₂³×C₂₃	1	2	yes	—
715	C₂×C₄⋊C₄	—	2	1	no	—
716	C₂×C₄⋊C₄	—	2	2	no	—
717	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
718	C₂×C₄²	—	2	1	no	—
719	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
720	#107	C₂³×C₂₃	1	2	yes	—
721	#107	C₂³×C₂₃	1	2	yes	—
722	#107	C₂³×C₂₃	1	2	yes	—
723	#107	C₂³×C₂₃	1	2	yes	—
724	#107	C₂³×C₂₃	1	2	yes	—
725	#107	C₂³×C₂₃	1	2	yes	—
726	#107	C₂³×C₂₃	1	2	yes	—
727	#106	C₂³×C₂₃	1	2	yes	—
728	#106	C₂³×C₂₃	1	2	yes	—
729	#106	C₂³×C₂₃	1	2	yes	—
730	#106	C₂³×C₂₃	1	2	yes	—
731	#106	C₂³×C₂₃	1	2	yes	—
732	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
733	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
734	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
735	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
736	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
737	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
738	#103	C₂³×C₂₃	1	2	yes	—
739	#103	C₂³×C₂₃	1	2	yes	—
740	#103	C₂³×C₂₃	1	2	yes	—
741	#103	C₂³×C₂₃	1	2	yes	—
742	#103	C₂³×C₂₃	1	2	yes	—
743	#103	C₂³×C₂₃	1	2	yes	—
744	#103	C₂³×C₂₃	1	2	yes	—
745	#102	C₂³×C₂₃	1	2	yes	—
746	#102	C₂³×C₂₃	1	2	yes	—
747	#102	C₂³×C₂₃	1	2	yes	—
748	#102	C₂³×C₂₃	1	2	yes	—
749	#102	C₂³×C₂₃	1	2	yes	—
750	#102	C₂³×C₂₃	1	2	yes	—
751	#102	C₂³×C₂₃	1	2	yes	—
752	#102	C₂³×C₂₃	1	2	yes	—
753	#102	C₂³×C₂₃	1	2	yes	—
754	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
755	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
756	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
757	#97	C₂³×C₂₃	1	1	yes	characteristic
758	#97	C₂³×C₂₃	1	1	yes	characteristic
759	#97	C₂³×C₂₃	1	2	yes	—
760	#97	C₂³×C₂₃	1	2	yes	—
761	#97	C₂³×C₂₃	1	2	yes	—
762	C₄×C₈	C₂³×C₂₃	1	2	yes	—
763	C₄×C₈	C₂³×C₂₃	1	2	yes	—
764	C₂₃	#61874	1	1	yes	characteristic, direct product factor, Sylow
765	#41	—	8	2	no	—
766	#41	—	8	2	no	—
767	C₂×Q₈	—	2	4	no	—
768	C₂×Q₈	—	2	1	no	—
769	C₂×Q₈	—	2	1	no	—
770	C₂×Q₈	—	2	1	no	—
771	C₂×Q₈	—	2	1	no	—
772	C₂×Q₈	—	2	2	no	—
773	C₂×Q₈	—	2	2	no	—
774	C₂×Q₈	—	2	2	no	—
775	C₂×Q₈	—	8	2	no	—
776	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
777	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
778	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
779	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
780	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
781	C₂×D₄	—	2	1	no	—
782	C₂×D₄	—	2	2	no	—
783	C₂×D₄	—	2	1	no	—
784	C₂×D₄	—	2	1	no	—
785	C₂×D₄	—	2	2	no	—
786	C₂×D₄	—	2	2	no	—
787	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
788	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
789	C₂²×C₄	—	2	1	no	—
790	C₂²×C₄	—	2	1	no	—
791	C₂²×C₄	—	2	1	no	—
792	C₂²×C₄	—	2	2	no	—
793	C₂²×C₄	—	2	2	no	—
794	C₂²×C₄	—	2	2	no	—
795	C₂²×C₄	—	2	2	no	—
796	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
797	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
798	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
799	Q₁₆	—	2	4	no	—
800	SD₁₆	—	2	4	no	—
801	SD₁₆	—	2	4	no	—
802	SD₁₆	—	2	4	no	—
803	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
804	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
805	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
806	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
807	C₄⋊C₄	—	2	1	no	—
808	C₄⋊C₄	—	2	2	no	—
809	C₄⋊C₄	—	2	2	no	—
810	C₄⋊C₄	—	2	2	no	—
811	C₄⋊C₄	—	2	2	no	—
812	C₄⋊C₄	—	2	1	no	—
813	C₄⋊C₄	—	2	2	no	—
814	C₄⋊C₄	—	2	2	no	—
815	C₄⋊C₄	—	2	2	no	—
816	C₄⋊C₄	—	2	2	no	—
817	C₄⋊C₄	—	2	1	no	—
818	C₄⋊C₄	—	2	1	no	—
819	C₄⋊C₄	—	2	1	no	—
820	C₄⋊C₄	—	2	2	no	—
821	C₄⋊C₄	—	2	1	no	—
822	C₄⋊C₄	—	2	2	no	—
823	C₄⋊C₄	—	2	1	no	—
824	C₄⋊C₄	—	2	2	no	—
825	C₄⋊C₄	—	2	2	no	—
826	C₄⋊C₄	—	2	2	no	—
827	C₄⋊C₄	—	2	2	no	—
828	C₄⋊C₄	—	2	2	no	—
829	C₄⋊C₄	—	2	2	no	—
830	C₄⋊C₄	—	2	2	no	—
831	C₄⋊C₄	—	2	2	no	—
832	C₄⋊C₄	—	2	1	no	—
833	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
834	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
835	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
836	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
837	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
838	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
839	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
840	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
841	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
842	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
843	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
844	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
845	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
846	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
847	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
848	C₂²⋊C₄	—	2	2	no	—
849	C₂²⋊C₄	—	2	1	no	—
850	C₂²⋊C₄	—	2	1	no	—
851	C₂²⋊C₄	—	2	1	no	—
852	C₂²⋊C₄	—	2	1	no	—
853	C₂²⋊C₄	—	2	2	no	—
854	C₂²⋊C₄	—	2	2	no	—
855	C₂²⋊C₄	—	2	2	no	—
856	C₂²⋊C₄	—	2	1	no	—
857	C₂²⋊C₄	—	2	2	no	—
858	C₂²⋊C₄	—	2	2	no	—
859	C₂²⋊C₄	—	2	2	no	—
860	C₂²⋊C₄	—	2	2	no	—
861	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
862	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
863	C₄²	—	2	2	no	—
864	C₄²	—	2	2	no	—
865	C₄²	—	2	1	no	—
866	C₄²	—	2	2	no	—
867	C₄²	—	2	2	no	—
868	C₄²	—	2	2	no	—
869	C₄²	—	2	2	no	—
870	C₄²	—	2	2	no	—
871	C₄²	—	2	2	no	—
872	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
873	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
874	C₄²	C₂⁴×C₂₃	1	2	yes	—
875	C₄²	C₂⁴×C₂₃	1	2	yes	—
876	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
877	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
878	C₂³	—	2	1	no	—
879	C₂³	—	2	2	no	—
880	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
881	Q₈	—	2	4	no	—
882	Q₈	—	2	2	no	—
883	Q₈	—	2	2	no	—
884	Q₈	—	4	1	no	—
885	Q₈	—	4	1	no	—
886	Q₈	—	4	2	no	—
887	Q₈	—	4	2	no	—
888	Q₈	—	4	2	no	—
889	Q₈	—	8	2	no	—
890	Q₈	—	8	1	no	—
891	Q₈	—	8	2	no	—
892	Q₈	—	8	2	no	—
893	Q₈	C₂₃×2₋¹⁺⁴	1	4	yes	—
894	D₄	—	2	2	no	—
895	D₄	—	2	2	no	—
896	D₄	—	2	2	no	—
897	D₄	—	4	2	no	—
898	D₄	—	8	2	no	—
899	D₄	—	8	1	no	—
900	D₄	—	8	2	no	—
901	D₄	—	8	2	no	—
902	D₄	—	8	1	no	—
903	C₂×C₄	—	2	4	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	2	1	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	1	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	1	no	—
913	C₂×C₄	—	4	1	no	—
914	C₂×C₄	—	4	1	no	—
915	C₂×C₄	—	4	2	no	—
916	C₂×C₄	—	8	2	no	—
917	C₂×C₄	—	8	2	no	—
918	C₂×C₄	—	8	2	no	—
919	C₂×C₄	—	8	2	no	—
920	C₂×C₄	—	8	1	no	—
921	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
922	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
923	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
924	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
925	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
926	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
927	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
928	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
929	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
930	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
931	C₈	—	2	2	no	—
932	C₈	—	2	2	no	—
933	C₈	—	2	2	no	—
934	C₈	—	2	2	no	—
935	C₂²	—	2	1	no	—
936	C₂²	—	2	1	no	—
937	C₂²	—	2	1	no	—
938	C₂²	—	4	1	no	—
939	C₂²	—	4	2	no	—
940	C₂²	—	4	1	no	—
941	C₂²	—	4	2	no	—
942	C₂²	—	4	2	no	—
943	C₂²	—	4	1	no	—
944	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
945	C₄	—	2	4	no	—
946	C₄	—	2	1	no	—
947	C₄	—	2	1	no	—
948	C₄	—	2	1	no	—
949	C₄	—	2	2	no	—
950	C₄	—	2	2	no	—
951	C₄	—	2	1	no	—
952	C₄	—	2	1	no	—
953	C₄	—	2	2	no	—
954	C₄	—	2	2	no	—
955	C₄	—	4	1	no	—
956	C₄	—	4	1	no	—
957	C₄	—	4	2	no	—
958	C₄	—	4	2	no	—
959	C₄	—	4	2	no	—
960	C₄	—	4	1	no	—
961	C₄	—	4	2	no	—
962	C₄	C₂×C₂₃×2₋¹⁺⁴	1	2	yes	—
963	C₂	—	4	1	no	—
964	C₂	—	8	1	no	—
965	C₂	—	8	2	no	—
966	C₂	C₂₃×#3486	1	1	yes	characteristic
967	C₂	C₂₃×#3585	1	1	yes	characteristic
968	C₂	C₂₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂₃×#3554	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂₃×#533 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₃×#3502	C₂	semidirect
3. C₂₃×#3390	C₂	semidirect
4. C₂₃×#3388	C₂	semidirect
5. C₂₃×#3386	C₂	semidirect
6. C₂₃×#3385	C₂	semidirect
7. C₂₃×#3375	C₂	semidirect
8. C₂₃×#3371	C₂	semidirect
9. C₂₃×#3371	C₂	semidirect
10. C₂₃×#3368	C₂	semidirect
11. C₂₃×#3243	C₂	semidirect
12. C₂₃×#3241	C₂	semidirect
13. C₂₃×#3240	C₂	semidirect
14. C₂₃×#3235	C₂	semidirect
15. C₂₃×#3126	C₂	semidirect
16. C₂₃×#3121	C₂	semidirect
17. C₂₃×#3117	C₂	semidirect
18. C₂₃×#3112	C₂	semidirect
19. C₂₃×#2987	C₂	semidirect
393. #61874	C₂₃	direct (N × H)
452. #3502	C₂×C₂₃	semidirect
453. #3390	C₂×C₂₃	semidirect
454. #3388	C₂×C₂₃	semidirect
455. #3386	C₂×C₂₃	semidirect
456. #3385	C₂×C₂₃	semidirect
457. #3375	C₂×C₂₃	semidirect
458. #3371	C₂×C₂₃	semidirect
459. #3371	C₂×C₂₃	semidirect
460. #3368	C₂×C₂₃	semidirect
461. #3243	C₂×C₂₃	semidirect
462. #3241	C₂×C₂₃	semidirect
463. #3240	C₂×C₂₃	semidirect
464. #3235	C₂×C₂₃	semidirect
465. #3126	C₂×C₂₃	semidirect
466. #3121	C₂×C₂₃	semidirect
467. #3117	C₂×C₂₃	semidirect
468. #3112	C₂×C₂₃	semidirect
469. #2987	C₂×C₂₃	semidirect
764. C₂₃	#61874	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×#3554	2
C₂₃×#3502	2
C₂₃×#3390	2
C₂₃×#3388	2
C₂₃×#3386	2
C₂₃×#3385	2
C₂₃×#3375	2
C₂₃×#3371	2
C₂₃×#3368	2
C₂₃×#3243	2
C₂₃×#3241	2
C₂₃×#3240	2
C₂₃×#3235	2
C₂₃×#3126	2
C₂₃×#3121	2
C₂₃×#3117	2
C₂₃×#3112	2
C₂₃×#2987	2
#61874	23

Subgroups — C23×#61874 #19209500

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61874 #19209500