Subgroups — C₂₃×#61713 #19209339

Order 5888.

1826 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3506	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#553	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3350	C₂	1	4	yes	maximal, complemented
4	C₂₃×#3347	C₂	1	4	yes	maximal, complemented
5	C₂₃×#3309	C₂	1	4	yes	maximal, complemented
6	C₂₃×#3307	C₂	1	4	yes	maximal, complemented
7	C₂₃×#3236	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#3234	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#3194	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3188	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3110	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3109	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3092	C₂	1	2	yes	maximal, complemented
14	C₂₃×#3091	C₂	1	2	yes	maximal, complemented
15	C₂₃×#2973	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#559	—	2	2	no	—
17	C₂₃×#556	C₂²	1	2	yes	complemented
18	C₂₃×#555	C₂²	1	2	yes	complemented
19	C₂₃×#553	—	2	2	no	—
20	C₂₃×#553	—	2	2	no	—
21	C₂₃×#553	—	2	2	no	—
22	C₂₃×#553	C₂²	1	4	yes	—
23	C₂₃×#553	C₂²	1	4	yes	—
24	C₂₃×#550	C₂²	1	2	yes	complemented
25	C₂₃×#547	C₂²	1	2	yes	complemented
26	C₂₃×#538	—	2	1	no	—
27	C₂₃×#538	—	2	1	no	—
28	C₂₃×#535	—	2	1	no	—
29	C₂₃×#533	C₂²	1	1	yes	characteristic
30	C₂₃×#532	C₂²	1	1	yes	characteristic
31	C₂×C₂₃×#126	—	2	1	no	—
32	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic
33	C₂₃×#525	C₂²	1	2	yes	—
34	C₂₃×#525	C₂²	1	2	yes	—
35	C₂×C₂₃×#123	—	2	1	no	—
36	C₂×C₂₃×#121	—	2	1	no	—
37	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
38	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
39	C₂₃×#520	—	2	1	no	—
40	C₂×C₄×D₄×C₂₃	—	2	1	no	—
41	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
43	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
44	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
45	C₂₃×#501	C₂²	1	2	yes	complemented
46	C₂₃×#501	C₂²	1	2	yes	complemented
47	C₂₃×#491	C₂²	1	2	yes	complemented
48	C₂₃×#490	C₂²	1	2	yes	complemented
49	C₂₃×#485	C₂²	1	4	yes	complemented
50	C₂₃×#484	C₂²	1	2	yes	—
51	C₂₃×#484	C₂²	1	2	yes	—
52	C₂₃×#483	C₂²	1	2	yes	—
53	C₂₃×#483	C₂²	1	4	yes	complemented
54	C₂₃×#482	C₂²	1	4	yes	complemented
55	C₂₃×#482	C₂²	1	4	yes	complemented
56	C₂₃×#482	C₂²	1	4	yes	complemented
57	C₂₃×#481	C₂²	1	2	yes	—
58	C₂₃×#481	C₂²	1	2	yes	—
59	C₂₃×#480	C₂²	1	2	yes	—
60	C₂₃×#480	C₂²	1	4	yes	complemented
61	C₂₃×#479	C₂²	1	4	yes	complemented
62	C₂₃×#478	C₂²	1	4	yes	complemented
63	C₂₃×#476	C₂²	1	2	yes	complemented
64	C₂₃×#474	C₂²	1	2	yes	complemented
65	C₂₃×#469	C₂²	1	4	yes	complemented
66	C₂₃×#468	C₂²	1	4	yes	complemented
67	C₂₃×#466	C₂²	1	4	yes	complemented
68	C₂₃×#465	C₂²	1	4	yes	complemented
69	C₂₃×#461	C₂²	1	2	yes	complemented
70	C₂₃×#459	C₂²	1	2	yes	complemented
71	C₂₃×#450	C₂²	1	2	yes	—
72	C₂₃×#449	C₂²	1	4	yes	complemented
73	C₂₃×#449	C₂²	1	4	yes	complemented
74	C₂₃×#447	C₂²	1	2	yes	—
75	C₂₃×#442	C₂²	1	4	yes	complemented
76	C₂₃×#440	C₂²	1	4	yes	complemented
77	C₂₃×#435	C₂²	1	4	yes	complemented
78	C₂₃×#435	C₂²	1	4	yes	complemented
79	C₂₃×#432	C₂²	1	1	yes	characteristic
80	C₂₃×#432	C₂²	1	1	yes	characteristic
81	C₂₃×#428	C₂²	1	4	yes	complemented
82	C₂₃×#427	C₂²	1	4	yes	complemented
83	C₂₃×#417	C₂²	1	4	yes	complemented
84	C₂₃×#416	C₂²	1	4	yes	complemented
85	C₂₃×#407	C₂²	1	2	yes	—
86	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	—
87	C₂×#41×C₂₃	—	2	1	no	—
88	C₂×#41×C₂₃	C₂³	1	2	yes	—
89	C₂×#41×C₂₃	C₂³	1	2	yes	—
90	C₂²×D₄×C₂₃	—	2	1	no	—
91	C₂²×D₄×C₂₃	—	2	1	no	—
92	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
93	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₂₃	—	2	1	no	—
95	C₂³×C₄×C₂₃	—	2	1	no	—
96	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
98	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
99	C₂×D₈×C₂₃	C₂³	1	4	yes	—
100	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
101	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
102	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
103	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
104	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
105	C₂₃×#127	—	2	2	no	—
106	C₂₃×#127	C₂³	1	1	yes	characteristic
107	C₂₃×#126	—	2	4	no	—
108	C₂₃×#126	—	2	4	no	—
109	C₂₃×#126	—	2	2	no	—
110	C₂₃×#126	—	2	2	no	—
111	C₂₃×#125	—	2	1	no	—
112	C₂₃×#125	—	2	1	no	—
113	C₂₃×#125	—	2	1	no	—
114	C₂₃×#125	C₂³	1	2	yes	—
115	C₂₃×#125	C₂³	1	2	yes	—
116	C₂₃×#124	—	2	2	no	—
117	C₂₃×#124	—	2	2	no	—
118	C₂₃×#124	—	2	2	no	—
119	C₂₃×#124	—	2	1	no	—
120	C₂₃×#123	—	2	2	no	—
121	C₂₃×#123	—	2	2	no	—
122	C₂₃×#123	—	2	2	no	—
123	C₂₃×#123	—	2	2	no	—
124	C₂₃×#123	—	2	4	no	—
125	C₂₃×#123	—	2	4	no	—
126	C₂₃×C₂²⋊Q₈	—	2	1	no	—
127	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
128	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
129	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
130	C₂₃×#121	—	2	2	no	—
131	C₂₃×#121	—	2	4	no	—
132	C₂₃×#121	—	2	4	no	—
133	C₂₃×#121	—	2	2	no	—
134	C₂₃×#121	—	2	2	no	—
135	C₂₃×#121	—	2	2	no	—
136	C₂₃×#121	—	2	1	no	—
137	C₂₃×#121	—	2	2	no	—
138	C₂₃×#121	—	2	2	no	—
139	C₂₃×#121	C₂³	1	2	yes	—
140	C₂₃×#121	C₂³	1	2	yes	—
141	C₂₃×#121	C₂³	1	4	yes	—
142	C₂₃×#121	C₂³	1	4	yes	—
143	C₂₃×#121	C₂³	1	2	yes	—
144	C₂₃×#120	—	2	2	no	—
145	C₂₃×#120	—	2	2	no	—
146	C₄×Q₈×C₂₃	—	2	2	no	—
147	C₄×Q₈×C₂₃	—	2	1	no	—
148	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
149	C₄×D₄×C₂₃	—	2	2	no	—
150	C₄×D₄×C₂₃	—	2	2	no	—
151	C₄×D₄×C₂₃	—	2	2	no	—
152	C₄×D₄×C₂₃	—	2	2	no	—
153	C₄×D₄×C₂₃	—	2	2	no	—
154	C₄×D₄×C₂₃	—	2	4	no	—
155	C₄×D₄×C₂₃	—	2	4	no	—
156	C₄×D₄×C₂₃	—	2	1	no	—
157	C₄×D₄×C₂₃	—	2	1	no	—
158	C₄×D₄×C₂₃	—	2	1	no	—
159	C₄×D₄×C₂₃	D₄	1	2	yes	—
160	C₄×D₄×C₂₃	D₄	1	2	yes	—
161	C₄×D₄×C₂₃	C₂³	1	2	yes	—
162	C₄×D₄×C₂₃	C₂³	1	2	yes	—
163	C₄×D₄×C₂₃	C₂³	1	2	yes	—
164	C₄×D₄×C₂₃	C₂³	1	2	yes	—
165	C₄×D₄×C₂₃	C₂³	1	2	yes	—
166	C₂₃×#117	—	2	2	no	—
167	C₂₃×#117	—	2	1	no	—
168	C₂₃×#117	—	2	2	no	—
169	C₂₃×#117	C₂³	1	4	yes	—
170	C₂₃×#117	C₂³	1	2	yes	—
171	C₂₃×#117	C₂³	1	2	yes	—
172	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
173	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
174	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
175	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
176	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
177	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
178	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
179	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
180	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
181	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
182	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
183	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
184	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
185	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
186	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
187	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
188	C₂×C₄²×C₂₃	—	2	1	no	—
189	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
190	C₂₃×#107	C₂³	1	4	yes	—
191	C₂₃×#107	C₂³	1	4	yes	—
192	C₂₃×#107	C₂³	1	4	yes	—
193	C₂₃×#106	C₂³	1	4	yes	—
194	C₂₃×#106	C₂³	1	4	yes	—
195	C₂₃×#106	C₂³	1	4	yes	—
196	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
197	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
198	C₂₃×#103	C₂³	1	4	yes	—
199	C₂₃×#103	C₂³	1	4	yes	—
200	C₂₃×#103	C₂³	1	4	yes	—
201	C₂₃×#102	C₂³	1	4	yes	—
202	C₂₃×#102	C₂³	1	4	yes	—
203	C₂₃×#102	C₂³	1	4	yes	—
204	C₂₃×#102	C₂³	1	4	yes	—
205	C₂₃×#102	C₂³	1	4	yes	—
206	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
207	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
208	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
209	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
210	C₂₃×#97	C₂³	1	2	yes	—
211	C₂₃×#97	C₂³	1	2	yes	—
212	C₂⁴×C₂₃	—	2	1	no	—
213	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
214	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
215	#41×C₂₃	—	4	4	no	—
216	#41×C₂₃	—	4	4	no	—
217	#41×C₂₃	—	4	4	no	—
218	C₂×Q₈×C₂₃	—	2	1	no	—
219	C₂×Q₈×C₂₃	—	2	1	no	—
220	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
221	C₂×D₄×C₂₃	—	2	2	no	—
222	C₂×D₄×C₂₃	—	2	4	no	—
223	C₂×D₄×C₂₃	—	2	2	no	—
224	C₂×D₄×C₂₃	—	2	2	no	—
225	C₂×D₄×C₂₃	—	2	2	no	—
226	C₂×D₄×C₂₃	—	2	2	no	—
227	C₂×D₄×C₂₃	—	2	4	no	—
228	C₂×D₄×C₂₃	—	2	1	no	—
229	C₂×D₄×C₂₃	—	2	1	no	—
230	C₂×D₄×C₂₃	—	2	1	no	—
231	C₂×D₄×C₂₃	—	4	2	no	—
232	C₂×D₄×C₂₃	—	4	2	no	—
233	C₂×D₄×C₂₃	—	4	4	no	—
234	C₂×D₄×C₂₃	—	8	2	no	—
235	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
236	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
237	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
238	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₂₃	—	2	1	no	—
240	C₂²×C₄×C₂₃	—	2	1	no	—
241	C₂²×C₄×C₂₃	—	2	1	no	—
242	C₂²×C₄×C₂₃	—	2	4	no	—
243	C₂²×C₄×C₂₃	—	2	2	no	—
244	C₂²×C₄×C₂₃	—	2	2	no	—
245	C₂²×C₄×C₂₃	—	2	2	no	—
246	C₂²×C₄×C₂₃	—	2	2	no	—
247	C₂²×C₄×C₂₃	—	2	2	no	—
248	C₂²×C₄×C₂₃	—	4	2	no	—
249	C₂²×C₄×C₂₃	—	4	2	no	—
250	C₂²×C₄×C₂₃	—	8	2	no	—
251	C₂²×C₄×C₂₃	—	8	2	no	—
252	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
253	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
254	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
255	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
256	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
257	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
258	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
261	SD₁₆×C₂₃	—	4	4	no	—
262	D₈×C₂₃	—	4	4	no	—
263	M₁₆×C₂₃	—	4	4	no	—
264	C₂×C₈×C₂₃	—	4	4	no	—
265	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
266	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
267	C₄⋊C₄×C₂₃	—	2	1	no	—
268	C₄⋊C₄×C₂₃	—	2	1	no	—
269	C₄⋊C₄×C₂₃	—	2	4	no	—
270	C₄⋊C₄×C₂₃	—	2	1	no	—
271	C₄⋊C₄×C₂₃	—	2	2	no	—
272	C₄⋊C₄×C₂₃	—	2	2	no	—
273	C₄⋊C₄×C₂₃	—	2	2	no	—
274	C₄⋊C₄×C₂₃	—	2	2	no	—
275	C₄⋊C₄×C₂₃	—	2	2	no	—
276	C₄⋊C₄×C₂₃	—	2	2	no	—
277	C₄⋊C₄×C₂₃	—	2	1	no	—
278	C₄⋊C₄×C₂₃	—	2	1	no	—
279	C₄⋊C₄×C₂₃	—	2	2	no	—
280	C₄⋊C₄×C₂₃	—	2	1	no	—
281	C₄⋊C₄×C₂₃	—	2	1	no	—
282	C₄⋊C₄×C₂₃	—	2	2	no	—
283	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
284	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
285	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
286	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
287	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
288	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
289	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
290	C₂²⋊C₄×C₂₃	—	2	4	no	—
291	C₂²⋊C₄×C₂₃	—	2	2	no	—
292	C₂²⋊C₄×C₂₃	—	2	2	no	—
293	C₂²⋊C₄×C₂₃	—	2	2	no	—
294	C₂²⋊C₄×C₂₃	—	2	2	no	—
295	C₂²⋊C₄×C₂₃	—	2	2	no	—
296	C₂²⋊C₄×C₂₃	—	2	4	no	—
297	C₂²⋊C₄×C₂₃	—	2	2	no	—
298	C₂²⋊C₄×C₂₃	—	2	2	no	—
299	C₂²⋊C₄×C₂₃	—	2	4	no	—
300	C₂²⋊C₄×C₂₃	—	2	2	no	—
301	C₂²⋊C₄×C₂₃	—	2	2	no	—
302	C₂²⋊C₄×C₂₃	—	2	2	no	—
303	C₂²⋊C₄×C₂₃	—	2	2	no	—
304	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
305	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
306	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
307	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
308	C₄²×C₂₃	—	2	4	no	—
309	C₄²×C₂₃	—	2	2	no	—
310	C₄²×C₂₃	—	2	2	no	—
311	C₄²×C₂₃	—	2	2	no	—
312	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
313	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
314	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
315	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
316	#61713	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
317	C₂³×C₂₃	—	2	2	no	—
318	C₂³×C₂₃	—	2	2	no	—
319	C₂³×C₂₃	—	2	2	no	—
320	C₂³×C₂₃	—	2	2	no	—
321	C₂³×C₂₃	—	4	1	no	—
322	C₂³×C₂₃	—	4	1	no	—
323	C₂³×C₂₃	—	4	1	no	—
324	C₂³×C₂₃	—	4	1	no	—
325	C₂³×C₂₃	—	4	2	no	—
326	C₂³×C₂₃	—	4	2	no	—
327	C₂³×C₂₃	—	4	2	no	—
328	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
329	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
330	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
331	Q₈×C₂₃	—	2	4	no	—
332	Q₈×C₂₃	—	4	2	no	—
333	Q₈×C₂₃	—	8	1	no	—
334	D₄×C₂₃	—	2	2	no	—
335	D₄×C₂₃	—	2	4	no	—
336	D₄×C₂₃	—	2	2	no	—
337	D₄×C₂₃	—	4	2	no	—
338	D₄×C₂₃	—	4	2	no	—
339	D₄×C₂₃	—	4	2	no	—
340	D₄×C₂₃	—	4	2	no	—
341	D₄×C₂₃	—	4	8	no	—
342	D₄×C₂₃	—	4	4	no	—
343	D₄×C₂₃	—	8	1	no	—
344	D₄×C₂₃	—	8	2	no	—
345	D₄×C₂₃	—	8	2	no	—
346	D₄×C₂₃	—	8	4	no	—
347	D₄×C₂₃	—	8	2	no	—
348	D₄×C₂₃	—	8	2	no	—
349	C₂×C₄×C₂₃	—	2	2	no	—
350	C₂×C₄×C₂₃	—	2	4	no	—
351	C₂×C₄×C₂₃	—	2	4	no	—
352	C₂×C₄×C₂₃	—	2	2	no	—
353	C₂×C₄×C₂₃	—	2	2	no	—
354	C₂×C₄×C₂₃	—	2	2	no	—
355	C₂×C₄×C₂₃	—	2	2	no	—
356	C₂×C₄×C₂₃	—	2	2	no	—
357	C₂×C₄×C₂₃	—	2	2	no	—
358	C₂×C₄×C₂₃	—	2	2	no	—
359	C₂×C₄×C₂₃	—	4	2	no	—
360	C₂×C₄×C₂₃	—	4	2	no	—
361	C₂×C₄×C₂₃	—	4	1	no	—
362	C₂×C₄×C₂₃	—	4	1	no	—
363	C₂×C₄×C₂₃	—	4	1	no	—
364	C₂×C₄×C₂₃	—	4	4	no	—
365	C₂×C₄×C₂₃	—	4	2	no	—
366	C₂×C₄×C₂₃	—	4	2	no	—
367	C₂×C₄×C₂₃	—	4	2	no	—
368	C₂×C₄×C₂₃	—	8	2	no	—
369	C₂×C₄×C₂₃	—	8	2	no	—
370	C₂×C₄×C₂₃	—	8	2	no	—
371	C₂×C₄×C₂₃	—	8	2	no	—
372	C₂×C₄×C₂₃	—	8	4	no	—
373	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
374	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
375	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
376	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
377	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
378	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
379	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
380	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
381	C₈×C₂₃	—	2	4	no	—
382	C₈×C₂₃	—	2	4	no	—
383	#3506	C₂×C₂₃	1	1	yes	characteristic, complemented
384	C₂×#553	C₂×C₂₃	1	1	yes	characteristic, complemented
385	#3350	C₂×C₂₃	1	4	yes	complemented
386	#3347	C₂×C₂₃	1	4	yes	complemented
387	#3309	C₂×C₂₃	1	4	yes	complemented
388	#3307	C₂×C₂₃	1	4	yes	complemented
389	#3236	C₂×C₂₃	1	1	yes	characteristic, complemented
390	#3234	C₂×C₂₃	1	1	yes	characteristic, complemented
391	#3194	C₂×C₂₃	1	2	yes	complemented
392	#3188	C₂×C₂₃	1	2	yes	complemented
393	#3110	C₂×C₂₃	1	1	yes	characteristic, complemented
394	#3109	C₂×C₂₃	1	1	yes	characteristic, complemented
395	#3092	C₂×C₂₃	1	2	yes	complemented
396	#3091	C₂×C₂₃	1	2	yes	complemented
397	#2973	C₂×C₂₃	1	1	yes	characteristic, complemented
398	C₂²×C₂₃	—	2	1	no	—
399	C₂²×C₂₃	—	2	1	no	—
400	C₂²×C₂₃	—	2	2	no	—
401	C₂²×C₂₃	—	2	2	no	—
402	C₂²×C₂₃	—	2	2	no	—
403	C₂²×C₂₃	—	2	2	no	—
404	C₂²×C₂₃	—	2	2	no	—
405	C₂²×C₂₃	—	2	2	no	—
406	C₂²×C₂₃	—	4	4	no	—
407	C₂²×C₂₃	—	4	2	no	—
408	C₂²×C₂₃	—	4	2	no	—
409	C₂²×C₂₃	—	4	2	no	—
410	C₂²×C₂₃	—	4	2	no	—
411	C₂²×C₂₃	—	4	2	no	—
412	C₂²×C₂₃	—	4	2	no	—
413	C₂²×C₂₃	—	8	2	no	—
414	C₂²×C₂₃	—	8	4	no	—
415	C₂²×C₂₃	#575	1	2	yes	—
416	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
417	C₄×C₂₃	—	2	1	no	—
418	C₄×C₂₃	—	2	1	no	—
419	C₄×C₂₃	—	2	1	no	—
420	C₄×C₂₃	—	2	2	no	—
421	C₄×C₂₃	—	2	2	no	—
422	C₄×C₂₃	—	2	1	no	—
423	C₄×C₂₃	—	2	1	no	—
424	C₄×C₂₃	—	4	2	no	—
425	C₄×C₂₃	—	4	2	no	—
426	C₄×C₂₃	—	4	2	no	—
427	C₄×C₂₃	—	4	2	no	—
428	C₄×C₂₃	—	4	2	no	—
429	C₄×C₂₃	—	4	2	no	—
430	C₄×C₂₃	#585	1	2	yes	—
431	#559	—	2	2	no	—
432	#556	C₂²×C₂₃	1	2	yes	complemented
433	#555	C₂²×C₂₃	1	2	yes	complemented
434	#553	—	2	2	no	—
435	#553	—	2	2	no	—
436	#553	—	2	2	no	—
437	#553	C₂²×C₂₃	1	4	yes	—
438	#553	C₂²×C₂₃	1	4	yes	—
439	#550	C₂²×C₂₃	1	2	yes	complemented
440	#547	C₂²×C₂₃	1	2	yes	complemented
441	#538	—	2	1	no	—
442	#538	—	2	1	no	—
443	#535	—	2	1	no	—
444	#533	C₂²×C₂₃	1	1	yes	characteristic
445	#532	C₂²×C₂₃	1	1	yes	characteristic
446	C₂×#126	—	2	1	no	—
447	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic
448	#525	C₂²×C₂₃	1	2	yes	—
449	#525	C₂²×C₂₃	1	2	yes	—
450	C₂×#123	—	2	1	no	—
451	C₂×#121	—	2	1	no	—
452	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
453	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
454	#520	—	2	1	no	—
455	C₂×C₄×D₄	—	2	1	no	—
456	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
457	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
458	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
459	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
460	#501	C₂²×C₂₃	1	2	yes	complemented
461	#501	C₂²×C₂₃	1	2	yes	complemented
462	#491	C₂²×C₂₃	1	2	yes	complemented
463	#490	C₂²×C₂₃	1	2	yes	complemented
464	#485	C₂²×C₂₃	1	4	yes	complemented
465	#484	C₂²×C₂₃	1	2	yes	—
466	#484	C₂²×C₂₃	1	2	yes	—
467	#483	C₂²×C₂₃	1	2	yes	—
468	#483	C₂²×C₂₃	1	4	yes	complemented
469	#482	C₂²×C₂₃	1	4	yes	complemented
470	#482	C₂²×C₂₃	1	4	yes	complemented
471	#482	C₂²×C₂₃	1	4	yes	complemented
472	#481	C₂²×C₂₃	1	2	yes	—
473	#481	C₂²×C₂₃	1	2	yes	—
474	#480	C₂²×C₂₃	1	2	yes	—
475	#480	C₂²×C₂₃	1	4	yes	complemented
476	#479	C₂²×C₂₃	1	4	yes	complemented
477	#478	C₂²×C₂₃	1	4	yes	complemented
478	#476	C₂²×C₂₃	1	2	yes	complemented
479	#474	C₂²×C₂₃	1	2	yes	complemented
480	#469	C₂²×C₂₃	1	4	yes	complemented
481	#468	C₂²×C₂₃	1	4	yes	complemented
482	#466	C₂²×C₂₃	1	4	yes	complemented
483	#465	C₂²×C₂₃	1	4	yes	complemented
484	#461	C₂²×C₂₃	1	2	yes	complemented
485	#459	C₂²×C₂₃	1	2	yes	complemented
486	#450	C₂²×C₂₃	1	2	yes	—
487	#449	C₂²×C₂₃	1	4	yes	complemented
488	#449	C₂²×C₂₃	1	4	yes	complemented
489	#447	C₂²×C₂₃	1	2	yes	—
490	#442	C₂²×C₂₃	1	4	yes	complemented
491	#440	C₂²×C₂₃	1	4	yes	complemented
492	#435	C₂²×C₂₃	1	4	yes	complemented
493	#435	C₂²×C₂₃	1	4	yes	complemented
494	#432	C₂²×C₂₃	1	1	yes	characteristic
495	#432	C₂²×C₂₃	1	1	yes	characteristic
496	#428	C₂²×C₂₃	1	4	yes	complemented
497	#427	C₂²×C₂₃	1	4	yes	complemented
498	#417	C₂²×C₂₃	1	4	yes	complemented
499	#416	C₂²×C₂₃	1	4	yes	complemented
500	#407	C₂²×C₂₃	1	2	yes	—
501	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	—
502	C₂×C₂₃	—	2	2	no	—
503	C₂×C₂₃	—	4	2	no	—
504	C₂×C₂₃	—	4	2	no	—
505	C₂×C₂₃	—	8	2	no	—
506	C₂×C₂₃	—	8	2	no	—
507	C₂×C₂₃	#3485	1	1	yes	characteristic
508	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
509	C₂×C₂₃	#3585	1	1	yes	characteristic
510	C₂×#41	—	2	1	no	—
511	C₂×#41	C₂³×C₂₃	1	2	yes	—
512	C₂×#41	C₂³×C₂₃	1	2	yes	—
513	C₂²×D₄	—	2	1	no	—
514	C₂²×D₄	—	2	1	no	—
515	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
516	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
517	C₂³×C₄	—	2	1	no	—
518	C₂³×C₄	—	2	1	no	—
519	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
520	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
521	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
522	C₂×D₈	C₂³×C₂₃	1	4	yes	—
523	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
524	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
525	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
526	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
527	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
528	#127	—	2	2	no	—
529	#127	C₂³×C₂₃	1	1	yes	characteristic
530	#126	—	2	4	no	—
531	#126	—	2	4	no	—
532	#126	—	2	2	no	—
533	#126	—	2	2	no	—
534	#125	—	2	1	no	—
535	#125	—	2	1	no	—
536	#125	—	2	1	no	—
537	#125	C₂³×C₂₃	1	2	yes	—
538	#125	C₂³×C₂₃	1	2	yes	—
539	#124	—	2	2	no	—
540	#124	—	2	2	no	—
541	#124	—	2	2	no	—
542	#124	—	2	1	no	—
543	#123	—	2	2	no	—
544	#123	—	2	2	no	—
545	#123	—	2	4	no	—
546	#123	—	2	4	no	—
547	#123	—	2	2	no	—
548	#123	—	2	2	no	—
549	C₂²⋊Q₈	—	2	1	no	—
550	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
551	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
552	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
553	#121	—	2	4	no	—
554	#121	—	2	4	no	—
555	#121	—	2	2	no	—
556	#121	—	2	2	no	—
557	#121	—	2	2	no	—
558	#121	—	2	2	no	—
559	#121	—	2	1	no	—
560	#121	—	2	2	no	—
561	#121	—	2	2	no	—
562	#121	C₂³×C₂₃	1	4	yes	—
563	#121	C₂³×C₂₃	1	4	yes	—
564	#121	C₂³×C₂₃	1	2	yes	—
565	#121	C₂³×C₂₃	1	2	yes	—
566	#121	C₂³×C₂₃	1	2	yes	—
567	#120	—	2	2	no	—
568	#120	—	2	2	no	—
569	C₄×Q₈	—	2	2	no	—
570	C₄×Q₈	—	2	1	no	—
571	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
572	C₄×D₄	—	2	2	no	—
573	C₄×D₄	—	2	2	no	—
574	C₄×D₄	—	2	2	no	—
575	C₄×D₄	—	2	2	no	—
576	C₄×D₄	—	2	2	no	—
577	C₄×D₄	—	2	4	no	—
578	C₄×D₄	—	2	4	no	—
579	C₄×D₄	—	2	1	no	—
580	C₄×D₄	—	2	1	no	—
581	C₄×D₄	—	2	1	no	—
582	C₄×D₄	D₄×C₂₃	1	2	yes	—
583	C₄×D₄	D₄×C₂₃	1	2	yes	—
584	C₄×D₄	C₂³×C₂₃	1	2	yes	—
585	C₄×D₄	C₂³×C₂₃	1	2	yes	—
586	C₄×D₄	C₂³×C₂₃	1	2	yes	—
587	C₄×D₄	C₂³×C₂₃	1	2	yes	—
588	C₄×D₄	C₂³×C₂₃	1	2	yes	—
589	#117	—	2	2	no	—
590	#117	—	2	1	no	—
591	#117	—	2	2	no	—
592	#117	C₂³×C₂₃	1	4	yes	—
593	#117	C₂³×C₂₃	1	2	yes	—
594	#117	C₂³×C₂₃	1	2	yes	—
595	C₂×C₄⋊C₄	—	2	1	no	—
596	C₂×C₄⋊C₄	—	2	2	no	—
597	C₂×C₄⋊C₄	—	2	1	no	—
598	C₂×C₄⋊C₄	—	2	1	no	—
599	C₂×C₄⋊C₄	—	2	2	no	—
600	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
601	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
602	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
603	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
604	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
605	C₂×C₂²⋊C₄	—	2	1	no	—
606	C₂×C₂²⋊C₄	—	2	1	no	—
607	C₂×C₂²⋊C₄	—	2	1	no	—
608	C₂×C₂²⋊C₄	—	2	1	no	—
609	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
610	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
611	C₂×C₄²	—	2	1	no	—
612	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
613	#107	C₂³×C₂₃	1	4	yes	—
614	#107	C₂³×C₂₃	1	4	yes	—
615	#107	C₂³×C₂₃	1	4	yes	—
616	#106	C₂³×C₂₃	1	4	yes	—
617	#106	C₂³×C₂₃	1	4	yes	—
618	#106	C₂³×C₂₃	1	4	yes	—
619	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
620	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
621	#103	C₂³×C₂₃	1	4	yes	—
622	#103	C₂³×C₂₃	1	4	yes	—
623	#103	C₂³×C₂₃	1	4	yes	—
624	#102	C₂³×C₂₃	1	4	yes	—
625	#102	C₂³×C₂₃	1	4	yes	—
626	#102	C₂³×C₂₃	1	4	yes	—
627	#102	C₂³×C₂₃	1	4	yes	—
628	#102	C₂³×C₂₃	1	4	yes	—
629	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
630	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
631	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
632	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
633	#97	C₂³×C₂₃	1	2	yes	—
634	#97	C₂³×C₂₃	1	2	yes	—
635	C₂₃	#61713	1	1	yes	characteristic, direct product factor, Sylow
636	C₂⁴	—	2	1	no	—
637	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
638	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
639	#41	—	4	4	no	—
640	#41	—	4	4	no	—
641	#41	—	4	4	no	—
642	C₂×Q₈	—	2	1	no	—
643	C₂×Q₈	—	2	1	no	—
644	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
645	C₂×D₄	—	2	2	no	—
646	C₂×D₄	—	2	4	no	—
647	C₂×D₄	—	2	2	no	—
648	C₂×D₄	—	2	2	no	—
649	C₂×D₄	—	2	2	no	—
650	C₂×D₄	—	2	2	no	—
651	C₂×D₄	—	2	4	no	—
652	C₂×D₄	—	2	1	no	—
653	C₂×D₄	—	2	1	no	—
654	C₂×D₄	—	2	1	no	—
655	C₂×D₄	—	4	2	no	—
656	C₂×D₄	—	4	2	no	—
657	C₂×D₄	—	4	4	no	—
658	C₂×D₄	—	8	2	no	—
659	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
660	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
661	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
662	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
663	C₂²×C₄	—	2	1	no	—
664	C₂²×C₄	—	2	1	no	—
665	C₂²×C₄	—	2	1	no	—
666	C₂²×C₄	—	2	4	no	—
667	C₂²×C₄	—	2	2	no	—
668	C₂²×C₄	—	2	2	no	—
669	C₂²×C₄	—	2	2	no	—
670	C₂²×C₄	—	2	2	no	—
671	C₂²×C₄	—	2	2	no	—
672	C₂²×C₄	—	4	2	no	—
673	C₂²×C₄	—	4	2	no	—
674	C₂²×C₄	—	8	2	no	—
675	C₂²×C₄	—	8	2	no	—
676	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
677	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
678	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
679	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
680	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
681	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
682	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
683	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
684	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
685	SD₁₆	—	4	4	no	—
686	D₈	—	4	4	no	—
687	M₁₆	—	4	4	no	—
688	C₂×C₈	—	4	4	no	—
689	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
690	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
691	C₄⋊C₄	—	2	1	no	—
692	C₄⋊C₄	—	2	1	no	—
693	C₄⋊C₄	—	2	4	no	—
694	C₄⋊C₄	—	2	1	no	—
695	C₄⋊C₄	—	2	2	no	—
696	C₄⋊C₄	—	2	2	no	—
697	C₄⋊C₄	—	2	2	no	—
698	C₄⋊C₄	—	2	2	no	—
699	C₄⋊C₄	—	2	2	no	—
700	C₄⋊C₄	—	2	2	no	—
701	C₄⋊C₄	—	2	1	no	—
702	C₄⋊C₄	—	2	1	no	—
703	C₄⋊C₄	—	2	2	no	—
704	C₄⋊C₄	—	2	1	no	—
705	C₄⋊C₄	—	2	1	no	—
706	C₄⋊C₄	—	2	2	no	—
707	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
708	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
709	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
710	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
711	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
712	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
713	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
714	C₂²⋊C₄	—	2	4	no	—
715	C₂²⋊C₄	—	2	2	no	—
716	C₂²⋊C₄	—	2	2	no	—
717	C₂²⋊C₄	—	2	2	no	—
718	C₂²⋊C₄	—	2	2	no	—
719	C₂²⋊C₄	—	2	2	no	—
720	C₂²⋊C₄	—	2	4	no	—
721	C₂²⋊C₄	—	2	2	no	—
722	C₂²⋊C₄	—	2	2	no	—
723	C₂²⋊C₄	—	2	4	no	—
724	C₂²⋊C₄	—	2	2	no	—
725	C₂²⋊C₄	—	2	2	no	—
726	C₂²⋊C₄	—	2	2	no	—
727	C₂²⋊C₄	—	2	2	no	—
728	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
729	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
730	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
731	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
732	C₄²	—	2	4	no	—
733	C₄²	—	2	2	no	—
734	C₄²	—	2	2	no	—
735	C₄²	—	2	2	no	—
736	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
737	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
738	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
739	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
740	C₂³	—	2	2	no	—
741	C₂³	—	2	2	no	—
742	C₂³	—	2	2	no	—
743	C₂³	—	2	2	no	—
744	C₂³	—	4	1	no	—
745	C₂³	—	4	1	no	—
746	C₂³	—	4	1	no	—
747	C₂³	—	4	1	no	—
748	C₂³	—	4	2	no	—
749	C₂³	—	4	2	no	—
750	C₂³	—	4	2	no	—
751	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
752	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
753	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
754	Q₈	—	2	4	no	—
755	Q₈	—	4	2	no	—
756	Q₈	—	8	1	no	—
757	D₄	—	2	2	no	—
758	D₄	—	2	4	no	—
759	D₄	—	2	2	no	—
760	D₄	—	4	2	no	—
761	D₄	—	4	2	no	—
762	D₄	—	4	2	no	—
763	D₄	—	4	2	no	—
764	D₄	—	4	8	no	—
765	D₄	—	4	4	no	—
766	D₄	—	8	1	no	—
767	D₄	—	8	4	no	—
768	D₄	—	8	2	no	—
769	D₄	—	8	2	no	—
770	D₄	—	8	2	no	—
771	D₄	—	8	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	4	no	—
774	C₂×C₄	—	2	4	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	4	2	no	—
783	C₂×C₄	—	4	2	no	—
784	C₂×C₄	—	4	1	no	—
785	C₂×C₄	—	4	1	no	—
786	C₂×C₄	—	4	1	no	—
787	C₂×C₄	—	4	4	no	—
788	C₂×C₄	—	4	2	no	—
789	C₂×C₄	—	4	2	no	—
790	C₂×C₄	—	4	2	no	—
791	C₂×C₄	—	8	2	no	—
792	C₂×C₄	—	8	2	no	—
793	C₂×C₄	—	8	2	no	—
794	C₂×C₄	—	8	2	no	—
795	C₂×C₄	—	8	4	no	—
796	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
797	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
798	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
799	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
800	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
801	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
802	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
803	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
804	C₈	—	2	4	no	—
805	C₈	—	2	4	no	—
806	C₂²	—	2	1	no	—
807	C₂²	—	2	1	no	—
808	C₂²	—	2	2	no	—
809	C₂²	—	2	2	no	—
810	C₂²	—	2	2	no	—
811	C₂²	—	2	2	no	—
812	C₂²	—	2	2	no	—
813	C₂²	—	2	2	no	—
814	C₂²	—	4	4	no	—
815	C₂²	—	4	2	no	—
816	C₂²	—	4	2	no	—
817	C₂²	—	4	2	no	—
818	C₂²	—	4	2	no	—
819	C₂²	—	4	2	no	—
820	C₂²	—	4	2	no	—
821	C₂²	—	8	2	no	—
822	C₂²	—	8	4	no	—
823	C₂²	C₂₃×#575	1	2	yes	—
824	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
825	C₄	—	2	1	no	—
826	C₄	—	2	2	no	—
827	C₄	—	2	2	no	—
828	C₄	—	2	1	no	—
829	C₄	—	2	1	no	—
830	C₄	—	2	1	no	—
831	C₄	—	2	1	no	—
832	C₄	—	4	2	no	—
833	C₄	—	4	2	no	—
834	C₄	—	4	2	no	—
835	C₄	—	4	2	no	—
836	C₄	—	4	2	no	—
837	C₄	—	4	2	no	—
838	C₄	C₂₃×#585	1	2	yes	—
839	C₂	—	2	2	no	—
840	C₂	—	4	2	no	—
841	C₂	—	4	2	no	—
842	C₂	—	8	2	no	—
843	C₂	—	8	2	no	—
844	C₂	C₂₃×#3485	1	1	yes	characteristic
845	C₂	C₂×C₂₃×#575	1	1	yes	characteristic
846	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×#3506	C₂	semidirect
2. C₂×C₂₃×#553	C₂	semidirect
3. C₂₃×#3350	C₂	semidirect
4. C₂₃×#3347	C₂	semidirect
5. C₂₃×#3309	C₂	semidirect
6. C₂₃×#3307	C₂	semidirect
7. C₂₃×#3236	C₂	semidirect
8. C₂₃×#3234	C₂	semidirect
9. C₂₃×#3194	C₂	semidirect
10. C₂₃×#3188	C₂	semidirect
11. C₂₃×#3110	C₂	semidirect
12. C₂₃×#3109	C₂	semidirect
13. C₂₃×#3092	C₂	semidirect
14. C₂₃×#3091	C₂	semidirect
15. C₂₃×#2973	C₂	semidirect
17. C₂₃×#556	C₂²	semidirect
18. C₂₃×#555	C₂²	semidirect
24. C₂₃×#550	C₂²	semidirect
25. C₂₃×#547	C₂²	semidirect
45. C₂₃×#501	C₂²	semidirect
46. C₂₃×#501	C₂²	semidirect
47. C₂₃×#491	C₂²	semidirect
48. C₂₃×#490	C₂²	semidirect
49. C₂₃×#485	C₂²	semidirect
53. C₂₃×#483	C₂²	semidirect
54. C₂₃×#482	C₂²	semidirect
55. C₂₃×#482	C₂²	semidirect
56. C₂₃×#482	C₂²	semidirect
60. C₂₃×#480	C₂²	semidirect
61. C₂₃×#479	C₂²	semidirect
62. C₂₃×#478	C₂²	semidirect
63. C₂₃×#476	C₂²	semidirect
64. C₂₃×#474	C₂²	semidirect
65. C₂₃×#469	C₂²	semidirect
66. C₂₃×#468	C₂²	semidirect
67. C₂₃×#466	C₂²	semidirect
68. C₂₃×#465	C₂²	semidirect
69. C₂₃×#461	C₂²	semidirect
70. C₂₃×#459	C₂²	semidirect
72. C₂₃×#449	C₂²	semidirect
73. C₂₃×#449	C₂²	semidirect
75. C₂₃×#442	C₂²	semidirect
76. C₂₃×#440	C₂²	semidirect
77. C₂₃×#435	C₂²	semidirect
78. C₂₃×#435	C₂²	semidirect
81. C₂₃×#428	C₂²	semidirect
82. C₂₃×#427	C₂²	semidirect
83. C₂₃×#417	C₂²	semidirect
84. C₂₃×#416	C₂²	semidirect
316. #61713	C₂₃	direct (N × H)
383. #3506	C₂×C₂₃	semidirect
384. C₂×#553	C₂×C₂₃	semidirect
385. #3350	C₂×C₂₃	semidirect
386. #3347	C₂×C₂₃	semidirect
387. #3309	C₂×C₂₃	semidirect
388. #3307	C₂×C₂₃	semidirect
389. #3236	C₂×C₂₃	semidirect
390. #3234	C₂×C₂₃	semidirect
391. #3194	C₂×C₂₃	semidirect
392. #3188	C₂×C₂₃	semidirect
393. #3110	C₂×C₂₃	semidirect
394. #3109	C₂×C₂₃	semidirect
395. #3092	C₂×C₂₃	semidirect
396. #3091	C₂×C₂₃	semidirect
397. #2973	C₂×C₂₃	semidirect
432. #556	C₂²×C₂₃	semidirect
433. #555	C₂²×C₂₃	semidirect
439. #550	C₂²×C₂₃	semidirect
440. #547	C₂²×C₂₃	semidirect
460. #501	C₂²×C₂₃	semidirect
461. #501	C₂²×C₂₃	semidirect
462. #491	C₂²×C₂₃	semidirect
463. #490	C₂²×C₂₃	semidirect
464. #485	C₂²×C₂₃	semidirect
468. #483	C₂²×C₂₃	semidirect
469. #482	C₂²×C₂₃	semidirect
470. #482	C₂²×C₂₃	semidirect
471. #482	C₂²×C₂₃	semidirect
475. #480	C₂²×C₂₃	semidirect
476. #479	C₂²×C₂₃	semidirect
477. #478	C₂²×C₂₃	semidirect
478. #476	C₂²×C₂₃	semidirect
479. #474	C₂²×C₂₃	semidirect
480. #469	C₂²×C₂₃	semidirect
481. #468	C₂²×C₂₃	semidirect
482. #466	C₂²×C₂₃	semidirect
483. #465	C₂²×C₂₃	semidirect
484. #461	C₂²×C₂₃	semidirect
485. #459	C₂²×C₂₃	semidirect
487. #449	C₂²×C₂₃	semidirect
488. #449	C₂²×C₂₃	semidirect
490. #442	C₂²×C₂₃	semidirect
491. #440	C₂²×C₂₃	semidirect
492. #435	C₂²×C₂₃	semidirect
493. #435	C₂²×C₂₃	semidirect
496. #428	C₂²×C₂₃	semidirect
497. #427	C₂²×C₂₃	semidirect
498. #417	C₂²×C₂₃	semidirect
499. #416	C₂²×C₂₃	semidirect
635. C₂₃	#61713	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×#3506	2
C₂×C₂₃×#553	2
C₂₃×#3350	2
C₂₃×#3347	2
C₂₃×#3309	2
C₂₃×#3307	2
C₂₃×#3236	2
C₂₃×#3234	2
C₂₃×#3194	2
C₂₃×#3188	2
C₂₃×#3110	2
C₂₃×#3109	2
C₂₃×#3092	2
C₂₃×#3091	2
C₂₃×#2973	2
#61713	23

Subgroups — C23×#61713 #19209339

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61713 #19209339