Subgroups — C₂₃×#61407 #19209033

Order 5888.

1922 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3507	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3506	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3401	C₂	1	4	yes	maximal, complemented
4	C₂₃×#3399	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3398	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3394	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3394	C₂	1	4	yes	maximal, complemented
8	C₂₃×#3392	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3154	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3147	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3046	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3045	C₂	1	2	yes	maximal, complemented
13	C₂₃×#3037	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3036	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#2960	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#2952	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×SD₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₂₃×#137	C₂²	1	2	yes	—
19	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
20	C₂×C₂₃×#135	C₂²	1	2	yes	—
21	C₂×C₂₃×#135	C₂²	1	2	yes	—
22	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
23	C₂₃×#559	C₂²	1	4	yes	—
24	C₂₃×#559	C₂²	1	2	yes	complemented
25	C₂₃×#557	C₂²	1	2	yes	complemented
26	C₂₃×#556	—	2	1	no	—
27	C₂₃×#556	C₂²	1	2	yes	—
28	C₂₃×#556	C₂²	1	4	yes	complemented
29	C₂₃×#555	—	2	1	no	—
30	C₂₃×#554	—	2	1	no	—
31	C₂₃×#553	—	2	2	no	—
32	C₂₃×#552	—	2	2	no	—
33	C₂₃×#550	C₂²	1	2	yes	—
34	C₂₃×#547	—	2	1	no	—
35	C₂₃×#539	—	2	2	no	—
36	C₂₃×#538	—	2	2	no	—
37	C₂₃×#536	C₂²	1	2	yes	—
38	C₂₃×#535	C₂²	1	2	yes	—
39	C₂₃×#533	C₂²	1	1	yes	characteristic
40	C₂₃×#532	C₂²	1	1	yes	characteristic
41	C₂₃×#532	C₂²	1	1	yes	characteristic
42	C₂₃×#529	—	2	2	no	—
43	C₂₃×#525	—	2	2	no	—
44	C₂₃×#520	C₂²	1	2	yes	—
45	C₂₃×#520	C₂²	1	2	yes	—
46	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
47	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
48	C₂₃×#497	C₂²	1	4	yes	—
49	C₂₃×#496	C₂²	1	4	yes	—
50	C₂₃×#495	C₂²	1	4	yes	—
51	C₂₃×#495	C₂²	1	2	yes	complemented
52	C₂₃×#495	C₂²	1	2	yes	complemented
53	C₂₃×#494	C₂²	1	1	yes	characteristic, complemented
54	C₂₃×#493	C₂²	1	1	yes	characteristic, complemented
55	C₂₃×#492	C₂²	1	4	yes	—
56	C₂₃×#492	C₂²	1	1	yes	characteristic, complemented
57	C₂₃×#492	C₂²	1	1	yes	characteristic, complemented
58	C₂₃×#464	C₂²	1	4	yes	—
59	C₂₃×#464	C₂²	1	4	yes	complemented
60	C₂₃×#464	C₂²	1	4	yes	complemented
61	C₂₃×#463	C₂²	1	4	yes	—
62	C₂₃×#463	C₂²	1	4	yes	—
63	C₂₃×#463	C₂²	1	4	yes	complemented
64	C₂₃×#462	C₂²	1	2	yes	complemented
65	C₂₃×#462	C₂²	1	4	yes	complemented
66	C₂₃×#461	C₂²	1	2	yes	—
67	C₂₃×#461	C₂²	1	4	yes	complemented
68	C₂₃×#460	C₂²	1	4	yes	—
69	C₂₃×#460	C₂²	1	2	yes	complemented
70	C₂₃×#459	C₂²	1	2	yes	—
71	C₂₃×#459	C₂²	1	4	yes	—
72	C₂₃×#446	C₂²	1	2	yes	complemented
73	C₂₃×#446	C₂²	1	2	yes	complemented
74	C₈×Q₈×C₂₃	C₂²	1	2	yes	complemented
75	C₈×Q₈×C₂₃	C₂²	1	2	yes	complemented
76	C₂₃×#442	C₂²	1	4	yes	complemented
77	C₂₃×#441	C₂²	1	4	yes	complemented
78	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
79	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
80	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
81	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
82	C₄×SD₁₆×C₂₃	C₂²	1	4	yes	complemented
83	C₄×SD₁₆×C₂₃	C₂²	1	4	yes	complemented
84	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
85	C₂₃×#424	C₂²	1	2	yes	—
86	C₂₃×#423	C₂²	1	1	yes	characteristic
87	C₂₃×#417	C₂²	1	2	yes	—
88	C₂₃×#417	C₂²	1	2	yes	—
89	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
90	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
91	C₂₃×#405	C₂²	1	2	yes	—
92	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
93	C₂×#41×C₂₃	—	2	2	no	—
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×D₄×C₂₃	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₂₃	—	2	1	no	—
99	C₂₃×#137	—	4	4	no	—
100	C₂₃×AGL(1,ℤ/8)	—	4	4	no	—
101	C₂₃×#135	—	2	8	no	—
102	C₂₃×#135	—	4	4	no	—
103	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
104	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
105	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
106	C₂×SD₁₆×C₂₃	—	2	4	no	—
107	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
108	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
109	C₂×SD₁₆×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×SD₁₆×C₂₃	C₂³	1	4	yes	—
114	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
115	C₂×D₈×C₂₃	C₂³	1	2	yes	—
116	C₂×D₈×C₂₃	C₂³	1	2	yes	—
117	C₂×D₈×C₂₃	C₂³	1	4	yes	—
118	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
119	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
120	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
121	C₂₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
122	C₂₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
123	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
124	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
125	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
126	C₂₃×#127	C₂³	1	1	yes	characteristic
127	C₂₃×#127	C₂³	1	4	yes	—
128	C₂₃×#127	C₂³	1	1	yes	characteristic
129	C₂₃×#126	—	2	4	no	—
130	C₂₃×#126	—	2	4	no	—
131	C₂₃×#126	—	2	4	no	—
132	C₂₃×#125	—	2	4	no	—
133	C₂₃×#125	—	2	2	no	—
134	C₂₃×#125	D₄	1	2	yes	—
135	C₂₃×#124	—	2	4	no	—
136	C₂₃×#124	—	2	2	no	—
137	C₂₃×#124	C₂³	1	4	yes	—
138	C₂₃×#124	C₂³	1	2	yes	—
139	C₂₃×#124	C₂³	1	4	yes	—
140	C₂₃×#124	C₂³	1	2	yes	—
141	C₂₃×#123	—	2	4	no	—
142	C₂₃×#123	—	2	4	no	—
143	C₂₃×#123	—	2	4	no	—
144	C₂₃×#123	—	2	4	no	—
145	C₂₃×C₂²⋊Q₈	—	2	2	no	—
146	C₂₃×C₂²⋊Q₈	—	2	4	no	—
147	C₂₃×C₂²⋊Q₈	—	2	2	no	—
148	C₂₃×C₂²⋊Q₈	—	2	2	no	—
149	C₂₃×C₂²⋊Q₈	D₄	1	2	yes	—
150	C₂₃×C₂²⋊Q₈	D₄	1	2	yes	—
151	C₂₃×#121	—	2	1	no	—
152	C₂₃×#121	—	2	1	no	—
153	C₂₃×#121	—	2	1	no	—
154	C₂₃×#121	—	2	1	no	—
155	C₂₃×#121	—	2	2	no	—
156	C₂₃×#121	—	2	4	no	—
157	C₂₃×#121	—	2	2	no	—
158	C₂₃×#121	—	2	2	no	—
159	C₂₃×#120	—	2	4	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	4	yes	—
164	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
165	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
166	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
167	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
168	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
169	C₄×D₄×C₂₃	—	2	4	no	—
170	C₄×D₄×C₂₃	—	2	2	no	—
171	C₄×D₄×C₂₃	—	2	4	no	—
172	C₄×D₄×C₂₃	—	2	4	no	—
173	C₄×D₄×C₂₃	—	2	1	no	—
174	C₄×D₄×C₂₃	—	2	1	no	—
175	C₄×D₄×C₂₃	—	2	1	no	—
176	C₄×D₄×C₂₃	—	2	1	no	—
177	C₄×D₄×C₂₃	—	2	1	no	—
178	C₄×D₄×C₂₃	—	2	1	no	—
179	C₄×D₄×C₂₃	C₂³	1	2	yes	—
180	C₄×D₄×C₂₃	C₂³	1	4	yes	—
181	C₄×D₄×C₂₃	C₂³	1	4	yes	—
182	C₄×D₄×C₂₃	C₂³	1	2	yes	—
183	C₂₃×#117	—	2	2	no	—
184	C₂₃×#117	—	2	4	no	—
185	C₂₃×#117	—	2	2	no	—
186	C₂₃×#117	—	2	2	no	—
187	C₂₃×#117	C₂³	1	2	yes	—
188	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
189	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
190	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
191	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
192	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
193	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
194	C₂×C₄²×C₂₃	—	2	1	no	—
195	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
196	C₂₃×#106	C₂³	1	2	yes	—
197	C₂₃×#106	C₂³	1	2	yes	—
198	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
199	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
200	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
201	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
202	C₂₃×#103	C₂³	1	2	yes	—
203	C₂₃×#103	C₂³	1	2	yes	—
204	C₂₃×#103	C₂³	1	4	yes	—
205	C₂₃×#103	C₂³	1	4	yes	—
206	C₂₃×#102	C₂³	1	2	yes	—
207	C₂₃×#102	C₂³	1	2	yes	—
208	C₂₃×#102	C₂³	1	4	yes	—
209	C₂₃×#102	C₂³	1	4	yes	—
210	C₂₃×#97	C₂³	1	4	yes	—
211	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
212	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
213	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
214	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
215	C₄×C₈×C₂₃	C₂³	1	4	yes	—
216	C₂⁴×C₂₃	—	2	1	no	—
217	#41×C₂₃	—	2	4	no	—
218	#41×C₂₃	—	2	4	no	—
219	#41×C₂₃	—	2	4	no	—
220	#41×C₂₃	—	2	4	no	—
221	#41×C₂₃	—	8	4	no	—
222	C₂×Q₈×C₂₃	—	2	1	no	—
223	C₂×Q₈×C₂₃	—	2	2	no	—
224	C₂×Q₈×C₂₃	—	2	2	no	—
225	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
226	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
227	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
228	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
229	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
230	C₂×D₄×C₂₃	—	2	2	no	—
231	C₂×D₄×C₂₃	—	2	2	no	—
232	C₂×D₄×C₂₃	—	2	1	no	—
233	C₂×D₄×C₂₃	—	2	1	no	—
234	C₂×D₄×C₂₃	—	2	1	no	—
235	C₂×D₄×C₂₃	—	2	4	no	—
236	C₂×D₄×C₂₃	—	2	1	no	—
237	C₂×D₄×C₂₃	—	2	1	no	—
238	C₂×D₄×C₂₃	—	2	4	no	—
239	C₂×D₄×C₂₃	—	2	2	no	—
240	C₂×D₄×C₂₃	—	2	2	no	—
241	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
242	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
243	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₂₃	—	2	1	no	—
245	C₂²×C₄×C₂₃	—	2	1	no	—
246	C₂²×C₄×C₂₃	—	2	1	no	—
247	C₂²×C₄×C₂₃	—	2	2	no	—
248	C₂²×C₄×C₂₃	—	2	2	no	—
249	C₂²×C₄×C₂₃	—	2	2	no	—
250	C₂²×C₄×C₂₃	—	2	4	no	—
251	C₂²×C₄×C₂₃	—	2	4	no	—
252	C₂²×C₄×C₂₃	—	2	2	no	—
253	C₂²×C₄×C₂₃	—	8	2	no	—
254	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
255	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
256	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
257	Q₁₆×C₂₃	—	2	4	no	—
258	Q₁₆×C₂₃	—	4	2	no	—
259	Q₁₆×C₂₃	—	4	4	no	—
260	SD₁₆×C₂₃	—	2	4	no	—
261	SD₁₆×C₂₃	—	2	4	no	—
262	SD₁₆×C₂₃	—	2	4	no	—
263	SD₁₆×C₂₃	—	2	4	no	—
264	SD₁₆×C₂₃	—	4	2	no	—
265	SD₁₆×C₂₃	—	4	2	no	—
266	SD₁₆×C₂₃	—	4	4	no	—
267	SD₁₆×C₂₃	—	4	4	no	—
268	D₈×C₂₃	—	2	4	no	—
269	D₈×C₂₃	—	4	2	no	—
270	D₈×C₂₃	—	4	4	no	—
271	M₁₆×C₂₃	—	2	4	no	—
272	C₂×C₈×C₂₃	—	2	2	no	—
273	C₂×C₈×C₂₃	#41	1	4	yes	complemented
274	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
275	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
276	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
277	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
278	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
279	C₄⋊C₄×C₂₃	—	2	1	no	—
280	C₄⋊C₄×C₂₃	—	2	1	no	—
281	C₄⋊C₄×C₂₃	—	2	4	no	—
282	C₄⋊C₄×C₂₃	—	2	4	no	—
283	C₄⋊C₄×C₂₃	—	2	2	no	—
284	C₄⋊C₄×C₂₃	—	2	2	no	—
285	C₄⋊C₄×C₂₃	—	2	1	no	—
286	C₄⋊C₄×C₂₃	—	2	4	no	—
287	C₄⋊C₄×C₂₃	—	2	1	no	—
288	C₄⋊C₄×C₂₃	—	2	1	no	—
289	C₄⋊C₄×C₂₃	—	2	1	no	—
290	C₄⋊C₄×C₂₃	—	2	4	no	—
291	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
292	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
293	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
294	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
295	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
296	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
297	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
298	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
299	C₂²⋊C₄×C₂₃	—	2	2	no	—
300	C₂²⋊C₄×C₂₃	—	2	2	no	—
301	C₂²⋊C₄×C₂₃	—	2	2	no	—
302	C₂²⋊C₄×C₂₃	—	2	4	no	—
303	C₂²⋊C₄×C₂₃	—	2	4	no	—
304	C₂²⋊C₄×C₂₃	—	2	4	no	—
305	C₂²⋊C₄×C₂₃	—	2	4	no	—
306	C₂²⋊C₄×C₂₃	—	2	2	no	—
307	C₂²⋊C₄×C₂₃	—	2	4	no	—
308	C₂²⋊C₄×C₂₃	—	2	2	no	—
309	C₂²⋊C₄×C₂₃	—	2	2	no	—
310	C₂²⋊C₄×C₂₃	—	2	4	no	—
311	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
312	C₄²×C₂₃	—	2	2	no	—
313	C₄²×C₂₃	—	2	2	no	—
314	C₄²×C₂₃	—	2	4	no	—
315	C₄²×C₂₃	—	2	4	no	—
316	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
317	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
318	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
319	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
320	C₄²×C₂₃	C₂⁴	1	4	yes	—
321	#61407	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
322	C₂³×C₂₃	—	2	2	no	—
323	C₂³×C₂₃	—	2	2	no	—
324	C₂³×C₂₃	—	2	2	no	—
325	C₂³×C₂₃	—	4	2	no	—
326	C₂³×C₂₃	—	8	1	no	—
327	C₂³×C₂₃	—	8	1	no	—
328	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
329	Q₈×C₂₃	—	2	4	no	—
330	Q₈×C₂₃	—	2	2	no	—
331	Q₈×C₂₃	—	2	2	no	—
332	Q₈×C₂₃	—	2	2	no	—
333	Q₈×C₂₃	—	2	2	no	—
334	Q₈×C₂₃	—	2	2	no	—
335	Q₈×C₂₃	—	2	2	no	—
336	Q₈×C₂₃	—	4	2	no	—
337	Q₈×C₂₃	—	4	2	no	—
338	D₄×C₂₃	—	2	2	no	—
339	D₄×C₂₃	—	2	2	no	—
340	D₄×C₂₃	—	2	2	no	—
341	D₄×C₂₃	—	2	2	no	—
342	D₄×C₂₃	—	2	2	no	—
343	D₄×C₂₃	—	2	2	no	—
344	D₄×C₂₃	—	4	4	no	—
345	D₄×C₂₃	—	4	4	no	—
346	D₄×C₂₃	—	4	2	no	—
347	D₄×C₂₃	—	4	2	no	—
348	D₄×C₂₃	—	4	2	no	—
349	D₄×C₂₃	—	8	1	no	—
350	D₄×C₂₃	—	8	1	no	—
351	D₄×C₂₃	—	8	4	no	—
352	D₄×C₂₃	—	8	4	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	1	no	—
360	C₂×C₄×C₂₃	—	4	2	no	—
361	C₂×C₄×C₂₃	—	4	4	no	—
362	C₂×C₄×C₂₃	—	4	4	no	—
363	C₂×C₄×C₂₃	—	4	4	no	—
364	C₂×C₄×C₂₃	—	8	4	no	—
365	C₂×C₄×C₂₃	—	8	2	no	—
366	C₂×C₄×C₂₃	—	8	4	no	—
367	C₂×C₄×C₂₃	—	8	1	no	—
368	C₂×C₄×C₂₃	—	8	1	no	—
369	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
370	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
371	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
372	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
373	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
374	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
375	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
376	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
377	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
378	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
379	C₈×C₂₃	—	2	1	no	—
380	C₈×C₂₃	—	2	1	no	—
381	C₈×C₂₃	—	2	4	no	—
382	C₈×C₂₃	C₂×#41	1	2	yes	—
383	C₈×C₂₃	C₂×#41	1	2	yes	—
384	#3507	C₂×C₂₃	1	1	yes	characteristic, complemented
385	#3506	C₂×C₂₃	1	1	yes	characteristic, complemented
386	#3401	C₂×C₂₃	1	4	yes	complemented
387	#3399	C₂×C₂₃	1	2	yes	complemented
388	#3398	C₂×C₂₃	1	2	yes	complemented
389	#3394	C₂×C₂₃	1	2	yes	complemented
390	#3394	C₂×C₂₃	1	4	yes	complemented
391	#3392	C₂×C₂₃	1	2	yes	complemented
392	#3154	C₂×C₂₃	1	2	yes	complemented
393	#3147	C₂×C₂₃	1	1	yes	characteristic, complemented
394	#3046	C₂×C₂₃	1	2	yes	complemented
395	#3045	C₂×C₂₃	1	2	yes	complemented
396	#3037	C₂×C₂₃	1	1	yes	characteristic, complemented
397	#3036	C₂×C₂₃	1	1	yes	characteristic, complemented
398	#2960	C₂×C₂₃	1	1	yes	characteristic, complemented
399	#2952	C₂×C₂₃	1	2	yes	complemented
400	C₂×C₄×SD₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
401	C₂²×C₂₃	—	2	1	no	—
402	C₂²×C₂₃	—	2	1	no	—
403	C₂²×C₂₃	—	4	2	no	—
404	C₂²×C₂₃	—	4	2	no	—
405	C₂²×C₂₃	—	4	2	no	—
406	C₂²×C₂₃	—	4	2	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	—	8	4	no	—
413	C₂²×C₂₃	#550	1	2	yes	—
414	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
415	C₄×C₂₃	—	2	1	no	—
416	C₄×C₂₃	—	2	1	no	—
417	C₄×C₂₃	—	2	4	no	—
418	C₄×C₂₃	—	2	1	no	—
419	C₄×C₂₃	—	2	4	no	—
420	C₄×C₂₃	—	4	2	no	—
421	C₄×C₂₃	—	4	2	no	—
422	C₄×C₂₃	—	4	2	no	—
423	C₄×C₂₃	—	4	2	no	—
424	C₄×C₂₃	—	4	2	no	—
425	C₄×C₂₃	#550	1	2	yes	—
426	C₄×C₂₃	#577	1	2	yes	—
427	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
428	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
429	C₂×#137	C₂²×C₂₃	1	2	yes	—
430	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	2	yes	—
431	C₂×#135	C₂²×C₂₃	1	2	yes	—
432	C₂×#135	C₂²×C₂₃	1	2	yes	—
433	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
434	#559	C₂²×C₂₃	1	4	yes	—
435	#559	C₂²×C₂₃	1	2	yes	complemented
436	#557	C₂²×C₂₃	1	2	yes	complemented
437	#556	—	2	1	no	—
438	#556	C₂²×C₂₃	1	2	yes	—
439	#556	C₂²×C₂₃	1	4	yes	complemented
440	#555	—	2	1	no	—
441	#554	—	2	1	no	—
442	#553	—	2	2	no	—
443	#552	—	2	2	no	—
444	#550	C₂²×C₂₃	1	2	yes	—
445	#547	—	2	1	no	—
446	#539	—	2	2	no	—
447	#538	—	2	2	no	—
448	#536	C₂²×C₂₃	1	2	yes	—
449	#535	C₂²×C₂₃	1	2	yes	—
450	#533	C₂²×C₂₃	1	1	yes	characteristic
451	#532	C₂²×C₂₃	1	1	yes	characteristic
452	#532	C₂²×C₂₃	1	1	yes	characteristic
453	#529	—	2	2	no	—
454	#525	—	2	2	no	—
455	#520	C₂²×C₂₃	1	2	yes	—
456	#520	C₂²×C₂₃	1	2	yes	—
457	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
458	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
459	#497	C₂²×C₂₃	1	4	yes	—
460	#496	C₂²×C₂₃	1	4	yes	—
461	#495	C₂²×C₂₃	1	4	yes	—
462	#495	C₂²×C₂₃	1	2	yes	complemented
463	#495	C₂²×C₂₃	1	2	yes	complemented
464	#494	C₂²×C₂₃	1	1	yes	characteristic, complemented
465	#493	C₂²×C₂₃	1	1	yes	characteristic, complemented
466	#492	C₂²×C₂₃	1	4	yes	—
467	#492	C₂²×C₂₃	1	1	yes	characteristic, complemented
468	#492	C₂²×C₂₃	1	1	yes	characteristic, complemented
469	#464	C₂²×C₂₃	1	4	yes	—
470	#464	C₂²×C₂₃	1	4	yes	complemented
471	#464	C₂²×C₂₃	1	4	yes	complemented
472	#463	C₂²×C₂₃	1	4	yes	—
473	#463	C₂²×C₂₃	1	4	yes	—
474	#463	C₂²×C₂₃	1	4	yes	complemented
475	#462	C₂²×C₂₃	1	2	yes	complemented
476	#462	C₂²×C₂₃	1	4	yes	complemented
477	#461	C₂²×C₂₃	1	2	yes	—
478	#461	C₂²×C₂₃	1	4	yes	complemented
479	#460	C₂²×C₂₃	1	4	yes	—
480	#460	C₂²×C₂₃	1	2	yes	complemented
481	#459	C₂²×C₂₃	1	2	yes	—
482	#459	C₂²×C₂₃	1	4	yes	—
483	#446	C₂²×C₂₃	1	2	yes	complemented
484	#446	C₂²×C₂₃	1	2	yes	complemented
485	C₈×Q₈	C₂²×C₂₃	1	2	yes	complemented
486	C₈×Q₈	C₂²×C₂₃	1	2	yes	complemented
487	#442	C₂²×C₂₃	1	4	yes	complemented
488	#441	C₂²×C₂₃	1	4	yes	complemented
489	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
490	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
491	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
492	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
493	C₄×SD₁₆	C₂²×C₂₃	1	4	yes	complemented
494	C₄×SD₁₆	C₂²×C₂₃	1	4	yes	complemented
495	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
496	#424	C₂²×C₂₃	1	2	yes	—
497	#423	C₂²×C₂₃	1	1	yes	characteristic
498	#417	C₂²×C₂₃	1	2	yes	—
499	#417	C₂²×C₂₃	1	2	yes	—
500	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
501	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
502	#405	C₂²×C₂₃	1	2	yes	—
503	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
504	C₂×C₂₃	—	2	2	no	—
505	C₂×C₂₃	—	8	2	no	—
506	C₂×C₂₃	—	8	2	no	—
507	C₂×C₂₃	—	8	2	no	—
508	C₂×C₂₃	C₂×#550	1	1	yes	characteristic
509	C₂×C₂₃	C₂×#577	1	1	yes	characteristic
510	C₂×C₂₃	#3584	1	1	yes	characteristic
511	C₂×#41	—	2	2	no	—
512	C₂×#41	C₂³×C₂₃	1	2	yes	—
513	C₂×#41	C₂³×C₂₃	1	2	yes	—
514	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
515	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
516	C₂³×C₄	—	2	1	no	—
517	#137	—	4	4	no	—
518	AGL(1,ℤ/8)	—	4	4	no	—
519	#135	—	2	8	no	—
520	#135	—	4	4	no	—
521	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
522	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
523	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
524	C₂×SD₁₆	—	2	4	no	—
525	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
526	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
527	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
528	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
529	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
530	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
531	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
532	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
533	C₂×D₈	C₂³×C₂₃	1	2	yes	—
534	C₂×D₈	C₂³×C₂₃	1	2	yes	—
535	C₂×D₈	C₂³×C₂₃	1	4	yes	—
536	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
537	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
538	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
539	C₄⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
540	C₄⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
541	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
542	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
543	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
544	#127	C₂³×C₂₃	1	1	yes	characteristic
545	#127	C₂³×C₂₃	1	1	yes	characteristic
546	#127	C₂³×C₂₃	1	4	yes	—
547	#126	—	2	4	no	—
548	#126	—	2	4	no	—
549	#126	—	2	4	no	—
550	#125	—	2	2	no	—
551	#125	—	2	4	no	—
552	#125	D₄×C₂₃	1	2	yes	—
553	#124	—	2	2	no	—
554	#124	—	2	4	no	—
555	#124	C₂³×C₂₃	1	2	yes	—
556	#124	C₂³×C₂₃	1	2	yes	—
557	#124	C₂³×C₂₃	1	4	yes	—
558	#124	C₂³×C₂₃	1	4	yes	—
559	#123	—	2	4	no	—
560	#123	—	2	4	no	—
561	#123	—	2	4	no	—
562	#123	—	2	4	no	—
563	C₂²⋊Q₈	—	2	2	no	—
564	C₂²⋊Q₈	—	2	4	no	—
565	C₂²⋊Q₈	—	2	2	no	—
566	C₂²⋊Q₈	—	2	2	no	—
567	C₂²⋊Q₈	D₄×C₂₃	1	2	yes	—
568	C₂²⋊Q₈	D₄×C₂₃	1	2	yes	—
569	#121	—	2	1	no	—
570	#121	—	2	1	no	—
571	#121	—	2	1	no	—
572	#121	—	2	1	no	—
573	#121	—	2	2	no	—
574	#121	—	2	2	no	—
575	#121	—	2	2	no	—
576	#121	—	2	4	no	—
577	#120	—	2	4	no	—
578	C₄×Q₈	—	2	2	no	—
579	C₄×Q₈	—	2	1	no	—
580	C₄×Q₈	—	2	1	no	—
581	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
582	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
583	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
584	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
585	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
586	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
587	C₄×D₄	—	2	4	no	—
588	C₄×D₄	—	2	2	no	—
589	C₄×D₄	—	2	4	no	—
590	C₄×D₄	—	2	4	no	—
591	C₄×D₄	—	2	1	no	—
592	C₄×D₄	—	2	1	no	—
593	C₄×D₄	—	2	1	no	—
594	C₄×D₄	—	2	1	no	—
595	C₄×D₄	—	2	1	no	—
596	C₄×D₄	—	2	1	no	—
597	C₄×D₄	C₂³×C₂₃	1	2	yes	—
598	C₄×D₄	C₂³×C₂₃	1	2	yes	—
599	C₄×D₄	C₂³×C₂₃	1	4	yes	—
600	C₄×D₄	C₂³×C₂₃	1	4	yes	—
601	#117	—	2	2	no	—
602	#117	—	2	2	no	—
603	#117	—	2	2	no	—
604	#117	—	2	4	no	—
605	#117	C₂³×C₂₃	1	2	yes	—
606	C₂×C₄⋊C₄	—	2	1	no	—
607	C₂×C₄⋊C₄	—	2	2	no	—
608	C₂×C₄⋊C₄	—	2	2	no	—
609	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
610	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
611	C₂×C₂²⋊C₄	—	2	1	no	—
612	C₂×C₄²	—	2	1	no	—
613	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
614	#106	C₂³×C₂₃	1	2	yes	—
615	#106	C₂³×C₂₃	1	2	yes	—
616	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
617	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
618	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
619	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
620	#103	C₂³×C₂₃	1	2	yes	—
621	#103	C₂³×C₂₃	1	2	yes	—
622	#103	C₂³×C₂₃	1	4	yes	—
623	#103	C₂³×C₂₃	1	4	yes	—
624	#102	C₂³×C₂₃	1	2	yes	—
625	#102	C₂³×C₂₃	1	2	yes	—
626	#102	C₂³×C₂₃	1	4	yes	—
627	#102	C₂³×C₂₃	1	4	yes	—
628	#97	C₂³×C₂₃	1	4	yes	—
629	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
630	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
631	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
632	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
633	C₄×C₈	C₂³×C₂₃	1	4	yes	—
634	C₂₃	#61407	1	1	yes	characteristic, direct product factor, Sylow
635	C₂⁴	—	2	1	no	—
636	#41	—	2	4	no	—
637	#41	—	2	4	no	—
638	#41	—	2	4	no	—
639	#41	—	2	4	no	—
640	#41	—	8	4	no	—
641	C₂×Q₈	—	2	1	no	—
642	C₂×Q₈	—	2	2	no	—
643	C₂×Q₈	—	2	2	no	—
644	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
645	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
646	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
647	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
648	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
649	C₂×D₄	—	2	2	no	—
650	C₂×D₄	—	2	2	no	—
651	C₂×D₄	—	2	1	no	—
652	C₂×D₄	—	2	1	no	—
653	C₂×D₄	—	2	1	no	—
654	C₂×D₄	—	2	4	no	—
655	C₂×D₄	—	2	1	no	—
656	C₂×D₄	—	2	1	no	—
657	C₂×D₄	—	2	4	no	—
658	C₂×D₄	—	2	2	no	—
659	C₂×D₄	—	2	2	no	—
660	C₂×D₄	C₂⁴×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	2	no	—
667	C₂²×C₄	—	2	2	no	—
668	C₂²×C₄	—	2	2	no	—
669	C₂²×C₄	—	2	4	no	—
670	C₂²×C₄	—	2	4	no	—
671	C₂²×C₄	—	2	2	no	—
672	C₂²×C₄	—	8	2	no	—
673	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
674	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
675	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
676	Q₁₆	—	2	4	no	—
677	Q₁₆	—	4	2	no	—
678	Q₁₆	—	4	4	no	—
679	SD₁₆	—	2	4	no	—
680	SD₁₆	—	2	4	no	—
681	SD₁₆	—	2	4	no	—
682	SD₁₆	—	2	4	no	—
683	SD₁₆	—	4	2	no	—
684	SD₁₆	—	4	2	no	—
685	SD₁₆	—	4	4	no	—
686	SD₁₆	—	4	4	no	—
687	D₈	—	2	4	no	—
688	D₈	—	4	2	no	—
689	D₈	—	4	4	no	—
690	M₁₆	—	2	4	no	—
691	C₂×C₈	—	2	2	no	—
692	C₂×C₈	#41×C₂₃	1	4	yes	complemented
693	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
694	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
695	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
696	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
697	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
698	C₄⋊C₄	—	2	1	no	—
699	C₄⋊C₄	—	2	1	no	—
700	C₄⋊C₄	—	2	4	no	—
701	C₄⋊C₄	—	2	4	no	—
702	C₄⋊C₄	—	2	2	no	—
703	C₄⋊C₄	—	2	2	no	—
704	C₄⋊C₄	—	2	1	no	—
705	C₄⋊C₄	—	2	4	no	—
706	C₄⋊C₄	—	2	1	no	—
707	C₄⋊C₄	—	2	1	no	—
708	C₄⋊C₄	—	2	1	no	—
709	C₄⋊C₄	—	2	4	no	—
710	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
711	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
712	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
713	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
714	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
715	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
716	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
717	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
718	C₂²⋊C₄	—	2	2	no	—
719	C₂²⋊C₄	—	2	2	no	—
720	C₂²⋊C₄	—	2	2	no	—
721	C₂²⋊C₄	—	2	4	no	—
722	C₂²⋊C₄	—	2	4	no	—
723	C₂²⋊C₄	—	2	4	no	—
724	C₂²⋊C₄	—	2	4	no	—
725	C₂²⋊C₄	—	2	2	no	—
726	C₂²⋊C₄	—	2	4	no	—
727	C₂²⋊C₄	—	2	2	no	—
728	C₂²⋊C₄	—	2	2	no	—
729	C₂²⋊C₄	—	2	4	no	—
730	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
731	C₄²	—	2	2	no	—
732	C₄²	—	2	2	no	—
733	C₄²	—	2	4	no	—
734	C₄²	—	2	4	no	—
735	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
736	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
737	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
738	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
739	C₄²	C₂⁴×C₂₃	1	4	yes	—
740	C₂³	—	2	2	no	—
741	C₂³	—	2	2	no	—
742	C₂³	—	2	2	no	—
743	C₂³	—	4	2	no	—
744	C₂³	—	8	1	no	—
745	C₂³	—	8	1	no	—
746	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
747	Q₈	—	2	4	no	—
748	Q₈	—	2	2	no	—
749	Q₈	—	2	2	no	—
750	Q₈	—	2	2	no	—
751	Q₈	—	2	2	no	—
752	Q₈	—	2	2	no	—
753	Q₈	—	2	2	no	—
754	Q₈	—	4	2	no	—
755	Q₈	—	4	2	no	—
756	D₄	—	2	2	no	—
757	D₄	—	2	2	no	—
758	D₄	—	2	2	no	—
759	D₄	—	2	2	no	—
760	D₄	—	2	2	no	—
761	D₄	—	2	2	no	—
762	D₄	—	4	4	no	—
763	D₄	—	4	4	no	—
764	D₄	—	4	2	no	—
765	D₄	—	4	2	no	—
766	D₄	—	4	2	no	—
767	D₄	—	8	4	no	—
768	D₄	—	8	1	no	—
769	D₄	—	8	1	no	—
770	D₄	—	8	4	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	4	1	no	—
778	C₂×C₄	—	4	2	no	—
779	C₂×C₄	—	4	4	no	—
780	C₂×C₄	—	4	4	no	—
781	C₂×C₄	—	4	4	no	—
782	C₂×C₄	—	8	2	no	—
783	C₂×C₄	—	8	4	no	—
784	C₂×C₄	—	8	4	no	—
785	C₂×C₄	—	8	1	no	—
786	C₂×C₄	—	8	1	no	—
787	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
788	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
789	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
790	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
791	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
792	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
793	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
794	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
795	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
796	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
797	C₈	—	2	1	no	—
798	C₈	—	2	1	no	—
799	C₈	—	2	4	no	—
800	C₈	C₂×#41×C₂₃	1	2	yes	—
801	C₈	C₂×#41×C₂₃	1	2	yes	—
802	C₂²	—	2	1	no	—
803	C₂²	—	2	1	no	—
804	C₂²	—	4	2	no	—
805	C₂²	—	4	2	no	—
806	C₂²	—	4	2	no	—
807	C₂²	—	4	2	no	—
808	C₂²	—	4	2	no	—
809	C₂²	—	4	2	no	—
810	C₂²	—	4	2	no	—
811	C₂²	—	4	2	no	—
812	C₂²	—	4	2	no	—
813	C₂²	—	8	4	no	—
814	C₂²	C₂₃×#550	1	2	yes	—
815	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
816	C₄	—	2	1	no	—
817	C₄	—	2	4	no	—
818	C₄	—	2	1	no	—
819	C₄	—	2	1	no	—
820	C₄	—	2	4	no	—
821	C₄	—	4	2	no	—
822	C₄	—	4	2	no	—
823	C₄	—	4	2	no	—
824	C₄	—	4	2	no	—
825	C₄	—	4	2	no	—
826	C₄	C₂₃×#550	1	2	yes	—
827	C₄	C₂₃×#577	1	2	yes	—
828	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
829	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
830	C₂	—	2	2	no	—
831	C₂	—	8	2	no	—
832	C₂	—	8	2	no	—
833	C₂	—	8	2	no	—
834	C₂	C₂×C₂₃×#550	1	1	yes	characteristic
835	C₂	C₂×C₂₃×#577	1	1	yes	characteristic
836	C₂	C₂₃×#3584	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×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3507	C₂	semidirect
2. C₂₃×#3506	C₂	semidirect
3. C₂₃×#3401	C₂	semidirect
4. C₂₃×#3399	C₂	semidirect
5. C₂₃×#3398	C₂	semidirect
6. C₂₃×#3394	C₂	semidirect
7. C₂₃×#3394	C₂	semidirect
8. C₂₃×#3392	C₂	semidirect
9. C₂₃×#3154	C₂	semidirect
10. C₂₃×#3147	C₂	semidirect
11. C₂₃×#3046	C₂	semidirect
12. C₂₃×#3045	C₂	semidirect
13. C₂₃×#3037	C₂	semidirect
14. C₂₃×#3036	C₂	semidirect
15. C₂₃×#2960	C₂	semidirect
16. C₂₃×#2952	C₂	semidirect
17. C₂×C₄×SD₁₆×C₂₃	C₂	semidirect
24. C₂₃×#559	C₂²	semidirect
25. C₂₃×#557	C₂²	semidirect
28. C₂₃×#556	C₂²	semidirect
51. C₂₃×#495	C₂²	semidirect
52. C₂₃×#495	C₂²	semidirect
53. C₂₃×#494	C₂²	semidirect
54. C₂₃×#493	C₂²	semidirect
56. C₂₃×#492	C₂²	semidirect
57. C₂₃×#492	C₂²	semidirect
59. C₂₃×#464	C₂²	semidirect
60. C₂₃×#464	C₂²	semidirect
63. C₂₃×#463	C₂²	semidirect
64. C₂₃×#462	C₂²	semidirect
65. C₂₃×#462	C₂²	semidirect
67. C₂₃×#461	C₂²	semidirect
69. C₂₃×#460	C₂²	semidirect
72. C₂₃×#446	C₂²	semidirect
73. C₂₃×#446	C₂²	semidirect
74. C₈×Q₈×C₂₃	C₂²	semidirect
75. C₈×Q₈×C₂₃	C₂²	semidirect
76. C₂₃×#442	C₂²	semidirect
77. C₂₃×#441	C₂²	semidirect
82. C₄×SD₁₆×C₂₃	C₂²	semidirect
83. C₄×SD₁₆×C₂₃	C₂²	semidirect
273. C₂×C₈×C₂₃	#41	semidirect
321. #61407	C₂₃	direct (N × H)
384. #3507	C₂×C₂₃	semidirect
385. #3506	C₂×C₂₃	semidirect
386. #3401	C₂×C₂₃	semidirect
387. #3399	C₂×C₂₃	semidirect
388. #3398	C₂×C₂₃	semidirect
389. #3394	C₂×C₂₃	semidirect
390. #3394	C₂×C₂₃	semidirect
391. #3392	C₂×C₂₃	semidirect
392. #3154	C₂×C₂₃	semidirect
393. #3147	C₂×C₂₃	semidirect
394. #3046	C₂×C₂₃	semidirect
395. #3045	C₂×C₂₃	semidirect
396. #3037	C₂×C₂₃	semidirect
397. #3036	C₂×C₂₃	semidirect
398. #2960	C₂×C₂₃	semidirect
399. #2952	C₂×C₂₃	semidirect
400. C₂×C₄×SD₁₆	C₂×C₂₃	semidirect
435. #559	C₂²×C₂₃	semidirect
436. #557	C₂²×C₂₃	semidirect
439. #556	C₂²×C₂₃	semidirect
462. #495	C₂²×C₂₃	semidirect
463. #495	C₂²×C₂₃	semidirect
464. #494	C₂²×C₂₃	semidirect
465. #493	C₂²×C₂₃	semidirect
467. #492	C₂²×C₂₃	semidirect
468. #492	C₂²×C₂₃	semidirect
470. #464	C₂²×C₂₃	semidirect
471. #464	C₂²×C₂₃	semidirect
474. #463	C₂²×C₂₃	semidirect
475. #462	C₂²×C₂₃	semidirect
476. #462	C₂²×C₂₃	semidirect
478. #461	C₂²×C₂₃	semidirect
480. #460	C₂²×C₂₃	semidirect
483. #446	C₂²×C₂₃	semidirect
484. #446	C₂²×C₂₃	semidirect
485. C₈×Q₈	C₂²×C₂₃	semidirect
486. C₈×Q₈	C₂²×C₂₃	semidirect
487. #442	C₂²×C₂₃	semidirect
488. #441	C₂²×C₂₃	semidirect
493. C₄×SD₁₆	C₂²×C₂₃	semidirect
494. C₄×SD₁₆	C₂²×C₂₃	semidirect
634. C₂₃	#61407	direct (N × H)
692. C₂×C₈	#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×#3507	2
C₂₃×#3506	2
C₂₃×#3401	2
C₂₃×#3399	2
C₂₃×#3398	2
C₂₃×#3394	2
C₂₃×#3392	2
C₂₃×#3154	2
C₂₃×#3147	2
C₂₃×#3046	2
C₂₃×#3045	2
C₂₃×#3037	2
C₂₃×#3036	2
C₂₃×#2960	2
C₂₃×#2952	2
C₂×C₄×SD₁₆×C₂₃	2
#61407	23

Subgroups — C23×#61407 #19209033

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61407 #19209033