Subgroups — C₂₃×#61080 #19208706

Order 5888.

2742 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#577	C₂	1	2	yes	maximal, complemented
2	C₂₃×#3497	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3496	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#3269	C₂	1	4	yes	maximal, complemented
5	C₂₃×#3268	C₂	1	4	yes	maximal, complemented
6	C₂₃×#3266	C₂	1	4	yes	maximal, complemented
7	C₂₃×#3265	C₂	1	4	yes	maximal, complemented
8	C₂₃×#3150	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#3061	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3037	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3036	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3013	C₂	1	2	yes	maximal, complemented
13	C₂₃×#3012	C₂	1	2	yes	maximal, complemented
14	C₂×C₂₃×#440	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#2932	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₃×2₋¹⁺⁴	C₂²	1	2	yes	complemented
17	C₂×C₂₃×H(5,𝔽₂)	C₂²	1	2	yes	—
18	C₂₃×#577	—	2	16	no	—
19	C₂×C₂₃×#137	C₂²	1	4	yes	complemented
20	C₂×C₂₃×#137	C₂²	1	2	yes	complemented
21	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
22	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
23	C₂×C₂₃×#135	C₂²	1	4	yes	complemented
24	C₂×C₂₃×#135	C₂²	1	2	yes	complemented
25	C₂×C₂₃×#135	C₂²	1	2	yes	complemented
26	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
27	C₂²×SD₁₆×C₂₃	C₂²	1	4	yes	complemented
28	C₂×C₂₃×#131	C₂²	1	2	yes	complemented
29	C₂₃×#550	—	2	1	no	—
30	C₂₃×#550	C₂²	1	2	yes	complemented
31	D₄×Q₈×C₂₃	—	2	1	no	—
32	D₄×Q₈×C₂₃	C₂²	1	2	yes	complemented
33	C₂₃×#548	—	2	2	no	—
34	C₂₃×#548	C₂²	1	4	yes	complemented
35	C₂₃×#547	—	2	1	no	—
36	C₂₃×#547	C₂²	1	2	yes	—
37	C₂₃×#546	—	2	2	no	—
38	C₂₃×#546	C₂²	1	4	yes	—
39	D₄²×C₂₃	—	2	1	no	—
40	D₄²×C₂₃	C₂²	1	2	yes	—
41	C₂₃×#537	—	2	2	no	—
42	C₂₃×#537	C₂²	1	2	yes	—
43	C₂₃×#537	C₂²	1	2	yes	complemented
44	C₂₃×#534	—	2	2	no	—
45	C₂₃×#532	—	2	2	no	—
46	C₂₃×#532	C₂²	1	1	yes	characteristic
47	C₂₃×#532	C₂²	1	1	yes	characteristic
48	C₂₃×#532	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₂₃×#121	—	2	2	no	—
50	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
52	C₂₃×#497	C₂²	1	2	yes	complemented
53	C₂₃×#497	C₂²	1	2	yes	complemented
54	C₂₃×#496	C₂²	1	2	yes	complemented
55	C₂₃×#496	C₂²	1	2	yes	complemented
56	C₂₃×#468	C₂²	1	4	yes	complemented
57	C₂₃×#468	C₂²	1	4	yes	complemented
58	C₂₃×#467	C₂²	1	4	yes	complemented
59	C₂₃×#466	C₂²	1	4	yes	complemented
60	C₂₃×#464	C₂²	1	4	yes	complemented
61	C₂₃×#463	C₂²	1	4	yes	complemented
62	C₂₃×#462	C₂²	1	2	yes	complemented
63	C₂₃×#461	C₂²	1	2	yes	complemented
64	C₂₃×#460	C₂²	1	2	yes	complemented
65	C₂₃×#459	C₂²	1	2	yes	complemented
66	C₂₃×#452	C₂²	1	4	yes	complemented
67	C₂₃×#452	C₂²	1	4	yes	complemented
68	C₂₃×#451	C₂²	1	4	yes	complemented
69	C₂₃×#450	C₂²	1	4	yes	complemented
70	C₂₃×#449	C₂²	1	4	yes	complemented
71	C₂₃×#449	C₂²	1	4	yes	complemented
72	C₂₃×#448	C₂²	1	4	yes	complemented
73	C₂₃×#447	C₂²	1	4	yes	complemented
74	C₂₃×#440	C₂²	1	4	yes	complemented
75	C₂₃×#440	C₂²	1	4	yes	complemented
76	C₂₃×#435	C₂²	1	4	yes	complemented
77	C₂₃×#435	C₂²	1	4	yes	complemented
78	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic, complemented
79	C₂₃×#423	C₂²	1	1	yes	characteristic, complemented
80	C₂₃×#417	C₂²	1	2	yes	complemented
81	C₂₃×#417	C₂²	1	2	yes	complemented
82	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic, complemented
83	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
84	C₂₃×#408	C₂²	1	2	yes	complemented
85	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic, complemented
86	C₂₃×2₋¹⁺⁴	—	2	8	no	—
87	C₂₃×2₋¹⁺⁴	—	4	4	no	—
88	C₂₃×H(5,𝔽₂)	—	2	8	no	—
89	C₂₃×H(5,𝔽₂)	—	4	4	no	—
90	C₂×#41×C₂₃	—	2	2	no	—
91	C₂×#41×C₂₃	—	2	2	no	—
92	C₂×#41×C₂₃	—	2	4	no	—
93	C₂×#41×C₂₃	C₂³	1	2	yes	—
94	C₂×#41×C₂₃	C₂³	1	2	yes	—
95	C₂×#41×C₂₃	C₂³	1	4	yes	—
96	C₂×#41×C₂₃	C₂³	1	4	yes	—
97	C₂×#41×C₂₃	C₂³	1	2	yes	—
98	C₂²×Q₈×C₂₃	—	2	2	no	—
99	C₂²×Q₈×C₂₃	C₂³	1	4	yes	—
100	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
101	C₂²×D₄×C₂₃	—	2	4	no	—
102	C₂²×D₄×C₂₃	—	2	2	no	—
103	C₂²×D₄×C₂₃	—	2	2	no	—
104	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
105	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₂₃	—	2	1	no	—
107	C₂₃×#137	—	2	8	no	—
108	C₂₃×#137	—	2	16	no	—
109	C₂₃×AGL(1,ℤ/8)	—	2	8	no	—
110	C₂₃×AGL(1,ℤ/8)	—	2	16	no	—
111	C₂₃×#135	—	2	16	no	—
112	C₂₃×#135	—	2	8	no	—
113	C₂₃×#135	—	4	4	no	—
114	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
115	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
116	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
117	C₂×SD₁₆×C₂₃	—	2	16	no	—
118	C₂×SD₁₆×C₂₃	D₄	1	8	yes	complemented
119	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
120	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
121	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
122	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
123	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
124	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
125	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
126	C₂×D₈×C₂₃	C₂³	1	4	yes	—
127	C₂×D₈×C₂₃	C₂³	1	2	yes	—
128	C₂×D₈×C₂₃	C₂³	1	2	yes	—
129	C₂₃×#131	—	2	8	no	—
130	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
131	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
132	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
133	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
134	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
135	C₂₃×C₄⋊Q₈	—	2	2	no	—
136	C₂₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
137	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
138	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
139	C₂₃×#127	—	2	2	no	—
140	C₂₃×#127	D₄	1	1	yes	characteristic
141	C₂₃×#127	C₂³	1	1	yes	characteristic
142	C₂₃×#127	C₂³	1	1	yes	characteristic
143	C₂₃×#124	—	2	4	no	—
144	C₂₃×#124	D₄	1	2	yes	—
145	C₂₃×#124	C₂³	1	2	yes	—
146	C₂₃×#124	C₂³	1	2	yes	—
147	C₂₃×#123	—	2	4	no	—
148	C₂₃×#123	—	2	4	no	—
149	C₂₃×C₂²⋊Q₈	—	2	2	no	—
150	C₂₃×C₂²⋊Q₈	—	2	2	no	—
151	C₂₃×C₂²⋊Q₈	—	2	4	no	—
152	C₂₃×C₂²⋊Q₈	—	2	4	no	—
153	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
154	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
155	C₂₃×#121	—	2	2	no	—
156	C₂₃×#121	—	2	2	no	—
157	C₂₃×#121	—	2	4	no	—
158	C₂₃×#121	—	2	4	no	—
159	C₂₃×#121	—	2	4	no	—
160	C₂₃×#121	—	2	2	no	—
161	C₂₃×#121	—	2	1	no	—
162	C₂₃×#121	—	2	1	no	—
163	C₂₃×#121	—	2	1	no	—
164	C₂₃×#121	—	2	1	no	—
165	C₂₃×#121	—	2	2	no	—
166	C₂₃×#121	—	2	4	no	—
167	C₂₃×#121	—	2	4	no	—
168	C₂₃×#121	D₄	1	2	yes	—
169	C₂₃×#121	D₄	1	2	yes	—
170	C₂₃×#121	C₂³	1	4	yes	—
171	C₂₃×#121	C₂³	1	4	yes	—
172	C₂₃×#120	—	2	4	no	—
173	C₂₃×#120	—	2	4	no	—
174	C₄×Q₈×C₂₃	—	2	1	no	—
175	C₄×Q₈×C₂₃	—	2	1	no	—
176	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
177	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
178	C₄×D₄×C₂₃	—	2	2	no	—
179	C₄×D₄×C₂₃	—	2	2	no	—
180	C₄×D₄×C₂₃	—	2	4	no	—
181	C₄×D₄×C₂₃	—	2	1	no	—
182	C₄×D₄×C₂₃	—	2	1	no	—
183	C₄×D₄×C₂₃	—	2	1	no	—
184	C₄×D₄×C₂₃	—	2	1	no	—
185	C₄×D₄×C₂₃	—	2	1	no	—
186	C₄×D₄×C₂₃	—	2	1	no	—
187	C₄×D₄×C₂₃	C₂³	1	2	yes	—
188	C₄×D₄×C₂₃	C₂³	1	2	yes	—
189	C₄×D₄×C₂₃	C₂³	1	2	yes	—
190	C₄×D₄×C₂₃	C₂³	1	2	yes	—
191	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
192	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
193	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
194	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
195	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
196	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
197	C₂×C₄²×C₂₃	—	2	1	no	—
198	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
199	C₂₃×#107	C₂³	1	4	yes	—
200	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
201	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
202	C₂₃×#103	C₂³	1	4	yes	—
203	C₂₃×#103	C₂³	1	4	yes	—
204	C₂₃×#103	C₂³	1	4	yes	—
205	C₂₃×#102	C₂³	1	4	yes	—
206	C₂₃×#102	C₂³	1	4	yes	—
207	C₂₃×#102	C₂³	1	4	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	—	2	4	no	—
214	#41×C₂₃	—	2	4	no	—
215	#41×C₂₃	—	2	4	no	—
216	#41×C₂₃	—	2	8	no	—
217	#41×C₂₃	—	2	8	no	—
218	#41×C₂₃	—	2	4	no	—
219	#41×C₂₃	—	2	4	no	—
220	#41×C₂₃	—	2	4	no	—
221	#41×C₂₃	—	2	4	no	—
222	#41×C₂₃	—	4	4	no	—
223	#41×C₂₃	—	4	4	no	—
224	#41×C₂₃	—	4	16	no	—
225	#41×C₂₃	—	4	8	no	—
226	#41×C₂₃	—	4	8	no	—
227	C₂×Q₈×C₂₃	—	2	1	no	—
228	C₂×Q₈×C₂₃	—	2	4	no	—
229	C₂×Q₈×C₂₃	—	2	2	no	—
230	C₂×Q₈×C₂₃	—	2	8	no	—
231	C₂×Q₈×C₂₃	—	4	4	no	—
232	C₂×Q₈×C₂₃	—	4	8	no	—
233	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
234	C₂×Q₈×C₂₃	C₂×D₄	1	4	yes	complemented
235	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
236	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
237	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
238	C₂×D₄×C₂₃	—	2	8	no	—
239	C₂×D₄×C₂₃	—	2	4	no	—
240	C₂×D₄×C₂₃	—	2	2	no	—
241	C₂×D₄×C₂₃	—	2	2	no	—
242	C₂×D₄×C₂₃	—	2	4	no	—
243	C₂×D₄×C₂₃	—	2	4	no	—
244	C₂×D₄×C₂₃	—	2	4	no	—
245	C₂×D₄×C₂₃	—	2	1	no	—
246	C₂×D₄×C₂₃	—	2	1	no	—
247	C₂×D₄×C₂₃	—	2	1	no	—
248	C₂×D₄×C₂₃	—	2	4	no	—
249	C₂×D₄×C₂₃	—	2	1	no	—
250	C₂×D₄×C₂₃	—	2	1	no	—
251	C₂×D₄×C₂₃	—	2	2	no	—
252	C₂×D₄×C₂₃	—	4	4	no	—
253	C₂×D₄×C₂₃	—	4	8	no	—
254	C₂×D₄×C₂₃	—	4	16	no	—
255	C₂×D₄×C₂₃	—	8	4	no	—
256	C₂×D₄×C₂₃	C₂×D₄	1	4	yes	—
257	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
258	C₂×D₄×C₂₃	C₂×D₄	1	4	yes	—
259	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
260	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
261	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
262	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
263	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₂₃	—	2	1	no	—
265	C₂²×C₄×C₂₃	—	2	4	no	—
266	C₂²×C₄×C₂₃	—	2	1	no	—
267	C₂²×C₄×C₂₃	—	2	1	no	—
268	C₂²×C₄×C₂₃	—	2	4	no	—
269	C₂²×C₄×C₂₃	—	2	2	no	—
270	C₂²×C₄×C₂₃	—	2	2	no	—
271	C₂²×C₄×C₂₃	—	2	4	no	—
272	C₂²×C₄×C₂₃	—	2	2	no	—
273	C₂²×C₄×C₂₃	—	2	2	no	—
274	C₂²×C₄×C₂₃	—	8	2	no	—
275	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
276	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
277	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
278	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
279	Q₁₆×C₂₃	—	2	8	no	—
280	Q₁₆×C₂₃	—	2	4	no	—
281	Q₁₆×C₂₃	—	4	2	no	—
282	SD₁₆×C₂₃	—	2	8	no	—
283	SD₁₆×C₂₃	—	2	8	no	—
284	SD₁₆×C₂₃	—	2	4	no	—
285	SD₁₆×C₂₃	—	2	4	no	—
286	SD₁₆×C₂₃	—	4	2	no	—
287	SD₁₆×C₂₃	—	4	2	no	—
288	SD₁₆×C₂₃	C₂×D₄	1	16	yes	complemented
289	D₈×C₂₃	—	2	8	no	—
290	D₈×C₂₃	—	2	4	no	—
291	D₈×C₂₃	—	4	2	no	—
292	M₁₆×C₂₃	—	2	4	no	—
293	M₁₆×C₂₃	—	2	8	no	—
294	C₂×C₈×C₂₃	—	2	2	no	—
295	C₂×C₈×C₂₃	—	2	8	no	—
296	C₂×C₈×C₂₃	C₂×D₄	1	4	yes	complemented
297	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
298	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
299	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
300	C₄⋊C₄×C₂₃	—	2	1	no	—
301	C₄⋊C₄×C₂₃	—	2	2	no	—
302	C₄⋊C₄×C₂₃	—	2	2	no	—
303	C₄⋊C₄×C₂₃	—	2	4	no	—
304	C₄⋊C₄×C₂₃	—	2	1	no	—
305	C₄⋊C₄×C₂₃	—	2	1	no	—
306	C₄⋊C₄×C₂₃	—	2	1	no	—
307	C₄⋊C₄×C₂₃	—	2	1	no	—
308	C₄⋊C₄×C₂₃	—	2	4	no	—
309	C₄⋊C₄×C₂₃	—	2	1	no	—
310	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
311	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
312	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
313	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
314	C₂²⋊C₄×C₂₃	—	2	4	no	—
315	C₂²⋊C₄×C₂₃	—	2	4	no	—
316	C₂²⋊C₄×C₂₃	—	2	2	no	—
317	C₂²⋊C₄×C₂₃	—	2	2	no	—
318	C₂²⋊C₄×C₂₃	—	2	2	no	—
319	C₂²⋊C₄×C₂₃	—	2	4	no	—
320	C₂²⋊C₄×C₂₃	—	2	2	no	—
321	C₂²⋊C₄×C₂₃	—	2	2	no	—
322	C₂²⋊C₄×C₂₃	—	2	2	no	—
323	C₂²⋊C₄×C₂₃	—	2	4	no	—
324	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
325	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
326	C₄²×C₂₃	—	2	2	no	—
327	C₄²×C₂₃	—	2	2	no	—
328	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
329	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
330	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
331	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
332	#61080	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
333	C₂³×C₂₃	—	2	2	no	—
334	C₂³×C₂₃	—	2	4	no	—
335	C₂³×C₂₃	—	2	2	no	—
336	C₂³×C₂₃	—	2	2	no	—
337	C₂³×C₂₃	—	4	8	no	—
338	C₂³×C₂₃	—	8	1	no	—
339	C₂³×C₂₃	—	8	1	no	—
340	C₂³×C₂₃	—	8	4	no	—
341	C₂³×C₂₃	—	8	4	no	—
342	C₂³×C₂₃	C₂²×D₄	1	4	yes	—
343	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
344	Q₈×C₂₃	—	2	4	no	—
345	Q₈×C₂₃	—	2	4	no	—
346	Q₈×C₂₃	—	2	2	no	—
347	Q₈×C₂₃	—	2	2	no	—
348	Q₈×C₂₃	—	2	2	no	—
349	Q₈×C₂₃	—	2	2	no	—
350	Q₈×C₂₃	—	2	2	no	—
351	Q₈×C₂₃	—	4	8	no	—
352	Q₈×C₂₃	C₂²×D₄	1	4	yes	—
353	D₄×C₂₃	—	2	8	no	—
354	D₄×C₂₃	—	2	4	no	—
355	D₄×C₂₃	—	2	4	no	—
356	D₄×C₂₃	—	2	2	no	—
357	D₄×C₂₃	—	2	2	no	—
358	D₄×C₂₃	—	2	2	no	—
359	D₄×C₂₃	—	2	2	no	—
360	D₄×C₂₃	—	2	2	no	—
361	D₄×C₂₃	—	4	2	no	—
362	D₄×C₂₃	—	4	2	no	—
363	D₄×C₂₃	—	4	8	no	—
364	D₄×C₂₃	—	4	8	no	—
365	D₄×C₂₃	—	4	2	no	—
366	D₄×C₂₃	—	4	2	no	—
367	D₄×C₂₃	—	4	8	no	—
368	D₄×C₂₃	—	4	4	no	—
369	D₄×C₂₃	—	4	4	no	—
370	D₄×C₂₃	—	8	1	no	—
371	D₄×C₂₃	—	8	1	no	—
372	D₄×C₂₃	—	8	4	no	—
373	D₄×C₂₃	—	8	4	no	—
374	D₄×C₂₃	C₂²×D₄	1	4	yes	—
375	C₂×C₄×C₂₃	—	2	4	no	—
376	C₂×C₄×C₂₃	—	2	2	no	—
377	C₂×C₄×C₂₃	—	2	4	no	—
378	C₂×C₄×C₂₃	—	2	4	no	—
379	C₂×C₄×C₂₃	—	2	2	no	—
380	C₂×C₄×C₂₃	—	2	2	no	—
381	C₂×C₄×C₂₃	—	2	2	no	—
382	C₂×C₄×C₂₃	—	2	2	no	—
383	C₂×C₄×C₂₃	—	4	1	no	—
384	C₂×C₄×C₂₃	—	4	1	no	—
385	C₂×C₄×C₂₃	—	4	8	no	—
386	C₂×C₄×C₂₃	—	4	8	no	—
387	C₂×C₄×C₂₃	—	4	8	no	—
388	C₂×C₄×C₂₃	—	4	4	no	—
389	C₂×C₄×C₂₃	—	4	4	no	—
390	C₂×C₄×C₂₃	—	4	4	no	—
391	C₂×C₄×C₂₃	—	8	2	no	—
392	C₂×C₄×C₂₃	—	8	1	no	—
393	C₂×C₄×C₂₃	—	8	1	no	—
394	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
395	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
396	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
397	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
398	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
399	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
400	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
401	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
402	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
403	C₈×C₂₃	—	2	4	no	—
404	C₈×C₂₃	—	2	2	no	—
405	C₈×C₂₃	C₂²×D₄	1	4	yes	—
406	C₂×#577	C₂×C₂₃	1	2	yes	complemented
407	#3497	C₂×C₂₃	1	1	yes	characteristic, complemented
408	#3496	C₂×C₂₃	1	1	yes	characteristic, complemented
409	#3269	C₂×C₂₃	1	4	yes	complemented
410	#3268	C₂×C₂₃	1	4	yes	complemented
411	#3266	C₂×C₂₃	1	4	yes	complemented
412	#3265	C₂×C₂₃	1	4	yes	complemented
413	#3150	C₂×C₂₃	1	1	yes	characteristic, complemented
414	#3061	C₂×C₂₃	1	2	yes	complemented
415	#3037	C₂×C₂₃	1	1	yes	characteristic, complemented
416	#3036	C₂×C₂₃	1	1	yes	characteristic, complemented
417	#3013	C₂×C₂₃	1	2	yes	complemented
418	#3012	C₂×C₂₃	1	2	yes	complemented
419	C₂×#440	C₂×C₂₃	1	1	yes	characteristic, complemented
420	#2932	C₂×C₂₃	1	1	yes	characteristic, complemented
421	C₂²×C₂₃	—	2	1	no	—
422	C₂²×C₂₃	—	2	1	no	—
423	C₂²×C₂₃	—	2	4	no	—
424	C₂²×C₂₃	—	2	4	no	—
425	C₂²×C₂₃	—	2	4	no	—
426	C₂²×C₂₃	—	2	4	no	—
427	C₂²×C₂₃	—	4	2	no	—
428	C₂²×C₂₃	—	4	2	no	—
429	C₂²×C₂₃	—	4	2	no	—
430	C₂²×C₂₃	—	4	2	no	—
431	C₂²×C₂₃	—	4	2	no	—
432	C₂²×C₂₃	—	4	2	no	—
433	C₂²×C₂₃	—	4	2	no	—
434	C₂²×C₂₃	—	4	2	no	—
435	C₂²×C₂₃	—	8	4	no	—
436	C₂²×C₂₃	—	16	8	no	—
437	C₂²×C₂₃	D₄²	1	2	yes	—
438	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
439	C₄×C₂₃	—	2	1	no	—
440	C₄×C₂₃	—	2	1	no	—
441	C₄×C₂₃	—	2	1	no	—
442	C₄×C₂₃	—	2	1	no	—
443	C₄×C₂₃	—	2	4	no	—
444	C₄×C₂₃	—	2	4	no	—
445	C₄×C₂₃	—	4	2	no	—
446	C₄×C₂₃	—	4	2	no	—
447	C₄×C₂₃	—	4	2	no	—
448	C₄×C₂₃	—	4	2	no	—
449	C₄×C₂₃	D₄²	1	2	yes	—
450	C₄×C₂₃	C₂³×D₄	1	1	yes	characteristic
451	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
452	C₂×2₋¹⁺⁴	C₂²×C₂₃	1	2	yes	complemented
453	C₂×H(5,𝔽₂)	C₂²×C₂₃	1	2	yes	—
454	#577	—	2	16	no	—
455	C₂×#137	C₂²×C₂₃	1	4	yes	complemented
456	C₂×#137	C₂²×C₂₃	1	2	yes	complemented
457	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	2	yes	—
458	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	4	yes	complemented
459	C₂×#135	C₂²×C₂₃	1	2	yes	complemented
460	C₂×#135	C₂²×C₂₃	1	4	yes	complemented
461	C₂×#135	C₂²×C₂₃	1	2	yes	complemented
462	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
463	C₂²×SD₁₆	C₂²×C₂₃	1	4	yes	complemented
464	C₂×#131	C₂²×C₂₃	1	2	yes	complemented
465	#550	—	2	1	no	—
466	#550	C₂²×C₂₃	1	2	yes	complemented
467	D₄×Q₈	—	2	1	no	—
468	D₄×Q₈	C₂²×C₂₃	1	2	yes	complemented
469	#548	—	2	2	no	—
470	#548	C₂²×C₂₃	1	4	yes	complemented
471	#547	—	2	1	no	—
472	#547	C₂²×C₂₃	1	2	yes	—
473	#546	—	2	2	no	—
474	#546	C₂²×C₂₃	1	4	yes	—
475	D₄²	—	2	1	no	—
476	D₄²	C₂²×C₂₃	1	2	yes	—
477	#537	—	2	2	no	—
478	#537	C₂²×C₂₃	1	2	yes	—
479	#537	C₂²×C₂₃	1	2	yes	complemented
480	#534	—	2	2	no	—
481	#532	—	2	2	no	—
482	#532	C₂²×C₂₃	1	1	yes	characteristic
483	#532	C₂²×C₂₃	1	1	yes	characteristic
484	#532	C₂²×C₂₃	1	1	yes	characteristic, complemented
485	C₂×#121	—	2	2	no	—
486	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
487	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
488	#497	C₂²×C₂₃	1	2	yes	complemented
489	#497	C₂²×C₂₃	1	2	yes	complemented
490	#496	C₂²×C₂₃	1	2	yes	complemented
491	#496	C₂²×C₂₃	1	2	yes	complemented
492	#468	C₂²×C₂₃	1	4	yes	complemented
493	#468	C₂²×C₂₃	1	4	yes	complemented
494	#467	C₂²×C₂₃	1	4	yes	complemented
495	#466	C₂²×C₂₃	1	4	yes	complemented
496	#464	C₂²×C₂₃	1	4	yes	complemented
497	#463	C₂²×C₂₃	1	4	yes	complemented
498	#462	C₂²×C₂₃	1	2	yes	complemented
499	#461	C₂²×C₂₃	1	2	yes	complemented
500	#460	C₂²×C₂₃	1	2	yes	complemented
501	#459	C₂²×C₂₃	1	2	yes	complemented
502	#452	C₂²×C₂₃	1	4	yes	complemented
503	#452	C₂²×C₂₃	1	4	yes	complemented
504	#451	C₂²×C₂₃	1	4	yes	complemented
505	#450	C₂²×C₂₃	1	4	yes	complemented
506	#449	C₂²×C₂₃	1	4	yes	complemented
507	#449	C₂²×C₂₃	1	4	yes	complemented
508	#448	C₂²×C₂₃	1	4	yes	complemented
509	#447	C₂²×C₂₃	1	4	yes	complemented
510	#440	C₂²×C₂₃	1	4	yes	complemented
511	#440	C₂²×C₂₃	1	4	yes	complemented
512	#435	C₂²×C₂₃	1	4	yes	complemented
513	#435	C₂²×C₂₃	1	4	yes	complemented
514	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic, complemented
515	#423	C₂²×C₂₃	1	1	yes	characteristic, complemented
516	#417	C₂²×C₂₃	1	2	yes	complemented
517	#417	C₂²×C₂₃	1	2	yes	complemented
518	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic, complemented
519	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
520	#408	C₂²×C₂₃	1	2	yes	complemented
521	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic, complemented
522	C₂×C₂₃	—	2	2	no	—
523	C₂×C₂₃	—	4	4	no	—
524	C₂×C₂₃	—	4	4	no	—
525	C₂×C₂₃	—	8	2	no	—
526	C₂×C₂₃	—	8	2	no	—
527	C₂×C₂₃	C₂×D₄²	1	1	yes	characteristic
528	C₂×C₂₃	#3585	1	1	yes	characteristic
529	C₂×C₂₃	#3586	1	1	yes	characteristic
530	2₋¹⁺⁴	—	2	8	no	—
531	2₋¹⁺⁴	—	4	4	no	—
532	H(5,𝔽₂)	—	2	8	no	—
533	H(5,𝔽₂)	—	4	4	no	—
534	C₂×#41	—	2	2	no	—
535	C₂×#41	—	2	4	no	—
536	C₂×#41	—	2	2	no	—
537	C₂×#41	C₂³×C₂₃	1	2	yes	—
538	C₂×#41	C₂³×C₂₃	1	2	yes	—
539	C₂×#41	C₂³×C₂₃	1	4	yes	—
540	C₂×#41	C₂³×C₂₃	1	4	yes	—
541	C₂×#41	C₂³×C₂₃	1	2	yes	—
542	C₂²×Q₈	—	2	2	no	—
543	C₂²×Q₈	C₂³×C₂₃	1	4	yes	—
544	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
545	C₂²×D₄	—	2	4	no	—
546	C₂²×D₄	—	2	2	no	—
547	C₂²×D₄	—	2	2	no	—
548	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
549	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
550	C₂³×C₄	—	2	1	no	—
551	#137	—	2	8	no	—
552	#137	—	2	16	no	—
553	AGL(1,ℤ/8)	—	2	8	no	—
554	AGL(1,ℤ/8)	—	2	16	no	—
555	#135	—	2	16	no	—
556	#135	—	2	8	no	—
557	#135	—	4	4	no	—
558	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
559	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
560	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
561	C₂×SD₁₆	—	2	16	no	—
562	C₂×SD₁₆	D₄×C₂₃	1	8	yes	complemented
563	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
564	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
565	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
566	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
567	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
568	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
569	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
570	C₂×D₈	C₂³×C₂₃	1	4	yes	—
571	C₂×D₈	C₂³×C₂₃	1	2	yes	—
572	C₂×D₈	C₂³×C₂₃	1	2	yes	—
573	#131	—	2	8	no	—
574	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
575	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
576	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
577	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
578	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
579	C₄⋊Q₈	—	2	2	no	—
580	C₄⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
581	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
582	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
583	#127	—	2	2	no	—
584	#127	D₄×C₂₃	1	1	yes	characteristic
585	#127	C₂³×C₂₃	1	1	yes	characteristic
586	#127	C₂³×C₂₃	1	1	yes	characteristic
587	#124	—	2	4	no	—
588	#124	D₄×C₂₃	1	2	yes	—
589	#124	C₂³×C₂₃	1	2	yes	—
590	#124	C₂³×C₂₃	1	2	yes	—
591	#123	—	2	4	no	—
592	#123	—	2	4	no	—
593	C₂²⋊Q₈	—	2	2	no	—
594	C₂²⋊Q₈	—	2	2	no	—
595	C₂²⋊Q₈	—	2	4	no	—
596	C₂²⋊Q₈	—	2	4	no	—
597	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
598	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
599	#121	—	2	4	no	—
600	#121	—	2	2	no	—
601	#121	—	2	4	no	—
602	#121	—	2	4	no	—
603	#121	—	2	2	no	—
604	#121	—	2	2	no	—
605	#121	—	2	1	no	—
606	#121	—	2	1	no	—
607	#121	—	2	1	no	—
608	#121	—	2	1	no	—
609	#121	—	2	2	no	—
610	#121	—	2	4	no	—
611	#121	—	2	4	no	—
612	#121	D₄×C₂₃	1	2	yes	—
613	#121	D₄×C₂₃	1	2	yes	—
614	#121	C₂³×C₂₃	1	4	yes	—
615	#121	C₂³×C₂₃	1	4	yes	—
616	#120	—	2	4	no	—
617	#120	—	2	4	no	—
618	C₄×Q₈	—	2	1	no	—
619	C₄×Q₈	—	2	1	no	—
620	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
621	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
622	C₄×D₄	—	2	2	no	—
623	C₄×D₄	—	2	2	no	—
624	C₄×D₄	—	2	4	no	—
625	C₄×D₄	—	2	1	no	—
626	C₄×D₄	—	2	1	no	—
627	C₄×D₄	—	2	1	no	—
628	C₄×D₄	—	2	1	no	—
629	C₄×D₄	—	2	1	no	—
630	C₄×D₄	—	2	1	no	—
631	C₄×D₄	C₂³×C₂₃	1	2	yes	—
632	C₄×D₄	C₂³×C₂₃	1	2	yes	—
633	C₄×D₄	C₂³×C₂₃	1	2	yes	—
634	C₄×D₄	C₂³×C₂₃	1	2	yes	—
635	C₂×C₄⋊C₄	—	2	1	no	—
636	C₂×C₄⋊C₄	—	2	2	no	—
637	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
638	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
639	C₂×C₂²⋊C₄	—	2	1	no	—
640	C₂×C₂²⋊C₄	—	2	4	no	—
641	C₂×C₄²	—	2	1	no	—
642	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
643	#107	C₂³×C₂₃	1	4	yes	—
644	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
645	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
646	#103	C₂³×C₂₃	1	4	yes	—
647	#103	C₂³×C₂₃	1	4	yes	—
648	#103	C₂³×C₂₃	1	4	yes	—
649	#102	C₂³×C₂₃	1	4	yes	—
650	#102	C₂³×C₂₃	1	4	yes	—
651	#102	C₂³×C₂₃	1	4	yes	—
652	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
653	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
654	#97	C₂³×C₂₃	1	2	yes	—
655	#97	C₂³×C₂₃	1	2	yes	—
656	C₂₃	#61080	1	1	yes	characteristic, direct product factor, Sylow
657	C₂⁴	—	2	1	no	—
658	C₂⁴	—	2	4	no	—
659	#41	—	2	4	no	—
660	#41	—	2	4	no	—
661	#41	—	2	8	no	—
662	#41	—	2	8	no	—
663	#41	—	2	4	no	—
664	#41	—	2	4	no	—
665	#41	—	2	4	no	—
666	#41	—	2	4	no	—
667	#41	—	4	4	no	—
668	#41	—	4	4	no	—
669	#41	—	4	16	no	—
670	#41	—	4	8	no	—
671	#41	—	4	8	no	—
672	C₂×Q₈	—	2	1	no	—
673	C₂×Q₈	—	2	4	no	—
674	C₂×Q₈	—	2	2	no	—
675	C₂×Q₈	—	2	8	no	—
676	C₂×Q₈	—	4	4	no	—
677	C₂×Q₈	—	4	8	no	—
678	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
679	C₂×Q₈	C₂×D₄×C₂₃	1	4	yes	complemented
680	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
681	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
682	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
683	C₂×D₄	—	2	8	no	—
684	C₂×D₄	—	2	4	no	—
685	C₂×D₄	—	2	2	no	—
686	C₂×D₄	—	2	2	no	—
687	C₂×D₄	—	2	4	no	—
688	C₂×D₄	—	2	4	no	—
689	C₂×D₄	—	2	4	no	—
690	C₂×D₄	—	2	1	no	—
691	C₂×D₄	—	2	1	no	—
692	C₂×D₄	—	2	1	no	—
693	C₂×D₄	—	2	4	no	—
694	C₂×D₄	—	2	1	no	—
695	C₂×D₄	—	2	1	no	—
696	C₂×D₄	—	2	2	no	—
697	C₂×D₄	—	4	4	no	—
698	C₂×D₄	—	4	8	no	—
699	C₂×D₄	—	4	16	no	—
700	C₂×D₄	—	8	4	no	—
701	C₂×D₄	C₂×D₄×C₂₃	1	4	yes	—
702	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
703	C₂×D₄	C₂×D₄×C₂₃	1	4	yes	—
704	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
705	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
706	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
707	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
708	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
709	C₂²×C₄	—	2	1	no	—
710	C₂²×C₄	—	2	4	no	—
711	C₂²×C₄	—	2	1	no	—
712	C₂²×C₄	—	2	1	no	—
713	C₂²×C₄	—	2	4	no	—
714	C₂²×C₄	—	2	2	no	—
715	C₂²×C₄	—	2	2	no	—
716	C₂²×C₄	—	2	4	no	—
717	C₂²×C₄	—	2	2	no	—
718	C₂²×C₄	—	2	2	no	—
719	C₂²×C₄	—	8	2	no	—
720	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
721	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
722	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
723	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
724	Q₁₆	—	2	8	no	—
725	Q₁₆	—	2	4	no	—
726	Q₁₆	—	4	2	no	—
727	SD₁₆	—	2	8	no	—
728	SD₁₆	—	2	8	no	—
729	SD₁₆	—	2	4	no	—
730	SD₁₆	—	2	4	no	—
731	SD₁₆	—	4	2	no	—
732	SD₁₆	—	4	2	no	—
733	SD₁₆	C₂×D₄×C₂₃	1	16	yes	complemented
734	D₈	—	2	8	no	—
735	D₈	—	2	4	no	—
736	D₈	—	4	2	no	—
737	M₁₆	—	2	4	no	—
738	M₁₆	—	2	8	no	—
739	C₂×C₈	—	2	2	no	—
740	C₂×C₈	—	2	8	no	—
741	C₂×C₈	C₂×D₄×C₂₃	1	4	yes	complemented
742	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
743	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
744	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
745	C₄⋊C₄	—	2	1	no	—
746	C₄⋊C₄	—	2	2	no	—
747	C₄⋊C₄	—	2	2	no	—
748	C₄⋊C₄	—	2	4	no	—
749	C₄⋊C₄	—	2	1	no	—
750	C₄⋊C₄	—	2	1	no	—
751	C₄⋊C₄	—	2	1	no	—
752	C₄⋊C₄	—	2	1	no	—
753	C₄⋊C₄	—	2	4	no	—
754	C₄⋊C₄	—	2	1	no	—
755	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
756	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
757	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
758	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
759	C₂²⋊C₄	—	2	4	no	—
760	C₂²⋊C₄	—	2	4	no	—
761	C₂²⋊C₄	—	2	2	no	—
762	C₂²⋊C₄	—	2	2	no	—
763	C₂²⋊C₄	—	2	2	no	—
764	C₂²⋊C₄	—	2	4	no	—
765	C₂²⋊C₄	—	2	2	no	—
766	C₂²⋊C₄	—	2	2	no	—
767	C₂²⋊C₄	—	2	2	no	—
768	C₂²⋊C₄	—	2	4	no	—
769	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
770	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
771	C₄²	—	2	2	no	—
772	C₄²	—	2	2	no	—
773	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
774	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
775	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
776	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
777	C₂³	—	2	2	no	—
778	C₂³	—	2	4	no	—
779	C₂³	—	2	2	no	—
780	C₂³	—	2	2	no	—
781	C₂³	—	4	8	no	—
782	C₂³	—	8	1	no	—
783	C₂³	—	8	1	no	—
784	C₂³	—	8	4	no	—
785	C₂³	—	8	4	no	—
786	C₂³	C₂²×D₄×C₂₃	1	4	yes	—
787	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
788	Q₈	—	2	2	no	—
789	Q₈	—	2	4	no	—
790	Q₈	—	2	4	no	—
791	Q₈	—	2	2	no	—
792	Q₈	—	2	2	no	—
793	Q₈	—	2	2	no	—
794	Q₈	—	2	2	no	—
795	Q₈	—	4	8	no	—
796	Q₈	C₂²×D₄×C₂₃	1	4	yes	—
797	D₄	—	2	8	no	—
798	D₄	—	2	2	no	—
799	D₄	—	2	2	no	—
800	D₄	—	2	2	no	—
801	D₄	—	2	2	no	—
802	D₄	—	2	2	no	—
803	D₄	—	2	4	no	—
804	D₄	—	2	4	no	—
805	D₄	—	4	2	no	—
806	D₄	—	4	2	no	—
807	D₄	—	4	8	no	—
808	D₄	—	4	8	no	—
809	D₄	—	4	2	no	—
810	D₄	—	4	2	no	—
811	D₄	—	4	8	no	—
812	D₄	—	4	4	no	—
813	D₄	—	4	4	no	—
814	D₄	—	8	1	no	—
815	D₄	—	8	1	no	—
816	D₄	—	8	4	no	—
817	D₄	—	8	4	no	—
818	D₄	C₂²×D₄×C₂₃	1	4	yes	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	4	no	—
821	C₂×C₄	—	2	4	no	—
822	C₂×C₄	—	2	4	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	4	1	no	—
828	C₂×C₄	—	4	1	no	—
829	C₂×C₄	—	4	8	no	—
830	C₂×C₄	—	4	8	no	—
831	C₂×C₄	—	4	8	no	—
832	C₂×C₄	—	4	4	no	—
833	C₂×C₄	—	4	4	no	—
834	C₂×C₄	—	4	4	no	—
835	C₂×C₄	—	8	2	no	—
836	C₂×C₄	—	8	1	no	—
837	C₂×C₄	—	8	1	no	—
838	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
839	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
840	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
841	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
842	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
843	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
844	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
845	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
846	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
847	C₈	—	2	4	no	—
848	C₈	—	2	2	no	—
849	C₈	C₂²×D₄×C₂₃	1	4	yes	—
850	C₂²	—	2	1	no	—
851	C₂²	—	2	1	no	—
852	C₂²	—	2	4	no	—
853	C₂²	—	2	4	no	—
854	C₂²	—	2	4	no	—
855	C₂²	—	2	4	no	—
856	C₂²	—	4	2	no	—
857	C₂²	—	4	2	no	—
858	C₂²	—	4	2	no	—
859	C₂²	—	4	2	no	—
860	C₂²	—	4	2	no	—
861	C₂²	—	4	2	no	—
862	C₂²	—	4	2	no	—
863	C₂²	—	4	2	no	—
864	C₂²	—	8	4	no	—
865	C₂²	—	16	8	no	—
866	C₂²	D₄²×C₂₃	1	2	yes	—
867	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
868	C₄	—	2	4	no	—
869	C₄	—	2	4	no	—
870	C₄	—	2	1	no	—
871	C₄	—	2	1	no	—
872	C₄	—	2	1	no	—
873	C₄	—	2	1	no	—
874	C₄	—	4	2	no	—
875	C₄	—	4	2	no	—
876	C₄	—	4	2	no	—
877	C₄	—	4	2	no	—
878	C₄	D₄²×C₂₃	1	2	yes	—
879	C₄	C₂³×D₄×C₂₃	1	1	yes	characteristic
880	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
881	C₂	—	2	2	no	—
882	C₂	—	4	4	no	—
883	C₂	—	4	4	no	—
884	C₂	—	8	2	no	—
885	C₂	—	8	2	no	—
886	C₂	C₂×D₄²×C₂₃	1	1	yes	characteristic
887	C₂	C₂₃×#3585	1	1	yes	characteristic
888	C₂	C₂₃×#3586	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. C₂×C₂₃×#577	C₂	semidirect
2. C₂₃×#3497	C₂	semidirect
3. C₂₃×#3496	C₂	semidirect
4. C₂₃×#3269	C₂	semidirect
5. C₂₃×#3268	C₂	semidirect
6. C₂₃×#3266	C₂	semidirect
7. C₂₃×#3265	C₂	semidirect
8. C₂₃×#3150	C₂	semidirect
9. C₂₃×#3061	C₂	semidirect
10. C₂₃×#3037	C₂	semidirect
11. C₂₃×#3036	C₂	semidirect
12. C₂₃×#3013	C₂	semidirect
13. C₂₃×#3012	C₂	semidirect
14. C₂×C₂₃×#440	C₂	semidirect
15. C₂₃×#2932	C₂	semidirect
16. C₂×C₂₃×2₋¹⁺⁴	C₂²	semidirect
19. C₂×C₂₃×#137	C₂²	semidirect
20. C₂×C₂₃×#137	C₂²	semidirect
22. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
23. C₂×C₂₃×#135	C₂²	semidirect
24. C₂×C₂₃×#135	C₂²	semidirect
25. C₂×C₂₃×#135	C₂²	semidirect
27. C₂²×SD₁₆×C₂₃	C₂²	semidirect
28. C₂×C₂₃×#131	C₂²	semidirect
30. C₂₃×#550	C₂²	semidirect
32. D₄×Q₈×C₂₃	C₂²	semidirect
34. C₂₃×#548	C₂²	semidirect
43. C₂₃×#537	C₂²	semidirect
48. C₂₃×#532	C₂²	semidirect
50. C₂×C₄×Q₈×C₂₃	C₂²	semidirect
52. C₂₃×#497	C₂²	semidirect
53. C₂₃×#497	C₂²	semidirect
54. C₂₃×#496	C₂²	semidirect
55. C₂₃×#496	C₂²	semidirect
56. C₂₃×#468	C₂²	semidirect
57. C₂₃×#468	C₂²	semidirect
58. C₂₃×#467	C₂²	semidirect
59. C₂₃×#466	C₂²	semidirect
60. C₂₃×#464	C₂²	semidirect
61. C₂₃×#463	C₂²	semidirect
62. C₂₃×#462	C₂²	semidirect
63. C₂₃×#461	C₂²	semidirect
64. C₂₃×#460	C₂²	semidirect
65. C₂₃×#459	C₂²	semidirect
66. C₂₃×#452	C₂²	semidirect
67. C₂₃×#452	C₂²	semidirect
68. C₂₃×#451	C₂²	semidirect
69. C₂₃×#450	C₂²	semidirect
70. C₂₃×#449	C₂²	semidirect
71. C₂₃×#449	C₂²	semidirect
72. C₂₃×#448	C₂²	semidirect
73. C₂₃×#447	C₂²	semidirect
74. C₂₃×#440	C₂²	semidirect
75. C₂₃×#440	C₂²	semidirect
76. C₂₃×#435	C₂²	semidirect
77. C₂₃×#435	C₂²	semidirect
78. C₂×C₂₃×#107	C₂²	semidirect
79. C₂₃×#423	C₂²	semidirect
80. C₂₃×#417	C₂²	semidirect
81. C₂₃×#417	C₂²	semidirect
82. C₂×C₂₃×#103	C₂²	semidirect
84. C₂₃×#408	C₂²	semidirect
85. C₂×C₂₃×#97	C₂²	semidirect
118. C₂×SD₁₆×C₂₃	D₄	semidirect
234. C₂×Q₈×C₂₃	C₂×D₄	semidirect
288. SD₁₆×C₂₃	C₂×D₄	semidirect
296. C₂×C₈×C₂₃	C₂×D₄	semidirect
332. #61080	C₂₃	direct (N × H)
406. C₂×#577	C₂×C₂₃	semidirect
407. #3497	C₂×C₂₃	semidirect
408. #3496	C₂×C₂₃	semidirect
409. #3269	C₂×C₂₃	semidirect
410. #3268	C₂×C₂₃	semidirect
411. #3266	C₂×C₂₃	semidirect
412. #3265	C₂×C₂₃	semidirect
413. #3150	C₂×C₂₃	semidirect
414. #3061	C₂×C₂₃	semidirect
415. #3037	C₂×C₂₃	semidirect
416. #3036	C₂×C₂₃	semidirect
417. #3013	C₂×C₂₃	semidirect
418. #3012	C₂×C₂₃	semidirect
419. C₂×#440	C₂×C₂₃	semidirect
420. #2932	C₂×C₂₃	semidirect
452. C₂×2₋¹⁺⁴	C₂²×C₂₃	semidirect
455. C₂×#137	C₂²×C₂₃	semidirect
456. C₂×#137	C₂²×C₂₃	semidirect
458. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
459. C₂×#135	C₂²×C₂₃	semidirect
460. C₂×#135	C₂²×C₂₃	semidirect
461. C₂×#135	C₂²×C₂₃	semidirect
463. C₂²×SD₁₆	C₂²×C₂₃	semidirect
464. C₂×#131	C₂²×C₂₃	semidirect
466. #550	C₂²×C₂₃	semidirect
468. D₄×Q₈	C₂²×C₂₃	semidirect
470. #548	C₂²×C₂₃	semidirect
479. #537	C₂²×C₂₃	semidirect
484. #532	C₂²×C₂₃	semidirect
486. C₂×C₄×Q₈	C₂²×C₂₃	semidirect
488. #497	C₂²×C₂₃	semidirect
489. #497	C₂²×C₂₃	semidirect
490. #496	C₂²×C₂₃	semidirect
491. #496	C₂²×C₂₃	semidirect
492. #468	C₂²×C₂₃	semidirect
493. #468	C₂²×C₂₃	semidirect
494. #467	C₂²×C₂₃	semidirect
495. #466	C₂²×C₂₃	semidirect
496. #464	C₂²×C₂₃	semidirect
497. #463	C₂²×C₂₃	semidirect
498. #462	C₂²×C₂₃	semidirect
499. #461	C₂²×C₂₃	semidirect
500. #460	C₂²×C₂₃	semidirect
501. #459	C₂²×C₂₃	semidirect
502. #452	C₂²×C₂₃	semidirect
503. #452	C₂²×C₂₃	semidirect
504. #451	C₂²×C₂₃	semidirect
505. #450	C₂²×C₂₃	semidirect
506. #449	C₂²×C₂₃	semidirect
507. #449	C₂²×C₂₃	semidirect
508. #448	C₂²×C₂₃	semidirect
509. #447	C₂²×C₂₃	semidirect
510. #440	C₂²×C₂₃	semidirect
511. #440	C₂²×C₂₃	semidirect
512. #435	C₂²×C₂₃	semidirect
513. #435	C₂²×C₂₃	semidirect
514. C₂×#107	C₂²×C₂₃	semidirect
515. #423	C₂²×C₂₃	semidirect
516. #417	C₂²×C₂₃	semidirect
517. #417	C₂²×C₂₃	semidirect
518. C₂×#103	C₂²×C₂₃	semidirect
520. #408	C₂²×C₂₃	semidirect
521. C₂×#97	C₂²×C₂₃	semidirect
562. C₂×SD₁₆	D₄×C₂₃	semidirect
656. C₂₃	#61080	direct (N × H)
679. C₂×Q₈	C₂×D₄×C₂₃	semidirect
733. SD₁₆	C₂×D₄×C₂₃	semidirect
741. C₂×C₈	C₂×D₄×C₂₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₂₃×#577	2
C₂₃×#3497	2
C₂₃×#3496	2
C₂₃×#3269	2
C₂₃×#3268	2
C₂₃×#3266	2
C₂₃×#3265	2
C₂₃×#3150	2
C₂₃×#3061	2
C₂₃×#3037	2
C₂₃×#3036	2
C₂₃×#3013	2
C₂₃×#3012	2
C₂×C₂₃×#440	2
C₂₃×#2932	2
#61080	23

Subgroups — C23×#61080 #19208706

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61080 #19208706