Subgroups — C₂₃×#61060 #19208686

Order 5888.

2686 conjugacy classes of subgroups.

The subgroup lattice has 1030 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	1	yes	maximal, characteristic, complemented
2	C₂²×C₂₃×#137	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3486	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#3485	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#3276	C₂	1	4	yes	maximal, complemented
6	C₂₃×#3275	C₂	1	4	yes	maximal, complemented
7	C₂₃×#3269	C₂	1	4	yes	maximal, complemented
8	C₂₃×#3266	C₂	1	4	yes	maximal, complemented
9	C₂₃×#3156	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3059	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3054	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3044	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3042	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3011	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3009	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#3005	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#3004	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#2949	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#2930	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₂₃×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
21	C₂×C₂₃×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
22	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
23	C₂³×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
24	C₂₃×#577	—	2	8	no	—
25	C₂×C₂₃×#137	—	2	8	no	—
26	C₂×C₂₃×#137	C₂²	1	1	yes	characteristic
27	C₂×C₂₃×#137	C₂²	1	1	yes	characteristic
28	C₂×C₂₃×#137	C₂²	1	4	yes	complemented
29	C₂×C₂₃×#137	C₂²	1	4	yes	complemented
30	C₂×C₂₃×#137	C₂²	1	2	yes	complemented
31	C₂×C₂₃×#137	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
33	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
34	C₂×C₂₃×#135	C₂²	1	1	yes	characteristic
35	C₂×C₂₃×#135	C₂²	1	2	yes	complemented
36	C₂²×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
37	C₂²×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
38	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
39	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
40	C₂²×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
41	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic
42	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
43	D₄×Q₈×C₂₃	—	2	2	no	—
44	D₄×Q₈×C₂₃	C₂²	1	4	yes	complemented
45	C₂₃×#548	—	2	2	no	—
46	C₂₃×#548	C₂²	1	4	yes	complemented
47	C₂₃×#547	—	2	2	no	—
48	C₂₃×#547	C₂²	1	4	yes	—
49	C₂₃×#546	—	2	2	no	—
50	C₂₃×#546	C₂²	1	4	yes	—
51	C₂₃×#536	—	2	2	no	—
52	C₂₃×#536	C₂²	1	1	yes	characteristic
53	C₂₃×#536	C₂²	1	1	yes	characteristic
54	C₂₃×#536	C₂²	1	1	yes	characteristic
55	C₂₃×#536	C₂²	1	1	yes	characteristic, complemented
56	C₂₃×#534	—	2	2	no	—
57	C₂₃×#525	—	2	2	no	—
58	C₂₃×#525	C₂²	1	1	yes	characteristic
59	C₂₃×#525	C₂²	1	1	yes	characteristic
60	C₂₃×#525	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₂₃×#123	—	2	2	no	—
62	C₂₃×#519	C₂²	1	1	yes	characteristic, complemented
63	C₂₃×#518	C₂²	1	1	yes	characteristic
64	C₂₃×#497	C₂²	1	2	yes	complemented
65	C₂₃×#497	C₂²	1	2	yes	complemented
66	C₂₃×#495	C₂²	1	2	yes	complemented
67	C₂₃×#494	C₂²	1	2	yes	complemented
68	C₂₃×#470	C₂²	1	4	yes	complemented
69	C₂₃×#470	C₂²	1	2	yes	complemented
70	C₂₃×#469	C₂²	1	2	yes	complemented
71	C₂₃×#468	C₂²	1	2	yes	complemented
72	C₂₃×#468	C₂²	1	2	yes	complemented
73	C₂₃×#467	C₂²	1	4	yes	complemented
74	C₂₃×#464	C₂²	1	4	yes	complemented
75	C₂₃×#463	C₂²	1	4	yes	complemented
76	C₂₃×#462	C₂²	1	4	yes	complemented
77	C₂₃×#461	C₂²	1	4	yes	complemented
78	C₂₃×#452	C₂²	1	4	yes	complemented
79	C₂₃×#452	C₂²	1	4	yes	complemented
80	C₂₃×#452	C₂²	1	4	yes	complemented
81	C₂₃×#451	C₂²	1	4	yes	complemented
82	C₂₃×#451	C₂²	1	4	yes	complemented
83	C₂₃×#450	C₂²	1	4	yes	complemented
84	C₂₃×#449	C₂²	1	4	yes	complemented
85	C₂₃×#448	C₂²	1	4	yes	complemented
86	C₂₃×#440	C₂²	1	4	yes	complemented
87	C₄×SD₁₆×C₂₃	C₂²	1	4	yes	complemented
88	C₂₃×#436	C₂²	1	4	yes	complemented
89	C₂₃×#435	C₂²	1	4	yes	complemented
90	C₂₃×#427	C₂²	1	1	yes	characteristic, complemented
91	C₂₃×#424	C₂²	1	1	yes	characteristic, complemented
92	C₂₃×#419	C₂²	1	1	yes	characteristic, complemented
93	C₂₃×#419	C₂²	1	1	yes	characteristic, complemented
94	C₂₃×#419	C₂²	1	1	yes	characteristic, complemented
95	C₂₃×#418	C₂²	1	1	yes	characteristic
96	C₂₃×#416	C₂²	1	1	yes	characteristic
97	C₂₃×#416	C₂²	1	1	yes	characteristic, complemented
98	C₂₃×#408	C₂²	1	1	yes	characteristic
99	C₂₃×#407	C₂²	1	1	yes	characteristic, complemented
100	C₂₃×#405	C₂²	1	1	yes	characteristic, complemented
101	C₂₃×2₋¹⁺⁴	—	2	4	no	—
102	C₂₃×2₋¹⁺⁴	—	4	2	no	—
103	C₂₃×H(5,𝔽₂)	—	2	4	no	—
104	C₂₃×H(5,𝔽₂)	—	4	2	no	—
105	C₂×#41×C₂₃	—	2	1	no	—
106	C₂×#41×C₂₃	—	2	1	no	—
107	C₂×#41×C₂₃	—	2	2	no	—
108	C₂×#41×C₂₃	—	2	2	no	—
109	C₂×#41×C₂₃	—	2	4	no	—
110	C₂×#41×C₂₃	—	4	2	no	—
111	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
112	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
113	C₂×#41×C₂₃	C₂³	1	2	yes	—
114	C₂×#41×C₂₃	C₂³	1	4	yes	—
115	C₂×#41×C₂₃	C₂³	1	2	yes	—
116	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
117	C₂²×Q₈×C₂₃	—	2	1	no	—
118	C₂²×Q₈×C₂₃	—	2	2	no	—
119	C₂²×Q₈×C₂₃	—	2	1	no	—
120	C₂²×Q₈×C₂₃	—	2	4	no	—
121	C₂²×Q₈×C₂₃	—	4	2	no	—
122	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
123	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
124	C₂²×Q₈×C₂₃	C₂³	1	4	yes	—
125	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
126	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
127	C₂²×D₄×C₂₃	—	2	1	no	—
128	C₂²×D₄×C₂₃	—	2	2	no	—
129	C₂²×D₄×C₂₃	—	2	1	no	—
130	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
131	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
132	C₂³×C₄×C₂₃	—	2	1	no	—
133	C₂³×C₄×C₂₃	—	2	1	no	—
134	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
135	C₂₃×#137	—	2	4	no	—
136	C₂₃×#137	—	2	16	no	—
137	C₂₃×#137	—	2	16	no	—
138	C₂₃×#137	—	2	8	no	—
139	C₂₃×#137	—	4	2	no	—
140	C₂₃×#137	—	4	2	no	—
141	C₂₃×AGL(1,ℤ/8)	—	2	4	no	—
142	C₂₃×AGL(1,ℤ/8)	—	2	8	no	—
143	C₂₃×#135	—	2	8	no	—
144	C₂₃×#135	—	2	4	no	—
145	C₂×Q₁₆×C₂₃	—	2	4	no	—
146	C₂×Q₁₆×C₂₃	—	2	4	no	—
147	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
148	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
149	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
150	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
151	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
152	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
153	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₂₃	—	2	4	no	—
155	C₂×SD₁₆×C₂₃	—	2	8	no	—
156	C₂×SD₁₆×C₂₃	D₄	1	8	yes	complemented
157	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
158	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
159	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
160	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
161	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
162	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
163	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
164	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
165	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
166	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
167	C₂×D₈×C₂₃	C₂³	1	2	yes	—
168	C₂₃×#131	—	2	4	no	—
169	C₂×M₁₆×C₂₃	—	2	4	no	—
170	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
171	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
172	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
173	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
174	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
175	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
176	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
177	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
178	C₂₃×C₄⋊Q₈	—	2	1	no	—
179	C₂₃×C₄⋊Q₈	—	2	1	no	—
180	C₂₃×C₄⋊Q₈	—	2	4	no	—
181	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
182	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
183	C₂₃×#124	—	2	1	no	—
184	C₂₃×#124	—	2	1	no	—
185	C₂₃×#124	—	2	4	no	—
186	C₂₃×#124	C₂³	1	2	yes	—
187	C₂₃×#124	C₂³	1	2	yes	—
188	C₂₃×#123	—	2	2	no	—
189	C₂₃×#123	—	2	2	no	—
190	C₂₃×#123	—	2	1	no	—
191	C₂₃×#123	—	2	1	no	—
192	C₂₃×#123	—	2	4	no	—
193	C₂₃×#123	—	2	4	no	—
194	C₂₃×#123	—	2	4	no	—
195	C₂₃×#123	—	2	2	no	—
196	C₂₃×#123	—	2	2	no	—
197	C₂₃×#123	D₄	1	2	yes	—
198	C₂₃×C₂²⋊Q₈	—	2	2	no	—
199	C₂₃×C₂²⋊Q₈	—	2	2	no	—
200	C₂₃×C₂²⋊Q₈	—	2	4	no	—
201	C₂₃×C₂²⋊Q₈	—	2	4	no	—
202	C₂₃×C₂²⋊Q₈	—	2	4	no	—
203	C₂₃×C₂²⋊Q₈	D₄	1	2	yes	—
204	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
205	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
206	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
207	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
208	C₂₃×#121	—	2	4	no	—
209	C₂₃×#121	—	2	4	no	—
210	C₂₃×#121	—	2	4	no	—
211	C₂₃×#121	D₄	1	2	yes	—
212	C₂₃×#121	C₂³	1	2	yes	—
213	C₂₃×#121	C₂³	1	2	yes	—
214	C₂₃×#120	—	2	1	no	—
215	C₂₃×#120	—	2	1	no	—
216	C₂₃×#120	—	2	4	no	—
217	C₂₃×#120	D₄	1	2	yes	—
218	C₄×Q₈×C₂₃	—	2	2	no	—
219	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
220	C₄×D₄×C₂₃	—	2	4	no	—
221	C₄×D₄×C₂₃	—	2	2	no	—
222	C₄×D₄×C₂₃	—	2	2	no	—
223	C₄×D₄×C₂₃	—	2	2	no	—
224	C₄×D₄×C₂₃	—	2	4	no	—
225	C₄×D₄×C₂₃	C₂³	1	4	yes	—
226	C₄×D₄×C₂₃	C₂³	1	4	yes	—
227	C₂₃×#117	—	2	2	no	—
228	C₂₃×#117	C₂³	1	1	yes	characteristic
229	C₂₃×#117	C₂³	1	1	yes	characteristic
230	C₂₃×#117	C₂³	1	1	yes	characteristic
231	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
232	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
233	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
234	C₂₃×#107	C₂³	1	2	yes	—
235	C₂₃×#106	C₂³	1	2	yes	—
236	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
237	C₂₃×#103	C₂³	1	2	yes	—
238	C₂₃×#103	C₂³	1	2	yes	—
239	C₂₃×#103	C₂³	1	4	yes	—
240	C₂₃×#103	C₂³	1	4	yes	—
241	C₂₃×#103	C₂³	1	4	yes	—
242	C₂₃×#102	C₂³	1	2	yes	—
243	C₂₃×#102	C₂³	1	2	yes	—
244	C₂₃×#102	C₂³	1	4	yes	—
245	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
246	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
247	C₂₃×#97	C₂³	1	2	yes	—
248	C₄×C₈×C₂₃	C₂³	1	2	yes	—
249	C₂⁴×C₂₃	—	2	1	no	—
250	C₂⁴×C₂₃	—	2	2	no	—
251	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
252	#41×C₂₃	—	2	2	no	—
253	#41×C₂₃	—	2	2	no	—
254	#41×C₂₃	—	2	4	no	—
255	#41×C₂₃	—	2	4	no	—
256	#41×C₂₃	—	2	8	no	—
257	#41×C₂₃	—	2	2	no	—
258	#41×C₂₃	—	2	2	no	—
259	#41×C₂₃	—	2	2	no	—
260	#41×C₂₃	—	2	2	no	—
261	#41×C₂₃	—	4	4	no	—
262	#41×C₂₃	—	4	2	no	—
263	#41×C₂₃	—	4	2	no	—
264	#41×C₂₃	—	4	8	no	—
265	#41×C₂₃	—	4	8	no	—
266	#41×C₂₃	—	4	4	no	—
267	#41×C₂₃	—	4	4	no	—
268	C₂×Q₈×C₂₃	—	2	1	no	—
269	C₂×Q₈×C₂₃	—	2	4	no	—
270	C₂×Q₈×C₂₃	—	2	1	no	—
271	C₂×Q₈×C₂₃	—	2	1	no	—
272	C₂×Q₈×C₂₃	—	2	2	no	—
273	C₂×Q₈×C₂₃	—	2	2	no	—
274	C₂×Q₈×C₂₃	—	2	4	no	—
275	C₂×Q₈×C₂₃	—	2	8	no	—
276	C₂×Q₈×C₂₃	—	2	2	no	—
277	C₂×Q₈×C₂₃	—	2	2	no	—
278	C₂×Q₈×C₂₃	—	2	2	no	—
279	C₂×Q₈×C₂₃	—	2	2	no	—
280	C₂×Q₈×C₂₃	—	4	4	no	—
281	C₂×Q₈×C₂₃	—	4	4	no	—
282	C₂×Q₈×C₂₃	—	4	2	no	—
283	C₂×Q₈×C₂₃	—	4	8	no	—
284	C₂×Q₈×C₂₃	—	4	4	no	—
285	C₂×Q₈×C₂₃	C₂×D₄	1	4	yes	—
286	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
287	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
288	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
289	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
290	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
291	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
292	C₂×D₄×C₂₃	—	2	4	no	—
293	C₂×D₄×C₂₃	—	2	2	no	—
294	C₂×D₄×C₂₃	—	2	4	no	—
295	C₂×D₄×C₂₃	—	2	1	no	—
296	C₂×D₄×C₂₃	—	2	1	no	—
297	C₂×D₄×C₂₃	—	2	2	no	—
298	C₂×D₄×C₂₃	—	2	2	no	—
299	C₂×D₄×C₂₃	—	2	2	no	—
300	C₂×D₄×C₂₃	—	2	1	no	—
301	C₂×D₄×C₂₃	—	2	2	no	—
302	C₂×D₄×C₂₃	—	2	2	no	—
303	C₂×D₄×C₂₃	—	4	2	no	—
304	C₂×D₄×C₂₃	—	4	4	no	—
305	C₂×D₄×C₂₃	—	4	8	no	—
306	C₂×D₄×C₂₃	—	4	4	no	—
307	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
308	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
309	C₂×D₄×C₂₃	C₂×D₄	1	4	yes	—
310	C₂×D₄×C₂₃	C₂×D₄	1	4	yes	—
311	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
312	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
313	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
314	C₂²×C₄×C₂₃	—	2	1	no	—
315	C₂²×C₄×C₂₃	—	2	2	no	—
316	C₂²×C₄×C₂₃	—	2	2	no	—
317	C₂²×C₄×C₂₃	—	2	4	no	—
318	C₂²×C₄×C₂₃	—	2	2	no	—
319	C₂²×C₄×C₂₃	—	2	1	no	—
320	C₂²×C₄×C₂₃	—	2	1	no	—
321	C₂²×C₄×C₂₃	—	2	4	no	—
322	C₂²×C₄×C₂₃	—	2	2	no	—
323	C₂²×C₄×C₂₃	—	2	1	no	—
324	C₂²×C₄×C₂₃	—	2	2	no	—
325	C₂²×C₄×C₂₃	—	2	1	no	—
326	C₂²×C₄×C₂₃	—	2	4	no	—
327	C₂²×C₄×C₂₃	—	4	4	no	—
328	C₂²×C₄×C₂₃	—	4	4	no	—
329	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
330	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
331	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
332	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
333	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
334	Q₁₆×C₂₃	—	2	8	no	—
335	Q₁₆×C₂₃	—	2	4	no	—
336	Q₁₆×C₂₃	—	2	4	no	—
337	Q₁₆×C₂₃	—	2	4	no	—
338	Q₁₆×C₂₃	—	2	2	no	—
339	Q₁₆×C₂₃	—	4	2	no	—
340	Q₁₆×C₂₃	—	4	2	no	—
341	SD₁₆×C₂₃	—	2	4	no	—
342	SD₁₆×C₂₃	—	2	4	no	—
343	SD₁₆×C₂₃	—	2	8	no	—
344	SD₁₆×C₂₃	—	2	2	no	—
345	SD₁₆×C₂₃	—	2	2	no	—
346	SD₁₆×C₂₃	—	4	2	no	—
347	SD₁₆×C₂₃	—	4	2	no	—
348	SD₁₆×C₂₃	C₂×D₄	1	8	yes	—
349	SD₁₆×C₂₃	C₂×D₄	1	8	yes	—
350	D₈×C₂₃	—	2	4	no	—
351	D₈×C₂₃	—	2	2	no	—
352	M₁₆×C₂₃	—	2	2	no	—
353	M₁₆×C₂₃	—	2	2	no	—
354	M₁₆×C₂₃	—	2	4	no	—
355	M₁₆×C₂₃	—	2	4	no	—
356	M₁₆×C₂₃	—	2	4	no	—
357	C₂×C₈×C₂₃	—	2	2	no	—
358	C₂×C₈×C₂₃	—	2	4	no	—
359	C₂×C₈×C₂₃	C₂×D₄	1	4	yes	—
360	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
361	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
362	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
363	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
364	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
365	C₄⋊C₄×C₂₃	—	2	2	no	—
366	C₄⋊C₄×C₂₃	—	2	4	no	—
367	C₄⋊C₄×C₂₃	—	2	4	no	—
368	C₄⋊C₄×C₂₃	—	2	4	no	—
369	C₄⋊C₄×C₂₃	—	2	4	no	—
370	C₄⋊C₄×C₂₃	—	2	4	no	—
371	C₄⋊C₄×C₂₃	—	2	2	no	—
372	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
373	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
374	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
375	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
376	C₂²⋊C₄×C₂₃	—	2	1	no	—
377	C₂²⋊C₄×C₂₃	—	2	4	no	—
378	C₂²⋊C₄×C₂₃	—	2	1	no	—
379	C₂²⋊C₄×C₂₃	—	2	2	no	—
380	C₂²⋊C₄×C₂₃	—	2	2	no	—
381	C₂²⋊C₄×C₂₃	—	2	4	no	—
382	C₂²⋊C₄×C₂₃	—	2	2	no	—
383	C₂²⋊C₄×C₂₃	—	2	4	no	—
384	C₂²⋊C₄×C₂₃	—	2	4	no	—
385	C₂²⋊C₄×C₂₃	—	2	4	no	—
386	C₂²⋊C₄×C₂₃	—	2	2	no	—
387	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
388	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
389	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
390	C₄²×C₂₃	—	2	4	no	—
391	C₄²×C₂₃	—	2	1	no	—
392	C₄²×C₂₃	—	2	1	no	—
393	C₄²×C₂₃	C₂⁴	1	2	yes	—
394	#61060	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
395	C₂³×C₂₃	—	2	2	no	—
396	C₂³×C₂₃	—	2	2	no	—
397	C₂³×C₂₃	—	2	4	no	—
398	C₂³×C₂₃	—	2	1	no	—
399	C₂³×C₂₃	—	2	1	no	—
400	C₂³×C₂₃	—	4	2	no	—
401	C₂³×C₂₃	—	4	4	no	—
402	C₂³×C₂₃	—	8	2	no	—
403	C₂³×C₂₃	—	8	4	no	—
404	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
405	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
406	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
407	Q₈×C₂₃	—	2	4	no	—
408	Q₈×C₂₃	—	2	2	no	—
409	Q₈×C₂₃	—	2	2	no	—
410	Q₈×C₂₃	—	2	1	no	—
411	Q₈×C₂₃	—	2	2	no	—
412	Q₈×C₂₃	—	2	1	no	—
413	Q₈×C₂₃	—	2	2	no	—
414	Q₈×C₂₃	—	2	2	no	—
415	Q₈×C₂₃	—	2	2	no	—
416	Q₈×C₂₃	—	2	1	no	—
417	Q₈×C₂₃	—	2	1	no	—
418	Q₈×C₂₃	—	4	8	no	—
419	Q₈×C₂₃	—	4	4	no	—
420	Q₈×C₂₃	—	4	2	no	—
421	Q₈×C₂₃	—	4	2	no	—
422	Q₈×C₂₃	C₂²×D₄	1	4	yes	—
423	D₄×C₂₃	—	2	4	no	—
424	D₄×C₂₃	—	2	4	no	—
425	D₄×C₂₃	—	2	2	no	—
426	D₄×C₂₃	—	2	1	no	—
427	D₄×C₂₃	—	2	1	no	—
428	D₄×C₂₃	—	2	2	no	—
429	D₄×C₂₃	—	2	1	no	—
430	D₄×C₂₃	—	2	1	no	—
431	D₄×C₂₃	—	4	4	no	—
432	D₄×C₂₃	—	4	4	no	—
433	D₄×C₂₃	—	4	4	no	—
434	D₄×C₂₃	—	4	4	no	—
435	D₄×C₂₃	—	4	8	no	—
436	D₄×C₂₃	—	4	4	no	—
437	D₄×C₂₃	—	4	2	no	—
438	D₄×C₂₃	—	4	2	no	—
439	D₄×C₂₃	—	8	2	no	—
440	D₄×C₂₃	C₂²×D₄	1	4	yes	—
441	C₂×C₄×C₂₃	—	2	2	no	—
442	C₂×C₄×C₂₃	—	2	4	no	—
443	C₂×C₄×C₂₃	—	2	2	no	—
444	C₂×C₄×C₂₃	—	2	4	no	—
445	C₂×C₄×C₂₃	—	2	2	no	—
446	C₂×C₄×C₂₃	—	2	2	no	—
447	C₂×C₄×C₂₃	—	2	2	no	—
448	C₂×C₄×C₂₃	—	2	2	no	—
449	C₂×C₄×C₂₃	—	2	2	no	—
450	C₂×C₄×C₂₃	—	2	2	no	—
451	C₂×C₄×C₂₃	—	2	2	no	—
452	C₂×C₄×C₂₃	—	2	2	no	—
453	C₂×C₄×C₂₃	—	2	1	no	—
454	C₂×C₄×C₂₃	—	2	1	no	—
455	C₂×C₄×C₂₃	—	4	4	no	—
456	C₂×C₄×C₂₃	—	4	8	no	—
457	C₂×C₄×C₂₃	—	4	8	no	—
458	C₂×C₄×C₂₃	—	4	4	no	—
459	C₂×C₄×C₂₃	—	4	4	no	—
460	C₂×C₄×C₂₃	—	4	2	no	—
461	C₂×C₄×C₂₃	—	4	2	no	—
462	C₂×C₄×C₂₃	—	4	2	no	—
463	C₂×C₄×C₂₃	—	4	2	no	—
464	C₂×C₄×C₂₃	—	8	4	no	—
465	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
466	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
467	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
468	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
469	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
470	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
471	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
472	C₈×C₂₃	—	2	2	no	—
473	C₈×C₂₃	—	2	2	no	—
474	C₈×C₂₃	—	2	2	no	—
475	C₈×C₂₃	C₂²×D₄	1	2	yes	—
476	C₈×C₂₃	C₂²×D₄	1	2	yes	—
477	C₂×#577	C₂×C₂₃	1	1	yes	characteristic, complemented
478	C₂²×#137	C₂×C₂₃	1	1	yes	characteristic, complemented
479	#3486	C₂×C₂₃	1	1	yes	characteristic, complemented
480	#3485	C₂×C₂₃	1	1	yes	characteristic, complemented
481	#3276	C₂×C₂₃	1	4	yes	complemented
482	#3275	C₂×C₂₃	1	4	yes	complemented
483	#3269	C₂×C₂₃	1	4	yes	complemented
484	#3266	C₂×C₂₃	1	4	yes	complemented
485	#3156	C₂×C₂₃	1	1	yes	characteristic, complemented
486	#3059	C₂×C₂₃	1	1	yes	characteristic, complemented
487	#3054	C₂×C₂₃	1	1	yes	characteristic, complemented
488	#3044	C₂×C₂₃	1	1	yes	characteristic, complemented
489	#3042	C₂×C₂₃	1	1	yes	characteristic, complemented
490	#3011	C₂×C₂₃	1	1	yes	characteristic, complemented
491	#3009	C₂×C₂₃	1	1	yes	characteristic, complemented
492	#3005	C₂×C₂₃	1	1	yes	characteristic, complemented
493	#3004	C₂×C₂₃	1	1	yes	characteristic, complemented
494	#2949	C₂×C₂₃	1	1	yes	characteristic, complemented
495	#2930	C₂×C₂₃	1	1	yes	characteristic, complemented
496	C₂²×C₂₃	—	2	2	no	—
497	C₂²×C₂₃	—	2	2	no	—
498	C₂²×C₂₃	—	2	4	no	—
499	C₂²×C₂₃	—	2	2	no	—
500	C₂²×C₂₃	—	2	2	no	—
501	C₂²×C₂₃	—	2	2	no	—
502	C₂²×C₂₃	—	2	4	no	—
503	C₂²×C₂₃	—	4	4	no	—
504	C₂²×C₂₃	—	4	4	no	—
505	C₂²×C₂₃	—	4	2	no	—
506	C₂²×C₂₃	—	4	2	no	—
507	C₂²×C₂₃	—	4	1	no	—
508	C₂²×C₂₃	—	4	1	no	—
509	C₂²×C₂₃	—	8	4	no	—
510	C₂²×C₂₃	—	16	4	no	—
511	C₂²×C₂₃	D₄²	1	2	yes	—
512	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
513	C₄×C₂₃	—	2	4	no	—
514	C₄×C₂₃	—	2	2	no	—
515	C₄×C₂₃	—	2	4	no	—
516	C₄×C₂₃	—	2	2	no	—
517	C₄×C₂₃	—	4	2	no	—
518	C₄×C₂₃	—	4	2	no	—
519	C₄×C₂₃	—	4	1	no	—
520	C₄×C₂₃	—	4	2	no	—
521	C₄×C₂₃	—	4	1	no	—
522	C₄×C₂₃	—	4	2	no	—
523	C₄×C₂₃	D₄²	1	2	yes	—
524	C₄×C₂₃	C₂³×D₄	1	1	yes	characteristic
525	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
526	C₂×2₋¹⁺⁴	C₂²×C₂₃	1	1	yes	characteristic
527	C₂×H(5,𝔽₂)	C₂²×C₂₃	1	1	yes	characteristic
528	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
529	C₂³×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
530	#577	—	2	8	no	—
531	C₂×#137	—	2	8	no	—
532	C₂×#137	C₂²×C₂₃	1	1	yes	characteristic
533	C₂×#137	C₂²×C₂₃	1	1	yes	characteristic
534	C₂×#137	C₂²×C₂₃	1	4	yes	complemented
535	C₂×#137	C₂²×C₂₃	1	4	yes	complemented
536	C₂×#137	C₂²×C₂₃	1	2	yes	complemented
537	C₂×#137	C₂²×C₂₃	1	1	yes	characteristic, complemented
538	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	1	yes	characteristic
539	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	2	yes	complemented
540	C₂×#135	C₂²×C₂₃	1	1	yes	characteristic
541	C₂×#135	C₂²×C₂₃	1	2	yes	complemented
542	C₂²×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
543	C₂²×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
544	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
545	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
546	C₂²×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
547	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic
548	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
549	D₄×Q₈	—	2	2	no	—
550	D₄×Q₈	C₂²×C₂₃	1	4	yes	complemented
551	#548	—	2	2	no	—
552	#548	C₂²×C₂₃	1	4	yes	complemented
553	#547	—	2	2	no	—
554	#547	C₂²×C₂₃	1	4	yes	—
555	#546	—	2	2	no	—
556	#546	C₂²×C₂₃	1	4	yes	—
557	#536	—	2	2	no	—
558	#536	C₂²×C₂₃	1	1	yes	characteristic
559	#536	C₂²×C₂₃	1	1	yes	characteristic
560	#536	C₂²×C₂₃	1	1	yes	characteristic
561	#536	C₂²×C₂₃	1	1	yes	characteristic, complemented
562	#534	—	2	2	no	—
563	#525	—	2	2	no	—
564	#525	C₂²×C₂₃	1	1	yes	characteristic
565	#525	C₂²×C₂₃	1	1	yes	characteristic
566	#525	C₂²×C₂₃	1	1	yes	characteristic, complemented
567	C₂×#123	—	2	2	no	—
568	#519	C₂²×C₂₃	1	1	yes	characteristic, complemented
569	#518	C₂²×C₂₃	1	1	yes	characteristic
570	#497	C₂²×C₂₃	1	2	yes	complemented
571	#497	C₂²×C₂₃	1	2	yes	complemented
572	#495	C₂²×C₂₃	1	2	yes	complemented
573	#494	C₂²×C₂₃	1	2	yes	complemented
574	#470	C₂²×C₂₃	1	4	yes	complemented
575	#470	C₂²×C₂₃	1	2	yes	complemented
576	#469	C₂²×C₂₃	1	2	yes	complemented
577	#468	C₂²×C₂₃	1	2	yes	complemented
578	#468	C₂²×C₂₃	1	2	yes	complemented
579	#467	C₂²×C₂₃	1	4	yes	complemented
580	#464	C₂²×C₂₃	1	4	yes	complemented
581	#463	C₂²×C₂₃	1	4	yes	complemented
582	#462	C₂²×C₂₃	1	4	yes	complemented
583	#461	C₂²×C₂₃	1	4	yes	complemented
584	#452	C₂²×C₂₃	1	4	yes	complemented
585	#452	C₂²×C₂₃	1	4	yes	complemented
586	#452	C₂²×C₂₃	1	4	yes	complemented
587	#451	C₂²×C₂₃	1	4	yes	complemented
588	#451	C₂²×C₂₃	1	4	yes	complemented
589	#450	C₂²×C₂₃	1	4	yes	complemented
590	#449	C₂²×C₂₃	1	4	yes	complemented
591	#448	C₂²×C₂₃	1	4	yes	complemented
592	#440	C₂²×C₂₃	1	4	yes	complemented
593	C₄×SD₁₆	C₂²×C₂₃	1	4	yes	complemented
594	#436	C₂²×C₂₃	1	4	yes	complemented
595	#435	C₂²×C₂₃	1	4	yes	complemented
596	#427	C₂²×C₂₃	1	1	yes	characteristic, complemented
597	#424	C₂²×C₂₃	1	1	yes	characteristic, complemented
598	#419	C₂²×C₂₃	1	1	yes	characteristic, complemented
599	#419	C₂²×C₂₃	1	1	yes	characteristic, complemented
600	#419	C₂²×C₂₃	1	1	yes	characteristic, complemented
601	#418	C₂²×C₂₃	1	1	yes	characteristic
602	#416	C₂²×C₂₃	1	1	yes	characteristic
603	#416	C₂²×C₂₃	1	1	yes	characteristic, complemented
604	#408	C₂²×C₂₃	1	1	yes	characteristic
605	#407	C₂²×C₂₃	1	1	yes	characteristic, complemented
606	#405	C₂²×C₂₃	1	1	yes	characteristic, complemented
607	C₂×C₂₃	—	2	2	no	—
608	C₂×C₂₃	—	4	2	no	—
609	C₂×C₂₃	—	4	2	no	—
610	C₂×C₂₃	—	4	4	no	—
611	C₂×C₂₃	—	8	1	no	—
612	C₂×C₂₃	—	8	1	no	—
613	C₂×C₂₃	C₂×D₄²	1	1	yes	characteristic
614	C₂×C₂₃	#3586	1	2	yes	—
615	2₋¹⁺⁴	—	2	4	no	—
616	2₋¹⁺⁴	—	4	2	no	—
617	H(5,𝔽₂)	—	2	4	no	—
618	H(5,𝔽₂)	—	4	2	no	—
619	C₂×#41	—	2	1	no	—
620	C₂×#41	—	2	2	no	—
621	C₂×#41	—	2	1	no	—
622	C₂×#41	—	2	2	no	—
623	C₂×#41	—	2	4	no	—
624	C₂×#41	—	4	2	no	—
625	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
626	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
627	C₂×#41	C₂³×C₂₃	1	4	yes	—
628	C₂×#41	C₂³×C₂₃	1	2	yes	—
629	C₂×#41	C₂³×C₂₃	1	2	yes	—
630	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
631	C₂²×Q₈	—	2	1	no	—
632	C₂²×Q₈	—	2	1	no	—
633	C₂²×Q₈	—	2	2	no	—
634	C₂²×Q₈	—	2	4	no	—
635	C₂²×Q₈	—	4	2	no	—
636	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
637	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
638	C₂²×Q₈	C₂³×C₂₃	1	4	yes	—
639	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
640	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
641	C₂²×D₄	—	2	1	no	—
642	C₂²×D₄	—	2	2	no	—
643	C₂²×D₄	—	2	1	no	—
644	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
645	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
646	C₂³×C₄	—	2	1	no	—
647	C₂³×C₄	—	2	1	no	—
648	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
649	#137	—	2	4	no	—
650	#137	—	2	16	no	—
651	#137	—	2	16	no	—
652	#137	—	2	8	no	—
653	#137	—	4	2	no	—
654	#137	—	4	2	no	—
655	AGL(1,ℤ/8)	—	2	4	no	—
656	AGL(1,ℤ/8)	—	2	8	no	—
657	#135	—	2	8	no	—
658	#135	—	2	4	no	—
659	C₂×Q₁₆	—	2	4	no	—
660	C₂×Q₁₆	—	2	4	no	—
661	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
662	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
663	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
664	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
665	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
666	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
667	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
668	C₂×SD₁₆	—	2	4	no	—
669	C₂×SD₁₆	—	2	8	no	—
670	C₂×SD₁₆	D₄×C₂₃	1	8	yes	complemented
671	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
672	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
673	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
674	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
675	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
676	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
677	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
678	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
679	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
680	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
681	C₂×D₈	C₂³×C₂₃	1	2	yes	—
682	#131	—	2	4	no	—
683	C₂×M₁₆	—	2	4	no	—
684	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
685	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
686	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
687	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
688	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
689	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
690	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
691	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
692	C₄⋊Q₈	—	2	1	no	—
693	C₄⋊Q₈	—	2	1	no	—
694	C₄⋊Q₈	—	2	4	no	—
695	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
696	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
697	#124	—	2	1	no	—
698	#124	—	2	1	no	—
699	#124	—	2	4	no	—
700	#124	C₂³×C₂₃	1	2	yes	—
701	#124	C₂³×C₂₃	1	2	yes	—
702	#123	—	2	2	no	—
703	#123	—	2	2	no	—
704	#123	—	2	1	no	—
705	#123	—	2	1	no	—
706	#123	—	2	4	no	—
707	#123	—	2	2	no	—
708	#123	—	2	4	no	—
709	#123	—	2	2	no	—
710	#123	—	2	4	no	—
711	#123	D₄×C₂₃	1	2	yes	—
712	C₂²⋊Q₈	—	2	4	no	—
713	C₂²⋊Q₈	—	2	2	no	—
714	C₂²⋊Q₈	—	2	2	no	—
715	C₂²⋊Q₈	—	2	4	no	—
716	C₂²⋊Q₈	—	2	4	no	—
717	C₂²⋊Q₈	D₄×C₂₃	1	2	yes	—
718	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
719	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
720	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
721	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
722	#121	—	2	4	no	—
723	#121	—	2	4	no	—
724	#121	—	2	4	no	—
725	#121	D₄×C₂₃	1	2	yes	—
726	#121	C₂³×C₂₃	1	2	yes	—
727	#121	C₂³×C₂₃	1	2	yes	—
728	#120	—	2	1	no	—
729	#120	—	2	1	no	—
730	#120	—	2	4	no	—
731	#120	D₄×C₂₃	1	2	yes	—
732	C₄×Q₈	—	2	2	no	—
733	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
734	C₄×D₄	—	2	4	no	—
735	C₄×D₄	—	2	2	no	—
736	C₄×D₄	—	2	2	no	—
737	C₄×D₄	—	2	2	no	—
738	C₄×D₄	—	2	4	no	—
739	C₄×D₄	C₂³×C₂₃	1	4	yes	—
740	C₄×D₄	C₂³×C₂₃	1	4	yes	—
741	#117	—	2	2	no	—
742	#117	C₂³×C₂₃	1	1	yes	characteristic
743	#117	C₂³×C₂₃	1	1	yes	characteristic
744	#117	C₂³×C₂₃	1	1	yes	characteristic
745	C₂×C₄⋊C₄	—	2	4	no	—
746	C₂×C₂²⋊C₄	—	2	2	no	—
747	C₂×C₂²⋊C₄	—	2	4	no	—
748	#107	C₂³×C₂₃	1	2	yes	—
749	#106	C₂³×C₂₃	1	2	yes	—
750	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
751	#103	C₂³×C₂₃	1	2	yes	—
752	#103	C₂³×C₂₃	1	2	yes	—
753	#103	C₂³×C₂₃	1	4	yes	—
754	#103	C₂³×C₂₃	1	4	yes	—
755	#103	C₂³×C₂₃	1	4	yes	—
756	#102	C₂³×C₂₃	1	2	yes	—
757	#102	C₂³×C₂₃	1	2	yes	—
758	#102	C₂³×C₂₃	1	4	yes	—
759	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
760	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
761	#97	C₂³×C₂₃	1	2	yes	—
762	C₄×C₈	C₂³×C₂₃	1	2	yes	—
763	C₂₃	#61060	1	1	yes	characteristic, direct product factor, Sylow
764	C₂⁴	—	2	1	no	—
765	C₂⁴	—	2	2	no	—
766	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
767	#41	—	2	2	no	—
768	#41	—	2	2	no	—
769	#41	—	2	4	no	—
770	#41	—	2	4	no	—
771	#41	—	2	8	no	—
772	#41	—	2	2	no	—
773	#41	—	2	2	no	—
774	#41	—	2	2	no	—
775	#41	—	2	2	no	—
776	#41	—	4	4	no	—
777	#41	—	4	2	no	—
778	#41	—	4	2	no	—
779	#41	—	4	8	no	—
780	#41	—	4	8	no	—
781	#41	—	4	4	no	—
782	#41	—	4	4	no	—
783	C₂×Q₈	—	2	1	no	—
784	C₂×Q₈	—	2	4	no	—
785	C₂×Q₈	—	2	1	no	—
786	C₂×Q₈	—	2	1	no	—
787	C₂×Q₈	—	2	2	no	—
788	C₂×Q₈	—	2	2	no	—
789	C₂×Q₈	—	2	4	no	—
790	C₂×Q₈	—	2	8	no	—
791	C₂×Q₈	—	2	2	no	—
792	C₂×Q₈	—	2	2	no	—
793	C₂×Q₈	—	2	2	no	—
794	C₂×Q₈	—	2	2	no	—
795	C₂×Q₈	—	4	4	no	—
796	C₂×Q₈	—	4	4	no	—
797	C₂×Q₈	—	4	2	no	—
798	C₂×Q₈	—	4	8	no	—
799	C₂×Q₈	—	4	4	no	—
800	C₂×Q₈	C₂×D₄×C₂₃	1	4	yes	—
801	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
802	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
803	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
804	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
805	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
806	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
807	C₂×D₄	—	2	4	no	—
808	C₂×D₄	—	2	2	no	—
809	C₂×D₄	—	2	4	no	—
810	C₂×D₄	—	2	1	no	—
811	C₂×D₄	—	2	1	no	—
812	C₂×D₄	—	2	2	no	—
813	C₂×D₄	—	2	2	no	—
814	C₂×D₄	—	2	2	no	—
815	C₂×D₄	—	2	1	no	—
816	C₂×D₄	—	2	2	no	—
817	C₂×D₄	—	2	2	no	—
818	C₂×D₄	—	4	2	no	—
819	C₂×D₄	—	4	4	no	—
820	C₂×D₄	—	4	8	no	—
821	C₂×D₄	—	4	4	no	—
822	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
823	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
824	C₂×D₄	C₂×D₄×C₂₃	1	4	yes	—
825	C₂×D₄	C₂×D₄×C₂₃	1	4	yes	—
826	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
827	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
828	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
829	C₂²×C₄	—	2	1	no	—
830	C₂²×C₄	—	2	2	no	—
831	C₂²×C₄	—	2	2	no	—
832	C₂²×C₄	—	2	4	no	—
833	C₂²×C₄	—	2	2	no	—
834	C₂²×C₄	—	2	1	no	—
835	C₂²×C₄	—	2	1	no	—
836	C₂²×C₄	—	2	4	no	—
837	C₂²×C₄	—	2	2	no	—
838	C₂²×C₄	—	2	1	no	—
839	C₂²×C₄	—	2	2	no	—
840	C₂²×C₄	—	2	1	no	—
841	C₂²×C₄	—	2	4	no	—
842	C₂²×C₄	—	4	4	no	—
843	C₂²×C₄	—	4	4	no	—
844	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
845	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
846	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
847	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
848	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
849	Q₁₆	—	2	8	no	—
850	Q₁₆	—	2	4	no	—
851	Q₁₆	—	2	4	no	—
852	Q₁₆	—	2	4	no	—
853	Q₁₆	—	2	2	no	—
854	Q₁₆	—	4	2	no	—
855	Q₁₆	—	4	2	no	—
856	SD₁₆	—	2	4	no	—
857	SD₁₆	—	2	4	no	—
858	SD₁₆	—	2	8	no	—
859	SD₁₆	—	2	2	no	—
860	SD₁₆	—	2	2	no	—
861	SD₁₆	—	4	2	no	—
862	SD₁₆	—	4	2	no	—
863	SD₁₆	C₂×D₄×C₂₃	1	8	yes	—
864	SD₁₆	C₂×D₄×C₂₃	1	8	yes	—
865	D₈	—	2	4	no	—
866	D₈	—	2	2	no	—
867	M₁₆	—	2	2	no	—
868	M₁₆	—	2	2	no	—
869	M₁₆	—	2	4	no	—
870	M₁₆	—	2	4	no	—
871	M₁₆	—	2	4	no	—
872	C₂×C₈	—	2	2	no	—
873	C₂×C₈	—	2	4	no	—
874	C₂×C₈	C₂×D₄×C₂₃	1	4	yes	—
875	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
876	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
877	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
878	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
879	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
880	C₄⋊C₄	—	2	2	no	—
881	C₄⋊C₄	—	2	4	no	—
882	C₄⋊C₄	—	2	4	no	—
883	C₄⋊C₄	—	2	4	no	—
884	C₄⋊C₄	—	2	4	no	—
885	C₄⋊C₄	—	2	4	no	—
886	C₄⋊C₄	—	2	2	no	—
887	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
888	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
889	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
890	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
891	C₂²⋊C₄	—	2	1	no	—
892	C₂²⋊C₄	—	2	4	no	—
893	C₂²⋊C₄	—	2	1	no	—
894	C₂²⋊C₄	—	2	2	no	—
895	C₂²⋊C₄	—	2	2	no	—
896	C₂²⋊C₄	—	2	4	no	—
897	C₂²⋊C₄	—	2	2	no	—
898	C₂²⋊C₄	—	2	4	no	—
899	C₂²⋊C₄	—	2	4	no	—
900	C₂²⋊C₄	—	2	4	no	—
901	C₂²⋊C₄	—	2	2	no	—
902	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
903	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
904	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
905	C₄²	—	2	4	no	—
906	C₄²	—	2	1	no	—
907	C₄²	—	2	1	no	—
908	C₄²	C₂⁴×C₂₃	1	2	yes	—
909	C₂³	—	2	2	no	—
910	C₂³	—	2	2	no	—
911	C₂³	—	2	4	no	—
912	C₂³	—	2	1	no	—
913	C₂³	—	2	1	no	—
914	C₂³	—	4	2	no	—
915	C₂³	—	4	4	no	—
916	C₂³	—	8	2	no	—
917	C₂³	—	8	4	no	—
918	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
919	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
920	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
921	Q₈	—	2	2	no	—
922	Q₈	—	2	4	no	—
923	Q₈	—	2	2	no	—
924	Q₈	—	2	1	no	—
925	Q₈	—	2	2	no	—
926	Q₈	—	2	1	no	—
927	Q₈	—	2	2	no	—
928	Q₈	—	2	2	no	—
929	Q₈	—	2	2	no	—
930	Q₈	—	2	1	no	—
931	Q₈	—	2	1	no	—
932	Q₈	—	4	8	no	—
933	Q₈	—	4	4	no	—
934	Q₈	—	4	2	no	—
935	Q₈	—	4	2	no	—
936	Q₈	C₂²×D₄×C₂₃	1	4	yes	—
937	D₄	—	2	4	no	—
938	D₄	—	2	1	no	—
939	D₄	—	2	1	no	—
940	D₄	—	2	2	no	—
941	D₄	—	2	1	no	—
942	D₄	—	2	1	no	—
943	D₄	—	2	4	no	—
944	D₄	—	2	2	no	—
945	D₄	—	4	4	no	—
946	D₄	—	4	4	no	—
947	D₄	—	4	4	no	—
948	D₄	—	4	4	no	—
949	D₄	—	4	8	no	—
950	D₄	—	4	4	no	—
951	D₄	—	4	2	no	—
952	D₄	—	4	2	no	—
953	D₄	—	8	2	no	—
954	D₄	C₂²×D₄×C₂₃	1	4	yes	—
955	C₂×C₄	—	2	2	no	—
956	C₂×C₄	—	2	2	no	—
957	C₂×C₄	—	2	4	no	—
958	C₂×C₄	—	2	2	no	—
959	C₂×C₄	—	2	2	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	2	2	no	—
962	C₂×C₄	—	2	4	no	—
963	C₂×C₄	—	2	2	no	—
964	C₂×C₄	—	2	2	no	—
965	C₂×C₄	—	2	2	no	—
966	C₂×C₄	—	2	2	no	—
967	C₂×C₄	—	2	1	no	—
968	C₂×C₄	—	2	1	no	—
969	C₂×C₄	—	4	4	no	—
970	C₂×C₄	—	4	8	no	—
971	C₂×C₄	—	4	8	no	—
972	C₂×C₄	—	4	4	no	—
973	C₂×C₄	—	4	4	no	—
974	C₂×C₄	—	4	2	no	—
975	C₂×C₄	—	4	2	no	—
976	C₂×C₄	—	4	2	no	—
977	C₂×C₄	—	4	2	no	—
978	C₂×C₄	—	8	4	no	—
979	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
980	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
981	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
982	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
983	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
984	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
985	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
986	C₈	—	2	2	no	—
987	C₈	—	2	2	no	—
988	C₈	—	2	2	no	—
989	C₈	C₂²×D₄×C₂₃	1	2	yes	—
990	C₈	C₂²×D₄×C₂₃	1	2	yes	—
991	C₂²	—	2	2	no	—
992	C₂²	—	2	2	no	—
993	C₂²	—	2	2	no	—
994	C₂²	—	2	4	no	—
995	C₂²	—	2	2	no	—
996	C₂²	—	2	4	no	—
997	C₂²	—	2	2	no	—
998	C₂²	—	4	4	no	—
999	C₂²	—	4	4	no	—
1000	C₂²	—	4	1	no	—
1001	C₂²	—	4	1	no	—
1002	C₂²	—	4	2	no	—
1003	C₂²	—	4	2	no	—
1004	C₂²	—	8	4	no	—
1005	C₂²	—	16	4	no	—
1006	C₂²	D₄²×C₂₃	1	2	yes	—
1007	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1008	C₄	—	2	2	no	—
1009	C₄	—	2	4	no	—
1010	C₄	—	2	2	no	—
1011	C₄	—	2	4	no	—
1012	C₄	—	4	1	no	—
1013	C₄	—	4	2	no	—
1014	C₄	—	4	1	no	—
1015	C₄	—	4	2	no	—
1016	C₄	—	4	2	no	—
1017	C₄	—	4	2	no	—
1018	C₄	D₄²×C₂₃	1	2	yes	—
1019	C₄	C₂³×D₄×C₂₃	1	1	yes	characteristic
1020	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1021	C₂	—	2	2	no	—
1022	C₂	—	4	2	no	—
1023	C₂	—	4	2	no	—
1024	C₂	—	4	4	no	—
1025	C₂	—	8	1	no	—
1026	C₂	—	8	1	no	—
1027	C₂	C₂×D₄²×C₂₃	1	1	yes	characteristic
1028	C₂	C₂₃×#3586	1	2	yes	—

	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×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#577	C₂	semidirect
2. C₂²×C₂₃×#137	C₂	semidirect
3. C₂₃×#3486	C₂	semidirect
4. C₂₃×#3485	C₂	semidirect
5. C₂₃×#3276	C₂	semidirect
6. C₂₃×#3275	C₂	semidirect
7. C₂₃×#3269	C₂	semidirect
8. C₂₃×#3266	C₂	semidirect
9. C₂₃×#3156	C₂	semidirect
10. C₂₃×#3059	C₂	semidirect
11. C₂₃×#3054	C₂	semidirect
12. C₂₃×#3044	C₂	semidirect
13. C₂₃×#3042	C₂	semidirect
14. C₂₃×#3011	C₂	semidirect
15. C₂₃×#3009	C₂	semidirect
16. C₂₃×#3005	C₂	semidirect
17. C₂₃×#3004	C₂	semidirect
18. C₂₃×#2949	C₂	semidirect
19. C₂₃×#2930	C₂	semidirect
23. C₂³×Q₈×C₂₃	C₂²	semidirect
28. C₂×C₂₃×#137	C₂²	semidirect
29. C₂×C₂₃×#137	C₂²	semidirect
30. C₂×C₂₃×#137	C₂²	semidirect
31. C₂×C₂₃×#137	C₂²	semidirect
33. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
35. C₂×C₂₃×#135	C₂²	semidirect
36. C₂²×Q₁₆×C₂₃	C₂²	semidirect
37. C₂²×Q₁₆×C₂₃	C₂²	semidirect
40. C₂²×SD₁₆×C₂₃	C₂²	semidirect
42. C₂²×M₁₆×C₂₃	C₂²	semidirect
44. D₄×Q₈×C₂₃	C₂²	semidirect
46. C₂₃×#548	C₂²	semidirect
55. C₂₃×#536	C₂²	semidirect
60. C₂₃×#525	C₂²	semidirect
62. C₂₃×#519	C₂²	semidirect
64. C₂₃×#497	C₂²	semidirect
65. C₂₃×#497	C₂²	semidirect
66. C₂₃×#495	C₂²	semidirect
67. C₂₃×#494	C₂²	semidirect
68. C₂₃×#470	C₂²	semidirect
69. C₂₃×#470	C₂²	semidirect
70. C₂₃×#469	C₂²	semidirect
71. C₂₃×#468	C₂²	semidirect
72. C₂₃×#468	C₂²	semidirect
73. C₂₃×#467	C₂²	semidirect
74. C₂₃×#464	C₂²	semidirect
75. C₂₃×#463	C₂²	semidirect
76. C₂₃×#462	C₂²	semidirect
77. C₂₃×#461	C₂²	semidirect
78. C₂₃×#452	C₂²	semidirect
79. C₂₃×#452	C₂²	semidirect
80. C₂₃×#452	C₂²	semidirect
81. C₂₃×#451	C₂²	semidirect
82. C₂₃×#451	C₂²	semidirect
83. C₂₃×#450	C₂²	semidirect
84. C₂₃×#449	C₂²	semidirect
85. C₂₃×#448	C₂²	semidirect
86. C₂₃×#440	C₂²	semidirect
87. C₄×SD₁₆×C₂₃	C₂²	semidirect
88. C₂₃×#436	C₂²	semidirect
89. C₂₃×#435	C₂²	semidirect
90. C₂₃×#427	C₂²	semidirect
91. C₂₃×#424	C₂²	semidirect
92. C₂₃×#419	C₂²	semidirect
93. C₂₃×#419	C₂²	semidirect
94. C₂₃×#419	C₂²	semidirect
97. C₂₃×#416	C₂²	semidirect
99. C₂₃×#407	C₂²	semidirect
100. C₂₃×#405	C₂²	semidirect
156. C₂×SD₁₆×C₂₃	D₄	semidirect
394. #61060	C₂₃	direct (N × H)
477. C₂×#577	C₂×C₂₃	semidirect
478. C₂²×#137	C₂×C₂₃	semidirect
479. #3486	C₂×C₂₃	semidirect
480. #3485	C₂×C₂₃	semidirect
481. #3276	C₂×C₂₃	semidirect
482. #3275	C₂×C₂₃	semidirect
483. #3269	C₂×C₂₃	semidirect
484. #3266	C₂×C₂₃	semidirect
485. #3156	C₂×C₂₃	semidirect
486. #3059	C₂×C₂₃	semidirect
487. #3054	C₂×C₂₃	semidirect
488. #3044	C₂×C₂₃	semidirect
489. #3042	C₂×C₂₃	semidirect
490. #3011	C₂×C₂₃	semidirect
491. #3009	C₂×C₂₃	semidirect
492. #3005	C₂×C₂₃	semidirect
493. #3004	C₂×C₂₃	semidirect
494. #2949	C₂×C₂₃	semidirect
495. #2930	C₂×C₂₃	semidirect
529. C₂³×Q₈	C₂²×C₂₃	semidirect
534. C₂×#137	C₂²×C₂₃	semidirect
535. C₂×#137	C₂²×C₂₃	semidirect
536. C₂×#137	C₂²×C₂₃	semidirect
537. C₂×#137	C₂²×C₂₃	semidirect
539. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
541. C₂×#135	C₂²×C₂₃	semidirect
542. C₂²×Q₁₆	C₂²×C₂₃	semidirect
543. C₂²×Q₁₆	C₂²×C₂₃	semidirect
546. C₂²×SD₁₆	C₂²×C₂₃	semidirect
548. C₂²×M₁₆	C₂²×C₂₃	semidirect
550. D₄×Q₈	C₂²×C₂₃	semidirect
552. #548	C₂²×C₂₃	semidirect
561. #536	C₂²×C₂₃	semidirect
566. #525	C₂²×C₂₃	semidirect
568. #519	C₂²×C₂₃	semidirect
570. #497	C₂²×C₂₃	semidirect
571. #497	C₂²×C₂₃	semidirect
572. #495	C₂²×C₂₃	semidirect
573. #494	C₂²×C₂₃	semidirect
574. #470	C₂²×C₂₃	semidirect
575. #470	C₂²×C₂₃	semidirect
576. #469	C₂²×C₂₃	semidirect
577. #468	C₂²×C₂₃	semidirect
578. #468	C₂²×C₂₃	semidirect
579. #467	C₂²×C₂₃	semidirect
580. #464	C₂²×C₂₃	semidirect
581. #463	C₂²×C₂₃	semidirect
582. #462	C₂²×C₂₃	semidirect
583. #461	C₂²×C₂₃	semidirect
584. #452	C₂²×C₂₃	semidirect
585. #452	C₂²×C₂₃	semidirect
586. #452	C₂²×C₂₃	semidirect
587. #451	C₂²×C₂₃	semidirect
588. #451	C₂²×C₂₃	semidirect
589. #450	C₂²×C₂₃	semidirect
590. #449	C₂²×C₂₃	semidirect
591. #448	C₂²×C₂₃	semidirect
592. #440	C₂²×C₂₃	semidirect
593. C₄×SD₁₆	C₂²×C₂₃	semidirect
594. #436	C₂²×C₂₃	semidirect
595. #435	C₂²×C₂₃	semidirect
596. #427	C₂²×C₂₃	semidirect
597. #424	C₂²×C₂₃	semidirect
598. #419	C₂²×C₂₃	semidirect
599. #419	C₂²×C₂₃	semidirect
600. #419	C₂²×C₂₃	semidirect
603. #416	C₂²×C₂₃	semidirect
605. #407	C₂²×C₂₃	semidirect
606. #405	C₂²×C₂₃	semidirect
670. C₂×SD₁₆	D₄×C₂₃	semidirect
763. C₂₃	#61060	direct (N × H)

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
C₂²×C₂₃×#137	2
C₂₃×#3486	2
C₂₃×#3485	2
C₂₃×#3276	2
C₂₃×#3275	2
C₂₃×#3269	2
C₂₃×#3266	2
C₂₃×#3156	2
C₂₃×#3059	2
C₂₃×#3054	2
C₂₃×#3044	2
C₂₃×#3042	2
C₂₃×#3011	2
C₂₃×#3009	2
C₂₃×#3005	2
C₂₃×#3004	2
C₂₃×#2949	2
C₂₃×#2930	2
#61060	23

Subgroups — C23×#61060 #19208686

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61060 #19208686