Subgroups — C₂₃×#21468 #19169094

Order 5888.

1320 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#568	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3002	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂₃×#444	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₂₃×#443	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2930	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#1876	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#1876	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#1871	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#1866	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#1866	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1855	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#1789	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#1765	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#1764	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#1753	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
17	C₂×C₂₃×#135	C₂²	1	1	yes	characteristic
18	C₂×C₂₃×#135	C₂²	1	1	yes	characteristic
19	C₂₃×#568	—	2	4	no	—
20	C₂₃×#568	—	2	4	no	—
21	C₂×C₂₃×#131	—	2	1	no	—
22	C₂×C₂₃×#131	—	2	1	no	—
23	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic
24	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic
25	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic
26	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic
27	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic, complemented
28	C₂²×M₁₆×C₂₃	—	2	1	no	—
29	C₂²×M₁₆×C₂₃	—	2	1	no	—
30	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
31	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
32	C₂₃×#525	C₂²	1	1	yes	characteristic
33	C₂₃×#452	C₄	1	1	yes	characteristic, complemented
34	C₂₃×#452	C₄	1	1	yes	characteristic, complemented
35	C₂₃×#451	C₄	1	1	yes	characteristic, complemented
36	C₂₃×#450	C₄	1	1	yes	characteristic, complemented
37	C₂₃×#449	C₄	1	1	yes	characteristic, complemented
38	C₂₃×#449	C₄	1	1	yes	characteristic, complemented
39	C₂₃×#448	C₄	1	1	yes	characteristic, complemented
40	C₂₃×#447	C₄	1	1	yes	characteristic, complemented
41	C₂₃×#444	—	2	4	no	—
42	C₂₃×#443	—	2	4	no	—
43	C₂₃×#436	—	2	1	no	—
44	C₂₃×#436	—	2	1	no	—
45	C₂₃×#435	—	2	1	no	—
46	C₂₃×#435	—	2	1	no	—
47	C₂×C₂₃×#108	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₂₃×#108	C₂²	1	1	yes	characteristic, complemented
49	C₂₃×#424	C₂²	1	1	yes	characteristic, complemented
50	C₂×C₂₃×#104	C₂²	1	1	yes	characteristic
51	C₂×C₂₃×#104	C₂²	1	1	yes	characteristic
52	C₂×C₂₃×#104	C₂²	1	1	yes	characteristic
53	C₂×C₂₃×#104	C₂²	1	1	yes	characteristic
54	C₂×C₂₃×#104	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₂₃×#104	C₂²	1	1	yes	characteristic, complemented
56	C₂₃×#416	C₂²	1	1	yes	characteristic
57	C₂₃×#416	C₂²	1	1	yes	characteristic
58	C₂₃×#408	C₂²	1	1	yes	characteristic, complemented
59	C₂₃×#407	C₂²	1	1	yes	characteristic
60	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
61	C₂₃×#405	C₂²	1	1	yes	characteristic, complemented
62	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic, complemented
63	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
64	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
65	C₂₃×#341	C₂²	1	1	yes	characteristic, complemented
66	C₂₃×#341	C₂²	1	1	yes	characteristic, complemented
67	C₂₃×#339	C₂²	1	1	yes	characteristic, complemented
68	C₂₃×#339	C₂²	1	1	yes	characteristic, complemented
69	C₂₃×#336	C₂²	1	1	yes	characteristic, complemented
70	C₂₃×#336	C₂²	1	1	yes	characteristic, complemented
71	C₂×#41×C₂₃	—	2	2	no	—
72	C₂×#41×C₂₃	—	2	2	no	—
73	C₂×#41×C₂₃	—	2	2	no	—
74	C₂×#41×C₂₃	—	2	2	no	—
75	C₂×#41×C₂₃	—	2	1	no	—
76	C₂×#41×C₂₃	—	2	1	no	—
77	C₂×#41×C₂₃	C₂×C₄	1	1	yes	characteristic
78	C₂×#41×C₂₃	C₂×C₄	1	1	yes	characteristic
79	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
80	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
81	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
82	C₂²×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
83	C₂²×D₄×C₂₃	—	2	1	no	—
84	C₂²×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
85	C₂³×C₄×C₂₃	—	2	1	no	—
86	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
87	C₂₃×#135	—	2	2	no	—
88	C₂₃×#135	—	2	2	no	—
89	C₂₃×#135	—	2	2	no	—
90	C₂₃×#135	—	2	2	no	—
91	C₂×Q₁₆×C₂₃	C₂×C₄	1	1	yes	characteristic
92	C₂×Q₁₆×C₂₃	C₂×C₄	1	1	yes	characteristic
93	C₂×SD₁₆×C₂₃	C₂×C₄	1	1	yes	characteristic
94	C₂×SD₁₆×C₂₃	C₂×C₄	1	1	yes	characteristic
95	C₂×SD₁₆×C₂₃	C₂×C₄	1	1	yes	characteristic
96	C₂×SD₁₆×C₂₃	C₂×C₄	1	1	yes	characteristic
97	C₂×D₈×C₂₃	C₂×C₄	1	1	yes	characteristic
98	C₂×D₈×C₂₃	C₂×C₄	1	1	yes	characteristic
99	C₂₃×#131	—	2	8	no	—
100	C₂₃×#131	—	2	8	no	—
101	C₂₃×#131	—	2	2	no	—
102	C₂₃×#131	—	2	2	no	—
103	C₂₃×#131	—	2	2	no	—
104	C₂₃×#131	—	2	2	no	—
105	C₂₃×#131	—	2	2	no	—
106	C₂₃×#131	—	2	2	no	—
107	C₂₃×#131	—	2	2	no	—
108	C₂₃×#131	—	2	2	no	—
109	C₂₃×#131	D₄	1	4	yes	complemented
110	C₂₃×#131	D₄	1	4	yes	complemented
111	C₂×M₁₆×C₂₃	—	2	8	no	—
112	C₂×M₁₆×C₂₃	—	2	8	no	—
113	C₂×M₁₆×C₂₃	—	2	1	no	—
114	C₂×M₁₆×C₂₃	—	2	2	no	—
115	C₂×M₁₆×C₂₃	—	2	2	no	—
116	C₂×M₁₆×C₂₃	—	2	1	no	—
117	C₂×M₁₆×C₂₃	—	2	1	no	—
118	C₂×M₁₆×C₂₃	—	2	1	no	—
119	C₂×M₁₆×C₂₃	—	2	1	no	—
120	C₂×M₁₆×C₂₃	—	2	2	no	—
121	C₂×M₁₆×C₂₃	—	2	2	no	—
122	C₂×M₁₆×C₂₃	—	2	1	no	—
123	C₂×M₁₆×C₂₃	D₄	1	1	yes	characteristic
124	C₂×M₁₆×C₂₃	D₄	1	1	yes	characteristic
125	C₂×M₁₆×C₂₃	D₄	1	1	yes	characteristic
126	C₂×M₁₆×C₂₃	D₄	1	1	yes	characteristic
127	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
128	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
129	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
130	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
131	C₂²×C₈×C₂₃	—	2	1	no	—
132	C₂²×C₈×C₂₃	—	2	1	no	—
133	C₂²×C₈×C₂₃	—	2	1	no	—
134	C₂²×C₈×C₂₃	—	2	1	no	—
135	C₂²×C₈×C₂₃	—	2	1	no	—
136	C₂²×C₈×C₂₃	—	2	1	no	—
137	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
138	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
139	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
140	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
141	C₂₃×#123	—	2	1	no	—
142	C₂₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
143	C₂₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
144	C₂₃×#121	C₂×C₄	1	1	yes	characteristic
145	C₂₃×#121	C₂×C₄	1	1	yes	characteristic
146	C₂₃×#120	—	2	1	no	—
147	C₄×D₄×C₂₃	—	2	1	no	—
148	C₄×D₄×C₂₃	—	2	1	no	—
149	C₂₃×#117	C₂³	1	1	yes	characteristic
150	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
151	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
152	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
153	C₂₃×#108	—	2	2	no	—
154	C₂₃×#108	—	2	2	no	—
155	C₂₃×C₄⋊C₈	—	2	1	no	—
156	C₂₃×C₄⋊C₈	—	2	1	no	—
157	C₂₃×#104	—	2	2	no	—
158	C₂₃×#104	—	2	2	no	—
159	C₂₃×#104	—	2	2	no	—
160	C₂₃×#104	—	2	2	no	—
161	C₂₃×#104	—	2	2	no	—
162	C₂₃×#104	—	2	2	no	—
163	C₂₃×#103	C₂×C₄	1	1	yes	characteristic
164	C₂₃×#103	C₂×C₄	1	1	yes	characteristic
165	C₂₃×#103	C₂×C₄	1	1	yes	characteristic
166	C₂₃×#103	C₂×C₄	1	1	yes	characteristic
167	C₂₃×#102	C₂×C₄	1	1	yes	characteristic
168	C₂₃×#102	C₂×C₄	1	1	yes	characteristic
169	C₂₃×#102	C₂×C₄	1	1	yes	characteristic
170	C₂₃×#102	C₂×C₄	1	1	yes	characteristic
171	C₂₃×C₂²⋊C₈	—	2	1	no	—
172	C₂₃×C₂²⋊C₈	—	2	1	no	—
173	C₂₃×C₂²⋊C₈	—	2	1	no	—
174	C₂₃×C₂²⋊C₈	—	2	1	no	—
175	C₂₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
176	C₂₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
177	C₂₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
178	C₂₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
179	C₂₃×#97	—	2	2	no	—
180	C₂₃×#97	—	2	1	no	—
181	C₄×C₈×C₂₃	—	2	2	no	—
182	C₄×C₈×C₂₃	—	2	1	no	—
183	C₂₃×#95	—	2	1	no	—
184	C₂⁴×C₂₃	—	2	1	no	—
185	C₂⁴×C₂₃	#41	1	1	yes	characteristic
186	#41×C₂₃	—	2	4	no	—
187	#41×C₂₃	—	2	4	no	—
188	#41×C₂₃	—	2	4	no	—
189	#41×C₂₃	—	2	4	no	—
190	#41×C₂₃	—	2	2	no	—
191	#41×C₂₃	—	2	2	no	—
192	#41×C₂₃	—	2	2	no	—
193	#41×C₂₃	—	2	2	no	—
194	#41×C₂₃	—	2	1	no	—
195	#41×C₂₃	—	2	1	no	—
196	#41×C₂₃	—	2	1	no	—
197	#41×C₂₃	—	2	1	no	—
198	#41×C₂₃	—	2	1	no	—
199	#41×C₂₃	—	2	1	no	—
200	#41×C₂₃	—	2	1	no	—
201	#41×C₂₃	—	2	1	no	—
202	#41×C₂₃	C₂×D₄	1	2	yes	—
203	#41×C₂₃	C₂×D₄	1	2	yes	—
204	#41×C₂₃	#41	1	2	yes	—
205	#41×C₂₃	#41	1	2	yes	—
206	C₂×Q₈×C₂₃	—	2	2	no	—
207	C₂×Q₈×C₂₃	—	2	2	no	—
208	C₂×Q₈×C₂₃	—	2	1	no	—
209	C₂×Q₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
210	C₂×Q₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
211	C₂×Q₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
212	C₂×D₄×C₂₃	—	2	4	no	—
213	C₂×D₄×C₂₃	—	2	4	no	—
214	C₂×D₄×C₂₃	—	2	1	no	—
215	C₂×D₄×C₂₃	—	2	1	no	—
216	C₂×D₄×C₂₃	—	2	1	no	—
217	C₂×D₄×C₂₃	—	2	1	no	—
218	C₂×D₄×C₂₃	—	2	2	no	—
219	C₂×D₄×C₂₃	—	2	2	no	—
220	C₂×D₄×C₂₃	—	2	1	no	—
221	C₂×D₄×C₂₃	—	2	1	no	—
222	C₂×D₄×C₂₃	—	2	1	no	—
223	C₂×D₄×C₂₃	—	2	1	no	—
224	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
225	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
226	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
227	C₂²×C₄×C₂₃	—	2	4	no	—
228	C₂²×C₄×C₂₃	—	2	4	no	—
229	C₂²×C₄×C₂₃	—	2	1	no	—
230	C₂²×C₄×C₂₃	—	2	1	no	—
231	C₂²×C₄×C₂₃	—	2	1	no	—
232	C₂²×C₄×C₂₃	—	2	1	no	—
233	C₂²×C₄×C₂₃	—	2	1	no	—
234	C₂²×C₄×C₂₃	—	2	1	no	—
235	C₂²×C₄×C₂₃	—	2	1	no	—
236	C₂²×C₄×C₂₃	—	2	1	no	—
237	C₂²×C₄×C₂₃	—	2	1	no	—
238	C₂²×C₄×C₂₃	—	2	1	no	—
239	C₂²×C₄×C₂₃	—	2	1	no	—
240	C₂²×C₄×C₂₃	—	2	1	no	—
241	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
242	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
243	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
244	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
245	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
246	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
247	Q₁₆×C₂₃	—	2	2	no	—
248	Q₁₆×C₂₃	—	2	2	no	—
249	SD₁₆×C₂₃	—	2	2	no	—
250	SD₁₆×C₂₃	—	2	2	no	—
251	SD₁₆×C₂₃	—	2	2	no	—
252	SD₁₆×C₂₃	—	2	2	no	—
253	D₈×C₂₃	—	2	2	no	—
254	D₈×C₂₃	—	2	2	no	—
255	M₁₆×C₂₃	—	2	4	no	—
256	M₁₆×C₂₃	—	2	4	no	—
257	M₁₆×C₂₃	—	2	4	no	—
258	M₁₆×C₂₃	—	2	1	no	—
259	M₁₆×C₂₃	—	2	1	no	—
260	M₁₆×C₂₃	—	2	2	no	—
261	M₁₆×C₂₃	—	2	2	no	—
262	M₁₆×C₂₃	—	2	4	no	—
263	M₁₆×C₂₃	—	2	4	no	—
264	M₁₆×C₂₃	—	2	2	no	—
265	M₁₆×C₂₃	—	2	2	no	—
266	M₁₆×C₂₃	—	2	1	no	—
267	M₁₆×C₂₃	—	2	1	no	—
268	M₁₆×C₂₃	—	2	1	no	—
269	M₁₆×C₂₃	—	2	1	no	—
270	M₁₆×C₂₃	—	4	2	no	—
271	M₁₆×C₂₃	C₂×D₄	1	2	yes	—
272	M₁₆×C₂₃	C₂×D₄	1	2	yes	—
273	C₂×C₈×C₂₃	—	2	4	no	—
274	C₂×C₈×C₂₃	—	2	4	no	—
275	C₂×C₈×C₂₃	—	2	4	no	—
276	C₂×C₈×C₂₃	—	2	1	no	—
277	C₂×C₈×C₂₃	—	2	1	no	—
278	C₂×C₈×C₂₃	—	2	1	no	—
279	C₂×C₈×C₂₃	—	2	1	no	—
280	C₂×C₈×C₂₃	—	2	1	no	—
281	C₂×C₈×C₂₃	—	2	1	no	—
282	C₂×C₈×C₂₃	—	2	1	no	—
283	C₂×C₈×C₂₃	—	2	1	no	—
284	C₂×C₈×C₂₃	—	2	4	no	—
285	C₂×C₈×C₂₃	—	2	4	no	—
286	C₂×C₈×C₂₃	—	2	1	no	—
287	C₂×C₈×C₂₃	—	2	1	no	—
288	C₂×C₈×C₂₃	—	4	2	no	—
289	C₂×C₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
290	C₂×C₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
291	C₂×C₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
292	C₂×C₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
293	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
294	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
295	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
296	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
297	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
298	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
299	C₄⋊C₄×C₂₃	—	2	1	no	—
300	C₄⋊C₄×C₂₃	—	2	1	no	—
301	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
302	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
303	C₂²⋊C₄×C₂₃	—	2	1	no	—
304	C₂²⋊C₄×C₂₃	—	2	1	no	—
305	C₂²⋊C₄×C₂₃	—	2	1	no	—
306	C₂²⋊C₄×C₂₃	—	2	1	no	—
307	C₂²⋊C₄×C₂₃	—	2	1	no	—
308	C₂²⋊C₄×C₂₃	—	4	2	no	—
309	C₄²×C₂₃	—	2	1	no	—
310	C₄²×C₂₃	—	2	1	no	—
311	C₄²×C₂₃	—	2	1	no	—
312	C₄²×C₂₃	—	2	1	no	—
313	C₄²×C₂₃	—	2	1	no	—
314	#21468	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
315	C₂³×C₂₃	—	2	4	no	—
316	C₂³×C₂₃	—	2	1	no	—
317	C₂³×C₂₃	—	2	1	no	—
318	C₂³×C₂₃	—	2	1	no	—
319	C₂³×C₂₃	—	2	1	no	—
320	C₂³×C₂₃	—	2	1	no	—
321	C₂³×C₂₃	—	4	1	no	—
322	C₂³×C₂₃	—	4	1	no	—
323	C₂³×C₂₃	—	8	1	no	—
324	C₂³×C₂₃	—	8	1	no	—
325	C₂³×C₂₃	C₄×D₄	1	1	yes	characteristic
326	C₂³×C₂₃	C₄×D₄	1	1	yes	characteristic
327	C₂³×C₂₃	C₂×#41	1	1	yes	characteristic
328	Q₈×C₂₃	—	2	4	no	—
329	Q₈×C₂₃	—	2	1	no	—
330	Q₈×C₂₃	—	2	1	no	—
331	Q₈×C₂₃	—	2	1	no	—
332	Q₈×C₂₃	—	2	1	no	—
333	Q₈×C₂₃	C₄×D₄	1	2	yes	—
334	Q₈×C₂₃	C₄×D₄	1	2	yes	—
335	D₄×C₂₃	—	2	4	no	—
336	D₄×C₂₃	—	2	4	no	—
337	D₄×C₂₃	—	2	4	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	1	no	—
343	D₄×C₂₃	—	2	1	no	—
344	D₄×C₂₃	—	2	1	no	—
345	D₄×C₂₃	—	2	1	no	—
346	D₄×C₂₃	—	4	1	no	—
347	D₄×C₂₃	—	4	1	no	—
348	D₄×C₂₃	—	8	1	no	—
349	D₄×C₂₃	—	8	1	no	—
350	D₄×C₂₃	C₄×D₄	1	2	yes	—
351	D₄×C₂₃	C₄×D₄	1	2	yes	—
352	C₂×C₄×C₂₃	—	2	4	no	—
353	C₂×C₄×C₂₃	—	2	4	no	—
354	C₂×C₄×C₂₃	—	2	4	no	—
355	C₂×C₄×C₂₃	—	2	1	no	—
356	C₂×C₄×C₂₃	—	2	1	no	—
357	C₂×C₄×C₂₃	—	2	1	no	—
358	C₂×C₄×C₂₃	—	2	1	no	—
359	C₂×C₄×C₂₃	—	2	1	no	—
360	C₂×C₄×C₂₃	—	2	1	no	—
361	C₂×C₄×C₂₃	—	2	1	no	—
362	C₂×C₄×C₂₃	—	2	1	no	—
363	C₂×C₄×C₂₃	—	2	2	no	—
364	C₂×C₄×C₂₃	—	2	2	no	—
365	C₂×C₄×C₂₃	—	2	1	no	—
366	C₂×C₄×C₂₃	—	2	1	no	—
367	C₂×C₄×C₂₃	—	2	1	no	—
368	C₂×C₄×C₂₃	—	2	2	no	—
369	C₂×C₄×C₂₃	—	2	2	no	—
370	C₂×C₄×C₂₃	—	2	1	no	—
371	C₂×C₄×C₂₃	—	2	2	no	—
372	C₂×C₄×C₂₃	—	2	1	no	—
373	C₂×C₄×C₂₃	—	2	1	no	—
374	C₂×C₄×C₂₃	—	2	1	no	—
375	C₂×C₄×C₂₃	—	4	1	no	—
376	C₂×C₄×C₂₃	—	4	1	no	—
377	C₂×C₄×C₂₃	—	4	1	no	—
378	C₂×C₄×C₂₃	—	4	1	no	—
379	C₂×C₄×C₂₃	—	4	1	no	—
380	C₂×C₄×C₂₃	—	4	1	no	—
381	C₂×C₄×C₂₃	—	4	1	no	—
382	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
383	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
384	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
385	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
386	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
387	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
388	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
389	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
390	C₈×C₂₃	—	2	1	no	—
391	C₈×C₂₃	—	2	1	no	—
392	C₈×C₂₃	—	2	1	no	—
393	C₈×C₂₃	—	2	1	no	—
394	C₈×C₂₃	—	2	2	no	—
395	C₈×C₂₃	—	2	2	no	—
396	C₈×C₂₃	—	2	1	no	—
397	C₈×C₂₃	—	2	1	no	—
398	C₈×C₂₃	—	4	1	no	—
399	C₈×C₂₃	—	4	1	no	—
400	C₈×C₂₃	#120	1	2	yes	—
401	C₈×C₂₃	#120	1	2	yes	—
402	C₂×#568	C₂×C₂₃	1	1	yes	characteristic, complemented
403	#3002	C₂×C₂₃	1	1	yes	characteristic
404	C₂×#444	C₂×C₂₃	1	1	yes	characteristic, complemented
405	C₂×#443	C₂×C₂₃	1	1	yes	characteristic, complemented
406	#2930	C₂×C₂₃	1	1	yes	characteristic, complemented
407	#1876	C₂×C₂₃	1	1	yes	characteristic, complemented
408	#1876	C₂×C₂₃	1	1	yes	characteristic, complemented
409	#1871	C₂×C₂₃	1	1	yes	characteristic, complemented
410	#1866	C₂×C₂₃	1	1	yes	characteristic, complemented
411	#1866	C₂×C₂₃	1	1	yes	characteristic, complemented
412	#1855	C₂×C₂₃	1	1	yes	characteristic, complemented
413	#1789	C₂×C₂₃	1	1	yes	characteristic, complemented
414	#1765	C₂×C₂₃	1	1	yes	characteristic, complemented
415	#1764	C₂×C₂₃	1	1	yes	characteristic, complemented
416	#1753	C₂×C₂₃	1	1	yes	characteristic, complemented
417	C₂²×C₂₃	—	2	1	no	—
418	C₂²×C₂₃	—	2	1	no	—
419	C₂²×C₂₃	—	2	1	no	—
420	C₂²×C₂₃	—	2	1	no	—
421	C₂²×C₂₃	—	2	1	no	—
422	C₂²×C₂₃	—	2	1	no	—
423	C₂²×C₂₃	—	2	1	no	—
424	C₂²×C₂₃	—	2	1	no	—
425	C₂²×C₂₃	—	2	2	no	—
426	C₂²×C₂₃	—	2	2	no	—
427	C₂²×C₂₃	—	4	1	no	—
428	C₂²×C₂₃	—	4	1	no	—
429	C₂²×C₂₃	—	4	1	no	—
430	C₂²×C₂₃	—	4	1	no	—
431	C₂²×C₂₃	—	4	1	no	—
432	C₂²×C₂₃	—	4	1	no	—
433	C₂²×C₂₃	—	4	1	no	—
434	C₂²×C₂₃	—	8	1	no	—
435	C₂²×C₂₃	—	8	1	no	—
436	C₂²×C₂₃	—	8	4	no	—
437	C₂²×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
438	C₂²×C₂₃	#525	1	1	yes	characteristic
439	C₂²×C₂₃	#525	1	1	yes	characteristic
440	C₄×C₂₃	—	2	1	no	—
441	C₄×C₂₃	—	2	2	no	—
442	C₄×C₂₃	—	2	2	no	—
443	C₄×C₂₃	—	2	1	no	—
444	C₄×C₂₃	—	4	2	no	—
445	C₄×C₂₃	—	4	1	no	—
446	C₄×C₂₃	—	4	1	no	—
447	C₄×C₂₃	—	4	1	no	—
448	C₄×C₂₃	—	8	1	no	—
449	C₄×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
450	C₄×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
451	C₄×C₂₃	C₂×#120	1	1	yes	characteristic
452	C₄×C₂₃	#525	1	1	yes	characteristic
453	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
454	C₂×#135	C₂²×C₂₃	1	1	yes	characteristic
455	C₂×#135	C₂²×C₂₃	1	1	yes	characteristic
456	#568	—	2	4	no	—
457	#568	—	2	4	no	—
458	C₂×#131	—	2	1	no	—
459	C₂×#131	—	2	1	no	—
460	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic
461	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic
462	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic
463	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic
464	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic, complemented
465	C₂²×M₁₆	—	2	1	no	—
466	C₂²×M₁₆	—	2	1	no	—
467	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
468	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
469	#525	C₂²×C₂₃	1	1	yes	characteristic
470	#452	C₄×C₂₃	1	1	yes	characteristic, complemented
471	#452	C₄×C₂₃	1	1	yes	characteristic, complemented
472	#451	C₄×C₂₃	1	1	yes	characteristic, complemented
473	#450	C₄×C₂₃	1	1	yes	characteristic, complemented
474	#449	C₄×C₂₃	1	1	yes	characteristic, complemented
475	#449	C₄×C₂₃	1	1	yes	characteristic, complemented
476	#448	C₄×C₂₃	1	1	yes	characteristic, complemented
477	#447	C₄×C₂₃	1	1	yes	characteristic, complemented
478	#444	—	2	4	no	—
479	#443	—	2	4	no	—
480	#436	—	2	1	no	—
481	#436	—	2	1	no	—
482	#435	—	2	1	no	—
483	#435	—	2	1	no	—
484	C₂×#108	C₂²×C₂₃	1	1	yes	characteristic, complemented
485	C₂×#108	C₂²×C₂₃	1	1	yes	characteristic, complemented
486	#424	C₂²×C₂₃	1	1	yes	characteristic, complemented
487	C₂×#104	C₂²×C₂₃	1	1	yes	characteristic
488	C₂×#104	C₂²×C₂₃	1	1	yes	characteristic
489	C₂×#104	C₂²×C₂₃	1	1	yes	characteristic
490	C₂×#104	C₂²×C₂₃	1	1	yes	characteristic
491	C₂×#104	C₂²×C₂₃	1	1	yes	characteristic, complemented
492	C₂×#104	C₂²×C₂₃	1	1	yes	characteristic, complemented
493	#416	C₂²×C₂₃	1	1	yes	characteristic
494	#416	C₂²×C₂₃	1	1	yes	characteristic
495	#408	C₂²×C₂₃	1	1	yes	characteristic, complemented
496	#407	C₂²×C₂₃	1	1	yes	characteristic
497	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
498	#405	C₂²×C₂₃	1	1	yes	characteristic, complemented
499	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic, complemented
500	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
501	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
502	#341	C₂²×C₂₃	1	1	yes	characteristic, complemented
503	#341	C₂²×C₂₃	1	1	yes	characteristic, complemented
504	#339	C₂²×C₂₃	1	1	yes	characteristic, complemented
505	#339	C₂²×C₂₃	1	1	yes	characteristic, complemented
506	#336	C₂²×C₂₃	1	1	yes	characteristic, complemented
507	#336	C₂²×C₂₃	1	1	yes	characteristic, complemented
508	C₂×C₂₃	—	2	1	no	—
509	C₂×C₂₃	—	2	1	no	—
510	C₂×C₂₃	—	4	1	no	—
511	C₂×C₂₃	—	4	1	no	—
512	C₂×C₂₃	—	4	2	no	—
513	C₂×C₂₃	—	4	2	no	—
514	C₂×C₂₃	—	8	1	no	—
515	C₂×C₂₃	C₄×#120	1	1	yes	characteristic
516	C₂×C₂₃	#2956	1	1	yes	characteristic
517	C₂×C₂₃	#2957	1	1	yes	characteristic
518	C₂×#41	—	2	2	no	—
519	C₂×#41	—	2	2	no	—
520	C₂×#41	—	2	2	no	—
521	C₂×#41	—	2	2	no	—
522	C₂×#41	—	2	1	no	—
523	C₂×#41	—	2	1	no	—
524	C₂×#41	C₂×C₄×C₂₃	1	1	yes	characteristic
525	C₂×#41	C₂×C₄×C₂₃	1	1	yes	characteristic
526	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
527	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
528	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
529	C₂²×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
530	C₂²×D₄	—	2	1	no	—
531	C₂²×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
532	C₂³×C₄	—	2	1	no	—
533	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
534	#135	—	2	2	no	—
535	#135	—	2	2	no	—
536	#135	—	2	2	no	—
537	#135	—	2	2	no	—
538	C₂×Q₁₆	C₂×C₄×C₂₃	1	1	yes	characteristic
539	C₂×Q₁₆	C₂×C₄×C₂₃	1	1	yes	characteristic
540	C₂×SD₁₆	C₂×C₄×C₂₃	1	1	yes	characteristic
541	C₂×SD₁₆	C₂×C₄×C₂₃	1	1	yes	characteristic
542	C₂×SD₁₆	C₂×C₄×C₂₃	1	1	yes	characteristic
543	C₂×SD₁₆	C₂×C₄×C₂₃	1	1	yes	characteristic
544	C₂×D₈	C₂×C₄×C₂₃	1	1	yes	characteristic
545	C₂×D₈	C₂×C₄×C₂₃	1	1	yes	characteristic
546	#131	—	2	8	no	—
547	#131	—	2	8	no	—
548	#131	—	2	2	no	—
549	#131	—	2	2	no	—
550	#131	—	2	2	no	—
551	#131	—	2	2	no	—
552	#131	—	2	2	no	—
553	#131	—	2	2	no	—
554	#131	—	2	2	no	—
555	#131	—	2	2	no	—
556	#131	D₄×C₂₃	1	4	yes	complemented
557	#131	D₄×C₂₃	1	4	yes	complemented
558	C₂×M₁₆	—	2	8	no	—
559	C₂×M₁₆	—	2	8	no	—
560	C₂×M₁₆	—	2	1	no	—
561	C₂×M₁₆	—	2	2	no	—
562	C₂×M₁₆	—	2	2	no	—
563	C₂×M₁₆	—	2	1	no	—
564	C₂×M₁₆	—	2	1	no	—
565	C₂×M₁₆	—	2	1	no	—
566	C₂×M₁₆	—	2	1	no	—
567	C₂×M₁₆	—	2	2	no	—
568	C₂×M₁₆	—	2	2	no	—
569	C₂×M₁₆	—	2	1	no	—
570	C₂×M₁₆	D₄×C₂₃	1	1	yes	characteristic
571	C₂×M₁₆	D₄×C₂₃	1	1	yes	characteristic
572	C₂×M₁₆	D₄×C₂₃	1	1	yes	characteristic
573	C₂×M₁₆	D₄×C₂₃	1	1	yes	characteristic
574	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
575	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
576	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
577	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
578	C₂²×C₈	—	2	1	no	—
579	C₂²×C₈	—	2	1	no	—
580	C₂²×C₈	—	2	1	no	—
581	C₂²×C₈	—	2	1	no	—
582	C₂²×C₈	—	2	1	no	—
583	C₂²×C₈	—	2	1	no	—
584	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
585	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
586	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
587	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
588	#123	—	2	1	no	—
589	C₂²⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
590	C₂²⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
591	#121	C₂×C₄×C₂₃	1	1	yes	characteristic
592	#121	C₂×C₄×C₂₃	1	1	yes	characteristic
593	#120	—	2	1	no	—
594	C₄×D₄	—	2	1	no	—
595	C₄×D₄	—	2	1	no	—
596	#117	C₂³×C₂₃	1	1	yes	characteristic
597	C₂×C₂²⋊C₄	—	2	1	no	—
598	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
599	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
600	#108	—	2	2	no	—
601	#108	—	2	2	no	—
602	C₄⋊C₈	—	2	1	no	—
603	C₄⋊C₈	—	2	1	no	—
604	#104	—	2	2	no	—
605	#104	—	2	2	no	—
606	#104	—	2	2	no	—
607	#104	—	2	2	no	—
608	#104	—	2	2	no	—
609	#104	—	2	2	no	—
610	#103	C₂×C₄×C₂₃	1	1	yes	characteristic
611	#103	C₂×C₄×C₂₃	1	1	yes	characteristic
612	#103	C₂×C₄×C₂₃	1	1	yes	characteristic
613	#103	C₂×C₄×C₂₃	1	1	yes	characteristic
614	#102	C₂×C₄×C₂₃	1	1	yes	characteristic
615	#102	C₂×C₄×C₂₃	1	1	yes	characteristic
616	#102	C₂×C₄×C₂₃	1	1	yes	characteristic
617	#102	C₂×C₄×C₂₃	1	1	yes	characteristic
618	C₂²⋊C₈	—	2	1	no	—
619	C₂²⋊C₈	—	2	1	no	—
620	C₂²⋊C₈	—	2	1	no	—
621	C₂²⋊C₈	—	2	1	no	—
622	C₂²⋊C₈	C₂×C₄×C₂₃	1	1	yes	characteristic
623	C₂²⋊C₈	C₂×C₄×C₂₃	1	1	yes	characteristic
624	C₂²⋊C₈	C₂×C₄×C₂₃	1	1	yes	characteristic
625	C₂²⋊C₈	C₂×C₄×C₂₃	1	1	yes	characteristic
626	#97	—	2	2	no	—
627	#97	—	2	1	no	—
628	C₄×C₈	—	2	2	no	—
629	C₄×C₈	—	2	1	no	—
630	#95	—	2	1	no	—
631	C₂₃	#21468	1	1	yes	characteristic, direct product factor, Sylow
632	C₂⁴	—	2	1	no	—
633	C₂⁴	#41×C₂₃	1	1	yes	characteristic
634	#41	—	2	4	no	—
635	#41	—	2	4	no	—
636	#41	—	2	4	no	—
637	#41	—	2	4	no	—
638	#41	—	2	2	no	—
639	#41	—	2	2	no	—
640	#41	—	2	2	no	—
641	#41	—	2	2	no	—
642	#41	—	2	1	no	—
643	#41	—	2	1	no	—
644	#41	—	2	1	no	—
645	#41	—	2	1	no	—
646	#41	—	2	1	no	—
647	#41	—	2	1	no	—
648	#41	—	2	1	no	—
649	#41	—	2	1	no	—
650	#41	C₂×D₄×C₂₃	1	2	yes	—
651	#41	C₂×D₄×C₂₃	1	2	yes	—
652	#41	#41×C₂₃	1	2	yes	—
653	#41	#41×C₂₃	1	2	yes	—
654	C₂×Q₈	—	2	2	no	—
655	C₂×Q₈	—	2	2	no	—
656	C₂×Q₈	—	2	1	no	—
657	C₂×Q₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
658	C₂×Q₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
659	C₂×Q₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
660	C₂×D₄	—	2	4	no	—
661	C₂×D₄	—	2	4	no	—
662	C₂×D₄	—	2	1	no	—
663	C₂×D₄	—	2	1	no	—
664	C₂×D₄	—	2	1	no	—
665	C₂×D₄	—	2	1	no	—
666	C₂×D₄	—	2	2	no	—
667	C₂×D₄	—	2	2	no	—
668	C₂×D₄	—	2	1	no	—
669	C₂×D₄	—	2	1	no	—
670	C₂×D₄	—	2	1	no	—
671	C₂×D₄	—	2	1	no	—
672	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
673	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
674	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
675	C₂²×C₄	—	2	4	no	—
676	C₂²×C₄	—	2	4	no	—
677	C₂²×C₄	—	2	1	no	—
678	C₂²×C₄	—	2	1	no	—
679	C₂²×C₄	—	2	1	no	—
680	C₂²×C₄	—	2	1	no	—
681	C₂²×C₄	—	2	1	no	—
682	C₂²×C₄	—	2	1	no	—
683	C₂²×C₄	—	2	1	no	—
684	C₂²×C₄	—	2	1	no	—
685	C₂²×C₄	—	2	1	no	—
686	C₂²×C₄	—	2	1	no	—
687	C₂²×C₄	—	2	1	no	—
688	C₂²×C₄	—	2	1	no	—
689	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
690	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
691	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
692	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
693	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
694	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
695	Q₁₆	—	2	2	no	—
696	Q₁₆	—	2	2	no	—
697	SD₁₆	—	2	2	no	—
698	SD₁₆	—	2	2	no	—
699	SD₁₆	—	2	2	no	—
700	SD₁₆	—	2	2	no	—
701	D₈	—	2	2	no	—
702	D₈	—	2	2	no	—
703	M₁₆	—	2	4	no	—
704	M₁₆	—	2	4	no	—
705	M₁₆	—	2	4	no	—
706	M₁₆	—	2	1	no	—
707	M₁₆	—	2	1	no	—
708	M₁₆	—	2	2	no	—
709	M₁₆	—	2	2	no	—
710	M₁₆	—	2	4	no	—
711	M₁₆	—	2	4	no	—
712	M₁₆	—	2	2	no	—
713	M₁₆	—	2	2	no	—
714	M₁₆	—	2	1	no	—
715	M₁₆	—	2	1	no	—
716	M₁₆	—	2	1	no	—
717	M₁₆	—	2	1	no	—
718	M₁₆	—	4	2	no	—
719	M₁₆	C₂×D₄×C₂₃	1	2	yes	—
720	M₁₆	C₂×D₄×C₂₃	1	2	yes	—
721	C₂×C₈	—	2	4	no	—
722	C₂×C₈	—	2	4	no	—
723	C₂×C₈	—	2	4	no	—
724	C₂×C₈	—	2	1	no	—
725	C₂×C₈	—	2	1	no	—
726	C₂×C₈	—	2	1	no	—
727	C₂×C₈	—	2	1	no	—
728	C₂×C₈	—	2	1	no	—
729	C₂×C₈	—	2	1	no	—
730	C₂×C₈	—	2	1	no	—
731	C₂×C₈	—	2	1	no	—
732	C₂×C₈	—	2	4	no	—
733	C₂×C₈	—	2	4	no	—
734	C₂×C₈	—	2	1	no	—
735	C₂×C₈	—	2	1	no	—
736	C₂×C₈	—	4	2	no	—
737	C₂×C₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
738	C₂×C₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
739	C₂×C₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
740	C₂×C₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
741	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
742	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
743	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
744	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
745	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
746	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
747	C₄⋊C₄	—	2	1	no	—
748	C₄⋊C₄	—	2	1	no	—
749	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
750	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
751	C₂²⋊C₄	—	2	1	no	—
752	C₂²⋊C₄	—	2	1	no	—
753	C₂²⋊C₄	—	2	1	no	—
754	C₂²⋊C₄	—	2	1	no	—
755	C₂²⋊C₄	—	2	1	no	—
756	C₂²⋊C₄	—	4	2	no	—
757	C₄²	—	2	1	no	—
758	C₄²	—	2	1	no	—
759	C₄²	—	2	1	no	—
760	C₄²	—	2	1	no	—
761	C₄²	—	2	1	no	—
762	C₂³	—	2	4	no	—
763	C₂³	—	2	1	no	—
764	C₂³	—	2	1	no	—
765	C₂³	—	2	1	no	—
766	C₂³	—	2	1	no	—
767	C₂³	—	2	1	no	—
768	C₂³	—	4	1	no	—
769	C₂³	—	4	1	no	—
770	C₂³	—	8	1	no	—
771	C₂³	—	8	1	no	—
772	C₂³	C₄×D₄×C₂₃	1	1	yes	characteristic
773	C₂³	C₄×D₄×C₂₃	1	1	yes	characteristic
774	C₂³	C₂×#41×C₂₃	1	1	yes	characteristic
775	Q₈	—	2	4	no	—
776	Q₈	—	2	1	no	—
777	Q₈	—	2	1	no	—
778	Q₈	—	2	1	no	—
779	Q₈	—	2	1	no	—
780	Q₈	C₄×D₄×C₂₃	1	2	yes	—
781	Q₈	C₄×D₄×C₂₃	1	2	yes	—
782	D₄	—	2	4	no	—
783	D₄	—	2	4	no	—
784	D₄	—	2	4	no	—
785	D₄	—	2	2	no	—
786	D₄	—	2	2	no	—
787	D₄	—	2	2	no	—
788	D₄	—	2	2	no	—
789	D₄	—	2	1	no	—
790	D₄	—	2	1	no	—
791	D₄	—	2	1	no	—
792	D₄	—	2	1	no	—
793	D₄	—	4	1	no	—
794	D₄	—	4	1	no	—
795	D₄	—	8	1	no	—
796	D₄	—	8	1	no	—
797	D₄	C₄×D₄×C₂₃	1	2	yes	—
798	D₄	C₄×D₄×C₂₃	1	2	yes	—
799	C₂×C₄	—	2	4	no	—
800	C₂×C₄	—	2	4	no	—
801	C₂×C₄	—	2	4	no	—
802	C₂×C₄	—	2	1	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	4	1	no	—
823	C₂×C₄	—	4	1	no	—
824	C₂×C₄	—	4	1	no	—
825	C₂×C₄	—	4	1	no	—
826	C₂×C₄	—	4	1	no	—
827	C₂×C₄	—	4	1	no	—
828	C₂×C₄	—	4	1	no	—
829	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
830	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
831	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
832	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
833	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
834	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
835	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
836	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
837	C₈	—	2	1	no	—
838	C₈	—	2	1	no	—
839	C₈	—	2	1	no	—
840	C₈	—	2	1	no	—
841	C₈	—	2	2	no	—
842	C₈	—	2	2	no	—
843	C₈	—	2	1	no	—
844	C₈	—	2	1	no	—
845	C₈	—	4	1	no	—
846	C₈	—	4	1	no	—
847	C₈	C₂₃×#120	1	2	yes	—
848	C₈	C₂₃×#120	1	2	yes	—
849	C₂²	—	2	1	no	—
850	C₂²	—	2	1	no	—
851	C₂²	—	2	1	no	—
852	C₂²	—	2	1	no	—
853	C₂²	—	2	1	no	—
854	C₂²	—	2	1	no	—
855	C₂²	—	2	1	no	—
856	C₂²	—	2	1	no	—
857	C₂²	—	2	2	no	—
858	C₂²	—	2	2	no	—
859	C₂²	—	4	1	no	—
860	C₂²	—	4	1	no	—
861	C₂²	—	4	1	no	—
862	C₂²	—	4	1	no	—
863	C₂²	—	4	1	no	—
864	C₂²	—	4	1	no	—
865	C₂²	—	4	1	no	—
866	C₂²	—	8	1	no	—
867	C₂²	—	8	1	no	—
868	C₂²	—	8	4	no	—
869	C₂²	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
870	C₂²	C₂₃×#525	1	1	yes	characteristic
871	C₂²	C₂₃×#525	1	1	yes	characteristic
872	C₄	—	2	1	no	—
873	C₄	—	2	2	no	—
874	C₄	—	2	2	no	—
875	C₄	—	2	1	no	—
876	C₄	—	4	2	no	—
877	C₄	—	4	1	no	—
878	C₄	—	4	1	no	—
879	C₄	—	4	1	no	—
880	C₄	—	8	1	no	—
881	C₄	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
882	C₄	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
883	C₄	C₂×C₂₃×#120	1	1	yes	characteristic
884	C₄	C₂₃×#525	1	1	yes	characteristic
885	C₂	—	2	1	no	—
886	C₂	—	2	1	no	—
887	C₂	—	4	1	no	—
888	C₂	—	4	1	no	—
889	C₂	—	4	2	no	—
890	C₂	—	4	2	no	—
891	C₂	—	8	1	no	—
892	C₂	C₄×C₂₃×#120	1	1	yes	characteristic
893	C₂	C₂₃×#2956	1	1	yes	characteristic
894	C₂	C₂₃×#2957	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₂₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
socle	C₂²×C₂₃	C₂×C₄×D₄
prime radical	C₂₃×#3002	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ C₂²×M₁₆×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#568	C₂	semidirect
3. C₂×C₂₃×#444	C₂	semidirect
4. C₂×C₂₃×#443	C₂	semidirect
5. C₂₃×#2930	C₂	semidirect
6. C₂₃×#1876	C₂	semidirect
7. C₂₃×#1876	C₂	semidirect
8. C₂₃×#1871	C₂	semidirect
9. C₂₃×#1866	C₂	semidirect
10. C₂₃×#1866	C₂	semidirect
11. C₂₃×#1855	C₂	semidirect
12. C₂₃×#1789	C₂	semidirect
13. C₂₃×#1765	C₂	semidirect
14. C₂₃×#1764	C₂	semidirect
15. C₂₃×#1753	C₂	semidirect
27. C₂×C₂₃×#131	C₂²	semidirect
33. C₂₃×#452	C₄	semidirect
34. C₂₃×#452	C₄	semidirect
35. C₂₃×#451	C₄	semidirect
36. C₂₃×#450	C₄	semidirect
37. C₂₃×#449	C₄	semidirect
38. C₂₃×#449	C₄	semidirect
39. C₂₃×#448	C₄	semidirect
40. C₂₃×#447	C₄	semidirect
47. C₂×C₂₃×#108	C₂²	semidirect
48. C₂×C₂₃×#108	C₂²	semidirect
49. C₂₃×#424	C₂²	semidirect
54. C₂×C₂₃×#104	C₂²	semidirect
55. C₂×C₂₃×#104	C₂²	semidirect
58. C₂₃×#408	C₂²	semidirect
61. C₂₃×#405	C₂²	semidirect
62. C₂×C₂₃×#97	C₂²	semidirect
63. C₂×C₄×C₈×C₂₃	C₂²	semidirect
65. C₂₃×#341	C₂²	semidirect
66. C₂₃×#341	C₂²	semidirect
67. C₂₃×#339	C₂²	semidirect
68. C₂₃×#339	C₂²	semidirect
69. C₂₃×#336	C₂²	semidirect
70. C₂₃×#336	C₂²	semidirect
109. C₂₃×#131	D₄	semidirect
110. C₂₃×#131	D₄	semidirect
314. #21468	C₂₃	direct (N × H)
402. C₂×#568	C₂×C₂₃	semidirect
404. C₂×#444	C₂×C₂₃	semidirect
405. C₂×#443	C₂×C₂₃	semidirect
406. #2930	C₂×C₂₃	semidirect
407. #1876	C₂×C₂₃	semidirect
408. #1876	C₂×C₂₃	semidirect
409. #1871	C₂×C₂₃	semidirect
410. #1866	C₂×C₂₃	semidirect
411. #1866	C₂×C₂₃	semidirect
412. #1855	C₂×C₂₃	semidirect
413. #1789	C₂×C₂₃	semidirect
414. #1765	C₂×C₂₃	semidirect
415. #1764	C₂×C₂₃	semidirect
416. #1753	C₂×C₂₃	semidirect
464. C₂×#131	C₂²×C₂₃	semidirect
470. #452	C₄×C₂₃	semidirect
471. #452	C₄×C₂₃	semidirect
472. #451	C₄×C₂₃	semidirect
473. #450	C₄×C₂₃	semidirect
474. #449	C₄×C₂₃	semidirect
475. #449	C₄×C₂₃	semidirect
476. #448	C₄×C₂₃	semidirect
477. #447	C₄×C₂₃	semidirect
484. C₂×#108	C₂²×C₂₃	semidirect
485. C₂×#108	C₂²×C₂₃	semidirect
486. #424	C₂²×C₂₃	semidirect
491. C₂×#104	C₂²×C₂₃	semidirect
492. C₂×#104	C₂²×C₂₃	semidirect
495. #408	C₂²×C₂₃	semidirect
498. #405	C₂²×C₂₃	semidirect
499. C₂×#97	C₂²×C₂₃	semidirect
500. C₂×C₄×C₈	C₂²×C₂₃	semidirect
502. #341	C₂²×C₂₃	semidirect
503. #341	C₂²×C₂₃	semidirect
504. #339	C₂²×C₂₃	semidirect
505. #339	C₂²×C₂₃	semidirect
506. #336	C₂²×C₂₃	semidirect
507. #336	C₂²×C₂₃	semidirect
556. #131	D₄×C₂₃	semidirect
557. #131	D₄×C₂₃	semidirect
631. C₂₃	#21468	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×#568	2
C₂₃×#3002	2
C₂×C₂₃×#444	2
C₂×C₂₃×#443	2
C₂₃×#2930	2
C₂₃×#1876	2
C₂₃×#1871	2
C₂₃×#1866	2
C₂₃×#1855	2
C₂₃×#1789	2
C₂₃×#1765	2
C₂₃×#1764	2
C₂₃×#1753	2
#21468	23

Subgroups — C23×#21468 #19169094

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#21468 #19169094