Subgroups — C₂₃×#60323 #19207949

Order 5888.

1940 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3481	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2994	C₂	1	2	yes	maximal, complemented
3	C₂₃×#2993	C₂	1	2	yes	maximal, complemented
4	C₂₃×#2991	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2990	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#2979	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#2976	C₂	1	4	yes	maximal, complemented
8	C₂₃×#2974	C₂	1	2	yes	maximal, complemented
9	C₂₃×#2972	C₂	1	2	yes	maximal, complemented
10	C₂₃×#2969	C₂	1	2	yes	maximal, complemented
11	C₂₃×#2966	C₂	1	2	yes	maximal, complemented
12	C₂₃×#2965	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈×#41×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
14	D₄×M₁₆×C₂₃	C₂	1	2	yes	maximal, complemented
15	C₂₃×#2933	C₂	1	4	yes	maximal, complemented
16	C₂₃×#2931	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₂₃×#436	C₂	1	2	yes	maximal, complemented
18	C₂×C₂₃×#131	C₂²	1	2	yes	complemented
19	C₂²×M₁₆×C₂₃	C₂²	1	4	yes	complemented
20	C₂₃×#559	C₄	1	1	yes	characteristic
21	C₂₃×#554	C₄	1	1	yes	characteristic
22	C₂₃×#554	C₄	1	1	yes	characteristic
23	C₂₃×#553	C₄	1	2	yes	—
24	C₂₃×#553	C₄	1	2	yes	—
25	C₂₃×#551	C₄	1	4	yes	—
26	C₂₃×#546	C₄	1	2	yes	—
27	C₂₃×#546	C₄	1	2	yes	—
28	D₄²×C₂₃	C₄	1	1	yes	characteristic
29	C₂₃×#532	C₂²	1	1	yes	characteristic
30	C₂₃×#529	C₂²	1	2	yes	—
31	C₂₃×#529	C₂²	1	2	yes	—
32	C₂₃×#525	C₂²	1	4	yes	—
33	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
34	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
37	C₂₃×#446	C₂²	1	1	yes	characteristic, complemented
38	C₂₃×#446	C₂²	1	1	yes	characteristic, complemented
39	C₂₃×#446	C₂²	1	2	yes	complemented
40	C₈×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
41	C₈×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
42	C₈×Q₈×C₂₃	C₂²	1	2	yes	complemented
43	C₂₃×#436	C₂²	1	1	yes	characteristic
44	C₂₃×#436	C₂²	1	2	yes	—
45	C₂₃×#436	C₂²	1	1	yes	characteristic
46	C₂₃×#436	C₂²	1	2	yes	complemented
47	C₂₃×#436	C₂²	1	4	yes	complemented
48	C₂₃×#436	C₂²	1	4	yes	complemented
49	C₂₃×#436	C₂²	1	2	yes	complemented
50	C₂₃×#436	C₂²	1	2	yes	complemented
51	C₂₃×#436	C₂²	1	4	yes	complemented
52	C₂₃×#436	C₂²	1	2	yes	complemented
53	C₂₃×#435	C₂²	1	2	yes	complemented
54	C₂₃×#435	C₂²	1	4	yes	complemented
55	C₂₃×#435	C₂²	1	4	yes	complemented
56	C₂₃×#435	C₂²	1	4	yes	complemented
57	C₂₃×#435	C₂²	1	4	yes	complemented
58	C₂₃×#435	C₂²	1	2	yes	complemented
59	C₂₃×#435	C₂²	1	4	yes	complemented
60	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic
61	C₈×D₄×C₂₃	C₂²	1	2	yes	—
62	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic
63	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
64	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
65	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
66	C₈×D₄×C₂₃	C₂²	1	4	yes	complemented
67	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
68	C₈×D₄×C₂₃	C₂²	1	4	yes	complemented
69	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
70	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
71	C₂₃×#433	C₂²	1	4	yes	complemented
72	C₂₃×#433	C₂²	1	4	yes	complemented
73	C₂₃×#432	C₂²	1	2	yes	complemented
74	C₂₃×#431	C₂²	1	2	yes	complemented
75	C₂₃×#431	C₂²	1	1	yes	characteristic, complemented
76	C₂₃×#431	C₂²	1	2	yes	complemented
77	C₂₃×#431	C₂²	1	1	yes	characteristic, complemented
78	C₂₃×#431	C₂²	1	2	yes	complemented
79	C₂₃×#424	C₂²	1	4	yes	complemented
80	C₂₃×#423	C₂²	1	1	yes	characteristic, complemented
81	C₂₃×#423	C₂²	1	2	yes	complemented
82	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	complemented
83	C₂₃×#408	C₂²	1	2	yes	complemented
84	C₂₃×#408	C₂²	1	4	yes	complemented
85	C₂₃×#407	C₂²	1	4	yes	complemented
86	C₂×C₂₃×C₂²⋊C₈	C₂²	1	4	yes	complemented
87	C₂×C₂₃×C₂²⋊C₈	C₂²	1	4	yes	complemented
88	C₂₃×#405	C₂²	1	4	yes	complemented
89	C₄×M₁₆×C₂₃	C₂²	1	2	yes	complemented
90	C₂×C₄×C₈×C₂₃	C₂²	1	2	yes	complemented
91	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
92	C₂×#41×C₂₃	C₂×C₄	1	1	yes	characteristic
93	C₂×#41×C₂₃	C₂×C₄	1	1	yes	characteristic
94	C₂×#41×C₂₃	C₂³	1	2	yes	—
95	C₂²×D₄×C₂₃	C₂×C₄	1	2	yes	—
96	C₂²×D₄×C₂₃	C₂×C₄	1	2	yes	—
97	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
98	C₂₃×#131	—	4	4	no	—
99	C₂×M₁₆×C₂₃	—	4	8	no	—
100	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
101	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
102	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
103	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
104	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
105	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
106	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
107	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
108	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
109	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
110	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
111	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
112	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
113	C₂₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
114	C₂₃×#127	C₂×C₄	1	1	yes	characteristic
115	C₂₃×#126	C₂×C₄	1	4	yes	—
116	C₂₃×#126	C₂×C₄	1	4	yes	—
117	C₂₃×#125	C₂×C₄	1	2	yes	—
118	C₂₃×#125	C₂×C₄	1	2	yes	—
119	C₂₃×#124	C₂×C₄	1	2	yes	—
120	C₂₃×#124	C₂×C₄	1	2	yes	—
121	C₂₃×#124	C₂×C₄	1	2	yes	—
122	C₂₃×#123	C₂×C₄	1	4	yes	—
123	C₂₃×#123	C₂×C₄	1	4	yes	—
124	C₂₃×#123	C₂×C₄	1	4	yes	—
125	C₂₃×#123	C₂×C₄	1	4	yes	—
126	C₂₃×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
127	C₂₃×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
128	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
129	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
130	C₂₃×#121	C₂×C₄	1	4	yes	—
131	C₂₃×#121	C₂×C₄	1	4	yes	—
132	C₂₃×#121	C₂×C₄	1	2	yes	—
133	C₂₃×#121	C₂×C₄	1	2	yes	—
134	C₂₃×#121	C₂×C₄	1	2	yes	—
135	C₂₃×#121	C₂×C₄	1	2	yes	—
136	C₂₃×#120	C₂×C₄	1	4	yes	—
137	C₂₃×#120	C₂×C₄	1	4	yes	—
138	C₄×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
139	C₄×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
140	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
141	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
142	C₄×D₄×C₂₃	C₂×C₄	1	4	yes	—
143	C₄×D₄×C₂₃	C₂×C₄	1	4	yes	—
144	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
145	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
146	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
147	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
148	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
149	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
150	C₄×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
151	C₄×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
152	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
153	C₄×D₄×C₂₃	C₂³	1	4	yes	—
154	C₄×D₄×C₂₃	C₂³	1	2	yes	—
155	C₄×D₄×C₂₃	C₂³	1	2	yes	—
156	C₄×D₄×C₂₃	C₂³	1	2	yes	—
157	C₄×D₄×C₂₃	C₂³	1	4	yes	—
158	C₄×D₄×C₂₃	C₂³	1	2	yes	—
159	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
160	C₂₃×#117	C₂×C₄	1	2	yes	—
161	C₂₃×#117	C₂×C₄	1	2	yes	—
162	C₂₃×#117	C₂×C₄	1	1	yes	characteristic
163	C₂₃×#117	C₂×C₄	1	1	yes	characteristic
164	C₂₃×#117	C₂³	1	4	yes	—
165	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
166	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
167	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	4	yes	—
168	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	4	yes	—
169	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
170	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
171	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
172	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
173	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
174	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
175	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
176	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
177	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
178	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
179	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
180	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
181	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
182	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
183	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
184	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
185	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
186	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
187	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
188	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
189	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
190	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
191	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
192	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
193	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
194	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
195	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
196	C₂₃×#97	C₂³	1	2	yes	—
197	C₂₃×#97	C₂³	1	2	yes	—
198	C₂₃×#97	C₂³	1	4	yes	—
199	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
200	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
201	C₄×C₈×C₂₃	C₂³	1	2	yes	—
202	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
203	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
204	C₄×C₈×C₂₃	C₂³	1	2	yes	—
205	C₄×C₈×C₂₃	C₂³	1	2	yes	—
206	C₄×C₈×C₂₃	C₂³	1	2	yes	—
207	C₄×C₈×C₂₃	C₂³	1	4	yes	—
208	C₂⁴×C₂₃	C₂²×C₄	1	4	yes	—
209	#41×C₂₃	—	2	4	no	—
210	#41×C₂₃	—	4	2	no	—
211	#41×C₂₃	—	4	2	no	—
212	#41×C₂₃	—	4	2	no	—
213	C₂×Q₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
214	C₂×Q₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
215	C₂×Q₈×C₂₃	C₂²×C₄	1	2	yes	—
216	C₂×D₄×C₂₃	—	2	8	no	—
217	C₂×D₄×C₂₃	—	4	4	no	—
218	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
219	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
220	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
221	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
222	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
223	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
224	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
225	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
226	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
227	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
228	C₂²×C₄×C₂₃	—	4	4	no	—
229	C₂²×C₄×C₂₃	—	4	4	no	—
230	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
231	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
232	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
233	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
234	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
235	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
236	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
237	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
238	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
239	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
240	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
241	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
243	M₁₆×C₂₃	—	2	4	no	—
244	M₁₆×C₂₃	—	2	8	no	—
245	M₁₆×C₂₃	—	4	4	no	—
246	M₁₆×C₂₃	—	4	4	no	—
247	M₁₆×C₂₃	—	4	2	no	—
248	M₁₆×C₂₃	—	4	2	no	—
249	C₂×C₈×C₂₃	—	2	4	no	—
250	C₂×C₈×C₂₃	—	2	2	no	—
251	C₂×C₈×C₂₃	—	4	2	no	—
252	C₂×C₈×C₂₃	—	4	4	no	—
253	C₂×C₈×C₂₃	—	4	1	no	—
254	C₂×C₈×C₂₃	—	4	4	no	—
255	C₂×C₈×C₂₃	—	4	4	no	—
256	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
257	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
258	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
259	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
260	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
261	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
262	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
263	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
264	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
265	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
266	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
267	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
268	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
269	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
270	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
271	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
272	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
273	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
274	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
275	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
276	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
277	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
278	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
279	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
280	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
281	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
282	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
283	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
284	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
285	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
286	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
287	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
288	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
289	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
290	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
291	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
292	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
293	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
294	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
295	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
296	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
297	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
298	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
299	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
300	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
301	C₄²×C₂₃	C₂⁴	1	2	yes	—
302	C₄²×C₂₃	C₂⁴	1	2	yes	—
303	#60323	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
304	C₂³×C₂₃	—	2	8	no	—
305	C₂³×C₂₃	—	4	4	no	—
306	C₂³×C₂₃	—	4	4	no	—
307	C₂³×C₂₃	C₂³×C₄	1	4	yes	—
308	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
309	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
310	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
311	Q₈×C₂₃	—	2	2	no	—
312	Q₈×C₂₃	—	2	2	no	—
313	Q₈×C₂₃	—	4	2	no	—
314	D₄×C₂₃	—	2	8	no	—
315	D₄×C₂₃	—	2	4	no	—
316	D₄×C₂₃	—	2	4	no	—
317	D₄×C₂₃	—	2	2	no	—
318	D₄×C₂₃	—	2	4	no	—
319	D₄×C₂₃	—	4	4	no	—
320	D₄×C₂₃	—	4	4	no	—
321	D₄×C₂₃	—	4	2	no	—
322	D₄×C₂₃	—	4	2	no	—
323	D₄×C₂₃	#131	1	4	yes	complemented
324	C₂×C₄×C₂₃	—	2	4	no	—
325	C₂×C₄×C₂₃	—	2	4	no	—
326	C₂×C₄×C₂₃	—	2	2	no	—
327	C₂×C₄×C₂₃	—	2	4	no	—
328	C₂×C₄×C₂₃	—	2	2	no	—
329	C₂×C₄×C₂₃	—	2	2	no	—
330	C₂×C₄×C₂₃	—	2	1	no	—
331	C₂×C₄×C₂₃	—	2	4	no	—
332	C₂×C₄×C₂₃	—	2	2	no	—
333	C₂×C₄×C₂₃	—	2	2	no	—
334	C₂×C₄×C₂₃	—	2	4	no	—
335	C₂×C₄×C₂₃	—	2	1	no	—
336	C₂×C₄×C₂₃	—	2	2	no	—
337	C₂×C₄×C₂₃	—	4	4	no	—
338	C₂×C₄×C₂₃	—	4	4	no	—
339	C₂×C₄×C₂₃	—	4	4	no	—
340	C₂×C₄×C₂₃	—	4	2	no	—
341	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
342	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
343	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
344	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
345	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
346	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
347	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
348	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
349	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
350	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
351	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
352	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
353	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
354	C₈×C₂₃	—	2	1	no	—
355	C₈×C₂₃	—	2	2	no	—
356	C₈×C₂₃	—	2	2	no	—
357	C₈×C₂₃	—	2	4	no	—
358	C₈×C₂₃	—	2	1	no	—
359	C₈×C₂₃	—	2	2	no	—
360	C₈×C₂₃	—	2	2	no	—
361	C₈×C₂₃	—	2	1	no	—
362	C₈×C₂₃	H(5,𝔽₂)	1	2	yes	—
363	#3481	C₂×C₂₃	1	1	yes	characteristic
364	#2994	C₂×C₂₃	1	2	yes	complemented
365	#2993	C₂×C₂₃	1	2	yes	complemented
366	#2991	C₂×C₂₃	1	1	yes	characteristic, complemented
367	#2990	C₂×C₂₃	1	1	yes	characteristic, complemented
368	#2979	C₂×C₂₃	1	1	yes	characteristic, complemented
369	#2976	C₂×C₂₃	1	4	yes	complemented
370	#2974	C₂×C₂₃	1	2	yes	complemented
371	#2972	C₂×C₂₃	1	2	yes	complemented
372	#2969	C₂×C₂₃	1	2	yes	complemented
373	#2966	C₂×C₂₃	1	2	yes	complemented
374	#2965	C₂×C₂₃	1	1	yes	characteristic, complemented
375	C₈×#41	C₂×C₂₃	1	1	yes	characteristic, complemented
376	D₄×M₁₆	C₂×C₂₃	1	2	yes	complemented
377	#2933	C₂×C₂₃	1	4	yes	complemented
378	#2931	C₂×C₂₃	1	1	yes	characteristic, complemented
379	C₂×#436	C₂×C₂₃	1	2	yes	complemented
380	C₂²×C₂₃	—	2	2	no	—
381	C₂²×C₂₃	—	2	2	no	—
382	C₂²×C₂₃	—	2	2	no	—
383	C₂²×C₂₃	—	2	4	no	—
384	C₂²×C₂₃	—	2	1	no	—
385	C₂²×C₂₃	—	2	1	no	—
386	C₂²×C₂₃	—	2	2	no	—
387	C₂²×C₂₃	—	2	4	no	—
388	C₂²×C₂₃	—	2	1	no	—
389	C₂²×C₂₃	—	2	2	no	—
390	C₂²×C₂₃	—	2	4	no	—
391	C₂²×C₂₃	—	8	8	no	—
392	C₂²×C₂₃	C₂×#131	1	4	yes	—
393	C₂²×C₂₃	C₂⁴×C₄	1	1	yes	characteristic
394	C₄×C₂₃	—	2	2	no	—
395	C₄×C₂₃	—	2	2	no	—
396	C₄×C₂₃	—	2	4	no	—
397	C₄×C₂₃	—	2	1	no	—
398	C₄×C₂₃	—	2	1	no	—
399	C₄×C₂₃	—	2	2	no	—
400	C₄×C₂₃	—	2	2	no	—
401	C₄×C₂₃	—	2	1	no	—
402	C₄×C₂₃	—	2	2	no	—
403	C₄×C₂₃	—	2	2	no	—
404	C₄×C₂₃	C₂×#131	1	2	yes	—
405	C₄×C₂₃	#568	1	2	yes	—
406	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
407	C₄×C₂₃	#585	1	1	yes	characteristic
408	C₂×#131	C₂²×C₂₃	1	2	yes	complemented
409	C₂²×M₁₆	C₂²×C₂₃	1	4	yes	complemented
410	#559	C₄×C₂₃	1	1	yes	characteristic
411	#554	C₄×C₂₃	1	1	yes	characteristic
412	#554	C₄×C₂₃	1	1	yes	characteristic
413	#553	C₄×C₂₃	1	2	yes	—
414	#553	C₄×C₂₃	1	2	yes	—
415	#551	C₄×C₂₃	1	4	yes	—
416	#546	C₄×C₂₃	1	2	yes	—
417	#546	C₄×C₂₃	1	2	yes	—
418	D₄²	C₄×C₂₃	1	1	yes	characteristic
419	#532	C₂²×C₂₃	1	1	yes	characteristic
420	#529	C₂²×C₂₃	1	2	yes	—
421	#529	C₂²×C₂₃	1	2	yes	—
422	#525	C₂²×C₂₃	1	4	yes	—
423	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
424	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
425	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
426	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
427	#446	C₂²×C₂₃	1	1	yes	characteristic, complemented
428	#446	C₂²×C₂₃	1	1	yes	characteristic, complemented
429	#446	C₂²×C₂₃	1	2	yes	complemented
430	C₈×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
431	C₈×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
432	C₈×Q₈	C₂²×C₂₃	1	2	yes	complemented
433	#436	C₂²×C₂₃	1	1	yes	characteristic
434	#436	C₂²×C₂₃	1	2	yes	—
435	#436	C₂²×C₂₃	1	1	yes	characteristic
436	#436	C₂²×C₂₃	1	2	yes	complemented
437	#436	C₂²×C₂₃	1	4	yes	complemented
438	#436	C₂²×C₂₃	1	4	yes	complemented
439	#436	C₂²×C₂₃	1	2	yes	complemented
440	#436	C₂²×C₂₃	1	2	yes	complemented
441	#436	C₂²×C₂₃	1	4	yes	complemented
442	#436	C₂²×C₂₃	1	2	yes	complemented
443	#435	C₂²×C₂₃	1	2	yes	complemented
444	#435	C₂²×C₂₃	1	4	yes	complemented
445	#435	C₂²×C₂₃	1	4	yes	complemented
446	#435	C₂²×C₂₃	1	4	yes	complemented
447	#435	C₂²×C₂₃	1	4	yes	complemented
448	#435	C₂²×C₂₃	1	2	yes	complemented
449	#435	C₂²×C₂₃	1	4	yes	complemented
450	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic
451	C₈×D₄	C₂²×C₂₃	1	2	yes	—
452	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic
453	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
454	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
455	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
456	C₈×D₄	C₂²×C₂₃	1	4	yes	complemented
457	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
458	C₈×D₄	C₂²×C₂₃	1	4	yes	complemented
459	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
460	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
461	#433	C₂²×C₂₃	1	4	yes	complemented
462	#433	C₂²×C₂₃	1	4	yes	complemented
463	#432	C₂²×C₂₃	1	2	yes	complemented
464	#431	C₂²×C₂₃	1	2	yes	complemented
465	#431	C₂²×C₂₃	1	1	yes	characteristic, complemented
466	#431	C₂²×C₂₃	1	2	yes	complemented
467	#431	C₂²×C₂₃	1	1	yes	characteristic, complemented
468	#431	C₂²×C₂₃	1	2	yes	complemented
469	#424	C₂²×C₂₃	1	4	yes	complemented
470	#423	C₂²×C₂₃	1	1	yes	characteristic, complemented
471	#423	C₂²×C₂₃	1	2	yes	complemented
472	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	complemented
473	#408	C₂²×C₂₃	1	2	yes	complemented
474	#408	C₂²×C₂₃	1	4	yes	complemented
475	#407	C₂²×C₂₃	1	4	yes	complemented
476	C₂×C₂²⋊C₈	C₂²×C₂₃	1	4	yes	complemented
477	C₂×C₂²⋊C₈	C₂²×C₂₃	1	4	yes	complemented
478	#405	C₂²×C₂₃	1	4	yes	complemented
479	C₄×M₁₆	C₂²×C₂₃	1	2	yes	complemented
480	C₂×C₄×C₈	C₂²×C₂₃	1	2	yes	complemented
481	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
482	C₂×C₂₃	—	2	4	no	—
483	C₂×C₂₃	—	4	1	no	—
484	C₂×C₂₃	—	4	4	no	—
485	C₂×C₂₃	—	4	2	no	—
486	C₂×C₂₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
487	C₂×C₂₃	C₂²×#131	1	1	yes	characteristic
488	C₂×C₂₃	C₂×#568	1	1	yes	characteristic
489	C₂×#41	C₂×C₄×C₂₃	1	1	yes	characteristic
490	C₂×#41	C₂×C₄×C₂₃	1	1	yes	characteristic
491	C₂×#41	C₂³×C₂₃	1	2	yes	—
492	C₂²×D₄	C₂×C₄×C₂₃	1	2	yes	—
493	C₂²×D₄	C₂×C₄×C₂₃	1	2	yes	—
494	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
495	#131	—	4	4	no	—
496	C₂×M₁₆	—	4	8	no	—
497	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
498	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
499	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
500	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
501	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
502	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
503	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
504	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
505	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
506	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
507	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
508	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
509	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
510	C₄⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
511	#127	C₂×C₄×C₂₃	1	1	yes	characteristic
512	#126	C₂×C₄×C₂₃	1	4	yes	—
513	#126	C₂×C₄×C₂₃	1	4	yes	—
514	#125	C₂×C₄×C₂₃	1	2	yes	—
515	#125	C₂×C₄×C₂₃	1	2	yes	—
516	#124	C₂×C₄×C₂₃	1	2	yes	—
517	#124	C₂×C₄×C₂₃	1	2	yes	—
518	#124	C₂×C₄×C₂₃	1	2	yes	—
519	#123	C₂×C₄×C₂₃	1	4	yes	—
520	#123	C₂×C₄×C₂₃	1	4	yes	—
521	#123	C₂×C₄×C₂₃	1	4	yes	—
522	#123	C₂×C₄×C₂₃	1	4	yes	—
523	C₂²⋊Q₈	C₂×C₄×C₂₃	1	4	yes	—
524	C₂²⋊Q₈	C₂×C₄×C₂₃	1	4	yes	—
525	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
526	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
527	#121	C₂×C₄×C₂₃	1	4	yes	—
528	#121	C₂×C₄×C₂₃	1	4	yes	—
529	#121	C₂×C₄×C₂₃	1	2	yes	—
530	#121	C₂×C₄×C₂₃	1	2	yes	—
531	#121	C₂×C₄×C₂₃	1	2	yes	—
532	#121	C₂×C₄×C₂₃	1	2	yes	—
533	#120	C₂×C₄×C₂₃	1	4	yes	—
534	#120	C₂×C₄×C₂₃	1	4	yes	—
535	C₄×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
536	C₄×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
537	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
538	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
539	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
540	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
541	C₄×D₄	C₂×C₄×C₂₃	1	4	yes	—
542	C₄×D₄	C₂×C₄×C₂₃	1	4	yes	—
543	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
544	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
545	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
546	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
547	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
548	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
549	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
550	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
551	C₄×D₄	C₂³×C₂₃	1	4	yes	—
552	C₄×D₄	C₂³×C₂₃	1	4	yes	—
553	C₄×D₄	C₂³×C₂₃	1	2	yes	—
554	C₄×D₄	C₂³×C₂₃	1	2	yes	—
555	C₄×D₄	C₂³×C₂₃	1	2	yes	—
556	C₄×D₄	C₂³×C₂₃	1	2	yes	—
557	#117	C₂×C₄×C₂₃	1	2	yes	—
558	#117	C₂×C₄×C₂₃	1	2	yes	—
559	#117	C₂×C₄×C₂₃	1	1	yes	characteristic
560	#117	C₂×C₄×C₂₃	1	1	yes	characteristic
561	#117	C₂³×C₂₃	1	4	yes	—
562	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
563	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
564	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	4	yes	—
565	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	4	yes	—
566	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
567	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
568	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
569	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
570	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
571	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
572	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
573	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
574	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
575	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
576	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
577	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
578	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
579	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
580	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
581	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
582	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
583	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
584	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
585	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
586	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
587	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
588	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
589	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
590	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
591	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
592	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
593	#97	C₂³×C₂₃	1	2	yes	—
594	#97	C₂³×C₂₃	1	2	yes	—
595	#97	C₂³×C₂₃	1	4	yes	—
596	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
597	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
598	C₄×C₈	C₂³×C₂₃	1	2	yes	—
599	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
600	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
601	C₄×C₈	C₂³×C₂₃	1	2	yes	—
602	C₄×C₈	C₂³×C₂₃	1	2	yes	—
603	C₄×C₈	C₂³×C₂₃	1	2	yes	—
604	C₄×C₈	C₂³×C₂₃	1	4	yes	—
605	C₂₃	#60323	1	1	yes	characteristic, direct product factor, Sylow
606	C₂⁴	C₂²×C₄×C₂₃	1	4	yes	—
607	#41	—	2	4	no	—
608	#41	—	4	2	no	—
609	#41	—	4	2	no	—
610	#41	—	4	2	no	—
611	C₂×Q₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
612	C₂×Q₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
613	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
614	C₂×D₄	—	2	8	no	—
615	C₂×D₄	—	4	4	no	—
616	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
617	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
618	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
619	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
620	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
621	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
622	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
623	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
624	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
625	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
626	C₂²×C₄	—	4	4	no	—
627	C₂²×C₄	—	4	4	no	—
628	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
629	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
630	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
631	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
632	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
633	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
634	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
635	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
636	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
637	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
638	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
639	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
640	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
641	M₁₆	—	2	4	no	—
642	M₁₆	—	2	8	no	—
643	M₁₆	—	4	4	no	—
644	M₁₆	—	4	4	no	—
645	M₁₆	—	4	2	no	—
646	M₁₆	—	4	2	no	—
647	C₂×C₈	—	2	4	no	—
648	C₂×C₈	—	2	2	no	—
649	C₂×C₈	—	4	4	no	—
650	C₂×C₈	—	4	4	no	—
651	C₂×C₈	—	4	2	no	—
652	C₂×C₈	—	4	4	no	—
653	C₂×C₈	—	4	1	no	—
654	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
655	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
656	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
657	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
658	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
659	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
660	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
661	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
662	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
663	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
664	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
665	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
666	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
667	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
668	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
669	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
670	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
671	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
672	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
673	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
674	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
675	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
676	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
677	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
678	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
679	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
680	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
681	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
682	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
683	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
684	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
685	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
686	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
687	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
688	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
689	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
690	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
691	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
692	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
693	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
694	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
695	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
696	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
697	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
698	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
699	C₄²	C₂⁴×C₂₃	1	2	yes	—
700	C₄²	C₂⁴×C₂₃	1	2	yes	—
701	C₂³	—	2	8	no	—
702	C₂³	—	4	4	no	—
703	C₂³	—	4	4	no	—
704	C₂³	C₂³×C₄×C₂₃	1	4	yes	—
705	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
706	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
707	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
708	Q₈	—	2	2	no	—
709	Q₈	—	2	2	no	—
710	Q₈	—	4	2	no	—
711	D₄	—	2	8	no	—
712	D₄	—	2	4	no	—
713	D₄	—	2	4	no	—
714	D₄	—	2	2	no	—
715	D₄	—	2	4	no	—
716	D₄	—	4	4	no	—
717	D₄	—	4	4	no	—
718	D₄	—	4	2	no	—
719	D₄	—	4	2	no	—
720	D₄	C₂₃×#131	1	4	yes	complemented
721	C₂×C₄	—	2	4	no	—
722	C₂×C₄	—	2	4	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	4	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	1	no	—
728	C₂×C₄	—	2	4	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	4	no	—
732	C₂×C₄	—	2	1	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	4	4	no	—
735	C₂×C₄	—	4	4	no	—
736	C₂×C₄	—	4	4	no	—
737	C₂×C₄	—	4	2	no	—
738	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
739	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
740	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
741	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
742	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
743	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
744	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
745	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
746	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
747	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
748	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
749	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
750	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
751	C₈	—	2	1	no	—
752	C₈	—	2	2	no	—
753	C₈	—	2	2	no	—
754	C₈	—	2	4	no	—
755	C₈	—	2	1	no	—
756	C₈	—	2	2	no	—
757	C₈	—	2	2	no	—
758	C₈	—	2	1	no	—
759	C₈	C₂₃×H(5,𝔽₂)	1	2	yes	—
760	C₂²	—	2	2	no	—
761	C₂²	—	2	2	no	—
762	C₂²	—	2	2	no	—
763	C₂²	—	2	4	no	—
764	C₂²	—	2	1	no	—
765	C₂²	—	2	1	no	—
766	C₂²	—	2	2	no	—
767	C₂²	—	2	4	no	—
768	C₂²	—	2	1	no	—
769	C₂²	—	2	2	no	—
770	C₂²	—	2	4	no	—
771	C₂²	—	8	8	no	—
772	C₂²	C₂×C₂₃×#131	1	4	yes	—
773	C₂²	C₂⁴×C₄×C₂₃	1	1	yes	characteristic
774	C₄	—	2	2	no	—
775	C₄	—	2	2	no	—
776	C₄	—	2	4	no	—
777	C₄	—	2	1	no	—
778	C₄	—	2	1	no	—
779	C₄	—	2	2	no	—
780	C₄	—	2	2	no	—
781	C₄	—	2	1	no	—
782	C₄	—	2	2	no	—
783	C₄	—	2	2	no	—
784	C₄	C₂×C₂₃×#131	1	2	yes	—
785	C₄	C₂₃×#568	1	2	yes	—
786	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
787	C₄	C₂₃×#585	1	1	yes	characteristic
788	C₂	—	2	4	no	—
789	C₂	—	4	2	no	—
790	C₂	—	4	4	no	—
791	C₂	—	4	1	no	—
792	C₂	C₄×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
793	C₂	C₂²×C₂₃×#131	1	1	yes	characteristic
794	C₂	C₂×C₂₃×#568	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₂₃
Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
socle	C₂²×C₂₃	C₂⁴×C₄
prime radical	C₂₃×#3481	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₃×#2994	C₂	semidirect
3. C₂₃×#2993	C₂	semidirect
4. C₂₃×#2991	C₂	semidirect
5. C₂₃×#2990	C₂	semidirect
6. C₂₃×#2979	C₂	semidirect
7. C₂₃×#2976	C₂	semidirect
8. C₂₃×#2974	C₂	semidirect
9. C₂₃×#2972	C₂	semidirect
10. C₂₃×#2969	C₂	semidirect
11. C₂₃×#2966	C₂	semidirect
12. C₂₃×#2965	C₂	semidirect
13. C₈×#41×C₂₃	C₂	semidirect
14. D₄×M₁₆×C₂₃	C₂	semidirect
15. C₂₃×#2933	C₂	semidirect
16. C₂₃×#2931	C₂	semidirect
17. C₂×C₂₃×#436	C₂	semidirect
18. C₂×C₂₃×#131	C₂²	semidirect
19. C₂²×M₁₆×C₂₃	C₂²	semidirect
37. C₂₃×#446	C₂²	semidirect
38. C₂₃×#446	C₂²	semidirect
39. C₂₃×#446	C₂²	semidirect
40. C₈×Q₈×C₂₃	C₂²	semidirect
41. C₈×Q₈×C₂₃	C₂²	semidirect
42. C₈×Q₈×C₂₃	C₂²	semidirect
46. C₂₃×#436	C₂²	semidirect
47. C₂₃×#436	C₂²	semidirect
48. C₂₃×#436	C₂²	semidirect
49. C₂₃×#436	C₂²	semidirect
50. C₂₃×#436	C₂²	semidirect
51. C₂₃×#436	C₂²	semidirect
52. C₂₃×#436	C₂²	semidirect
53. C₂₃×#435	C₂²	semidirect
54. C₂₃×#435	C₂²	semidirect
55. C₂₃×#435	C₂²	semidirect
56. C₂₃×#435	C₂²	semidirect
57. C₂₃×#435	C₂²	semidirect
58. C₂₃×#435	C₂²	semidirect
59. C₂₃×#435	C₂²	semidirect
63. C₈×D₄×C₂₃	C₂²	semidirect
64. C₈×D₄×C₂₃	C₂²	semidirect
65. C₈×D₄×C₂₃	C₂²	semidirect
66. C₈×D₄×C₂₃	C₂²	semidirect
67. C₈×D₄×C₂₃	C₂²	semidirect
68. C₈×D₄×C₂₃	C₂²	semidirect
69. C₈×D₄×C₂₃	C₂²	semidirect
70. C₈×D₄×C₂₃	C₂²	semidirect
71. C₂₃×#433	C₂²	semidirect
72. C₂₃×#433	C₂²	semidirect
73. C₂₃×#432	C₂²	semidirect
74. C₂₃×#431	C₂²	semidirect
75. C₂₃×#431	C₂²	semidirect
76. C₂₃×#431	C₂²	semidirect
77. C₂₃×#431	C₂²	semidirect
78. C₂₃×#431	C₂²	semidirect
79. C₂₃×#424	C₂²	semidirect
80. C₂₃×#423	C₂²	semidirect
81. C₂₃×#423	C₂²	semidirect
82. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
83. C₂₃×#408	C₂²	semidirect
84. C₂₃×#408	C₂²	semidirect
85. C₂₃×#407	C₂²	semidirect
86. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
87. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
88. C₂₃×#405	C₂²	semidirect
89. C₄×M₁₆×C₂₃	C₂²	semidirect
90. C₂×C₄×C₈×C₂₃	C₂²	semidirect
91. C₂×C₄×C₈×C₂₃	C₂²	semidirect
303. #60323	C₂₃	direct (N × H)
323. D₄×C₂₃	#131	semidirect
364. #2994	C₂×C₂₃	semidirect
365. #2993	C₂×C₂₃	semidirect
366. #2991	C₂×C₂₃	semidirect
367. #2990	C₂×C₂₃	semidirect
368. #2979	C₂×C₂₃	semidirect
369. #2976	C₂×C₂₃	semidirect
370. #2974	C₂×C₂₃	semidirect
371. #2972	C₂×C₂₃	semidirect
372. #2969	C₂×C₂₃	semidirect
373. #2966	C₂×C₂₃	semidirect
374. #2965	C₂×C₂₃	semidirect
375. C₈×#41	C₂×C₂₃	semidirect
376. D₄×M₁₆	C₂×C₂₃	semidirect
377. #2933	C₂×C₂₃	semidirect
378. #2931	C₂×C₂₃	semidirect
379. C₂×#436	C₂×C₂₃	semidirect
408. C₂×#131	C₂²×C₂₃	semidirect
409. C₂²×M₁₆	C₂²×C₂₃	semidirect
427. #446	C₂²×C₂₃	semidirect
428. #446	C₂²×C₂₃	semidirect
429. #446	C₂²×C₂₃	semidirect
430. C₈×Q₈	C₂²×C₂₃	semidirect
431. C₈×Q₈	C₂²×C₂₃	semidirect
432. C₈×Q₈	C₂²×C₂₃	semidirect
436. #436	C₂²×C₂₃	semidirect
437. #436	C₂²×C₂₃	semidirect
438. #436	C₂²×C₂₃	semidirect
439. #436	C₂²×C₂₃	semidirect
440. #436	C₂²×C₂₃	semidirect
441. #436	C₂²×C₂₃	semidirect
442. #436	C₂²×C₂₃	semidirect
443. #435	C₂²×C₂₃	semidirect
444. #435	C₂²×C₂₃	semidirect
445. #435	C₂²×C₂₃	semidirect
446. #435	C₂²×C₂₃	semidirect
447. #435	C₂²×C₂₃	semidirect
448. #435	C₂²×C₂₃	semidirect
449. #435	C₂²×C₂₃	semidirect
453. C₈×D₄	C₂²×C₂₃	semidirect
454. C₈×D₄	C₂²×C₂₃	semidirect
455. C₈×D₄	C₂²×C₂₃	semidirect
456. C₈×D₄	C₂²×C₂₃	semidirect
457. C₈×D₄	C₂²×C₂₃	semidirect
458. C₈×D₄	C₂²×C₂₃	semidirect
459. C₈×D₄	C₂²×C₂₃	semidirect
460. C₈×D₄	C₂²×C₂₃	semidirect
461. #433	C₂²×C₂₃	semidirect
462. #433	C₂²×C₂₃	semidirect
463. #432	C₂²×C₂₃	semidirect
464. #431	C₂²×C₂₃	semidirect
465. #431	C₂²×C₂₃	semidirect
466. #431	C₂²×C₂₃	semidirect
467. #431	C₂²×C₂₃	semidirect
468. #431	C₂²×C₂₃	semidirect
469. #424	C₂²×C₂₃	semidirect
470. #423	C₂²×C₂₃	semidirect
471. #423	C₂²×C₂₃	semidirect
472. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
473. #408	C₂²×C₂₃	semidirect
474. #408	C₂²×C₂₃	semidirect
475. #407	C₂²×C₂₃	semidirect
476. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
477. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
478. #405	C₂²×C₂₃	semidirect
479. C₄×M₁₆	C₂²×C₂₃	semidirect
480. C₂×C₄×C₈	C₂²×C₂₃	semidirect
481. C₂×C₄×C₈	C₂²×C₂₃	semidirect
605. C₂₃	#60323	direct (N × H)
720. D₄	C₂₃×#131	semidirect

Maximal subgroups

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

subgroup	index
C₂₃×#3481	2
C₂₃×#2994	2
C₂₃×#2993	2
C₂₃×#2991	2
C₂₃×#2990	2
C₂₃×#2979	2
C₂₃×#2976	2
C₂₃×#2974	2
C₂₃×#2972	2
C₂₃×#2969	2
C₂₃×#2966	2
C₂₃×#2965	2
C₈×#41×C₂₃	2
D₄×M₁₆×C₂₃	2
C₂₃×#2933	2
C₂₃×#2931	2
C₂×C₂₃×#436	2
#60323	23

Subgroups — C23×#60323 #19207949

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60323 #19207949