Subgroups — C₂₃×#60297 #19207923

Order 5888.

1684 conjugacy classes of subgroups.

The subgroup lattice has 942 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3455	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2995	C₂	1	2	yes	maximal, complemented
3	C₂₃×#2994	C₂	1	2	yes	maximal, complemented
4	C₂₃×#2993	C₂	1	2	yes	maximal, complemented
5	C₂₃×#2992	C₂	1	2	yes	maximal, complemented
6	C₂₃×#2987	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#2986	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#2981	C₂	1	2	yes	maximal, complemented
9	C₂₃×#2978	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#2977	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#2976	C₂	1	2	yes	maximal, complemented
12	C₂₃×#2969	C₂	1	2	yes	maximal, complemented
13	C₂₃×#2968	C₂	1	2	yes	maximal, complemented
14	C₂₃×#2967	C₂	1	2	yes	maximal, complemented
15	C₂₃×#2966	C₂	1	2	yes	maximal, complemented
16	C₂₃×#2925	C₂	1	2	yes	maximal, complemented
17	C₂₃×#2924	C₂	1	2	yes	maximal, complemented
18	C₂₃×#2923	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#2922	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#542	C₄	1	2	yes	—
21	C₂₃×#542	C₄	1	2	yes	—
22	C₂₃×#541	C₄	1	2	yes	—
23	C₂₃×#540	C₄	1	2	yes	—
24	C₂₃×#539	C₄	1	2	yes	—
25	C₂₃×#539	C₄	1	2	yes	—
26	C₂₃×#538	C₄	1	2	yes	—
27	C₂₃×#538	C₄	1	2	yes	—
28	C₂₃×#533	C₂²	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×#529	C₂²	1	2	yes	—
33	C₂₃×#529	C₂²	1	2	yes	—
34	C₂₃×#525	C₂²	1	1	yes	characteristic
35	C₂₃×#525	C₂²	1	1	yes	characteristic
36	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
37	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
38	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
39	C₂₃×#446	C₂²	1	2	yes	complemented
40	C₂₃×#446	C₂²	1	2	yes	complemented
41	C₂₃×#446	C₂²	1	2	yes	complemented
42	C₂₃×#446	C₂²	1	2	yes	complemented
43	C₂₃×#446	C₂²	1	2	yes	complemented
44	C₂₃×#446	C₂²	1	2	yes	complemented
45	C₈×Q₈×C₂₃	C₂²	1	2	yes	complemented
46	C₈×Q₈×C₂₃	C₂²	1	2	yes	complemented
47	C₂₃×#436	C₂²	1	2	yes	—
48	C₂₃×#436	C₂²	1	2	yes	—
49	C₂₃×#436	C₂²	1	2	yes	—
50	C₂₃×#436	C₂²	1	2	yes	—
51	C₂₃×#436	C₂²	1	2	yes	complemented
52	C₂₃×#436	C₂²	1	2	yes	complemented
53	C₂₃×#435	C₂²	1	2	yes	—
54	C₂₃×#435	C₂²	1	2	yes	—
55	C₂₃×#435	C₂²	1	2	yes	—
56	C₂₃×#435	C₂²	1	2	yes	—
57	C₂₃×#435	C₂²	1	2	yes	—
58	C₂₃×#435	C₂²	1	2	yes	—
59	C₂₃×#435	C₂²	1	2	yes	—
60	C₂₃×#435	C₂²	1	2	yes	—
61	C₂₃×#435	C₂²	1	2	yes	complemented
62	C₂₃×#435	C₂²	1	2	yes	complemented
63	C₂₃×#435	C₂²	1	2	yes	complemented
64	C₂₃×#435	C₂²	1	2	yes	complemented
65	C₈×D₄×C₂₃	C₂²	1	2	yes	—
66	C₈×D₄×C₂₃	C₂²	1	2	yes	—
67	C₈×D₄×C₂₃	C₂²	1	2	yes	—
68	C₈×D₄×C₂₃	C₂²	1	2	yes	—
69	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
70	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
71	C₂₃×#433	C₂²	1	1	yes	characteristic
72	C₂₃×#433	C₂²	1	1	yes	characteristic
73	C₂₃×#433	C₂²	1	1	yes	characteristic
74	C₂₃×#433	C₂²	1	1	yes	characteristic
75	C₂₃×#433	C₂²	1	2	yes	—
76	C₂₃×#433	C₂²	1	2	yes	—
77	C₂₃×#433	C₂²	1	2	yes	—
78	C₂₃×#433	C₂²	1	2	yes	—
79	C₂₃×#433	C₂²	1	2	yes	—
80	C₂₃×#433	C₂²	1	2	yes	—
81	C₂₃×#433	C₂²	1	1	yes	characteristic, complemented
82	C₂₃×#433	C₂²	1	1	yes	characteristic, complemented
83	C₂₃×#433	C₂²	1	1	yes	characteristic, complemented
84	C₂₃×#433	C₂²	1	1	yes	characteristic, complemented
85	C₂₃×#433	C₂²	1	2	yes	complemented
86	C₂₃×#433	C₂²	1	2	yes	complemented
87	C₂₃×#432	C₂²	1	2	yes	—
88	C₂₃×#432	C₂²	1	2	yes	—
89	C₂₃×#432	C₂²	1	2	yes	complemented
90	C₂₃×#432	C₂²	1	2	yes	complemented
91	C₂₃×#431	C₂²	1	2	yes	—
92	C₂₃×#431	C₂²	1	2	yes	—
93	C₂₃×#431	C₂²	1	2	yes	complemented
94	C₂₃×#431	C₂²	1	2	yes	complemented
95	C₂₃×#424	C₂²	1	2	yes	—
96	C₂₃×#424	C₂²	1	2	yes	—
97	C₂₃×#424	C₂²	1	2	yes	complemented
98	C₂₃×#424	C₂²	1	2	yes	complemented
99	C₂₃×#423	C₂²	1	2	yes	complemented
100	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	complemented
101	C₂₃×#408	C₂²	1	2	yes	—
102	C₂₃×#408	C₂²	1	2	yes	—
103	C₂₃×#408	C₂²	1	2	yes	—
104	C₂₃×#408	C₂²	1	2	yes	—
105	C₂₃×#407	C₂²	1	2	yes	—
106	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	—
107	C₂₃×#405	C₂²	1	2	yes	—
108	C₂₃×#405	C₂²	1	2	yes	—
109	C₂₃×#405	C₂²	1	2	yes	complemented
110	C₂₃×#405	C₂²	1	2	yes	complemented
111	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
112	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
113	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic, complemented
114	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
115	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
116	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
118	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
119	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
120	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
121	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
122	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
123	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
124	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
125	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
126	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
127	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
128	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
129	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
130	C₂₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
131	C₂₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
132	C₂₃×#127	C₂×C₄	1	1	yes	characteristic
133	C₂₃×#126	C₂×C₄	1	2	yes	—
134	C₂₃×#126	C₂×C₄	1	2	yes	—
135	C₂₃×#126	C₂×C₄	1	2	yes	—
136	C₂₃×#126	C₂×C₄	1	2	yes	—
137	C₂₃×#126	C₂×C₄	1	2	yes	—
138	C₂₃×#126	C₂×C₄	1	2	yes	—
139	C₂₃×#126	C₂×C₄	1	2	yes	—
140	C₂₃×#126	C₂×C₄	1	2	yes	—
141	C₂₃×#125	C₂×C₄	1	2	yes	—
142	C₂₃×#125	C₂×C₄	1	2	yes	—
143	C₂₃×#125	C₂×C₄	1	2	yes	—
144	C₂₃×#125	C₂×C₄	1	2	yes	—
145	C₂₃×#125	C₂×C₄	1	2	yes	—
146	C₂₃×#124	C₂×C₄	1	2	yes	—
147	C₂₃×#124	C₂×C₄	1	2	yes	—
148	C₂₃×#124	C₂×C₄	1	2	yes	—
149	C₂₃×#124	C₂×C₄	1	2	yes	—
150	C₂₃×#124	C₂×C₄	1	1	yes	characteristic
151	C₂₃×#124	C₂×C₄	1	1	yes	characteristic
152	C₂₃×#123	C₂×C₄	1	1	yes	characteristic
153	C₂₃×#123	C₂×C₄	1	1	yes	characteristic
154	C₂₃×#123	C₂×C₄	1	2	yes	—
155	C₂₃×#123	C₂×C₄	1	2	yes	—
156	C₂₃×#123	C₂×C₄	1	2	yes	—
157	C₂₃×#123	C₂×C₄	1	2	yes	—
158	C₂₃×#123	C₂×C₄	1	2	yes	—
159	C₂₃×#123	C₂×C₄	1	2	yes	—
160	C₂₃×#123	C₂×C₄	1	2	yes	—
161	C₂₃×#123	C₂×C₄	1	2	yes	—
162	C₂₃×#123	C₂×C₄	1	2	yes	—
163	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
164	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
165	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
166	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
167	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
168	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
169	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
170	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
171	C₂₃×#121	C₂×C₄	1	2	yes	—
172	C₂₃×#121	C₂×C₄	1	2	yes	—
173	C₂₃×#121	C₂×C₄	1	2	yes	—
174	C₂₃×#121	C₂×C₄	1	2	yes	—
175	C₂₃×#121	C₂×C₄	1	2	yes	—
176	C₂₃×#121	C₂×C₄	1	2	yes	—
177	C₂₃×#121	C₂×C₄	1	2	yes	—
178	C₂₃×#121	C₂×C₄	1	2	yes	—
179	C₂₃×#120	C₂×C₄	1	1	yes	characteristic
180	C₂₃×#120	C₂×C₄	1	1	yes	characteristic
181	C₂₃×#120	C₂×C₄	1	2	yes	—
182	C₄×Q₈×C₂₃	C₂×C₄	1	2	yes	—
183	C₄×Q₈×C₂₃	C₂×C₄	1	2	yes	—
184	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
185	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
186	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
187	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
188	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
189	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
190	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
191	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
192	C₄×D₄×C₂₃	C₂³	1	2	yes	—
193	C₄×D₄×C₂₃	C₂³	1	2	yes	—
194	C₄×D₄×C₂₃	C₂³	1	2	yes	—
195	C₄×D₄×C₂₃	C₂³	1	2	yes	—
196	C₄×D₄×C₂₃	C₂³	1	2	yes	—
197	C₄×D₄×C₂₃	C₂³	1	2	yes	—
198	C₂₃×#117	C₂×C₄	1	2	yes	—
199	C₂₃×#117	C₂×C₄	1	2	yes	—
200	C₂₃×#117	C₂³	1	2	yes	—
201	C₂₃×#117	C₂³	1	2	yes	—
202	C₂₃×#117	C₂³	1	2	yes	—
203	C₂₃×#117	C₂³	1	1	yes	characteristic
204	C₂₃×#117	C₂³	1	1	yes	characteristic
205	C₂₃×#117	C₂³	1	1	yes	characteristic
206	C₂₃×#117	C₂³	1	1	yes	characteristic
207	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
208	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
209	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
210	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
211	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
212	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
213	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
214	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
215	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
216	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
217	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
218	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
219	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
220	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
221	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
222	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
223	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
224	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
225	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
226	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
227	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
228	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
229	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
230	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
231	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
232	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
233	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
234	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
235	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
236	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
237	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
238	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
239	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
240	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
241	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
242	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
243	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
244	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
245	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
246	C₂₃×#97	C₂³	1	2	yes	—
247	C₂₃×#97	C₂³	1	1	yes	characteristic
248	C₂₃×#97	C₂³	1	1	yes	characteristic
249	C₂₃×#97	C₂³	1	2	yes	—
250	C₂₃×#97	C₂³	1	1	yes	characteristic
251	C₂₃×#97	C₂³	1	1	yes	characteristic
252	C₂₃×#97	C₂³	1	2	yes	—
253	C₂₃×#97	C₂³	1	2	yes	—
254	C₂₃×#97	C₂³	1	2	yes	—
255	C₂₃×#97	C₂³	1	2	yes	—
256	C₄×C₈×C₂₃	C₂³	1	2	yes	—
257	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
258	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
259	C₄×C₈×C₂₃	C₂³	1	2	yes	—
260	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
261	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
262	C₄×C₈×C₂₃	C₂³	1	2	yes	—
263	C₄×C₈×C₂₃	C₂³	1	2	yes	—
264	C₄×C₈×C₂₃	C₂³	1	2	yes	—
265	C₄×C₈×C₂₃	C₂³	1	2	yes	—
266	C₂⁴×C₂₃	C₂²×C₄	1	1	yes	characteristic
267	#41×C₂₃	—	4	2	no	—
268	#41×C₂₃	—	4	2	no	—
269	C₂×Q₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
270	C₂×Q₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
271	C₂×Q₈×C₂₃	C₂²×C₄	1	2	yes	—
272	C₂×Q₈×C₂₃	C₂²×C₄	1	2	yes	—
273	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
274	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
275	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
276	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
277	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
278	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
279	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
280	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
281	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
282	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
283	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
284	C₂²×C₄×C₂₃	—	4	2	no	—
285	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
286	C₂²×C₄×C₂₃	C₂²×C₄	1	2	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	1	yes	characteristic
292	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
293	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
294	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
295	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
296	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
297	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
298	M₁₆×C₂₃	—	4	2	no	—
299	M₁₆×C₂₃	—	4	2	no	—
300	M₁₆×C₂₃	—	4	2	no	—
301	M₁₆×C₂₃	—	4	2	no	—
302	M₁₆×C₂₃	—	4	2	no	—
303	M₁₆×C₂₃	—	4	2	no	—
304	C₂×C₈×C₂₃	—	4	2	no	—
305	C₂×C₈×C₂₃	—	4	2	no	—
306	C₂×C₈×C₂₃	—	4	2	no	—
307	C₂×C₈×C₂₃	—	4	2	no	—
308	C₂×C₈×C₂₃	—	4	2	no	—
309	C₂×C₈×C₂₃	—	4	2	no	—
310	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
311	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
312	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
313	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
314	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
315	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
316	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
317	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
318	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
319	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
320	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
321	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
322	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
323	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
324	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
325	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
326	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
327	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
328	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
329	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
330	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
331	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
332	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
333	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
334	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
335	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
336	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
337	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
338	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
339	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
340	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
341	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
342	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
343	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
344	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
345	C₂²⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
346	C₂²⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
347	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
348	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
349	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
350	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
351	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
352	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
353	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
354	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
355	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
356	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
357	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
358	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
359	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
360	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
361	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
362	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
363	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
364	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
365	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
366	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
367	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
368	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
369	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
370	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
371	C₄²×C₂₃	C₂⁴	1	2	yes	—
372	C₄²×C₂₃	C₂⁴	1	2	yes	—
373	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
374	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
375	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
376	#60297	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
377	C₂³×C₂₃	—	4	1	no	—
378	C₂³×C₂₃	—	4	2	no	—
379	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
380	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
381	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
382	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
383	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
384	Q₈×C₂₃	—	4	2	no	—
385	Q₈×C₂₃	—	4	2	no	—
386	Q₈×C₂₃	—	4	1	no	—
387	Q₈×C₂₃	—	4	1	no	—
388	D₄×C₂₃	—	4	2	no	—
389	D₄×C₂₃	—	4	2	no	—
390	D₄×C₂₃	—	4	2	no	—
391	D₄×C₂₃	—	4	2	no	—
392	D₄×C₂₃	—	4	2	no	—
393	D₄×C₂₃	—	4	2	no	—
394	D₄×C₂₃	—	4	1	no	—
395	D₄×C₂₃	—	4	1	no	—
396	D₄×C₂₃	—	4	2	no	—
397	D₄×C₂₃	—	4	1	no	—
398	D₄×C₂₃	—	4	1	no	—
399	C₂×C₄×C₂₃	—	2	2	no	—
400	C₂×C₄×C₂₃	—	2	2	no	—
401	C₂×C₄×C₂₃	—	2	2	no	—
402	C₂×C₄×C₂₃	—	2	2	no	—
403	C₂×C₄×C₂₃	—	2	2	no	—
404	C₂×C₄×C₂₃	—	2	2	no	—
405	C₂×C₄×C₂₃	—	2	2	no	—
406	C₂×C₄×C₂₃	—	4	1	no	—
407	C₂×C₄×C₂₃	—	4	2	no	—
408	C₂×C₄×C₂₃	—	4	2	no	—
409	C₂×C₄×C₂₃	—	4	2	no	—
410	C₂×C₄×C₂₃	—	4	2	no	—
411	C₂×C₄×C₂₃	—	4	2	no	—
412	C₂×C₄×C₂₃	—	4	2	no	—
413	C₂×C₄×C₂₃	—	4	2	no	—
414	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
415	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
416	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
417	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
418	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
419	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
420	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
421	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
422	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
423	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
424	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
425	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
426	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
427	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
428	C₈×C₂₃	—	2	2	no	—
429	C₈×C₂₃	—	2	2	no	—
430	C₈×C₂₃	—	2	2	no	—
431	C₈×C₂₃	—	2	2	no	—
432	C₈×C₂₃	—	2	2	no	—
433	C₈×C₂₃	—	2	2	no	—
434	C₈×C₂₃	—	2	2	no	—
435	C₈×C₂₃	—	2	2	no	—
436	#3455	C₂×C₂₃	1	1	yes	characteristic
437	#2995	C₂×C₂₃	1	2	yes	complemented
438	#2994	C₂×C₂₃	1	2	yes	complemented
439	#2993	C₂×C₂₃	1	2	yes	complemented
440	#2992	C₂×C₂₃	1	2	yes	complemented
441	#2987	C₂×C₂₃	1	1	yes	characteristic, complemented
442	#2986	C₂×C₂₃	1	1	yes	characteristic, complemented
443	#2981	C₂×C₂₃	1	2	yes	complemented
444	#2978	C₂×C₂₃	1	1	yes	characteristic, complemented
445	#2977	C₂×C₂₃	1	1	yes	characteristic, complemented
446	#2976	C₂×C₂₃	1	2	yes	complemented
447	#2969	C₂×C₂₃	1	2	yes	complemented
448	#2968	C₂×C₂₃	1	2	yes	complemented
449	#2967	C₂×C₂₃	1	2	yes	complemented
450	#2966	C₂×C₂₃	1	2	yes	complemented
451	#2925	C₂×C₂₃	1	2	yes	complemented
452	#2924	C₂×C₂₃	1	2	yes	complemented
453	#2923	C₂×C₂₃	1	1	yes	characteristic, complemented
454	#2922	C₂×C₂₃	1	1	yes	characteristic, complemented
455	C₂²×C₂₃	—	2	1	no	—
456	C₂²×C₂₃	—	2	2	no	—
457	C₂²×C₂₃	—	2	2	no	—
458	C₂²×C₂₃	—	2	1	no	—
459	C₂²×C₂₃	—	2	1	no	—
460	C₂²×C₂₃	—	2	2	no	—
461	C₂²×C₂₃	—	2	2	no	—
462	C₂²×C₂₃	—	2	2	no	—
463	C₂²×C₂₃	—	2	2	no	—
464	C₂²×C₂₃	—	2	2	no	—
465	C₂²×C₂₃	—	2	2	no	—
466	C₂²×C₂₃	—	2	2	no	—
467	C₂²×C₂₃	—	8	2	no	—
468	C₂²×C₂₃	C₂⁴×C₄	1	1	yes	characteristic
469	C₄×C₂₃	—	2	2	no	—
470	C₄×C₂₃	—	2	1	no	—
471	C₄×C₂₃	—	2	2	no	—
472	C₄×C₂₃	—	2	1	no	—
473	C₄×C₂₃	—	2	1	no	—
474	C₄×C₂₃	—	2	2	no	—
475	C₄×C₂₃	—	2	2	no	—
476	C₄×C₂₃	—	2	2	no	—
477	C₄×C₂₃	—	2	2	no	—
478	C₄×C₂₃	—	2	2	no	—
479	C₄×C₂₃	—	2	2	no	—
480	C₄×C₂₃	—	2	2	no	—
481	C₄×C₂₃	—	2	2	no	—
482	C₄×C₂₃	#585	1	2	yes	—
483	#542	C₄×C₂₃	1	2	yes	—
484	#542	C₄×C₂₃	1	2	yes	—
485	#541	C₄×C₂₃	1	2	yes	—
486	#540	C₄×C₂₃	1	2	yes	—
487	#539	C₄×C₂₃	1	2	yes	—
488	#539	C₄×C₂₃	1	2	yes	—
489	#538	C₄×C₂₃	1	2	yes	—
490	#538	C₄×C₂₃	1	2	yes	—
491	#533	C₂²×C₂₃	1	1	yes	characteristic
492	#532	C₂²×C₂₃	1	1	yes	characteristic
493	#529	C₂²×C₂₃	1	2	yes	—
494	#529	C₂²×C₂₃	1	2	yes	—
495	#529	C₂²×C₂₃	1	2	yes	—
496	#529	C₂²×C₂₃	1	2	yes	—
497	#525	C₂²×C₂₃	1	1	yes	characteristic
498	#525	C₂²×C₂₃	1	1	yes	characteristic
499	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
500	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
501	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
502	#446	C₂²×C₂₃	1	2	yes	complemented
503	#446	C₂²×C₂₃	1	2	yes	complemented
504	#446	C₂²×C₂₃	1	2	yes	complemented
505	#446	C₂²×C₂₃	1	2	yes	complemented
506	#446	C₂²×C₂₃	1	2	yes	complemented
507	#446	C₂²×C₂₃	1	2	yes	complemented
508	C₈×Q₈	C₂²×C₂₃	1	2	yes	complemented
509	C₈×Q₈	C₂²×C₂₃	1	2	yes	complemented
510	#436	C₂²×C₂₃	1	2	yes	—
511	#436	C₂²×C₂₃	1	2	yes	—
512	#436	C₂²×C₂₃	1	2	yes	—
513	#436	C₂²×C₂₃	1	2	yes	—
514	#436	C₂²×C₂₃	1	2	yes	complemented
515	#436	C₂²×C₂₃	1	2	yes	complemented
516	#435	C₂²×C₂₃	1	2	yes	—
517	#435	C₂²×C₂₃	1	2	yes	—
518	#435	C₂²×C₂₃	1	2	yes	—
519	#435	C₂²×C₂₃	1	2	yes	—
520	#435	C₂²×C₂₃	1	2	yes	—
521	#435	C₂²×C₂₃	1	2	yes	—
522	#435	C₂²×C₂₃	1	2	yes	—
523	#435	C₂²×C₂₃	1	2	yes	—
524	#435	C₂²×C₂₃	1	2	yes	complemented
525	#435	C₂²×C₂₃	1	2	yes	complemented
526	#435	C₂²×C₂₃	1	2	yes	complemented
527	#435	C₂²×C₂₃	1	2	yes	complemented
528	C₈×D₄	C₂²×C₂₃	1	2	yes	—
529	C₈×D₄	C₂²×C₂₃	1	2	yes	—
530	C₈×D₄	C₂²×C₂₃	1	2	yes	—
531	C₈×D₄	C₂²×C₂₃	1	2	yes	—
532	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
533	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
534	#433	C₂²×C₂₃	1	1	yes	characteristic
535	#433	C₂²×C₂₃	1	1	yes	characteristic
536	#433	C₂²×C₂₃	1	1	yes	characteristic
537	#433	C₂²×C₂₃	1	1	yes	characteristic
538	#433	C₂²×C₂₃	1	2	yes	—
539	#433	C₂²×C₂₃	1	2	yes	—
540	#433	C₂²×C₂₃	1	2	yes	—
541	#433	C₂²×C₂₃	1	2	yes	—
542	#433	C₂²×C₂₃	1	2	yes	—
543	#433	C₂²×C₂₃	1	2	yes	—
544	#433	C₂²×C₂₃	1	1	yes	characteristic, complemented
545	#433	C₂²×C₂₃	1	1	yes	characteristic, complemented
546	#433	C₂²×C₂₃	1	1	yes	characteristic, complemented
547	#433	C₂²×C₂₃	1	1	yes	characteristic, complemented
548	#433	C₂²×C₂₃	1	2	yes	complemented
549	#433	C₂²×C₂₃	1	2	yes	complemented
550	#432	C₂²×C₂₃	1	2	yes	—
551	#432	C₂²×C₂₃	1	2	yes	—
552	#432	C₂²×C₂₃	1	2	yes	complemented
553	#432	C₂²×C₂₃	1	2	yes	complemented
554	#431	C₂²×C₂₃	1	2	yes	—
555	#431	C₂²×C₂₃	1	2	yes	—
556	#431	C₂²×C₂₃	1	2	yes	complemented
557	#431	C₂²×C₂₃	1	2	yes	complemented
558	#424	C₂²×C₂₃	1	2	yes	—
559	#424	C₂²×C₂₃	1	2	yes	—
560	#424	C₂²×C₂₃	1	2	yes	complemented
561	#424	C₂²×C₂₃	1	2	yes	complemented
562	#423	C₂²×C₂₃	1	2	yes	complemented
563	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	complemented
564	#408	C₂²×C₂₃	1	2	yes	—
565	#408	C₂²×C₂₃	1	2	yes	—
566	#408	C₂²×C₂₃	1	2	yes	—
567	#408	C₂²×C₂₃	1	2	yes	—
568	#407	C₂²×C₂₃	1	2	yes	—
569	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	—
570	#405	C₂²×C₂₃	1	2	yes	—
571	#405	C₂²×C₂₃	1	2	yes	—
572	#405	C₂²×C₂₃	1	2	yes	complemented
573	#405	C₂²×C₂₃	1	2	yes	complemented
574	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
575	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
576	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic, complemented
577	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
578	C₂×C₂₃	—	4	2	no	—
579	C₂×C₂₃	—	4	1	no	—
580	C₂×C₂₃	—	4	1	no	—
581	C₂×C₂₃	—	4	1	no	—
582	C₂×C₂₃	—	4	2	no	—
583	C₂×C₂₃	#3428	1	1	yes	characteristic
584	C₂×C₂₃	#3573	1	2	yes	—
585	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
586	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
587	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
588	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
589	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
590	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
591	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
592	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
593	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
594	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
595	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
596	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
597	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
598	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
599	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
600	C₄⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
601	C₄⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
602	#127	C₂×C₄×C₂₃	1	1	yes	characteristic
603	#126	C₂×C₄×C₂₃	1	2	yes	—
604	#126	C₂×C₄×C₂₃	1	2	yes	—
605	#126	C₂×C₄×C₂₃	1	2	yes	—
606	#126	C₂×C₄×C₂₃	1	2	yes	—
607	#126	C₂×C₄×C₂₃	1	2	yes	—
608	#126	C₂×C₄×C₂₃	1	2	yes	—
609	#126	C₂×C₄×C₂₃	1	2	yes	—
610	#126	C₂×C₄×C₂₃	1	2	yes	—
611	#125	C₂×C₄×C₂₃	1	2	yes	—
612	#125	C₂×C₄×C₂₃	1	2	yes	—
613	#125	C₂×C₄×C₂₃	1	2	yes	—
614	#125	C₂×C₄×C₂₃	1	2	yes	—
615	#125	C₂×C₄×C₂₃	1	2	yes	—
616	#124	C₂×C₄×C₂₃	1	2	yes	—
617	#124	C₂×C₄×C₂₃	1	2	yes	—
618	#124	C₂×C₄×C₂₃	1	2	yes	—
619	#124	C₂×C₄×C₂₃	1	2	yes	—
620	#124	C₂×C₄×C₂₃	1	1	yes	characteristic
621	#124	C₂×C₄×C₂₃	1	1	yes	characteristic
622	#123	C₂×C₄×C₂₃	1	1	yes	characteristic
623	#123	C₂×C₄×C₂₃	1	1	yes	characteristic
624	#123	C₂×C₄×C₂₃	1	2	yes	—
625	#123	C₂×C₄×C₂₃	1	2	yes	—
626	#123	C₂×C₄×C₂₃	1	2	yes	—
627	#123	C₂×C₄×C₂₃	1	2	yes	—
628	#123	C₂×C₄×C₂₃	1	2	yes	—
629	#123	C₂×C₄×C₂₃	1	2	yes	—
630	#123	C₂×C₄×C₂₃	1	2	yes	—
631	#123	C₂×C₄×C₂₃	1	2	yes	—
632	#123	C₂×C₄×C₂₃	1	2	yes	—
633	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
634	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
635	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
636	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
637	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
638	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
639	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
640	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
641	#121	C₂×C₄×C₂₃	1	2	yes	—
642	#121	C₂×C₄×C₂₃	1	2	yes	—
643	#121	C₂×C₄×C₂₃	1	2	yes	—
644	#121	C₂×C₄×C₂₃	1	2	yes	—
645	#121	C₂×C₄×C₂₃	1	2	yes	—
646	#121	C₂×C₄×C₂₃	1	2	yes	—
647	#121	C₂×C₄×C₂₃	1	2	yes	—
648	#121	C₂×C₄×C₂₃	1	2	yes	—
649	#120	C₂×C₄×C₂₃	1	1	yes	characteristic
650	#120	C₂×C₄×C₂₃	1	1	yes	characteristic
651	#120	C₂×C₄×C₂₃	1	2	yes	—
652	C₄×Q₈	C₂×C₄×C₂₃	1	2	yes	—
653	C₄×Q₈	C₂×C₄×C₂₃	1	2	yes	—
654	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
655	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
656	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
657	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
658	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
659	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
660	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
661	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
662	C₄×D₄	C₂³×C₂₃	1	2	yes	—
663	C₄×D₄	C₂³×C₂₃	1	2	yes	—
664	C₄×D₄	C₂³×C₂₃	1	2	yes	—
665	C₄×D₄	C₂³×C₂₃	1	2	yes	—
666	C₄×D₄	C₂³×C₂₃	1	2	yes	—
667	C₄×D₄	C₂³×C₂₃	1	2	yes	—
668	#117	C₂×C₄×C₂₃	1	2	yes	—
669	#117	C₂×C₄×C₂₃	1	2	yes	—
670	#117	C₂³×C₂₃	1	2	yes	—
671	#117	C₂³×C₂₃	1	2	yes	—
672	#117	C₂³×C₂₃	1	1	yes	characteristic
673	#117	C₂³×C₂₃	1	1	yes	characteristic
674	#117	C₂³×C₂₃	1	2	yes	—
675	#117	C₂³×C₂₃	1	1	yes	characteristic
676	#117	C₂³×C₂₃	1	1	yes	characteristic
677	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
678	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
679	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
680	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
681	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
682	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
683	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
684	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
685	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
686	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
687	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
688	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
689	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
690	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
691	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
692	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
693	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
694	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
695	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
696	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
697	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
698	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
699	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
700	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
701	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
702	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
703	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
704	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
705	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
706	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
707	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
708	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
709	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
710	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
711	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
712	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
713	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
714	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
715	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
716	#97	C₂³×C₂₃	1	2	yes	—
717	#97	C₂³×C₂₃	1	1	yes	characteristic
718	#97	C₂³×C₂₃	1	1	yes	characteristic
719	#97	C₂³×C₂₃	1	2	yes	—
720	#97	C₂³×C₂₃	1	1	yes	characteristic
721	#97	C₂³×C₂₃	1	1	yes	characteristic
722	#97	C₂³×C₂₃	1	2	yes	—
723	#97	C₂³×C₂₃	1	2	yes	—
724	#97	C₂³×C₂₃	1	2	yes	—
725	#97	C₂³×C₂₃	1	2	yes	—
726	C₄×C₈	C₂³×C₂₃	1	2	yes	—
727	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
728	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
729	C₄×C₈	C₂³×C₂₃	1	2	yes	—
730	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
731	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
732	C₄×C₈	C₂³×C₂₃	1	2	yes	—
733	C₄×C₈	C₂³×C₂₃	1	2	yes	—
734	C₄×C₈	C₂³×C₂₃	1	2	yes	—
735	C₄×C₈	C₂³×C₂₃	1	2	yes	—
736	C₂₃	#60297	1	1	yes	characteristic, direct product factor, Sylow
737	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
738	#41	—	4	2	no	—
739	#41	—	4	2	no	—
740	C₂×Q₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
741	C₂×Q₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
742	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
743	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
744	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
745	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
746	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
747	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
748	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
749	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
750	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
751	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
752	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
753	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
754	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
755	C₂²×C₄	—	4	2	no	—
756	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
757	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
758	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
759	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
760	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
761	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
762	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
763	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
764	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
765	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
766	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
767	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
768	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
769	M₁₆	—	4	2	no	—
770	M₁₆	—	4	2	no	—
771	M₁₆	—	4	2	no	—
772	M₁₆	—	4	2	no	—
773	M₁₆	—	4	2	no	—
774	M₁₆	—	4	2	no	—
775	C₂×C₈	—	4	2	no	—
776	C₂×C₈	—	4	2	no	—
777	C₂×C₈	—	4	2	no	—
778	C₂×C₈	—	4	2	no	—
779	C₂×C₈	—	4	2	no	—
780	C₂×C₈	—	4	2	no	—
781	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
782	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
783	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
784	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
785	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
786	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
787	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
788	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
789	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
790	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
791	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
792	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
793	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
794	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
795	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
796	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
797	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
798	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
799	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
800	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
801	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
802	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
803	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
804	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
805	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
806	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
807	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
808	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
809	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
810	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
811	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
812	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
813	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
814	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
815	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
816	C₂²⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
817	C₂²⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
818	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
819	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
820	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
821	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
822	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
823	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
824	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
825	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
826	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
827	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
828	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
829	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
830	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
831	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
832	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
833	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
834	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
835	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
836	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
837	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
838	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
839	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
840	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
841	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
842	C₄²	C₂⁴×C₂₃	1	2	yes	—
843	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
844	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
845	C₄²	C₂⁴×C₂₃	1	2	yes	—
846	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
847	C₂³	—	4	1	no	—
848	C₂³	—	4	2	no	—
849	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
850	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
851	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
852	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
853	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
854	Q₈	—	4	1	no	—
855	Q₈	—	4	1	no	—
856	Q₈	—	4	2	no	—
857	Q₈	—	4	2	no	—
858	D₄	—	4	1	no	—
859	D₄	—	4	1	no	—
860	D₄	—	4	2	no	—
861	D₄	—	4	1	no	—
862	D₄	—	4	1	no	—
863	D₄	—	4	2	no	—
864	D₄	—	4	2	no	—
865	D₄	—	4	2	no	—
866	D₄	—	4	2	no	—
867	D₄	—	4	2	no	—
868	D₄	—	4	2	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	4	2	no	—
877	C₂×C₄	—	4	1	no	—
878	C₂×C₄	—	4	2	no	—
879	C₂×C₄	—	4	2	no	—
880	C₂×C₄	—	4	2	no	—
881	C₂×C₄	—	4	2	no	—
882	C₂×C₄	—	4	2	no	—
883	C₂×C₄	—	4	2	no	—
884	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
885	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
886	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
887	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
888	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
889	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
890	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
891	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
892	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
893	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
894	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
895	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
896	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
897	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
898	C₈	—	2	2	no	—
899	C₈	—	2	2	no	—
900	C₈	—	2	2	no	—
901	C₈	—	2	2	no	—
902	C₈	—	2	2	no	—
903	C₈	—	2	2	no	—
904	C₈	—	2	2	no	—
905	C₈	—	2	2	no	—
906	C₂²	—	2	1	no	—
907	C₂²	—	2	2	no	—
908	C₂²	—	2	2	no	—
909	C₂²	—	2	1	no	—
910	C₂²	—	2	1	no	—
911	C₂²	—	2	2	no	—
912	C₂²	—	2	2	no	—
913	C₂²	—	2	2	no	—
914	C₂²	—	2	2	no	—
915	C₂²	—	2	2	no	—
916	C₂²	—	2	2	no	—
917	C₂²	—	2	2	no	—
918	C₂²	—	8	2	no	—
919	C₂²	C₂⁴×C₄×C₂₃	1	1	yes	characteristic
920	C₄	—	2	1	no	—
921	C₄	—	2	2	no	—
922	C₄	—	2	2	no	—
923	C₄	—	2	1	no	—
924	C₄	—	2	1	no	—
925	C₄	—	2	2	no	—
926	C₄	—	2	2	no	—
927	C₄	—	2	2	no	—
928	C₄	—	2	2	no	—
929	C₄	—	2	2	no	—
930	C₄	—	2	2	no	—
931	C₄	—	2	2	no	—
932	C₄	—	2	2	no	—
933	C₄	C₂₃×#585	1	2	yes	—
934	C₂	—	4	1	no	—
935	C₂	—	4	2	no	—
936	C₂	—	4	2	no	—
937	C₂	—	4	1	no	—
938	C₂	—	4	1	no	—
939	C₂	C₂₃×#3428	1	1	yes	characteristic
940	C₂	C₂₃×#3573	1	2	yes	—

	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×#3455	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×#2995	C₂	semidirect
3. C₂₃×#2994	C₂	semidirect
4. C₂₃×#2993	C₂	semidirect
5. C₂₃×#2992	C₂	semidirect
6. C₂₃×#2987	C₂	semidirect
7. C₂₃×#2986	C₂	semidirect
8. C₂₃×#2981	C₂	semidirect
9. C₂₃×#2978	C₂	semidirect
10. C₂₃×#2977	C₂	semidirect
11. C₂₃×#2976	C₂	semidirect
12. C₂₃×#2969	C₂	semidirect
13. C₂₃×#2968	C₂	semidirect
14. C₂₃×#2967	C₂	semidirect
15. C₂₃×#2966	C₂	semidirect
16. C₂₃×#2925	C₂	semidirect
17. C₂₃×#2924	C₂	semidirect
18. C₂₃×#2923	C₂	semidirect
19. C₂₃×#2922	C₂	semidirect
39. C₂₃×#446	C₂²	semidirect
40. C₂₃×#446	C₂²	semidirect
41. C₂₃×#446	C₂²	semidirect
42. C₂₃×#446	C₂²	semidirect
43. C₂₃×#446	C₂²	semidirect
44. C₂₃×#446	C₂²	semidirect
45. C₈×Q₈×C₂₃	C₂²	semidirect
46. C₈×Q₈×C₂₃	C₂²	semidirect
51. C₂₃×#436	C₂²	semidirect
52. C₂₃×#436	C₂²	semidirect
61. C₂₃×#435	C₂²	semidirect
62. C₂₃×#435	C₂²	semidirect
63. C₂₃×#435	C₂²	semidirect
64. C₂₃×#435	C₂²	semidirect
69. C₈×D₄×C₂₃	C₂²	semidirect
70. C₈×D₄×C₂₃	C₂²	semidirect
81. C₂₃×#433	C₂²	semidirect
82. C₂₃×#433	C₂²	semidirect
83. C₂₃×#433	C₂²	semidirect
84. C₂₃×#433	C₂²	semidirect
85. C₂₃×#433	C₂²	semidirect
86. C₂₃×#433	C₂²	semidirect
89. C₂₃×#432	C₂²	semidirect
90. C₂₃×#432	C₂²	semidirect
93. C₂₃×#431	C₂²	semidirect
94. C₂₃×#431	C₂²	semidirect
97. C₂₃×#424	C₂²	semidirect
98. C₂₃×#424	C₂²	semidirect
99. C₂₃×#423	C₂²	semidirect
100. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
109. C₂₃×#405	C₂²	semidirect
110. C₂₃×#405	C₂²	semidirect
111. C₄×M₁₆×C₂₃	C₂²	semidirect
112. C₄×M₁₆×C₂₃	C₂²	semidirect
113. C₂×C₂₃×#97	C₂²	semidirect
114. C₂×C₄×C₈×C₂₃	C₂²	semidirect
376. #60297	C₂₃	direct (N × H)
437. #2995	C₂×C₂₃	semidirect
438. #2994	C₂×C₂₃	semidirect
439. #2993	C₂×C₂₃	semidirect
440. #2992	C₂×C₂₃	semidirect
441. #2987	C₂×C₂₃	semidirect
442. #2986	C₂×C₂₃	semidirect
443. #2981	C₂×C₂₃	semidirect
444. #2978	C₂×C₂₃	semidirect
445. #2977	C₂×C₂₃	semidirect
446. #2976	C₂×C₂₃	semidirect
447. #2969	C₂×C₂₃	semidirect
448. #2968	C₂×C₂₃	semidirect
449. #2967	C₂×C₂₃	semidirect
450. #2966	C₂×C₂₃	semidirect
451. #2925	C₂×C₂₃	semidirect
452. #2924	C₂×C₂₃	semidirect
453. #2923	C₂×C₂₃	semidirect
454. #2922	C₂×C₂₃	semidirect
502. #446	C₂²×C₂₃	semidirect
503. #446	C₂²×C₂₃	semidirect
504. #446	C₂²×C₂₃	semidirect
505. #446	C₂²×C₂₃	semidirect
506. #446	C₂²×C₂₃	semidirect
507. #446	C₂²×C₂₃	semidirect
508. C₈×Q₈	C₂²×C₂₃	semidirect
509. C₈×Q₈	C₂²×C₂₃	semidirect
514. #436	C₂²×C₂₃	semidirect
515. #436	C₂²×C₂₃	semidirect
524. #435	C₂²×C₂₃	semidirect
525. #435	C₂²×C₂₃	semidirect
526. #435	C₂²×C₂₃	semidirect
527. #435	C₂²×C₂₃	semidirect
532. C₈×D₄	C₂²×C₂₃	semidirect
533. C₈×D₄	C₂²×C₂₃	semidirect
544. #433	C₂²×C₂₃	semidirect
545. #433	C₂²×C₂₃	semidirect
546. #433	C₂²×C₂₃	semidirect
547. #433	C₂²×C₂₃	semidirect
548. #433	C₂²×C₂₃	semidirect
549. #433	C₂²×C₂₃	semidirect
552. #432	C₂²×C₂₃	semidirect
553. #432	C₂²×C₂₃	semidirect
556. #431	C₂²×C₂₃	semidirect
557. #431	C₂²×C₂₃	semidirect
560. #424	C₂²×C₂₃	semidirect
561. #424	C₂²×C₂₃	semidirect
562. #423	C₂²×C₂₃	semidirect
563. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
572. #405	C₂²×C₂₃	semidirect
573. #405	C₂²×C₂₃	semidirect
574. C₄×M₁₆	C₂²×C₂₃	semidirect
575. C₄×M₁₆	C₂²×C₂₃	semidirect
576. C₂×#97	C₂²×C₂₃	semidirect
577. C₂×C₄×C₈	C₂²×C₂₃	semidirect
736. C₂₃	#60297	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₃×#3455	2
C₂₃×#2995	2
C₂₃×#2994	2
C₂₃×#2993	2
C₂₃×#2992	2
C₂₃×#2987	2
C₂₃×#2986	2
C₂₃×#2981	2
C₂₃×#2978	2
C₂₃×#2977	2
C₂₃×#2976	2
C₂₃×#2969	2
C₂₃×#2968	2
C₂₃×#2967	2
C₂₃×#2966	2
C₂₃×#2925	2
C₂₃×#2924	2
C₂₃×#2923	2
C₂₃×#2922	2
#60297	23

Subgroups — C23×#60297 #19207923

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60297 #19207923