Subgroups — C₂₃×#60340 #19207966

Order 5888.

1666 conjugacy classes of subgroups.

The subgroup lattice has 944 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3461	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×#2992	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2992	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#2992	C₂	1	2	yes	maximal, complemented
7	C₂₃×#2990	C₂	1	2	yes	maximal, complemented
8	C₂₃×#2987	C₂	1	2	yes	maximal, complemented
9	C₂₃×#2985	C₂	1	2	yes	maximal, complemented
10	C₂₃×#2983	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#2970	C₂	1	2	yes	maximal, complemented
12	C₂₃×#2968	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	1	yes	maximal, characteristic, complemented
16	C₂₃×#2966	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#2962	C₂	1	2	yes	maximal, complemented
18	C₂₃×#2961	C₂	1	2	yes	maximal, complemented
19	C₂×C₂₃×#446	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#544	C₄	1	1	yes	characteristic
21	C₂₃×#542	C₄	1	2	yes	—
22	C₂₃×#542	C₄	1	2	yes	—
23	C₂₃×#541	C₄	1	2	yes	—
24	C₂₃×#541	C₄	1	2	yes	—
25	C₂₃×#539	C₄	1	1	yes	characteristic
26	C₂₃×#539	C₄	1	1	yes	characteristic
27	C₂₃×#539	C₄	1	2	yes	—
28	C₂₃×#537	C₄	1	1	yes	characteristic
29	C₂₃×#536	C₄	1	2	yes	—
30	C₂₃×#533	C₂²	1	2	yes	—
31	C₂₃×#533	C₂²	1	2	yes	—
32	C₂₃×#529	C₂²	1	1	yes	characteristic
33	C₂₃×#529	C₂²	1	1	yes	characteristic
34	C₂₃×#529	C₂²	1	2	yes	—
35	C₂₃×#529	C₂²	1	2	yes	—
36	C₂₃×#529	C₂²	1	2	yes	—
37	C₄×#41×C₂₃	C₂²	1	2	yes	—
38	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
39	C₂₃×#446	C₂²	1	2	yes	—
40	C₂₃×#446	C₂²	1	2	yes	—
41	C₂₃×#446	C₂²	1	2	yes	—
42	C₂₃×#446	C₂²	1	2	yes	—
43	C₂₃×#446	C₂²	1	1	yes	characteristic
44	C₂₃×#446	C₂²	1	2	yes	—
45	C₂₃×#446	C₂²	1	2	yes	—
46	C₂₃×#446	C₂²	1	2	yes	—
47	C₂₃×#446	C₂²	1	2	yes	—
48	C₂₃×#446	C₂²	1	2	yes	—
49	C₂₃×#446	C₂²	1	2	yes	—
50	C₂₃×#446	C₂²	1	2	yes	—
51	C₂₃×#446	C₂²	1	2	yes	—
52	C₂₃×#446	C₂²	1	2	yes	—
53	C₂₃×#446	C₂²	1	1	yes	characteristic
54	C₂₃×#446	C₂²	1	2	yes	—
55	C₂₃×#446	C₂²	1	2	yes	—
56	C₂₃×#446	C₂²	1	2	yes	—
57	C₂₃×#446	C₂²	1	2	yes	—
58	C₈×Q₈×C₂₃	C₂²	1	1	yes	characteristic
59	C₈×Q₈×C₂₃	C₂²	1	2	yes	—
60	C₈×Q₈×C₂₃	C₂²	1	1	yes	characteristic
61	C₂₃×#436	C₂²	1	1	yes	characteristic
62	C₂₃×#436	C₂²	1	1	yes	characteristic
63	C₂₃×#436	C₂²	1	2	yes	—
64	C₂₃×#435	C₂²	1	2	yes	—
65	C₂₃×#435	C₂²	1	2	yes	—
66	C₂₃×#435	C₂²	1	2	yes	—
67	C₂₃×#435	C₂²	1	2	yes	—
68	C₂₃×#435	C₂²	1	2	yes	—
69	C₂₃×#435	C₂²	1	2	yes	—
70	C₂₃×#435	C₂²	1	2	yes	—
71	C₂₃×#435	C₂²	1	2	yes	—
72	C₂₃×#435	C₂²	1	2	yes	—
73	C₂₃×#435	C₂²	1	2	yes	—
74	C₂₃×#435	C₂²	1	2	yes	—
75	C₂₃×#435	C₂²	1	2	yes	—
76	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic
77	C₈×D₄×C₂₃	C₂²	1	2	yes	—
78	C₈×D₄×C₂₃	C₂²	1	2	yes	—
79	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic
80	C₈×D₄×C₂₃	C₂²	1	2	yes	—
81	C₈×D₄×C₂₃	C₂²	1	2	yes	—
82	C₈×D₄×C₂₃	C₂²	1	2	yes	—
83	C₂₃×#433	C₂²	1	2	yes	—
84	C₂₃×#433	C₂²	1	2	yes	—
85	C₂₃×#433	C₂²	1	2	yes	—
86	C₂₃×#433	C₂²	1	2	yes	—
87	C₂₃×#433	C₂²	1	2	yes	—
88	C₂₃×#433	C₂²	1	2	yes	—
89	C₂₃×#433	C₂²	1	2	yes	—
90	C₂₃×#433	C₂²	1	2	yes	—
91	C₂₃×#432	C₂²	1	1	yes	characteristic
92	C₂₃×#432	C₂²	1	1	yes	characteristic
93	C₂₃×#432	C₂²	1	2	yes	—
94	C₂₃×#432	C₂²	1	2	yes	—
95	C₂₃×#432	C₂²	1	2	yes	—
96	C₂₃×#432	C₂²	1	2	yes	—
97	C₂₃×#431	C₂²	1	2	yes	—
98	C₂₃×#431	C₂²	1	2	yes	—
99	C₂₃×#424	C₂²	1	2	yes	—
100	C₂₃×#424	C₂²	1	2	yes	—
101	C₂₃×#424	C₂²	1	2	yes	—
102	C₂₃×#424	C₂²	1	2	yes	—
103	C₂₃×#423	C₂²	1	2	yes	—
104	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
105	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
106	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
107	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
108	C₂₃×#405	C₂²	1	2	yes	—
109	C₂₃×#405	C₂²	1	2	yes	—
110	C₂₃×#405	C₂²	1	2	yes	—
111	C₂₃×#405	C₂²	1	2	yes	—
112	C₄×M₁₆×C₂₃	C₂²	1	2	yes	—
113	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
114	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
115	C₂×C₂₃×#97	C₂²	1	2	yes	—
116	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
117	C₂×#41×C₂₃	C₂×C₄	1	2	yes	—
118	C₂²×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
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	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
124	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
125	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
126	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
127	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
128	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
129	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
130	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
131	C₂₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
132	C₂₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
133	C₂₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
134	C₂₃×C₄⋊Q₈	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×#126	C₂×C₄	1	2	yes	—
142	C₂₃×#126	C₂×C₄	1	2	yes	—
143	C₂₃×#125	C₂×C₄	1	1	yes	characteristic
144	C₂₃×#125	C₂×C₄	1	1	yes	characteristic
145	C₂₃×#125	C₂×C₄	1	2	yes	—
146	C₂₃×#125	C₂×C₄	1	2	yes	—
147	C₂₃×#125	C₂×C₄	1	2	yes	—
148	C₂₃×#125	C₂×C₄	1	2	yes	—
149	C₂₃×#125	C₂×C₄	1	2	yes	—
150	C₂₃×#125	C₂×C₄	1	2	yes	—
151	C₂₃×#125	C₂×C₄	1	2	yes	—
152	C₂₃×#124	C₂×C₄	1	2	yes	—
153	C₂₃×#124	C₂×C₄	1	2	yes	—
154	C₂₃×#124	C₂×C₄	1	1	yes	characteristic
155	C₂₃×#124	C₂×C₄	1	1	yes	characteristic
156	C₂₃×#124	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×#123	C₂×C₄	1	2	yes	—
164	C₂₃×#123	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	1	yes	characteristic
168	C₂₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
169	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
170	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
171	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
172	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
173	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
174	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
175	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
176	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
177	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
178	C₂₃×#121	C₂×C₄	1	1	yes	characteristic
179	C₂₃×#121	C₂×C₄	1	1	yes	characteristic
180	C₂₃×#121	C₂×C₄	1	2	yes	—
181	C₂₃×#121	C₂×C₄	1	2	yes	—
182	C₂₃×#121	C₂×C₄	1	2	yes	—
183	C₄×Q₈×C₂₃	C₂×C₄	1	2	yes	—
184	C₄×Q₈×C₂₃	C₂×C₄	1	2	yes	—
185	C₄×Q₈×C₂₃	C₂×C₄	1	2	yes	—
186	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
187	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
188	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
189	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
190	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
191	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
192	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
193	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
194	C₄×D₄×C₂₃	C₂×C₄	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	1	yes	characteristic
198	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
199	C₄×D₄×C₂₃	C₂³	1	2	yes	—
200	C₄×D₄×C₂₃	C₂³	1	2	yes	—
201	C₂₃×#117	C₂×C₄	1	2	yes	—
202	C₂₃×#117	C₂×C₄	1	2	yes	—
203	C₂₃×#117	C₂×C₄	1	2	yes	—
204	C₂₃×#117	C₂³	1	2	yes	—
205	C₂₃×#117	C₂³	1	2	yes	—
206	C₂₃×#117	C₂³	1	2	yes	—
207	C₂₃×#117	C₂³	1	2	yes	—
208	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
209	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
210	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
211	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
212	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
213	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
214	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
215	C₂×C₄²×C₂₃	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	1	yes	characteristic
229	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
230	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
231	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
232	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
233	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
234	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
235	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
236	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
237	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
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×C₂²⋊C₈	C₂³	1	2	yes	—
247	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
248	C₂₃×#97	C₂³	1	2	yes	—
249	C₂₃×#97	C₂³	1	2	yes	—
250	C₂₃×#97	C₂³	1	2	yes	—
251	C₂₃×#97	C₂³	1	2	yes	—
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	C₂₃×#97	C₂³	1	2	yes	—
257	C₂₃×#97	C₂³	1	2	yes	—
258	C₂₃×#97	C₂³	1	2	yes	—
259	C₂₃×#97	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	1	yes	characteristic
263	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
264	C₄×C₈×C₂₃	C₂³	1	2	yes	—
265	C₄×C₈×C₂₃	C₂³	1	2	yes	—
266	C₄×C₈×C₂₃	C₂³	1	2	yes	—
267	C₄×C₈×C₂₃	C₂³	1	2	yes	—
268	C₄×C₈×C₂₃	C₂³	1	2	yes	—
269	C₄×C₈×C₂₃	C₂³	1	2	yes	—
270	#41×C₂₃	—	4	4	no	—
271	C₂×Q₈×C₂₃	—	4	2	no	—
272	C₂×Q₈×C₂₃	C₂²×C₄	1	2	yes	—
273	C₂×Q₈×C₂₃	C₂²×C₄	1	2	yes	—
274	C₂×Q₈×C₂₃	C₂²×C₄	1	2	yes	—
275	C₂×Q₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
276	C₂×Q₈×C₂₃	C₂²×C₄	1	2	yes	—
277	C₂×Q₈×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	1	yes	characteristic
282	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
283	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
284	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
285	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
286	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
287	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
288	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
289	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
290	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
291	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
292	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
293	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
294	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
295	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
296	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
297	M₁₆×C₂₃	—	2	4	no	—
298	M₁₆×C₂₃	—	4	2	no	—
299	M₁₆×C₂₃	—	4	2	no	—
300	M₁₆×C₂₃	—	4	2	no	—
301	C₂×C₈×C₂₃	—	2	2	no	—
302	C₂×C₈×C₂₃	—	2	4	no	—
303	C₂×C₈×C₂₃	—	4	2	no	—
304	C₂×C₈×C₂₃	—	4	1	no	—
305	C₂×C₈×C₂₃	—	4	1	no	—
306	C₂×C₈×C₂₃	—	4	1	no	—
307	C₂×C₈×C₂₃	—	4	2	no	—
308	C₂×C₈×C₂₃	—	4	2	no	—
309	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
314	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
315	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
316	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
317	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
318	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
340	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
341	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
342	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
343	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
344	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
345	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
346	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
347	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
348	C₄⋊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	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
364	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
365	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
366	C₂²⋊C₄×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	C₂²×C₄	1	2	yes	—
371	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
372	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
373	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
374	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
375	C₄²×C₂₃	C₂⁴	1	2	yes	—
376	C₄²×C₂₃	C₂⁴	1	2	yes	—
377	C₄²×C₂₃	C₂⁴	1	2	yes	—
378	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
379	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
380	C₄²×C₂₃	C₂⁴	1	2	yes	—
381	#60340	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
382	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
383	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
384	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
385	Q₈×C₂₃	—	4	2	no	—
386	Q₈×C₂₃	—	4	2	no	—
387	Q₈×C₂₃	—	4	1	no	—
388	Q₈×C₂₃	—	4	2	no	—
389	Q₈×C₂₃	—	4	1	no	—
390	Q₈×C₂₃	—	4	2	no	—
391	D₄×C₂₃	—	2	4	no	—
392	D₄×C₂₃	—	2	4	no	—
393	D₄×C₂₃	—	4	1	no	—
394	D₄×C₂₃	—	4	1	no	—
395	D₄×C₂₃	—	4	2	no	—
396	D₄×C₂₃	—	4	2	no	—
397	C₂×C₄×C₂₃	—	2	2	no	—
398	C₂×C₄×C₂₃	—	2	2	no	—
399	C₂×C₄×C₂₃	—	2	2	no	—
400	C₂×C₄×C₂₃	—	2	1	no	—
401	C₂×C₄×C₂₃	—	2	2	no	—
402	C₂×C₄×C₂₃	—	2	2	no	—
403	C₂×C₄×C₂₃	—	2	1	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	1	no	—
410	C₂×C₄×C₂₃	—	4	1	no	—
411	C₂×C₄×C₂₃	—	4	2	no	—
412	C₂×C₄×C₂₃	—	4	2	no	—
413	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
414	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
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	1	yes	characteristic
426	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
427	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
428	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
429	C₈×C₂₃	—	2	1	no	—
430	C₈×C₂₃	—	2	2	no	—
431	C₈×C₂₃	—	2	2	no	—
432	C₈×C₂₃	—	2	1	no	—
433	C₈×C₂₃	—	2	2	no	—
434	C₈×C₂₃	—	2	2	no	—
435	C₈×C₂₃	—	2	2	no	—
436	C₈×C₂₃	—	2	1	no	—
437	C₈×C₂₃	—	2	2	no	—
438	C₈×C₂₃	2₋¹⁺⁴	1	2	yes	—
439	#3461	C₂×C₂₃	1	1	yes	characteristic
440	#2995	C₂×C₂₃	1	2	yes	complemented
441	#2994	C₂×C₂₃	1	2	yes	complemented
442	#2992	C₂×C₂₃	1	1	yes	characteristic, complemented
443	#2992	C₂×C₂₃	1	1	yes	characteristic, complemented
444	#2992	C₂×C₂₃	1	2	yes	complemented
445	#2990	C₂×C₂₃	1	2	yes	complemented
446	#2987	C₂×C₂₃	1	2	yes	complemented
447	#2985	C₂×C₂₃	1	2	yes	complemented
448	#2983	C₂×C₂₃	1	1	yes	characteristic, complemented
449	#2970	C₂×C₂₃	1	2	yes	complemented
450	#2968	C₂×C₂₃	1	2	yes	complemented
451	#2968	C₂×C₂₃	1	2	yes	complemented
452	#2967	C₂×C₂₃	1	2	yes	complemented
453	#2966	C₂×C₂₃	1	1	yes	characteristic, complemented
454	#2966	C₂×C₂₃	1	1	yes	characteristic, complemented
455	#2962	C₂×C₂₃	1	2	yes	complemented
456	#2961	C₂×C₂₃	1	2	yes	complemented
457	C₂×#446	C₂×C₂₃	1	1	yes	characteristic, complemented
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	#568	1	2	yes	—
467	C₂²×C₂₃	C₂⁴×C₄	1	1	yes	characteristic
468	C₄×C₂₃	—	2	1	no	—
469	C₄×C₂₃	—	2	2	no	—
470	C₄×C₂₃	—	2	2	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	1	no	—
479	C₄×C₂₃	—	2	1	no	—
480	C₄×C₂₃	—	2	2	no	—
481	C₄×C₂₃	—	2	2	no	—
482	C₄×C₂₃	—	2	2	no	—
483	C₄×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
484	C₄×C₂₃	#585	1	1	yes	characteristic
485	#544	C₄×C₂₃	1	1	yes	characteristic
486	#542	C₄×C₂₃	1	2	yes	—
487	#542	C₄×C₂₃	1	2	yes	—
488	#541	C₄×C₂₃	1	2	yes	—
489	#541	C₄×C₂₃	1	2	yes	—
490	#539	C₄×C₂₃	1	1	yes	characteristic
491	#539	C₄×C₂₃	1	1	yes	characteristic
492	#539	C₄×C₂₃	1	2	yes	—
493	#537	C₄×C₂₃	1	1	yes	characteristic
494	#536	C₄×C₂₃	1	2	yes	—
495	#533	C₂²×C₂₃	1	2	yes	—
496	#533	C₂²×C₂₃	1	2	yes	—
497	#529	C₂²×C₂₃	1	1	yes	characteristic
498	#529	C₂²×C₂₃	1	1	yes	characteristic
499	#529	C₂²×C₂₃	1	2	yes	—
500	#529	C₂²×C₂₃	1	2	yes	—
501	#529	C₂²×C₂₃	1	2	yes	—
502	C₄×#41	C₂²×C₂₃	1	2	yes	—
503	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
504	#446	C₂²×C₂₃	1	2	yes	—
505	#446	C₂²×C₂₃	1	2	yes	—
506	#446	C₂²×C₂₃	1	2	yes	—
507	#446	C₂²×C₂₃	1	2	yes	—
508	#446	C₂²×C₂₃	1	1	yes	characteristic
509	#446	C₂²×C₂₃	1	2	yes	—
510	#446	C₂²×C₂₃	1	2	yes	—
511	#446	C₂²×C₂₃	1	2	yes	—
512	#446	C₂²×C₂₃	1	2	yes	—
513	#446	C₂²×C₂₃	1	2	yes	—
514	#446	C₂²×C₂₃	1	2	yes	—
515	#446	C₂²×C₂₃	1	2	yes	—
516	#446	C₂²×C₂₃	1	2	yes	—
517	#446	C₂²×C₂₃	1	2	yes	—
518	#446	C₂²×C₂₃	1	1	yes	characteristic
519	#446	C₂²×C₂₃	1	2	yes	—
520	#446	C₂²×C₂₃	1	2	yes	—
521	#446	C₂²×C₂₃	1	2	yes	—
522	#446	C₂²×C₂₃	1	2	yes	—
523	C₈×Q₈	C₂²×C₂₃	1	1	yes	characteristic
524	C₈×Q₈	C₂²×C₂₃	1	2	yes	—
525	C₈×Q₈	C₂²×C₂₃	1	1	yes	characteristic
526	#436	C₂²×C₂₃	1	1	yes	characteristic
527	#436	C₂²×C₂₃	1	1	yes	characteristic
528	#436	C₂²×C₂₃	1	2	yes	—
529	#435	C₂²×C₂₃	1	2	yes	—
530	#435	C₂²×C₂₃	1	2	yes	—
531	#435	C₂²×C₂₃	1	2	yes	—
532	#435	C₂²×C₂₃	1	2	yes	—
533	#435	C₂²×C₂₃	1	2	yes	—
534	#435	C₂²×C₂₃	1	2	yes	—
535	#435	C₂²×C₂₃	1	2	yes	—
536	#435	C₂²×C₂₃	1	2	yes	—
537	#435	C₂²×C₂₃	1	2	yes	—
538	#435	C₂²×C₂₃	1	2	yes	—
539	#435	C₂²×C₂₃	1	2	yes	—
540	#435	C₂²×C₂₃	1	2	yes	—
541	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic
542	C₈×D₄	C₂²×C₂₃	1	2	yes	—
543	C₈×D₄	C₂²×C₂₃	1	2	yes	—
544	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic
545	C₈×D₄	C₂²×C₂₃	1	2	yes	—
546	C₈×D₄	C₂²×C₂₃	1	2	yes	—
547	C₈×D₄	C₂²×C₂₃	1	2	yes	—
548	#433	C₂²×C₂₃	1	2	yes	—
549	#433	C₂²×C₂₃	1	2	yes	—
550	#433	C₂²×C₂₃	1	2	yes	—
551	#433	C₂²×C₂₃	1	2	yes	—
552	#433	C₂²×C₂₃	1	2	yes	—
553	#433	C₂²×C₂₃	1	2	yes	—
554	#433	C₂²×C₂₃	1	2	yes	—
555	#433	C₂²×C₂₃	1	2	yes	—
556	#432	C₂²×C₂₃	1	1	yes	characteristic
557	#432	C₂²×C₂₃	1	1	yes	characteristic
558	#432	C₂²×C₂₃	1	2	yes	—
559	#432	C₂²×C₂₃	1	2	yes	—
560	#432	C₂²×C₂₃	1	2	yes	—
561	#432	C₂²×C₂₃	1	2	yes	—
562	#431	C₂²×C₂₃	1	2	yes	—
563	#431	C₂²×C₂₃	1	2	yes	—
564	#424	C₂²×C₂₃	1	2	yes	—
565	#424	C₂²×C₂₃	1	2	yes	—
566	#424	C₂²×C₂₃	1	2	yes	—
567	#424	C₂²×C₂₃	1	2	yes	—
568	#423	C₂²×C₂₃	1	2	yes	—
569	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
570	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
571	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
572	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
573	#405	C₂²×C₂₃	1	2	yes	—
574	#405	C₂²×C₂₃	1	2	yes	—
575	#405	C₂²×C₂₃	1	2	yes	—
576	#405	C₂²×C₂₃	1	2	yes	—
577	C₄×M₁₆	C₂²×C₂₃	1	2	yes	—
578	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
579	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
580	C₂×#97	C₂²×C₂₃	1	2	yes	—
581	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
582	C₂×C₂₃	—	2	2	no	—
583	C₂×C₂₃	—	4	2	no	—
584	C₂×C₂₃	—	4	2	no	—
585	C₂×C₂₃	C₄×2₋¹⁺⁴	1	1	yes	characteristic
586	C₂×C₂₃	C₂×#568	1	1	yes	characteristic
587	C₂×C₂₃	#3573	1	1	yes	characteristic
588	C₂×#41	C₂×C₄×C₂₃	1	2	yes	—
589	C₂²×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
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	1	yes	characteristic
595	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
596	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
597	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
598	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
599	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
600	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
601	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
602	C₄⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
603	C₄⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
604	C₄⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
605	C₄⋊Q₈	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	#126	C₂×C₄×C₂₃	1	2	yes	—
612	#126	C₂×C₄×C₂₃	1	2	yes	—
613	#126	C₂×C₄×C₂₃	1	2	yes	—
614	#125	C₂×C₄×C₂₃	1	1	yes	characteristic
615	#125	C₂×C₄×C₂₃	1	1	yes	characteristic
616	#125	C₂×C₄×C₂₃	1	2	yes	—
617	#125	C₂×C₄×C₂₃	1	2	yes	—
618	#125	C₂×C₄×C₂₃	1	2	yes	—
619	#125	C₂×C₄×C₂₃	1	2	yes	—
620	#125	C₂×C₄×C₂₃	1	2	yes	—
621	#125	C₂×C₄×C₂₃	1	2	yes	—
622	#125	C₂×C₄×C₂₃	1	2	yes	—
623	#124	C₂×C₄×C₂₃	1	2	yes	—
624	#124	C₂×C₄×C₂₃	1	2	yes	—
625	#124	C₂×C₄×C₂₃	1	1	yes	characteristic
626	#124	C₂×C₄×C₂₃	1	1	yes	characteristic
627	#124	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	#123	C₂×C₄×C₂₃	1	2	yes	—
634	#123	C₂×C₄×C₂₃	1	2	yes	—
635	#123	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	1	yes	characteristic
639	C₂²⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
640	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
641	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
642	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
643	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
644	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
645	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
646	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
647	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
648	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
649	#121	C₂×C₄×C₂₃	1	1	yes	characteristic
650	#121	C₂×C₄×C₂₃	1	1	yes	characteristic
651	#121	C₂×C₄×C₂₃	1	2	yes	—
652	#121	C₂×C₄×C₂₃	1	2	yes	—
653	#121	C₂×C₄×C₂₃	1	2	yes	—
654	C₄×Q₈	C₂×C₄×C₂₃	1	2	yes	—
655	C₄×Q₈	C₂×C₄×C₂₃	1	2	yes	—
656	C₄×Q₈	C₂×C₄×C₂₃	1	2	yes	—
657	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
658	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
659	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
660	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
661	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
662	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
663	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
664	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
665	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
666	C₄×D₄	C₂³×C₂₃	1	2	yes	—
667	C₄×D₄	C₂³×C₂₃	1	2	yes	—
668	C₄×D₄	C₂³×C₂₃	1	2	yes	—
669	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
670	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
671	C₄×D₄	C₂³×C₂₃	1	2	yes	—
672	#117	C₂×C₄×C₂₃	1	2	yes	—
673	#117	C₂×C₄×C₂₃	1	2	yes	—
674	#117	C₂×C₄×C₂₃	1	2	yes	—
675	#117	C₂³×C₂₃	1	2	yes	—
676	#117	C₂³×C₂₃	1	2	yes	—
677	#117	C₂³×C₂₃	1	2	yes	—
678	#117	C₂³×C₂₃	1	2	yes	—
679	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
680	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
681	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
682	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
683	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
684	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
685	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
686	C₂×C₄²	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	1	yes	characteristic
700	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
701	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
702	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
703	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
704	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
705	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
706	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
707	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
708	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
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	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
717	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
718	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
719	#97	C₂³×C₂₃	1	2	yes	—
720	#97	C₂³×C₂₃	1	2	yes	—
721	#97	C₂³×C₂₃	1	2	yes	—
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	#97	C₂³×C₂₃	1	2	yes	—
727	#97	C₂³×C₂₃	1	2	yes	—
728	#97	C₂³×C₂₃	1	2	yes	—
729	#97	C₂³×C₂₃	1	2	yes	—
730	#97	C₂³×C₂₃	1	2	yes	—
731	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
732	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
733	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
734	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
735	C₄×C₈	C₂³×C₂₃	1	2	yes	—
736	C₄×C₈	C₂³×C₂₃	1	2	yes	—
737	C₄×C₈	C₂³×C₂₃	1	2	yes	—
738	C₄×C₈	C₂³×C₂₃	1	2	yes	—
739	C₄×C₈	C₂³×C₂₃	1	2	yes	—
740	C₄×C₈	C₂³×C₂₃	1	2	yes	—
741	C₂₃	#60340	1	1	yes	characteristic, direct product factor, Sylow
742	#41	—	4	4	no	—
743	C₂×Q₈	—	4	2	no	—
744	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
745	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
746	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
747	C₂×Q₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
748	C₂×Q₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
749	C₂×Q₈	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	1	yes	characteristic
754	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
755	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
756	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
757	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
758	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
759	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
760	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
761	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
762	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
763	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
764	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
765	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
766	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
767	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
768	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
769	M₁₆	—	2	4	no	—
770	M₁₆	—	4	2	no	—
771	M₁₆	—	4	2	no	—
772	M₁₆	—	4	2	no	—
773	C₂×C₈	—	2	2	no	—
774	C₂×C₈	—	2	4	no	—
775	C₂×C₈	—	4	2	no	—
776	C₂×C₈	—	4	1	no	—
777	C₂×C₈	—	4	1	no	—
778	C₂×C₈	—	4	1	no	—
779	C₂×C₈	—	4	2	no	—
780	C₂×C₈	—	4	2	no	—
781	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
782	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
783	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
784	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
785	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
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	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
790	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
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	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
812	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
813	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
814	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
815	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
816	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
817	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
818	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
819	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
820	C₄⋊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	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
835	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
836	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
837	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
838	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
839	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
840	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
841	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
842	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
843	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
844	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
845	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
846	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
847	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
848	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
849	C₄²	C₂⁴×C₂₃	1	2	yes	—
850	C₄²	C₂⁴×C₂₃	1	2	yes	—
851	C₄²	C₂⁴×C₂₃	1	2	yes	—
852	C₄²	C₂⁴×C₂₃	1	2	yes	—
853	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
854	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
855	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
856	Q₈	—	4	2	no	—
857	Q₈	—	4	2	no	—
858	Q₈	—	4	2	no	—
859	Q₈	—	4	1	no	—
860	Q₈	—	4	1	no	—
861	Q₈	—	4	2	no	—
862	D₄	—	2	4	no	—
863	D₄	—	2	4	no	—
864	D₄	—	4	2	no	—
865	D₄	—	4	1	no	—
866	D₄	—	4	1	no	—
867	D₄	—	4	2	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	1	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	4	2	no	—
878	C₂×C₄	—	4	2	no	—
879	C₂×C₄	—	4	1	no	—
880	C₂×C₄	—	4	2	no	—
881	C₂×C₄	—	4	2	no	—
882	C₂×C₄	—	4	1	no	—
883	C₂×C₄	—	4	1	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	2	yes	—
889	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
890	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
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	1	yes	characteristic
897	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
898	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
899	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
900	C₈	—	2	1	no	—
901	C₈	—	2	2	no	—
902	C₈	—	2	2	no	—
903	C₈	—	2	1	no	—
904	C₈	—	2	2	no	—
905	C₈	—	2	2	no	—
906	C₈	—	2	2	no	—
907	C₈	—	2	1	no	—
908	C₈	—	2	2	no	—
909	C₈	C₂₃×2₋¹⁺⁴	1	2	yes	—
910	C₂²	—	2	1	no	—
911	C₂²	—	2	1	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	C₂₃×#568	1	2	yes	—
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	2	no	—
924	C₄	—	2	1	no	—
925	C₄	—	2	1	no	—
926	C₄	—	2	2	no	—
927	C₄	—	2	2	no	—
928	C₄	—	2	2	no	—
929	C₄	—	2	2	no	—
930	C₄	—	2	1	no	—
931	C₄	—	2	1	no	—
932	C₄	—	2	2	no	—
933	C₄	—	2	2	no	—
934	C₄	—	2	2	no	—
935	C₄	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
936	C₄	C₂₃×#585	1	1	yes	characteristic
937	C₂	—	2	2	no	—
938	C₂	—	4	2	no	—
939	C₂	—	4	2	no	—
940	C₂	C₄×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
941	C₂	C₂×C₂₃×#568	1	1	yes	characteristic
942	C₂	C₂₃×#3573	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×#537	C₄
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×#2992	C₂	semidirect
5. C₂₃×#2992	C₂	semidirect
6. C₂₃×#2992	C₂	semidirect
7. C₂₃×#2990	C₂	semidirect
8. C₂₃×#2987	C₂	semidirect
9. C₂₃×#2985	C₂	semidirect
10. C₂₃×#2983	C₂	semidirect
11. C₂₃×#2970	C₂	semidirect
12. C₂₃×#2968	C₂	semidirect
13. C₂₃×#2968	C₂	semidirect
14. C₂₃×#2967	C₂	semidirect
15. C₂₃×#2966	C₂	semidirect
16. C₂₃×#2966	C₂	semidirect
17. C₂₃×#2962	C₂	semidirect
18. C₂₃×#2961	C₂	semidirect
19. C₂×C₂₃×#446	C₂	semidirect
381. #60340	C₂₃	direct (N × H)
440. #2995	C₂×C₂₃	semidirect
441. #2994	C₂×C₂₃	semidirect
442. #2992	C₂×C₂₃	semidirect
443. #2992	C₂×C₂₃	semidirect
444. #2992	C₂×C₂₃	semidirect
445. #2990	C₂×C₂₃	semidirect
446. #2987	C₂×C₂₃	semidirect
447. #2985	C₂×C₂₃	semidirect
448. #2983	C₂×C₂₃	semidirect
449. #2970	C₂×C₂₃	semidirect
450. #2968	C₂×C₂₃	semidirect
451. #2968	C₂×C₂₃	semidirect
452. #2967	C₂×C₂₃	semidirect
453. #2966	C₂×C₂₃	semidirect
454. #2966	C₂×C₂₃	semidirect
455. #2962	C₂×C₂₃	semidirect
456. #2961	C₂×C₂₃	semidirect
457. C₂×#446	C₂×C₂₃	semidirect
741. C₂₃	#60340	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×#3461	2
C₂₃×#2995	2
C₂₃×#2994	2
C₂₃×#2992	2
C₂₃×#2990	2
C₂₃×#2987	2
C₂₃×#2985	2
C₂₃×#2983	2
C₂₃×#2970	2
C₂₃×#2968	2
C₂₃×#2967	2
C₂₃×#2966	2
C₂₃×#2962	2
C₂₃×#2961	2
C₂×C₂₃×#446	2
#60340	23

Subgroups — C23×#60340 #19207966

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60340 #19207966