Subgroups — C₂₃×#60339 #19207965

Order 5888.

1710 conjugacy classes of subgroups.

The subgroup lattice has 748 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×#2994	C₂	1	4	yes	maximal, complemented
3	C₂₃×#2994	C₂	1	2	yes	maximal, complemented
4	C₂₃×#2993	C₂	1	2	yes	maximal, complemented
5	C₂₃×#2989	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#2988	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#2986	C₂	1	2	yes	maximal, complemented
8	C₂₃×#2985	C₂	1	2	yes	maximal, complemented
9	C₂₃×#2982	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#2969	C₂	1	2	yes	maximal, complemented
11	C₂₃×#2968	C₂	1	4	yes	maximal, complemented
12	C₂₃×#2966	C₂	1	2	yes	maximal, complemented
13	C₂₃×#2965	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈×#41×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#2962	C₂	1	2	yes	maximal, complemented
16	C₂₃×#2960	C₂	1	2	yes	maximal, complemented
17	C₂×C₂₃×#446	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#544	C₄	1	1	yes	characteristic
19	C₂₃×#542	C₄	1	2	yes	—
20	C₂₃×#542	C₄	1	2	yes	—
21	C₂₃×#541	C₄	1	2	yes	—
22	C₂₃×#541	C₄	1	2	yes	—
23	C₂₃×#539	C₄	1	4	yes	—
24	C₂₃×#537	C₄	1	1	yes	characteristic
25	C₂₃×#536	C₄	1	1	yes	characteristic
26	C₂₃×#536	C₄	1	1	yes	characteristic
27	C₂₃×#533	C₂²	1	2	yes	—
28	C₂₃×#533	C₂²	1	2	yes	—
29	C₂₃×#529	C₂²	1	2	yes	—
30	C₂₃×#529	C₂²	1	4	yes	—
31	C₂₃×#529	C₂²	1	2	yes	—
32	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
33	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
34	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
35	C₂₃×#446	C₂²	1	2	yes	—
36	C₂₃×#446	C₂²	1	2	yes	—
37	C₂₃×#446	C₂²	1	2	yes	—
38	C₂₃×#446	C₂²	1	2	yes	—
39	C₂₃×#446	C₂²	1	1	yes	characteristic
40	C₂₃×#446	C₂²	1	4	yes	—
41	C₂₃×#446	C₂²	1	4	yes	—
42	C₂₃×#446	C₂²	1	2	yes	—
43	C₂₃×#446	C₂²	1	1	yes	characteristic
44	C₂₃×#446	C₂²	1	4	yes	—
45	C₈×Q₈×C₂₃	C₂²	1	2	yes	—
46	C₈×Q₈×C₂₃	C₂²	1	2	yes	—
47	C₈×Q₈×C₂₃	C₂²	1	4	yes	—
48	C₈×Q₈×C₂₃	C₂²	1	1	yes	characteristic
49	C₈×Q₈×C₂₃	C₂²	1	2	yes	—
50	C₈×Q₈×C₂₃	C₂²	1	1	yes	characteristic
51	C₈×Q₈×C₂₃	C₂²	1	2	yes	—
52	C₈×Q₈×C₂₃	C₂²	1	2	yes	—
53	C₂₃×#436	C₂²	1	1	yes	characteristic
54	C₂₃×#436	C₂²	1	1	yes	characteristic
55	C₂₃×#436	C₂²	1	2	yes	—
56	C₂₃×#436	C₂²	1	4	yes	—
57	C₂₃×#435	C₂²	1	2	yes	—
58	C₂₃×#435	C₂²	1	2	yes	—
59	C₂₃×#435	C₂²	1	4	yes	—
60	C₂₃×#435	C₂²	1	4	yes	—
61	C₂₃×#435	C₂²	1	4	yes	—
62	C₈×D₄×C₂₃	C₂²	1	2	yes	—
63	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic
64	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic
65	C₈×D₄×C₂₃	C₂²	1	2	yes	—
66	C₈×D₄×C₂₃	C₂²	1	2	yes	—
67	C₈×D₄×C₂₃	C₂²	1	4	yes	—
68	C₈×D₄×C₂₃	C₂²	1	4	yes	—
69	C₂₃×#433	C₂²	1	4	yes	—
70	C₂₃×#433	C₂²	1	4	yes	—
71	C₂₃×#433	C₂²	1	4	yes	—
72	C₂₃×#433	C₂²	1	4	yes	—
73	C₂₃×#432	C₂²	1	2	yes	—
74	C₂₃×#431	C₂²	1	1	yes	characteristic
75	C₂₃×#431	C₂²	1	2	yes	—
76	C₂₃×#431	C₂²	1	1	yes	characteristic
77	C₂₃×#431	C₂²	1	2	yes	—
78	C₂₃×#431	C₂²	1	4	yes	—
79	C₂₃×#431	C₂²	1	2	yes	—
80	C₂₃×#424	C₂²	1	4	yes	—
81	C₂₃×#424	C₂²	1	4	yes	—
82	C₂₃×#423	C₂²	1	2	yes	—
83	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
84	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
85	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
86	C₂₃×#405	C₂²	1	4	yes	—
87	C₂₃×#405	C₂²	1	4	yes	—
88	C₄×M₁₆×C₂₃	C₂²	1	2	yes	—
89	C₂×C₂₃×#97	C₂²	1	2	yes	—
90	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
91	C₂×C₄×C₈×C₂₃	C₂²	1	2	yes	—
92	C₂×#41×C₂₃	C₂×C₄	1	1	yes	characteristic
93	C₂×#41×C₂₃	C₂×C₄	1	1	yes	characteristic
94	C₂²×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
95	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
96	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
97	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
98	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
99	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
100	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
101	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
102	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
103	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
104	C₂₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
105	C₂₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
106	C₂₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
107	C₂₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
108	C₂₃×#126	C₂×C₄	1	4	yes	—
109	C₂₃×#126	C₂×C₄	1	4	yes	—
110	C₂₃×#126	C₂×C₄	1	4	yes	—
111	C₂₃×#126	C₂×C₄	1	4	yes	—
112	C₂₃×#125	C₂×C₄	1	4	yes	—
113	C₂₃×#125	C₂×C₄	1	2	yes	—
114	C₂₃×#125	C₂×C₄	1	2	yes	—
115	C₂₃×#125	C₂×C₄	1	4	yes	—
116	C₂₃×#125	C₂×C₄	1	4	yes	—
117	C₂₃×#124	C₂×C₄	1	2	yes	—
118	C₂₃×#124	C₂×C₄	1	2	yes	—
119	C₂₃×#124	C₂×C₄	1	4	yes	—
120	C₂₃×#123	C₂×C₄	1	4	yes	—
121	C₂₃×#123	C₂×C₄	1	4	yes	—
122	C₂₃×#123	C₂×C₄	1	4	yes	—
123	C₂₃×#123	C₂×C₄	1	4	yes	—
124	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
125	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
126	C₂₃×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
127	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
128	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
129	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
130	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
131	C₂₃×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
132	C₂₃×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
133	C₂₃×#121	C₂×C₄	1	4	yes	—
134	C₂₃×#121	C₂×C₄	1	2	yes	—
135	C₂₃×#121	C₂×C₄	1	2	yes	—
136	C₄×Q₈×C₂₃	C₂×C₄	1	2	yes	—
137	C₄×Q₈×C₂₃	C₂×C₄	1	2	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	2	yes	—
141	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
142	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
143	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
144	C₄×Q₈×C₂₃	C₂³	1	4	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	1	yes	characteristic
148	C₄×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
149	C₄×D₄×C₂₃	C₂³	1	2	yes	—
150	C₄×D₄×C₂₃	C₂³	1	2	yes	—
151	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
152	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
153	C₄×D₄×C₂₃	C₂³	1	4	yes	—
154	C₂₃×#117	C₂×C₄	1	1	yes	characteristic
155	C₂₃×#117	C₂×C₄	1	1	yes	characteristic
156	C₂₃×#117	C₂×C₄	1	2	yes	—
157	C₂₃×#117	C₂×C₄	1	2	yes	—
158	C₂₃×#117	C₂³	1	4	yes	—
159	C₂₃×#117	C₂³	1	4	yes	—
160	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
161	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
162	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
163	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
164	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
165	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
166	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
167	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
168	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
169	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
170	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
171	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
172	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
173	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
174	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
175	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
176	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
177	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
178	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
179	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
180	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
181	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
182	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
183	C₂₃×C₂²⋊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	4	yes	—
187	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
188	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
189	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
190	C₂₃×#97	C₂³	1	4	yes	—
191	C₂₃×#97	C₂³	1	4	yes	—
192	C₂₃×#97	C₂³	1	2	yes	—
193	C₂₃×#97	C₂³	1	2	yes	—
194	C₂₃×#97	C₂³	1	4	yes	—
195	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
196	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
197	C₄×C₈×C₂₃	C₂³	1	2	yes	—
198	C₄×C₈×C₂₃	C₂³	1	2	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	2	yes	—
203	C₄×C₈×C₂₃	C₂³	1	4	yes	—
204	C₄×C₈×C₂₃	C₂³	1	4	yes	—
205	C₄×C₈×C₂₃	C₂³	1	4	yes	—
206	#41×C₂₃	—	2	4	no	—
207	#41×C₂₃	—	2	4	no	—
208	C₂×Q₈×C₂₃	—	2	4	no	—
209	C₂×Q₈×C₂₃	C₂²×C₄	1	2	yes	—
210	C₂×Q₈×C₂₃	C₂²×C₄	1	2	yes	—
211	C₂×Q₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
212	C₂×Q₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
213	C₂×Q₈×C₂₃	C₂²×C₄	1	4	yes	—
214	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
215	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
216	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
217	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
218	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
219	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
220	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
221	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
222	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
223	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
224	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
225	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
226	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
227	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
228	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
229	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
230	M₁₆×C₂₃	—	2	4	no	—
231	M₁₆×C₂₃	—	4	4	no	—
232	M₁₆×C₂₃	—	4	2	no	—
233	C₂×C₈×C₂₃	—	2	2	no	—
234	C₂×C₈×C₂₃	—	2	4	no	—
235	C₂×C₈×C₂₃	—	4	2	no	—
236	C₂×C₈×C₂₃	—	4	4	no	—
237	C₂×C₈×C₂₃	—	4	1	no	—
238	C₂×C₈×C₂₃	—	4	2	no	—
239	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
240	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
241	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
242	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
243	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
244	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
245	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
246	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
247	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
248	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
249	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
250	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
251	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
252	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
253	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
254	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
255	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
256	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
257	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
258	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
259	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
260	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
261	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
262	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
263	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
264	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
265	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
266	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
267	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
268	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
269	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
270	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
271	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
272	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
273	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
274	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
275	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
276	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
277	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
278	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
279	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
280	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
281	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
282	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
283	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
284	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
285	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
286	C₄²×C₂₃	C₂²×C₄	1	4	yes	—
287	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
288	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
289	C₄²×C₂₃	C₂⁴	1	2	yes	—
290	C₄²×C₂₃	C₂⁴	1	4	yes	—
291	C₄²×C₂₃	C₂⁴	1	2	yes	—
292	#60339	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
293	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
294	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
295	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
296	Q₈×C₂₃	—	2	4	no	—
297	Q₈×C₂₃	—	2	4	no	—
298	Q₈×C₂₃	—	2	2	no	—
299	Q₈×C₂₃	—	2	2	no	—
300	Q₈×C₂₃	—	4	4	no	—
301	D₄×C₂₃	—	2	4	no	—
302	D₄×C₂₃	—	2	4	no	—
303	D₄×C₂₃	—	2	2	no	—
304	D₄×C₂₃	—	2	2	no	—
305	D₄×C₂₃	—	4	4	no	—
306	C₂×C₄×C₂₃	—	2	4	no	—
307	C₂×C₄×C₂₃	—	2	4	no	—
308	C₂×C₄×C₂₃	—	2	4	no	—
309	C₂×C₄×C₂₃	—	2	1	no	—
310	C₂×C₄×C₂₃	—	2	2	no	—
311	C₂×C₄×C₂₃	—	2	2	no	—
312	C₂×C₄×C₂₃	—	2	1	no	—
313	C₂×C₄×C₂₃	—	2	2	no	—
314	C₂×C₄×C₂₃	—	2	2	no	—
315	C₂×C₄×C₂₃	—	4	1	no	—
316	C₂×C₄×C₂₃	—	4	2	no	—
317	C₂×C₄×C₂₃	—	4	2	no	—
318	C₂×C₄×C₂₃	—	4	2	no	—
319	C₂×C₄×C₂₃	#131	1	4	yes	—
320	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
321	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
322	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
323	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
324	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
325	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
326	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
327	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
328	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
329	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
330	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
331	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
332	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
333	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
334	C₈×C₂₃	—	2	2	no	—
335	C₈×C₂₃	—	2	1	no	—
336	C₈×C₂₃	—	2	2	no	—
337	C₈×C₂₃	—	2	1	no	—
338	C₈×C₂₃	—	2	2	no	—
339	C₈×C₂₃	—	2	4	no	—
340	C₈×C₂₃	—	2	1	no	—
341	C₈×C₂₃	—	2	2	no	—
342	C₈×C₂₃	2₋¹⁺⁴	1	2	yes	—
343	#3461	C₂×C₂₃	1	1	yes	characteristic
344	#2994	C₂×C₂₃	1	4	yes	complemented
345	#2994	C₂×C₂₃	1	2	yes	complemented
346	#2993	C₂×C₂₃	1	2	yes	complemented
347	#2989	C₂×C₂₃	1	1	yes	characteristic, complemented
348	#2988	C₂×C₂₃	1	1	yes	characteristic, complemented
349	#2986	C₂×C₂₃	1	2	yes	complemented
350	#2985	C₂×C₂₃	1	2	yes	complemented
351	#2982	C₂×C₂₃	1	1	yes	characteristic, complemented
352	#2969	C₂×C₂₃	1	2	yes	complemented
353	#2968	C₂×C₂₃	1	4	yes	complemented
354	#2966	C₂×C₂₃	1	2	yes	complemented
355	#2965	C₂×C₂₃	1	1	yes	characteristic, complemented
356	C₈×#41	C₂×C₂₃	1	1	yes	characteristic, complemented
357	#2962	C₂×C₂₃	1	2	yes	complemented
358	#2960	C₂×C₂₃	1	2	yes	complemented
359	C₂×#446	C₂×C₂₃	1	1	yes	characteristic, complemented
360	C₂²×C₂₃	—	2	1	no	—
361	C₂²×C₂₃	—	2	1	no	—
362	C₂²×C₂₃	—	2	2	no	—
363	C₂²×C₂₃	—	2	2	no	—
364	C₂²×C₂₃	—	2	2	no	—
365	C₂²×C₂₃	—	2	2	no	—
366	C₂²×C₂₃	—	2	2	no	—
367	C₂²×C₂₃	—	2	2	no	—
368	C₂²×C₂₃	C₂×#131	1	2	yes	—
369	C₂²×C₂₃	C₂⁴×C₄	1	1	yes	characteristic
370	C₄×C₂₃	—	2	1	no	—
371	C₄×C₂₃	—	2	2	no	—
372	C₄×C₂₃	—	2	2	no	—
373	C₄×C₂₃	—	2	2	no	—
374	C₄×C₂₃	—	2	2	no	—
375	C₄×C₂₃	—	2	4	no	—
376	C₄×C₂₃	—	2	1	no	—
377	C₄×C₂₃	—	2	1	no	—
378	C₄×C₂₃	—	2	4	no	—
379	C₄×C₂₃	—	2	2	no	—
380	C₄×C₂₃	—	2	2	no	—
381	C₄×C₂₃	C₂×#131	1	2	yes	—
382	C₄×C₂₃	C₂×#131	1	2	yes	—
383	C₄×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
384	C₄×C₂₃	#585	1	1	yes	characteristic
385	#544	C₄×C₂₃	1	1	yes	characteristic
386	#542	C₄×C₂₃	1	2	yes	—
387	#542	C₄×C₂₃	1	2	yes	—
388	#541	C₄×C₂₃	1	2	yes	—
389	#541	C₄×C₂₃	1	2	yes	—
390	#539	C₄×C₂₃	1	4	yes	—
391	#537	C₄×C₂₃	1	1	yes	characteristic
392	#536	C₄×C₂₃	1	1	yes	characteristic
393	#536	C₄×C₂₃	1	1	yes	characteristic
394	#533	C₂²×C₂₃	1	2	yes	—
395	#533	C₂²×C₂₃	1	2	yes	—
396	#529	C₂²×C₂₃	1	2	yes	—
397	#529	C₂²×C₂₃	1	4	yes	—
398	#529	C₂²×C₂₃	1	2	yes	—
399	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
400	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
401	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
402	#446	C₂²×C₂₃	1	2	yes	—
403	#446	C₂²×C₂₃	1	2	yes	—
404	#446	C₂²×C₂₃	1	2	yes	—
405	#446	C₂²×C₂₃	1	2	yes	—
406	#446	C₂²×C₂₃	1	1	yes	characteristic
407	#446	C₂²×C₂₃	1	4	yes	—
408	#446	C₂²×C₂₃	1	4	yes	—
409	#446	C₂²×C₂₃	1	2	yes	—
410	#446	C₂²×C₂₃	1	1	yes	characteristic
411	#446	C₂²×C₂₃	1	4	yes	—
412	C₈×Q₈	C₂²×C₂₃	1	2	yes	—
413	C₈×Q₈	C₂²×C₂₃	1	2	yes	—
414	C₈×Q₈	C₂²×C₂₃	1	4	yes	—
415	C₈×Q₈	C₂²×C₂₃	1	1	yes	characteristic
416	C₈×Q₈	C₂²×C₂₃	1	2	yes	—
417	C₈×Q₈	C₂²×C₂₃	1	1	yes	characteristic
418	C₈×Q₈	C₂²×C₂₃	1	2	yes	—
419	C₈×Q₈	C₂²×C₂₃	1	2	yes	—
420	#436	C₂²×C₂₃	1	1	yes	characteristic
421	#436	C₂²×C₂₃	1	1	yes	characteristic
422	#436	C₂²×C₂₃	1	2	yes	—
423	#436	C₂²×C₂₃	1	4	yes	—
424	#435	C₂²×C₂₃	1	2	yes	—
425	#435	C₂²×C₂₃	1	2	yes	—
426	#435	C₂²×C₂₃	1	4	yes	—
427	#435	C₂²×C₂₃	1	4	yes	—
428	#435	C₂²×C₂₃	1	4	yes	—
429	C₈×D₄	C₂²×C₂₃	1	2	yes	—
430	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic
431	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic
432	C₈×D₄	C₂²×C₂₃	1	2	yes	—
433	C₈×D₄	C₂²×C₂₃	1	2	yes	—
434	C₈×D₄	C₂²×C₂₃	1	4	yes	—
435	C₈×D₄	C₂²×C₂₃	1	4	yes	—
436	#433	C₂²×C₂₃	1	4	yes	—
437	#433	C₂²×C₂₃	1	4	yes	—
438	#433	C₂²×C₂₃	1	4	yes	—
439	#433	C₂²×C₂₃	1	4	yes	—
440	#432	C₂²×C₂₃	1	2	yes	—
441	#431	C₂²×C₂₃	1	1	yes	characteristic
442	#431	C₂²×C₂₃	1	2	yes	—
443	#431	C₂²×C₂₃	1	1	yes	characteristic
444	#431	C₂²×C₂₃	1	2	yes	—
445	#431	C₂²×C₂₃	1	4	yes	—
446	#431	C₂²×C₂₃	1	2	yes	—
447	#424	C₂²×C₂₃	1	4	yes	—
448	#424	C₂²×C₂₃	1	4	yes	—
449	#423	C₂²×C₂₃	1	2	yes	—
450	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
451	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
452	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
453	#405	C₂²×C₂₃	1	4	yes	—
454	#405	C₂²×C₂₃	1	4	yes	—
455	C₄×M₁₆	C₂²×C₂₃	1	2	yes	—
456	C₂×#97	C₂²×C₂₃	1	2	yes	—
457	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
458	C₂×C₄×C₈	C₂²×C₂₃	1	2	yes	—
459	C₂×C₂₃	—	2	2	no	—
460	C₂×C₂₃	—	4	2	no	—
461	C₂×C₂₃	—	4	2	no	—
462	C₂×C₂₃	C₄×2₋¹⁺⁴	1	1	yes	characteristic
463	C₂×C₂₃	C₂²×#131	1	1	yes	characteristic
464	C₂×C₂₃	#3573	1	1	yes	characteristic
465	C₂×#41	C₂×C₄×C₂₃	1	1	yes	characteristic
466	C₂×#41	C₂×C₄×C₂₃	1	1	yes	characteristic
467	C₂²×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
468	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
469	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
470	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
471	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
472	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
473	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
474	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
475	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
476	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
477	C₄⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
478	C₄⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
479	C₄⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
480	C₄⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
481	#126	C₂×C₄×C₂₃	1	4	yes	—
482	#126	C₂×C₄×C₂₃	1	4	yes	—
483	#126	C₂×C₄×C₂₃	1	4	yes	—
484	#126	C₂×C₄×C₂₃	1	4	yes	—
485	#125	C₂×C₄×C₂₃	1	4	yes	—
486	#125	C₂×C₄×C₂₃	1	2	yes	—
487	#125	C₂×C₄×C₂₃	1	2	yes	—
488	#125	C₂×C₄×C₂₃	1	4	yes	—
489	#125	C₂×C₄×C₂₃	1	4	yes	—
490	#124	C₂×C₄×C₂₃	1	2	yes	—
491	#124	C₂×C₄×C₂₃	1	2	yes	—
492	#124	C₂×C₄×C₂₃	1	4	yes	—
493	#123	C₂×C₄×C₂₃	1	4	yes	—
494	#123	C₂×C₄×C₂₃	1	4	yes	—
495	#123	C₂×C₄×C₂₃	1	4	yes	—
496	#123	C₂×C₄×C₂₃	1	4	yes	—
497	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
498	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
499	C₂²⋊Q₈	C₂×C₄×C₂₃	1	4	yes	—
500	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
501	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
502	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
503	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
504	C₂²⋊Q₈	C₂×C₄×C₂₃	1	4	yes	—
505	C₂²⋊Q₈	C₂×C₄×C₂₃	1	4	yes	—
506	#121	C₂×C₄×C₂₃	1	4	yes	—
507	#121	C₂×C₄×C₂₃	1	2	yes	—
508	#121	C₂×C₄×C₂₃	1	2	yes	—
509	C₄×Q₈	C₂×C₄×C₂₃	1	2	yes	—
510	C₄×Q₈	C₂×C₄×C₂₃	1	2	yes	—
511	C₄×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
512	C₄×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
513	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
514	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
515	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
516	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
517	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
518	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
519	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
520	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
521	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
522	C₄×D₄	C₂³×C₂₃	1	2	yes	—
523	C₄×D₄	C₂³×C₂₃	1	2	yes	—
524	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
525	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
526	C₄×D₄	C₂³×C₂₃	1	4	yes	—
527	#117	C₂×C₄×C₂₃	1	1	yes	characteristic
528	#117	C₂×C₄×C₂₃	1	1	yes	characteristic
529	#117	C₂×C₄×C₂₃	1	2	yes	—
530	#117	C₂×C₄×C₂₃	1	2	yes	—
531	#117	C₂³×C₂₃	1	4	yes	—
532	#117	C₂³×C₂₃	1	4	yes	—
533	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
534	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
535	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
536	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
537	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
538	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
539	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
540	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
541	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
542	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
543	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
544	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
545	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
546	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
547	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
548	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
549	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
550	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
551	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
552	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
553	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
554	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
555	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
556	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
557	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
558	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
559	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
560	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
561	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
562	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
563	#97	C₂³×C₂₃	1	4	yes	—
564	#97	C₂³×C₂₃	1	4	yes	—
565	#97	C₂³×C₂₃	1	2	yes	—
566	#97	C₂³×C₂₃	1	2	yes	—
567	#97	C₂³×C₂₃	1	4	yes	—
568	C₄×C₈	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	2	yes	—
572	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
573	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
574	C₄×C₈	C₂³×C₂₃	1	2	yes	—
575	C₄×C₈	C₂³×C₂₃	1	2	yes	—
576	C₄×C₈	C₂³×C₂₃	1	4	yes	—
577	C₄×C₈	C₂³×C₂₃	1	4	yes	—
578	C₄×C₈	C₂³×C₂₃	1	4	yes	—
579	C₂₃	#60339	1	1	yes	characteristic, direct product factor, Sylow
580	#41	—	2	4	no	—
581	#41	—	2	4	no	—
582	C₂×Q₈	—	2	4	no	—
583	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
584	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
585	C₂×Q₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
586	C₂×Q₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
587	C₂×Q₈	C₂²×C₄×C₂₃	1	4	yes	—
588	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
589	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
590	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
591	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
592	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
593	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
594	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
595	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
596	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
597	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
598	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
599	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
600	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
601	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
602	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
603	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
604	M₁₆	—	2	4	no	—
605	M₁₆	—	4	4	no	—
606	M₁₆	—	4	2	no	—
607	C₂×C₈	—	2	2	no	—
608	C₂×C₈	—	2	4	no	—
609	C₂×C₈	—	4	2	no	—
610	C₂×C₈	—	4	4	no	—
611	C₂×C₈	—	4	1	no	—
612	C₂×C₈	—	4	2	no	—
613	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
614	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
615	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
616	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
617	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
618	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
619	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
620	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
621	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
622	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
623	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
624	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
625	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
626	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
627	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
628	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
629	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
630	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
631	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
632	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
633	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
634	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
635	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
636	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
637	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
638	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
639	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
640	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
641	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
642	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
643	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
644	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
645	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
646	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
647	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
648	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
649	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
650	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
651	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
652	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
653	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
654	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
655	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
656	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
657	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
658	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
659	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
660	C₄²	C₂²×C₄×C₂₃	1	4	yes	—
661	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
662	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
663	C₄²	C₂⁴×C₂₃	1	2	yes	—
664	C₄²	C₂⁴×C₂₃	1	2	yes	—
665	C₄²	C₂⁴×C₂₃	1	4	yes	—
666	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
667	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
668	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
669	Q₈	—	2	4	no	—
670	Q₈	—	2	4	no	—
671	Q₈	—	2	2	no	—
672	Q₈	—	2	2	no	—
673	Q₈	—	4	4	no	—
674	D₄	—	2	4	no	—
675	D₄	—	2	4	no	—
676	D₄	—	2	2	no	—
677	D₄	—	2	2	no	—
678	D₄	—	4	4	no	—
679	C₂×C₄	—	2	4	no	—
680	C₂×C₄	—	2	4	no	—
681	C₂×C₄	—	2	4	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	4	1	no	—
689	C₂×C₄	—	4	2	no	—
690	C₂×C₄	—	4	2	no	—
691	C₂×C₄	—	4	2	no	—
692	C₂×C₄	C₂₃×#131	1	4	yes	—
693	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
694	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
695	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
696	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
697	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
698	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
699	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
700	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
701	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
702	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
703	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
704	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
705	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
706	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
707	C₈	—	2	2	no	—
708	C₈	—	2	1	no	—
709	C₈	—	2	2	no	—
710	C₈	—	2	1	no	—
711	C₈	—	2	2	no	—
712	C₈	—	2	4	no	—
713	C₈	—	2	1	no	—
714	C₈	—	2	2	no	—
715	C₈	C₂₃×2₋¹⁺⁴	1	2	yes	—
716	C₂²	—	2	1	no	—
717	C₂²	—	2	1	no	—
718	C₂²	—	2	2	no	—
719	C₂²	—	2	2	no	—
720	C₂²	—	2	2	no	—
721	C₂²	—	2	2	no	—
722	C₂²	—	2	2	no	—
723	C₂²	—	2	2	no	—
724	C₂²	C₂×C₂₃×#131	1	2	yes	—
725	C₂²	C₂⁴×C₄×C₂₃	1	1	yes	characteristic
726	C₄	—	2	1	no	—
727	C₄	—	2	2	no	—
728	C₄	—	2	2	no	—
729	C₄	—	2	2	no	—
730	C₄	—	2	2	no	—
731	C₄	—	2	4	no	—
732	C₄	—	2	1	no	—
733	C₄	—	2	1	no	—
734	C₄	—	2	4	no	—
735	C₄	—	2	2	no	—
736	C₄	—	2	2	no	—
737	C₄	C₂×C₂₃×#131	1	2	yes	—
738	C₄	C₂×C₂₃×#131	1	2	yes	—
739	C₄	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
740	C₄	C₂₃×#585	1	1	yes	characteristic
741	C₂	—	2	2	no	—
742	C₂	—	4	2	no	—
743	C₂	—	4	2	no	—
744	C₂	C₄×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
745	C₂	C₂²×C₂₃×#131	1	1	yes	characteristic
746	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×#2994	C₂	semidirect
3. C₂₃×#2994	C₂	semidirect
4. C₂₃×#2993	C₂	semidirect
5. C₂₃×#2989	C₂	semidirect
6. C₂₃×#2988	C₂	semidirect
7. C₂₃×#2986	C₂	semidirect
8. C₂₃×#2985	C₂	semidirect
9. C₂₃×#2982	C₂	semidirect
10. C₂₃×#2969	C₂	semidirect
11. C₂₃×#2968	C₂	semidirect
12. C₂₃×#2966	C₂	semidirect
13. C₂₃×#2965	C₂	semidirect
14. C₈×#41×C₂₃	C₂	semidirect
15. C₂₃×#2962	C₂	semidirect
16. C₂₃×#2960	C₂	semidirect
17. C₂×C₂₃×#446	C₂	semidirect
292. #60339	C₂₃	direct (N × H)
344. #2994	C₂×C₂₃	semidirect
345. #2994	C₂×C₂₃	semidirect
346. #2993	C₂×C₂₃	semidirect
347. #2989	C₂×C₂₃	semidirect
348. #2988	C₂×C₂₃	semidirect
349. #2986	C₂×C₂₃	semidirect
350. #2985	C₂×C₂₃	semidirect
351. #2982	C₂×C₂₃	semidirect
352. #2969	C₂×C₂₃	semidirect
353. #2968	C₂×C₂₃	semidirect
354. #2966	C₂×C₂₃	semidirect
355. #2965	C₂×C₂₃	semidirect
356. C₈×#41	C₂×C₂₃	semidirect
357. #2962	C₂×C₂₃	semidirect
358. #2960	C₂×C₂₃	semidirect
359. C₂×#446	C₂×C₂₃	semidirect
579. C₂₃	#60339	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×#2994	2
C₂₃×#2993	2
C₂₃×#2989	2
C₂₃×#2988	2
C₂₃×#2986	2
C₂₃×#2985	2
C₂₃×#2982	2
C₂₃×#2969	2
C₂₃×#2968	2
C₂₃×#2966	2
C₂₃×#2965	2
C₈×#41×C₂₃	2
C₂₃×#2962	2
C₂₃×#2960	2
C₂×C₂₃×#446	2
#60339	23

Subgroups — C23×#60339 #19207965

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60339 #19207965