Subgroups — C₂₃×#35007 #19182633

Order 5888.

2756 conjugacy classes of subgroups.

The subgroup lattice has 1222 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#538	C₂	1	2	yes	maximal, complemented
2	C₂₃×#2860	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#2858	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#2856	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2854	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#2662	C₂	1	2	yes	maximal, complemented
7	C₂₃×#2661	C₂	1	2	yes	maximal, complemented
8	C₂₃×#2555	C₂	1	2	yes	maximal, complemented
9	C₂₃×#2554	C₂	1	2	yes	maximal, complemented
10	C₂₃×#2512	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#2491	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#2472	C₂	1	2	yes	maximal, complemented
13	C₂₃×#2445	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#2440	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#2433	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#2428	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#2424	C₂	1	2	yes	maximal, complemented
18	C₂₃×#2416	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#2408	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#2321	C₂	1	2	yes	maximal, complemented
21	C₄×C₂₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₂₃×#390	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄²×D₄×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂³×D₄×C₂₃	C₂²	1	1	yes	characteristic
25	C₂₃×#538	—	2	16	no	—
26	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic
28	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic
29	C₂×C₂₃×#126	C₂²	1	2	yes	complemented
30	C₂×C₂₃×#126	C₂²	1	2	yes	complemented
31	C₂×C₂₃×#124	C₂²	1	2	yes	complemented
32	C₂×C₂₃×#124	C₂²	1	2	yes	complemented
33	C₂×C₂₃×#124	C₂²	1	2	yes	complemented
34	C₂×C₂₃×#123	C₂²	1	2	yes	complemented
35	C₂×C₂₃×#123	C₂²	1	2	yes	complemented
36	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
37	C₂×C₂₃×#121	C₂²	1	2	yes	—
38	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
39	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
40	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
41	C₂×C₂₃×#121	C₂²	1	2	yes	complemented
42	C₂×C₂₃×#121	C₂²	1	2	yes	complemented
43	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₂₃×#121	C₂²	1	2	yes	complemented
45	C₂×C₂₃×#120	C₂²	1	2	yes	—
46	C₂×C₂₃×#120	C₂²	1	2	yes	—
47	C₂×C₂₃×#120	C₂²	1	2	yes	—
48	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
49	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
50	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
51	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
52	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
53	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
54	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
55	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
56	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
57	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic, complemented
58	C₂₃×#398	C₂²	1	2	yes	complemented
59	C₂₃×#397	C₂²	1	2	yes	complemented
60	C₂₃×#396	C₂²	1	2	yes	complemented
61	C₂₃×#396	C₂²	1	2	yes	complemented
62	C₂₃×#395	C₂²	1	2	yes	complemented
63	C₂₃×#394	C₂²	1	2	yes	—
64	C₂₃×#394	C₂²	1	2	yes	complemented
65	C₂₃×#394	C₂²	1	2	yes	complemented
66	C₂₃×#394	C₂²	1	2	yes	complemented
67	C₂₃×#394	C₂²	1	2	yes	complemented
68	C₂₃×#394	C₂²	1	2	yes	complemented
69	C₂₃×#393	C₂²	1	2	yes	complemented
70	C₂₃×#392	C₂²	1	2	yes	—
71	C₂₃×#392	C₂²	1	2	yes	—
72	C₂₃×#392	C₂²	1	2	yes	—
73	C₂₃×#392	C₂²	1	2	yes	complemented
74	C₂₃×#390	C₂²	1	2	yes	—
75	C₂₃×#390	C₂²	1	1	yes	characteristic
76	C₂₃×#390	C₂²	1	1	yes	characteristic
77	C₂₃×#390	C₂²	1	1	yes	characteristic
78	C₂₃×#390	C₂²	1	1	yes	characteristic
79	C₂₃×#390	C₂²	1	1	yes	characteristic
80	C₂₃×#390	C₂²	1	1	yes	characteristic
81	C₂₃×#390	C₂²	1	2	yes	—
82	C₂₃×#390	C₂²	1	1	yes	characteristic
83	C₂₃×#390	C₂²	1	1	yes	characteristic
84	C₂₃×#390	C₂²	1	2	yes	complemented
85	C₂₃×#390	C₂²	1	2	yes	complemented
86	C₂₃×#390	C₂²	1	1	yes	characteristic, complemented
87	C₂₃×#390	C₂²	1	2	yes	complemented
88	C₂₃×#390	C₂²	1	2	yes	complemented
89	C₂₃×#390	C₂²	1	1	yes	characteristic, complemented
90	C₂₃×#389	C₂²	1	1	yes	characteristic, complemented
91	C₂₃×#389	C₂²	1	1	yes	characteristic, complemented
92	C₂₃×#389	C₂²	1	1	yes	characteristic, complemented
93	C₂₃×#389	C₂²	1	1	yes	characteristic, complemented
94	C₂₃×#388	C₂²	1	2	yes	complemented
95	C₂₃×#388	C₂²	1	2	yes	complemented
96	C₂₃×#388	C₂²	1	2	yes	complemented
97	C₂₃×#388	C₂²	1	2	yes	complemented
98	C₂₃×#388	C₂²	1	2	yes	complemented
99	C₂₃×#388	C₂²	1	2	yes	complemented
100	C₂₃×#388	C₂²	1	2	yes	complemented
101	C₂₃×#388	C₂²	1	2	yes	complemented
102	C₂₃×#386	C₂²	1	2	yes	—
103	C₂₃×#386	C₂²	1	2	yes	—
104	C₂₃×#386	C₂²	1	2	yes	complemented
105	C₂₃×#386	C₂²	1	2	yes	complemented
106	C₂₃×#386	C₂²	1	2	yes	complemented
107	C₂₃×#385	C₂²	1	2	yes	—
108	C₂₃×#384	C₂²	1	1	yes	characteristic, complemented
109	C₂₃×#380	C₂²	1	1	yes	characteristic
110	C₂₃×#380	C₂²	1	1	yes	characteristic, complemented
111	C₂₃×#379	C₂²	1	2	yes	—
112	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
113	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
114	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
115	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
116	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
117	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
118	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
119	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
120	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
121	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
122	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	complemented
123	C₄³×C₂₃	C₂²	1	1	yes	characteristic, complemented
124	C₂⁵×C₂₃	C₂³	1	2	yes	—
125	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
126	C₂²×D₄×C₂₃	—	2	4	no	—
127	C₂²×D₄×C₂₃	—	4	2	no	—
128	C₂²×D₄×C₂₃	—	4	2	no	—
129	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
130	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
131	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
132	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
133	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
134	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
135	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
136	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
137	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
138	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
139	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
140	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
141	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
142	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
143	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
144	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
145	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
146	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
147	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
148	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
149	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
150	C₂₃×C₄⋊Q₈	—	4	2	no	—
151	C₂₃×#127	—	4	2	no	—
152	C₂₃×#127	—	4	2	no	—
153	C₂₃×#126	—	2	8	no	—
154	C₂₃×#126	—	2	8	no	—
155	C₂₃×#124	—	2	8	no	—
156	C₂₃×#124	—	2	8	no	—
157	C₂₃×#124	—	4	4	no	—
158	C₂₃×#123	—	2	8	no	—
159	C₂₃×#123	—	2	8	no	—
160	C₂₃×C₂²⋊Q₈	—	2	8	no	—
161	C₂₃×#121	—	2	8	no	—
162	C₂₃×#121	—	2	8	no	—
163	C₂₃×#121	—	2	4	no	—
164	C₂₃×#121	—	2	8	no	—
165	C₂₃×#121	—	4	4	no	—
166	C₂₃×#121	—	4	2	no	—
167	C₂₃×#121	—	4	2	no	—
168	C₂₃×#121	—	4	2	no	—
169	C₂₃×#120	—	2	8	no	—
170	C₂₃×#120	—	2	8	no	—
171	C₂₃×#120	—	2	8	no	—
172	C₄×D₄×C₂₃	—	2	8	no	—
173	C₄×D₄×C₂₃	—	2	4	no	—
174	C₄×D₄×C₂₃	—	2	4	no	—
175	C₄×D₄×C₂₃	—	4	2	no	—
176	C₄×D₄×C₂₃	D₄	1	8	yes	complemented
177	C₂×C₄⋊C₄×C₂₃	—	4	2	no	—
178	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
179	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
180	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
181	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
182	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
183	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
184	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
185	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
186	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
187	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
188	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
189	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
190	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
191	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
192	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
193	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
194	C₂×C₂²⋊C₄×C₂₃	—	2	8	no	—
195	C₂×C₂²⋊C₄×C₂₃	—	4	4	no	—
196	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
197	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
198	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
199	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
201	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
202	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
203	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
204	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
205	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
206	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
207	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
208	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
209	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
210	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
211	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
212	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
213	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
214	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
215	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
216	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
217	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
218	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
219	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
220	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
221	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
222	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
223	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
224	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
225	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
226	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
227	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
228	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
229	C₂×C₄²×C₂₃	—	4	2	no	—
230	C₂×C₄²×C₂₃	—	4	2	no	—
231	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
232	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
233	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
234	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
235	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
236	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
237	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
238	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
239	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
240	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
241	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
242	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
243	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
244	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
245	C₂₃×#95	C₂³	1	1	yes	characteristic
246	C₂₃×#95	C₂³	1	1	yes	characteristic
247	C₂₃×#95	C₂³	1	1	yes	characteristic
248	C₂₃×#95	C₂³	1	1	yes	characteristic
249	C₂₃×#95	C₂³	1	1	yes	characteristic
250	C₂₃×#95	C₂³	1	1	yes	characteristic
251	C₂₃×#95	C₂³	1	2	yes	—
252	C₂₃×#95	C₂³	1	2	yes	—
253	C₂₃×#95	C₂³	1	2	yes	—
254	C₂₃×#95	C₂³	1	2	yes	—
255	C₂₃×#95	C₂³	1	2	yes	—
256	C₂₃×#95	C₂³	1	2	yes	—
257	C₂₃×#95	C₂³	1	2	yes	—
258	C₂⁴×C₂₃	—	2	4	no	—
259	C₂⁴×C₂₃	—	2	4	no	—
260	C₂⁴×C₂₃	—	2	4	no	—
261	C₂⁴×C₂₃	—	4	2	no	—
262	C₂⁴×C₂₃	—	4	2	no	—
263	C₂⁴×C₂₃	—	4	2	no	—
264	C₂⁴×C₂₃	—	4	2	no	—
265	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
266	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
267	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
268	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
269	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
270	C₂×Q₈×C₂₃	—	2	4	no	—
271	C₂×Q₈×C₂₃	—	4	2	no	—
272	C₂×Q₈×C₂₃	—	4	2	no	—
273	C₂×D₄×C₂₃	—	2	2	no	—
274	C₂×D₄×C₂₃	—	2	2	no	—
275	C₂×D₄×C₂₃	—	2	4	no	—
276	C₂×D₄×C₂₃	—	2	4	no	—
277	C₂×D₄×C₂₃	—	2	4	no	—
278	C₂×D₄×C₂₃	—	2	4	no	—
279	C₂×D₄×C₂₃	—	2	4	no	—
280	C₂×D₄×C₂₃	—	2	4	no	—
281	C₂×D₄×C₂₃	—	2	4	no	—
282	C₂×D₄×C₂₃	—	2	4	no	—
283	C₂×D₄×C₂₃	—	2	2	no	—
284	C₂×D₄×C₂₃	—	2	4	no	—
285	C₂×D₄×C₂₃	—	2	2	no	—
286	C₂×D₄×C₂₃	—	2	2	no	—
287	C₂×D₄×C₂₃	—	2	4	no	—
288	C₂×D₄×C₂₃	—	2	4	no	—
289	C₂×D₄×C₂₃	—	2	2	no	—
290	C₂×D₄×C₂₃	—	2	2	no	—
291	C₂×D₄×C₂₃	—	2	2	no	—
292	C₂×D₄×C₂₃	—	2	2	no	—
293	C₂×D₄×C₂₃	—	2	2	no	—
294	C₂×D₄×C₂₃	—	2	2	no	—
295	C₂×D₄×C₂₃	—	4	2	no	—
296	C₂×D₄×C₂₃	—	4	2	no	—
297	C₂×D₄×C₂₃	—	4	16	no	—
298	C₂×D₄×C₂₃	—	4	2	no	—
299	C₂×D₄×C₂₃	—	4	2	no	—
300	C₂×D₄×C₂₃	—	4	2	no	—
301	C₂×D₄×C₂₃	—	4	2	no	—
302	C₂×D₄×C₂₃	—	4	2	no	—
303	C₂×D₄×C₂₃	—	4	2	no	—
304	C₂×D₄×C₂₃	—	4	2	no	—
305	C₂×D₄×C₂₃	—	4	2	no	—
306	C₂×D₄×C₂₃	—	4	2	no	—
307	C₂×D₄×C₂₃	—	4	2	no	—
308	C₂×D₄×C₂₃	—	4	2	no	—
309	C₂×D₄×C₂₃	—	4	2	no	—
310	C₂×D₄×C₂₃	—	4	2	no	—
311	C₂×D₄×C₂₃	—	4	2	no	—
312	C₂×D₄×C₂₃	C₂×D₄	1	4	yes	—
313	C₂²×C₄×C₂₃	—	2	2	no	—
314	C₂²×C₄×C₂₃	—	2	2	no	—
315	C₂²×C₄×C₂₃	—	2	2	no	—
316	C₂²×C₄×C₂₃	—	2	4	no	—
317	C₂²×C₄×C₂₃	—	2	2	no	—
318	C₂²×C₄×C₂₃	—	2	2	no	—
319	C₂²×C₄×C₂₃	—	2	2	no	—
320	C₂²×C₄×C₂₃	—	2	2	no	—
321	C₂²×C₄×C₂₃	—	2	2	no	—
322	C₂²×C₄×C₂₃	—	2	2	no	—
323	C₂²×C₄×C₂₃	—	2	4	no	—
324	C₂²×C₄×C₂₃	—	4	1	no	—
325	C₂²×C₄×C₂₃	—	4	1	no	—
326	C₂²×C₄×C₂₃	—	4	1	no	—
327	C₂²×C₄×C₂₃	—	4	1	no	—
328	C₂²×C₄×C₂₃	—	4	1	no	—
329	C₂²×C₄×C₂₃	—	4	1	no	—
330	C₂²×C₄×C₂₃	—	4	2	no	—
331	C₂²×C₄×C₂₃	—	4	2	no	—
332	C₂²×C₄×C₂₃	—	4	2	no	—
333	C₂²×C₄×C₂₃	—	4	2	no	—
334	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
335	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	complemented
336	C₂²×C₄×C₂₃	#41	1	4	yes	—
337	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
338	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
339	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
340	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
341	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
342	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
343	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
344	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
345	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
346	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
347	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
348	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
349	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
350	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
351	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
352	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
353	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
354	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
355	C₄⋊C₄×C₂₃	—	2	4	no	—
356	C₄⋊C₄×C₂₃	—	2	4	no	—
357	C₄⋊C₄×C₂₃	—	2	4	no	—
358	C₄⋊C₄×C₂₃	—	2	4	no	—
359	C₄⋊C₄×C₂₃	—	2	4	no	—
360	C₄⋊C₄×C₂₃	—	2	2	no	—
361	C₄⋊C₄×C₂₃	—	2	2	no	—
362	C₄⋊C₄×C₂₃	—	2	2	no	—
363	C₄⋊C₄×C₂₃	—	2	2	no	—
364	C₄⋊C₄×C₂₃	—	2	2	no	—
365	C₄⋊C₄×C₂₃	—	2	2	no	—
366	C₄⋊C₄×C₂₃	—	2	2	no	—
367	C₄⋊C₄×C₂₃	—	4	2	no	—
368	C₄⋊C₄×C₂₃	—	4	2	no	—
369	C₄⋊C₄×C₂₃	—	4	2	no	—
370	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	complemented
371	C₂²⋊C₄×C₂₃	—	2	4	no	—
372	C₂²⋊C₄×C₂₃	—	2	4	no	—
373	C₂²⋊C₄×C₂₃	—	2	2	no	—
374	C₂²⋊C₄×C₂₃	—	2	4	no	—
375	C₂²⋊C₄×C₂₃	—	2	4	no	—
376	C₂²⋊C₄×C₂₃	—	2	4	no	—
377	C₂²⋊C₄×C₂₃	—	2	4	no	—
378	C₂²⋊C₄×C₂₃	—	2	4	no	—
379	C₂²⋊C₄×C₂₃	—	2	4	no	—
380	C₂²⋊C₄×C₂₃	—	2	4	no	—
381	C₂²⋊C₄×C₂₃	—	2	4	no	—
382	C₂²⋊C₄×C₂₃	—	2	4	no	—
383	C₂²⋊C₄×C₂₃	—	2	4	no	—
384	C₂²⋊C₄×C₂₃	—	2	2	no	—
385	C₂²⋊C₄×C₂₃	—	2	2	no	—
386	C₂²⋊C₄×C₂₃	—	2	4	no	—
387	C₂²⋊C₄×C₂₃	—	2	4	no	—
388	C₂²⋊C₄×C₂₃	—	2	4	no	—
389	C₂²⋊C₄×C₂₃	—	2	4	no	—
390	C₂²⋊C₄×C₂₃	—	2	4	no	—
391	C₂²⋊C₄×C₂₃	—	2	4	no	—
392	C₂²⋊C₄×C₂₃	—	4	2	no	—
393	C₂²⋊C₄×C₂₃	—	4	2	no	—
394	C₂²⋊C₄×C₂₃	—	4	2	no	—
395	C₂²⋊C₄×C₂₃	—	4	2	no	—
396	C₂²⋊C₄×C₂₃	—	4	2	no	—
397	C₂²⋊C₄×C₂₃	—	4	2	no	—
398	C₂²⋊C₄×C₂₃	—	4	2	no	—
399	C₂²⋊C₄×C₂₃	—	4	2	no	—
400	C₂²⋊C₄×C₂₃	—	4	2	no	—
401	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
402	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	complemented
403	C₂²⋊C₄×C₂₃	#41	1	4	yes	—
404	C₄²×C₂₃	—	2	4	no	—
405	C₄²×C₂₃	—	2	2	no	—
406	C₄²×C₂₃	—	2	2	no	—
407	C₄²×C₂₃	—	2	2	no	—
408	C₄²×C₂₃	—	2	2	no	—
409	C₄²×C₂₃	—	2	2	no	—
410	C₄²×C₂₃	—	2	2	no	—
411	C₄²×C₂₃	—	2	2	no	—
412	C₄²×C₂₃	—	4	1	no	—
413	C₄²×C₂₃	—	4	1	no	—
414	C₄²×C₂₃	—	4	1	no	—
415	C₄²×C₂₃	—	4	1	no	—
416	C₄²×C₂₃	—	4	1	no	—
417	C₄²×C₂₃	C₂×D₄	1	4	yes	complemented
418	#35007	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
419	C₂³×C₂₃	—	2	1	no	—
420	C₂³×C₂₃	—	2	1	no	—
421	C₂³×C₂₃	—	2	1	no	—
422	C₂³×C₂₃	—	2	1	no	—
423	C₂³×C₂₃	—	2	1	no	—
424	C₂³×C₂₃	—	2	1	no	—
425	C₂³×C₂₃	—	2	1	no	—
426	C₂³×C₂₃	—	2	1	no	—
427	C₂³×C₂₃	—	2	1	no	—
428	C₂³×C₂₃	—	2	1	no	—
429	C₂³×C₂₃	—	2	2	no	—
430	C₂³×C₂₃	—	2	2	no	—
431	C₂³×C₂₃	—	2	2	no	—
432	C₂³×C₂₃	—	2	2	no	—
433	C₂³×C₂₃	—	2	2	no	—
434	C₂³×C₂₃	—	2	2	no	—
435	C₂³×C₂₃	—	2	2	no	—
436	C₂³×C₂₃	—	2	2	no	—
437	C₂³×C₂₃	—	2	2	no	—
438	C₂³×C₂₃	—	2	2	no	—
439	C₂³×C₂₃	—	2	2	no	—
440	C₂³×C₂₃	—	2	2	no	—
441	C₂³×C₂₃	—	2	2	no	—
442	C₂³×C₂₃	—	2	2	no	—
443	C₂³×C₂₃	—	2	2	no	—
444	C₂³×C₂₃	—	2	2	no	—
445	C₂³×C₂₃	—	2	2	no	—
446	C₂³×C₂₃	—	2	2	no	—
447	C₂³×C₂₃	—	2	2	no	—
448	C₂³×C₂₃	—	2	2	no	—
449	C₂³×C₂₃	—	2	2	no	—
450	C₂³×C₂₃	—	4	8	no	—
451	C₂³×C₂₃	—	4	8	no	—
452	C₂³×C₂₃	—	4	8	no	—
453	C₂³×C₂₃	—	8	4	no	—
454	C₂³×C₂₃	—	8	4	no	—
455	C₂³×C₂₃	—	8	4	no	—
456	C₂³×C₂₃	—	8	4	no	—
457	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
458	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
459	C₂³×C₂₃	C₂×#41	1	2	yes	—
460	C₂³×C₂₃	C₂×#41	1	2	yes	—
461	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
462	Q₈×C₂₃	—	8	4	no	—
463	D₄×C₂₃	—	2	8	no	—
464	D₄×C₂₃	—	4	8	no	—
465	D₄×C₂₃	—	4	8	no	—
466	D₄×C₂₃	—	4	4	no	—
467	D₄×C₂₃	—	4	4	no	—
468	D₄×C₂₃	—	4	4	no	—
469	D₄×C₂₃	—	8	4	no	—
470	D₄×C₂₃	—	8	4	no	—
471	D₄×C₂₃	—	8	4	no	—
472	D₄×C₂₃	—	8	4	no	—
473	D₄×C₂₃	—	8	4	no	—
474	D₄×C₂₃	—	8	4	no	—
475	D₄×C₂₃	—	8	4	no	—
476	C₂×C₄×C₂₃	—	2	1	no	—
477	C₂×C₄×C₂₃	—	2	1	no	—
478	C₂×C₄×C₂₃	—	2	1	no	—
479	C₂×C₄×C₂₃	—	2	1	no	—
480	C₂×C₄×C₂₃	—	2	1	no	—
481	C₂×C₄×C₂₃	—	2	1	no	—
482	C₂×C₄×C₂₃	—	2	1	no	—
483	C₂×C₄×C₂₃	—	2	1	no	—
484	C₂×C₄×C₂₃	—	2	1	no	—
485	C₂×C₄×C₂₃	—	2	1	no	—
486	C₂×C₄×C₂₃	—	2	1	no	—
487	C₂×C₄×C₂₃	—	2	1	no	—
488	C₂×C₄×C₂₃	—	2	1	no	—
489	C₂×C₄×C₂₃	—	2	1	no	—
490	C₂×C₄×C₂₃	—	2	1	no	—
491	C₂×C₄×C₂₃	—	2	1	no	—
492	C₂×C₄×C₂₃	—	2	1	no	—
493	C₂×C₄×C₂₃	—	2	1	no	—
494	C₂×C₄×C₂₃	—	2	8	no	—
495	C₂×C₄×C₂₃	—	2	2	no	—
496	C₂×C₄×C₂₃	—	2	2	no	—
497	C₂×C₄×C₂₃	—	2	2	no	—
498	C₂×C₄×C₂₃	—	2	2	no	—
499	C₂×C₄×C₂₃	—	2	2	no	—
500	C₂×C₄×C₂₃	—	2	1	no	—
501	C₂×C₄×C₂₃	—	2	2	no	—
502	C₂×C₄×C₂₃	—	2	1	no	—
503	C₂×C₄×C₂₃	—	2	1	no	—
504	C₂×C₄×C₂₃	—	2	2	no	—
505	C₂×C₄×C₂₃	—	2	1	no	—
506	C₂×C₄×C₂₃	—	2	1	no	—
507	C₂×C₄×C₂₃	—	2	1	no	—
508	C₂×C₄×C₂₃	—	2	2	no	—
509	C₂×C₄×C₂₃	—	2	2	no	—
510	C₂×C₄×C₂₃	—	2	2	no	—
511	C₂×C₄×C₂₃	—	2	1	no	—
512	C₂×C₄×C₂₃	—	2	1	no	—
513	C₂×C₄×C₂₃	—	2	2	no	—
514	C₂×C₄×C₂₃	—	2	2	no	—
515	C₂×C₄×C₂₃	—	2	2	no	—
516	C₂×C₄×C₂₃	—	2	2	no	—
517	C₂×C₄×C₂₃	—	2	1	no	—
518	C₂×C₄×C₂₃	—	2	2	no	—
519	C₂×C₄×C₂₃	—	4	4	no	—
520	C₂×C₄×C₂₃	—	4	4	no	—
521	C₂×C₄×C₂₃	—	4	4	no	—
522	C₂×C₄×C₂₃	—	4	4	no	—
523	C₂×C₄×C₂₃	—	4	4	no	—
524	C₂×C₄×C₂₃	—	8	4	no	—
525	C₂×C₄×C₂₃	—	8	4	no	—
526	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
527	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
528	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
529	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
530	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
531	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
532	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
533	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
534	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
535	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
536	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
537	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
538	C₂×#538	C₂×C₂₃	1	2	yes	complemented
539	#2860	C₂×C₂₃	1	1	yes	characteristic, complemented
540	#2858	C₂×C₂₃	1	1	yes	characteristic, complemented
541	#2856	C₂×C₂₃	1	1	yes	characteristic, complemented
542	#2854	C₂×C₂₃	1	1	yes	characteristic, complemented
543	#2662	C₂×C₂₃	1	2	yes	complemented
544	#2661	C₂×C₂₃	1	2	yes	complemented
545	#2555	C₂×C₂₃	1	2	yes	complemented
546	#2554	C₂×C₂₃	1	2	yes	complemented
547	#2512	C₂×C₂₃	1	1	yes	characteristic, complemented
548	#2491	C₂×C₂₃	1	1	yes	characteristic, complemented
549	#2472	C₂×C₂₃	1	2	yes	complemented
550	#2445	C₂×C₂₃	1	1	yes	characteristic, complemented
551	#2440	C₂×C₂₃	1	1	yes	characteristic, complemented
552	#2433	C₂×C₂₃	1	1	yes	characteristic, complemented
553	#2428	C₂×C₂₃	1	1	yes	characteristic, complemented
554	#2424	C₂×C₂₃	1	2	yes	complemented
555	#2416	C₂×C₂₃	1	1	yes	characteristic, complemented
556	#2408	C₂×C₂₃	1	1	yes	characteristic, complemented
557	#2321	C₂×C₂₃	1	2	yes	complemented
558	C₄×#121	C₂×C₂₃	1	1	yes	characteristic, complemented
559	C₂×#390	C₂×C₂₃	1	1	yes	characteristic, complemented
560	C₄²×D₄	C₂×C₂₃	1	1	yes	characteristic, complemented
561	C₂²×C₂₃	—	2	2	no	—
562	C₂²×C₂₃	—	2	2	no	—
563	C₂²×C₂₃	—	2	2	no	—
564	C₂²×C₂₃	—	2	2	no	—
565	C₂²×C₂₃	—	2	2	no	—
566	C₂²×C₂₃	—	2	2	no	—
567	C₂²×C₂₃	—	2	2	no	—
568	C₂²×C₂₃	—	2	2	no	—
569	C₂²×C₂₃	—	2	2	no	—
570	C₂²×C₂₃	—	4	1	no	—
571	C₂²×C₂₃	—	4	1	no	—
572	C₂²×C₂₃	—	4	1	no	—
573	C₂²×C₂₃	—	4	1	no	—
574	C₂²×C₂₃	—	4	2	no	—
575	C₂²×C₂₃	—	4	2	no	—
576	C₂²×C₂₃	—	4	2	no	—
577	C₂²×C₂₃	—	4	2	no	—
578	C₂²×C₂₃	—	4	2	no	—
579	C₂²×C₂₃	—	4	2	no	—
580	C₂²×C₂₃	—	4	2	no	—
581	C₂²×C₂₃	—	4	2	no	—
582	C₂²×C₂₃	—	4	2	no	—
583	C₂²×C₂₃	—	4	2	no	—
584	C₂²×C₂₃	—	4	2	no	—
585	C₂²×C₂₃	—	4	2	no	—
586	C₂²×C₂₃	—	4	2	no	—
587	C₂²×C₂₃	—	4	2	no	—
588	C₂²×C₂₃	—	4	2	no	—
589	C₂²×C₂₃	—	4	2	no	—
590	C₂²×C₂₃	—	4	2	no	—
591	C₂²×C₂₃	—	4	2	no	—
592	C₂²×C₂₃	—	4	2	no	—
593	C₂²×C₂₃	—	4	2	no	—
594	C₂²×C₂₃	—	4	2	no	—
595	C₂²×C₂₃	—	8	16	no	—
596	C₂²×C₂₃	#532	1	4	yes	—
597	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
598	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
599	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
600	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
601	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
602	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
603	C₂²×C₂₃	#585	1	1	yes	characteristic
604	C₄×C₂₃	—	2	2	no	—
605	C₄×C₂₃	—	2	2	no	—
606	C₄×C₂₃	—	2	2	no	—
607	C₄×C₂₃	—	2	2	no	—
608	C₄×C₂₃	—	2	2	no	—
609	C₄×C₂₃	—	2	2	no	—
610	C₄×C₂₃	—	2	2	no	—
611	C₄×C₂₃	—	2	2	no	—
612	C₄×C₂₃	—	2	2	no	—
613	C₄×C₂₃	—	4	2	no	—
614	C₄×C₂₃	—	4	1	no	—
615	C₄×C₂₃	—	4	1	no	—
616	C₄×C₂₃	—	4	2	no	—
617	C₄×C₂₃	—	4	2	no	—
618	C₄×C₂₃	—	4	2	no	—
619	C₄×C₂₃	—	4	2	no	—
620	C₄×C₂₃	—	4	1	no	—
621	C₄×C₂₃	#538	1	4	yes	complemented
622	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic
623	#538	—	2	16	no	—
624	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
625	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic
626	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic
627	C₂×#126	C₂²×C₂₃	1	2	yes	complemented
628	C₂×#126	C₂²×C₂₃	1	2	yes	complemented
629	C₂×#124	C₂²×C₂₃	1	2	yes	complemented
630	C₂×#124	C₂²×C₂₃	1	2	yes	complemented
631	C₂×#124	C₂²×C₂₃	1	2	yes	complemented
632	C₂×#123	C₂²×C₂₃	1	2	yes	complemented
633	C₂×#123	C₂²×C₂₃	1	2	yes	complemented
634	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
635	C₂×#121	C₂²×C₂₃	1	2	yes	—
636	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
637	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
638	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
639	C₂×#121	C₂²×C₂₃	1	2	yes	complemented
640	C₂×#121	C₂²×C₂₃	1	2	yes	complemented
641	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic, complemented
642	C₂×#121	C₂²×C₂₃	1	2	yes	complemented
643	C₂×#120	C₂²×C₂₃	1	2	yes	—
644	C₂×#120	C₂²×C₂₃	1	2	yes	—
645	C₂×#120	C₂²×C₂₃	1	2	yes	—
646	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
647	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
648	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
649	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
650	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
651	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
652	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
653	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
654	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
655	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic, complemented
656	#398	C₂²×C₂₃	1	2	yes	complemented
657	#397	C₂²×C₂₃	1	2	yes	complemented
658	#396	C₂²×C₂₃	1	2	yes	complemented
659	#396	C₂²×C₂₃	1	2	yes	complemented
660	#395	C₂²×C₂₃	1	2	yes	complemented
661	#394	C₂²×C₂₃	1	2	yes	—
662	#394	C₂²×C₂₃	1	2	yes	complemented
663	#394	C₂²×C₂₃	1	2	yes	complemented
664	#394	C₂²×C₂₃	1	2	yes	complemented
665	#394	C₂²×C₂₃	1	2	yes	complemented
666	#394	C₂²×C₂₃	1	2	yes	complemented
667	#393	C₂²×C₂₃	1	2	yes	complemented
668	#392	C₂²×C₂₃	1	2	yes	—
669	#392	C₂²×C₂₃	1	2	yes	—
670	#392	C₂²×C₂₃	1	2	yes	—
671	#392	C₂²×C₂₃	1	2	yes	complemented
672	#390	C₂²×C₂₃	1	1	yes	characteristic
673	#390	C₂²×C₂₃	1	1	yes	characteristic
674	#390	C₂²×C₂₃	1	1	yes	characteristic
675	#390	C₂²×C₂₃	1	1	yes	characteristic
676	#390	C₂²×C₂₃	1	1	yes	characteristic
677	#390	C₂²×C₂₃	1	1	yes	characteristic
678	#390	C₂²×C₂₃	1	2	yes	—
679	#390	C₂²×C₂₃	1	1	yes	characteristic
680	#390	C₂²×C₂₃	1	1	yes	characteristic
681	#390	C₂²×C₂₃	1	2	yes	—
682	#390	C₂²×C₂₃	1	2	yes	complemented
683	#390	C₂²×C₂₃	1	2	yes	complemented
684	#390	C₂²×C₂₃	1	1	yes	characteristic, complemented
685	#390	C₂²×C₂₃	1	2	yes	complemented
686	#390	C₂²×C₂₃	1	1	yes	characteristic, complemented
687	#390	C₂²×C₂₃	1	2	yes	complemented
688	#389	C₂²×C₂₃	1	1	yes	characteristic, complemented
689	#389	C₂²×C₂₃	1	1	yes	characteristic, complemented
690	#389	C₂²×C₂₃	1	1	yes	characteristic, complemented
691	#389	C₂²×C₂₃	1	1	yes	characteristic, complemented
692	#388	C₂²×C₂₃	1	2	yes	complemented
693	#388	C₂²×C₂₃	1	2	yes	complemented
694	#388	C₂²×C₂₃	1	2	yes	complemented
695	#388	C₂²×C₂₃	1	2	yes	complemented
696	#388	C₂²×C₂₃	1	2	yes	complemented
697	#388	C₂²×C₂₃	1	2	yes	complemented
698	#388	C₂²×C₂₃	1	2	yes	complemented
699	#388	C₂²×C₂₃	1	2	yes	complemented
700	#386	C₂²×C₂₃	1	2	yes	—
701	#386	C₂²×C₂₃	1	2	yes	—
702	#386	C₂²×C₂₃	1	2	yes	complemented
703	#386	C₂²×C₂₃	1	2	yes	complemented
704	#386	C₂²×C₂₃	1	2	yes	complemented
705	#385	C₂²×C₂₃	1	2	yes	—
706	#384	C₂²×C₂₃	1	1	yes	characteristic, complemented
707	#380	C₂²×C₂₃	1	1	yes	characteristic
708	#380	C₂²×C₂₃	1	1	yes	characteristic, complemented
709	#379	C₂²×C₂₃	1	2	yes	—
710	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
711	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
712	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
713	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
714	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
715	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
716	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
717	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
718	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
719	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
720	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	complemented
721	C₄³	C₂²×C₂₃	1	1	yes	characteristic, complemented
722	C₂×C₂₃	—	2	4	no	—
723	C₂×C₂₃	—	4	2	no	—
724	C₂×C₂₃	—	8	2	no	—
725	C₂×C₂₃	—	8	2	no	—
726	C₂×C₂₃	—	8	2	no	—
727	C₂×C₂₃	C₂×#532	1	1	yes	characteristic
728	C₂×C₂₃	C₂×#538	1	1	yes	characteristic
729	C₂×C₂₃	#3460	1	1	yes	characteristic
730	C₂×C₂₃	#3496	1	1	yes	characteristic
731	C₂×C₂₃	#3498	1	1	yes	characteristic
732	C₂×C₂₃	#3514	1	1	yes	characteristic
733	C₂×C₂₃	#3519	1	1	yes	characteristic
734	C₂⁵	C₂³×C₂₃	1	2	yes	—
735	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
736	C₂²×D₄	—	2	4	no	—
737	C₂²×D₄	—	4	2	no	—
738	C₂²×D₄	—	4	2	no	—
739	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
740	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
741	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
742	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
743	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
744	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
745	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
746	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
747	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
748	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
749	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
750	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
751	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
752	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
753	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
754	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
755	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
756	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
757	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
758	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
759	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
760	C₄⋊Q₈	—	4	2	no	—
761	#127	—	4	2	no	—
762	#127	—	4	2	no	—
763	#126	—	2	8	no	—
764	#126	—	2	8	no	—
765	#124	—	2	8	no	—
766	#124	—	2	8	no	—
767	#124	—	4	4	no	—
768	#123	—	2	8	no	—
769	#123	—	2	8	no	—
770	C₂²⋊Q₈	—	2	8	no	—
771	#121	—	2	8	no	—
772	#121	—	2	8	no	—
773	#121	—	2	4	no	—
774	#121	—	2	8	no	—
775	#121	—	4	4	no	—
776	#121	—	4	2	no	—
777	#121	—	4	2	no	—
778	#121	—	4	2	no	—
779	#120	—	2	8	no	—
780	#120	—	2	8	no	—
781	#120	—	2	8	no	—
782	C₄×D₄	—	2	8	no	—
783	C₄×D₄	—	2	4	no	—
784	C₄×D₄	—	2	4	no	—
785	C₄×D₄	—	4	2	no	—
786	C₄×D₄	D₄×C₂₃	1	8	yes	complemented
787	C₂×C₄⋊C₄	—	4	2	no	—
788	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
789	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
790	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
791	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
792	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
793	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
794	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
795	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
796	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
797	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
798	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
799	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
800	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
801	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
802	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
803	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
804	C₂×C₂²⋊C₄	—	2	8	no	—
805	C₂×C₂²⋊C₄	—	4	4	no	—
806	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
807	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
808	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
809	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
810	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
811	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
812	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
813	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
814	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
815	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
816	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
817	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
818	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
819	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
820	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
821	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
822	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
823	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
824	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
825	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
826	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
827	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
828	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
829	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
830	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
831	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
832	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
833	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
834	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
835	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
836	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
837	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
838	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
839	C₂×C₄²	—	4	2	no	—
840	C₂×C₄²	—	4	2	no	—
841	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
842	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
843	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
844	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
845	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
846	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
847	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
848	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
849	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
850	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
851	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
852	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
853	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
854	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
855	#95	C₂³×C₂₃	1	1	yes	characteristic
856	#95	C₂³×C₂₃	1	1	yes	characteristic
857	#95	C₂³×C₂₃	1	1	yes	characteristic
858	#95	C₂³×C₂₃	1	1	yes	characteristic
859	#95	C₂³×C₂₃	1	1	yes	characteristic
860	#95	C₂³×C₂₃	1	1	yes	characteristic
861	#95	C₂³×C₂₃	1	2	yes	—
862	#95	C₂³×C₂₃	1	2	yes	—
863	#95	C₂³×C₂₃	1	2	yes	—
864	#95	C₂³×C₂₃	1	2	yes	—
865	#95	C₂³×C₂₃	1	2	yes	—
866	#95	C₂³×C₂₃	1	2	yes	—
867	#95	C₂³×C₂₃	1	2	yes	—
868	C₂₃	#35007	1	1	yes	characteristic, direct product factor, Sylow
869	C₂⁴	—	2	4	no	—
870	C₂⁴	—	2	4	no	—
871	C₂⁴	—	2	4	no	—
872	C₂⁴	—	4	2	no	—
873	C₂⁴	—	4	2	no	—
874	C₂⁴	—	4	2	no	—
875	C₂⁴	—	4	2	no	—
876	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
877	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
878	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
879	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
880	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
881	C₂×Q₈	—	2	4	no	—
882	C₂×Q₈	—	4	2	no	—
883	C₂×Q₈	—	4	2	no	—
884	C₂×D₄	—	2	2	no	—
885	C₂×D₄	—	2	2	no	—
886	C₂×D₄	—	2	4	no	—
887	C₂×D₄	—	2	4	no	—
888	C₂×D₄	—	2	4	no	—
889	C₂×D₄	—	2	4	no	—
890	C₂×D₄	—	2	4	no	—
891	C₂×D₄	—	2	4	no	—
892	C₂×D₄	—	2	4	no	—
893	C₂×D₄	—	2	4	no	—
894	C₂×D₄	—	2	2	no	—
895	C₂×D₄	—	2	4	no	—
896	C₂×D₄	—	2	2	no	—
897	C₂×D₄	—	2	2	no	—
898	C₂×D₄	—	2	4	no	—
899	C₂×D₄	—	2	4	no	—
900	C₂×D₄	—	2	2	no	—
901	C₂×D₄	—	2	2	no	—
902	C₂×D₄	—	2	2	no	—
903	C₂×D₄	—	2	2	no	—
904	C₂×D₄	—	2	2	no	—
905	C₂×D₄	—	2	2	no	—
906	C₂×D₄	—	4	2	no	—
907	C₂×D₄	—	4	2	no	—
908	C₂×D₄	—	4	16	no	—
909	C₂×D₄	—	4	2	no	—
910	C₂×D₄	—	4	2	no	—
911	C₂×D₄	—	4	2	no	—
912	C₂×D₄	—	4	2	no	—
913	C₂×D₄	—	4	2	no	—
914	C₂×D₄	—	4	2	no	—
915	C₂×D₄	—	4	2	no	—
916	C₂×D₄	—	4	2	no	—
917	C₂×D₄	—	4	2	no	—
918	C₂×D₄	—	4	2	no	—
919	C₂×D₄	—	4	2	no	—
920	C₂×D₄	—	4	2	no	—
921	C₂×D₄	—	4	2	no	—
922	C₂×D₄	—	4	2	no	—
923	C₂×D₄	C₂×D₄×C₂₃	1	4	yes	—
924	C₂²×C₄	—	2	2	no	—
925	C₂²×C₄	—	2	2	no	—
926	C₂²×C₄	—	2	2	no	—
927	C₂²×C₄	—	2	4	no	—
928	C₂²×C₄	—	2	2	no	—
929	C₂²×C₄	—	2	2	no	—
930	C₂²×C₄	—	2	2	no	—
931	C₂²×C₄	—	2	2	no	—
932	C₂²×C₄	—	2	2	no	—
933	C₂²×C₄	—	2	2	no	—
934	C₂²×C₄	—	2	4	no	—
935	C₂²×C₄	—	4	1	no	—
936	C₂²×C₄	—	4	1	no	—
937	C₂²×C₄	—	4	1	no	—
938	C₂²×C₄	—	4	1	no	—
939	C₂²×C₄	—	4	1	no	—
940	C₂²×C₄	—	4	1	no	—
941	C₂²×C₄	—	4	2	no	—
942	C₂²×C₄	—	4	2	no	—
943	C₂²×C₄	—	4	2	no	—
944	C₂²×C₄	—	4	2	no	—
945	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
946	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	complemented
947	C₂²×C₄	#41×C₂₃	1	4	yes	—
948	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
949	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
950	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
951	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
952	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
953	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
954	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
955	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
956	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
957	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
958	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
959	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
960	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
961	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
962	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
963	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
964	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
965	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
966	C₄⋊C₄	—	2	4	no	—
967	C₄⋊C₄	—	2	4	no	—
968	C₄⋊C₄	—	2	4	no	—
969	C₄⋊C₄	—	2	4	no	—
970	C₄⋊C₄	—	2	4	no	—
971	C₄⋊C₄	—	2	2	no	—
972	C₄⋊C₄	—	2	2	no	—
973	C₄⋊C₄	—	2	2	no	—
974	C₄⋊C₄	—	2	2	no	—
975	C₄⋊C₄	—	2	2	no	—
976	C₄⋊C₄	—	2	2	no	—
977	C₄⋊C₄	—	2	2	no	—
978	C₄⋊C₄	—	4	2	no	—
979	C₄⋊C₄	—	4	2	no	—
980	C₄⋊C₄	—	4	2	no	—
981	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	complemented
982	C₂²⋊C₄	—	2	4	no	—
983	C₂²⋊C₄	—	2	4	no	—
984	C₂²⋊C₄	—	2	2	no	—
985	C₂²⋊C₄	—	2	4	no	—
986	C₂²⋊C₄	—	2	4	no	—
987	C₂²⋊C₄	—	2	4	no	—
988	C₂²⋊C₄	—	2	4	no	—
989	C₂²⋊C₄	—	2	4	no	—
990	C₂²⋊C₄	—	2	4	no	—
991	C₂²⋊C₄	—	2	4	no	—
992	C₂²⋊C₄	—	2	4	no	—
993	C₂²⋊C₄	—	2	4	no	—
994	C₂²⋊C₄	—	2	4	no	—
995	C₂²⋊C₄	—	2	2	no	—
996	C₂²⋊C₄	—	2	2	no	—
997	C₂²⋊C₄	—	2	4	no	—
998	C₂²⋊C₄	—	2	4	no	—
999	C₂²⋊C₄	—	2	4	no	—
1000	C₂²⋊C₄	—	2	4	no	—
1001	C₂²⋊C₄	—	2	4	no	—
1002	C₂²⋊C₄	—	2	4	no	—
1003	C₂²⋊C₄	—	4	2	no	—
1004	C₂²⋊C₄	—	4	2	no	—
1005	C₂²⋊C₄	—	4	2	no	—
1006	C₂²⋊C₄	—	4	2	no	—
1007	C₂²⋊C₄	—	4	2	no	—
1008	C₂²⋊C₄	—	4	2	no	—
1009	C₂²⋊C₄	—	4	2	no	—
1010	C₂²⋊C₄	—	4	2	no	—
1011	C₂²⋊C₄	—	4	2	no	—
1012	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
1013	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	complemented
1014	C₂²⋊C₄	#41×C₂₃	1	4	yes	—
1015	C₄²	—	2	4	no	—
1016	C₄²	—	2	2	no	—
1017	C₄²	—	2	2	no	—
1018	C₄²	—	2	2	no	—
1019	C₄²	—	2	2	no	—
1020	C₄²	—	2	2	no	—
1021	C₄²	—	2	2	no	—
1022	C₄²	—	2	2	no	—
1023	C₄²	—	4	1	no	—
1024	C₄²	—	4	1	no	—
1025	C₄²	—	4	1	no	—
1026	C₄²	—	4	1	no	—
1027	C₄²	—	4	1	no	—
1028	C₄²	C₂×D₄×C₂₃	1	4	yes	complemented
1029	C₂³	—	2	1	no	—
1030	C₂³	—	2	1	no	—
1031	C₂³	—	2	1	no	—
1032	C₂³	—	2	1	no	—
1033	C₂³	—	2	1	no	—
1034	C₂³	—	2	1	no	—
1035	C₂³	—	2	1	no	—
1036	C₂³	—	2	1	no	—
1037	C₂³	—	2	1	no	—
1038	C₂³	—	2	1	no	—
1039	C₂³	—	2	2	no	—
1040	C₂³	—	2	2	no	—
1041	C₂³	—	2	2	no	—
1042	C₂³	—	2	2	no	—
1043	C₂³	—	2	2	no	—
1044	C₂³	—	2	2	no	—
1045	C₂³	—	2	2	no	—
1046	C₂³	—	2	2	no	—
1047	C₂³	—	2	2	no	—
1048	C₂³	—	2	2	no	—
1049	C₂³	—	2	2	no	—
1050	C₂³	—	2	2	no	—
1051	C₂³	—	2	2	no	—
1052	C₂³	—	2	2	no	—
1053	C₂³	—	2	2	no	—
1054	C₂³	—	2	2	no	—
1055	C₂³	—	2	2	no	—
1056	C₂³	—	2	2	no	—
1057	C₂³	—	2	2	no	—
1058	C₂³	—	2	2	no	—
1059	C₂³	—	2	2	no	—
1060	C₂³	—	4	8	no	—
1061	C₂³	—	4	8	no	—
1062	C₂³	—	4	8	no	—
1063	C₂³	—	8	4	no	—
1064	C₂³	—	8	4	no	—
1065	C₂³	—	8	4	no	—
1066	C₂³	—	8	4	no	—
1067	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
1068	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
1069	C₂³	C₂×#41×C₂₃	1	2	yes	—
1070	C₂³	C₂×#41×C₂₃	1	2	yes	—
1071	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
1072	Q₈	—	8	4	no	—
1073	D₄	—	2	8	no	—
1074	D₄	—	4	8	no	—
1075	D₄	—	4	8	no	—
1076	D₄	—	4	4	no	—
1077	D₄	—	4	4	no	—
1078	D₄	—	4	4	no	—
1079	D₄	—	8	4	no	—
1080	D₄	—	8	4	no	—
1081	D₄	—	8	4	no	—
1082	D₄	—	8	4	no	—
1083	D₄	—	8	4	no	—
1084	D₄	—	8	4	no	—
1085	D₄	—	8	4	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	1	no	—
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	2	1	no	—
1092	C₂×C₄	—	2	1	no	—
1093	C₂×C₄	—	2	1	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	2	1	no	—
1096	C₂×C₄	—	2	1	no	—
1097	C₂×C₄	—	2	1	no	—
1098	C₂×C₄	—	2	1	no	—
1099	C₂×C₄	—	2	1	no	—
1100	C₂×C₄	—	2	1	no	—
1101	C₂×C₄	—	2	1	no	—
1102	C₂×C₄	—	2	1	no	—
1103	C₂×C₄	—	2	1	no	—
1104	C₂×C₄	—	2	8	no	—
1105	C₂×C₄	—	2	2	no	—
1106	C₂×C₄	—	2	2	no	—
1107	C₂×C₄	—	2	2	no	—
1108	C₂×C₄	—	2	2	no	—
1109	C₂×C₄	—	2	2	no	—
1110	C₂×C₄	—	2	1	no	—
1111	C₂×C₄	—	2	2	no	—
1112	C₂×C₄	—	2	1	no	—
1113	C₂×C₄	—	2	1	no	—
1114	C₂×C₄	—	2	2	no	—
1115	C₂×C₄	—	2	1	no	—
1116	C₂×C₄	—	2	1	no	—
1117	C₂×C₄	—	2	1	no	—
1118	C₂×C₄	—	2	2	no	—
1119	C₂×C₄	—	2	2	no	—
1120	C₂×C₄	—	2	2	no	—
1121	C₂×C₄	—	2	1	no	—
1122	C₂×C₄	—	2	1	no	—
1123	C₂×C₄	—	2	2	no	—
1124	C₂×C₄	—	2	2	no	—
1125	C₂×C₄	—	2	2	no	—
1126	C₂×C₄	—	2	2	no	—
1127	C₂×C₄	—	2	1	no	—
1128	C₂×C₄	—	2	2	no	—
1129	C₂×C₄	—	4	4	no	—
1130	C₂×C₄	—	4	4	no	—
1131	C₂×C₄	—	4	4	no	—
1132	C₂×C₄	—	4	4	no	—
1133	C₂×C₄	—	4	4	no	—
1134	C₂×C₄	—	8	4	no	—
1135	C₂×C₄	—	8	4	no	—
1136	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1137	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1138	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1139	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1140	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1141	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
1142	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
1143	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
1144	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
1145	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
1146	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
1147	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
1148	C₂²	—	2	2	no	—
1149	C₂²	—	2	2	no	—
1150	C₂²	—	2	2	no	—
1151	C₂²	—	2	2	no	—
1152	C₂²	—	2	2	no	—
1153	C₂²	—	2	2	no	—
1154	C₂²	—	2	2	no	—
1155	C₂²	—	2	2	no	—
1156	C₂²	—	2	2	no	—
1157	C₂²	—	4	1	no	—
1158	C₂²	—	4	1	no	—
1159	C₂²	—	4	1	no	—
1160	C₂²	—	4	1	no	—
1161	C₂²	—	4	2	no	—
1162	C₂²	—	4	2	no	—
1163	C₂²	—	4	2	no	—
1164	C₂²	—	4	2	no	—
1165	C₂²	—	4	2	no	—
1166	C₂²	—	4	2	no	—
1167	C₂²	—	4	2	no	—
1168	C₂²	—	4	2	no	—
1169	C₂²	—	4	2	no	—
1170	C₂²	—	4	2	no	—
1171	C₂²	—	4	2	no	—
1172	C₂²	—	4	2	no	—
1173	C₂²	—	4	2	no	—
1174	C₂²	—	4	2	no	—
1175	C₂²	—	4	2	no	—
1176	C₂²	—	4	2	no	—
1177	C₂²	—	4	2	no	—
1178	C₂²	—	4	2	no	—
1179	C₂²	—	4	2	no	—
1180	C₂²	—	4	2	no	—
1181	C₂²	—	4	2	no	—
1182	C₂²	—	8	16	no	—
1183	C₂²	C₂₃×#532	1	4	yes	—
1184	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1185	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
1186	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
1187	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1188	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1189	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1190	C₂²	C₂₃×#585	1	1	yes	characteristic
1191	C₄	—	2	2	no	—
1192	C₄	—	2	2	no	—
1193	C₄	—	2	2	no	—
1194	C₄	—	2	2	no	—
1195	C₄	—	2	2	no	—
1196	C₄	—	2	2	no	—
1197	C₄	—	2	2	no	—
1198	C₄	—	2	2	no	—
1199	C₄	—	2	2	no	—
1200	C₄	—	4	2	no	—
1201	C₄	—	4	1	no	—
1202	C₄	—	4	1	no	—
1203	C₄	—	4	2	no	—
1204	C₄	—	4	2	no	—
1205	C₄	—	4	2	no	—
1206	C₄	—	4	2	no	—
1207	C₄	—	4	1	no	—
1208	C₄	C₂₃×#538	1	4	yes	complemented
1209	C₂	—	2	4	no	—
1210	C₂	—	4	2	no	—
1211	C₂	—	8	2	no	—
1212	C₂	—	8	2	no	—
1213	C₂	—	8	2	no	—
1214	C₂	C₂×C₂₃×#532	1	1	yes	characteristic
1215	C₂	C₂×C₂₃×#538	1	1	yes	characteristic
1216	C₂	C₂₃×#3460	1	1	yes	characteristic
1217	C₂	C₂₃×#3496	1	1	yes	characteristic
1218	C₂	C₂₃×#3498	1	1	yes	characteristic
1219	C₂	C₂₃×#3514	1	1	yes	characteristic
1220	C₂	C₂₃×#3519	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₂₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#538	C₂	semidirect
2. C₂₃×#2860	C₂	semidirect
3. C₂₃×#2858	C₂	semidirect
4. C₂₃×#2856	C₂	semidirect
5. C₂₃×#2854	C₂	semidirect
6. C₂₃×#2662	C₂	semidirect
7. C₂₃×#2661	C₂	semidirect
8. C₂₃×#2555	C₂	semidirect
9. C₂₃×#2554	C₂	semidirect
10. C₂₃×#2512	C₂	semidirect
11. C₂₃×#2491	C₂	semidirect
12. C₂₃×#2472	C₂	semidirect
13. C₂₃×#2445	C₂	semidirect
14. C₂₃×#2440	C₂	semidirect
15. C₂₃×#2433	C₂	semidirect
16. C₂₃×#2428	C₂	semidirect
17. C₂₃×#2424	C₂	semidirect
18. C₂₃×#2416	C₂	semidirect
19. C₂₃×#2408	C₂	semidirect
20. C₂₃×#2321	C₂	semidirect
21. C₄×C₂₃×#121	C₂	semidirect
22. C₂×C₂₃×#390	C₂	semidirect
23. C₄²×D₄×C₂₃	C₂	semidirect
26. C₂×C₂₃×C₄⋊Q₈	C₂²	semidirect
29. C₂×C₂₃×#126	C₂²	semidirect
30. C₂×C₂₃×#126	C₂²	semidirect
31. C₂×C₂₃×#124	C₂²	semidirect
32. C₂×C₂₃×#124	C₂²	semidirect
33. C₂×C₂₃×#124	C₂²	semidirect
34. C₂×C₂₃×#123	C₂²	semidirect
35. C₂×C₂₃×#123	C₂²	semidirect
41. C₂×C₂₃×#121	C₂²	semidirect
42. C₂×C₂₃×#121	C₂²	semidirect
43. C₂×C₂₃×#121	C₂²	semidirect
44. C₂×C₂₃×#121	C₂²	semidirect
52. C₂×C₄×D₄×C₂₃	C₂²	semidirect
57. C₂²×C₄²×C₂₃	C₂²	semidirect
58. C₂₃×#398	C₂²	semidirect
59. C₂₃×#397	C₂²	semidirect
60. C₂₃×#396	C₂²	semidirect
61. C₂₃×#396	C₂²	semidirect
62. C₂₃×#395	C₂²	semidirect
64. C₂₃×#394	C₂²	semidirect
65. C₂₃×#394	C₂²	semidirect
66. C₂₃×#394	C₂²	semidirect
67. C₂₃×#394	C₂²	semidirect
68. C₂₃×#394	C₂²	semidirect
69. C₂₃×#393	C₂²	semidirect
73. C₂₃×#392	C₂²	semidirect
84. C₂₃×#390	C₂²	semidirect
85. C₂₃×#390	C₂²	semidirect
86. C₂₃×#390	C₂²	semidirect
87. C₂₃×#390	C₂²	semidirect
88. C₂₃×#390	C₂²	semidirect
89. C₂₃×#390	C₂²	semidirect
90. C₂₃×#389	C₂²	semidirect
91. C₂₃×#389	C₂²	semidirect
92. C₂₃×#389	C₂²	semidirect
93. C₂₃×#389	C₂²	semidirect
94. C₂₃×#388	C₂²	semidirect
95. C₂₃×#388	C₂²	semidirect
96. C₂₃×#388	C₂²	semidirect
97. C₂₃×#388	C₂²	semidirect
98. C₂₃×#388	C₂²	semidirect
99. C₂₃×#388	C₂²	semidirect
100. C₂₃×#388	C₂²	semidirect
101. C₂₃×#388	C₂²	semidirect
104. C₂₃×#386	C₂²	semidirect
105. C₂₃×#386	C₂²	semidirect
106. C₂₃×#386	C₂²	semidirect
108. C₂₃×#384	C₂²	semidirect
110. C₂₃×#380	C₂²	semidirect
112. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
113. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
114. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
115. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
119. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
120. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
121. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
122. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
123. C₄³×C₂₃	C₂²	semidirect
176. C₄×D₄×C₂₃	D₄	semidirect
335. C₂²×C₄×C₂₃	C₂×D₄	semidirect
370. C₄⋊C₄×C₂₃	C₂×D₄	semidirect
402. C₂²⋊C₄×C₂₃	C₂×D₄	semidirect
417. C₄²×C₂₃	C₂×D₄	semidirect
418. #35007	C₂₃	direct (N × H)
538. C₂×#538	C₂×C₂₃	semidirect
539. #2860	C₂×C₂₃	semidirect
540. #2858	C₂×C₂₃	semidirect
541. #2856	C₂×C₂₃	semidirect
542. #2854	C₂×C₂₃	semidirect
543. #2662	C₂×C₂₃	semidirect
544. #2661	C₂×C₂₃	semidirect
545. #2555	C₂×C₂₃	semidirect
546. #2554	C₂×C₂₃	semidirect
547. #2512	C₂×C₂₃	semidirect
548. #2491	C₂×C₂₃	semidirect
549. #2472	C₂×C₂₃	semidirect
550. #2445	C₂×C₂₃	semidirect
551. #2440	C₂×C₂₃	semidirect
552. #2433	C₂×C₂₃	semidirect
553. #2428	C₂×C₂₃	semidirect
554. #2424	C₂×C₂₃	semidirect
555. #2416	C₂×C₂₃	semidirect
556. #2408	C₂×C₂₃	semidirect
557. #2321	C₂×C₂₃	semidirect
558. C₄×#121	C₂×C₂₃	semidirect
559. C₂×#390	C₂×C₂₃	semidirect
560. C₄²×D₄	C₂×C₂₃	semidirect
621. C₄×C₂₃	#538	semidirect
624. C₂×C₄⋊Q₈	C₂²×C₂₃	semidirect
627. C₂×#126	C₂²×C₂₃	semidirect
628. C₂×#126	C₂²×C₂₃	semidirect
629. C₂×#124	C₂²×C₂₃	semidirect
630. C₂×#124	C₂²×C₂₃	semidirect
631. C₂×#124	C₂²×C₂₃	semidirect
632. C₂×#123	C₂²×C₂₃	semidirect
633. C₂×#123	C₂²×C₂₃	semidirect
639. C₂×#121	C₂²×C₂₃	semidirect
640. C₂×#121	C₂²×C₂₃	semidirect
641. C₂×#121	C₂²×C₂₃	semidirect
642. C₂×#121	C₂²×C₂₃	semidirect
650. C₂×C₄×D₄	C₂²×C₂₃	semidirect
655. C₂²×C₄²	C₂²×C₂₃	semidirect
656. #398	C₂²×C₂₃	semidirect
657. #397	C₂²×C₂₃	semidirect
658. #396	C₂²×C₂₃	semidirect
659. #396	C₂²×C₂₃	semidirect
660. #395	C₂²×C₂₃	semidirect
662. #394	C₂²×C₂₃	semidirect
663. #394	C₂²×C₂₃	semidirect
664. #394	C₂²×C₂₃	semidirect
665. #394	C₂²×C₂₃	semidirect
666. #394	C₂²×C₂₃	semidirect
667. #393	C₂²×C₂₃	semidirect
671. #392	C₂²×C₂₃	semidirect
682. #390	C₂²×C₂₃	semidirect
683. #390	C₂²×C₂₃	semidirect
684. #390	C₂²×C₂₃	semidirect
685. #390	C₂²×C₂₃	semidirect
686. #390	C₂²×C₂₃	semidirect
687. #390	C₂²×C₂₃	semidirect
688. #389	C₂²×C₂₃	semidirect
689. #389	C₂²×C₂₃	semidirect
690. #389	C₂²×C₂₃	semidirect
691. #389	C₂²×C₂₃	semidirect
692. #388	C₂²×C₂₃	semidirect
693. #388	C₂²×C₂₃	semidirect
694. #388	C₂²×C₂₃	semidirect
695. #388	C₂²×C₂₃	semidirect
696. #388	C₂²×C₂₃	semidirect
697. #388	C₂²×C₂₃	semidirect
698. #388	C₂²×C₂₃	semidirect
699. #388	C₂²×C₂₃	semidirect
702. #386	C₂²×C₂₃	semidirect
703. #386	C₂²×C₂₃	semidirect
704. #386	C₂²×C₂₃	semidirect
706. #384	C₂²×C₂₃	semidirect
708. #380	C₂²×C₂₃	semidirect
710. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
711. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
712. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
713. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
717. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
718. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
719. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
720. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
721. C₄³	C₂²×C₂₃	semidirect
786. C₄×D₄	D₄×C₂₃	semidirect
868. C₂₃	#35007	direct (N × H)
946. C₂²×C₄	C₂×D₄×C₂₃	semidirect
981. C₄⋊C₄	C₂×D₄×C₂₃	semidirect
1013. C₂²⋊C₄	C₂×D₄×C₂₃	semidirect
1028. C₄²	C₂×D₄×C₂₃	semidirect
1208. C₄	C₂₃×#538	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#538	2
C₂₃×#2860	2
C₂₃×#2858	2
C₂₃×#2856	2
C₂₃×#2854	2
C₂₃×#2662	2
C₂₃×#2661	2
C₂₃×#2555	2
C₂₃×#2554	2
C₂₃×#2512	2
C₂₃×#2491	2
C₂₃×#2472	2
C₂₃×#2445	2
C₂₃×#2440	2
C₂₃×#2433	2
C₂₃×#2428	2
C₂₃×#2424	2
C₂₃×#2416	2
C₂₃×#2408	2
C₂₃×#2321	2
C₄×C₂₃×#121	2
C₂×C₂₃×#390	2
C₄²×D₄×C₂₃	2
#35007	23

Subgroups — C23×#35007 #19182633

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#35007 #19182633