Subgroups — C₂×C₂₃×#3300 #19208744

Order 5888.

2146 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#552	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#548	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#3300	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₂₃×#488	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₂₃×#485	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₂₃×#480	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₂₃×#479	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₂₃×#467	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₂₃×#465	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₂₃×#464	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₂₃×#452	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₂₃×#451	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₄×Q₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₈×D₄×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₂₃×#416	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₂₃×#103	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
18	C₂³×Q₈×C₂₃	C₂²	1	1	yes	characteristic
19	C₂²×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
20	C₂²×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
21	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
22	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
23	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
24	C₂₃×#552	—	2	4	no	—
25	C₂₃×#552	C₂²	1	8	yes	complemented
26	C₂₃×#548	—	2	4	no	—
27	C₂₃×#548	C₂²	1	8	yes	—
28	C₂×C₂₃×#126	—	2	1	no	—
29	C₂×C₂₃×#125	—	2	1	no	—
30	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic
31	C₂×C₂₃×#124	—	2	1	no	—
32	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
33	C₂×C₂₃×#123	—	2	1	no	—
34	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
35	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
36	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
37	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
38	C₂×C₂₃×#121	—	2	1	no	—
39	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
40	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
41	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₂₃	—	2	1	no	—
43	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
44	C₂×C₂₃×#117	—	2	1	no	—
45	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
46	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
47	C₂₃×#488	C₂²	1	8	yes	complemented
48	C₂₃×#485	C₂²	1	8	yes	complemented
49	C₂₃×#480	C₂²	1	8	yes	complemented
50	C₂₃×#479	C₂²	1	8	yes	complemented
51	C₂₃×#467	C₂²	1	8	yes	complemented
52	C₂₃×#465	C₂²	1	8	yes	complemented
53	C₂₃×#464	C₂²	1	8	yes	complemented
54	C₂₃×#452	C₂²	1	8	yes	complemented
55	C₂₃×#451	C₂²	1	8	yes	complemented
56	C₄×Q₁₆×C₂₃	C₂²	1	8	yes	complemented
57	C₈×D₄×C₂₃	C₂²	1	8	yes	complemented
58	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
59	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
60	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
61	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
62	C₂₃×#416	C₂²	1	8	yes	complemented
63	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
64	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
65	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
66	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
67	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
68	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
69	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
70	C₂×C₂₃×#103	C₂²	1	8	yes	complemented
71	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
72	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
73	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
74	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
75	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
76	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
77	C₂×#41×C₂₃	—	2	2	no	—
78	C₂×#41×C₂₃	—	2	4	no	—
79	C₂×#41×C₂₃	—	4	2	no	—
80	C₂×#41×C₂₃	C₂³	1	4	yes	—
81	C₂²×Q₈×C₂₃	—	2	2	no	—
82	C₂²×Q₈×C₂₃	—	2	1	no	—
83	C₂²×Q₈×C₂₃	—	2	4	no	—
84	C₂²×Q₈×C₂₃	—	4	2	no	—
85	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
86	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
87	C₂²×Q₈×C₂₃	C₂³	1	4	yes	—
88	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
89	C₂²×D₄×C₂₃	—	2	1	no	—
90	C₂²×D₄×C₂₃	—	2	1	no	—
91	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
92	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₂₃	—	2	1	no	—
94	C₂³×C₄×C₂₃	—	2	1	no	—
95	C₂³×C₄×C₂₃	—	2	1	no	—
96	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
98	C₂×Q₁₆×C₂₃	—	2	4	no	—
99	C₂×Q₁₆×C₂₃	—	4	2	no	—
100	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
101	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
102	C₂×SD₁₆×C₂₃	—	4	2	no	—
103	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
104	C₂²×C₈×C₂₃	—	4	2	no	—
105	C₂²×C₈×C₂₃	—	4	2	no	—
106	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
107	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
108	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
109	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
110	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
111	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
112	C₂₃×#126	—	2	8	no	—
113	C₂₃×#125	—	2	8	no	—
114	C₂₃×#125	—	2	2	no	—
115	C₂₃×#125	C₂³	1	4	yes	—
116	C₂₃×#124	—	2	8	no	—
117	C₂₃×#124	—	2	2	no	—
118	C₂₃×#124	C₂³	1	4	yes	—
119	C₂₃×#123	—	2	8	no	—
120	C₂₃×C₂²⋊Q₈	—	2	2	no	—
121	C₂₃×C₂²⋊Q₈	—	2	2	no	—
122	C₂₃×C₂²⋊Q₈	—	2	2	no	—
123	C₂₃×C₂²⋊Q₈	—	2	8	no	—
124	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
125	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
126	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
127	C₂₃×#121	—	2	8	no	—
128	C₂₃×#121	—	2	2	no	—
129	C₂₃×#121	C₂³	1	4	yes	—
130	C₄×Q₈×C₂₃	—	2	2	no	—
131	C₄×Q₈×C₂₃	—	2	2	no	—
132	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
133	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
134	C₄×D₄×C₂₃	—	2	8	no	—
135	C₄×D₄×C₂₃	D₄	1	4	yes	—
136	C₄×D₄×C₂₃	C₂³	1	4	yes	—
137	C₂₃×#117	—	2	2	no	—
138	C₂₃×#117	—	2	8	no	—
139	C₂₃×#117	C₂³	1	4	yes	—
140	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
141	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
142	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
143	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
144	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
145	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
146	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
147	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
148	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
149	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
150	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
151	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
152	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
153	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
154	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
155	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
156	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
157	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
158	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
159	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
160	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
161	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
162	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
163	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
164	C₂×C₄²×C₂₃	—	2	1	no	—
165	C₂×C₄²×C₂₃	—	2	1	no	—
166	C₂×C₄²×C₂₃	—	2	1	no	—
167	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
168	C₂₃×#107	C₂³	1	4	yes	—
169	C₂₃×#107	C₂³	1	4	yes	—
170	C₂₃×#106	C₂³	1	4	yes	—
171	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
172	C₂₃×#103	C₂³	1	4	yes	—
173	C₂₃×#103	C₂³	1	4	yes	—
174	C₂₃×#103	C₂³	1	4	yes	—
175	C₂₃×#103	C₂³	1	4	yes	—
176	C₂₃×#103	C₂³	1	4	yes	—
177	C₂₃×#103	C₂³	1	4	yes	—
178	C₂₃×#103	C₂³	1	4	yes	—
179	C₂₃×#102	C₂³	1	4	yes	—
180	C₂₃×#102	C₂³	1	4	yes	—
181	C₂₃×#102	C₂³	1	4	yes	—
182	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
183	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
184	C₄×C₈×C₂₃	C₂³	1	4	yes	—
185	C₂⁴×C₂₃	—	2	1	no	—
186	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
187	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
188	#41×C₂₃	—	2	8	no	—
189	#41×C₂₃	—	4	4	no	—
190	#41×C₂₃	—	4	8	no	—
191	C₂×Q₈×C₂₃	—	2	1	no	—
192	C₂×Q₈×C₂₃	—	2	1	no	—
193	C₂×Q₈×C₂₃	—	2	4	no	—
194	C₂×Q₈×C₂₃	—	2	1	no	—
195	C₂×Q₈×C₂₃	—	2	2	no	—
196	C₂×Q₈×C₂₃	—	2	8	no	—
197	C₂×Q₈×C₂₃	—	2	2	no	—
198	C₂×Q₈×C₂₃	—	2	2	no	—
199	C₂×Q₈×C₂₃	—	2	2	no	—
200	C₂×Q₈×C₂₃	—	2	2	no	—
201	C₂×Q₈×C₂₃	—	4	4	no	—
202	C₂×Q₈×C₂₃	—	4	4	no	—
203	C₂×Q₈×C₂₃	—	4	8	no	—
204	C₂×Q₈×C₂₃	#41	1	4	yes	—
205	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
206	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
207	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
208	C₂×D₄×C₂₃	—	2	4	no	—
209	C₂×D₄×C₂₃	—	2	4	no	—
210	C₂×D₄×C₂₃	—	2	4	no	—
211	C₂×D₄×C₂₃	—	2	1	no	—
212	C₂×D₄×C₂₃	—	2	2	no	—
213	C₂×D₄×C₂₃	—	2	2	no	—
214	C₂×D₄×C₂₃	—	4	4	no	—
215	C₂×D₄×C₂₃	—	4	4	no	—
216	C₂×D₄×C₂₃	C₂×D₄	1	4	yes	—
217	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₂₃	—	2	1	no	—
219	C₂²×C₄×C₂₃	—	2	2	no	—
220	C₂²×C₄×C₂₃	—	2	2	no	—
221	C₂²×C₄×C₂₃	—	2	2	no	—
222	C₂²×C₄×C₂₃	—	2	2	no	—
223	C₂²×C₄×C₂₃	—	2	4	no	—
224	C₂²×C₄×C₂₃	—	2	4	no	—
225	C₂²×C₄×C₂₃	—	2	1	no	—
226	C₂²×C₄×C₂₃	—	2	1	no	—
227	C₂²×C₄×C₂₃	—	2	1	no	—
228	C₂²×C₄×C₂₃	—	2	1	no	—
229	C₂²×C₄×C₂₃	—	2	1	no	—
230	C₂²×C₄×C₂₃	—	2	1	no	—
231	C₂²×C₄×C₂₃	—	2	4	no	—
232	C₂²×C₄×C₂₃	—	4	4	no	—
233	C₂²×C₄×C₂₃	—	4	4	no	—
234	C₂²×C₄×C₂₃	—	4	4	no	—
235	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
236	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
237	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
238	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
239	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
240	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
241	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
244	Q₁₆×C₂₃	—	2	8	no	—
245	Q₁₆×C₂₃	—	4	4	no	—
246	SD₁₆×C₂₃	—	4	4	no	—
247	C₂×C₈×C₂₃	—	2	2	no	—
248	C₂×C₈×C₂₃	—	2	2	no	—
249	C₂×C₈×C₂₃	—	2	2	no	—
250	C₂×C₈×C₂₃	—	2	2	no	—
251	C₂×C₈×C₂₃	—	4	4	no	—
252	C₂×C₈×C₂₃	—	4	4	no	—
253	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
254	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
255	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
256	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
257	C₄⋊C₄×C₂₃	—	2	1	no	—
258	C₄⋊C₄×C₂₃	—	2	1	no	—
259	C₄⋊C₄×C₂₃	—	2	4	no	—
260	C₄⋊C₄×C₂₃	—	2	4	no	—
261	C₄⋊C₄×C₂₃	—	2	4	no	—
262	C₄⋊C₄×C₂₃	—	2	4	no	—
263	C₄⋊C₄×C₂₃	—	2	4	no	—
264	C₄⋊C₄×C₂₃	—	2	4	no	—
265	C₄⋊C₄×C₂₃	—	2	4	no	—
266	C₄⋊C₄×C₂₃	—	2	4	no	—
267	C₄⋊C₄×C₂₃	—	2	1	no	—
268	C₄⋊C₄×C₂₃	—	2	1	no	—
269	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
270	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
271	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
272	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
273	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
274	C₂²⋊C₄×C₂₃	—	2	4	no	—
275	C₂²⋊C₄×C₂₃	—	2	4	no	—
276	C₂²⋊C₄×C₂₃	—	2	4	no	—
277	C₂²⋊C₄×C₂₃	—	2	4	no	—
278	C₂²⋊C₄×C₂₃	—	2	4	no	—
279	C₂²⋊C₄×C₂₃	—	2	4	no	—
280	C₂²⋊C₄×C₂₃	—	2	4	no	—
281	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
282	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
283	C₄²×C₂₃	—	2	4	no	—
284	C₄²×C₂₃	—	2	4	no	—
285	C₄²×C₂₃	—	2	4	no	—
286	C₄²×C₂₃	C₂×D₄	1	2	yes	—
287	C₄²×C₂₃	C₂⁴	1	2	yes	—
288	C₂×#3300	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
289	C₂³×C₂₃	—	2	2	no	—
290	C₂³×C₂₃	—	2	2	no	—
291	C₂³×C₂₃	—	2	2	no	—
292	C₂³×C₂₃	—	2	2	no	—
293	C₂³×C₂₃	—	2	2	no	—
294	C₂³×C₂₃	—	2	2	no	—
295	C₂³×C₂₃	—	4	2	no	—
296	C₂³×C₂₃	—	4	2	no	—
297	C₂³×C₂₃	—	4	2	no	—
298	C₂³×C₂₃	#135	1	4	yes	—
299	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
300	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
301	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
302	Q₈×C₂₃	—	2	4	no	—
303	Q₈×C₂₃	—	2	2	no	—
304	Q₈×C₂₃	—	2	2	no	—
305	Q₈×C₂₃	—	2	2	no	—
306	Q₈×C₂₃	—	2	2	no	—
307	Q₈×C₂₃	—	2	2	no	—
308	Q₈×C₂₃	—	4	8	no	—
309	Q₈×C₂₃	—	4	2	no	—
310	Q₈×C₂₃	—	4	2	no	—
311	Q₈×C₂₃	C₂×#41	1	4	yes	—
312	D₄×C₂₃	—	2	8	no	—
313	D₄×C₂₃	—	2	2	no	—
314	D₄×C₂₃	—	2	2	no	—
315	D₄×C₂₃	—	4	8	no	—
316	D₄×C₂₃	—	4	8	no	—
317	D₄×C₂₃	—	4	2	no	—
318	C₂×C₄×C₂₃	—	2	2	no	—
319	C₂×C₄×C₂₃	—	2	2	no	—
320	C₂×C₄×C₂₃	—	2	4	no	—
321	C₂×C₄×C₂₃	—	2	2	no	—
322	C₂×C₄×C₂₃	—	2	2	no	—
323	C₂×C₄×C₂₃	—	2	2	no	—
324	C₂×C₄×C₂₃	—	2	4	no	—
325	C₂×C₄×C₂₃	—	2	4	no	—
326	C₂×C₄×C₂₃	—	2	2	no	—
327	C₂×C₄×C₂₃	—	2	2	no	—
328	C₂×C₄×C₂₃	—	2	2	no	—
329	C₂×C₄×C₂₃	—	2	2	no	—
330	C₂×C₄×C₂₃	—	2	2	no	—
331	C₂×C₄×C₂₃	—	2	2	no	—
332	C₂×C₄×C₂₃	—	2	2	no	—
333	C₂×C₄×C₂₃	—	2	2	no	—
334	C₂×C₄×C₂₃	—	2	2	no	—
335	C₂×C₄×C₂₃	—	2	2	no	—
336	C₂×C₄×C₂₃	—	4	8	no	—
337	C₂×C₄×C₂₃	—	4	8	no	—
338	C₂×C₄×C₂₃	—	4	2	no	—
339	C₂×C₄×C₂₃	—	4	2	no	—
340	C₂×C₄×C₂₃	—	4	8	no	—
341	C₂×C₄×C₂₃	—	4	2	no	—
342	C₂×C₄×C₂₃	—	4	2	no	—
343	C₂×C₄×C₂₃	—	4	2	no	—
344	C₂×C₄×C₂₃	—	4	2	no	—
345	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
346	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
347	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
348	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
349	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
350	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
351	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
352	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
353	C₈×C₂₃	—	2	2	no	—
354	C₈×C₂₃	—	2	2	no	—
355	C₈×C₂₃	—	2	2	no	—
356	C₈×C₂₃	—	2	2	no	—
357	C₂×#552	C₂×C₂₃	1	1	yes	characteristic, complemented
358	C₂×#548	C₂×C₂₃	1	1	yes	characteristic
359	#3300	C₂×C₂₃	1	16	yes	direct product factor
360	C₂×#488	C₂×C₂₃	1	1	yes	characteristic, complemented
361	C₂×#485	C₂×C₂₃	1	1	yes	characteristic, complemented
362	C₂×#480	C₂×C₂₃	1	1	yes	characteristic, complemented
363	C₂×#479	C₂×C₂₃	1	1	yes	characteristic, complemented
364	C₂×#467	C₂×C₂₃	1	1	yes	characteristic, complemented
365	C₂×#465	C₂×C₂₃	1	1	yes	characteristic, complemented
366	C₂×#464	C₂×C₂₃	1	1	yes	characteristic, complemented
367	C₂×#452	C₂×C₂₃	1	1	yes	characteristic, complemented
368	C₂×#451	C₂×C₂₃	1	1	yes	characteristic, complemented
369	C₂×C₄×Q₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
370	C₂×C₈×D₄	C₂×C₂₃	1	1	yes	characteristic, complemented
371	C₂×#416	C₂×C₂₃	1	1	yes	characteristic, complemented
372	C₂²×#103	C₂×C₂₃	1	1	yes	characteristic, complemented
373	C₂²×C₂₃	—	2	2	no	—
374	C₂²×C₂₃	—	2	8	no	—
375	C₂²×C₂₃	—	2	2	no	—
376	C₂²×C₂₃	—	2	2	no	—
377	C₂²×C₂₃	—	2	2	no	—
378	C₂²×C₂₃	—	2	2	no	—
379	C₂²×C₂₃	—	4	4	no	—
380	C₂²×C₂₃	—	4	2	no	—
381	C₂²×C₂₃	—	4	2	no	—
382	C₂²×C₂₃	—	4	2	no	—
383	C₂²×C₂₃	—	8	4	no	—
384	C₂²×C₂₃	#546	1	2	yes	—
385	C₂²×C₂₃	C₂×#135	1	4	yes	—
386	C₂²×C₂₃	C₂×#135	1	2	yes	—
387	C₂²×C₂₃	#578	1	2	yes	—
388	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
389	C₄×C₂₃	—	2	2	no	—
390	C₄×C₂₃	—	2	2	no	—
391	C₄×C₂₃	—	2	4	no	—
392	C₄×C₂₃	—	2	2	no	—
393	C₄×C₂₃	—	2	2	no	—
394	C₄×C₂₃	—	4	2	no	—
395	C₄×C₂₃	—	4	2	no	—
396	C₄×C₂₃	—	4	2	no	—
397	C₄×C₂₃	—	4	2	no	—
398	C₄×C₂₃	—	4	2	no	—
399	C₄×C₂₃	—	4	2	no	—
400	C₄×C₂₃	#546	1	2	yes	—
401	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
402	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
403	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
404	C₂³×Q₈	C₂²×C₂₃	1	1	yes	characteristic
405	C₂²×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
406	C₂²×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
407	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
408	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
409	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
410	#552	—	2	4	no	—
411	#552	C₂²×C₂₃	1	8	yes	complemented
412	#548	—	2	4	no	—
413	#548	C₂²×C₂₃	1	8	yes	—
414	C₂×#126	—	2	1	no	—
415	C₂×#125	—	2	1	no	—
416	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic
417	C₂×#124	—	2	1	no	—
418	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
419	C₂×#123	—	2	1	no	—
420	C₂×C₂²⋊Q₈	—	2	1	no	—
421	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
422	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
423	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
424	C₂×#121	—	2	1	no	—
425	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
426	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
427	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
428	C₂×C₄×D₄	—	2	1	no	—
429	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
430	C₂×#117	—	2	1	no	—
431	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
432	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
433	#488	C₂²×C₂₃	1	8	yes	complemented
434	#485	C₂²×C₂₃	1	8	yes	complemented
435	#480	C₂²×C₂₃	1	8	yes	complemented
436	#479	C₂²×C₂₃	1	8	yes	complemented
437	#467	C₂²×C₂₃	1	8	yes	complemented
438	#465	C₂²×C₂₃	1	8	yes	complemented
439	#464	C₂²×C₂₃	1	8	yes	complemented
440	#452	C₂²×C₂₃	1	8	yes	complemented
441	#451	C₂²×C₂₃	1	8	yes	complemented
442	C₄×Q₁₆	C₂²×C₂₃	1	8	yes	complemented
443	C₈×D₄	C₂²×C₂₃	1	8	yes	complemented
444	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
445	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
446	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
447	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
448	#416	C₂²×C₂₃	1	8	yes	complemented
449	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
450	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
451	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
452	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
453	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
454	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
455	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
456	C₂×#103	C₂²×C₂₃	1	8	yes	complemented
457	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
458	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
459	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
460	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
461	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
462	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
463	C₂×C₂₃	—	2	4	no	—
464	C₂×C₂₃	—	4	2	no	—
465	C₂×C₂₃	—	8	2	no	—
466	C₂×C₂₃	#3300	1	4	yes	direct product factor
467	C₂×C₂₃	C₂×#546	1	1	yes	characteristic
468	C₂×C₂₃	C₂²×#135	1	1	yes	characteristic
469	C₂×C₂₃	C₂×#578	1	1	yes	characteristic
470	C₂×#41	—	2	2	no	—
471	C₂×#41	—	2	4	no	—
472	C₂×#41	—	4	2	no	—
473	C₂×#41	C₂³×C₂₃	1	4	yes	—
474	C₂²×Q₈	—	2	1	no	—
475	C₂²×Q₈	—	2	2	no	—
476	C₂²×Q₈	—	2	4	no	—
477	C₂²×Q₈	—	4	2	no	—
478	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
479	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
480	C₂²×Q₈	C₂³×C₂₃	1	4	yes	—
481	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
482	C₂²×D₄	—	2	1	no	—
483	C₂²×D₄	—	2	1	no	—
484	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
485	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
486	C₂³×C₄	—	2	1	no	—
487	C₂³×C₄	—	2	1	no	—
488	C₂³×C₄	—	2	1	no	—
489	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
490	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
491	C₂×Q₁₆	—	2	4	no	—
492	C₂×Q₁₆	—	4	2	no	—
493	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
494	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
495	C₂×SD₁₆	—	4	2	no	—
496	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
497	C₂²×C₈	—	4	2	no	—
498	C₂²×C₈	—	4	2	no	—
499	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
500	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
501	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
502	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
503	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
504	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
505	#126	—	2	8	no	—
506	#125	—	2	8	no	—
507	#125	—	2	2	no	—
508	#125	C₂³×C₂₃	1	4	yes	—
509	#124	—	2	8	no	—
510	#124	—	2	2	no	—
511	#124	C₂³×C₂₃	1	4	yes	—
512	#123	—	2	8	no	—
513	C₂²⋊Q₈	—	2	2	no	—
514	C₂²⋊Q₈	—	2	2	no	—
515	C₂²⋊Q₈	—	2	2	no	—
516	C₂²⋊Q₈	—	2	8	no	—
517	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
518	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
519	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
520	#121	—	2	8	no	—
521	#121	—	2	2	no	—
522	#121	C₂³×C₂₃	1	4	yes	—
523	C₄×Q₈	—	2	2	no	—
524	C₄×Q₈	—	2	2	no	—
525	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
526	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
527	C₄×D₄	—	2	8	no	—
528	C₄×D₄	D₄×C₂₃	1	4	yes	—
529	C₄×D₄	C₂³×C₂₃	1	4	yes	—
530	#117	—	2	2	no	—
531	#117	—	2	8	no	—
532	#117	C₂³×C₂₃	1	4	yes	—
533	C₂×C₄⋊C₄	—	2	1	no	—
534	C₂×C₄⋊C₄	—	2	2	no	—
535	C₂×C₄⋊C₄	—	2	1	no	—
536	C₂×C₄⋊C₄	—	2	1	no	—
537	C₂×C₄⋊C₄	—	2	1	no	—
538	C₂×C₄⋊C₄	—	2	1	no	—
539	C₂×C₄⋊C₄	—	2	1	no	—
540	C₂×C₄⋊C₄	—	2	1	no	—
541	C₂×C₄⋊C₄	—	2	1	no	—
542	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
543	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
544	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
545	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
546	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
547	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
548	C₂×C₂²⋊C₄	—	2	1	no	—
549	C₂×C₂²⋊C₄	—	2	1	no	—
550	C₂×C₂²⋊C₄	—	2	1	no	—
551	C₂×C₂²⋊C₄	—	2	1	no	—
552	C₂×C₂²⋊C₄	—	2	1	no	—
553	C₂×C₂²⋊C₄	—	2	1	no	—
554	C₂×C₂²⋊C₄	—	2	1	no	—
555	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
556	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
557	C₂×C₄²	—	2	1	no	—
558	C₂×C₄²	—	2	1	no	—
559	C₂×C₄²	—	2	1	no	—
560	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
561	#107	C₂³×C₂₃	1	4	yes	—
562	#107	C₂³×C₂₃	1	4	yes	—
563	#106	C₂³×C₂₃	1	4	yes	—
564	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
565	#103	C₂³×C₂₃	1	4	yes	—
566	#103	C₂³×C₂₃	1	4	yes	—
567	#103	C₂³×C₂₃	1	4	yes	—
568	#103	C₂³×C₂₃	1	4	yes	—
569	#103	C₂³×C₂₃	1	4	yes	—
570	#103	C₂³×C₂₃	1	4	yes	—
571	#103	C₂³×C₂₃	1	4	yes	—
572	#102	C₂³×C₂₃	1	4	yes	—
573	#102	C₂³×C₂₃	1	4	yes	—
574	#102	C₂³×C₂₃	1	4	yes	—
575	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
576	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
577	C₄×C₈	C₂³×C₂₃	1	4	yes	—
578	C₂₃	C₂×#3300	1	1	yes	characteristic, direct product factor, Sylow
579	C₂⁴	—	2	1	no	—
580	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
581	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
582	#41	—	2	8	no	—
583	#41	—	4	4	no	—
584	#41	—	4	8	no	—
585	C₂×Q₈	—	2	1	no	—
586	C₂×Q₈	—	2	1	no	—
587	C₂×Q₈	—	2	4	no	—
588	C₂×Q₈	—	2	1	no	—
589	C₂×Q₈	—	2	2	no	—
590	C₂×Q₈	—	2	8	no	—
591	C₂×Q₈	—	2	2	no	—
592	C₂×Q₈	—	2	2	no	—
593	C₂×Q₈	—	2	2	no	—
594	C₂×Q₈	—	2	2	no	—
595	C₂×Q₈	—	4	4	no	—
596	C₂×Q₈	—	4	4	no	—
597	C₂×Q₈	—	4	8	no	—
598	C₂×Q₈	#41×C₂₃	1	4	yes	—
599	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
600	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
601	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
602	C₂×D₄	—	2	4	no	—
603	C₂×D₄	—	2	4	no	—
604	C₂×D₄	—	2	4	no	—
605	C₂×D₄	—	2	1	no	—
606	C₂×D₄	—	2	2	no	—
607	C₂×D₄	—	2	2	no	—
608	C₂×D₄	—	4	4	no	—
609	C₂×D₄	—	4	4	no	—
610	C₂×D₄	C₂×D₄×C₂₃	1	4	yes	—
611	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
612	C₂²×C₄	—	2	1	no	—
613	C₂²×C₄	—	2	2	no	—
614	C₂²×C₄	—	2	2	no	—
615	C₂²×C₄	—	2	2	no	—
616	C₂²×C₄	—	2	2	no	—
617	C₂²×C₄	—	2	1	no	—
618	C₂²×C₄	—	2	1	no	—
619	C₂²×C₄	—	2	1	no	—
620	C₂²×C₄	—	2	1	no	—
621	C₂²×C₄	—	2	1	no	—
622	C₂²×C₄	—	2	1	no	—
623	C₂²×C₄	—	2	4	no	—
624	C₂²×C₄	—	2	4	no	—
625	C₂²×C₄	—	2	4	no	—
626	C₂²×C₄	—	4	4	no	—
627	C₂²×C₄	—	4	4	no	—
628	C₂²×C₄	—	4	4	no	—
629	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
630	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
631	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
632	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
633	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
634	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
635	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
636	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
637	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
638	Q₁₆	—	2	8	no	—
639	Q₁₆	—	4	4	no	—
640	SD₁₆	—	4	4	no	—
641	C₂×C₈	—	2	2	no	—
642	C₂×C₈	—	2	2	no	—
643	C₂×C₈	—	2	2	no	—
644	C₂×C₈	—	2	2	no	—
645	C₂×C₈	—	4	4	no	—
646	C₂×C₈	—	4	4	no	—
647	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
648	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
649	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
650	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
651	C₄⋊C₄	—	2	1	no	—
652	C₄⋊C₄	—	2	1	no	—
653	C₄⋊C₄	—	2	4	no	—
654	C₄⋊C₄	—	2	4	no	—
655	C₄⋊C₄	—	2	4	no	—
656	C₄⋊C₄	—	2	4	no	—
657	C₄⋊C₄	—	2	4	no	—
658	C₄⋊C₄	—	2	4	no	—
659	C₄⋊C₄	—	2	4	no	—
660	C₄⋊C₄	—	2	4	no	—
661	C₄⋊C₄	—	2	1	no	—
662	C₄⋊C₄	—	2	1	no	—
663	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
664	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
665	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
666	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
667	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
668	C₂²⋊C₄	—	2	4	no	—
669	C₂²⋊C₄	—	2	4	no	—
670	C₂²⋊C₄	—	2	4	no	—
671	C₂²⋊C₄	—	2	4	no	—
672	C₂²⋊C₄	—	2	4	no	—
673	C₂²⋊C₄	—	2	4	no	—
674	C₂²⋊C₄	—	2	4	no	—
675	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
676	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
677	C₄²	—	2	4	no	—
678	C₄²	—	2	4	no	—
679	C₄²	—	2	4	no	—
680	C₄²	C₂×D₄×C₂₃	1	2	yes	—
681	C₄²	C₂⁴×C₂₃	1	2	yes	—
682	C₂³	—	2	2	no	—
683	C₂³	—	2	2	no	—
684	C₂³	—	2	2	no	—
685	C₂³	—	2	2	no	—
686	C₂³	—	2	2	no	—
687	C₂³	—	2	2	no	—
688	C₂³	—	4	2	no	—
689	C₂³	—	4	2	no	—
690	C₂³	—	4	2	no	—
691	C₂³	C₂₃×#135	1	4	yes	—
692	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
693	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
694	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
695	Q₈	—	2	2	no	—
696	Q₈	—	2	4	no	—
697	Q₈	—	2	2	no	—
698	Q₈	—	2	2	no	—
699	Q₈	—	2	2	no	—
700	Q₈	—	2	2	no	—
701	Q₈	—	4	8	no	—
702	Q₈	—	4	2	no	—
703	Q₈	—	4	2	no	—
704	Q₈	C₂×#41×C₂₃	1	4	yes	—
705	D₄	—	2	8	no	—
706	D₄	—	2	2	no	—
707	D₄	—	2	2	no	—
708	D₄	—	4	8	no	—
709	D₄	—	4	8	no	—
710	D₄	—	4	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	4	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	4	no	—
722	C₂×C₄	—	2	4	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	4	8	no	—
730	C₂×C₄	—	4	8	no	—
731	C₂×C₄	—	4	8	no	—
732	C₂×C₄	—	4	2	no	—
733	C₂×C₄	—	4	2	no	—
734	C₂×C₄	—	4	2	no	—
735	C₂×C₄	—	4	2	no	—
736	C₂×C₄	—	4	2	no	—
737	C₂×C₄	—	4	2	no	—
738	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
739	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
740	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
741	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
742	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
743	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
744	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
745	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
746	C₈	—	2	2	no	—
747	C₈	—	2	2	no	—
748	C₈	—	2	2	no	—
749	C₈	—	2	2	no	—
750	C₂²	—	2	2	no	—
751	C₂²	—	2	8	no	—
752	C₂²	—	2	2	no	—
753	C₂²	—	2	2	no	—
754	C₂²	—	2	2	no	—
755	C₂²	—	2	2	no	—
756	C₂²	—	4	4	no	—
757	C₂²	—	4	2	no	—
758	C₂²	—	4	2	no	—
759	C₂²	—	4	2	no	—
760	C₂²	—	8	4	no	—
761	C₂²	C₂₃×#546	1	2	yes	—
762	C₂²	C₂×C₂₃×#135	1	4	yes	—
763	C₂²	C₂×C₂₃×#135	1	2	yes	—
764	C₂²	C₂₃×#578	1	2	yes	—
765	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
766	C₄	—	2	2	no	—
767	C₄	—	2	2	no	—
768	C₄	—	2	4	no	—
769	C₄	—	2	2	no	—
770	C₄	—	2	2	no	—
771	C₄	—	4	2	no	—
772	C₄	—	4	2	no	—
773	C₄	—	4	2	no	—
774	C₄	—	4	2	no	—
775	C₄	—	4	2	no	—
776	C₄	—	4	2	no	—
777	C₄	C₂₃×#546	1	2	yes	—
778	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
779	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
780	C₂	—	2	4	no	—
781	C₂	—	4	2	no	—
782	C₂	—	8	2	no	—
783	C₂	C₂₃×#3300	1	4	yes	direct product factor
784	C₂	C₂×C₂₃×#546	1	1	yes	characteristic
785	C₂	C₂²×C₂₃×#135	1	1	yes	characteristic
786	C₂	C₂×C₂₃×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂×C₂₃×#548	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₂×C₄×D₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#552	C₂	semidirect
3. C₂₃×#3300	C₂	direct (N × H)
4. C₂×C₂₃×#488	C₂	semidirect
5. C₂×C₂₃×#485	C₂	semidirect
6. C₂×C₂₃×#480	C₂	semidirect
7. C₂×C₂₃×#479	C₂	semidirect
8. C₂×C₂₃×#467	C₂	semidirect
9. C₂×C₂₃×#465	C₂	semidirect
10. C₂×C₂₃×#464	C₂	semidirect
11. C₂×C₂₃×#452	C₂	semidirect
12. C₂×C₂₃×#451	C₂	semidirect
13. C₂×C₄×Q₁₆×C₂₃	C₂	semidirect
14. C₂×C₈×D₄×C₂₃	C₂	semidirect
15. C₂×C₂₃×#416	C₂	semidirect
16. C₂²×C₂₃×#103	C₂	semidirect
25. C₂₃×#552	C₂²	semidirect
47. C₂₃×#488	C₂²	semidirect
48. C₂₃×#485	C₂²	semidirect
49. C₂₃×#480	C₂²	semidirect
50. C₂₃×#479	C₂²	semidirect
51. C₂₃×#467	C₂²	semidirect
52. C₂₃×#465	C₂²	semidirect
53. C₂₃×#464	C₂²	semidirect
54. C₂₃×#452	C₂²	semidirect
55. C₂₃×#451	C₂²	semidirect
56. C₄×Q₁₆×C₂₃	C₂²	semidirect
57. C₈×D₄×C₂₃	C₂²	semidirect
62. C₂₃×#416	C₂²	semidirect
70. C₂×C₂₃×#103	C₂²	semidirect
288. C₂×#3300	C₂₃	direct (N × H)
357. C₂×#552	C₂×C₂₃	semidirect
359. #3300	C₂×C₂₃	direct (N × H)
360. C₂×#488	C₂×C₂₃	semidirect
361. C₂×#485	C₂×C₂₃	semidirect
362. C₂×#480	C₂×C₂₃	semidirect
363. C₂×#479	C₂×C₂₃	semidirect
364. C₂×#467	C₂×C₂₃	semidirect
365. C₂×#465	C₂×C₂₃	semidirect
366. C₂×#464	C₂×C₂₃	semidirect
367. C₂×#452	C₂×C₂₃	semidirect
368. C₂×#451	C₂×C₂₃	semidirect
369. C₂×C₄×Q₁₆	C₂×C₂₃	semidirect
370. C₂×C₈×D₄	C₂×C₂₃	semidirect
371. C₂×#416	C₂×C₂₃	semidirect
372. C₂²×#103	C₂×C₂₃	semidirect
411. #552	C₂²×C₂₃	semidirect
433. #488	C₂²×C₂₃	semidirect
434. #485	C₂²×C₂₃	semidirect
435. #480	C₂²×C₂₃	semidirect
436. #479	C₂²×C₂₃	semidirect
437. #467	C₂²×C₂₃	semidirect
438. #465	C₂²×C₂₃	semidirect
439. #464	C₂²×C₂₃	semidirect
440. #452	C₂²×C₂₃	semidirect
441. #451	C₂²×C₂₃	semidirect
442. C₄×Q₁₆	C₂²×C₂₃	semidirect
443. C₈×D₄	C₂²×C₂₃	semidirect
448. #416	C₂²×C₂₃	semidirect
456. C₂×#103	C₂²×C₂₃	semidirect
466. C₂×C₂₃	#3300	direct (N × H)
578. C₂₃	C₂×#3300	direct (N × H)
783. C₂	C₂₃×#3300	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#552	2
C₂×C₂₃×#548	2
C₂₃×#3300	2
C₂×C₂₃×#488	2
C₂×C₂₃×#485	2
C₂×C₂₃×#480	2
C₂×C₂₃×#479	2
C₂×C₂₃×#467	2
C₂×C₂₃×#465	2
C₂×C₂₃×#464	2
C₂×C₂₃×#452	2
C₂×C₂₃×#451	2
C₂×C₄×Q₁₆×C₂₃	2
C₂×C₈×D₄×C₂₃	2
C₂×C₂₃×#416	2
C₂²×C₂₃×#103	2
C₂×#3300	23

Subgroups — C2×C23×#3300 #19208744

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#3300 #19208744