Subgroups — C₄×C₂₃×#553 #19181790

Order 5888.

2600 conjugacy classes of subgroups.

The subgroup lattice has 1064 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#553	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2374	C₂	1	2	yes	maximal, complemented
3	C₂₃×#2373	C₂	1	2	yes	maximal, complemented
4	C₂₃×#2370	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2364	C₂	1	2	yes	maximal, complemented
6	C₂₃×#2363	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#2361	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#2357	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#2353	C₂	1	2	yes	maximal, complemented
10	C₂₃×#2352	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#2347	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#2345	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×C₂₃×#125	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₂₃×#126	C₂	1	2	yes	maximal, complemented
15	C₄×C₂₃×#123	C₂	1	2	yes	maximal, complemented
16	C₄×C₂₃×#121	C₂	1	2	yes	maximal, complemented
17	C₄×C₂₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×C₂₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄²×D₄×C₂₃	C₂	1	2	yes	maximal, complemented
20	C₄²×D₄×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄²×D₄×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×C₂₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₄×C₄⋊C₄×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂₃×#553	C₄	1	16	yes	direct product factor
25	C₂×C₂₃×#126	C₂²	1	2	yes	—
26	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic
27	C₂×C₂₃×#123	C₂²	1	2	yes	—
28	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
29	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
30	C₂×C₂₃×#121	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
38	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
40	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
41	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
42	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
43	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
44	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
45	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
46	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
47	C₂²×C₄²×C₂₃	C₂²	1	2	yes	—
48	C₂²×C₄²×C₂₃	C₂²	1	2	yes	—
49	C₂₃×#390	C₂²	1	1	yes	characteristic
50	C₂₃×#390	C₂²	1	1	yes	characteristic
51	C₂₃×#390	C₂²	1	2	yes	—
52	C₂₃×#389	C₂²	1	1	yes	characteristic
53	C₂₃×#389	C₂²	1	1	yes	characteristic
54	C₂₃×#389	C₂²	1	2	yes	—
55	C₂₃×#389	C₂²	1	1	yes	characteristic
56	C₂₃×#389	C₂²	1	1	yes	characteristic
57	C₂₃×#388	C₂²	1	2	yes	—
58	C₂₃×#388	C₂²	1	2	yes	—
59	C₂₃×#388	C₂²	1	2	yes	—
60	C₂₃×#388	C₂²	1	2	yes	—
61	C₂₃×#388	C₂²	1	2	yes	—
62	C₂₃×#388	C₂²	1	2	yes	—
63	C₂₃×#388	C₂²	1	2	yes	—
64	C₂₃×#388	C₂²	1	2	yes	—
65	C₂₃×#388	C₂²	1	2	yes	—
66	C₂₃×#387	C₂²	1	2	yes	—
67	C₂₃×#387	C₂²	1	2	yes	—
68	C₂₃×#387	C₂²	1	2	yes	—
69	C₂₃×#387	C₂²	1	2	yes	—
70	C₂₃×#387	C₂²	1	2	yes	—
71	C₂₃×#387	C₂²	1	2	yes	—
72	C₂₃×#387	C₂²	1	2	yes	—
73	C₂₃×#386	C₂²	1	2	yes	—
74	C₂₃×#386	C₂²	1	2	yes	—
75	C₂₃×#386	C₂²	1	2	yes	—
76	C₂₃×#386	C₂²	1	2	yes	—
77	C₂₃×#386	C₂²	1	2	yes	—
78	C₂₃×#385	C₂²	1	2	yes	—
79	C₂₃×#383	C₂²	1	2	yes	—
80	C₂₃×#382	C₂²	1	1	yes	characteristic
81	C₂₃×#381	C₂²	1	2	yes	—
82	C₂₃×#380	C₂²	1	1	yes	characteristic
83	C₂₃×#380	C₂²	1	2	yes	—
84	C₂₃×#380	C₂²	1	1	yes	characteristic
85	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
86	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
87	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
88	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
89	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
90	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
91	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
92	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
93	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
94	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
95	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
96	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
97	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
98	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
99	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
100	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
101	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
102	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
103	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
104	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
105	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
106	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
107	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
108	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
109	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
110	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
111	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
112	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
113	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
114	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
115	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
116	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
117	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
118	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
119	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
120	C₂₃×#376	C₂²	1	2	yes	—
121	C₂×C₂₃×#95	C₂²	1	2	yes	—
122	C₄³×C₂₃	C₂²	1	2	yes	—
123	C₄³×C₂₃	C₂²	1	1	yes	characteristic
124	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
125	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
126	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
127	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
128	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
130	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
132	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
133	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
134	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
135	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
136	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
137	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
138	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
139	C₂₃×#126	C₂×C₄	1	16	yes	complemented
140	C₂₃×#125	C₂×C₄	1	8	yes	complemented
141	C₂₃×#123	C₂×C₄	1	16	yes	complemented
142	C₂₃×#121	C₂×C₄	1	16	yes	complemented
143	C₂₃×#121	C₂×C₄	1	8	yes	complemented
144	C₂₃×#121	C₂×C₄	1	8	yes	complemented
145	C₄×D₄×C₂₃	—	2	8	no	—
146	C₄×D₄×C₂₃	—	2	4	no	—
147	C₄×D₄×C₂₃	—	2	4	no	—
148	C₄×D₄×C₂₃	—	2	8	no	—
149	C₄×D₄×C₂₃	—	2	4	no	—
150	C₄×D₄×C₂₃	—	2	4	no	—
151	C₄×D₄×C₂₃	—	4	4	no	—
152	C₄×D₄×C₂₃	C₂×C₄	1	16	yes	complemented
153	C₄×D₄×C₂₃	C₂×C₄	1	8	yes	complemented
154	C₄×D₄×C₂₃	C₂×C₄	1	8	yes	complemented
155	C₂₃×#117	—	2	4	no	—
156	C₂₃×#117	C₂×C₄	1	8	yes	complemented
157	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
158	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	8	yes	complemented
159	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
160	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
161	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
162	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
165	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
167	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
169	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
170	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
171	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
172	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
173	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
174	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
175	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
176	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
177	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
178	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
179	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
180	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
181	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
183	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
184	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
185	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
186	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
187	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
188	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
189	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
190	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
191	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
192	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
193	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
194	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₂₃	—	2	4	no	—
197	C₂×C₄²×C₂₃	—	2	4	no	—
198	C₂×C₄²×C₂₃	—	4	4	no	—
199	C₂×C₄²×C₂₃	—	4	4	no	—
200	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
201	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
203	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
204	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
205	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
206	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
208	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
209	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
210	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
211	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
212	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
213	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
214	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
215	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
216	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
217	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
218	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
219	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
220	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
221	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
222	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
223	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
224	C₂₃×#95	C₂³	1	2	yes	—
225	C₂₃×#95	C₂³	1	2	yes	—
226	C₂₃×#95	C₂³	1	2	yes	—
227	C₂₃×#95	C₂³	1	2	yes	—
228	C₂₃×#95	C₂³	1	2	yes	—
229	C₂₃×#95	C₂³	1	2	yes	—
230	C₂₃×#95	C₂³	1	2	yes	—
231	C₂₃×#95	C₂³	1	1	yes	characteristic
232	C₂₃×#95	C₂³	1	1	yes	characteristic
233	C₂₃×#95	C₂³	1	2	yes	—
234	C₂₃×#95	C₂³	1	2	yes	—
235	C₂₃×#95	C₂³	1	1	yes	characteristic
236	C₂₃×#95	C₂³	1	2	yes	—
237	C₂₃×#95	C₂³	1	1	yes	characteristic
238	C₂₃×#95	C₂³	1	1	yes	characteristic
239	C₂₃×#95	C₂³	1	2	yes	—
240	C₂₃×#95	C₂³	1	2	yes	—
241	C₂₃×#95	C₂³	1	2	yes	—
242	C₂₃×#95	C₂³	1	1	yes	characteristic
243	C₂₃×#95	C₂³	1	2	yes	—
244	C₂₃×#95	C₂³	1	2	yes	—
245	C₂₃×#95	C₂³	1	2	yes	—
246	C₂₃×#95	C₂³	1	2	yes	—
247	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
248	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
249	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
250	C₂×D₄×C₂₃	—	2	2	no	—
251	C₂×D₄×C₂₃	—	2	4	no	—
252	C₂×D₄×C₂₃	—	2	2	no	—
253	C₂×D₄×C₂₃	—	2	4	no	—
254	C₂×D₄×C₂₃	—	2	2	no	—
255	C₂×D₄×C₂₃	—	2	2	no	—
256	C₂×D₄×C₂₃	—	4	2	no	—
257	C₂×D₄×C₂₃	—	4	2	no	—
258	C₂×D₄×C₂₃	C₂²×C₄	1	8	yes	—
259	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
260	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
261	C₂×D₄×C₂₃	C₂²×C₄	1	8	yes	—
262	C₂²×C₄×C₂₃	—	2	2	no	—
263	C₂²×C₄×C₂₃	—	2	2	no	—
264	C₂²×C₄×C₂₃	—	2	2	no	—
265	C₂²×C₄×C₂₃	—	2	2	no	—
266	C₂²×C₄×C₂₃	—	2	2	no	—
267	C₂²×C₄×C₂₃	—	2	2	no	—
268	C₂²×C₄×C₂₃	—	2	2	no	—
269	C₂²×C₄×C₂₃	—	2	4	no	—
270	C₂²×C₄×C₂₃	—	2	2	no	—
271	C₂²×C₄×C₂₃	—	2	2	no	—
272	C₂²×C₄×C₂₃	—	2	2	no	—
273	C₂²×C₄×C₂₃	—	2	4	no	—
274	C₂²×C₄×C₂₃	—	2	2	no	—
275	C₂²×C₄×C₂₃	—	2	4	no	—
276	C₂²×C₄×C₂₃	—	2	4	no	—
277	C₂²×C₄×C₂₃	—	2	2	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	—	2	2	no	—
282	C₂²×C₄×C₂₃	—	4	2	no	—
283	C₂²×C₄×C₂₃	—	4	2	no	—
284	C₂²×C₄×C₂₃	—	4	2	no	—
285	C₂²×C₄×C₂₃	—	4	2	no	—
286	C₂²×C₄×C₂₃	—	4	1	no	—
287	C₂²×C₄×C₂₃	—	4	2	no	—
288	C₂²×C₄×C₂₃	—	4	2	no	—
289	C₂²×C₄×C₂₃	—	4	1	no	—
290	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
291	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
292	C₂²×C₄×C₂₃	C₂²×C₄	1	8	yes	—
293	C₂²×C₄×C₂₃	C₂²×C₄	1	8	yes	—
294	C₂²×C₄×C₂₃	#41	1	4	yes	—
295	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
296	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
297	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
298	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
299	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
300	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
301	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
302	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
303	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
304	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
305	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
306	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
307	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
308	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
309	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
310	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
311	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
312	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
313	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
314	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
315	C₄⋊C₄×C₂₃	—	2	4	no	—
316	C₄⋊C₄×C₂₃	—	2	2	no	—
317	C₄⋊C₄×C₂₃	—	2	2	no	—
318	C₄⋊C₄×C₂₃	—	2	2	no	—
319	C₄⋊C₄×C₂₃	—	2	4	no	—
320	C₄⋊C₄×C₂₃	—	2	4	no	—
321	C₄⋊C₄×C₂₃	—	2	2	no	—
322	C₄⋊C₄×C₂₃	—	2	2	no	—
323	C₄⋊C₄×C₂₃	—	4	2	no	—
324	C₄⋊C₄×C₂₃	—	4	2	no	—
325	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
326	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
327	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
328	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
329	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
330	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
331	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
332	C₄⋊C₄×C₂₃	#41	1	4	yes	—
333	C₂²⋊C₄×C₂₃	—	2	2	no	—
334	C₂²⋊C₄×C₂₃	—	2	4	no	—
335	C₂²⋊C₄×C₂₃	—	2	4	no	—
336	C₂²⋊C₄×C₂₃	—	2	4	no	—
337	C₂²⋊C₄×C₂₃	—	2	2	no	—
338	C₂²⋊C₄×C₂₃	—	2	4	no	—
339	C₂²⋊C₄×C₂₃	—	2	4	no	—
340	C₂²⋊C₄×C₂₃	—	2	4	no	—
341	C₂²⋊C₄×C₂₃	—	2	2	no	—
342	C₂²⋊C₄×C₂₃	—	4	2	no	—
343	C₂²⋊C₄×C₂₃	—	4	2	no	—
344	C₂²⋊C₄×C₂₃	—	4	2	no	—
345	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
346	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
347	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
348	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
349	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
350	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
351	C₂²⋊C₄×C₂₃	#41	1	4	yes	—
352	C₄²×C₂₃	—	2	2	no	—
353	C₄²×C₂₃	—	2	2	no	—
354	C₄²×C₂₃	—	2	2	no	—
355	C₄²×C₂₃	—	2	2	no	—
356	C₄²×C₂₃	—	2	2	no	—
357	C₄²×C₂₃	—	2	2	no	—
358	C₄²×C₂₃	—	2	4	no	—
359	C₄²×C₂₃	—	2	4	no	—
360	C₄²×C₂₃	—	2	2	no	—
361	C₄²×C₂₃	—	2	4	no	—
362	C₄²×C₂₃	—	2	2	no	—
363	C₄²×C₂₃	—	2	2	no	—
364	C₄²×C₂₃	—	2	2	no	—
365	C₄²×C₂₃	—	2	4	no	—
366	C₄²×C₂₃	—	2	4	no	—
367	C₄²×C₂₃	—	4	2	no	—
368	C₄²×C₂₃	—	4	2	no	—
369	C₄²×C₂₃	—	4	2	no	—
370	C₄²×C₂₃	—	4	2	no	—
371	C₄²×C₂₃	—	4	2	no	—
372	C₄²×C₂₃	—	4	1	no	—
373	C₄²×C₂₃	C₂²×C₄	1	8	yes	—
374	C₄²×C₂₃	C₂²×C₄	1	4	yes	—
375	C₄²×C₂₃	#41	1	4	yes	—
376	C₄×#553	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
377	C₂³×C₂₃	—	2	1	no	—
378	C₂³×C₂₃	—	2	1	no	—
379	C₂³×C₂₃	—	2	1	no	—
380	C₂³×C₂₃	—	2	1	no	—
381	C₂³×C₂₃	—	2	1	no	—
382	C₂³×C₂₃	—	2	2	no	—
383	C₂³×C₂₃	—	2	2	no	—
384	C₂³×C₂₃	—	2	1	no	—
385	C₂³×C₂₃	—	2	1	no	—
386	C₂³×C₂₃	—	2	2	no	—
387	C₂³×C₂₃	—	2	2	no	—
388	C₂³×C₂₃	—	2	1	no	—
389	C₂³×C₂₃	—	2	1	no	—
390	C₂³×C₂₃	—	2	2	no	—
391	C₂³×C₂₃	—	2	2	no	—
392	C₂³×C₂₃	—	2	1	no	—
393	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
394	C₂³×C₂₃	C₂³×C₄	1	4	yes	—
395	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
396	C₂³×C₂₃	C₂×#41	1	2	yes	—
397	C₂³×C₂₃	C₂×#41	1	2	yes	—
398	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
399	D₄×C₂₃	—	2	16	no	—
400	D₄×C₂₃	—	2	8	no	—
401	D₄×C₂₃	—	2	8	no	—
402	D₄×C₂₃	—	4	8	no	—
403	C₂×C₄×C₂₃	—	2	1	no	—
404	C₂×C₄×C₂₃	—	2	1	no	—
405	C₂×C₄×C₂₃	—	2	1	no	—
406	C₂×C₄×C₂₃	—	2	1	no	—
407	C₂×C₄×C₂₃	—	2	1	no	—
408	C₂×C₄×C₂₃	—	2	1	no	—
409	C₂×C₄×C₂₃	—	2	2	no	—
410	C₂×C₄×C₂₃	—	2	2	no	—
411	C₂×C₄×C₂₃	—	2	1	no	—
412	C₂×C₄×C₂₃	—	2	1	no	—
413	C₂×C₄×C₂₃	—	2	2	no	—
414	C₂×C₄×C₂₃	—	2	1	no	—
415	C₂×C₄×C₂₃	—	2	1	no	—
416	C₂×C₄×C₂₃	—	2	1	no	—
417	C₂×C₄×C₂₃	—	2	2	no	—
418	C₂×C₄×C₂₃	—	2	1	no	—
419	C₂×C₄×C₂₃	—	2	2	no	—
420	C₂×C₄×C₂₃	—	2	2	no	—
421	C₂×C₄×C₂₃	—	2	1	no	—
422	C₂×C₄×C₂₃	—	2	1	no	—
423	C₂×C₄×C₂₃	—	2	2	no	—
424	C₂×C₄×C₂₃	—	2	1	no	—
425	C₂×C₄×C₂₃	—	2	1	no	—
426	C₂×C₄×C₂₃	—	2	2	no	—
427	C₂×C₄×C₂₃	—	2	8	no	—
428	C₂×C₄×C₂₃	—	2	8	no	—
429	C₂×C₄×C₂₃	—	2	8	no	—
430	C₂×C₄×C₂₃	—	2	1	no	—
431	C₂×C₄×C₂₃	—	2	1	no	—
432	C₂×C₄×C₂₃	—	2	1	no	—
433	C₂×C₄×C₂₃	—	2	2	no	—
434	C₂×C₄×C₂₃	—	2	1	no	—
435	C₂×C₄×C₂₃	—	2	2	no	—
436	C₂×C₄×C₂₃	—	2	2	no	—
437	C₂×C₄×C₂₃	—	2	1	no	—
438	C₂×C₄×C₂₃	—	2	2	no	—
439	C₂×C₄×C₂₃	—	2	1	no	—
440	C₂×C₄×C₂₃	—	2	2	no	—
441	C₂×C₄×C₂₃	—	2	2	no	—
442	C₂×C₄×C₂₃	—	2	2	no	—
443	C₂×C₄×C₂₃	—	2	2	no	—
444	C₂×C₄×C₂₃	—	2	1	no	—
445	C₂×C₄×C₂₃	—	2	2	no	—
446	C₂×C₄×C₂₃	—	2	1	no	—
447	C₂×C₄×C₂₃	—	2	1	no	—
448	C₂×C₄×C₂₃	—	4	8	no	—
449	C₂×C₄×C₂₃	—	4	8	no	—
450	C₂×C₄×C₂₃	—	4	4	no	—
451	C₂×C₄×C₂₃	—	4	8	no	—
452	C₂×C₄×C₂₃	—	4	4	no	—
453	C₂×C₄×C₂₃	—	4	8	no	—
454	C₂×C₄×C₂₃	—	4	4	no	—
455	C₂×C₄×C₂₃	—	4	8	no	—
456	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
457	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
458	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
459	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
460	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
461	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
462	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
463	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
464	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
465	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
466	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
467	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
468	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
469	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
470	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
471	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
472	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
473	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
474	C₂×#553	C₂×C₂₃	1	1	yes	characteristic
475	#2374	C₂×C₂₃	1	2	yes	complemented
476	#2373	C₂×C₂₃	1	2	yes	complemented
477	#2370	C₂×C₂₃	1	1	yes	characteristic, complemented
478	#2364	C₂×C₂₃	1	2	yes	complemented
479	#2363	C₂×C₂₃	1	1	yes	characteristic, complemented
480	#2361	C₂×C₂₃	1	1	yes	characteristic, complemented
481	#2357	C₂×C₂₃	1	1	yes	characteristic, complemented
482	#2353	C₂×C₂₃	1	2	yes	complemented
483	#2352	C₂×C₂₃	1	1	yes	characteristic, complemented
484	#2347	C₂×C₂₃	1	1	yes	characteristic, complemented
485	#2345	C₂×C₂₃	1	1	yes	characteristic, complemented
486	C₄×#125	C₂×C₂₃	1	1	yes	characteristic, complemented
487	C₄×#126	C₂×C₂₃	1	2	yes	complemented
488	C₄×#123	C₂×C₂₃	1	2	yes	complemented
489	C₄×#121	C₂×C₂₃	1	1	yes	characteristic, complemented
490	C₄×#121	C₂×C₂₃	1	2	yes	complemented
491	C₄×#121	C₂×C₂₃	1	1	yes	characteristic, complemented
492	C₄²×D₄	C₂×C₂₃	1	1	yes	characteristic, complemented
493	C₄²×D₄	C₂×C₂₃	1	2	yes	complemented
494	C₄²×D₄	C₂×C₂₃	1	1	yes	characteristic, complemented
495	C₄×#117	C₂×C₂₃	1	1	yes	characteristic, complemented
496	C₂×C₄×C₄⋊C₄	C₂×C₂₃	1	1	yes	characteristic, complemented
497	C₂²×C₂₃	—	2	2	no	—
498	C₂²×C₂₃	—	2	2	no	—
499	C₂²×C₂₃	—	2	2	no	—
500	C₂²×C₂₃	—	2	2	no	—
501	C₂²×C₂₃	—	2	2	no	—
502	C₂²×C₂₃	—	2	2	no	—
503	C₂²×C₂₃	—	2	2	no	—
504	C₂²×C₂₃	—	2	2	no	—
505	C₂²×C₂₃	—	2	4	no	—
506	C₂²×C₂₃	—	2	4	no	—
507	C₂²×C₂₃	—	2	4	no	—
508	C₂²×C₂₃	—	2	2	no	—
509	C₂²×C₂₃	—	4	2	no	—
510	C₂²×C₂₃	—	4	1	no	—
511	C₂²×C₂₃	—	4	1	no	—
512	C₂²×C₂₃	—	4	2	no	—
513	C₂²×C₂₃	—	4	1	no	—
514	C₂²×C₂₃	—	4	2	no	—
515	C₂²×C₂₃	—	4	2	no	—
516	C₂²×C₂₃	—	4	1	no	—
517	C₂²×C₂₃	C₄×#41	1	4	yes	—
518	C₂²×C₂₃	C₂⁴×C₄	1	1	yes	characteristic
519	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
520	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
521	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
522	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
523	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
524	C₂²×C₂₃	#585	1	1	yes	characteristic
525	C₄×C₂₃	—	2	2	no	—
526	C₄×C₂₃	—	2	2	no	—
527	C₄×C₂₃	—	2	4	no	—
528	C₄×C₂₃	—	2	2	no	—
529	C₄×C₂₃	—	2	2	no	—
530	C₄×C₂₃	—	2	4	no	—
531	C₄×C₂₃	—	2	4	no	—
532	C₄×C₂₃	—	2	2	no	—
533	C₄×C₂₃	—	2	2	no	—
534	C₄×C₂₃	—	2	2	no	—
535	C₄×C₂₃	—	2	2	no	—
536	C₄×C₂₃	—	2	4	no	—
537	C₄×C₂₃	—	4	1	no	—
538	C₄×C₂₃	—	4	2	no	—
539	C₄×C₂₃	—	4	1	no	—
540	C₄×C₂₃	—	4	1	no	—
541	C₄×C₂₃	—	4	2	no	—
542	C₄×C₂₃	—	4	2	no	—
543	C₄×C₂₃	C₄×#41	1	4	yes	—
544	C₄×C₂₃	#553	1	4	yes	direct product factor
545	#553	C₄×C₂₃	1	16	yes	direct product factor
546	C₂×#126	C₂²×C₂₃	1	2	yes	—
547	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic
548	C₂×#123	C₂²×C₂₃	1	2	yes	—
549	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
550	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
551	C₂×#121	C₂²×C₂₃	1	2	yes	—
552	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
553	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
554	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
555	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
556	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
557	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
558	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
559	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
560	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
561	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
562	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
563	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
564	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
565	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
566	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
567	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
568	C₂²×C₄²	C₂²×C₂₃	1	2	yes	—
569	C₂²×C₄²	C₂²×C₂₃	1	2	yes	—
570	#390	C₂²×C₂₃	1	1	yes	characteristic
571	#390	C₂²×C₂₃	1	1	yes	characteristic
572	#390	C₂²×C₂₃	1	2	yes	—
573	#389	C₂²×C₂₃	1	1	yes	characteristic
574	#389	C₂²×C₂₃	1	1	yes	characteristic
575	#389	C₂²×C₂₃	1	1	yes	characteristic
576	#389	C₂²×C₂₃	1	1	yes	characteristic
577	#389	C₂²×C₂₃	1	2	yes	—
578	#388	C₂²×C₂₃	1	2	yes	—
579	#388	C₂²×C₂₃	1	2	yes	—
580	#388	C₂²×C₂₃	1	2	yes	—
581	#388	C₂²×C₂₃	1	2	yes	—
582	#388	C₂²×C₂₃	1	2	yes	—
583	#388	C₂²×C₂₃	1	2	yes	—
584	#388	C₂²×C₂₃	1	2	yes	—
585	#388	C₂²×C₂₃	1	2	yes	—
586	#388	C₂²×C₂₃	1	2	yes	—
587	#387	C₂²×C₂₃	1	2	yes	—
588	#387	C₂²×C₂₃	1	2	yes	—
589	#387	C₂²×C₂₃	1	2	yes	—
590	#387	C₂²×C₂₃	1	2	yes	—
591	#387	C₂²×C₂₃	1	2	yes	—
592	#387	C₂²×C₂₃	1	2	yes	—
593	#387	C₂²×C₂₃	1	2	yes	—
594	#386	C₂²×C₂₃	1	2	yes	—
595	#386	C₂²×C₂₃	1	2	yes	—
596	#386	C₂²×C₂₃	1	2	yes	—
597	#386	C₂²×C₂₃	1	2	yes	—
598	#386	C₂²×C₂₃	1	2	yes	—
599	#385	C₂²×C₂₃	1	2	yes	—
600	#383	C₂²×C₂₃	1	2	yes	—
601	#382	C₂²×C₂₃	1	1	yes	characteristic
602	#381	C₂²×C₂₃	1	2	yes	—
603	#380	C₂²×C₂₃	1	1	yes	characteristic
604	#380	C₂²×C₂₃	1	2	yes	—
605	#380	C₂²×C₂₃	1	1	yes	characteristic
606	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
607	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
608	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
609	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
610	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
611	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
612	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
613	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
614	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
615	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
616	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
617	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
618	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
619	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
620	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
621	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
622	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
623	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
624	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
625	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
626	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
627	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
628	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
629	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
630	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
631	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
632	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
633	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
634	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
635	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
636	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
637	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
638	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
639	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
640	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
641	#376	C₂²×C₂₃	1	2	yes	—
642	C₂×#95	C₂²×C₂₃	1	2	yes	—
643	C₄³	C₂²×C₂₃	1	2	yes	—
644	C₄³	C₂²×C₂₃	1	1	yes	characteristic
645	C₂×C₂₃	—	2	4	no	—
646	C₂×C₂₃	—	4	2	no	—
647	C₂×C₂₃	—	4	4	no	—
648	C₂×C₂₃	C₂×C₄×#41	1	1	yes	characteristic
649	C₂×C₂₃	C₂×C₄×#41	1	1	yes	characteristic
650	C₂×C₂₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
651	C₂×C₂₃	C₂×#553	1	1	yes	characteristic
652	C₂×C₂₃	#3475	1	1	yes	characteristic
653	C₂×C₂₃	#3480	1	1	yes	characteristic
654	C₂×C₂₃	#3481	1	1	yes	characteristic
655	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
656	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
657	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
658	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
659	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
660	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
661	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
662	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
663	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
664	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
665	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
666	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
667	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
668	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
669	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
670	#126	C₂×C₄×C₂₃	1	16	yes	complemented
671	#125	C₂×C₄×C₂₃	1	8	yes	complemented
672	#123	C₂×C₄×C₂₃	1	16	yes	complemented
673	#121	C₂×C₄×C₂₃	1	16	yes	complemented
674	#121	C₂×C₄×C₂₃	1	8	yes	complemented
675	#121	C₂×C₄×C₂₃	1	8	yes	complemented
676	C₄×D₄	—	2	8	no	—
677	C₄×D₄	—	2	4	no	—
678	C₄×D₄	—	2	4	no	—
679	C₄×D₄	—	2	8	no	—
680	C₄×D₄	—	2	4	no	—
681	C₄×D₄	—	2	4	no	—
682	C₄×D₄	—	4	4	no	—
683	C₄×D₄	C₂×C₄×C₂₃	1	16	yes	complemented
684	C₄×D₄	C₂×C₄×C₂₃	1	8	yes	complemented
685	C₄×D₄	C₂×C₄×C₂₃	1	8	yes	complemented
686	#117	—	2	4	no	—
687	#117	C₂×C₄×C₂₃	1	8	yes	complemented
688	C₂×C₄⋊C₄	—	2	4	no	—
689	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	8	yes	complemented
690	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
691	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
692	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
693	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
694	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
695	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
696	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
697	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
698	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
699	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
700	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
701	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
702	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
703	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
704	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
705	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
706	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
707	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
708	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
709	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
710	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
711	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
712	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
713	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
714	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
715	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
716	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
717	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
718	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
719	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
720	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
721	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
722	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
723	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
724	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
725	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
726	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
727	C₂×C₄²	—	2	4	no	—
728	C₂×C₄²	—	2	4	no	—
729	C₂×C₄²	—	4	4	no	—
730	C₂×C₄²	—	4	4	no	—
731	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
732	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
733	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
734	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
735	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
736	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
737	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
738	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
739	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
740	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
741	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
742	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
743	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
744	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
745	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
746	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
747	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
748	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
749	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
750	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
751	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
752	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
753	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
754	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
755	#95	C₂³×C₂₃	1	2	yes	—
756	#95	C₂³×C₂₃	1	2	yes	—
757	#95	C₂³×C₂₃	1	2	yes	—
758	#95	C₂³×C₂₃	1	2	yes	—
759	#95	C₂³×C₂₃	1	2	yes	—
760	#95	C₂³×C₂₃	1	2	yes	—
761	#95	C₂³×C₂₃	1	2	yes	—
762	#95	C₂³×C₂₃	1	1	yes	characteristic
763	#95	C₂³×C₂₃	1	1	yes	characteristic
764	#95	C₂³×C₂₃	1	2	yes	—
765	#95	C₂³×C₂₃	1	2	yes	—
766	#95	C₂³×C₂₃	1	1	yes	characteristic
767	#95	C₂³×C₂₃	1	2	yes	—
768	#95	C₂³×C₂₃	1	1	yes	characteristic
769	#95	C₂³×C₂₃	1	1	yes	characteristic
770	#95	C₂³×C₂₃	1	2	yes	—
771	#95	C₂³×C₂₃	1	2	yes	—
772	#95	C₂³×C₂₃	1	2	yes	—
773	#95	C₂³×C₂₃	1	1	yes	characteristic
774	#95	C₂³×C₂₃	1	2	yes	—
775	#95	C₂³×C₂₃	1	2	yes	—
776	#95	C₂³×C₂₃	1	2	yes	—
777	#95	C₂³×C₂₃	1	2	yes	—
778	C₂₃	C₄×#553	1	1	yes	characteristic, direct product factor, Sylow
779	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
780	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
781	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
782	C₂×D₄	—	2	4	no	—
783	C₂×D₄	—	2	2	no	—
784	C₂×D₄	—	2	2	no	—
785	C₂×D₄	—	2	4	no	—
786	C₂×D₄	—	2	2	no	—
787	C₂×D₄	—	2	2	no	—
788	C₂×D₄	—	4	2	no	—
789	C₂×D₄	—	4	2	no	—
790	C₂×D₄	C₂²×C₄×C₂₃	1	8	yes	—
791	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
792	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
793	C₂×D₄	C₂²×C₄×C₂₃	1	8	yes	—
794	C₂²×C₄	—	2	2	no	—
795	C₂²×C₄	—	2	2	no	—
796	C₂²×C₄	—	2	2	no	—
797	C₂²×C₄	—	2	2	no	—
798	C₂²×C₄	—	2	2	no	—
799	C₂²×C₄	—	2	2	no	—
800	C₂²×C₄	—	2	4	no	—
801	C₂²×C₄	—	2	2	no	—
802	C₂²×C₄	—	2	2	no	—
803	C₂²×C₄	—	2	2	no	—
804	C₂²×C₄	—	2	2	no	—
805	C₂²×C₄	—	2	4	no	—
806	C₂²×C₄	—	2	2	no	—
807	C₂²×C₄	—	2	4	no	—
808	C₂²×C₄	—	2	4	no	—
809	C₂²×C₄	—	2	2	no	—
810	C₂²×C₄	—	2	4	no	—
811	C₂²×C₄	—	2	4	no	—
812	C₂²×C₄	—	2	4	no	—
813	C₂²×C₄	—	2	2	no	—
814	C₂²×C₄	—	4	2	no	—
815	C₂²×C₄	—	4	2	no	—
816	C₂²×C₄	—	4	2	no	—
817	C₂²×C₄	—	4	2	no	—
818	C₂²×C₄	—	4	1	no	—
819	C₂²×C₄	—	4	2	no	—
820	C₂²×C₄	—	4	2	no	—
821	C₂²×C₄	—	4	1	no	—
822	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
823	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
824	C₂²×C₄	C₂²×C₄×C₂₃	1	8	yes	—
825	C₂²×C₄	C₂²×C₄×C₂₃	1	8	yes	—
826	C₂²×C₄	#41×C₂₃	1	4	yes	—
827	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
828	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
829	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
830	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
831	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
832	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
833	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
834	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
835	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
836	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
837	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
838	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
839	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
840	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
841	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
842	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
843	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
844	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
845	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
846	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
847	C₄⋊C₄	—	2	4	no	—
848	C₄⋊C₄	—	2	2	no	—
849	C₄⋊C₄	—	2	2	no	—
850	C₄⋊C₄	—	2	2	no	—
851	C₄⋊C₄	—	2	4	no	—
852	C₄⋊C₄	—	2	4	no	—
853	C₄⋊C₄	—	2	2	no	—
854	C₄⋊C₄	—	2	2	no	—
855	C₄⋊C₄	—	4	2	no	—
856	C₄⋊C₄	—	4	2	no	—
857	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
858	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
859	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
860	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
861	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
862	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
863	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
864	C₄⋊C₄	#41×C₂₃	1	4	yes	—
865	C₂²⋊C₄	—	2	2	no	—
866	C₂²⋊C₄	—	2	4	no	—
867	C₂²⋊C₄	—	2	4	no	—
868	C₂²⋊C₄	—	2	4	no	—
869	C₂²⋊C₄	—	2	2	no	—
870	C₂²⋊C₄	—	2	4	no	—
871	C₂²⋊C₄	—	2	4	no	—
872	C₂²⋊C₄	—	2	4	no	—
873	C₂²⋊C₄	—	2	2	no	—
874	C₂²⋊C₄	—	4	2	no	—
875	C₂²⋊C₄	—	4	2	no	—
876	C₂²⋊C₄	—	4	2	no	—
877	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
878	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
879	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
880	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
881	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
882	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
883	C₂²⋊C₄	#41×C₂₃	1	4	yes	—
884	C₄²	—	2	2	no	—
885	C₄²	—	2	2	no	—
886	C₄²	—	2	2	no	—
887	C₄²	—	2	2	no	—
888	C₄²	—	2	2	no	—
889	C₄²	—	2	2	no	—
890	C₄²	—	2	4	no	—
891	C₄²	—	2	4	no	—
892	C₄²	—	2	2	no	—
893	C₄²	—	2	4	no	—
894	C₄²	—	2	2	no	—
895	C₄²	—	2	2	no	—
896	C₄²	—	2	2	no	—
897	C₄²	—	2	4	no	—
898	C₄²	—	2	4	no	—
899	C₄²	—	4	2	no	—
900	C₄²	—	4	2	no	—
901	C₄²	—	4	2	no	—
902	C₄²	—	4	2	no	—
903	C₄²	—	4	2	no	—
904	C₄²	—	4	1	no	—
905	C₄²	C₂²×C₄×C₂₃	1	8	yes	—
906	C₄²	C₂²×C₄×C₂₃	1	4	yes	—
907	C₄²	#41×C₂₃	1	4	yes	—
908	C₂³	—	2	1	no	—
909	C₂³	—	2	1	no	—
910	C₂³	—	2	1	no	—
911	C₂³	—	2	1	no	—
912	C₂³	—	2	1	no	—
913	C₂³	—	2	2	no	—
914	C₂³	—	2	2	no	—
915	C₂³	—	2	1	no	—
916	C₂³	—	2	1	no	—
917	C₂³	—	2	2	no	—
918	C₂³	—	2	2	no	—
919	C₂³	—	2	1	no	—
920	C₂³	—	2	1	no	—
921	C₂³	—	2	2	no	—
922	C₂³	—	2	2	no	—
923	C₂³	—	2	1	no	—
924	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
925	C₂³	C₂³×C₄×C₂₃	1	4	yes	—
926	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
927	C₂³	C₂×#41×C₂₃	1	2	yes	—
928	C₂³	C₂×#41×C₂₃	1	2	yes	—
929	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
930	D₄	—	2	16	no	—
931	D₄	—	2	8	no	—
932	D₄	—	2	8	no	—
933	D₄	—	4	8	no	—
934	C₂×C₄	—	2	1	no	—
935	C₂×C₄	—	2	1	no	—
936	C₂×C₄	—	2	1	no	—
937	C₂×C₄	—	2	1	no	—
938	C₂×C₄	—	2	1	no	—
939	C₂×C₄	—	2	2	no	—
940	C₂×C₄	—	2	1	no	—
941	C₂×C₄	—	2	2	no	—
942	C₂×C₄	—	2	1	no	—
943	C₂×C₄	—	2	1	no	—
944	C₂×C₄	—	2	2	no	—
945	C₂×C₄	—	2	1	no	—
946	C₂×C₄	—	2	1	no	—
947	C₂×C₄	—	2	1	no	—
948	C₂×C₄	—	2	2	no	—
949	C₂×C₄	—	2	1	no	—
950	C₂×C₄	—	2	2	no	—
951	C₂×C₄	—	2	2	no	—
952	C₂×C₄	—	2	1	no	—
953	C₂×C₄	—	2	1	no	—
954	C₂×C₄	—	2	2	no	—
955	C₂×C₄	—	2	1	no	—
956	C₂×C₄	—	2	1	no	—
957	C₂×C₄	—	2	2	no	—
958	C₂×C₄	—	2	8	no	—
959	C₂×C₄	—	2	8	no	—
960	C₂×C₄	—	2	8	no	—
961	C₂×C₄	—	2	1	no	—
962	C₂×C₄	—	2	1	no	—
963	C₂×C₄	—	2	1	no	—
964	C₂×C₄	—	2	2	no	—
965	C₂×C₄	—	2	1	no	—
966	C₂×C₄	—	2	2	no	—
967	C₂×C₄	—	2	2	no	—
968	C₂×C₄	—	2	1	no	—
969	C₂×C₄	—	2	2	no	—
970	C₂×C₄	—	2	1	no	—
971	C₂×C₄	—	2	2	no	—
972	C₂×C₄	—	2	2	no	—
973	C₂×C₄	—	2	2	no	—
974	C₂×C₄	—	2	2	no	—
975	C₂×C₄	—	2	1	no	—
976	C₂×C₄	—	2	2	no	—
977	C₂×C₄	—	2	1	no	—
978	C₂×C₄	—	2	1	no	—
979	C₂×C₄	—	4	8	no	—
980	C₂×C₄	—	4	8	no	—
981	C₂×C₄	—	4	4	no	—
982	C₂×C₄	—	4	8	no	—
983	C₂×C₄	—	4	4	no	—
984	C₂×C₄	—	4	8	no	—
985	C₂×C₄	—	4	4	no	—
986	C₂×C₄	—	4	8	no	—
987	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
988	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
989	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
990	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
991	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
992	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
993	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
994	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
995	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
996	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
997	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
998	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
999	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
1000	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
1001	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
1002	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
1003	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
1004	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
1005	C₂²	—	2	2	no	—
1006	C₂²	—	2	2	no	—
1007	C₂²	—	2	2	no	—
1008	C₂²	—	2	2	no	—
1009	C₂²	—	2	2	no	—
1010	C₂²	—	2	2	no	—
1011	C₂²	—	2	2	no	—
1012	C₂²	—	2	2	no	—
1013	C₂²	—	2	4	no	—
1014	C₂²	—	2	4	no	—
1015	C₂²	—	2	4	no	—
1016	C₂²	—	2	2	no	—
1017	C₂²	—	4	2	no	—
1018	C₂²	—	4	1	no	—
1019	C₂²	—	4	1	no	—
1020	C₂²	—	4	2	no	—
1021	C₂²	—	4	1	no	—
1022	C₂²	—	4	2	no	—
1023	C₂²	—	4	2	no	—
1024	C₂²	—	4	1	no	—
1025	C₂²	C₄×#41×C₂₃	1	4	yes	—
1026	C₂²	C₂⁴×C₄×C₂₃	1	1	yes	characteristic
1027	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
1028	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
1029	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
1030	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
1031	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1032	C₂²	C₂₃×#585	1	1	yes	characteristic
1033	C₄	—	2	2	no	—
1034	C₄	—	2	2	no	—
1035	C₄	—	2	4	no	—
1036	C₄	—	2	2	no	—
1037	C₄	—	2	2	no	—
1038	C₄	—	2	4	no	—
1039	C₄	—	2	4	no	—
1040	C₄	—	2	2	no	—
1041	C₄	—	2	2	no	—
1042	C₄	—	2	2	no	—
1043	C₄	—	2	2	no	—
1044	C₄	—	2	4	no	—
1045	C₄	—	4	1	no	—
1046	C₄	—	4	2	no	—
1047	C₄	—	4	1	no	—
1048	C₄	—	4	1	no	—
1049	C₄	—	4	2	no	—
1050	C₄	—	4	2	no	—
1051	C₄	C₄×#41×C₂₃	1	4	yes	—
1052	C₄	C₂₃×#553	1	4	yes	direct product factor
1053	C₂	—	2	4	no	—
1054	C₂	—	4	2	no	—
1055	C₂	—	4	4	no	—
1056	C₂	C₂×C₄×#41×C₂₃	1	1	yes	characteristic
1057	C₂	C₂×C₄×#41×C₂₃	1	1	yes	characteristic
1058	C₂	C₄×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1059	C₂	C₂×C₂₃×#553	1	1	yes	characteristic
1060	C₂	C₂₃×#3475	1	1	yes	characteristic
1061	C₂	C₂₃×#3480	1	1	yes	characteristic
1062	C₂	C₂₃×#3481	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₂₃	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₂₃
Frattini, cosocle	C₂³	C₂⁵×C₂₃
socle	C₂³×C₂₃	C₂⁵
prime radical	C₂×C₂₃×#553	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₃×#2374	C₂	semidirect
3. C₂₃×#2373	C₂	semidirect
4. C₂₃×#2370	C₂	semidirect
5. C₂₃×#2364	C₂	semidirect
6. C₂₃×#2363	C₂	semidirect
7. C₂₃×#2361	C₂	semidirect
8. C₂₃×#2357	C₂	semidirect
9. C₂₃×#2353	C₂	semidirect
10. C₂₃×#2352	C₂	semidirect
11. C₂₃×#2347	C₂	semidirect
12. C₂₃×#2345	C₂	semidirect
13. C₄×C₂₃×#125	C₂	semidirect
14. C₄×C₂₃×#126	C₂	semidirect
15. C₄×C₂₃×#123	C₂	semidirect
16. C₄×C₂₃×#121	C₂	semidirect
17. C₄×C₂₃×#121	C₂	semidirect
18. C₄×C₂₃×#121	C₂	semidirect
19. C₄²×D₄×C₂₃	C₂	semidirect
20. C₄²×D₄×C₂₃	C₂	semidirect
21. C₄²×D₄×C₂₃	C₂	semidirect
22. C₄×C₂₃×#117	C₂	semidirect
23. C₂×C₄×C₄⋊C₄×C₂₃	C₂	semidirect
24. C₂₃×#553	C₄	direct (N × H)
139. C₂₃×#126	C₂×C₄	semidirect
140. C₂₃×#125	C₂×C₄	semidirect
141. C₂₃×#123	C₂×C₄	semidirect
142. C₂₃×#121	C₂×C₄	semidirect
143. C₂₃×#121	C₂×C₄	semidirect
144. C₂₃×#121	C₂×C₄	semidirect
152. C₄×D₄×C₂₃	C₂×C₄	semidirect
153. C₄×D₄×C₂₃	C₂×C₄	semidirect
154. C₄×D₄×C₂₃	C₂×C₄	semidirect
156. C₂₃×#117	C₂×C₄	semidirect
158. C₂×C₄⋊C₄×C₂₃	C₂×C₄	semidirect
376. C₄×#553	C₂₃	direct (N × H)
475. #2374	C₂×C₂₃	semidirect
476. #2373	C₂×C₂₃	semidirect
477. #2370	C₂×C₂₃	semidirect
478. #2364	C₂×C₂₃	semidirect
479. #2363	C₂×C₂₃	semidirect
480. #2361	C₂×C₂₃	semidirect
481. #2357	C₂×C₂₃	semidirect
482. #2353	C₂×C₂₃	semidirect
483. #2352	C₂×C₂₃	semidirect
484. #2347	C₂×C₂₃	semidirect
485. #2345	C₂×C₂₃	semidirect
486. C₄×#125	C₂×C₂₃	semidirect
487. C₄×#126	C₂×C₂₃	semidirect
488. C₄×#123	C₂×C₂₃	semidirect
489. C₄×#121	C₂×C₂₃	semidirect
490. C₄×#121	C₂×C₂₃	semidirect
491. C₄×#121	C₂×C₂₃	semidirect
492. C₄²×D₄	C₂×C₂₃	semidirect
493. C₄²×D₄	C₂×C₂₃	semidirect
494. C₄²×D₄	C₂×C₂₃	semidirect
495. C₄×#117	C₂×C₂₃	semidirect
496. C₂×C₄×C₄⋊C₄	C₂×C₂₃	semidirect
544. C₄×C₂₃	#553	direct (N × H)
545. #553	C₄×C₂₃	direct (N × H)
670. #126	C₂×C₄×C₂₃	semidirect
671. #125	C₂×C₄×C₂₃	semidirect
672. #123	C₂×C₄×C₂₃	semidirect
673. #121	C₂×C₄×C₂₃	semidirect
674. #121	C₂×C₄×C₂₃	semidirect
675. #121	C₂×C₄×C₂₃	semidirect
683. C₄×D₄	C₂×C₄×C₂₃	semidirect
684. C₄×D₄	C₂×C₄×C₂₃	semidirect
685. C₄×D₄	C₂×C₄×C₂₃	semidirect
687. #117	C₂×C₄×C₂₃	semidirect
689. C₂×C₄⋊C₄	C₂×C₄×C₂₃	semidirect
778. C₂₃	C₄×#553	direct (N × H)
1052. C₄	C₂₃×#553	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×#553	2
C₂₃×#2374	2
C₂₃×#2373	2
C₂₃×#2370	2
C₂₃×#2364	2
C₂₃×#2363	2
C₂₃×#2361	2
C₂₃×#2357	2
C₂₃×#2353	2
C₂₃×#2352	2
C₂₃×#2347	2
C₂₃×#2345	2
C₄×C₂₃×#125	2
C₄×C₂₃×#126	2
C₄×C₂₃×#123	2
C₄×C₂₃×#121	2
C₄²×D₄×C₂₃	2
C₄×C₂₃×#117	2
C₂×C₄×C₄⋊C₄×C₂₃	2
C₄×#553	23

Subgroups — C4×C23×#553 #19181790

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₂₃×#553 #19181790