Subgroups — #14415742

Order 1920.

1088 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#6710	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₄×C₂²⋊D₅	C₂	1	1	yes	maximal, characteristic
3	C₂×D₅×#208	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5207	C₂	1	1	yes	maximal, characteristic, complemented
5	#11748507	C₂	1	2	yes	maximal, complemented
6	#11748494	C₂	1	2	yes	maximal, complemented
7	#11748493	C₂	1	2	yes	maximal, complemented
8	#11748431	C₂	1	1	yes	maximal, characteristic, complemented
9	#11748341	C₂	1	1	yes	maximal, characteristic, complemented
10	#11748339	C₂	1	2	yes	maximal, complemented
11	Dic₅×#208	C₂	1	1	yes	maximal, characteristic, complemented
12	#10610359	—	3	1	no	maximal, Hall
13	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₂²⋊D₅	C₄	1	1	yes	characteristic
15	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
16	C₂×#6710	—	2	4	no	—
17	C₂×#6710	C₂²	1	1	yes	characteristic
18	C₂×#6710	C₂²	1	1	yes	characteristic
19	C₂×#6710	C₂²	1	2	yes	complemented
20	C₂²×C₃⋊#168	C₂²	1	2	yes	complemented
21	C₂×C₅×#208	C₂²	1	1	yes	characteristic
22	C₂×C₅×#208	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₂²⋊Dic₅	C₄	1	1	yes	characteristic
24	C₃×C₄×C₂²⋊D₅	C₄	1	1	yes	characteristic
25	C₃×C₄×C₂²⋊D₅	C₄	1	1	yes	characteristic
26	C₃×C₄×C₂²⋊D₅	C₄	1	1	yes	characteristic
27	C₃×C₄×C₂²⋊D₅	C₄	1	1	yes	characteristic
28	C₃×C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
29	C₃×C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
30	C₃×C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
31	C₃×C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
32	C₂×C₃×#685	C₄	1	1	yes	characteristic
33	C₂×C₃×#683	C₄	1	1	yes	characteristic
34	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
35	C₂×#6649	C₂²	1	2	yes	complemented
36	D₅×#208	—	2	4	no	—
37	C₂×D₅×C₃⋊C₈	C₂²	1	2	yes	complemented
38	C₅×#830	C₂²	1	2	yes	complemented
39	C₅×#830	C₂²	1	2	yes	complemented
40	#90982	C₂²	1	2	yes	complemented
41	#90982	C₂²	1	2	yes	complemented
42	#90955	C₂²	1	2	yes	complemented
43	#90955	C₂²	1	2	yes	complemented
44	#90952	C₂²	1	2	yes	complemented
45	Dic₅×C₃⋊C₈	C₂²	1	2	yes	complemented
46	D₄×#208	—	5	1	no	maximal, Hall
47	C₂×C₄×C₂²⋊D₅	D₃	1	1	yes	characteristic
48	C₂²×#681	—	3	1	no	—
49	C₂×D₅×M₁₆	—	3	1	no	—
50	C₅×#407	—	3	1	no	—
51	#65415	—	3	1	no	—
52	#65407	—	3	1	no	—
53	M₁₆×Dic₅	—	3	1	no	—
54	#65019	—	3	2	no	—
55	#65018	—	3	2	no	—
56	#65017	—	3	2	no	—
57	#65014	—	3	2	no	—
58	C₂⁴×C₃×C₅	C₂×C₄	1	1	yes	characteristic
59	C₂³×C₃×D₅	C₂×C₄	1	1	yes	characteristic
60	C₂²×C₃×C₄×C₅	—	2	2	no	—
61	C₂²×C₃×C₄×C₅	—	2	2	no	—
62	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
63	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
64	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
65	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
66	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
67	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
68	C₂×C₃×C₂²⋊D₅	—	2	4	no	—
69	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
70	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
71	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
72	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
73	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
74	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
75	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
76	C₂×C₃×C₄×D₅	—	2	2	no	—
77	C₂×C₃×C₄×D₅	—	2	2	no	—
78	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
79	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
80	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
81	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
82	#6710	—	2	2	no	—
83	#6710	—	2	4	no	—
84	#6710	D₄	1	4	yes	complemented
85	C₂×C₃⋊#168	—	2	4	no	—
86	C₂×C₃⋊#168	C₂³	1	2	yes	—
87	C₂×C₃⋊#168	C₂³	1	2	yes	—
88	C₅×#208	—	2	2	no	—
89	C₅×#208	—	2	2	no	—
90	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
91	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
92	C₃×C₂²⋊Dic₅	C₂×C₄	1	1	yes	characteristic
93	C₃×C₂²⋊Dic₅	C₂×C₄	1	1	yes	characteristic
94	C₃×C₂²⋊Dic₅	C₂×C₄	1	1	yes	characteristic
95	C₃×C₂²⋊Dic₅	C₂×C₄	1	1	yes	characteristic
96	C₃×#685	C₂×C₄	1	1	yes	characteristic
97	C₃×#685	C₂×C₄	1	1	yes	characteristic
98	C₃×#685	C₂×C₄	1	1	yes	characteristic
99	C₃×#685	C₂×C₄	1	1	yes	characteristic
100	C₃×#683	C₂×C₄	1	1	yes	characteristic
101	C₃×#683	C₂×C₄	1	1	yes	characteristic
102	C₃×#683	C₂×C₄	1	1	yes	characteristic
103	C₃×#683	C₂×C₄	1	1	yes	characteristic
104	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
105	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
106	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
107	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
108	#6649	—	2	4	no	—
109	D₅×C₃⋊C₈	—	2	4	no	—
110	C₂×C₃×C₄×D₄	—	5	1	no	—
111	C₂²×#208	—	5	1	no	—
112	C₂²×#208	—	5	1	no	—
113	#5207	—	5	1	no	—
114	#5207	D₅	1	1	yes	characteristic, complemented
115	#5012	—	5	2	no	—
116	#5011	—	5	2	no	—
117	#5011	—	5	2	no	—
118	D₄×C₃⋊C₈	—	5	2	no	—
119	#4924	—	5	1	no	—
120	C₄×#208	—	5	1	no	—
121	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
122	C₂²×C₂²⋊D₅	Dic₃	1	1	yes	characteristic
123	C₂²×C₄×D₅	C₂×D₃	1	1	yes	characteristic
124	C₂×C₅×M₁₆	—	3	1	no	—
125	C₂×C₅×M₁₆	—	3	1	no	—
126	C₂×C₂²⋊Dic₅	Dic₃	1	1	yes	characteristic
127	C₄×C₂²⋊D₅	Dic₃	1	1	yes	characteristic
128	C₄×C₂²⋊D₅	Dic₃	1	1	yes	characteristic
129	C₄×C₂²⋊D₅	Dic₃	1	1	yes	characteristic
130	C₄×C₂²⋊D₅	Dic₃	1	1	yes	characteristic
131	C₄×C₂²⋊D₅	C₂×D₃	1	1	yes	characteristic
132	C₄×C₂²⋊D₅	C₂×D₃	1	1	yes	characteristic
133	C₄×C₂²⋊D₅	C₂×D₃	1	1	yes	characteristic
134	C₄×C₂²⋊D₅	C₂×D₃	1	1	yes	characteristic
135	C₂×#685	Dic₃	1	1	yes	characteristic
136	C₂×#683	Dic₃	1	1	yes	characteristic
137	C₂×C₄×Dic₅	C₂×D₃	1	1	yes	characteristic
138	C₂×#681	—	3	1	no	—
139	C₂×#681	—	3	1	no	—
140	C₂×#681	—	3	2	no	—
141	C₂×#681	—	6	4	no	—
142	C₂²×#168	—	3	2	no	—
143	D₅×M₁₆	—	6	4	no	—
144	C₂×#676	—	3	2	no	—
145	C₂×C₈×D₅	—	3	2	no	—
146	C₅×C₂²⋊C₈	—	3	2	no	—
147	C₅×C₂²⋊C₈	—	3	2	no	—
148	#3952	—	3	2	no	—
149	#3952	—	3	2	no	—
150	#3947	—	3	2	no	—
151	#3946	—	3	2	no	—
152	#3946	—	3	2	no	—
153	C₈×Dic₅	—	3	2	no	—
154	D₄×M₁₆	—	15	1	no	Sylow
155	C₂³×C₃×C₅	—	2	2	no	—
156	C₂³×C₃×C₅	—	2	2	no	—
157	C₂³×C₃×C₅	—	4	1	no	—
158	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
159	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
160	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
161	C₂²×C₃×D₅	—	2	2	no	—
162	C₂²×C₃×D₅	—	2	2	no	—
163	C₂²×C₃×D₅	—	4	1	no	—
164	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
165	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
166	C₂×C₃×C₄×C₅	—	2	2	no	—
167	C₂×C₃×C₄×C₅	—	2	2	no	—
168	C₂×C₃×C₄×C₅	—	2	2	no	—
169	C₂×C₃×C₄×C₅	—	2	1	no	—
170	C₂×C₃×C₄×C₅	—	2	1	no	—
171	C₂×C₃×C₄×C₅	—	2	1	no	—
172	C₂×C₃×C₄×C₅	—	2	1	no	—
173	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
174	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
175	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
176	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
177	C₂×C₃×C₄×C₅	#41	1	2	yes	—
178	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
179	C₃×C₂²⋊D₅	—	2	2	no	—
180	C₃×C₂²⋊D₅	—	2	2	no	—
181	C₃×C₂²⋊D₅	—	2	2	no	—
182	C₃×C₂²⋊D₅	M₁₆	1	4	yes	complemented
183	C₂×C₃×Dic₅	—	2	2	no	—
184	C₂×C₃×Dic₅	—	2	2	no	—
185	C₂×C₃×Dic₅	—	4	1	no	—
186	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
187	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
188	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
189	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
190	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
191	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
192	C₃×C₄×D₅	—	2	2	no	—
193	C₃×C₄×D₅	—	2	2	no	—
194	C₃×C₄×D₅	—	2	1	no	—
195	C₃×C₄×D₅	—	2	1	no	—
196	C₃×C₄×D₅	—	2	1	no	—
197	C₃×C₄×D₅	—	2	1	no	—
198	C₃⋊#168	—	2	2	no	—
199	C₃⋊#168	C₂×D₄	1	4	yes	complemented
200	C₅×C₃⋊C₈	—	2	2	no	—
201	C₅×C₃⋊C₈	—	2	2	no	—
202	C₂²×C₃×D₄	—	5	1	no	—
203	C₂³×C₃×C₄	—	5	1	no	—
204	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
205	C₃×C₄×D₄	—	5	1	no	—
206	C₃×C₄×D₄	—	5	1	no	—
207	C₃×C₄×D₄	—	5	1	no	—
208	C₃×C₄×D₄	—	5	1	no	—
209	C₃×C₄×D₄	—	5	1	no	—
210	C₃×C₄×D₄	—	5	1	no	—
211	C₃×C₄×D₄	—	5	1	no	—
212	C₃×C₄×D₄	—	5	1	no	—
213	C₂×C₃×C₄⋊C₄	—	5	1	no	—
214	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
215	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
216	C₂×C₃×C₄²	—	5	1	no	—
217	C₂×#208	—	5	1	no	—
218	C₂×#208	—	5	1	no	—
219	C₂×#208	—	5	2	no	—
220	C₂×#208	—	5	2	no	—
221	C₂×#208	—	10	4	no	—
222	C₂×#208	—	10	4	no	—
223	C₂×#208	C₂×D₅	1	1	yes	characteristic
224	C₂×#208	C₂×D₅	1	1	yes	characteristic
225	C₂²×C₃⋊C₈	—	5	2	no	—
226	C₂²×C₃⋊C₈	—	5	2	no	—
227	#830	—	5	2	no	—
228	#830	—	5	2	no	—
229	#830	C₂×D₅	1	2	yes	complemented
230	#830	C₂×D₅	1	2	yes	complemented
231	C₄⋊(C₃⋊C₈)	—	5	2	no	—
232	C₄⋊(C₃⋊C₈)	—	5	2	no	—
233	#803	—	5	2	no	—
234	C₄×C₃⋊C₈	—	5	2	no	—
235	C₂⁴×C₅	C₂×Dic₃	1	1	yes	characteristic
236	C₂³×D₅	C₂×Dic₃	1	1	yes	characteristic
237	C₂²×C₄×C₅	—	2	2	no	—
238	C₂²×C₄×C₅	—	2	2	no	—
239	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
240	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
241	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
242	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
243	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
244	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
245	C₂×C₂²⋊D₅	—	2	4	no	—
246	C₂×C₂²⋊D₅	C₂×Dic₃	1	1	yes	characteristic
247	C₂×C₂²⋊D₅	C₂×Dic₃	1	1	yes	characteristic
248	C₂×C₂²⋊D₅	C₂×Dic₃	1	1	yes	characteristic
249	C₂×C₂²⋊D₅	C₂×Dic₃	1	1	yes	characteristic
250	C₂²×Dic₅	C₂×Dic₃	1	1	yes	characteristic
251	C₂²×Dic₅	C₂×Dic₃	1	1	yes	characteristic
252	C₂²×Dic₅	C₂×Dic₃	1	1	yes	characteristic
253	C₂×C₄×D₅	—	2	2	no	—
254	C₂×C₄×D₅	—	2	2	no	—
255	C₂×C₄×D₅	C₂×Dic₃	1	1	yes	characteristic
256	C₂×C₄×D₅	C₂×Dic₃	1	1	yes	characteristic
257	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
258	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
259	C₅×M₁₆	—	6	2	no	—
260	C₅×M₁₆	—	6	2	no	—
261	C₂×C₅×C₈	—	3	2	no	—
262	C₂×C₅×C₈	—	3	2	no	—
263	C₂²⋊Dic₅	C₂×Dic₃	1	1	yes	characteristic
264	C₂²⋊Dic₅	C₂×Dic₃	1	1	yes	characteristic
265	C₂²⋊Dic₅	C₂×Dic₃	1	1	yes	characteristic
266	C₂²⋊Dic₅	C₂×Dic₃	1	1	yes	characteristic
267	#685	C₂×Dic₃	1	1	yes	characteristic
268	#685	C₂×Dic₃	1	1	yes	characteristic
269	#685	C₂×Dic₃	1	1	yes	characteristic
270	#685	C₂×Dic₃	1	1	yes	characteristic
271	#683	C₂×Dic₃	1	1	yes	characteristic
272	#683	C₂×Dic₃	1	1	yes	characteristic
273	#683	C₂×Dic₃	1	1	yes	characteristic
274	#683	C₂×Dic₃	1	1	yes	characteristic
275	C₄×Dic₅	C₂×Dic₃	1	1	yes	characteristic
276	C₄×Dic₅	C₂×Dic₃	1	1	yes	characteristic
277	C₄×Dic₅	C₂²×D₃	1	1	yes	characteristic
278	C₄×Dic₅	C₂²×D₃	1	1	yes	characteristic
279	#681	—	3	4	no	—
280	#681	—	6	4	no	—
281	#681	—	6	2	no	—
282	C₂×#168	—	3	2	no	—
283	C₂×#168	—	3	2	no	—
284	C₂×#168	—	6	4	no	—
285	#676	—	6	4	no	—
286	C₈×D₅	—	6	4	no	—
287	C₂²×M₁₆	—	15	1	no	—
288	C₂²×M₁₆	—	15	1	no	—
289	C₂×C₄×D₄	—	5	1	no	—
290	#436	—	15	2	no	—
291	#435	—	15	2	no	—
292	#435	—	15	2	no	—
293	C₈×D₄	—	15	2	no	—
294	#423	—	15	1	no	—
295	#407	—	3	1	no	—
296	#407	—	15	1	no	—
297	C₄×M₁₆	—	15	1	no	—
298	C₂²×C₃×C₅	—	2	1	no	—
299	C₂²×C₃×C₅	—	2	1	no	—
300	C₂²×C₃×C₅	—	2	1	no	—
301	C₂²×C₃×C₅	—	2	1	no	—
302	C₂²×C₃×C₅	—	2	1	no	—
303	C₂²×C₃×C₅	—	2	1	no	—
304	C₂²×C₃×C₅	—	2	1	no	—
305	C₂²×C₃×C₅	—	4	4	no	—
306	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
307	C₂²×C₃×C₅	C₂×M₁₆	1	2	yes	complemented
308	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
309	C₂×C₃×D₅	—	2	1	no	—
310	C₂×C₃×D₅	—	2	1	no	—
311	C₂×C₃×D₅	—	2	1	no	—
312	C₂×C₃×D₅	—	2	1	no	—
313	C₂×C₃×D₅	—	2	1	no	—
314	C₂×C₃×D₅	—	4	4	no	—
315	C₂×C₃×D₅	C₂×M₁₆	1	2	yes	complemented
316	C₃×C₄×C₅	—	2	1	no	—
317	C₃×C₄×C₅	—	2	1	no	—
318	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
319	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
320	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
321	C₃×Dic₅	—	2	1	no	—
322	C₃×Dic₅	—	2	1	no	—
323	C₃×Dic₅	—	2	1	no	—
324	C₃×Dic₅	—	2	1	no	—
325	C₃×Dic₅	—	2	1	no	—
326	C₃×Dic₅	C₂×M₁₆	1	2	yes	complemented
327	C₂⁴×C₃	—	5	1	no	—
328	C₂⁴×C₃	C₄×D₅	1	1	yes	characteristic
329	C₂×C₃×D₄	—	5	1	no	—
330	C₂×C₃×D₄	—	5	1	no	—
331	C₂×C₃×D₄	—	5	1	no	—
332	C₂×C₃×D₄	—	5	1	no	—
333	C₂×C₃×D₄	—	10	4	no	—
334	C₂²×C₃×C₄	—	2	2	no	—
335	C₂²×C₃×C₄	—	2	2	no	—
336	C₂²×C₃×C₄	—	5	1	no	—
337	C₂²×C₃×C₄	—	5	1	no	—
338	C₂²×C₃×C₄	—	5	1	no	—
339	C₂²×C₃×C₄	—	5	1	no	—
340	C₂²×C₃×C₄	—	5	1	no	—
341	C₂²×C₃×C₄	—	5	1	no	—
342	C₂²×C₃×C₄	—	5	1	no	—
343	C₂²×C₃×C₄	—	10	2	no	—
344	C₂²×C₃×C₄	—	10	2	no	—
345	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
346	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
347	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
348	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
349	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
350	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
351	C₃×C₄⋊C₄	—	5	1	no	—
352	C₃×C₄⋊C₄	—	5	1	no	—
353	C₃×C₄⋊C₄	—	5	1	no	—
354	C₃×C₄⋊C₄	—	5	1	no	—
355	C₃×C₂²⋊C₄	—	5	1	no	—
356	C₃×C₂²⋊C₄	—	5	1	no	—
357	C₃×C₂²⋊C₄	—	5	1	no	—
358	C₃×C₂²⋊C₄	—	5	1	no	—
359	C₃×C₂²⋊C₄	—	5	1	no	—
360	C₃×C₂²⋊C₄	—	5	1	no	—
361	C₃×C₂²⋊C₄	—	5	1	no	—
362	C₃×C₂²⋊C₄	—	5	1	no	—
363	C₃×C₄²	—	5	1	no	—
364	C₃×C₄²	—	5	1	no	—
365	C₃×C₄²	—	5	1	no	—
366	C₃×C₄²	—	5	1	no	—
367	#208	—	2	2	no	—
368	#208	—	2	2	no	—
369	#208	—	5	4	no	—
370	#208	—	10	4	no	—
371	#208	—	10	4	no	—
372	#208	—	10	2	no	—
373	C₂×C₃⋊C₈	—	5	2	no	—
374	C₂×C₃⋊C₈	—	5	2	no	—
375	C₂×C₃⋊C₈	—	10	4	no	—
376	C₂×C₃⋊C₈	—	10	4	no	—
377	C₂×C₃⋊C₈	C₂²×D₅	1	2	yes	—
378	C₂×C₃⋊C₈	C₂²×D₅	1	2	yes	—
379	C₂³×C₅	—	2	2	no	—
380	C₂³×C₅	—	2	2	no	—
381	C₂³×C₅	—	4	1	no	—
382	C₂³×C₅	C₂²×Dic₃	1	1	yes	characteristic
383	C₂³×C₅	C₂²×Dic₃	1	1	yes	characteristic
384	C₂³×C₅	C₂²×Dic₃	1	1	yes	characteristic
385	C₂²×D₅	—	2	2	no	—
386	C₂²×D₅	—	2	2	no	—
387	C₂²×D₅	—	4	1	no	—
388	C₂²×D₅	C₂²×Dic₃	1	1	yes	characteristic
389	C₂²×D₅	C₂²×Dic₃	1	1	yes	characteristic
390	C₂×C₄×C₅	—	2	2	no	—
391	C₂×C₄×C₅	—	2	2	no	—
392	C₂×C₄×C₅	—	2	2	no	—
393	C₂×C₄×C₅	—	2	1	no	—
394	C₂×C₄×C₅	—	2	1	no	—
395	C₂×C₄×C₅	—	2	1	no	—
396	C₂×C₄×C₅	—	2	1	no	—
397	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
398	C₂×C₄×C₅	#237	1	2	yes	—
399	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
400	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
401	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
402	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
403	C₂²⋊D₅	—	2	2	no	—
404	C₂²⋊D₅	—	2	2	no	—
405	C₂²⋊D₅	—	2	2	no	—
406	C₂²⋊D₅	#208	1	4	yes	complemented
407	C₂×Dic₅	—	2	2	no	—
408	C₂×Dic₅	—	2	2	no	—
409	C₂×Dic₅	—	4	1	no	—
410	C₂×Dic₅	C₂²×Dic₃	1	1	yes	characteristic
411	C₂×Dic₅	C₂²×Dic₃	1	1	yes	characteristic
412	C₂×Dic₅	C₂²×Dic₃	1	1	yes	characteristic
413	C₂×Dic₅	C₂²×Dic₃	1	1	yes	characteristic
414	C₂×Dic₅	C₂²×Dic₃	1	1	yes	characteristic
415	C₂×Dic₅	C₂²×Dic₃	1	1	yes	characteristic
416	C₄×D₅	—	2	2	no	—
417	C₄×D₅	—	2	2	no	—
418	C₄×D₅	—	2	1	no	—
419	C₄×D₅	—	2	1	no	—
420	C₄×D₅	—	2	1	no	—
421	C₄×D₅	—	2	1	no	—
422	C₅×C₈	—	6	2	no	—
423	C₅×C₈	—	6	2	no	—
424	#168	—	3	4	no	—
425	#168	—	6	2	no	—
426	C₂²×D₄	—	5	1	no	—
427	C₂³×C₄	—	5	1	no	—
428	C₂³×C₄	D₃×D₅	1	1	yes	characteristic
429	C₂×M₁₆	—	3	1	no	—
430	C₂×M₁₆	—	3	1	no	—
431	C₂×M₁₆	—	15	2	no	—
432	C₂×M₁₆	—	15	1	no	—
433	C₂×M₁₆	—	15	1	no	—
434	C₂×M₁₆	—	15	2	no	—
435	C₂×M₁₆	—	30	4	no	—
436	C₂×M₁₆	—	30	4	no	—
437	C₂²×C₈	—	15	2	no	—
438	C₂²×C₈	—	15	2	no	—
439	C₄×D₄	—	5	1	no	—
440	C₄×D₄	—	5	1	no	—
441	C₄×D₄	—	5	1	no	—
442	C₄×D₄	—	5	1	no	—
443	C₄×D₄	—	5	1	no	—
444	C₄×D₄	—	5	1	no	—
445	C₄×D₄	—	5	1	no	—
446	C₄×D₄	—	5	1	no	—
447	C₂×C₄⋊C₄	—	5	1	no	—
448	C₂×C₂²⋊C₄	—	5	1	no	—
449	C₂×C₂²⋊C₄	—	5	1	no	—
450	C₂×C₄²	—	5	1	no	—
451	C₄⋊C₈	—	15	2	no	—
452	C₄⋊C₈	—	15	2	no	—
453	C₂²⋊C₈	—	3	2	no	—
454	C₂²⋊C₈	—	3	2	no	—
455	C₂²⋊C₈	—	15	2	no	—
456	C₂²⋊C₈	—	15	2	no	—
457	#97	—	15	2	no	—
458	C₄×C₈	—	15	2	no	—
459	C₂×C₃×C₅	—	2	2	no	—
460	C₂×C₃×C₅	—	2	2	no	—
461	C₂×C₃×C₅	—	4	1	no	—
462	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
463	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
464	C₂×C₃×C₅	#568	1	1	yes	characteristic
465	C₃×D₅	—	2	2	no	—
466	C₃×D₅	—	4	1	no	—
467	C₂³×C₃	—	2	2	no	—
468	C₂³×C₃	—	2	2	no	—
469	C₂³×C₃	—	4	1	no	—
470	C₂³×C₃	—	5	1	no	—
471	C₂³×C₃	—	5	1	no	—
472	C₂³×C₃	—	10	2	no	—
473	C₂³×C₃	—	10	2	no	—
474	C₂³×C₃	—	20	1	no	—
475	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
476	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
477	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
478	C₃×D₄	—	5	4	no	—
479	C₃×D₄	—	10	2	no	—
480	C₃×D₄	—	10	2	no	—
481	C₃×D₄	—	10	2	no	—
482	C₂×C₃×C₄	—	2	2	no	—
483	C₂×C₃×C₄	—	2	1	no	—
484	C₂×C₃×C₄	—	2	1	no	—
485	C₂×C₃×C₄	—	2	1	no	—
486	C₂×C₃×C₄	—	2	1	no	—
487	C₂×C₃×C₄	—	2	2	no	—
488	C₂×C₃×C₄	—	2	2	no	—
489	C₂×C₃×C₄	—	5	1	no	—
490	C₂×C₃×C₄	—	5	1	no	—
491	C₂×C₃×C₄	—	5	1	no	—
492	C₂×C₃×C₄	—	5	1	no	—
493	C₂×C₃×C₄	—	5	1	no	—
494	C₂×C₃×C₄	—	5	1	no	—
495	C₂×C₃×C₄	—	10	2	no	—
496	C₂×C₃×C₄	—	10	2	no	—
497	C₂×C₃×C₄	—	10	1	no	—
498	C₂×C₃×C₄	—	10	1	no	—
499	C₂×C₃×C₄	—	10	1	no	—
500	C₂×C₃×C₄	—	10	1	no	—
501	C₂×C₃×C₄	—	10	2	no	—
502	C₂×C₃×C₄	—	10	2	no	—
503	C₂×C₃×C₄	—	20	1	no	—
504	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
505	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
506	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
507	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
508	C₂×C₃×C₄	#711	1	2	yes	—
509	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
510	C₃⋊C₈	—	2	2	no	—
511	C₃⋊C₈	—	2	2	no	—
512	C₃⋊C₈	—	5	4	no	—
513	C₃⋊C₈	—	10	2	no	—
514	C₂²×C₅	—	2	1	no	—
515	C₂²×C₅	—	2	1	no	—
516	C₂²×C₅	—	2	1	no	—
517	C₂²×C₅	—	2	1	no	—
518	C₂²×C₅	—	2	1	no	—
519	C₂²×C₅	—	2	1	no	—
520	C₂²×C₅	—	2	1	no	—
521	C₂²×C₅	—	4	4	no	—
522	C₂²×C₅	C₂×#208	1	2	yes	complemented
523	C₂²×C₅	D₄×Dic₃	1	2	yes	—
524	C₂²×C₅	C₂³×Dic₃	1	1	yes	characteristic
525	C₂×D₅	—	2	1	no	—
526	C₂×D₅	—	2	1	no	—
527	C₂×D₅	—	2	1	no	—
528	C₂×D₅	—	2	1	no	—
529	C₂×D₅	—	2	1	no	—
530	C₂×D₅	—	4	4	no	—
531	C₂×D₅	C₂×#208	1	2	yes	complemented
532	C₄×C₅	—	2	1	no	—
533	C₄×C₅	—	2	1	no	—
534	C₄×C₅	D₄×Dic₃	1	2	yes	—
535	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
536	C₄×C₅	C₂×#237	1	1	yes	characteristic
537	Dic₅	—	2	1	no	—
538	Dic₅	—	2	1	no	—
539	Dic₅	—	2	1	no	—
540	Dic₅	—	2	1	no	—
541	Dic₅	—	2	1	no	—
542	Dic₅	C₂×#208	1	2	yes	complemented
543	C₂⁴	—	5	1	no	—
544	C₂⁴	D₅×Dic₃	1	1	yes	characteristic
545	C₂×D₄	—	5	1	no	—
546	C₂×D₄	—	5	1	no	—
547	C₂×D₄	—	5	1	no	—
548	C₂×D₄	—	5	1	no	—
549	C₂×D₄	—	10	4	no	—
550	C₂²×C₄	—	2	2	no	—
551	C₂²×C₄	—	2	2	no	—
552	C₂²×C₄	—	5	1	no	—
553	C₂²×C₄	—	5	1	no	—
554	C₂²×C₄	—	5	1	no	—
555	C₂²×C₄	—	5	1	no	—
556	C₂²×C₄	—	5	1	no	—
557	C₂²×C₄	—	5	1	no	—
558	C₂²×C₄	—	5	1	no	—
559	C₂²×C₄	—	10	2	no	—
560	C₂²×C₄	—	10	2	no	—
561	C₂²×C₄	D₅×Dic₃	1	1	yes	characteristic
562	C₂²×C₄	D₅×Dic₃	1	1	yes	characteristic
563	C₂²×C₄	D₅×Dic₃	1	1	yes	characteristic
564	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
565	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
566	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
567	M₁₆	—	6	2	no	—
568	M₁₆	—	6	2	no	—
569	M₁₆	—	15	4	no	—
570	M₁₆	—	30	4	no	—
571	M₁₆	—	30	4	no	—
572	M₁₆	—	30	2	no	—
573	C₂×C₈	—	3	2	no	—
574	C₂×C₈	—	3	2	no	—
575	C₂×C₈	—	15	2	no	—
576	C₂×C₈	—	15	2	no	—
577	C₂×C₈	—	30	4	no	—
578	C₂×C₈	—	30	4	no	—
579	C₄⋊C₄	—	5	1	no	—
580	C₄⋊C₄	—	5	1	no	—
581	C₄⋊C₄	—	5	1	no	—
582	C₄⋊C₄	—	5	1	no	—
583	C₂²⋊C₄	—	5	1	no	—
584	C₂²⋊C₄	—	5	1	no	—
585	C₂²⋊C₄	—	5	1	no	—
586	C₂²⋊C₄	—	5	1	no	—
587	C₂²⋊C₄	—	5	1	no	—
588	C₂²⋊C₄	—	5	1	no	—
589	C₂²⋊C₄	—	5	1	no	—
590	C₂²⋊C₄	—	5	1	no	—
591	C₄²	—	5	1	no	—
592	C₄²	—	5	1	no	—
593	C₄²	—	5	1	no	—
594	C₄²	—	5	1	no	—
595	C₃×C₅	D₄×M₁₆	1	1	yes	characteristic, complemented, Hall
596	C₂²×C₃	—	2	1	no	—
597	C₂²×C₃	—	2	1	no	—
598	C₂²×C₃	—	2	1	no	—
599	C₂²×C₃	—	2	1	no	—
600	C₂²×C₃	—	2	1	no	—
601	C₂²×C₃	—	2	1	no	—
602	C₂²×C₃	—	2	1	no	—
603	C₂²×C₃	—	4	4	no	—
604	C₂²×C₃	—	5	2	no	—
605	C₂²×C₃	—	10	1	no	—
606	C₂²×C₃	—	10	1	no	—
607	C₂²×C₃	—	10	1	no	—
608	C₂²×C₃	—	10	1	no	—
609	C₂²×C₃	—	10	1	no	—
610	C₂²×C₃	—	20	4	no	—
611	C₂²×C₃	#4027	1	2	yes	—
612	C₂²×C₃	D₅×M₁₆	1	2	yes	complemented
613	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
614	C₃×C₄	—	2	1	no	—
615	C₃×C₄	—	2	1	no	—
616	C₃×C₄	—	5	2	no	—
617	C₃×C₄	—	10	1	no	—
618	C₃×C₄	—	10	1	no	—
619	C₃×C₄	—	10	1	no	—
620	C₃×C₄	—	10	1	no	—
621	C₃×C₄	—	10	1	no	—
622	C₃×C₄	#4027	1	2	yes	—
623	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
624	C₃×C₄	C₂×#711	1	1	yes	characteristic
625	C₂×C₅	—	2	2	no	—
626	C₂×C₅	—	2	2	no	—
627	C₂×C₅	—	4	1	no	—
628	C₂×C₅	C₂²×#208	1	1	yes	characteristic
629	C₂×C₅	C₂×D₄×Dic₃	1	1	yes	characteristic
630	C₂×C₅	#5819	1	1	yes	characteristic
631	D₅	—	2	2	no	—
632	D₅	—	4	1	no	—
633	C₂³	—	2	2	no	—
634	C₂³	—	2	2	no	—
635	C₂³	—	4	1	no	—
636	C₂³	—	5	1	no	—
637	C₂³	—	5	1	no	—
638	C₂³	—	10	2	no	—
639	C₂³	—	10	2	no	—
640	C₂³	—	20	1	no	—
641	C₂³	C₂×D₅×Dic₃	1	1	yes	characteristic
642	C₂³	C₂×D₅×Dic₃	1	1	yes	characteristic
643	C₂³	C₂×D₅×Dic₃	1	1	yes	characteristic
644	D₄	—	5	4	no	—
645	D₄	—	10	2	no	—
646	D₄	—	10	2	no	—
647	D₄	—	10	2	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	2	1	no	—
650	C₂×C₄	—	2	1	no	—
651	C₂×C₄	—	2	1	no	—
652	C₂×C₄	—	2	1	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	5	1	no	—
656	C₂×C₄	—	5	1	no	—
657	C₂×C₄	—	5	1	no	—
658	C₂×C₄	—	5	1	no	—
659	C₂×C₄	—	5	1	no	—
660	C₂×C₄	—	5	1	no	—
661	C₂×C₄	—	10	2	no	—
662	C₂×C₄	—	10	2	no	—
663	C₂×C₄	—	10	1	no	—
664	C₂×C₄	—	10	1	no	—
665	C₂×C₄	—	10	1	no	—
666	C₂×C₄	—	10	1	no	—
667	C₂×C₄	—	10	2	no	—
668	C₂×C₄	—	10	2	no	—
669	C₂×C₄	—	20	1	no	—
670	C₂×C₄	C₂×D₅×Dic₃	1	1	yes	characteristic
671	C₂×C₄	C₂×D₅×Dic₃	1	1	yes	characteristic
672	C₂×C₄	C₂×D₅×Dic₃	1	1	yes	characteristic
673	C₂×C₄	#6780	1	2	yes	—
674	C₂×C₄	#6790	1	2	yes	—
675	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
676	C₈	—	6	2	no	—
677	C₈	—	6	2	no	—
678	C₈	—	15	4	no	—
679	C₈	—	30	2	no	—
680	C₂×C₃	—	2	2	no	—
681	C₂×C₃	—	2	2	no	—
682	C₂×C₃	—	4	1	no	—
683	C₂×C₃	—	10	2	no	—
684	C₂×C₃	—	20	1	no	—
685	C₂×C₃	C₂×#4027	1	1	yes	characteristic
686	C₂×C₃	C₂×D₅×M₁₆	1	1	yes	characteristic
687	C₂×C₃	#66079	1	1	yes	characteristic
688	C₅	D₄×#208	1	1	yes	characteristic, complemented, Sylow
689	C₂²	—	2	1	no	—
690	C₂²	—	2	1	no	—
691	C₂²	—	2	1	no	—
692	C₂²	—	2	1	no	—
693	C₂²	—	2	1	no	—
694	C₂²	—	2	1	no	—
695	C₂²	—	2	1	no	—
696	C₂²	—	4	4	no	—
697	C₂²	—	5	2	no	—
698	C₂²	—	10	1	no	—
699	C₂²	—	10	1	no	—
700	C₂²	—	10	1	no	—
701	C₂²	—	10	1	no	—
702	C₂²	—	10	1	no	—
703	C₂²	—	20	4	no	—
704	C₂²	D₅×#208	1	2	yes	complemented
705	C₂²	#91559	1	2	yes	—
706	C₂²	C₂²×D₅×Dic₃	1	1	yes	characteristic
707	C₄	—	2	1	no	—
708	C₄	—	2	1	no	—
709	C₄	—	5	2	no	—
710	C₄	—	10	1	no	—
711	C₄	—	10	1	no	—
712	C₄	—	10	1	no	—
713	C₄	—	10	1	no	—
714	C₄	—	10	1	no	—
715	C₄	#91559	1	2	yes	—
716	C₄	C₂×#6780	1	1	yes	characteristic
717	C₄	C₂×#6790	1	1	yes	characteristic
718	C₃	#10610359	1	1	yes	characteristic, complemented, Sylow
719	C₂	—	2	2	no	—
720	C₂	—	2	2	no	—
721	C₂	—	4	1	no	—
722	C₂	—	10	2	no	—
723	C₂	—	20	1	no	—
724	C₂	C₂×D₅×#208	1	1	yes	characteristic
725	C₂	#11754120	1	1	yes	characteristic
726	C₂	C₂×#91559	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₃×D₅
commutator, socle	C₂²×C₃×C₅	C₂³×C₄
Fitting	C₂³×C₃×C₄×C₅	C₂²
prime radical	C₂²×C₃×C₂²⋊D₅	C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₂³×C₄	D₃×D₅
hypocenter	C₃×C₅	D₄×M₁₆
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄

Complements

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

N	H ≅ G/N	type
1. C₂²×#6710	C₂	semidirect
3. C₂×D₅×#208	C₂	semidirect
4. C₅×#5207	C₂	semidirect
5. #11748507	C₂	semidirect
6. #11748494	C₂	semidirect
7. #11748493	C₂	semidirect
8. #11748431	C₂	semidirect
9. #11748341	C₂	semidirect
10. #11748339	C₂	semidirect
11. Dic₅×#208	C₂	semidirect
19. C₂×#6710	C₂²	semidirect
20. C₂²×C₃⋊#168	C₂²	semidirect
35. C₂×#6649	C₂²	semidirect
37. C₂×D₅×C₃⋊C₈	C₂²	semidirect
38. C₅×#830	C₂²	semidirect
39. C₅×#830	C₂²	semidirect
40. #90982	C₂²	semidirect
41. #90982	C₂²	semidirect
42. #90955	C₂²	semidirect
43. #90955	C₂²	semidirect
44. #90952	C₂²	semidirect
45. Dic₅×C₃⋊C₈	C₂²	semidirect
84. #6710	D₄	semidirect
114. #5207	D₅	semidirect
182. C₃×C₂²⋊D₅	M₁₆	semidirect
199. C₃⋊#168	C₂×D₄	semidirect
229. #830	C₂×D₅	semidirect
230. #830	C₂×D₅	semidirect
307. C₂²×C₃×C₅	C₂×M₁₆	semidirect
315. C₂×C₃×D₅	C₂×M₁₆	semidirect
326. C₃×Dic₅	C₂×M₁₆	semidirect
406. C₂²⋊D₅	#208	semidirect
522. C₂²×C₅	C₂×#208	semidirect
531. C₂×D₅	C₂×#208	semidirect
542. Dic₅	C₂×#208	semidirect
595. C₃×C₅	D₄×M₁₆	semidirect
612. C₂²×C₃	D₅×M₁₆	semidirect
688. C₅	D₄×#208	semidirect
704. C₂²	D₅×#208	semidirect
718. C₃	#10610359	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#6710	2
C₂×C₃×C₄×C₂²⋊D₅	2
C₂×D₅×#208	2
C₅×#5207	2
#11748507	2
#11748494	2
#11748493	2
#11748431	2
#11748341	2
#11748339	2
Dic₅×#208	2
#10610359	3
D₄×#208	5