Subgroups — C₅×#82735 #14424102

Order 1920.

1508 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×#235	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#942	C₂	1	2	yes	maximal, complemented
4	C₅×#5207	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5050	C₂	1	2	yes	maximal, complemented
6	C₅×#5047	C₂	1	4	yes	maximal, complemented
7	C₅×#5046	C₂	1	2	yes	maximal, complemented
8	C₅×#4966	C₂	1	2	yes	maximal, complemented
9	C₅×#3007	—	3	1	no	maximal, Hall
10	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
11	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
12	C₂²×C₅×#67	—	2	1	no	—
13	C₂×C₅×#235	—	2	1	no	—
14	C₂×C₅×#235	—	2	1	no	—
15	C₂×C₅×#235	—	2	8	no	—
16	C₂×C₅×#235	C₂²	1	2	yes	—
17	C₂×C₅×#235	C₂²	1	2	yes	—
18	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
19	C₂²×C₄×C₅×D₃	—	2	1	no	—
20	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
21	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
22	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
23	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
24	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
25	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
26	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₃×C₅×C₂²⋊C₄	—	2	1	no	—
28	C₂×C₅×#216	C₂²	1	4	yes	complemented
29	C₅×#942	—	2	8	no	—
30	C₂×C₅×#215	C₂²	1	4	yes	complemented
31	C₂×C₅×#208	C₂²	1	2	yes	complemented
32	C₅×#830	C₂²	1	2	yes	—
33	C₅×#830	C₂²	1	2	yes	complemented
34	C₅×#810	C₂²	1	4	yes	complemented
35	C₅×#809	C₂²	1	4	yes	complemented
36	#82735	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
37	C₂²×C₅×#41	—	3	1	no	—
38	C₂×C₅×#137	—	3	2	no	—
39	C₂×C₅×C₂²⋊Q₈	D₃	1	1	yes	characteristic, complemented
40	C₅×#452	—	3	4	no	—
41	C₅×#451	—	3	2	no	—
42	C₅×#450	—	3	2	no	—
43	C₅×#417	—	3	2	no	—
44	C₅×#407	—	3	1	no	—
45	C₂⁴×C₃×C₅	D₄	1	1	yes	characteristic
46	C₂³×C₅×D₃	—	2	1	no	—
47	C₂×C₃×C₅×Q₈	—	2	1	no	—
48	C₂×C₃×C₅×Q₈	—	2	4	no	—
49	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
50	C₂²×C₃×C₄×C₅	—	2	4	no	—
51	C₂²×C₃×C₄×C₅	—	2	1	no	—
52	C₂²×C₃×C₄×C₅	—	2	1	no	—
53	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
54	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
55	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
56	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
57	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
58	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
59	C₂×C₅×#67	—	2	8	no	—
60	C₂×C₅×#67	—	2	2	no	—
61	C₂×C₅×#67	—	2	2	no	—
62	C₂²×C₅×Dic₃	—	2	1	no	—
63	C₅×#235	—	2	8	no	—
64	C₅×#235	—	2	8	no	—
65	C₅×#235	—	2	4	no	—
66	C₅×#235	—	2	4	no	—
67	C₅×#235	—	2	4	no	—
68	C₅×#235	D₄	1	8	yes	—
69	C₂×C₅×D₁₂	—	2	1	no	—
70	C₂×C₅×D₁₂	—	2	4	no	—
71	C₂×C₅×D₁₂	C₂³	1	2	yes	—
72	C₂×C₄×C₅×D₃	—	2	8	no	—
73	C₂×C₄×C₅×D₃	—	2	2	no	—
74	C₂×C₄×C₅×D₃	—	2	2	no	—
75	C₂×C₅×Dic₆	—	2	1	no	—
76	C₂×C₅×Dic₆	—	2	4	no	—
77	C₂×C₅×Dic₆	C₂³	1	2	yes	—
78	C₃×C₅×C₄⋊C₄	—	2	2	no	—
79	C₃×C₅×C₄⋊C₄	—	2	2	no	—
80	C₃×C₅×C₄⋊C₄	—	2	1	no	—
81	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
82	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
83	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
84	C₅×#216	—	2	8	no	—
85	C₅×#215	—	2	8	no	—
86	C₅×#208	—	2	4	no	—
87	C₂×C₅×C₃⋊C₈	C₂³	1	4	yes	—
88	C₂²×#235	C₂×C₅	1	1	yes	characteristic
89	C₂×C₃×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
90	C₂×#942	C₂×C₅	1	2	yes	complemented
91	#5207	C₂×C₅	1	1	yes	characteristic, complemented
92	#5050	C₂×C₅	1	2	yes	complemented
93	#5047	C₂×C₅	1	4	yes	complemented
94	#5046	C₂×C₅	1	2	yes	complemented
95	#4966	C₂×C₅	1	2	yes	complemented
96	C₂×C₅×#41	—	3	2	no	—
97	C₂×C₅×#41	—	3	2	no	—
98	C₂×C₅×#41	—	6	8	no	—
99	C₂×C₅×#41	—	6	1	no	—
100	C₂×C₅×#41	—	6	1	no	—
101	C₂²×C₅×Q₈	—	3	1	no	—
102	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
103	C₂²×C₅×D₄	—	3	1	no	—
104	C₂²×C₅×D₄	—	6	1	no	—
105	C₂³×C₄×C₅	—	6	1	no	—
106	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
107	C₅×#137	—	6	8	no	—
108	C₂×C₅×Q₁₆	—	3	4	no	—
109	C₂×C₅×SD₁₆	—	3	4	no	—
110	C₂×C₅×M₁₆	—	3	2	no	—
111	C₅×C₂²⋊Q₈	—	2	1	no	—
112	C₅×C₂²⋊Q₈	—	2	1	no	—
113	C₅×C₂²⋊Q₈	C₂×D₃	1	2	yes	—
114	C₅×C₂²⋊Q₈	C₂×D₃	1	2	yes	complemented
115	C₂×C₅×C₄⋊C₄	—	2	1	no	—
116	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
117	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
118	C₅×#103	—	3	4	no	—
119	C₅×#102	—	3	4	no	—
120	C₅×C₂²⋊C₈	—	3	2	no	—
121	C₅×C₂²⋊C₈	—	3	2	no	—
122	#3007	—	3	1	no	Sylow
123	C₂³×C₃×C₅	—	2	2	no	—
124	C₂³×C₃×C₅	—	2	2	no	—
125	C₂³×C₃×C₅	—	4	1	no	—
126	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
127	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
128	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₅×D₃	—	2	4	no	—
130	C₂²×C₅×D₃	—	2	2	no	—
131	C₂²×C₅×D₃	—	4	2	no	—
132	C₂²×C₅×D₃	—	4	2	no	—
133	C₃×C₅×Q₈	—	2	4	no	—
134	C₃×C₅×Q₈	—	4	2	no	—
135	C₂×C₃×C₄×C₅	—	2	2	no	—
136	C₂×C₃×C₄×C₅	—	2	2	no	—
137	C₂×C₃×C₄×C₅	—	2	2	no	—
138	C₂×C₃×C₄×C₅	—	2	2	no	—
139	C₂×C₃×C₄×C₅	—	2	2	no	—
140	C₂×C₃×C₄×C₅	—	2	2	no	—
141	C₂×C₃×C₄×C₅	—	2	2	no	—
142	C₂×C₃×C₄×C₅	—	4	2	no	—
143	C₂×C₃×C₄×C₅	—	4	2	no	—
144	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
145	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
146	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
147	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
148	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
149	C₅×#67	—	2	8	no	—
150	C₅×#67	—	2	8	no	—
151	C₂×C₅×Dic₃	—	2	4	no	—
152	C₂×C₅×Dic₃	—	2	2	no	—
153	C₅×D₁₂	—	2	4	no	—
154	C₅×D₁₂	—	2	2	no	—
155	C₅×D₁₂	C₂×D₄	1	4	yes	—
156	C₄×C₅×D₃	—	2	8	no	—
157	C₄×C₅×D₃	—	2	8	no	—
158	C₅×Dic₆	—	2	4	no	—
159	C₅×Dic₆	—	2	2	no	—
160	C₅×Dic₆	C₂×D₄	1	4	yes	—
161	C₅×C₃⋊C₈	—	2	4	no	—
162	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
163	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
164	C₂²×#67	—	2	1	no	—
165	C₂×#235	—	2	1	no	—
166	C₂×#235	—	2	1	no	—
167	C₂×#235	—	2	8	no	—
168	C₂×#235	C₂²×C₅	1	2	yes	—
169	C₂×#235	C₂²×C₅	1	2	yes	—
170	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
171	C₂²×C₄×D₃	—	2	1	no	—
172	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
173	C₃×C₂²⋊Q₈	—	2	1	no	—
174	C₃×C₂²⋊Q₈	—	2	1	no	—
175	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
176	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
177	C₂×C₃×C₄⋊C₄	—	2	1	no	—
178	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
179	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
180	C₂×#216	C₂²×C₅	1	4	yes	complemented
181	#942	—	2	8	no	—
182	C₂×#215	C₂²×C₅	1	4	yes	complemented
183	C₂×#208	C₂²×C₅	1	2	yes	complemented
184	#830	C₂²×C₅	1	2	yes	—
185	#830	C₂²×C₅	1	2	yes	complemented
186	#810	C₂²×C₅	1	4	yes	complemented
187	#809	C₂²×C₅	1	4	yes	complemented
188	C₂⁴×C₅	—	6	1	no	—
189	C₂⁴×C₅	#67	1	1	yes	characteristic
190	C₅×#41	—	3	8	no	—
191	C₅×#41	—	6	4	no	—
192	C₅×#41	—	6	4	no	—
193	C₅×#41	—	6	8	no	—
194	C₅×#41	—	6	8	no	—
195	C₅×#41	—	6	4	no	—
196	C₂×C₅×Q₈	—	2	1	no	—
197	C₂×C₅×Q₈	—	2	4	no	—
198	C₂×C₅×Q₈	—	3	2	no	—
199	C₂×C₅×Q₈	—	6	4	no	—
200	C₂×C₅×Q₈	—	6	1	no	—
201	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
202	C₂×C₅×D₄	—	3	2	no	—
203	C₂×C₅×D₄	—	6	4	no	—
204	C₂×C₅×D₄	—	6	8	no	—
205	C₂×C₅×D₄	—	6	2	no	—
206	C₂×C₅×D₄	—	6	2	no	—
207	C₂×C₅×D₄	—	6	1	no	—
208	C₂²×C₄×C₅	—	2	4	no	—
209	C₂²×C₄×C₅	—	2	1	no	—
210	C₂²×C₄×C₅	—	2	1	no	—
211	C₂²×C₄×C₅	—	6	8	no	—
212	C₂²×C₄×C₅	—	6	1	no	—
213	C₂²×C₄×C₅	—	6	2	no	—
214	C₂²×C₄×C₅	—	6	2	no	—
215	C₂²×C₄×C₅	#67	1	1	yes	characteristic
216	C₂²×C₄×C₅	#67	1	1	yes	characteristic
217	C₂²×C₄×C₅	#67	1	1	yes	characteristic
218	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
219	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
220	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
221	C₅×Q₁₆	—	6	8	no	—
222	C₅×SD₁₆	—	6	8	no	—
223	C₅×M₁₆	—	6	4	no	—
224	C₂×C₅×C₈	—	3	4	no	—
225	C₅×C₄⋊C₄	—	2	2	no	—
226	C₅×C₄⋊C₄	—	2	2	no	—
227	C₅×C₄⋊C₄	—	2	1	no	—
228	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
229	C₅×C₂²⋊C₄	—	2	2	no	—
230	C₅×C₂²⋊C₄	—	2	2	no	—
231	C₂²×#41	—	3	1	no	—
232	C₂×#137	—	3	2	no	—
233	C₂×C₂²⋊Q₈	C₅×D₃	1	1	yes	characteristic, complemented
234	#452	—	3	4	no	—
235	#451	—	3	2	no	—
236	#450	—	3	2	no	—
237	#417	—	3	2	no	—
238	#407	—	3	1	no	—
239	C₂²×C₃×C₅	—	2	1	no	—
240	C₂²×C₃×C₅	—	2	1	no	—
241	C₂²×C₃×C₅	—	2	1	no	—
242	C₂²×C₃×C₅	—	2	1	no	—
243	C₂²×C₃×C₅	—	2	1	no	—
244	C₂²×C₃×C₅	—	2	1	no	—
245	C₂²×C₃×C₅	—	2	1	no	—
246	C₂²×C₃×C₅	—	4	4	no	—
247	C₂²×C₃×C₅	#120	1	2	yes	—
248	C₂²×C₃×C₅	#137	1	2	yes	complemented
249	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
250	C₂×C₅×D₃	—	2	4	no	—
251	C₂×C₅×D₃	—	4	8	no	—
252	C₂×C₅×D₃	—	4	2	no	—
253	C₂×C₅×D₃	—	4	2	no	—
254	C₃×C₄×C₅	—	2	1	no	—
255	C₃×C₄×C₅	—	2	1	no	—
256	C₃×C₄×C₅	—	4	2	no	—
257	C₃×C₄×C₅	—	4	2	no	—
258	C₃×C₄×C₅	#120	1	2	yes	—
259	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
260	C₅×Dic₃	—	2	4	no	—
261	C₂⁴×C₃	C₅×D₄	1	1	yes	characteristic
262	C₂³×D₃	—	2	1	no	—
263	C₂×C₃×Q₈	—	2	1	no	—
264	C₂×C₃×Q₈	—	2	4	no	—
265	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
266	C₂²×C₃×C₄	—	2	4	no	—
267	C₂²×C₃×C₄	—	2	1	no	—
268	C₂²×C₃×C₄	—	2	1	no	—
269	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
270	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
271	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
272	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
273	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
274	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
275	C₂×#67	—	2	8	no	—
276	C₂×#67	—	2	2	no	—
277	C₂×#67	—	2	2	no	—
278	C₂²×Dic₃	—	2	1	no	—
279	#235	—	2	8	no	—
280	#235	—	2	8	no	—
281	#235	—	2	4	no	—
282	#235	—	2	4	no	—
283	#235	—	2	4	no	—
284	#235	C₅×D₄	1	8	yes	—
285	C₂×D₁₂	—	2	1	no	—
286	C₂×D₁₂	—	2	4	no	—
287	C₂×D₁₂	C₂³×C₅	1	2	yes	—
288	C₂×C₄×D₃	—	2	8	no	—
289	C₂×C₄×D₃	—	2	2	no	—
290	C₂×C₄×D₃	—	2	2	no	—
291	C₂×Dic₆	—	2	1	no	—
292	C₂×Dic₆	—	2	4	no	—
293	C₂×Dic₆	C₂³×C₅	1	2	yes	—
294	C₃×C₄⋊C₄	—	2	2	no	—
295	C₃×C₄⋊C₄	—	2	2	no	—
296	C₃×C₄⋊C₄	—	2	1	no	—
297	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
298	C₃×C₂²⋊C₄	—	2	2	no	—
299	C₃×C₂²⋊C₄	—	2	2	no	—
300	#216	—	2	8	no	—
301	#215	—	2	8	no	—
302	#208	—	2	4	no	—
303	C₂×C₃⋊C₈	C₂³×C₅	1	4	yes	—
304	C₂³×C₅	—	2	2	no	—
305	C₂³×C₅	—	2	2	no	—
306	C₂³×C₅	—	4	1	no	—
307	C₂³×C₅	—	6	4	no	—
308	C₂³×C₅	—	6	2	no	—
309	C₂³×C₅	—	12	2	no	—
310	C₂³×C₅	—	12	2	no	—
311	C₂³×C₅	C₂×#67	1	1	yes	characteristic
312	C₂³×C₅	C₂×#67	1	1	yes	characteristic
313	C₂³×C₅	C₂×#67	1	1	yes	characteristic
314	C₅×Q₈	—	2	4	no	—
315	C₅×Q₈	—	3	4	no	—
316	C₅×Q₈	—	4	2	no	—
317	C₅×Q₈	—	6	4	no	—
318	C₅×Q₈	—	6	2	no	—
319	C₅×D₄	—	3	4	no	—
320	C₅×D₄	—	6	4	no	—
321	C₅×D₄	—	6	8	no	—
322	C₅×D₄	—	6	8	no	—
323	C₅×D₄	—	6	2	no	—
324	C₂×C₄×C₅	—	2	2	no	—
325	C₂×C₄×C₅	—	2	2	no	—
326	C₂×C₄×C₅	—	2	2	no	—
327	C₂×C₄×C₅	—	2	2	no	—
328	C₂×C₄×C₅	—	2	2	no	—
329	C₂×C₄×C₅	—	2	2	no	—
330	C₂×C₄×C₅	—	2	2	no	—
331	C₂×C₄×C₅	—	4	2	no	—
332	C₂×C₄×C₅	—	4	2	no	—
333	C₂×C₄×C₅	—	6	8	no	—
334	C₂×C₄×C₅	—	6	4	no	—
335	C₂×C₄×C₅	—	6	2	no	—
336	C₂×C₄×C₅	—	6	8	no	—
337	C₂×C₄×C₅	D₃×D₄	1	4	yes	—
338	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
339	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
340	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
341	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
342	C₅×C₈	—	6	4	no	—
343	C₂×#41	—	3	2	no	—
344	C₂×#41	—	3	2	no	—
345	C₂×#41	—	6	8	no	—
346	C₂×#41	—	6	1	no	—
347	C₂×#41	—	6	1	no	—
348	C₂²×Q₈	—	3	1	no	—
349	C₂²×Q₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
350	C₂²×D₄	—	3	1	no	—
351	C₂²×D₄	—	6	1	no	—
352	C₂³×C₄	—	6	1	no	—
353	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
354	#137	—	6	8	no	—
355	C₂×Q₁₆	—	3	4	no	—
356	C₂×SD₁₆	—	3	4	no	—
357	C₂×M₁₆	—	3	2	no	—
358	C₂²⋊Q₈	—	2	1	no	—
359	C₂²⋊Q₈	—	2	1	no	—
360	C₂²⋊Q₈	C₂×C₅×D₃	1	2	yes	—
361	C₂²⋊Q₈	C₂×C₅×D₃	1	2	yes	complemented
362	C₂×C₄⋊C₄	—	2	1	no	—
363	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
364	C₂×C₂²⋊C₄	—	2	1	no	—
365	#103	—	3	4	no	—
366	#102	—	3	4	no	—
367	C₂²⋊C₈	—	3	2	no	—
368	C₂²⋊C₈	—	3	2	no	—
369	C₂×C₃×C₅	—	2	2	no	—
370	C₂×C₃×C₅	—	2	2	no	—
371	C₂×C₃×C₅	—	4	1	no	—
372	C₂×C₃×C₅	C₂×#120	1	1	yes	characteristic
373	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
374	C₂×C₃×C₅	#575	1	1	yes	characteristic
375	C₅×D₃	—	4	4	no	—
376	C₂³×C₃	—	2	2	no	—
377	C₂³×C₃	—	2	2	no	—
378	C₂³×C₃	—	4	1	no	—
379	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
380	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
381	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
382	C₂²×D₃	—	2	4	no	—
383	C₂²×D₃	—	2	2	no	—
384	C₂²×D₃	—	4	2	no	—
385	C₂²×D₃	—	4	2	no	—
386	C₃×Q₈	—	2	4	no	—
387	C₃×Q₈	—	4	2	no	—
388	C₂×C₃×C₄	—	2	2	no	—
389	C₂×C₃×C₄	—	2	2	no	—
390	C₂×C₃×C₄	—	2	2	no	—
391	C₂×C₃×C₄	—	2	2	no	—
392	C₂×C₃×C₄	—	2	2	no	—
393	C₂×C₃×C₄	—	2	2	no	—
394	C₂×C₃×C₄	—	2	2	no	—
395	C₂×C₃×C₄	—	4	2	no	—
396	C₂×C₃×C₄	—	4	2	no	—
397	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
398	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
399	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
400	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
401	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
402	#67	—	2	8	no	—
403	#67	—	2	8	no	—
404	C₂×Dic₃	—	2	4	no	—
405	C₂×Dic₃	—	2	2	no	—
406	D₁₂	—	2	4	no	—
407	D₁₂	—	2	2	no	—
408	D₁₂	C₂×C₅×D₄	1	4	yes	—
409	C₄×D₃	—	2	8	no	—
410	C₄×D₃	—	2	8	no	—
411	Dic₆	—	2	4	no	—
412	Dic₆	—	2	2	no	—
413	Dic₆	C₂×C₅×D₄	1	4	yes	—
414	C₃⋊C₈	—	2	4	no	—
415	C₂²×C₅	—	2	1	no	—
416	C₂²×C₅	—	2	1	no	—
417	C₂²×C₅	—	2	1	no	—
418	C₂²×C₅	—	2	1	no	—
419	C₂²×C₅	—	2	1	no	—
420	C₂²×C₅	—	2	1	no	—
421	C₂²×C₅	—	2	1	no	—
422	C₂²×C₅	—	4	4	no	—
423	C₂²×C₅	—	6	4	no	—
424	C₂²×C₅	—	12	8	no	—
425	C₂²×C₅	—	12	2	no	—
426	C₂²×C₅	—	12	2	no	—
427	C₂²×C₅	#937	1	2	yes	—
428	C₂²×C₅	#942	1	2	yes	complemented
429	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
430	C₄×C₅	—	2	1	no	—
431	C₄×C₅	—	2	1	no	—
432	C₄×C₅	—	4	2	no	—
433	C₄×C₅	—	4	2	no	—
434	C₄×C₅	—	6	4	no	—
435	C₄×C₅	#937	1	2	yes	—
436	C₄×C₅	C₂×D₃×D₄	1	2	yes	—
437	C₂⁴	—	6	1	no	—
438	C₂⁴	C₅×#67	1	1	yes	characteristic
439	#41	—	3	8	no	—
440	#41	—	6	4	no	—
441	#41	—	6	4	no	—
442	#41	—	6	8	no	—
443	#41	—	6	8	no	—
444	#41	—	6	4	no	—
445	C₂×Q₈	—	2	1	no	—
446	C₂×Q₈	—	2	4	no	—
447	C₂×Q₈	—	3	2	no	—
448	C₂×Q₈	—	6	4	no	—
449	C₂×Q₈	—	6	1	no	—
450	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
451	C₂×D₄	—	3	2	no	—
452	C₂×D₄	—	6	4	no	—
453	C₂×D₄	—	6	8	no	—
454	C₂×D₄	—	6	2	no	—
455	C₂×D₄	—	6	2	no	—
456	C₂×D₄	—	6	1	no	—
457	C₂²×C₄	—	2	4	no	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	6	8	no	—
461	C₂²×C₄	—	6	1	no	—
462	C₂²×C₄	—	6	2	no	—
463	C₂²×C₄	—	6	2	no	—
464	C₂²×C₄	C₅×#67	1	1	yes	characteristic
465	C₂²×C₄	C₅×#67	1	1	yes	characteristic
466	C₂²×C₄	C₅×#67	1	1	yes	characteristic
467	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
468	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
469	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
470	Q₁₆	—	6	8	no	—
471	SD₁₆	—	6	8	no	—
472	M₁₆	—	6	4	no	—
473	C₂×C₈	—	3	4	no	—
474	C₄⋊C₄	—	2	2	no	—
475	C₄⋊C₄	—	2	2	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
478	C₂²⋊C₄	—	2	2	no	—
479	C₂²⋊C₄	—	2	2	no	—
480	C₃×C₅	#3007	1	1	yes	characteristic, complemented, Hall
481	C₂²×C₃	—	2	1	no	—
482	C₂²×C₃	—	2	1	no	—
483	C₂²×C₃	—	2	1	no	—
484	C₂²×C₃	—	2	1	no	—
485	C₂²×C₃	—	2	1	no	—
486	C₂²×C₃	—	2	1	no	—
487	C₂²×C₃	—	2	1	no	—
488	C₂²×C₃	—	4	4	no	—
489	C₂²×C₃	C₅×#120	1	2	yes	—
490	C₂²×C₃	C₅×#137	1	2	yes	complemented
491	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
492	C₂×D₃	—	2	4	no	—
493	C₂×D₃	—	4	8	no	—
494	C₂×D₃	—	4	2	no	—
495	C₂×D₃	—	4	2	no	—
496	C₃×C₄	—	2	1	no	—
497	C₃×C₄	—	2	1	no	—
498	C₃×C₄	—	4	2	no	—
499	C₃×C₄	—	4	2	no	—
500	C₃×C₄	C₅×#120	1	2	yes	—
501	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
502	Dic₃	—	2	4	no	—
503	C₂×C₅	—	2	2	no	—
504	C₂×C₅	—	2	2	no	—
505	C₂×C₅	—	4	1	no	—
506	C₂×C₅	—	12	4	no	—
507	C₂×C₅	C₂×#937	1	1	yes	characteristic
508	C₂×C₅	C₂×#942	1	1	yes	characteristic
509	C₂×C₅	#5822	1	1	yes	characteristic
510	C₂³	—	2	2	no	—
511	C₂³	—	2	2	no	—
512	C₂³	—	4	1	no	—
513	C₂³	—	6	4	no	—
514	C₂³	—	6	2	no	—
515	C₂³	—	12	2	no	—
516	C₂³	—	12	2	no	—
517	C₂³	C₂×C₅×#67	1	1	yes	characteristic
518	C₂³	C₂×C₅×#67	1	1	yes	characteristic
519	C₂³	C₂×C₅×#67	1	1	yes	characteristic
520	Q₈	—	2	4	no	—
521	Q₈	—	3	4	no	—
522	Q₈	—	4	2	no	—
523	Q₈	—	6	4	no	—
524	Q₈	—	6	2	no	—
525	D₄	—	3	4	no	—
526	D₄	—	6	4	no	—
527	D₄	—	6	8	no	—
528	D₄	—	6	8	no	—
529	D₄	—	6	2	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	4	2	no	—
538	C₂×C₄	—	4	2	no	—
539	C₂×C₄	—	6	8	no	—
540	C₂×C₄	—	6	4	no	—
541	C₂×C₄	—	6	2	no	—
542	C₂×C₄	—	6	8	no	—
543	C₂×C₄	C₅×D₃×D₄	1	4	yes	—
544	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
545	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
546	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
547	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
548	C₈	—	6	4	no	—
549	C₂×C₃	—	2	2	no	—
550	C₂×C₃	—	2	2	no	—
551	C₂×C₃	—	4	1	no	—
552	C₂×C₃	C₂×C₅×#120	1	1	yes	characteristic
553	C₂×C₃	C₂×C₅×#137	1	1	yes	characteristic
554	C₂×C₃	C₅×#575	1	1	yes	characteristic
555	D₃	—	4	4	no	—
556	C₅	#82735	1	1	yes	characteristic, direct product factor, Sylow
557	C₂²	—	2	1	no	—
558	C₂²	—	2	1	no	—
559	C₂²	—	2	1	no	—
560	C₂²	—	2	1	no	—
561	C₂²	—	2	1	no	—
562	C₂²	—	2	1	no	—
563	C₂²	—	2	1	no	—
564	C₂²	—	4	4	no	—
565	C₂²	—	6	4	no	—
566	C₂²	—	12	8	no	—
567	C₂²	—	12	2	no	—
568	C₂²	—	12	2	no	—
569	C₂²	C₅×#937	1	2	yes	—
570	C₂²	C₅×#942	1	2	yes	complemented
571	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
572	C₄	—	2	1	no	—
573	C₄	—	2	1	no	—
574	C₄	—	4	2	no	—
575	C₄	—	4	2	no	—
576	C₄	—	6	4	no	—
577	C₄	C₅×#937	1	2	yes	—
578	C₄	C₂×C₅×D₃×D₄	1	2	yes	—
579	C₃	C₅×#3007	1	1	yes	characteristic, complemented, Sylow
580	C₂	—	2	2	no	—
581	C₂	—	2	2	no	—
582	C₂	—	4	1	no	—
583	C₂	—	12	4	no	—
584	C₂	C₂×C₅×#937	1	1	yes	characteristic
585	C₂	C₂×C₅×#942	1	1	yes	characteristic
586	C₂	C₅×#5822	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂²×#67
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂×C₃×C₅×C₂²⋊Q₈	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂²×C₅×#235	C₂
hypercenter	C₂×C₅×C₂²⋊Q₈	D₃
hypocenter	C₃	C₅×#3007
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂³×C₄×C₅ ◁ C₂×C₅×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₅×C₂²⋊Q₈	C₂	semidirect
3. C₂×C₅×#942	C₂	semidirect
4. C₅×#5207	C₂	semidirect
5. C₅×#5050	C₂	semidirect
6. C₅×#5047	C₂	semidirect
7. C₅×#5046	C₂	semidirect
8. C₅×#4966	C₂	semidirect
10. C₂²×C₃×C₅×Q₈	C₂²	semidirect
24. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
26. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
28. C₂×C₅×#216	C₂²	semidirect
30. C₂×C₅×#215	C₂²	semidirect
31. C₂×C₅×#208	C₂²	semidirect
33. C₅×#830	C₂²	semidirect
34. C₅×#810	C₂²	semidirect
35. C₅×#809	C₂²	semidirect
36. #82735	C₅	direct (N × H)
39. C₂×C₅×C₂²⋊Q₈	D₃	semidirect
89. C₂×C₃×C₂²⋊Q₈	C₂×C₅	semidirect
90. C₂×#942	C₂×C₅	semidirect
91. #5207	C₂×C₅	semidirect
92. #5050	C₂×C₅	semidirect
93. #5047	C₂×C₅	semidirect
94. #5046	C₂×C₅	semidirect
95. #4966	C₂×C₅	semidirect
102. C₂²×C₅×Q₈	C₂×D₃	semidirect
114. C₅×C₂²⋊Q₈	C₂×D₃	semidirect
116. C₂×C₅×C₄⋊C₄	C₂×D₃	semidirect
162. C₂²×C₃×Q₈	C₂²×C₅	semidirect
176. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
178. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
180. C₂×#216	C₂²×C₅	semidirect
182. C₂×#215	C₂²×C₅	semidirect
183. C₂×#208	C₂²×C₅	semidirect
185. #830	C₂²×C₅	semidirect
186. #810	C₂²×C₅	semidirect
187. #809	C₂²×C₅	semidirect
233. C₂×C₂²⋊Q₈	C₅×D₃	semidirect
248. C₂²×C₃×C₅	#137	semidirect
349. C₂²×Q₈	C₂×C₅×D₃	semidirect
361. C₂²⋊Q₈	C₂×C₅×D₃	semidirect
363. C₂×C₄⋊C₄	C₂×C₅×D₃	semidirect
428. C₂²×C₅	#942	semidirect
480. C₃×C₅	#3007	semidirect
490. C₂²×C₃	C₅×#137	semidirect
556. C₅	#82735	direct (N × H)
570. C₂²	C₅×#942	semidirect
579. C₃	C₅×#3007	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₅×#235	2
C₂×C₃×C₅×C₂²⋊Q₈	2
C₂×C₅×#942	2
C₅×#5207	2
C₅×#5050	2
C₅×#5047	2
C₅×#5046	2
C₅×#4966	2
C₅×#3007	3
#82735	5

Subgroups — C5×#82735 #14424102

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#82735 #14424102