Subgroups — C₅×#86294 #14480629

Order 1920.

3112 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×#237	C₂	1	2	yes	maximal, complemented
2	C₃×C₅×#534	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5804	C₂	1	2	yes	maximal, complemented
4	C₅×#5656	C₂	1	4	yes	maximal, complemented
5	C₅×#5648	C₂	1	4	yes	maximal, complemented
6	C₅×#5597	C₂	1	4	yes	maximal, complemented
7	C₅×#5596	C₂	1	4	yes	maximal, complemented
8	C₅×#5592	C₂	1	4	yes	maximal, complemented
9	C₅×#5586	C₂	1	4	yes	maximal, complemented
10	C₅×#5493	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅×#877	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3449	—	3	1	no	maximal, Hall
13	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
14	C₂²×C₅×#67	C₂²	1	2	yes	—
15	C₂²×C₅×#67	C₂²	1	2	yes	complemented
16	C₂³×C₅×Dic₃	C₂²	1	1	yes	characteristic
17	C₂³×C₅×Dic₃	C₂²	1	2	yes	complemented
18	C₂×C₅×#237	—	2	16	no	—
19	C₂×C₅×#237	C₂²	1	4	yes	—
20	C₂×C₅×#237	C₂²	1	4	yes	—
21	C₂×C₅×#237	C₂²	1	4	yes	complemented
22	C₂×C₅×#237	C₂²	1	4	yes	complemented
23	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	complemented
24	C₂²×C₅×Dic₆	C₂²	1	2	yes	complemented
25	C₃×C₅×#123	C₂²	1	4	yes	complemented
26	C₃×C₅×#121	C₂²	1	4	yes	complemented
27	C₃×C₅×#120	C₂²	1	4	yes	complemented
28	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
29	C₅×#953	C₂²	1	4	yes	complemented
30	C₂×C₅×#217	C₂²	1	1	yes	characteristic
31	C₅×#940	C₂²	1	4	yes	complemented
32	C₅×#939	C₂²	1	8	yes	complemented
33	C₅×#939	C₂²	1	8	yes	complemented
34	C₅×#937	C₂²	1	4	yes	complemented
35	C₅×#935	C₂²	1	4	yes	complemented
36	C₅×D₄×Dic₃	C₂²	1	4	yes	complemented
37	C₅×#930	C₂²	1	4	yes	complemented
38	C₅×#929	C₂²	1	4	yes	complemented
39	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	complemented
40	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	complemented
41	C₅×#896	C₂²	1	8	yes	complemented
42	C₅×#893	C₂²	1	4	yes	complemented
43	C₅×#888	C₂²	1	4	yes	complemented
44	C₅×#886	C₂²	1	4	yes	complemented
45	C₅×#885	C₂²	1	8	yes	complemented
46	C₅×#884	C₂²	1	8	yes	complemented
47	C₅×#882	C₂²	1	4	yes	complemented
48	C₅×#67⋊C₄	C₂²	1	8	yes	complemented
49	C₅×#878	C₂²	1	8	yes	complemented
50	C₅×#877	C₂²	1	4	yes	complemented
51	C₅×#877	C₂²	1	4	yes	complemented
52	#86294	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
53	C₂²×C₅×#41	—	3	2	no	—
54	C₅×#537	—	3	4	no	—
55	C₅×#536	—	3	4	no	—
56	C₅×#535	—	3	4	no	—
57	C₅×#534	—	3	2	no	—
58	C₅×#534	—	3	1	no	—
59	C₅×#534	D₃	1	1	yes	characteristic, complemented
60	C₅×#532	—	3	4	no	—
61	C₅×#525	—	3	4	no	—
62	C₅×#525	—	3	4	no	—
63	C₂×C₅×#117	—	3	1	no	—
64	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
65	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
66	C₂³×C₅×D₃	C₂³	1	2	yes	—
67	C₂×C₃×C₅×D₄	—	2	8	no	—
68	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
69	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
70	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
71	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
72	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
73	C₂×C₅×#67	—	2	8	no	—
74	C₂×C₅×#67	—	2	8	no	—
75	C₂×C₅×#67	C₂³	1	4	yes	—
76	C₂×C₅×#67	C₂³	1	4	yes	—
77	C₂×C₅×#67	C₂³	1	4	yes	—
78	C₂×C₅×#67	C₂³	1	4	yes	—
79	C₂×C₅×#67	C₂³	1	8	yes	—
80	C₂²×C₅×Dic₃	—	2	8	no	—
81	C₂²×C₅×Dic₃	D₄	1	8	yes	complemented
82	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
83	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
84	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
85	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
86	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
87	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
88	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
89	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
90	C₅×#237	—	2	16	no	—
91	C₅×#237	—	2	16	no	—
92	C₅×#237	—	2	16	no	—
93	C₅×#237	—	2	16	no	—
94	C₂×C₅×D₁₂	C₂³	1	4	yes	—
95	C₂×C₄×C₅×D₃	—	2	8	no	—
96	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
97	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
98	C₂×C₅×Dic₆	—	2	8	no	—
99	C₂×C₅×Dic₆	C₂³	1	4	yes	—
100	C₂×C₅×Dic₆	C₂³	1	4	yes	—
101	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
102	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
103	C₃×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
104	C₅×#217	C₂³	1	4	yes	—
105	C₅×#217	C₂³	1	8	yes	—
106	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
107	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
108	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
109	C₅×Dic₃⋊C₄	C₂³	1	8	yes	—
110	C₅×Dic₃⋊C₄	C₂³	1	8	yes	—
111	C₄×C₅×Dic₃	C₂³	1	4	yes	—
112	C₄×C₅×Dic₃	C₂³	1	4	yes	—
113	C₂²×#237	C₂×C₅	1	2	yes	complemented
114	C₃×#534	C₂×C₅	1	1	yes	characteristic, complemented
115	#5804	C₂×C₅	1	2	yes	complemented
116	#5656	C₂×C₅	1	4	yes	complemented
117	#5648	C₂×C₅	1	4	yes	complemented
118	#5597	C₂×C₅	1	4	yes	complemented
119	#5596	C₂×C₅	1	4	yes	complemented
120	#5592	C₂×C₅	1	4	yes	complemented
121	#5586	C₂×C₅	1	4	yes	complemented
122	#5493	C₂×C₅	1	1	yes	characteristic, complemented
123	C₂×#877	C₂×C₅	1	1	yes	characteristic, complemented
124	C₂×C₅×#41	—	3	4	no	—
125	C₂×C₅×#41	—	3	4	no	—
126	C₂×C₅×#41	—	3	4	no	—
127	C₂×C₅×#41	—	3	4	no	—
128	C₂×C₅×#41	—	6	16	no	—
129	C₂²×C₅×Q₈	—	3	2	no	—
130	C₂²×C₅×D₄	—	3	2	no	—
131	C₂²×C₅×D₄	—	3	2	no	—
132	C₂²×C₅×D₄	C₂×D₃	1	2	yes	—
133	C₂³×C₄×C₅	—	3	1	no	—
134	C₂³×C₄×C₅	—	3	2	no	—
135	C₂³×C₄×C₅	—	3	2	no	—
136	C₅×C₄⋊Q₈	—	3	4	no	—
137	C₅×#127	—	3	4	no	—
138	C₅×#124	—	3	8	no	—
139	C₅×#123	—	3	4	no	—
140	C₅×#123	—	3	4	no	—
141	C₅×#123	—	3	4	no	—
142	C₅×#123	C₂×D₃	1	4	yes	complemented
143	C₅×C₂²⋊Q₈	—	3	8	no	—
144	C₅×C₂²⋊Q₈	—	3	8	no	—
145	C₅×#121	—	3	8	no	—
146	C₅×#121	—	3	8	no	—
147	C₅×#121	—	3	4	no	—
148	C₅×#121	—	3	8	no	—
149	C₅×#121	C₂×D₃	1	4	yes	complemented
150	C₅×#120	—	3	4	no	—
151	C₅×#120	—	3	4	no	—
152	C₅×#120	—	3	4	no	—
153	C₅×#120	C₂×D₃	1	4	yes	complemented
154	C₄×C₅×D₄	—	3	4	no	—
155	C₄×C₅×D₄	—	3	4	no	—
156	C₄×C₅×D₄	—	3	8	no	—
157	C₅×#117	—	3	4	no	—
158	C₅×#117	—	3	4	no	—
159	C₂×C₅×C₄⋊C₄	—	3	2	no	—
160	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
161	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
162	C₂×C₄²×C₅	—	3	2	no	—
163	#3449	—	3	1	no	Sylow
164	C₂³×C₃×C₅	—	2	4	no	—
165	C₂³×C₃×C₅	—	4	2	no	—
166	C₂³×C₃×C₅	—	4	4	no	—
167	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
168	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
169	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
170	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
171	C₂²×C₅×D₃	—	2	4	no	—
172	C₂²×C₅×D₃	—	4	4	no	—
173	C₂²×C₅×D₃	C₂⁴	1	4	yes	—
174	C₃×C₅×D₄	—	2	8	no	—
175	C₃×C₅×D₄	—	2	8	no	—
176	C₃×C₅×D₄	—	4	4	no	—
177	C₂×C₃×C₄×C₅	—	2	4	no	—
178	C₂×C₃×C₄×C₅	—	4	2	no	—
179	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
180	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
181	C₅×#67	—	2	8	no	—
182	C₅×#67	—	2	8	no	—
183	C₅×#67	—	2	8	no	—
184	C₅×#67	—	2	8	no	—
185	C₅×#67	—	4	8	no	—
186	C₂×C₅×Dic₃	—	2	4	no	—
187	C₂×C₅×Dic₃	—	2	8	no	—
188	C₂×C₅×Dic₃	—	2	8	no	—
189	C₂×C₅×Dic₃	—	4	2	no	—
190	C₂×C₅×Dic₃	C₂×D₄	1	8	yes	—
191	C₂×C₅×Dic₃	C₂×D₄	1	8	yes	—
192	C₂×C₅×Dic₃	C₂×D₄	1	4	yes	—
193	C₂×C₅×Dic₃	C₂×D₄	1	4	yes	—
194	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
195	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
196	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
197	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
198	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
199	C₅×D₁₂	—	4	4	no	—
200	C₄×C₅×D₃	—	2	8	no	—
201	C₄×C₅×D₃	—	2	8	no	—
202	C₅×Dic₆	—	2	8	no	—
203	C₅×Dic₆	—	2	8	no	—
204	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
205	C₂²×#67	C₂²×C₅	1	2	yes	—
206	C₂²×#67	C₂²×C₅	1	2	yes	complemented
207	C₂³×Dic₃	C₂²×C₅	1	1	yes	characteristic
208	C₂³×Dic₃	C₂²×C₅	1	2	yes	complemented
209	C₂×#237	—	2	16	no	—
210	C₂×#237	C₂²×C₅	1	4	yes	—
211	C₂×#237	C₂²×C₅	1	4	yes	—
212	C₂×#237	C₂²×C₅	1	4	yes	complemented
213	C₂×#237	C₂²×C₅	1	4	yes	complemented
214	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	complemented
215	C₂²×Dic₆	C₂²×C₅	1	2	yes	complemented
216	C₃×#123	C₂²×C₅	1	4	yes	complemented
217	C₃×#121	C₂²×C₅	1	4	yes	complemented
218	C₃×#120	C₂²×C₅	1	4	yes	complemented
219	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
220	#953	C₂²×C₅	1	4	yes	complemented
221	C₂×#217	C₂²×C₅	1	1	yes	characteristic
222	#940	C₂²×C₅	1	4	yes	complemented
223	#939	C₂²×C₅	1	8	yes	complemented
224	#939	C₂²×C₅	1	8	yes	complemented
225	#937	C₂²×C₅	1	4	yes	complemented
226	#935	C₂²×C₅	1	4	yes	complemented
227	D₄×Dic₃	C₂²×C₅	1	4	yes	complemented
228	#930	C₂²×C₅	1	4	yes	complemented
229	#929	C₂²×C₅	1	4	yes	complemented
230	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	complemented
231	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	complemented
232	#896	C₂²×C₅	1	8	yes	complemented
233	#893	C₂²×C₅	1	4	yes	complemented
234	#888	C₂²×C₅	1	4	yes	complemented
235	#886	C₂²×C₅	1	4	yes	complemented
236	#885	C₂²×C₅	1	8	yes	complemented
237	#884	C₂²×C₅	1	8	yes	complemented
238	#882	C₂²×C₅	1	4	yes	complemented
239	#67⋊C₄	C₂²×C₅	1	8	yes	complemented
240	#878	C₂²×C₅	1	8	yes	complemented
241	#877	C₂²×C₅	1	4	yes	complemented
242	#877	C₂²×C₅	1	4	yes	complemented
243	C₂⁴×C₅	—	3	2	no	—
244	C₂⁴×C₅	C₂²×D₃	1	2	yes	—
245	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
246	C₅×#41	—	6	16	no	—
247	C₅×#41	—	6	16	no	—
248	C₅×#41	—	6	16	no	—
249	C₅×#41	—	6	16	no	—
250	C₂×C₅×Q₈	—	3	4	no	—
251	C₂×C₅×Q₈	—	3	4	no	—
252	C₂×C₅×Q₈	—	6	8	no	—
253	C₂×C₅×D₄	—	2	8	no	—
254	C₂×C₅×D₄	—	3	4	no	—
255	C₂×C₅×D₄	—	3	4	no	—
256	C₂×C₅×D₄	—	3	4	no	—
257	C₂×C₅×D₄	—	3	4	no	—
258	C₂×C₅×D₄	—	3	8	no	—
259	C₂×C₅×D₄	—	3	4	no	—
260	C₂×C₅×D₄	—	6	8	no	—
261	C₂×C₅×D₄	—	6	8	no	—
262	C₂×C₅×D₄	C₂²×D₃	1	4	yes	—
263	C₂×C₅×D₄	C₂²×D₃	1	4	yes	—
264	C₂×C₅×D₄	C₂²×D₃	1	4	yes	—
265	C₂²×C₄×C₅	—	3	8	no	—
266	C₂²×C₄×C₅	—	3	1	no	—
267	C₂²×C₄×C₅	—	3	1	no	—
268	C₂²×C₄×C₅	—	3	2	no	—
269	C₂²×C₄×C₅	—	3	2	no	—
270	C₂²×C₄×C₅	—	3	4	no	—
271	C₂²×C₄×C₅	—	3	4	no	—
272	C₂²×C₄×C₅	—	3	2	no	—
273	C₂²×C₄×C₅	—	3	2	no	—
274	C₂²×C₄×C₅	—	3	4	no	—
275	C₂²×C₄×C₅	—	3	4	no	—
276	C₂²×C₄×C₅	—	6	8	no	—
277	C₂²×C₄×C₅	—	6	8	no	—
278	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
279	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
280	C₅×C₄⋊C₄	—	3	8	no	—
281	C₅×C₄⋊C₄	—	3	8	no	—
282	C₅×C₄⋊C₄	—	3	4	no	—
283	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
284	C₅×C₂²⋊C₄	—	3	4	no	—
285	C₅×C₂²⋊C₄	—	3	8	no	—
286	C₅×C₂²⋊C₄	—	3	8	no	—
287	C₅×C₂²⋊C₄	—	3	8	no	—
288	C₅×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
289	C₅×C₂²⋊C₄	C₂²×D₃	1	8	yes	—
290	C₄²×C₅	—	3	4	no	—
291	C₄²×C₅	—	3	4	no	—
292	C₂²×#41	—	3	2	no	—
293	#537	—	3	4	no	—
294	#536	—	3	4	no	—
295	#535	—	3	4	no	—
296	#534	—	3	2	no	—
297	#534	—	3	1	no	—
298	#534	C₅×D₃	1	1	yes	characteristic, complemented
299	#532	—	3	4	no	—
300	#525	—	3	4	no	—
301	#525	—	3	4	no	—
302	C₂×#117	—	3	1	no	—
303	C₂²×C₃×C₅	—	2	2	no	—
304	C₂²×C₃×C₅	—	2	4	no	—
305	C₂²×C₃×C₅	—	2	4	no	—
306	C₂²×C₃×C₅	—	2	8	no	—
307	C₂²×C₃×C₅	—	4	4	no	—
308	C₂²×C₃×C₅	—	4	8	no	—
309	C₂²×C₃×C₅	C₂²×D₄	1	4	yes	—
310	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
311	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
312	C₂×C₅×D₃	—	2	4	no	—
313	C₂×C₅×D₃	—	2	8	no	—
314	C₂×C₅×D₃	—	4	8	no	—
315	C₃×C₄×C₅	—	2	4	no	—
316	C₃×C₄×C₅	—	2	4	no	—
317	C₅×Dic₃	—	2	4	no	—
318	C₅×Dic₃	—	2	4	no	—
319	C₅×Dic₃	C₂²×D₄	1	2	yes	—
320	C₅×Dic₃	C₂²×D₄	1	4	yes	—
321	C₅×Dic₃	C₂²×D₄	1	2	yes	—
322	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
323	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
324	C₂³×D₃	C₂³×C₅	1	2	yes	—
325	C₂×C₃×D₄	—	2	8	no	—
326	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
327	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
328	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
329	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
330	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
331	C₂×#67	—	2	8	no	—
332	C₂×#67	—	2	8	no	—
333	C₂×#67	C₂³×C₅	1	4	yes	—
334	C₂×#67	C₂³×C₅	1	4	yes	—
335	C₂×#67	C₂³×C₅	1	4	yes	—
336	C₂×#67	C₂³×C₅	1	4	yes	—
337	C₂×#67	C₂³×C₅	1	8	yes	—
338	C₂²×Dic₃	—	2	8	no	—
339	C₂²×Dic₃	C₅×D₄	1	8	yes	complemented
340	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
341	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
342	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
343	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
344	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
345	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
346	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
347	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
348	#237	—	2	16	no	—
349	#237	—	2	16	no	—
350	#237	—	2	16	no	—
351	#237	—	2	16	no	—
352	C₂×D₁₂	C₂³×C₅	1	4	yes	—
353	C₂×C₄×D₃	—	2	8	no	—
354	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
355	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
356	C₂×Dic₆	—	2	8	no	—
357	C₂×Dic₆	C₂³×C₅	1	4	yes	—
358	C₂×Dic₆	C₂³×C₅	1	4	yes	—
359	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
360	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
361	C₃×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
362	#217	C₂³×C₅	1	4	yes	—
363	#217	C₂³×C₅	1	8	yes	—
364	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
365	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
366	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
367	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
368	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
369	C₄×Dic₃	C₂³×C₅	1	4	yes	—
370	C₄×Dic₃	C₂³×C₅	1	4	yes	—
371	C₂³×C₅	—	2	4	no	—
372	C₂³×C₅	—	3	4	no	—
373	C₂³×C₅	—	4	2	no	—
374	C₂³×C₅	—	4	4	no	—
375	C₂³×C₅	—	6	4	no	—
376	C₂³×C₅	—	12	4	no	—
377	C₂³×C₅	D₃×D₄	1	4	yes	—
378	C₂³×C₅	C₂³×D₃	1	4	yes	—
379	C₂³×C₅	C₂³×D₃	1	2	yes	—
380	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
381	C₅×Q₈	—	6	8	no	—
382	C₅×Q₈	—	6	8	no	—
383	C₅×D₄	—	2	8	no	—
384	C₅×D₄	—	2	8	no	—
385	C₅×D₄	—	4	4	no	—
386	C₅×D₄	—	6	8	no	—
387	C₅×D₄	—	6	8	no	—
388	C₅×D₄	—	6	8	no	—
389	C₅×D₄	—	6	8	no	—
390	C₅×D₄	—	12	4	no	—
391	C₅×D₄	—	12	8	no	—
392	C₂×C₄×C₅	—	2	4	no	—
393	C₂×C₄×C₅	—	3	8	no	—
394	C₂×C₄×C₅	—	3	8	no	—
395	C₂×C₄×C₅	—	3	4	no	—
396	C₂×C₄×C₅	—	3	4	no	—
397	C₂×C₄×C₅	—	3	1	no	—
398	C₂×C₄×C₅	—	3	1	no	—
399	C₂×C₄×C₅	—	3	2	no	—
400	C₂×C₄×C₅	—	3	4	no	—
401	C₂×C₄×C₅	—	3	4	no	—
402	C₂×C₄×C₅	—	4	2	no	—
403	C₂×C₄×C₅	—	6	8	no	—
404	C₂×C₄×C₅	—	6	8	no	—
405	C₂×C₄×C₅	—	6	8	no	—
406	C₂×C₄×C₅	—	6	8	no	—
407	C₂×C₄×C₅	—	6	4	no	—
408	C₂×C₄×C₅	—	12	2	no	—
409	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
410	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
411	C₂×#41	—	3	4	no	—
412	C₂×#41	—	3	4	no	—
413	C₂×#41	—	3	4	no	—
414	C₂×#41	—	3	4	no	—
415	C₂×#41	—	6	16	no	—
416	C₂²×Q₈	—	3	2	no	—
417	C₂²×D₄	—	3	2	no	—
418	C₂²×D₄	—	3	2	no	—
419	C₂²×D₄	C₂×C₅×D₃	1	2	yes	—
420	C₂³×C₄	—	3	1	no	—
421	C₂³×C₄	—	3	2	no	—
422	C₂³×C₄	—	3	2	no	—
423	C₄⋊Q₈	—	3	4	no	—
424	#127	—	3	4	no	—
425	#124	—	3	8	no	—
426	#123	—	3	4	no	—
427	#123	—	3	4	no	—
428	#123	—	3	4	no	—
429	#123	C₂×C₅×D₃	1	4	yes	complemented
430	C₂²⋊Q₈	—	3	8	no	—
431	C₂²⋊Q₈	—	3	8	no	—
432	#121	—	3	8	no	—
433	#121	—	3	8	no	—
434	#121	—	3	4	no	—
435	#121	—	3	8	no	—
436	#121	C₂×C₅×D₃	1	4	yes	complemented
437	#120	—	3	4	no	—
438	#120	—	3	4	no	—
439	#120	—	3	4	no	—
440	#120	C₂×C₅×D₃	1	4	yes	complemented
441	C₄×D₄	—	3	4	no	—
442	C₄×D₄	—	3	4	no	—
443	C₄×D₄	—	3	8	no	—
444	#117	—	3	4	no	—
445	#117	—	3	4	no	—
446	C₂×C₄⋊C₄	—	3	2	no	—
447	C₂×C₂²⋊C₄	—	3	1	no	—
448	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
449	C₂×C₄²	—	3	2	no	—
450	C₂×C₃×C₅	—	2	4	no	—
451	C₂×C₃×C₅	—	2	2	no	—
452	C₂×C₃×C₅	—	4	4	no	—
453	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
454	C₂×C₃×C₅	#585	1	2	yes	—
455	C₅×D₃	—	4	4	no	—
456	C₂³×C₃	—	2	4	no	—
457	C₂³×C₃	—	4	2	no	—
458	C₂³×C₃	—	4	4	no	—
459	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
460	C₂³×C₃	C₂⁴×C₅	1	4	yes	—
461	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
462	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
463	C₂²×D₃	—	2	4	no	—
464	C₂²×D₃	—	4	4	no	—
465	C₂²×D₃	C₂⁴×C₅	1	4	yes	—
466	C₃×D₄	—	2	8	no	—
467	C₃×D₄	—	2	8	no	—
468	C₃×D₄	—	4	4	no	—
469	C₂×C₃×C₄	—	2	4	no	—
470	C₂×C₃×C₄	—	4	2	no	—
471	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
472	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
473	#67	—	2	8	no	—
474	#67	—	2	8	no	—
475	#67	—	2	8	no	—
476	#67	—	2	8	no	—
477	#67	—	4	8	no	—
478	C₂×Dic₃	—	2	4	no	—
479	C₂×Dic₃	—	2	8	no	—
480	C₂×Dic₃	—	2	8	no	—
481	C₂×Dic₃	—	4	2	no	—
482	C₂×Dic₃	C₂×C₅×D₄	1	8	yes	—
483	C₂×Dic₃	C₂×C₅×D₄	1	8	yes	—
484	C₂×Dic₃	C₂×C₅×D₄	1	4	yes	—
485	C₂×Dic₃	C₂×C₅×D₄	1	4	yes	—
486	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
487	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
488	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
489	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
490	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
491	D₁₂	—	4	4	no	—
492	C₄×D₃	—	2	8	no	—
493	C₄×D₃	—	2	8	no	—
494	Dic₆	—	2	8	no	—
495	Dic₆	—	2	8	no	—
496	C₂²×C₅	—	2	2	no	—
497	C₂²×C₅	—	2	4	no	—
498	C₂²×C₅	—	2	4	no	—
499	C₂²×C₅	—	2	8	no	—
500	C₂²×C₅	—	4	4	no	—
501	C₂²×C₅	—	4	8	no	—
502	C₂²×C₅	—	6	4	no	—
503	C₂²×C₅	—	6	8	no	—
504	C₂²×C₅	—	12	8	no	—
505	C₂²×C₅	C₂×D₃×D₄	1	4	yes	—
506	C₂²×C₅	C₂×D₃×D₄	1	2	yes	—
507	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
508	C₄×C₅	—	2	4	no	—
509	C₄×C₅	—	2	4	no	—
510	C₄×C₅	—	3	2	no	—
511	C₄×C₅	—	3	4	no	—
512	C₄×C₅	—	3	2	no	—
513	C₄×C₅	—	6	4	no	—
514	C₄×C₅	—	6	4	no	—
515	C₂⁴	—	3	2	no	—
516	C₂⁴	C₂²×C₅×D₃	1	2	yes	—
517	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
518	#41	—	6	16	no	—
519	#41	—	6	16	no	—
520	#41	—	6	16	no	—
521	#41	—	6	16	no	—
522	C₂×Q₈	—	3	4	no	—
523	C₂×Q₈	—	3	4	no	—
524	C₂×Q₈	—	6	8	no	—
525	C₂×D₄	—	2	8	no	—
526	C₂×D₄	—	3	4	no	—
527	C₂×D₄	—	3	4	no	—
528	C₂×D₄	—	3	4	no	—
529	C₂×D₄	—	3	4	no	—
530	C₂×D₄	—	3	8	no	—
531	C₂×D₄	—	3	4	no	—
532	C₂×D₄	—	6	8	no	—
533	C₂×D₄	—	6	8	no	—
534	C₂×D₄	C₂²×C₅×D₃	1	4	yes	—
535	C₂×D₄	C₂²×C₅×D₃	1	4	yes	—
536	C₂×D₄	C₂²×C₅×D₃	1	4	yes	—
537	C₂²×C₄	—	3	8	no	—
538	C₂²×C₄	—	3	1	no	—
539	C₂²×C₄	—	3	1	no	—
540	C₂²×C₄	—	3	2	no	—
541	C₂²×C₄	—	3	2	no	—
542	C₂²×C₄	—	3	4	no	—
543	C₂²×C₄	—	3	4	no	—
544	C₂²×C₄	—	3	2	no	—
545	C₂²×C₄	—	3	2	no	—
546	C₂²×C₄	—	3	4	no	—
547	C₂²×C₄	—	3	4	no	—
548	C₂²×C₄	—	6	8	no	—
549	C₂²×C₄	—	6	8	no	—
550	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
551	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
552	C₄⋊C₄	—	3	8	no	—
553	C₄⋊C₄	—	3	8	no	—
554	C₄⋊C₄	—	3	4	no	—
555	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
556	C₂²⋊C₄	—	3	4	no	—
557	C₂²⋊C₄	—	3	8	no	—
558	C₂²⋊C₄	—	3	8	no	—
559	C₂²⋊C₄	—	3	8	no	—
560	C₂²⋊C₄	C₂²×C₅×D₃	1	4	yes	—
561	C₂²⋊C₄	C₂²×C₅×D₃	1	8	yes	—
562	C₄²	—	3	4	no	—
563	C₄²	—	3	4	no	—
564	C₃×C₅	#3449	1	1	yes	characteristic, complemented, Hall
565	C₂²×C₃	—	2	2	no	—
566	C₂²×C₃	—	2	4	no	—
567	C₂²×C₃	—	2	4	no	—
568	C₂²×C₃	—	2	8	no	—
569	C₂²×C₃	—	4	4	no	—
570	C₂²×C₃	—	4	8	no	—
571	C₂²×C₃	C₂²×C₅×D₄	1	4	yes	—
572	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
573	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
574	C₂×D₃	—	2	4	no	—
575	C₂×D₃	—	2	8	no	—
576	C₂×D₃	—	4	8	no	—
577	C₃×C₄	—	2	4	no	—
578	C₃×C₄	—	2	4	no	—
579	Dic₃	—	2	4	no	—
580	Dic₃	—	2	4	no	—
581	Dic₃	C₂²×C₅×D₄	1	2	yes	—
582	Dic₃	C₂²×C₅×D₄	1	4	yes	—
583	Dic₃	C₂²×C₅×D₄	1	2	yes	—
584	C₂×C₅	—	2	4	no	—
585	C₂×C₅	—	2	2	no	—
586	C₂×C₅	—	4	4	no	—
587	C₂×C₅	—	12	4	no	—
588	C₂×C₅	C₂²×D₃×D₄	1	1	yes	characteristic
589	C₂×C₅	#5966	1	2	yes	—
590	C₂³	—	2	4	no	—
591	C₂³	—	3	4	no	—
592	C₂³	—	4	2	no	—
593	C₂³	—	4	4	no	—
594	C₂³	—	6	4	no	—
595	C₂³	—	12	4	no	—
596	C₂³	C₅×D₃×D₄	1	4	yes	—
597	C₂³	C₂³×C₅×D₃	1	4	yes	—
598	C₂³	C₂³×C₅×D₃	1	2	yes	—
599	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
600	Q₈	—	6	8	no	—
601	Q₈	—	6	8	no	—
602	D₄	—	2	8	no	—
603	D₄	—	2	8	no	—
604	D₄	—	4	4	no	—
605	D₄	—	6	8	no	—
606	D₄	—	6	8	no	—
607	D₄	—	6	8	no	—
608	D₄	—	6	8	no	—
609	D₄	—	12	4	no	—
610	D₄	—	12	8	no	—
611	C₂×C₄	—	2	4	no	—
612	C₂×C₄	—	3	8	no	—
613	C₂×C₄	—	3	8	no	—
614	C₂×C₄	—	3	4	no	—
615	C₂×C₄	—	3	4	no	—
616	C₂×C₄	—	3	1	no	—
617	C₂×C₄	—	3	1	no	—
618	C₂×C₄	—	3	2	no	—
619	C₂×C₄	—	3	4	no	—
620	C₂×C₄	—	3	4	no	—
621	C₂×C₄	—	4	2	no	—
622	C₂×C₄	—	6	8	no	—
623	C₂×C₄	—	6	8	no	—
624	C₂×C₄	—	6	8	no	—
625	C₂×C₄	—	6	8	no	—
626	C₂×C₄	—	6	4	no	—
627	C₂×C₄	—	12	2	no	—
628	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
629	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
630	C₂×C₃	—	2	4	no	—
631	C₂×C₃	—	2	2	no	—
632	C₂×C₃	—	4	4	no	—
633	C₂×C₃	C₂³×C₅×D₄	1	1	yes	characteristic
634	C₂×C₃	C₅×#585	1	2	yes	—
635	D₃	—	4	4	no	—
636	C₅	#86294	1	1	yes	characteristic, direct product factor, Sylow
637	C₂²	—	2	2	no	—
638	C₂²	—	2	4	no	—
639	C₂²	—	2	4	no	—
640	C₂²	—	2	8	no	—
641	C₂²	—	4	4	no	—
642	C₂²	—	4	8	no	—
643	C₂²	—	6	4	no	—
644	C₂²	—	6	8	no	—
645	C₂²	—	12	8	no	—
646	C₂²	C₂×C₅×D₃×D₄	1	4	yes	—
647	C₂²	C₂×C₅×D₃×D₄	1	2	yes	—
648	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
649	C₄	—	2	4	no	—
650	C₄	—	2	4	no	—
651	C₄	—	3	2	no	—
652	C₄	—	3	4	no	—
653	C₄	—	3	2	no	—
654	C₄	—	6	4	no	—
655	C₄	—	6	4	no	—
656	C₃	C₅×#3449	1	1	yes	characteristic, complemented, Sylow
657	C₂	—	2	4	no	—
658	C₂	—	2	2	no	—
659	C₂	—	4	4	no	—
660	C₂	—	12	4	no	—
661	C₂	C₂²×C₅×D₃×D₄	1	1	yes	characteristic
662	C₂	C₅×#5966	1	2	yes	—

	subgroup	G/H
center	C₂²×C₅	C₂⁴×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₃×C₅×#534	C₂
socle	C₂²×C₃×C₅	C₂⁵
hypercenter	C₅×#534	D₃
hypocenter	C₃	C₅×#3449
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₅×#534

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×#237	C₂	semidirect
2. C₃×C₅×#534	C₂	semidirect
3. C₅×#5804	C₂	semidirect
4. C₅×#5656	C₂	semidirect
5. C₅×#5648	C₂	semidirect
6. C₅×#5597	C₂	semidirect
7. C₅×#5596	C₂	semidirect
8. C₅×#5592	C₂	semidirect
9. C₅×#5586	C₂	semidirect
10. C₅×#5493	C₂	semidirect
11. C₂×C₅×#877	C₂	semidirect
15. C₂²×C₅×#67	C₂²	semidirect
17. C₂³×C₅×Dic₃	C₂²	semidirect
21. C₂×C₅×#237	C₂²	semidirect
22. C₂×C₅×#237	C₂²	semidirect
23. C₂²×C₄×C₅×D₃	C₂²	semidirect
24. C₂²×C₅×Dic₆	C₂²	semidirect
25. C₃×C₅×#123	C₂²	semidirect
26. C₃×C₅×#121	C₂²	semidirect
27. C₃×C₅×#120	C₂²	semidirect
29. C₅×#953	C₂²	semidirect
31. C₅×#940	C₂²	semidirect
32. C₅×#939	C₂²	semidirect
33. C₅×#939	C₂²	semidirect
34. C₅×#937	C₂²	semidirect
35. C₅×#935	C₂²	semidirect
36. C₅×D₄×Dic₃	C₂²	semidirect
37. C₅×#930	C₂²	semidirect
38. C₅×#929	C₂²	semidirect
39. C₂×C₅×Dic₃⋊C₄	C₂²	semidirect
40. C₂×C₄×C₅×Dic₃	C₂²	semidirect
41. C₅×#896	C₂²	semidirect
42. C₅×#893	C₂²	semidirect
43. C₅×#888	C₂²	semidirect
44. C₅×#886	C₂²	semidirect
45. C₅×#885	C₂²	semidirect
46. C₅×#884	C₂²	semidirect
47. C₅×#882	C₂²	semidirect
48. C₅×#67⋊C₄	C₂²	semidirect
49. C₅×#878	C₂²	semidirect
50. C₅×#877	C₂²	semidirect
51. C₅×#877	C₂²	semidirect
52. #86294	C₅	direct (N × H)
59. C₅×#534	D₃	semidirect
81. C₂²×C₅×Dic₃	D₄	semidirect
113. C₂²×#237	C₂×C₅	semidirect
114. C₃×#534	C₂×C₅	semidirect
115. #5804	C₂×C₅	semidirect
116. #5656	C₂×C₅	semidirect
117. #5648	C₂×C₅	semidirect
118. #5597	C₂×C₅	semidirect
119. #5596	C₂×C₅	semidirect
120. #5592	C₂×C₅	semidirect
121. #5586	C₂×C₅	semidirect
122. #5493	C₂×C₅	semidirect
123. C₂×#877	C₂×C₅	semidirect
142. C₅×#123	C₂×D₃	semidirect
149. C₅×#121	C₂×D₃	semidirect
153. C₅×#120	C₂×D₃	semidirect
206. C₂²×#67	C₂²×C₅	semidirect
208. C₂³×Dic₃	C₂²×C₅	semidirect
212. C₂×#237	C₂²×C₅	semidirect
213. C₂×#237	C₂²×C₅	semidirect
214. C₂²×C₄×D₃	C₂²×C₅	semidirect
215. C₂²×Dic₆	C₂²×C₅	semidirect
216. C₃×#123	C₂²×C₅	semidirect
217. C₃×#121	C₂²×C₅	semidirect
218. C₃×#120	C₂²×C₅	semidirect
220. #953	C₂²×C₅	semidirect
222. #940	C₂²×C₅	semidirect
223. #939	C₂²×C₅	semidirect
224. #939	C₂²×C₅	semidirect
225. #937	C₂²×C₅	semidirect
226. #935	C₂²×C₅	semidirect
227. D₄×Dic₃	C₂²×C₅	semidirect
228. #930	C₂²×C₅	semidirect
229. #929	C₂²×C₅	semidirect
230. C₂×Dic₃⋊C₄	C₂²×C₅	semidirect
231. C₂×C₄×Dic₃	C₂²×C₅	semidirect
232. #896	C₂²×C₅	semidirect
233. #893	C₂²×C₅	semidirect
234. #888	C₂²×C₅	semidirect
235. #886	C₂²×C₅	semidirect
236. #885	C₂²×C₅	semidirect
237. #884	C₂²×C₅	semidirect
238. #882	C₂²×C₅	semidirect
239. #67⋊C₄	C₂²×C₅	semidirect
240. #878	C₂²×C₅	semidirect
241. #877	C₂²×C₅	semidirect
242. #877	C₂²×C₅	semidirect
298. #534	C₅×D₃	semidirect
339. C₂²×Dic₃	C₅×D₄	semidirect
429. #123	C₂×C₅×D₃	semidirect
436. #121	C₂×C₅×D₃	semidirect
440. #120	C₂×C₅×D₃	semidirect
564. C₃×C₅	#3449	semidirect
636. C₅	#86294	direct (N × H)
656. C₃	C₅×#3449	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₅×#237	2
C₃×C₅×#534	2
C₅×#5804	2
C₅×#5656	2
C₅×#5648	2
C₅×#5597	2
C₅×#5596	2
C₅×#5592	2
C₅×#5586	2
C₅×#5493	2
C₂×C₅×#877	2
C₅×#3449	3
#86294	5

Subgroups — C5×#86294 #14480629

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#86294 #14480629