Subgroups — C₅×#82507 #14430225

Order 1920.

776 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×C₅×#41	C₂	1	1	yes	maximal, characteristic
2	C₅×#5470	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5233	C₂	1	2	yes	maximal
4	C₅×#5022	C₂	1	2	yes	maximal, complemented
5	C₅×#5021	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5020	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5009	C₂	1	2	yes	maximal, complemented
8	C₅×#5008	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#5007	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4998	C₂	1	2	yes	maximal, complemented
11	C₂×C₅×C₄⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3076	—	3	1	no	maximal, Hall
13	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
14	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
15	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
16	C₃×C₄×C₅×D₄	—	2	1	no	—
17	C₃×C₄×C₅×D₄	—	2	1	no	—
18	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
19	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
20	C₃×C₅×#117	—	2	1	no	—
21	C₃×C₅×#117	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₄²×C₅	—	2	1	no	—
23	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
24	C₅×#926	C₂²	1	2	yes	—
25	C₅×#924	—	2	1	no	—
26	C₅×#924	—	2	1	no	—
27	C₂²×C₅×C₃⋊C₈	C₂²	1	2	yes	—
28	C₅×#870	C₂²	1	2	yes	—
29	C₅×#869	C₂²	1	1	yes	characteristic
30	C₅×#869	C₂²	1	1	yes	characteristic
31	C₄×C₅×Dic₆	—	2	1	no	—
32	C₄×C₅×Dic₆	—	2	1	no	—
33	C₅×#835	C₂²	1	2	yes	—
34	C₅×#835	C₂²	1	2	yes	—
35	C₅×#832	C₂²	1	2	yes	—
36	C₅×#832	C₂²	1	2	yes	—
37	C₅×#808	C₂²	1	2	yes	—
38	C₅×#808	C₂²	1	2	yes	—
39	C₅×#807	C₂²	1	2	yes	—
40	C₅×#807	C₂²	1	2	yes	—
41	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
42	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
43	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	2	yes	—
44	#82507	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
45	C₅×#533	—	3	1	no	—
46	C₄×C₅×#41	D₃	1	1	yes	characteristic
47	C₅×#479	—	3	2	no	—
48	C₅×#478	—	3	2	no	—
49	C₅×#477	—	3	1	no	—
50	C₅×#476	—	3	1	no	—
51	C₅×#475	—	3	1	no	—
52	C₅×#474	—	3	1	no	—
53	C₅×#427	—	3	2	no	—
54	C₂×C₅×C₄⋊C₈	—	3	1	no	—
55	C₅×#416	—	3	2	no	—
56	C₃×C₅×#41	—	2	2	no	—
57	C₃×C₅×#41	Q₈	1	4	yes	complemented
58	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
59	C₂×C₃×C₅×D₄	—	2	1	no	—
60	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
61	C₂²×C₃×C₄×C₅	—	2	1	no	—
62	C₂²×C₃×C₄×C₅	—	2	1	no	—
63	C₂²×C₃×C₄×C₅	—	2	1	no	—
64	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
65	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
66	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
67	C₂×C₅×Dic₆	—	2	1	no	—
68	C₂×C₅×Dic₆	—	2	1	no	—
69	C₃×C₅×C₄⋊C₄	—	2	1	no	—
70	C₃×C₅×C₄⋊C₄	—	2	1	no	—
71	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
72	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
73	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
74	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
75	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
76	C₃×C₄²×C₅	—	2	1	no	—
77	C₃×C₄²×C₅	—	2	1	no	—
78	C₃×C₄²×C₅	—	2	1	no	—
79	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
80	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
81	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
82	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
83	C₅×#217	—	2	2	no	—
84	C₅×C₄⋊Dic₃	—	2	1	no	—
85	C₅×C₄⋊Dic₃	—	2	1	no	—
86	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
87	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
88	C₅×Dic₃⋊C₄	—	2	2	no	—
89	C₅×Dic₃⋊C₄	—	2	2	no	—
90	C₄×C₅×Dic₃	—	2	2	no	—
91	C₂×C₅×C₃⋊C₈	—	2	4	no	—
92	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
93	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
94	C₃×C₄×#41	C₂×C₅	1	1	yes	characteristic
95	#5470	C₂×C₅	1	1	yes	characteristic, complemented
96	#5233	C₂×C₅	1	2	yes	—
97	#5022	C₂×C₅	1	2	yes	complemented
98	#5021	C₂×C₅	1	1	yes	characteristic, complemented
99	#5020	C₂×C₅	1	1	yes	characteristic, complemented
100	#5009	C₂×C₅	1	2	yes	complemented
101	#5008	C₂×C₅	1	1	yes	characteristic, complemented
102	#5007	C₂×C₅	1	1	yes	characteristic, complemented
103	#4998	C₂×C₅	1	2	yes	complemented
104	C₂×C₄⋊(C₃⋊C₈)	C₂×C₅	1	1	yes	characteristic, complemented
105	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
106	C₂²×C₅×C₈	—	3	2	no	—
107	C₅×C₄⋊Q₈	—	3	1	no	—
108	C₅×C₄⋊Q₈	—	3	1	no	—
109	C₅×#125	—	3	2	no	—
110	C₅×C₂²⋊Q₈	—	6	1	no	—
111	C₅×C₂²⋊Q₈	—	6	1	no	—
112	C₄×C₅×Q₈	—	6	1	no	—
113	C₄×C₅×Q₈	—	6	1	no	—
114	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
115	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
116	C₄×C₅×D₄	—	2	1	no	—
117	C₄×C₅×D₄	—	2	1	no	—
118	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
119	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
120	C₅×#117	—	2	1	no	—
121	C₅×#117	—	3	2	no	—
122	C₅×#117	C₂×D₃	1	1	yes	characteristic
123	C₂×C₄²×C₅	—	2	1	no	—
124	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
125	C₅×#107	—	3	2	no	—
126	C₅×#107	—	3	2	no	—
127	C₅×#106	—	3	2	no	—
128	C₅×#106	—	3	2	no	—
129	C₅×C₄⋊C₈	—	3	1	no	—
130	C₅×C₄⋊C₈	—	3	1	no	—
131	C₅×C₄⋊C₈	—	3	2	no	—
132	C₅×#103	—	3	2	no	—
133	C₅×#103	—	3	2	no	—
134	C₅×#102	—	3	2	no	—
135	C₅×#102	—	3	2	no	—
136	#3076	—	3	1	no	Sylow
137	C₂³×C₃×C₅	—	2	1	no	—
138	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
139	C₃×C₅×Q₈	—	2	1	no	—
140	C₃×C₅×Q₈	C₂×Q₈	1	2	yes	—
141	C₃×C₅×D₄	—	2	4	no	—
142	C₃×C₅×D₄	—	2	1	no	—
143	C₃×C₅×D₄	C₂×Q₈	1	2	yes	—
144	C₂×C₃×C₄×C₅	—	2	1	no	—
145	C₂×C₃×C₄×C₅	—	2	4	no	—
146	C₂×C₃×C₄×C₅	—	2	2	no	—
147	C₂×C₃×C₄×C₅	—	2	1	no	—
148	C₂×C₃×C₄×C₅	—	2	1	no	—
149	C₂×C₃×C₄×C₅	—	4	1	no	—
150	C₂×C₃×C₄×C₅	—	4	2	no	—
151	C₂×C₃×C₄×C₅	—	4	2	no	—
152	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
153	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
154	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
155	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
156	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
157	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
158	C₂×C₃×C₄×C₅	#41	1	2	yes	—
159	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
160	C₂×C₅×Dic₃	—	2	2	no	—
161	C₂×C₅×Dic₃	—	2	2	no	—
162	C₅×Dic₆	—	4	2	no	—
163	C₅×Dic₆	—	4	2	no	—
164	C₅×C₃⋊C₈	—	2	2	no	—
165	C₅×C₃⋊C₈	—	2	2	no	—
166	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
167	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
168	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
169	C₃×C₄×D₄	—	2	1	no	—
170	C₃×C₄×D₄	—	2	1	no	—
171	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
172	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
173	C₃×#117	—	2	1	no	—
174	C₃×#117	C₂²×C₅	1	1	yes	characteristic
175	C₂×C₃×C₄²	—	2	1	no	—
176	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
177	#926	C₂²×C₅	1	2	yes	—
178	#924	—	2	1	no	—
179	#924	—	2	1	no	—
180	C₂²×C₃⋊C₈	C₂²×C₅	1	2	yes	—
181	#870	C₂²×C₅	1	2	yes	—
182	#869	C₂²×C₅	1	1	yes	characteristic
183	#869	C₂²×C₅	1	1	yes	characteristic
184	C₄×Dic₆	—	2	1	no	—
185	C₄×Dic₆	—	2	1	no	—
186	#835	C₂²×C₅	1	2	yes	—
187	#835	C₂²×C₅	1	2	yes	—
188	#832	C₂²×C₅	1	2	yes	—
189	#832	C₂²×C₅	1	2	yes	—
190	#808	C₂²×C₅	1	2	yes	—
191	#808	C₂²×C₅	1	2	yes	—
192	#807	C₂²×C₅	1	2	yes	—
193	#807	C₂²×C₅	1	2	yes	—
194	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic
195	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic
196	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	2	yes	—
197	C₅×#41	—	2	2	no	—
198	C₅×#41	Dic₆	1	4	yes	complemented
199	C₂×C₅×Q₈	—	6	1	no	—
200	C₂×C₅×Q₈	—	6	1	no	—
201	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
202	C₂×C₅×D₄	—	2	1	no	—
203	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
204	C₂²×C₄×C₅	—	2	1	no	—
205	C₂²×C₄×C₅	—	2	1	no	—
206	C₂²×C₄×C₅	—	2	1	no	—
207	C₂²×C₄×C₅	#67	1	1	yes	characteristic
208	C₂²×C₄×C₅	#67	1	1	yes	characteristic
209	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
210	C₂×C₅×C₈	—	3	2	no	—
211	C₂×C₅×C₈	—	3	2	no	—
212	C₂×C₅×C₈	—	6	4	no	—
213	C₅×C₄⋊C₄	—	2	1	no	—
214	C₅×C₄⋊C₄	—	2	1	no	—
215	C₅×C₄⋊C₄	—	3	2	no	—
216	C₅×C₄⋊C₄	—	3	2	no	—
217	C₅×C₄⋊C₄	—	6	2	no	—
218	C₅×C₄⋊C₄	—	6	2	no	—
219	C₅×C₄⋊C₄	—	6	1	no	—
220	C₅×C₄⋊C₄	—	6	1	no	—
221	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
222	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
223	C₅×C₂²⋊C₄	—	2	1	no	—
224	C₅×C₂²⋊C₄	—	2	1	no	—
225	C₅×C₂²⋊C₄	—	2	1	no	—
226	C₅×C₂²⋊C₄	—	6	2	no	—
227	C₄²×C₅	—	2	1	no	—
228	C₄²×C₅	—	2	1	no	—
229	C₄²×C₅	—	2	1	no	—
230	C₄²×C₅	—	6	2	no	—
231	C₄²×C₅	#67	1	1	yes	characteristic
232	C₄²×C₅	#67	1	1	yes	characteristic
233	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
234	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
235	#533	—	3	1	no	—
236	C₄×#41	C₅×D₃	1	1	yes	characteristic
237	#479	—	3	2	no	—
238	#478	—	3	2	no	—
239	#477	—	3	1	no	—
240	#476	—	3	1	no	—
241	#475	—	3	1	no	—
242	#474	—	3	1	no	—
243	#427	—	3	2	no	—
244	C₂×C₄⋊C₈	—	3	1	no	—
245	#416	—	3	2	no	—
246	C₂²×C₃×C₅	—	2	1	no	—
247	C₂²×C₃×C₅	—	2	1	no	—
248	C₂²×C₃×C₅	—	2	2	no	—
249	C₂²×C₃×C₅	—	4	1	no	—
250	C₂²×C₃×C₅	—	4	1	no	—
251	C₂²×C₃×C₅	C₂²⋊Q₈	1	2	yes	—
252	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
253	C₃×C₄×C₅	—	2	2	no	—
254	C₃×C₄×C₅	—	2	1	no	—
255	C₃×C₄×C₅	—	2	1	no	—
256	C₃×C₄×C₅	—	2	1	no	—
257	C₃×C₄×C₅	—	4	1	no	—
258	C₃×C₄×C₅	—	4	1	no	—
259	C₃×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
260	C₃×C₄×C₅	#135	1	2	yes	—
261	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
262	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
263	C₅×Dic₃	—	4	2	no	—
264	C₅×Dic₃	—	4	2	no	—
265	C₃×#41	—	2	2	no	—
266	C₃×#41	C₅×Q₈	1	4	yes	complemented
267	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
268	C₂×C₃×D₄	—	2	1	no	—
269	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
270	C₂²×C₃×C₄	—	2	1	no	—
271	C₂²×C₃×C₄	—	2	1	no	—
272	C₂²×C₃×C₄	—	2	1	no	—
273	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
274	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
275	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
276	C₂×Dic₆	—	2	1	no	—
277	C₂×Dic₆	—	2	1	no	—
278	C₃×C₄⋊C₄	—	2	1	no	—
279	C₃×C₄⋊C₄	—	2	1	no	—
280	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
281	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
282	C₃×C₂²⋊C₄	—	2	1	no	—
283	C₃×C₂²⋊C₄	—	2	1	no	—
284	C₃×C₂²⋊C₄	—	2	1	no	—
285	C₃×C₄²	—	2	1	no	—
286	C₃×C₄²	—	2	1	no	—
287	C₃×C₄²	—	2	1	no	—
288	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
289	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
290	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
291	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
292	#217	—	2	2	no	—
293	C₄⋊Dic₃	—	2	1	no	—
294	C₄⋊Dic₃	—	2	1	no	—
295	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
296	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
297	Dic₃⋊C₄	—	2	2	no	—
298	Dic₃⋊C₄	—	2	2	no	—
299	C₄×Dic₃	—	2	2	no	—
300	C₂×C₃⋊C₈	—	2	4	no	—
301	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
302	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
303	C₂³×C₅	—	2	1	no	—
304	C₂³×C₅	C₂×#67	1	1	yes	characteristic
305	C₅×Q₈	—	2	1	no	—
306	C₅×Q₈	—	12	2	no	—
307	C₅×Q₈	—	12	2	no	—
308	C₅×Q₈	C₂×Dic₆	1	2	yes	—
309	C₅×D₄	—	2	4	no	—
310	C₅×D₄	—	2	1	no	—
311	C₅×D₄	C₂×Dic₆	1	2	yes	—
312	C₂×C₄×C₅	—	2	1	no	—
313	C₂×C₄×C₅	—	2	4	no	—
314	C₂×C₄×C₅	—	2	2	no	—
315	C₂×C₄×C₅	—	2	1	no	—
316	C₂×C₄×C₅	—	2	1	no	—
317	C₂×C₄×C₅	—	4	1	no	—
318	C₂×C₄×C₅	—	4	2	no	—
319	C₂×C₄×C₅	—	4	2	no	—
320	C₂×C₄×C₅	—	6	2	no	—
321	C₂×C₄×C₅	—	6	2	no	—
322	C₂×C₄×C₅	C₂×Dic₆	1	2	yes	—
323	C₂×C₄×C₅	#235	1	2	yes	—
324	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
325	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
326	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
327	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
328	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
329	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
330	C₅×C₈	—	6	2	no	—
331	C₅×C₈	—	6	2	no	—
332	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
333	C₂²×C₈	—	3	2	no	—
334	C₄⋊Q₈	—	3	1	no	—
335	C₄⋊Q₈	—	3	1	no	—
336	#125	—	3	2	no	—
337	C₂²⋊Q₈	—	6	1	no	—
338	C₂²⋊Q₈	—	6	1	no	—
339	C₄×Q₈	—	6	1	no	—
340	C₄×Q₈	—	6	1	no	—
341	C₄×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
342	C₄×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
343	C₄×D₄	—	2	1	no	—
344	C₄×D₄	—	2	1	no	—
345	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic
346	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic
347	#117	—	2	1	no	—
348	#117	—	3	2	no	—
349	#117	C₂×C₅×D₃	1	1	yes	characteristic
350	C₂×C₄²	—	2	1	no	—
351	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
352	#107	—	3	2	no	—
353	#107	—	3	2	no	—
354	#106	—	3	2	no	—
355	#106	—	3	2	no	—
356	C₄⋊C₈	—	3	1	no	—
357	C₄⋊C₈	—	3	1	no	—
358	C₄⋊C₈	—	3	2	no	—
359	#103	—	3	2	no	—
360	#103	—	3	2	no	—
361	#102	—	3	2	no	—
362	#102	—	3	2	no	—
363	C₂×C₃×C₅	—	2	2	no	—
364	C₂×C₃×C₅	—	4	2	no	—
365	C₂×C₃×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
366	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
367	C₂×C₃×C₅	#575	1	1	yes	characteristic
368	C₂³×C₃	—	2	1	no	—
369	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
370	C₃×Q₈	—	2	1	no	—
371	C₃×Q₈	C₂×C₅×Q₈	1	2	yes	—
372	C₃×D₄	—	2	4	no	—
373	C₃×D₄	—	2	1	no	—
374	C₃×D₄	C₂×C₅×Q₈	1	2	yes	—
375	C₂×C₃×C₄	—	2	1	no	—
376	C₂×C₃×C₄	—	2	4	no	—
377	C₂×C₃×C₄	—	2	2	no	—
378	C₂×C₃×C₄	—	2	1	no	—
379	C₂×C₃×C₄	—	2	1	no	—
380	C₂×C₃×C₄	—	4	1	no	—
381	C₂×C₃×C₄	—	4	2	no	—
382	C₂×C₃×C₄	—	4	2	no	—
383	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
384	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
385	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
386	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
387	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
388	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
389	C₂×C₃×C₄	C₅×#41	1	2	yes	—
390	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
391	C₂×Dic₃	—	2	2	no	—
392	C₂×Dic₃	—	2	2	no	—
393	Dic₆	—	4	2	no	—
394	Dic₆	—	4	2	no	—
395	C₃⋊C₈	—	2	2	no	—
396	C₃⋊C₈	—	2	2	no	—
397	C₂²×C₅	—	2	1	no	—
398	C₂²×C₅	—	2	1	no	—
399	C₂²×C₅	—	2	2	no	—
400	C₂²×C₅	—	4	1	no	—
401	C₂²×C₅	—	4	1	no	—
402	C₂²×C₅	#924	1	2	yes	—
403	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
404	C₄×C₅	—	2	2	no	—
405	C₄×C₅	—	2	1	no	—
406	C₄×C₅	—	2	1	no	—
407	C₄×C₅	—	2	1	no	—
408	C₄×C₅	—	4	1	no	—
409	C₄×C₅	—	4	1	no	—
410	C₄×C₅	—	12	2	no	—
411	C₄×C₅	—	12	2	no	—
412	C₄×C₅	#924	1	2	yes	—
413	C₄×C₅	#950	1	2	yes	—
414	C₄×C₅	C₂²×Dic₆	1	1	yes	characteristic
415	C₄×C₅	C₂×#235	1	1	yes	characteristic
416	#41	—	2	2	no	—
417	#41	C₅×Dic₆	1	4	yes	complemented
418	C₂×Q₈	—	6	1	no	—
419	C₂×Q₈	—	6	1	no	—
420	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
421	C₂×D₄	—	2	1	no	—
422	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	C₅×#67	1	1	yes	characteristic
427	C₂²×C₄	C₅×#67	1	1	yes	characteristic
428	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
429	C₂×C₈	—	3	2	no	—
430	C₂×C₈	—	3	2	no	—
431	C₂×C₈	—	6	4	no	—
432	C₄⋊C₄	—	2	1	no	—
433	C₄⋊C₄	—	2	1	no	—
434	C₄⋊C₄	—	3	2	no	—
435	C₄⋊C₄	—	3	2	no	—
436	C₄⋊C₄	—	6	2	no	—
437	C₄⋊C₄	—	6	2	no	—
438	C₄⋊C₄	—	6	1	no	—
439	C₄⋊C₄	—	6	1	no	—
440	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
441	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
442	C₂²⋊C₄	—	2	1	no	—
443	C₂²⋊C₄	—	2	1	no	—
444	C₂²⋊C₄	—	2	1	no	—
445	C₂²⋊C₄	—	6	2	no	—
446	C₄²	—	2	1	no	—
447	C₄²	—	2	1	no	—
448	C₄²	—	2	1	no	—
449	C₄²	—	6	2	no	—
450	C₄²	C₅×#67	1	1	yes	characteristic
451	C₄²	C₅×#67	1	1	yes	characteristic
452	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
453	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
454	C₃×C₅	#3076	1	1	yes	characteristic, complemented, Hall
455	C₂²×C₃	—	2	1	no	—
456	C₂²×C₃	—	2	1	no	—
457	C₂²×C₃	—	2	2	no	—
458	C₂²×C₃	—	4	1	no	—
459	C₂²×C₃	—	4	1	no	—
460	C₂²×C₃	C₅×C₂²⋊Q₈	1	2	yes	—
461	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
462	C₃×C₄	—	2	2	no	—
463	C₃×C₄	—	2	1	no	—
464	C₃×C₄	—	2	1	no	—
465	C₃×C₄	—	2	1	no	—
466	C₃×C₄	—	4	1	no	—
467	C₃×C₄	—	4	1	no	—
468	C₃×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
469	C₃×C₄	C₅×#135	1	2	yes	—
470	C₃×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
471	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
472	Dic₃	—	4	2	no	—
473	Dic₃	—	4	2	no	—
474	C₂×C₅	—	2	2	no	—
475	C₂×C₅	—	4	2	no	—
476	C₂×C₅	C₂×#924	1	1	yes	characteristic
477	C₂×C₅	C₂×#950	1	1	yes	characteristic
478	C₂×C₅	#5822	1	1	yes	characteristic
479	C₂³	—	2	1	no	—
480	C₂³	C₂×C₅×#67	1	1	yes	characteristic
481	Q₈	—	2	1	no	—
482	Q₈	—	12	2	no	—
483	Q₈	—	12	2	no	—
484	Q₈	C₂×C₅×Dic₆	1	2	yes	—
485	D₄	—	2	4	no	—
486	D₄	—	2	1	no	—
487	D₄	C₂×C₅×Dic₆	1	2	yes	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	4	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	4	1	no	—
494	C₂×C₄	—	4	2	no	—
495	C₂×C₄	—	4	2	no	—
496	C₂×C₄	—	6	2	no	—
497	C₂×C₄	—	6	2	no	—
498	C₂×C₄	C₂×C₅×Dic₆	1	2	yes	—
499	C₂×C₄	C₅×#235	1	2	yes	—
500	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
501	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
502	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
503	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
504	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
505	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
506	C₈	—	6	2	no	—
507	C₈	—	6	2	no	—
508	C₂×C₃	—	2	2	no	—
509	C₂×C₃	—	4	2	no	—
510	C₂×C₃	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
511	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
512	C₂×C₃	C₅×#575	1	1	yes	characteristic
513	C₅	#82507	1	1	yes	characteristic, direct product factor, Sylow
514	C₂²	—	2	1	no	—
515	C₂²	—	2	1	no	—
516	C₂²	—	2	2	no	—
517	C₂²	—	4	1	no	—
518	C₂²	—	4	1	no	—
519	C₂²	C₅×#924	1	2	yes	—
520	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
521	C₄	—	2	2	no	—
522	C₄	—	2	1	no	—
523	C₄	—	2	1	no	—
524	C₄	—	2	1	no	—
525	C₄	—	4	1	no	—
526	C₄	—	4	1	no	—
527	C₄	—	12	2	no	—
528	C₄	—	12	2	no	—
529	C₄	C₅×#924	1	2	yes	—
530	C₄	C₅×#950	1	2	yes	—
531	C₄	C₂²×C₅×Dic₆	1	1	yes	characteristic
532	C₄	C₂×C₅×#235	1	1	yes	characteristic
533	C₃	C₅×#3076	1	1	yes	characteristic, complemented, Sylow
534	C₂	—	2	2	no	—
535	C₂	—	4	2	no	—
536	C₂	C₂×C₅×#924	1	1	yes	characteristic
537	C₂	C₂×C₅×#950	1	1	yes	characteristic
538	C₂	C₅×#5822	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂×#67
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₄×C₅×#41	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₃×C₅×#41	C₂²
hypercenter	C₄×C₅×#41	D₃
hypocenter	C₃	C₅×#3076
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₄²×C₅ ◁ C₄×C₅×#41

Complements

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

N	H ≅ G/N	type
2. C₅×#5470	C₂	semidirect
4. C₅×#5022	C₂	semidirect
5. C₅×#5021	C₂	semidirect
6. C₅×#5020	C₂	semidirect
7. C₅×#5009	C₂	semidirect
8. C₅×#5008	C₂	semidirect
9. C₅×#5007	C₂	semidirect
10. C₅×#4998	C₂	semidirect
11. C₂×C₅×C₄⋊(C₃⋊C₈)	C₂	semidirect
44. #82507	C₅	direct (N × H)
57. C₃×C₅×#41	Q₈	semidirect
95. #5470	C₂×C₅	semidirect
97. #5022	C₂×C₅	semidirect
98. #5021	C₂×C₅	semidirect
99. #5020	C₂×C₅	semidirect
100. #5009	C₂×C₅	semidirect
101. #5008	C₂×C₅	semidirect
102. #5007	C₂×C₅	semidirect
103. #4998	C₂×C₅	semidirect
104. C₂×C₄⋊(C₃⋊C₈)	C₂×C₅	semidirect
198. C₅×#41	Dic₆	semidirect
266. C₃×#41	C₅×Q₈	semidirect
417. #41	C₅×Dic₆	semidirect
454. C₃×C₅	#3076	semidirect
513. C₅	#82507	direct (N × H)
533. C₃	C₅×#3076	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄×C₅×#41	2
C₅×#5470	2
C₅×#5233	2
C₅×#5022	2
C₅×#5021	2
C₅×#5020	2
C₅×#5009	2
C₅×#5008	2
C₅×#5007	2
C₅×#4998	2
C₂×C₅×C₄⋊(C₃⋊C₈)	2
C₅×#3076	3
#82507	5

Subgroups — C5×#82507 #14430225

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#82507 #14430225