Subgroups — C₅×#83349 #14430207

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×C₅×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₅×#235	C₂	1	1	yes	maximal, characteristic
3	C₅×#5094	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5091	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5087	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5084	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5066	C₂	1	2	yes	maximal, complemented
8	C₅×#5063	C₂	1	2	yes	maximal, complemented
9	C₅×#5002	C₂	1	2	yes	maximal
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×C₅×#235	C₂²	1	1	yes	characteristic
14	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₃×C₅×#125	C₂²	1	2	yes	—
17	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
18	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
19	C₃×C₄×C₅×Q₈	—	2	1	no	—
20	C₃×C₄×C₅×Q₈	—	2	1	no	—
21	C₃×C₅×#117	C₂²	1	2	yes	—
22	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
23	C₄×C₅×#67	—	2	1	no	—
24	C₄×C₅×#67	—	2	1	no	—
25	C₅×#926	C₂²	1	1	yes	characteristic
26	C₂²×C₅×C₃⋊C₈	C₂²	1	2	yes	—
27	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
28	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
29	C₅×#872	—	2	1	no	—
30	C₄²×C₅×D₃	—	2	1	no	—
31	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
32	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
33	C₅×#810	C₂²	1	2	yes	—
34	C₅×#810	C₂²	1	2	yes	—
35	C₅×#809	C₂²	1	2	yes	—
36	C₅×#809	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	2	yes	—
42	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
43	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
44	#83349	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
45	C₅×#533	D₃	1	1	yes	characteristic, complemented
46	C₄×C₅×#41	—	3	1	no	—
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	C₂×C₃×C₅×Q₈	—	2	1	no	—
57	C₂×C₃×C₅×Q₈	—	2	1	no	—
58	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
59	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
60	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
61	C₂×C₅×#67	—	2	1	no	—
62	C₅×#235	—	2	2	no	—
63	C₅×#235	Q₈	1	4	yes	complemented
64	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
65	C₂×C₄×C₅×D₃	—	2	1	no	—
66	C₂×C₄×C₅×D₃	—	2	1	no	—
67	C₂×C₄×C₅×D₃	—	2	1	no	—
68	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
69	C₃×C₅×C₄⋊C₄	—	2	2	no	—
70	C₃×C₅×C₄⋊C₄	—	2	2	no	—
71	C₃×C₅×C₄⋊C₄	—	2	1	no	—
72	C₃×C₅×C₄⋊C₄	—	2	1	no	—
73	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
74	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
75	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
76	C₃×C₄²×C₅	—	2	2	no	—
77	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
78	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
79	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
80	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
81	C₅×#217	—	2	1	no	—
82	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
83	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
84	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
85	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
86	C₅×Dic₃⋊C₄	—	2	1	no	—
87	C₅×Dic₃⋊C₄	—	2	1	no	—
88	C₄×C₅×Dic₃	—	2	1	no	—
89	C₄×C₅×Dic₃	—	2	1	no	—
90	C₄×C₅×Dic₃	—	2	1	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×#533	C₂×C₅	1	1	yes	characteristic, complemented
95	C₄×#235	C₂×C₅	1	1	yes	characteristic
96	#5094	C₂×C₅	1	1	yes	characteristic, complemented
97	#5091	C₂×C₅	1	1	yes	characteristic, complemented
98	#5087	C₂×C₅	1	1	yes	characteristic, complemented
99	#5084	C₂×C₅	1	1	yes	characteristic, complemented
100	#5066	C₂×C₅	1	2	yes	complemented
101	#5063	C₂×C₅	1	2	yes	complemented
102	#5002	C₂×C₅	1	2	yes	—
103	#4998	C₂×C₅	1	2	yes	complemented
104	C₂×C₄⋊(C₃⋊C₈)	C₂×C₅	1	1	yes	characteristic, complemented
105	C₂×C₅×#41	—	3	1	no	—
106	C₂²×C₅×C₈	—	3	2	no	—
107	C₅×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic
108	C₅×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic
109	C₅×#125	C₂×D₃	1	2	yes	—
110	C₅×C₂²⋊Q₈	—	2	1	no	—
111	C₅×C₂²⋊Q₈	—	2	1	no	—
112	C₄×C₅×Q₈	—	2	1	no	—
113	C₄×C₅×Q₈	—	2	1	no	—
114	C₄×C₅×Q₈	—	3	1	no	—
115	C₄×C₅×Q₈	—	3	1	no	—
116	C₄×C₅×D₄	—	3	1	no	—
117	C₄×C₅×D₄	—	3	1	no	—
118	C₄×C₅×D₄	—	6	1	no	—
119	C₄×C₅×D₄	—	6	1	no	—
120	C₅×#117	—	3	1	no	—
121	C₅×#117	—	6	1	no	—
122	C₅×#117	C₂×D₃	1	2	yes	—
123	C₂×C₄²×C₅	—	6	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	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₅×D₃	—	2	1	no	—
139	C₃×C₅×Q₈	—	4	2	no	—
140	C₃×C₅×Q₈	—	4	2	no	—
141	C₂×C₃×C₄×C₅	—	2	2	no	—
142	C₂×C₃×C₄×C₅	—	2	2	no	—
143	C₂×C₃×C₄×C₅	—	2	2	no	—
144	C₂×C₃×C₄×C₅	—	4	1	no	—
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	1	yes	characteristic
148	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
149	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
150	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
151	C₂×C₃×C₄×C₅	#41	1	2	yes	—
152	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
153	C₅×#67	—	2	4	no	—
154	C₂×C₅×Dic₃	—	2	1	no	—
155	C₂×C₅×Dic₃	—	2	1	no	—
156	C₂×C₅×Dic₃	—	2	1	no	—
157	C₅×D₁₂	—	2	1	no	—
158	C₅×D₁₂	C₂×Q₈	1	2	yes	—
159	C₄×C₅×D₃	—	2	4	no	—
160	C₄×C₅×D₃	—	4	2	no	—
161	C₄×C₅×D₃	—	4	2	no	—
162	C₅×Dic₆	—	2	1	no	—
163	C₅×Dic₆	C₂×Q₈	1	2	yes	—
164	C₅×C₃⋊C₈	—	2	2	no	—
165	C₅×C₃⋊C₈	—	2	2	no	—
166	C₂×#235	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×#125	C₂²×C₅	1	2	yes	—
170	C₃×C₂²⋊Q₈	—	2	1	no	—
171	C₃×C₂²⋊Q₈	—	2	1	no	—
172	C₃×C₄×Q₈	—	2	1	no	—
173	C₃×C₄×Q₈	—	2	1	no	—
174	C₃×#117	C₂²×C₅	1	2	yes	—
175	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
176	C₄×#67	—	2	1	no	—
177	C₄×#67	—	2	1	no	—
178	#926	C₂²×C₅	1	1	yes	characteristic
179	C₂²×C₃⋊C₈	C₂²×C₅	1	2	yes	—
180	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
181	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
182	#872	—	2	1	no	—
183	C₄²×D₃	—	2	1	no	—
184	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic
185	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic
186	#810	C₂²×C₅	1	2	yes	—
187	#810	C₂²×C₅	1	2	yes	—
188	#809	C₂²×C₅	1	2	yes	—
189	#809	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	2	yes	—
195	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic
196	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic
197	C₅×#41	—	3	4	no	—
198	C₅×#41	—	6	2	no	—
199	C₂×C₅×Q₈	—	2	1	no	—
200	C₂×C₅×Q₈	—	2	1	no	—
201	C₂×C₅×Q₈	—	3	1	no	—
202	C₂×C₅×D₄	—	3	1	no	—
203	C₂×C₅×D₄	—	6	1	no	—
204	C₂²×C₄×C₅	—	6	1	no	—
205	C₂²×C₄×C₅	—	6	1	no	—
206	C₂²×C₄×C₅	—	6	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	2	no	—
214	C₅×C₄⋊C₄	—	2	2	no	—
215	C₅×C₄⋊C₄	—	2	1	no	—
216	C₅×C₄⋊C₄	—	2	1	no	—
217	C₅×C₄⋊C₄	—	3	1	no	—
218	C₅×C₄⋊C₄	—	3	1	no	—
219	C₅×C₄⋊C₄	—	6	1	no	—
220	C₅×C₄⋊C₄	—	6	1	no	—
221	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
222	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
223	C₅×C₂²⋊C₄	—	2	2	no	—
224	C₅×C₂²⋊C₄	—	6	1	no	—
225	C₅×C₂²⋊C₄	—	6	1	no	—
226	C₅×C₂²⋊C₄	—	6	1	no	—
227	C₄²×C₅	—	2	2	no	—
228	C₄²×C₅	—	6	1	no	—
229	C₄²×C₅	—	6	1	no	—
230	C₄²×C₅	—	6	1	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	C₅×D₃	1	1	yes	characteristic, complemented
236	C₄×#41	—	3	1	no	—
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	C₂²⋊Q₈	1	2	yes	—
249	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
250	C₂×C₅×D₃	—	2	2	no	—
251	C₂×C₅×D₃	—	4	1	no	—
252	C₂×C₅×D₃	—	4	1	no	—
253	C₃×C₄×C₅	—	2	1	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	C₂²⋊Q₈	1	2	yes	—
259	C₃×C₄×C₅	#135	1	2	yes	—
260	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
261	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
262	C₅×Dic₃	—	2	2	no	—
263	C₅×Dic₃	—	4	1	no	—
264	C₅×Dic₃	—	4	1	no	—
265	C₂×C₃×Q₈	—	2	1	no	—
266	C₂×C₃×Q₈	—	2	1	no	—
267	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
268	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
269	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
270	C₂×#67	—	2	1	no	—
271	#235	—	2	2	no	—
272	#235	C₅×Q₈	1	4	yes	complemented
273	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
274	C₂×C₄×D₃	—	2	1	no	—
275	C₂×C₄×D₃	—	2	1	no	—
276	C₂×C₄×D₃	—	2	1	no	—
277	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
278	C₃×C₄⋊C₄	—	2	2	no	—
279	C₃×C₄⋊C₄	—	2	2	no	—
280	C₃×C₄⋊C₄	—	2	1	no	—
281	C₃×C₄⋊C₄	—	2	1	no	—
282	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
283	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
284	C₃×C₂²⋊C₄	—	2	2	no	—
285	C₃×C₄²	—	2	2	no	—
286	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
287	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
288	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
289	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
290	#217	—	2	1	no	—
291	(C₂×D₃)⋊C₄	—	2	1	no	—
292	(C₂×D₃)⋊C₄	—	2	1	no	—
293	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
294	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
295	Dic₃⋊C₄	—	2	1	no	—
296	Dic₃⋊C₄	—	2	1	no	—
297	C₄×Dic₃	—	2	1	no	—
298	C₄×Dic₃	—	2	1	no	—
299	C₄×Dic₃	—	2	1	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	—	6	1	no	—
304	C₂³×C₅	C₂×#67	1	1	yes	characteristic
305	C₅×Q₈	—	3	2	no	—
306	C₅×Q₈	—	4	2	no	—
307	C₅×Q₈	—	4	2	no	—
308	C₅×Q₈	—	6	1	no	—
309	C₅×D₄	—	3	2	no	—
310	C₅×D₄	—	6	4	no	—
311	C₅×D₄	—	6	1	no	—
312	C₂×C₄×C₅	—	2	2	no	—
313	C₂×C₄×C₅	—	2	2	no	—
314	C₂×C₄×C₅	—	2	2	no	—
315	C₂×C₄×C₅	—	4	1	no	—
316	C₂×C₄×C₅	—	6	1	no	—
317	C₂×C₄×C₅	—	6	4	no	—
318	C₂×C₄×C₅	—	6	1	no	—
319	C₂×C₄×C₅	—	6	1	no	—
320	C₂×C₄×C₅	—	12	2	no	—
321	C₂×C₄×C₅	—	12	2	no	—
322	C₂×C₄×C₅	D₃×Q₈	1	2	yes	—
323	C₂×C₄×C₅	#239	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	—	3	1	no	—
333	C₂²×C₈	—	3	2	no	—
334	C₄⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic
335	C₄⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic
336	#125	C₂×C₅×D₃	1	2	yes	—
337	C₂²⋊Q₈	—	2	1	no	—
338	C₂²⋊Q₈	—	2	1	no	—
339	C₄×Q₈	—	2	1	no	—
340	C₄×Q₈	—	2	1	no	—
341	C₄×Q₈	—	3	1	no	—
342	C₄×Q₈	—	3	1	no	—
343	C₄×D₄	—	3	1	no	—
344	C₄×D₄	—	3	1	no	—
345	C₄×D₄	—	6	1	no	—
346	C₄×D₄	—	6	1	no	—
347	#117	—	3	1	no	—
348	#117	—	6	1	no	—
349	#117	C₂×C₅×D₃	1	2	yes	—
350	C₂×C₄²	—	6	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	C₂×C₂²⋊Q₈	1	1	yes	characteristic
365	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
366	C₂×C₃×C₅	#575	1	1	yes	characteristic
367	C₅×D₃	—	4	2	no	—
368	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
369	C₂²×D₃	—	2	1	no	—
370	C₃×Q₈	—	4	2	no	—
371	C₃×Q₈	—	4	2	no	—
372	C₂×C₃×C₄	—	2	2	no	—
373	C₂×C₃×C₄	—	2	2	no	—
374	C₂×C₃×C₄	—	2	2	no	—
375	C₂×C₃×C₄	—	4	1	no	—
376	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
377	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
378	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
379	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
380	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
381	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
382	C₂×C₃×C₄	C₅×#41	1	2	yes	—
383	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
384	#67	—	2	4	no	—
385	C₂×Dic₃	—	2	1	no	—
386	C₂×Dic₃	—	2	1	no	—
387	C₂×Dic₃	—	2	1	no	—
388	D₁₂	—	2	1	no	—
389	D₁₂	C₂×C₅×Q₈	1	2	yes	—
390	C₄×D₃	—	2	4	no	—
391	C₄×D₃	—	4	2	no	—
392	C₄×D₃	—	4	2	no	—
393	Dic₆	—	2	1	no	—
394	Dic₆	C₂×C₅×Q₈	1	2	yes	—
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	—	6	2	no	—
400	C₂²×C₅	—	12	1	no	—
401	C₂²×C₅	—	12	1	no	—
402	C₂²×C₅	#946	1	2	yes	—
403	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
404	C₄×C₅	—	2	1	no	—
405	C₄×C₅	—	2	1	no	—
406	C₄×C₅	—	2	1	no	—
407	C₄×C₅	—	4	2	no	—
408	C₄×C₅	—	4	2	no	—
409	C₄×C₅	—	6	2	no	—
410	C₄×C₅	—	12	1	no	—
411	C₄×C₅	—	12	1	no	—
412	C₄×C₅	#946	1	2	yes	—
413	C₄×C₅	#950	1	2	yes	—
414	C₄×C₅	C₂×D₃×Q₈	1	1	yes	characteristic
415	C₄×C₅	C₂×#239	1	1	yes	characteristic
416	#41	—	3	4	no	—
417	#41	—	6	2	no	—
418	C₂×Q₈	—	2	1	no	—
419	C₂×Q₈	—	2	1	no	—
420	C₂×Q₈	—	3	1	no	—
421	C₂×D₄	—	3	1	no	—
422	C₂×D₄	—	6	1	no	—
423	C₂²×C₄	—	6	1	no	—
424	C₂²×C₄	—	6	1	no	—
425	C₂²×C₄	—	6	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	2	no	—
433	C₄⋊C₄	—	2	2	no	—
434	C₄⋊C₄	—	2	1	no	—
435	C₄⋊C₄	—	2	1	no	—
436	C₄⋊C₄	—	3	1	no	—
437	C₄⋊C₄	—	3	1	no	—
438	C₄⋊C₄	—	6	1	no	—
439	C₄⋊C₄	—	6	1	no	—
440	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
441	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
442	C₂²⋊C₄	—	2	2	no	—
443	C₂²⋊C₄	—	6	1	no	—
444	C₂²⋊C₄	—	6	1	no	—
445	C₂²⋊C₄	—	6	1	no	—
446	C₄²	—	2	2	no	—
447	C₄²	—	6	1	no	—
448	C₄²	—	6	1	no	—
449	C₄²	—	6	1	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	C₅×C₂²⋊Q₈	1	2	yes	—
458	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
459	C₂×D₃	—	2	2	no	—
460	C₂×D₃	—	4	1	no	—
461	C₂×D₃	—	4	1	no	—
462	C₃×C₄	—	2	1	no	—
463	C₃×C₄	—	2	1	no	—
464	C₃×C₄	—	2	1	no	—
465	C₃×C₄	—	4	2	no	—
466	C₃×C₄	—	4	2	no	—
467	C₃×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
468	C₃×C₄	C₅×#135	1	2	yes	—
469	C₃×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
470	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
471	Dic₃	—	2	2	no	—
472	Dic₃	—	4	1	no	—
473	Dic₃	—	4	1	no	—
474	C₂×C₅	—	2	2	no	—
475	C₂×C₅	—	12	2	no	—
476	C₂×C₅	C₂×#946	1	1	yes	characteristic
477	C₂×C₅	C₂×#950	1	1	yes	characteristic
478	C₂×C₅	#5822	1	1	yes	characteristic
479	C₂³	—	6	1	no	—
480	C₂³	C₂×C₅×#67	1	1	yes	characteristic
481	Q₈	—	3	2	no	—
482	Q₈	—	4	2	no	—
483	Q₈	—	4	2	no	—
484	Q₈	—	6	1	no	—
485	D₄	—	3	2	no	—
486	D₄	—	6	4	no	—
487	D₄	—	6	1	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	4	1	no	—
492	C₂×C₄	—	6	1	no	—
493	C₂×C₄	—	6	4	no	—
494	C₂×C₄	—	6	1	no	—
495	C₂×C₄	—	6	1	no	—
496	C₂×C₄	—	12	2	no	—
497	C₂×C₄	—	12	2	no	—
498	C₂×C₄	C₅×D₃×Q₈	1	2	yes	—
499	C₂×C₄	C₅×#239	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	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
510	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
511	C₂×C₃	C₅×#575	1	1	yes	characteristic
512	D₃	—	4	2	no	—
513	C₅	#83349	1	1	yes	characteristic, direct product factor, Sylow
514	C₂²	—	2	1	no	—
515	C₂²	—	2	1	no	—
516	C₂²	—	6	2	no	—
517	C₂²	—	12	1	no	—
518	C₂²	—	12	1	no	—
519	C₂²	C₅×#946	1	2	yes	—
520	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
521	C₄	—	2	1	no	—
522	C₄	—	2	1	no	—
523	C₄	—	2	1	no	—
524	C₄	—	4	2	no	—
525	C₄	—	4	2	no	—
526	C₄	—	6	2	no	—
527	C₄	—	12	1	no	—
528	C₄	—	12	1	no	—
529	C₄	C₅×#946	1	2	yes	—
530	C₄	C₅×#950	1	2	yes	—
531	C₄	C₂×C₅×D₃×Q₈	1	1	yes	characteristic
532	C₄	C₂×C₅×#239	1	1	yes	characteristic
533	C₃	C₅×#3076	1	1	yes	characteristic, complemented, Sylow
534	C₂	—	2	2	no	—
535	C₂	—	12	2	no	—
536	C₂	C₂×C₅×#946	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×C₅×#533	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₅×#235	C₂²
hypercenter	C₅×#533	D₃
hypocenter	C₃	C₅×#3076
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₄²×C₅ ◁ C₅×#533

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#533	C₂	semidirect
3. C₅×#5094	C₂	semidirect
4. C₅×#5091	C₂	semidirect
5. C₅×#5087	C₂	semidirect
6. C₅×#5084	C₂	semidirect
7. C₅×#5066	C₂	semidirect
8. C₅×#5063	C₂	semidirect
10. C₅×#4998	C₂	semidirect
11. C₂×C₅×C₄⋊(C₃⋊C₈)	C₂	semidirect
44. #83349	C₅	direct (N × H)
45. C₅×#533	D₃	semidirect
63. C₅×#235	Q₈	semidirect
94. C₃×#533	C₂×C₅	semidirect
96. #5094	C₂×C₅	semidirect
97. #5091	C₂×C₅	semidirect
98. #5087	C₂×C₅	semidirect
99. #5084	C₂×C₅	semidirect
100. #5066	C₂×C₅	semidirect
101. #5063	C₂×C₅	semidirect
103. #4998	C₂×C₅	semidirect
104. C₂×C₄⋊(C₃⋊C₈)	C₂×C₅	semidirect
235. #533	C₅×D₃	semidirect
272. #235	C₅×Q₈	semidirect
454. C₃×C₅	#3076	semidirect
513. C₅	#83349	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×C₅×#533	2
C₄×C₅×#235	2
C₅×#5094	2
C₅×#5091	2
C₅×#5087	2
C₅×#5084	2
C₅×#5066	2
C₅×#5063	2
C₅×#5002	2
C₅×#4998	2
C₂×C₅×C₄⋊(C₃⋊C₈)	2
C₅×#3076	3
#83349	5

Subgroups — C5×#83349 #14430207

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#83349 #14430207