Subgroups — C₅×#79078 #14418666

Order 1920.

712 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5517	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#424	C₂	1	1	yes	maximal, characteristic
3	C₅×#5119	C₂	1	1	yes	maximal, characteristic
4	C₅×Dic₃×M₁₆	C₂	1	1	yes	maximal, characteristic
5	C₅×#5101	C₂	1	1	yes	maximal, characteristic
6	C₂×C₅×Dic₃⋊C₈	C₂	1	1	yes	maximal, characteristic
7	C₅×#4997	C₂	1	1	yes	maximal, characteristic
8	C₅×#4831	C₂	1	2	yes	maximal, complemented
9	C₅×#4830	C₂	1	2	yes	maximal, complemented
10	C₅×#4828	C₂	1	2	yes	maximal, complemented
11	C₅×#4828	C₂	1	2	yes	maximal, complemented
12	C₅×#2962	—	3	1	no	maximal, Hall
13	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
15	C₃×C₅×#117	C₂²	1	1	yes	characteristic
16	C₅×#926	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
18	C₂×C₅×#208	C₂²	1	1	yes	characteristic
19	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
20	C₅×#890	C₄	1	1	yes	characteristic
21	C₅×#890	C₄	1	1	yes	characteristic
22	C₅×#888	C₄	1	1	yes	characteristic
23	C₅×#888	C₄	1	1	yes	characteristic
24	C₅×#878	C₄	1	2	yes	—
25	C₅×#878	C₄	1	2	yes	—
26	C₄×C₅×Dic₆	C₂²	1	2	yes	—
27	C₄×C₅×Dic₆	C₂²	1	2	yes	—
28	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	—
29	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	—
30	C₅×#815	C₂²	1	2	yes	—
31	C₅×#815	C₂²	1	2	yes	—
32	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
33	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
34	C₅×Dic₃⋊C₈	C₂²	1	2	yes	—
35	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
36	C₅×Dic₃⋊C₈	C₂²	1	2	yes	—
37	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
38	C₅×C₈×Dic₃	C₂²	1	2	yes	—
39	C₅×C₈×Dic₃	C₂²	1	2	yes	—
40	C₅×#803	C₂²	1	2	yes	—
41	C₄×C₅×C₃⋊C₈	C₂²	1	2	yes	—
42	#79078	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
43	C₅×#533	—	3	1	no	—
44	C₅×#446	—	3	2	no	—
45	C₅×#446	—	3	2	no	—
46	C₅×#446	—	3	2	no	—
47	C₅×C₈×Q₈	—	3	2	no	—
48	C₅×#424	—	3	1	no	—
49	C₅×#424	D₃	1	1	yes	characteristic
50	C₂×C₅×C₄⋊C₈	—	3	1	no	—
51	C₅×#405	—	3	1	no	—
52	C₅×#405	—	3	1	no	—
53	C₄×C₅×M₁₆	—	3	1	no	—
54	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
55	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
56	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
57	C₂×C₅×Dic₆	C₂×C₄	1	2	yes	—
58	C₂×C₅×Dic₆	C₂×C₄	1	2	yes	—
59	C₃×C₅×M₁₆	—	2	2	no	—
60	C₂×C₃×C₅×C₈	—	2	2	no	—
61	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
62	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
63	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
64	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
65	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
66	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
67	C₃×C₄²×C₅	C₂³	1	2	yes	—
68	C₅×#217	C₂×C₄	1	2	yes	—
69	C₅×C₄⋊Dic₃	C₂×C₄	1	2	yes	—
70	C₅×C₄⋊Dic₃	C₂×C₄	1	2	yes	—
71	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
72	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
73	C₅×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
74	C₅×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
75	C₅×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
76	C₅×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
77	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
78	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
79	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
80	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
81	C₄×C₅×Dic₃	C₂³	1	2	yes	—
82	C₅×#208	Q₈	1	4	yes	complemented
83	C₂×C₅×C₃⋊C₈	—	2	2	no	—
84	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
85	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
86	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
87	#5517	C₂×C₅	1	1	yes	characteristic
88	C₃×#424	C₂×C₅	1	1	yes	characteristic
89	#5119	C₂×C₅	1	1	yes	characteristic
90	Dic₃×M₁₆	C₂×C₅	1	1	yes	characteristic
91	#5101	C₂×C₅	1	1	yes	characteristic
92	C₂×Dic₃⋊C₈	C₂×C₅	1	1	yes	characteristic
93	#4997	C₂×C₅	1	1	yes	characteristic
94	#4831	C₂×C₅	1	2	yes	complemented
95	#4830	C₂×C₅	1	2	yes	complemented
96	#4828	C₂×C₅	1	2	yes	complemented
97	#4828	C₂×C₅	1	2	yes	complemented
98	C₂×C₅×M₁₆	—	3	1	no	—
99	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
100	C₂²×C₅×C₈	—	3	1	no	—
101	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
102	C₅×C₄⋊Q₈	—	3	1	no	—
103	C₅×C₄⋊Q₈	—	3	1	no	—
104	C₅×#125	—	3	1	no	—
105	C₅×#125	—	3	1	no	—
106	C₅×C₂²⋊Q₈	—	3	2	no	—
107	C₅×C₂²⋊Q₈	—	3	2	no	—
108	C₄×C₅×Q₈	—	3	2	no	—
109	C₄×C₅×Q₈	—	3	2	no	—
110	C₅×#117	—	3	1	no	—
111	C₅×#117	C₂×D₃	1	1	yes	characteristic
112	C₂×C₄²×C₅	—	3	1	no	—
113	C₅×C₄⋊C₈	—	3	1	no	—
114	C₅×C₄⋊C₈	—	3	1	no	—
115	C₅×C₄⋊C₈	—	3	1	no	—
116	C₅×C₄⋊C₈	—	3	1	no	—
117	C₅×C₄⋊C₈	—	3	2	no	—
118	C₅×C₄⋊C₈	—	3	2	no	—
119	C₅×C₄⋊C₈	C₂×D₃	1	2	yes	—
120	C₅×C₄⋊C₈	C₂×D₃	1	2	yes	—
121	C₅×#97	—	3	2	no	—
122	C₅×#97	—	3	2	no	—
123	C₅×#97	—	3	2	no	—
124	C₄×C₅×C₈	—	3	2	no	—
125	C₄×C₅×C₈	—	3	2	no	—
126	C₄×C₅×C₈	—	3	2	no	—
127	#2962	—	3	1	no	Sylow
128	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
130	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
131	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
133	C₂×C₃×C₄×C₅	#41	1	2	yes	—
134	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
135	C₂×C₅×Dic₃	—	2	2	no	—
136	C₂×C₅×Dic₃	—	4	1	no	—
137	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
141	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
142	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
143	C₅×Dic₆	—	2	4	no	—
144	C₅×Dic₆	—	4	2	no	—
145	C₃×C₅×C₈	—	2	1	no	—
146	C₃×C₅×C₈	—	2	1	no	—
147	C₃×C₅×C₈	—	2	2	no	—
148	C₅×C₃⋊C₈	—	2	1	no	—
149	C₅×C₃⋊C₈	—	2	1	no	—
150	C₅×C₃⋊C₈	C₂×Q₈	1	4	yes	—
151	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
152	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
153	C₃×#117	C₂²×C₅	1	1	yes	characteristic
154	#926	C₂²×C₅	1	1	yes	characteristic
155	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
156	C₂×#208	C₂²×C₅	1	1	yes	characteristic
157	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
158	#890	C₄×C₅	1	1	yes	characteristic
159	#890	C₄×C₅	1	1	yes	characteristic
160	#888	C₄×C₅	1	1	yes	characteristic
161	#888	C₄×C₅	1	1	yes	characteristic
162	#878	C₄×C₅	1	2	yes	—
163	#878	C₄×C₅	1	2	yes	—
164	C₄×Dic₆	C₂²×C₅	1	2	yes	—
165	C₄×Dic₆	C₂²×C₅	1	2	yes	—
166	C₃×C₄⋊C₈	C₂²×C₅	1	2	yes	—
167	C₃×C₄⋊C₈	C₂²×C₅	1	2	yes	—
168	#815	C₂²×C₅	1	2	yes	—
169	#815	C₂²×C₅	1	2	yes	—
170	Dic₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
171	Dic₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
172	Dic₃⋊C₈	C₂²×C₅	1	2	yes	—
173	Dic₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
174	Dic₃⋊C₈	C₂²×C₅	1	2	yes	—
175	Dic₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
176	C₈×Dic₃	C₂²×C₅	1	2	yes	—
177	C₈×Dic₃	C₂²×C₅	1	2	yes	—
178	#803	C₂²×C₅	1	2	yes	—
179	C₄×C₃⋊C₈	C₂²×C₅	1	2	yes	—
180	C₂×C₅×Q₈	—	3	2	no	—
181	C₂×C₅×Q₈	—	3	2	no	—
182	C₂²×C₄×C₅	—	3	1	no	—
183	C₂²×C₄×C₅	—	3	1	no	—
184	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
185	C₅×M₁₆	—	2	2	no	—
186	C₅×M₁₆	—	3	4	no	—
187	C₂×C₅×C₈	—	2	2	no	—
188	C₂×C₅×C₈	—	3	2	no	—
189	C₂×C₅×C₈	—	3	1	no	—
190	C₂×C₅×C₈	—	3	1	no	—
191	C₂×C₅×C₈	—	6	2	no	—
192	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
193	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
194	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
195	C₅×C₄⋊C₄	—	3	1	no	—
196	C₅×C₄⋊C₄	—	3	1	no	—
197	C₅×C₄⋊C₄	—	3	2	no	—
198	C₅×C₄⋊C₄	—	3	2	no	—
199	C₅×C₄⋊C₄	—	3	2	no	—
200	C₅×C₄⋊C₄	—	3	2	no	—
201	C₅×C₄⋊C₄	—	3	2	no	—
202	C₅×C₄⋊C₄	—	3	2	no	—
203	C₅×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
204	C₅×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
205	C₅×C₂²⋊C₄	—	3	2	no	—
206	C₅×C₂²⋊C₄	C₄×D₃	1	2	yes	—
207	C₄²×C₅	—	3	1	no	—
208	C₄²×C₅	—	3	1	no	—
209	C₄²×C₅	—	3	1	no	—
210	C₄²×C₅	—	3	1	no	—
211	C₄²×C₅	—	3	2	no	—
212	C₄²×C₅	C₂²×D₃	1	2	yes	—
213	#533	—	3	1	no	—
214	#446	—	3	2	no	—
215	#446	—	3	2	no	—
216	#446	—	3	2	no	—
217	C₈×Q₈	—	3	2	no	—
218	#424	—	3	1	no	—
219	#424	C₅×D₃	1	1	yes	characteristic
220	C₂×C₄⋊C₈	—	3	1	no	—
221	#405	—	3	1	no	—
222	#405	—	3	1	no	—
223	C₄×M₁₆	—	3	1	no	—
224	C₂²×C₃×C₅	—	2	1	no	—
225	C₂²×C₃×C₅	—	2	1	no	—
226	C₂²×C₃×C₅	C₄×Q₈	1	2	yes	—
227	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
228	C₃×C₄×C₅	—	2	2	no	—
229	C₃×C₄×C₅	—	2	2	no	—
230	C₃×C₄×C₅	C₄×Q₈	1	2	yes	—
231	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
232	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
233	C₅×Dic₃	—	2	2	no	—
234	C₅×Dic₃	—	2	1	no	—
235	C₅×Dic₃	—	2	1	no	—
236	C₅×Dic₃	—	2	2	no	—
237	C₅×Dic₃	—	2	1	no	—
238	C₅×Dic₃	#131	1	2	yes	—
239	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
240	C₂²×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
241	C₂²×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
242	C₂×Dic₆	C₂×C₄×C₅	1	2	yes	—
243	C₂×Dic₆	C₂×C₄×C₅	1	2	yes	—
244	C₃×M₁₆	—	2	2	no	—
245	C₂×C₃×C₈	—	2	2	no	—
246	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
247	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
248	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
249	C₃×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
250	C₃×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
251	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
252	C₃×C₄²	C₂³×C₅	1	2	yes	—
253	#217	C₂×C₄×C₅	1	2	yes	—
254	C₄⋊Dic₃	C₂×C₄×C₅	1	2	yes	—
255	C₄⋊Dic₃	C₂×C₄×C₅	1	2	yes	—
256	C₄⋊Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
257	C₄⋊Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
258	Dic₃⋊C₄	C₂×C₄×C₅	1	2	yes	—
259	Dic₃⋊C₄	C₂×C₄×C₅	1	2	yes	—
260	Dic₃⋊C₄	C₂×C₄×C₅	1	2	yes	—
261	Dic₃⋊C₄	C₂×C₄×C₅	1	2	yes	—
262	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
263	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
264	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
265	C₄×Dic₃	C₂³×C₅	1	2	yes	—
266	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
267	#208	C₅×Q₈	1	4	yes	complemented
268	C₂×C₃⋊C₈	—	2	2	no	—
269	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
270	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
271	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
272	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
273	C₅×Q₈	—	6	4	no	—
274	C₅×Q₈	—	12	2	no	—
275	C₂×C₄×C₅	—	3	1	no	—
276	C₂×C₄×C₅	—	3	1	no	—
277	C₂×C₄×C₅	—	3	1	no	—
278	C₂×C₄×C₅	—	3	1	no	—
279	C₂×C₄×C₅	—	3	2	no	—
280	C₂×C₄×C₅	—	3	2	no	—
281	C₂×C₄×C₅	—	6	2	no	—
282	C₂×C₄×C₅	—	12	1	no	—
283	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
284	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
285	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
286	C₂×C₄×C₅	#237	1	2	yes	—
287	C₂×C₄×C₅	D₃×Q₈	1	2	yes	—
288	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
289	C₅×C₈	—	2	1	no	—
290	C₅×C₈	—	2	1	no	—
291	C₅×C₈	—	2	2	no	—
292	C₅×C₈	—	3	4	no	—
293	C₅×C₈	—	6	1	no	—
294	C₅×C₈	—	6	1	no	—
295	C₂×M₁₆	—	3	1	no	—
296	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
297	C₂²×C₈	—	3	1	no	—
298	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
299	C₄⋊Q₈	—	3	1	no	—
300	C₄⋊Q₈	—	3	1	no	—
301	#125	—	3	1	no	—
302	#125	—	3	1	no	—
303	C₂²⋊Q₈	—	3	2	no	—
304	C₂²⋊Q₈	—	3	2	no	—
305	C₄×Q₈	—	3	2	no	—
306	C₄×Q₈	—	3	2	no	—
307	#117	—	3	1	no	—
308	#117	C₂×C₅×D₃	1	1	yes	characteristic
309	C₂×C₄²	—	3	1	no	—
310	C₄⋊C₈	—	3	1	no	—
311	C₄⋊C₈	—	3	1	no	—
312	C₄⋊C₈	—	3	1	no	—
313	C₄⋊C₈	—	3	1	no	—
314	C₄⋊C₈	—	3	2	no	—
315	C₄⋊C₈	—	3	2	no	—
316	C₄⋊C₈	C₂×C₅×D₃	1	2	yes	—
317	C₄⋊C₈	C₂×C₅×D₃	1	2	yes	—
318	#97	—	3	2	no	—
319	#97	—	3	2	no	—
320	#97	—	3	2	no	—
321	C₄×C₈	—	3	2	no	—
322	C₄×C₈	—	3	2	no	—
323	C₄×C₈	—	3	2	no	—
324	C₂×C₃×C₅	—	2	2	no	—
325	C₂×C₃×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
326	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
327	C₂×C₃×C₅	#568	1	1	yes	characteristic
328	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
329	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
330	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
331	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
332	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
333	C₂×C₃×C₄	C₅×#41	1	2	yes	—
334	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
335	C₂×Dic₃	—	2	2	no	—
336	C₂×Dic₃	—	4	1	no	—
337	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
338	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
339	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
340	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
341	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
342	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
343	Dic₆	—	2	4	no	—
344	Dic₆	—	4	2	no	—
345	C₃×C₈	—	2	1	no	—
346	C₃×C₈	—	2	1	no	—
347	C₃×C₈	—	2	2	no	—
348	C₃⋊C₈	—	2	1	no	—
349	C₃⋊C₈	—	2	1	no	—
350	C₃⋊C₈	C₂×C₅×Q₈	1	4	yes	—
351	C₂²×C₅	—	2	1	no	—
352	C₂²×C₅	—	2	1	no	—
353	C₂²×C₅	#887	1	2	yes	—
354	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
355	C₄×C₅	—	2	2	no	—
356	C₄×C₅	—	2	2	no	—
357	C₄×C₅	—	3	2	no	—
358	C₄×C₅	—	6	1	no	—
359	C₄×C₅	—	6	2	no	—
360	C₄×C₅	—	6	1	no	—
361	C₄×C₅	—	6	1	no	—
362	C₄×C₅	—	6	2	no	—
363	C₄×C₅	#887	1	2	yes	—
364	C₄×C₅	C₂×#237	1	1	yes	characteristic
365	C₄×C₅	C₂×D₃×Q₈	1	1	yes	characteristic
366	C₂×Q₈	—	3	2	no	—
367	C₂×Q₈	—	3	2	no	—
368	C₂²×C₄	—	3	1	no	—
369	C₂²×C₄	—	3	1	no	—
370	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
371	M₁₆	—	2	2	no	—
372	M₁₆	—	3	4	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	3	2	no	—
375	C₂×C₈	—	3	1	no	—
376	C₂×C₈	—	3	1	no	—
377	C₂×C₈	—	6	2	no	—
378	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
379	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
380	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
381	C₄⋊C₄	—	3	1	no	—
382	C₄⋊C₄	—	3	1	no	—
383	C₄⋊C₄	—	3	2	no	—
384	C₄⋊C₄	—	3	2	no	—
385	C₄⋊C₄	—	3	2	no	—
386	C₄⋊C₄	—	3	2	no	—
387	C₄⋊C₄	—	3	2	no	—
388	C₄⋊C₄	—	3	2	no	—
389	C₄⋊C₄	C₄×C₅×D₃	1	1	yes	characteristic
390	C₄⋊C₄	C₄×C₅×D₃	1	1	yes	characteristic
391	C₂²⋊C₄	—	3	2	no	—
392	C₂²⋊C₄	C₄×C₅×D₃	1	2	yes	—
393	C₄²	—	3	1	no	—
394	C₄²	—	3	1	no	—
395	C₄²	—	3	1	no	—
396	C₄²	—	3	2	no	—
397	C₄²	—	3	1	no	—
398	C₄²	C₂²×C₅×D₃	1	2	yes	—
399	C₃×C₅	#2962	1	1	yes	characteristic, complemented, Hall
400	C₂²×C₃	—	2	1	no	—
401	C₂²×C₃	—	2	1	no	—
402	C₂²×C₃	C₄×C₅×Q₈	1	2	yes	—
403	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
404	C₃×C₄	—	2	2	no	—
405	C₃×C₄	—	2	2	no	—
406	C₃×C₄	C₄×C₅×Q₈	1	2	yes	—
407	C₃×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
408	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
409	Dic₃	—	2	2	no	—
410	Dic₃	—	2	1	no	—
411	Dic₃	—	2	1	no	—
412	Dic₃	—	2	2	no	—
413	Dic₃	—	2	1	no	—
414	Dic₃	C₅×#131	1	2	yes	—
415	C₂×C₅	—	2	2	no	—
416	C₂×C₅	C₂×#887	1	1	yes	characteristic
417	C₂×C₅	D₃×#131	1	1	yes	characteristic
418	C₂×C₅	#5750	1	1	yes	characteristic
419	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
420	Q₈	—	6	4	no	—
421	Q₈	—	12	2	no	—
422	C₂×C₄	—	3	1	no	—
423	C₂×C₄	—	3	1	no	—
424	C₂×C₄	—	3	1	no	—
425	C₂×C₄	—	3	1	no	—
426	C₂×C₄	—	3	2	no	—
427	C₂×C₄	—	3	2	no	—
428	C₂×C₄	—	6	2	no	—
429	C₂×C₄	—	12	1	no	—
430	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
431	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
432	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
433	C₂×C₄	C₅×#237	1	2	yes	—
434	C₂×C₄	C₅×D₃×Q₈	1	2	yes	—
435	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
436	C₈	—	2	1	no	—
437	C₈	—	2	1	no	—
438	C₈	—	2	2	no	—
439	C₈	—	3	4	no	—
440	C₈	—	6	1	no	—
441	C₈	—	6	1	no	—
442	C₂×C₃	—	2	2	no	—
443	C₂×C₃	C₂×C₄×C₅×Q₈	1	1	yes	characteristic
444	C₂×C₃	C₂×C₅×#131	1	1	yes	characteristic
445	C₂×C₃	C₅×#568	1	1	yes	characteristic
446	C₅	#79078	1	1	yes	characteristic, direct product factor, Sylow
447	C₂²	—	2	1	no	—
448	C₂²	—	2	1	no	—
449	C₂²	C₅×#887	1	2	yes	—
450	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
451	C₄	—	2	2	no	—
452	C₄	—	2	2	no	—
453	C₄	—	3	2	no	—
454	C₄	—	6	1	no	—
455	C₄	—	6	2	no	—
456	C₄	—	6	1	no	—
457	C₄	—	6	1	no	—
458	C₄	—	6	2	no	—
459	C₄	C₅×#887	1	2	yes	—
460	C₄	C₂×C₅×#237	1	1	yes	characteristic
461	C₄	C₂×C₅×D₃×Q₈	1	1	yes	characteristic
462	C₃	C₅×#2962	1	1	yes	characteristic, complemented, Sylow
463	C₂	—	2	2	no	—
464	C₂	C₂×C₅×#887	1	1	yes	characteristic
465	C₂	C₅×D₃×#131	1	1	yes	characteristic
466	C₂	C₅×#5750	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#424	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂³×C₃×C₅	C₂²×C₄
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₅×#424	D₃
hypocenter	C₃	C₅×#2962
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₅×#424

Complements

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

N	H ≅ G/N	type
8. C₅×#4831	C₂	semidirect
9. C₅×#4830	C₂	semidirect
10. C₅×#4828	C₂	semidirect
11. C₅×#4828	C₂	semidirect
42. #79078	C₅	direct (N × H)
82. C₅×#208	Q₈	semidirect
94. #4831	C₂×C₅	semidirect
95. #4830	C₂×C₅	semidirect
96. #4828	C₂×C₅	semidirect
97. #4828	C₂×C₅	semidirect
267. #208	C₅×Q₈	semidirect
399. C₃×C₅	#2962	semidirect
446. C₅	#79078	direct (N × H)
462. C₃	C₅×#2962	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5517	2
C₃×C₅×#424	2
C₅×#5119	2
C₅×Dic₃×M₁₆	2
C₅×#5101	2
C₂×C₅×Dic₃⋊C₈	2
C₅×#4997	2
C₅×#4831	2
C₅×#4830	2
C₅×#4828	2
C₅×#2962	3
#79078	5

Subgroups — C5×#79078 #14418666

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#79078 #14418666