Subgroups — C₅×#21315 #11944035

Order 1280.

1142 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#544	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#424	C₂	1	1	yes	maximal, characteristic
3	C₅×#2274	C₂	1	1	yes	maximal, characteristic
4	C₅×#1989	C₂	1	2	yes	maximal, complemented
5	C₅×#1989	C₂	1	2	yes	maximal, complemented
6	C₅×#1988	C₂	1	2	yes	maximal, complemented
7	C₅×#1987	C₂	1	2	yes	maximal, complemented
8	C₅×#1736	C₂	1	1	yes	maximal, characteristic
9	C₅×#1736	C₂	1	1	yes	maximal, characteristic
10	C₅×#1735	C₂	1	1	yes	maximal, characteristic
11	C₂×C₅×#340	C₂	1	1	yes	maximal, characteristic
12	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
13	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
14	C₅×#544	—	2	4	no	—
15	C₅×#544	C₄	1	8	yes	complemented
16	C₂×C₅×C₄⋊Q₈	—	2	1	no	—
17	C₂×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
18	C₂×C₅×#125	—	2	1	no	—
19	C₂×C₅×#125	C₂²	1	2	yes	—
20	C₂×C₅×C₂²⋊Q₈	—	2	2	no	—
21	C₂×C₅×#117	C₂²	1	1	yes	characteristic
22	C₂×C₅×#117	C₂²	1	1	yes	characteristic
23	C₂×C₅×#117	C₂²	1	1	yes	characteristic
24	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₅×#424	—	2	4	no	—
27	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
28	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
29	C₄×C₅×C₄⋊C₄	—	2	1	no	—
30	C₄×C₅×C₄⋊C₄	—	2	1	no	—
31	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
32	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
33	C₄×C₅×C₂²⋊C₄	—	2	2	no	—
34	C₅×#340	C₂²	1	1	yes	characteristic
35	C₅×#340	C₂²	1	2	yes	—
36	C₅×#340	C₂²	1	2	yes	—
37	C₅×#340	C₂²	1	2	yes	—
38	C₅×#340	C₂²	1	1	yes	characteristic
39	C₅×#340	C₂²	1	2	yes	—
40	C₅×#340	C₂²	1	2	yes	—
41	C₅×#340	C₂²	1	1	yes	characteristic
42	C₅×#340	C₂²	1	1	yes	characteristic
43	C₅×#340	C₂²	1	2	yes	—
44	#21315	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
45	C₂²×C₅×Q₈	—	2	2	no	—
46	C₂³×C₄×C₅	—	2	1	no	—
47	C₂³×C₄×C₅	—	2	1	no	—
48	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
49	C₂×C₅×M₁₆	—	2	2	no	—
50	C₂×C₅×M₁₆	—	2	2	no	—
51	C₂×C₅×M₁₆	—	2	2	no	—
52	C₂²×C₅×C₈	—	2	2	no	—
53	C₂²×C₅×C₈	—	2	2	no	—
54	C₂²×C₅×C₈	—	2	2	no	—
55	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
56	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
57	C₂²×C₅×C₈	C₂³	1	2	yes	—
58	C₅×C₄⋊Q₈	—	2	8	no	—
59	C₅×C₄⋊Q₈	—	2	4	no	—
60	C₅×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
61	C₅×#125	—	2	8	no	—
62	C₅×#125	—	2	4	no	—
63	C₅×#125	C₂×C₄	1	8	yes	complemented
64	C₅×C₂²⋊Q₈	—	2	16	no	—
65	C₅×#117	—	2	2	no	—
66	C₅×#117	—	2	2	no	—
67	C₅×#117	C₂×C₄	1	4	yes	—
68	C₅×#117	C₂×C₄	1	4	yes	—
69	C₅×#117	D₄	1	4	yes	—
70	C₅×#117	Q₈	1	4	yes	complemented
71	C₂×C₅×C₄⋊C₄	—	2	1	no	—
72	C₂×C₅×C₄⋊C₄	—	2	1	no	—
73	C₂×C₅×C₄⋊C₄	—	2	2	no	—
74	C₂×C₅×C₄⋊C₄	—	2	2	no	—
75	C₂×C₅×C₄⋊C₄	—	2	2	no	—
76	C₂×C₅×C₄⋊C₄	—	2	2	no	—
77	C₂×C₅×C₄⋊C₄	—	2	2	no	—
78	C₂×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
79	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
80	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
81	C₂×C₅×C₄⋊C₄	Q₈	1	4	yes	complemented
82	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
83	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
84	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
85	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
86	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
87	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
88	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
89	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
90	C₂×C₅×C₂²⋊C₄	D₄	1	2	yes	—
91	C₂×C₄²×C₅	—	2	1	no	—
92	C₂×C₄²×C₅	—	2	1	no	—
93	C₂×C₄²×C₅	—	2	2	no	—
94	C₂×C₄²×C₅	—	2	2	no	—
95	C₂×C₄²×C₅	C₂³	1	2	yes	—
96	C₅×C₄⋊C₈	—	2	4	no	—
97	C₅×C₄⋊C₈	—	2	4	no	—
98	C₅×#95	—	2	2	no	—
99	C₅×#95	—	2	2	no	—
100	C₂×#544	C₂×C₅	1	1	yes	characteristic
101	C₂×#424	C₂×C₅	1	1	yes	characteristic
102	#2274	C₂×C₅	1	1	yes	characteristic
103	#1989	C₂×C₅	1	2	yes	complemented
104	#1989	C₂×C₅	1	2	yes	complemented
105	#1988	C₂×C₅	1	2	yes	complemented
106	#1987	C₂×C₅	1	2	yes	complemented
107	#1736	C₂×C₅	1	1	yes	characteristic
108	#1736	C₂×C₅	1	1	yes	characteristic
109	#1735	C₂×C₅	1	1	yes	characteristic
110	C₂×#340	C₂×C₅	1	1	yes	characteristic
111	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
112	C₂×C₅×Q₈	—	2	8	no	—
113	C₂×C₅×Q₈	—	8	2	no	—
114	C₂×C₅×Q₈	—	8	2	no	—
115	C₂²×C₄×C₅	—	2	1	no	—
116	C₂²×C₄×C₅	—	2	1	no	—
117	C₂²×C₄×C₅	—	2	2	no	—
118	C₂²×C₄×C₅	—	2	1	no	—
119	C₂²×C₄×C₅	—	2	1	no	—
120	C₂²×C₄×C₅	—	2	2	no	—
121	C₂²×C₄×C₅	—	2	4	no	—
122	C₂²×C₄×C₅	—	2	4	no	—
123	C₂²×C₄×C₅	—	8	1	no	—
124	C₂²×C₄×C₅	—	8	1	no	—
125	C₂²×C₄×C₅	—	8	1	no	—
126	C₂²×C₄×C₅	—	8	1	no	—
127	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
128	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
132	C₂²×C₄×C₅	C₂×Q₈	1	2	yes	—
133	C₂²×C₄×C₅	C₂×Q₈	1	2	yes	—
134	C₂²×C₄×C₅	#41	1	2	yes	—
135	C₂²×C₄×C₅	#41	1	2	yes	—
136	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
137	C₅×M₁₆	—	4	4	no	—
138	C₂×C₅×C₈	—	2	1	no	—
139	C₂×C₅×C₈	—	2	1	no	—
140	C₂×C₅×C₈	—	2	2	no	—
141	C₂×C₅×C₈	—	2	1	no	—
142	C₂×C₅×C₈	—	2	1	no	—
143	C₂×C₅×C₈	—	2	1	no	—
144	C₂×C₅×C₈	—	2	1	no	—
145	C₂×C₅×C₈	—	2	2	no	—
146	C₂×C₅×C₈	—	2	2	no	—
147	C₂×C₅×C₈	—	4	4	no	—
148	C₅×C₄⋊C₄	—	2	4	no	—
149	C₅×C₄⋊C₄	—	2	8	no	—
150	C₅×C₄⋊C₄	—	2	8	no	—
151	C₅×C₄⋊C₄	—	2	8	no	—
152	C₅×C₄⋊C₄	—	2	4	no	—
153	C₅×C₄⋊C₄	—	2	2	no	—
154	C₅×C₄⋊C₄	—	2	1	no	—
155	C₅×C₄⋊C₄	—	2	1	no	—
156	C₅×C₄⋊C₄	—	2	2	no	—
157	C₅×C₄⋊C₄	—	2	1	no	—
158	C₅×C₄⋊C₄	—	2	1	no	—
159	C₅×C₄⋊C₄	C₂²⋊C₄	1	4	yes	—
160	C₅×C₄⋊C₄	C₂²⋊C₄	1	4	yes	—
161	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
162	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
163	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
164	C₅×C₄⋊C₄	C₂×Q₈	1	4	yes	—
165	C₅×C₄⋊C₄	C₂×Q₈	1	2	yes	—
166	C₅×C₄⋊C₄	C₂×Q₈	1	2	yes	—
167	C₅×C₂²⋊C₄	—	2	4	no	—
168	C₅×C₂²⋊C₄	—	2	4	no	—
169	C₅×C₂²⋊C₄	C₂²⋊C₄	1	8	yes	—
170	C₄²×C₅	—	2	4	no	—
171	C₄²×C₅	—	2	4	no	—
172	C₄²×C₅	—	8	2	no	—
173	C₄²×C₅	—	8	2	no	—
174	C₄²×C₅	C₂²×C₄	1	4	yes	—
175	C₄²×C₅	C₂×D₄	1	4	yes	—
176	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
177	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
178	#544	—	2	4	no	—
179	#544	C₄×C₅	1	8	yes	complemented
180	C₂×C₄⋊Q₈	—	2	1	no	—
181	C₂×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
182	C₂×#125	—	2	1	no	—
183	C₂×#125	C₂²×C₅	1	2	yes	—
184	C₂×C₂²⋊Q₈	—	2	2	no	—
185	C₂×#117	C₂²×C₅	1	1	yes	characteristic
186	C₂×#117	C₂²×C₅	1	1	yes	characteristic
187	C₂×#117	C₂²×C₅	1	1	yes	characteristic
188	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
189	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
190	#424	—	2	4	no	—
191	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
192	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
193	C₄×C₄⋊C₄	—	2	1	no	—
194	C₄×C₄⋊C₄	—	2	1	no	—
195	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
196	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
197	C₄×C₂²⋊C₄	—	2	2	no	—
198	#340	C₂²×C₅	1	1	yes	characteristic
199	#340	C₂²×C₅	1	2	yes	—
200	#340	C₂²×C₅	1	2	yes	—
201	#340	C₂²×C₅	1	2	yes	—
202	#340	C₂²×C₅	1	1	yes	characteristic
203	#340	C₂²×C₅	1	2	yes	—
204	#340	C₂²×C₅	1	2	yes	—
205	#340	C₂²×C₅	1	1	yes	characteristic
206	#340	C₂²×C₅	1	1	yes	characteristic
207	#340	C₂²×C₅	1	2	yes	—
208	C₂³×C₅	—	2	1	no	—
209	C₂³×C₅	—	2	1	no	—
210	C₂³×C₅	—	2	1	no	—
211	C₂³×C₅	—	2	1	no	—
212	C₂³×C₅	C₂×C₂²⋊C₄	1	2	yes	—
213	C₂³×C₅	C₂²⋊Q₈	1	2	yes	—
214	C₂³×C₅	C₂²⋊Q₈	1	2	yes	—
215	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
216	C₅×Q₈	—	8	8	no	—
217	C₂×C₄×C₅	—	2	2	no	—
218	C₂×C₄×C₅	—	2	2	no	—
219	C₂×C₄×C₅	—	2	2	no	—
220	C₂×C₄×C₅	—	2	2	no	—
221	C₂×C₄×C₅	—	2	2	no	—
222	C₂×C₄×C₅	—	2	2	no	—
223	C₂×C₄×C₅	—	2	4	no	—
224	C₂×C₄×C₅	—	2	2	no	—
225	C₂×C₄×C₅	—	2	2	no	—
226	C₂×C₄×C₅	—	2	4	no	—
227	C₂×C₄×C₅	—	4	1	no	—
228	C₂×C₄×C₅	—	4	2	no	—
229	C₂×C₄×C₅	—	4	2	no	—
230	C₂×C₄×C₅	—	4	1	no	—
231	C₂×C₄×C₅	—	4	1	no	—
232	C₂×C₄×C₅	—	4	2	no	—
233	C₂×C₄×C₅	—	4	1	no	—
234	C₂×C₄×C₅	—	4	1	no	—
235	C₂×C₄×C₅	—	4	2	no	—
236	C₂×C₄×C₅	—	4	1	no	—
237	C₂×C₄×C₅	—	4	1	no	—
238	C₂×C₄×C₅	—	4	1	no	—
239	C₂×C₄×C₅	—	8	4	no	—
240	C₂×C₄×C₅	—	8	4	no	—
241	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	4	yes	—
242	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	4	yes	—
243	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
244	C₂×C₄×C₅	C₄×Q₈	1	4	yes	—
245	C₂×C₄×C₅	C₄×Q₈	1	4	yes	—
246	C₂×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
247	C₂×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
248	C₂×C₄×C₅	#124	1	4	yes	—
249	C₂×C₄×C₅	C₄⋊Q₈	1	4	yes	—
250	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
251	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
252	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
253	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
254	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
255	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
256	C₅×C₈	—	4	1	no	—
257	C₅×C₈	—	4	1	no	—
258	C₅×C₈	—	4	2	no	—
259	C₂²×Q₈	—	2	2	no	—
260	C₂³×C₄	—	2	1	no	—
261	C₂³×C₄	—	2	1	no	—
262	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
263	C₂×M₁₆	—	2	2	no	—
264	C₂×M₁₆	—	2	2	no	—
265	C₂×M₁₆	—	2	2	no	—
266	C₂²×C₈	—	2	2	no	—
267	C₂²×C₈	—	2	2	no	—
268	C₂²×C₈	—	2	2	no	—
269	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
270	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
271	C₂²×C₈	C₂³×C₅	1	2	yes	—
272	C₄⋊Q₈	—	2	8	no	—
273	C₄⋊Q₈	—	2	4	no	—
274	C₄⋊Q₈	C₂×C₄×C₅	1	8	yes	complemented
275	#125	—	2	8	no	—
276	#125	—	2	4	no	—
277	#125	C₂×C₄×C₅	1	8	yes	complemented
278	C₂²⋊Q₈	—	2	16	no	—
279	#117	—	2	2	no	—
280	#117	—	2	2	no	—
281	#117	C₂×C₄×C₅	1	4	yes	—
282	#117	C₂×C₄×C₅	1	4	yes	—
283	#117	C₅×D₄	1	4	yes	—
284	#117	C₅×Q₈	1	4	yes	complemented
285	C₂×C₄⋊C₄	—	2	1	no	—
286	C₂×C₄⋊C₄	—	2	2	no	—
287	C₂×C₄⋊C₄	—	2	1	no	—
288	C₂×C₄⋊C₄	—	2	2	no	—
289	C₂×C₄⋊C₄	—	2	2	no	—
290	C₂×C₄⋊C₄	—	2	2	no	—
291	C₂×C₄⋊C₄	—	2	2	no	—
292	C₂×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	—
293	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
294	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
295	C₂×C₄⋊C₄	C₅×Q₈	1	4	yes	complemented
296	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
297	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
298	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
299	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
300	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
301	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
302	C₂×C₂²⋊C₄	—	2	1	no	—
303	C₂×C₂²⋊C₄	—	2	1	no	—
304	C₂×C₂²⋊C₄	C₅×D₄	1	2	yes	—
305	C₂×C₄²	—	2	1	no	—
306	C₂×C₄²	—	2	1	no	—
307	C₂×C₄²	—	2	2	no	—
308	C₂×C₄²	—	2	2	no	—
309	C₂×C₄²	C₂³×C₅	1	2	yes	—
310	C₄⋊C₈	—	2	4	no	—
311	C₄⋊C₈	—	2	4	no	—
312	#95	—	2	2	no	—
313	#95	—	2	2	no	—
314	C₂²×C₅	—	2	2	no	—
315	C₂²×C₅	—	2	2	no	—
316	C₂²×C₅	—	2	2	no	—
317	C₂²×C₅	—	2	2	no	—
318	C₂²×C₅	—	2	2	no	—
319	C₂²×C₅	—	2	2	no	—
320	C₂²×C₅	#391	1	4	yes	—
321	C₂²×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
322	C₂²×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
323	C₂²×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
324	C₂²×C₅	#576	1	1	yes	characteristic
325	C₂²×C₅	#577	1	1	yes	characteristic
326	C₂²×C₅	#577	1	1	yes	characteristic
327	C₂²×C₅	#578	1	1	yes	characteristic
328	C₄×C₅	—	2	4	no	—
329	C₄×C₅	—	2	4	no	—
330	C₄×C₅	—	4	4	no	—
331	C₄×C₅	—	4	2	no	—
332	C₄×C₅	—	4	2	no	—
333	C₄×C₅	—	4	4	no	—
334	C₄×C₅	—	4	2	no	—
335	C₄×C₅	—	4	2	no	—
336	C₄×C₅	#391	1	4	yes	—
337	C₄×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
338	C₄×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
339	C₄×C₅	C₂×#124	1	1	yes	characteristic
340	C₄×C₅	C₂×C₄⋊Q₈	1	1	yes	characteristic
341	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
342	C₂×Q₈	—	2	8	no	—
343	C₂×Q₈	—	8	2	no	—
344	C₂×Q₈	—	8	2	no	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	4	no	—
352	C₂²×C₄	—	2	4	no	—
353	C₂²×C₄	—	8	1	no	—
354	C₂²×C₄	—	8	1	no	—
355	C₂²×C₄	—	8	1	no	—
356	C₂²×C₄	—	8	1	no	—
357	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
358	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
359	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
360	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
361	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
362	C₂²×C₄	C₂×C₅×Q₈	1	2	yes	—
363	C₂²×C₄	C₂×C₅×Q₈	1	2	yes	—
364	C₂²×C₄	C₅×#41	1	2	yes	—
365	C₂²×C₄	C₅×#41	1	2	yes	—
366	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
367	M₁₆	—	4	4	no	—
368	C₂×C₈	—	2	1	no	—
369	C₂×C₈	—	2	1	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	2	1	no	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	—	2	1	no	—
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	4	4	no	—
378	C₄⋊C₄	—	2	4	no	—
379	C₄⋊C₄	—	2	8	no	—
380	C₄⋊C₄	—	2	8	no	—
381	C₄⋊C₄	—	2	8	no	—
382	C₄⋊C₄	—	2	4	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	C₅×C₂²⋊C₄	1	4	yes	—
390	C₄⋊C₄	C₅×C₂²⋊C₄	1	4	yes	—
391	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
392	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
393	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
394	C₄⋊C₄	C₂×C₅×Q₈	1	4	yes	—
395	C₄⋊C₄	C₂×C₅×Q₈	1	2	yes	—
396	C₄⋊C₄	C₂×C₅×Q₈	1	2	yes	—
397	C₂²⋊C₄	—	2	4	no	—
398	C₂²⋊C₄	—	2	4	no	—
399	C₂²⋊C₄	C₅×C₂²⋊C₄	1	8	yes	—
400	C₄²	—	2	4	no	—
401	C₄²	—	2	4	no	—
402	C₄²	—	8	2	no	—
403	C₄²	—	8	2	no	—
404	C₄²	C₂²×C₄×C₅	1	4	yes	—
405	C₄²	C₂×C₅×D₄	1	4	yes	—
406	C₂×C₅	—	2	4	no	—
407	C₂×C₅	C₂×#391	1	1	yes	characteristic
408	C₂×C₅	#2897	1	1	yes	characteristic
409	C₂×C₅	#2898	1	1	yes	characteristic
410	C₂×C₅	#3081	1	1	yes	characteristic
411	C₂×C₅	#3082	1	1	yes	characteristic
412	C₂×C₅	#3083	1	1	yes	characteristic
413	C₂×C₅	#3084	1	1	yes	characteristic
414	C₂³	—	2	1	no	—
415	C₂³	—	2	1	no	—
416	C₂³	—	2	1	no	—
417	C₂³	—	2	1	no	—
418	C₂³	C₂×C₅×C₂²⋊C₄	1	2	yes	—
419	C₂³	C₅×C₂²⋊Q₈	1	2	yes	—
420	C₂³	C₅×C₂²⋊Q₈	1	2	yes	—
421	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
422	Q₈	—	8	8	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	4	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	4	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	8	4	no	—
446	C₂×C₄	—	8	4	no	—
447	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	4	yes	—
448	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	4	yes	—
449	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
450	C₂×C₄	C₄×C₅×Q₈	1	4	yes	—
451	C₂×C₄	C₄×C₅×Q₈	1	4	yes	—
452	C₂×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
453	C₂×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
454	C₂×C₄	C₅×#124	1	4	yes	—
455	C₂×C₄	C₅×C₄⋊Q₈	1	4	yes	—
456	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
457	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
458	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
459	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
460	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
461	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
462	C₈	—	4	1	no	—
463	C₈	—	4	1	no	—
464	C₈	—	4	2	no	—
465	C₅	#21315	1	1	yes	characteristic, direct product factor, Sylow
466	C₂²	—	2	2	no	—
467	C₂²	—	2	2	no	—
468	C₂²	—	2	2	no	—
469	C₂²	—	2	2	no	—
470	C₂²	—	2	2	no	—
471	C₂²	—	2	2	no	—
472	C₂²	C₅×#391	1	4	yes	—
473	C₂²	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
474	C₂²	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
475	C₂²	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
476	C₂²	C₅×#576	1	1	yes	characteristic
477	C₂²	C₅×#577	1	1	yes	characteristic
478	C₂²	C₅×#577	1	1	yes	characteristic
479	C₂²	C₅×#578	1	1	yes	characteristic
480	C₄	—	2	4	no	—
481	C₄	—	2	4	no	—
482	C₄	—	4	4	no	—
483	C₄	—	4	2	no	—
484	C₄	—	4	2	no	—
485	C₄	—	4	4	no	—
486	C₄	—	4	2	no	—
487	C₄	—	4	2	no	—
488	C₄	C₅×#391	1	4	yes	—
489	C₄	C₂×C₄×C₅×Q₈	1	1	yes	characteristic
490	C₄	C₂×C₄×C₅×Q₈	1	1	yes	characteristic
491	C₄	C₂×C₅×#124	1	1	yes	characteristic
492	C₄	C₂×C₅×C₄⋊Q₈	1	1	yes	characteristic
493	C₂	—	2	4	no	—
494	C₂	C₂×C₅×#391	1	1	yes	characteristic
495	C₂	C₅×#2897	1	1	yes	characteristic
496	C₂	C₅×#2898	1	1	yes	characteristic
497	C₂	C₅×#3081	1	1	yes	characteristic
498	C₂	C₅×#3082	1	1	yes	characteristic
499	C₂	C₅×#3083	1	1	yes	characteristic
500	C₂	C₅×#3084	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₂⁴×C₅	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₅×#117 ◁ G

Complements

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

N	H ≅ G/N	type
4. C₅×#1989	C₂	semidirect
5. C₅×#1989	C₂	semidirect
6. C₅×#1988	C₂	semidirect
7. C₅×#1987	C₂	semidirect
15. C₅×#544	C₄	semidirect
44. #21315	C₅	direct (N × H)
60. C₅×C₄⋊Q₈	C₂×C₄	semidirect
63. C₅×#125	C₂×C₄	semidirect
70. C₅×#117	Q₈	semidirect
81. C₂×C₅×C₄⋊C₄	Q₈	semidirect
103. #1989	C₂×C₅	semidirect
104. #1989	C₂×C₅	semidirect
105. #1988	C₂×C₅	semidirect
106. #1987	C₂×C₅	semidirect
179. #544	C₄×C₅	semidirect
274. C₄⋊Q₈	C₂×C₄×C₅	semidirect
277. #125	C₂×C₄×C₅	semidirect
284. #117	C₅×Q₈	semidirect
295. C₂×C₄⋊C₄	C₅×Q₈	semidirect
465. C₅	#21315	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×#544	2
C₂×C₅×#424	2
C₅×#2274	2
C₅×#1989	2
C₅×#1988	2
C₅×#1987	2
C₅×#1736	2
C₅×#1735	2
C₂×C₅×#340	2
#21315	5

Subgroups — C5×#21315 #11944035

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#21315 #11944035