Subgroups — C₅×#17868 #11940588

Order 1280.

688 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2965	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×C₈×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₅×#135	C₂	1	1	yes	maximal, characteristic
4	C₅×#1588	C₂	1	2	yes	maximal, complemented
5	C₅×#1587	C₂	1	2	yes	maximal, complemented
6	C₅×#1586	C₂	1	2	yes	maximal, complemented
7	C₅×#1585	C₂	1	2	yes	maximal, complemented
8	C₅×#1564	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1476	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1476	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅×#322	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#135	C₄	1	1	yes	characteristic
13	C₄×C₅×#41	C₂²	1	1	yes	characteristic
14	C₄×C₅×#41	C₂²	1	1	yes	characteristic
15	C₅×#446	C₂²	1	2	yes	—
16	C₅×C₈×Q₈	C₂²	1	2	yes	—
17	C₄×C₅×Q₁₆	C₄	1	1	yes	characteristic
18	C₄×C₅×Q₁₆	C₂²	1	1	yes	characteristic
19	C₄×C₅×SD₁₆	C₄	1	1	yes	characteristic
20	C₄×C₅×SD₁₆	C₄	1	1	yes	characteristic
21	C₄×C₅×SD₁₆	C₂²	1	1	yes	characteristic
22	C₄×C₅×SD₁₆	C₂²	1	1	yes	characteristic
23	C₄×C₅×D₈	C₄	1	1	yes	characteristic
24	C₄×C₅×D₈	C₂²	1	1	yes	characteristic
25	C₅×#436	C₂²	1	2	yes	—
26	C₅×#435	—	2	2	no	—
27	C₅×C₈×D₄	—	2	2	no	—
28	C₅×C₈×D₄	C₂²	1	2	yes	—
29	C₅×#431	—	2	1	no	—
30	C₅×#431	—	2	1	no	—
31	C₅×#431	C₂²	1	1	yes	characteristic
32	C₅×#431	C₂²	1	1	yes	characteristic
33	C₅×#427	C₄	1	1	yes	characteristic
34	C₅×#416	C₄	1	1	yes	characteristic
35	C₅×#416	C₄	1	1	yes	characteristic
36	C₄×C₅×M₁₆	—	2	1	no	—
37	C₂×C₄×C₅×C₈	—	2	1	no	—
38	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
41	C₅×#335	C₂²	1	2	yes	—
42	C₅×#334	C₂²	1	2	yes	—
43	C₅×Q₈⋊C₈	C₂²	1	2	yes	—
44	C₅×Q₈⋊C₈	C₂²	1	2	yes	—
45	C₅×D₄⋊C₈	C₂²	1	2	yes	—
46	C₅×D₄⋊C₈	C₂²	1	2	yes	—
47	C₅×#322	C₂²	1	2	yes	—
48	C₅×#322	C₂²	1	2	yes	—
49	#17868	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
50	C₂×C₅×#41	C₂×C₄	1	1	yes	characteristic
51	C₂×C₅×#41	C₂×C₄	1	1	yes	characteristic
52	C₅×#135	—	2	4	no	—
53	C₂×C₅×Q₁₆	C₂×C₄	1	1	yes	characteristic
54	C₂×C₅×SD₁₆	C₂×C₄	1	1	yes	characteristic
55	C₂×C₅×SD₁₆	C₂×C₄	1	1	yes	characteristic
56	C₂×C₅×D₈	C₂×C₄	1	1	yes	characteristic
57	C₂×C₅×M₁₆	—	2	2	no	—
58	C₂²×C₅×C₈	—	2	1	no	—
59	C₂²×C₅×C₈	—	2	2	no	—
60	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
61	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
62	C₂²×C₅×C₈	D₄	1	2	yes	—
63	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
64	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
65	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
66	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
67	C₄×C₅×D₄	—	2	1	no	—
68	C₄×C₅×D₄	—	2	1	no	—
69	C₄×C₅×D₄	—	2	1	no	—
70	C₄×C₅×D₄	—	2	1	no	—
71	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
72	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
73	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
74	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
75	C₅×#117	—	2	1	no	—
76	C₅×#117	—	2	1	no	—
77	C₅×#117	C₂×C₄	1	1	yes	characteristic
78	C₅×#117	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄²×C₅	—	2	1	no	—
80	C₂×C₄²×C₅	—	2	1	no	—
81	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
82	C₅×#107	C₂×C₄	1	1	yes	characteristic
83	C₅×#107	C₂×C₄	1	1	yes	characteristic
84	C₅×#106	C₂×C₄	1	1	yes	characteristic
85	C₅×#106	C₂×C₄	1	1	yes	characteristic
86	C₅×C₄⋊C₈	—	2	2	no	—
87	C₅×C₄⋊C₈	—	2	2	no	—
88	C₅×C₄⋊C₈	C₂³	1	2	yes	—
89	C₅×C₄⋊C₈	C₂³	1	2	yes	—
90	C₅×#103	C₂×C₄	1	1	yes	characteristic
91	C₅×#103	C₂×C₄	1	1	yes	characteristic
92	C₅×#103	C₂×C₄	1	1	yes	characteristic
93	C₅×#103	C₂×C₄	1	1	yes	characteristic
94	C₅×#102	C₂×C₄	1	1	yes	characteristic
95	C₅×#102	C₂×C₄	1	1	yes	characteristic
96	C₅×#102	C₂×C₄	1	1	yes	characteristic
97	C₅×#102	C₂×C₄	1	1	yes	characteristic
98	C₅×C₂²⋊C₈	—	2	1	no	—
99	C₅×C₂²⋊C₈	—	2	1	no	—
100	C₅×C₂²⋊C₈	—	2	2	no	—
101	C₅×C₂²⋊C₈	—	2	2	no	—
102	C₅×#97	—	2	2	no	—
103	C₄×C₅×C₈	—	2	2	no	—
104	C₄×C₅×C₈	—	2	1	no	—
105	C₄×C₅×C₈	—	2	1	no	—
106	C₄×C₅×C₈	—	2	1	no	—
107	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
108	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
109	C₄×C₅×C₈	D₄	1	1	yes	characteristic
110	C₄×C₅×C₈	D₄	1	1	yes	characteristic
111	C₄×C₅×C₈	C₂³	1	2	yes	—
112	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
113	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
114	C₄×C₅×C₈	C₂³	1	2	yes	—
115	#2965	C₂×C₅	1	1	yes	characteristic, complemented
116	C₈×#41	C₂×C₅	1	1	yes	characteristic, complemented
117	C₄×#135	C₂×C₅	1	1	yes	characteristic
118	#1588	C₂×C₅	1	2	yes	complemented
119	#1587	C₂×C₅	1	2	yes	complemented
120	#1586	C₂×C₅	1	2	yes	complemented
121	#1585	C₂×C₅	1	2	yes	complemented
122	#1564	C₂×C₅	1	1	yes	characteristic, complemented
123	#1476	C₂×C₅	1	1	yes	characteristic, complemented
124	#1476	C₂×C₅	1	1	yes	characteristic, complemented
125	C₂×#322	C₂×C₅	1	1	yes	characteristic, complemented
126	C₅×#41	—	2	2	no	—
127	C₅×#41	—	2	2	no	—
128	C₅×#41	—	2	2	no	—
129	C₅×#41	M₁₆	1	4	yes	complemented
130	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₅×D₄	—	2	1	no	—
133	C₂×C₅×D₄	—	2	1	no	—
134	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₄×C₅	—	2	1	no	—
137	C₂²×C₄×C₅	—	2	1	no	—
138	C₂²×C₄×C₅	—	2	1	no	—
139	C₂²×C₄×C₅	—	2	1	no	—
140	C₂²×C₄×C₅	—	2	1	no	—
141	C₂²×C₄×C₅	—	2	1	no	—
142	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
143	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₅	#41	1	1	yes	characteristic
145	C₅×Q₁₆	—	2	2	no	—
146	C₅×SD₁₆	—	2	2	no	—
147	C₅×SD₁₆	—	2	2	no	—
148	C₅×D₈	—	2	2	no	—
149	C₅×M₁₆	—	4	4	no	—
150	C₂×C₅×C₈	—	2	4	no	—
151	C₂×C₅×C₈	—	2	2	no	—
152	C₂×C₅×C₈	—	2	2	no	—
153	C₂×C₅×C₈	—	2	2	no	—
154	C₂×C₅×C₈	—	2	2	no	—
155	C₂×C₅×C₈	—	2	2	no	—
156	C₂×C₅×C₈	—	4	2	no	—
157	C₂×C₅×C₈	—	4	4	no	—
158	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
159	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
160	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
161	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
162	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
163	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
164	C₅×C₄⋊C₄	—	2	1	no	—
165	C₅×C₄⋊C₄	—	2	1	no	—
166	C₅×C₄⋊C₄	—	2	1	no	—
167	C₅×C₄⋊C₄	—	2	1	no	—
168	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
169	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
170	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
171	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
172	C₅×C₂²⋊C₄	—	2	1	no	—
173	C₅×C₂²⋊C₄	—	2	1	no	—
174	C₅×C₂²⋊C₄	—	2	1	no	—
175	C₅×C₂²⋊C₄	—	2	1	no	—
176	C₅×C₂²⋊C₄	—	2	1	no	—
177	C₅×C₂²⋊C₄	—	2	1	no	—
178	C₄²×C₅	—	2	1	no	—
179	C₄²×C₅	—	2	1	no	—
180	C₄²×C₅	—	2	1	no	—
181	C₄²×C₅	—	2	1	no	—
182	C₄²×C₅	—	2	1	no	—
183	C₄²×C₅	—	2	1	no	—
184	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
185	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
186	C₄²×C₅	#41	1	1	yes	characteristic
187	C₄²×C₅	C₂⁴	1	1	yes	characteristic
188	C₂×#135	C₄×C₅	1	1	yes	characteristic
189	C₄×#41	C₂²×C₅	1	1	yes	characteristic
190	C₄×#41	C₂²×C₅	1	1	yes	characteristic
191	#446	C₂²×C₅	1	2	yes	—
192	C₈×Q₈	C₂²×C₅	1	2	yes	—
193	C₄×Q₁₆	C₄×C₅	1	1	yes	characteristic
194	C₄×Q₁₆	C₂²×C₅	1	1	yes	characteristic
195	C₄×SD₁₆	C₄×C₅	1	1	yes	characteristic
196	C₄×SD₁₆	C₄×C₅	1	1	yes	characteristic
197	C₄×SD₁₆	C₂²×C₅	1	1	yes	characteristic
198	C₄×SD₁₆	C₂²×C₅	1	1	yes	characteristic
199	C₄×D₈	C₄×C₅	1	1	yes	characteristic
200	C₄×D₈	C₂²×C₅	1	1	yes	characteristic
201	#436	C₂²×C₅	1	2	yes	—
202	#435	—	2	2	no	—
203	C₈×D₄	—	2	2	no	—
204	C₈×D₄	C₂²×C₅	1	2	yes	—
205	#431	—	2	1	no	—
206	#431	—	2	1	no	—
207	#431	C₂²×C₅	1	1	yes	characteristic
208	#431	C₂²×C₅	1	1	yes	characteristic
209	#427	C₄×C₅	1	1	yes	characteristic
210	#416	C₄×C₅	1	1	yes	characteristic
211	#416	C₄×C₅	1	1	yes	characteristic
212	C₄×M₁₆	—	2	1	no	—
213	C₂×C₄×C₈	—	2	1	no	—
214	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
215	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
216	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
217	#335	C₂²×C₅	1	2	yes	—
218	#334	C₂²×C₅	1	2	yes	—
219	Q₈⋊C₈	C₂²×C₅	1	2	yes	—
220	Q₈⋊C₈	C₂²×C₅	1	2	yes	—
221	D₄⋊C₈	C₂²×C₅	1	2	yes	—
222	D₄⋊C₈	C₂²×C₅	1	2	yes	—
223	#322	C₂²×C₅	1	2	yes	—
224	#322	C₂²×C₅	1	2	yes	—
225	C₂³×C₅	—	2	1	no	—
226	C₂³×C₅	—	2	1	no	—
227	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
228	C₅×Q₈	—	2	1	no	—
229	C₅×Q₈	—	2	1	no	—
230	C₅×Q₈	—	2	1	no	—
231	C₅×Q₈	C₂×M₁₆	1	2	yes	—
232	C₅×D₄	—	2	4	no	—
233	C₅×D₄	—	2	1	no	—
234	C₅×D₄	—	2	1	no	—
235	C₅×D₄	—	2	1	no	—
236	C₅×D₄	—	4	2	no	—
237	C₅×D₄	C₂×M₁₆	1	2	yes	—
238	C₂×C₄×C₅	—	2	1	no	—
239	C₂×C₄×C₅	—	2	2	no	—
240	C₂×C₄×C₅	—	2	4	no	—
241	C₂×C₄×C₅	—	2	2	no	—
242	C₂×C₄×C₅	—	2	1	no	—
243	C₂×C₄×C₅	—	2	1	no	—
244	C₂×C₄×C₅	—	2	1	no	—
245	C₂×C₄×C₅	—	2	1	no	—
246	C₂×C₄×C₅	—	2	1	no	—
247	C₂×C₄×C₅	—	4	2	no	—
248	C₂×C₄×C₅	—	4	2	no	—
249	C₂×C₄×C₅	—	4	2	no	—
250	C₂×C₄×C₅	—	4	2	no	—
251	C₂×C₄×C₅	—	4	2	no	—
252	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
253	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
254	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
255	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
256	C₂×C₄×C₅	#131	1	2	yes	—
257	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
258	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
259	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
260	C₅×C₈	—	2	4	no	—
261	C₅×C₈	—	2	1	no	—
262	C₅×C₈	—	2	1	no	—
263	C₅×C₈	—	2	1	no	—
264	C₅×C₈	—	2	1	no	—
265	C₅×C₈	—	2	2	no	—
266	C₅×C₈	—	2	2	no	—
267	C₅×C₈	—	4	2	no	—
268	C₅×C₈	—	4	2	no	—
269	C₂×#41	C₂×C₄×C₅	1	1	yes	characteristic
270	C₂×#41	C₂×C₄×C₅	1	1	yes	characteristic
271	#135	—	2	4	no	—
272	C₂×Q₁₆	C₂×C₄×C₅	1	1	yes	characteristic
273	C₂×SD₁₆	C₂×C₄×C₅	1	1	yes	characteristic
274	C₂×SD₁₆	C₂×C₄×C₅	1	1	yes	characteristic
275	C₂×D₈	C₂×C₄×C₅	1	1	yes	characteristic
276	C₂×M₁₆	—	2	2	no	—
277	C₂²×C₈	—	2	1	no	—
278	C₂²×C₈	—	2	2	no	—
279	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
280	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
281	C₂²×C₈	C₅×D₄	1	2	yes	—
282	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
283	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
284	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
285	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
286	C₄×D₄	—	2	1	no	—
287	C₄×D₄	—	2	1	no	—
288	C₄×D₄	—	2	1	no	—
289	C₄×D₄	—	2	1	no	—
290	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
291	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
292	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
293	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
294	#117	—	2	1	no	—
295	#117	—	2	1	no	—
296	#117	C₂×C₄×C₅	1	1	yes	characteristic
297	#117	C₂×C₄×C₅	1	1	yes	characteristic
298	C₂×C₄²	—	2	1	no	—
299	C₂×C₄²	—	2	1	no	—
300	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
301	#107	C₂×C₄×C₅	1	1	yes	characteristic
302	#107	C₂×C₄×C₅	1	1	yes	characteristic
303	#106	C₂×C₄×C₅	1	1	yes	characteristic
304	#106	C₂×C₄×C₅	1	1	yes	characteristic
305	C₄⋊C₈	—	2	2	no	—
306	C₄⋊C₈	—	2	2	no	—
307	C₄⋊C₈	C₂³×C₅	1	2	yes	—
308	C₄⋊C₈	C₂³×C₅	1	2	yes	—
309	#103	C₂×C₄×C₅	1	1	yes	characteristic
310	#103	C₂×C₄×C₅	1	1	yes	characteristic
311	#103	C₂×C₄×C₅	1	1	yes	characteristic
312	#103	C₂×C₄×C₅	1	1	yes	characteristic
313	#102	C₂×C₄×C₅	1	1	yes	characteristic
314	#102	C₂×C₄×C₅	1	1	yes	characteristic
315	#102	C₂×C₄×C₅	1	1	yes	characteristic
316	#102	C₂×C₄×C₅	1	1	yes	characteristic
317	C₂²⋊C₈	—	2	1	no	—
318	C₂²⋊C₈	—	2	1	no	—
319	C₂²⋊C₈	—	2	2	no	—
320	C₂²⋊C₈	—	2	2	no	—
321	#97	—	2	2	no	—
322	C₄×C₈	—	2	2	no	—
323	C₄×C₈	—	2	1	no	—
324	C₄×C₈	—	2	1	no	—
325	C₄×C₈	—	2	1	no	—
326	C₄×C₈	C₂×C₄×C₅	1	1	yes	characteristic
327	C₄×C₈	C₂×C₄×C₅	1	1	yes	characteristic
328	C₄×C₈	C₅×D₄	1	1	yes	characteristic
329	C₄×C₈	C₅×D₄	1	1	yes	characteristic
330	C₄×C₈	C₂³×C₅	1	2	yes	—
331	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
332	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
333	C₄×C₈	C₂³×C₅	1	2	yes	—
334	C₂²×C₅	—	2	1	no	—
335	C₂²×C₅	—	2	1	no	—
336	C₂²×C₅	—	2	2	no	—
337	C₂²×C₅	—	4	1	no	—
338	C₂²×C₅	—	4	1	no	—
339	C₂²×C₅	—	4	1	no	—
340	C₂²×C₅	—	4	1	no	—
341	C₂²×C₅	—	4	1	no	—
342	C₂²×C₅	#435	1	2	yes	—
343	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
344	C₄×C₅	—	2	2	no	—
345	C₄×C₅	—	2	1	no	—
346	C₄×C₅	—	2	1	no	—
347	C₄×C₅	—	4	1	no	—
348	C₄×C₅	—	4	1	no	—
349	C₄×C₅	—	4	1	no	—
350	C₄×C₅	—	4	1	no	—
351	C₄×C₅	—	4	1	no	—
352	C₄×C₅	#435	1	2	yes	—
353	C₄×C₅	#443	1	2	yes	—
354	C₄×C₅	C₂²×M₁₆	1	1	yes	characteristic
355	C₄×C₅	C₂×#131	1	1	yes	characteristic
356	C₄×C₅	#575	1	2	yes	—
357	#41	—	2	2	no	—
358	#41	—	2	2	no	—
359	#41	—	2	2	no	—
360	#41	C₅×M₁₆	1	4	yes	complemented
361	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
362	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
363	C₂×D₄	—	2	1	no	—
364	C₂×D₄	—	2	1	no	—
365	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
366	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
374	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
375	C₂²×C₄	C₅×#41	1	1	yes	characteristic
376	Q₁₆	—	2	2	no	—
377	SD₁₆	—	2	2	no	—
378	SD₁₆	—	2	2	no	—
379	D₈	—	2	2	no	—
380	M₁₆	—	4	4	no	—
381	C₂×C₈	—	2	4	no	—
382	C₂×C₈	—	2	2	no	—
383	C₂×C₈	—	2	2	no	—
384	C₂×C₈	—	2	2	no	—
385	C₂×C₈	—	2	2	no	—
386	C₂×C₈	—	2	2	no	—
387	C₂×C₈	—	4	2	no	—
388	C₂×C₈	—	4	4	no	—
389	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
390	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
391	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
392	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
393	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
394	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
395	C₄⋊C₄	—	2	1	no	—
396	C₄⋊C₄	—	2	1	no	—
397	C₄⋊C₄	—	2	1	no	—
398	C₄⋊C₄	—	2	1	no	—
399	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
400	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
401	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
402	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
403	C₂²⋊C₄	—	2	1	no	—
404	C₂²⋊C₄	—	2	1	no	—
405	C₂²⋊C₄	—	2	1	no	—
406	C₂²⋊C₄	—	2	1	no	—
407	C₂²⋊C₄	—	2	1	no	—
408	C₂²⋊C₄	—	2	1	no	—
409	C₄²	—	2	1	no	—
410	C₄²	—	2	1	no	—
411	C₄²	—	2	1	no	—
412	C₄²	—	2	1	no	—
413	C₄²	—	2	1	no	—
414	C₄²	—	2	1	no	—
415	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
416	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
417	C₄²	C₅×#41	1	1	yes	characteristic
418	C₄²	C₂⁴×C₅	1	1	yes	characteristic
419	C₂×C₅	—	2	2	no	—
420	C₂×C₅	—	4	2	no	—
421	C₂×C₅	—	8	1	no	—
422	C₂×C₅	C₂×#435	1	1	yes	characteristic
423	C₂×C₅	#2943	1	1	yes	characteristic
424	C₂×C₅	C₂×#443	1	1	yes	characteristic
425	C₂³	—	2	1	no	—
426	C₂³	—	2	1	no	—
427	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
428	Q₈	—	2	1	no	—
429	Q₈	—	2	1	no	—
430	Q₈	—	2	1	no	—
431	Q₈	C₂×C₅×M₁₆	1	2	yes	—
432	D₄	—	2	4	no	—
433	D₄	—	2	1	no	—
434	D₄	—	2	1	no	—
435	D₄	—	2	1	no	—
436	D₄	—	4	2	no	—
437	D₄	C₂×C₅×M₁₆	1	2	yes	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	4	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
453	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
454	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
455	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
456	C₂×C₄	C₅×#131	1	2	yes	—
457	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
458	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
459	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
460	C₈	—	2	4	no	—
461	C₈	—	2	1	no	—
462	C₈	—	2	1	no	—
463	C₈	—	2	1	no	—
464	C₈	—	2	1	no	—
465	C₈	—	2	2	no	—
466	C₈	—	2	2	no	—
467	C₈	—	4	2	no	—
468	C₈	—	4	2	no	—
469	C₅	#17868	1	1	yes	characteristic, direct product factor, Sylow
470	C₂²	—	2	1	no	—
471	C₂²	—	2	1	no	—
472	C₂²	—	2	2	no	—
473	C₂²	—	4	1	no	—
474	C₂²	—	4	1	no	—
475	C₂²	—	4	1	no	—
476	C₂²	—	4	1	no	—
477	C₂²	—	4	1	no	—
478	C₂²	C₅×#435	1	2	yes	—
479	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
480	C₄	—	2	2	no	—
481	C₄	—	2	1	no	—
482	C₄	—	2	1	no	—
483	C₄	—	4	1	no	—
484	C₄	—	4	1	no	—
485	C₄	—	4	1	no	—
486	C₄	—	4	1	no	—
487	C₄	—	4	1	no	—
488	C₄	C₅×#435	1	2	yes	—
489	C₄	C₅×#443	1	2	yes	—
490	C₄	C₂²×C₅×M₁₆	1	1	yes	characteristic
491	C₄	C₂×C₅×#131	1	1	yes	characteristic
492	C₄	C₅×#575	1	2	yes	—
493	C₂	—	2	2	no	—
494	C₂	—	4	2	no	—
495	C₂	—	8	1	no	—
496	C₂	C₂×C₅×#435	1	1	yes	characteristic
497	C₂	C₅×#2943	1	1	yes	characteristic
498	C₂	C₂×C₅×#443	1	1	yes	characteristic

	subgroup	G/H
center	C₄²×C₅	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₄²	C₂⁴×C₅
socle	C₂²×C₅	C₂×C₄×D₄
prime radical	C₂×C₅×#135	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄²×C₅ ◁ C₂×C₄×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#2965	C₂	semidirect
2. C₅×C₈×#41	C₂	semidirect
4. C₅×#1588	C₂	semidirect
5. C₅×#1587	C₂	semidirect
6. C₅×#1586	C₂	semidirect
7. C₅×#1585	C₂	semidirect
8. C₅×#1564	C₂	semidirect
9. C₅×#1476	C₂	semidirect
10. C₅×#1476	C₂	semidirect
11. C₂×C₅×#322	C₂	semidirect
49. #17868	C₅	direct (N × H)
115. #2965	C₂×C₅	semidirect
116. C₈×#41	C₂×C₅	semidirect
118. #1588	C₂×C₅	semidirect
119. #1587	C₂×C₅	semidirect
120. #1586	C₂×C₅	semidirect
121. #1585	C₂×C₅	semidirect
122. #1564	C₂×C₅	semidirect
123. #1476	C₂×C₅	semidirect
124. #1476	C₂×C₅	semidirect
125. C₂×#322	C₂×C₅	semidirect
129. C₅×#41	M₁₆	semidirect
360. #41	C₅×M₁₆	semidirect
469. C₅	#17868	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#2965	2
C₅×C₈×#41	2
C₄×C₅×#135	2
C₅×#1588	2
C₅×#1587	2
C₅×#1586	2
C₅×#1585	2
C₅×#1564	2
C₅×#1476	2
C₂×C₅×#322	2
#17868	5

Subgroups — C5×#17868 #11940588

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#17868 #11940588