Subgroups — C₅×#18026 #11940746

Order 1280.

656 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3100	C₂	1	1	yes	maximal, characteristic
2	C₅×#2979	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2974	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1594	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1589	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1586	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1586	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1581	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1581	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1580	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×C₈×D₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1572	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1496	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1478	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1454	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#532	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
18	C₅×#480	C₄	1	1	yes	characteristic
19	C₅×#480	C₄	1	1	yes	characteristic
20	C₅×#474	C₄	1	1	yes	characteristic
21	C₅×#474	C₄	1	1	yes	characteristic
22	C₅×#459	C₄	1	1	yes	characteristic
23	C₅×#459	C₄	1	1	yes	characteristic
24	C₅×#447	C₄	1	1	yes	characteristic
25	C₅×#447	C₄	1	1	yes	characteristic
26	C₄×C₅×D₈	C₂²	1	1	yes	characteristic
27	C₄×C₅×D₈	C₂²	1	1	yes	characteristic
28	C₄×C₅×D₈	C₂²	1	1	yes	characteristic
29	C₄×C₅×D₈	C₂²	1	1	yes	characteristic
30	C₅×#436	—	2	1	no	—
31	C₅×#436	C₂²	1	1	yes	characteristic
32	C₅×#436	C₂²	1	1	yes	characteristic
33	C₅×#436	C₂²	1	1	yes	characteristic, complemented
34	C₅×#436	C₂²	1	1	yes	characteristic, complemented
35	C₅×#435	—	2	1	no	—
36	C₅×#435	—	2	1	no	—
37	C₅×C₈×D₄	—	2	1	no	—
38	C₅×C₈×D₄	C₂²	1	1	yes	characteristic
39	C₅×C₈×D₄	C₂²	1	1	yes	characteristic
40	C₅×C₈×D₄	C₂²	1	1	yes	characteristic, complemented
41	C₅×C₈×D₄	C₂²	1	1	yes	characteristic, complemented
42	C₅×#432	C₂²	1	1	yes	characteristic
43	C₅×#431	C₂²	1	1	yes	characteristic
44	C₅×#431	C₂²	1	1	yes	characteristic
45	C₅×#431	C₂²	1	1	yes	characteristic
46	C₅×#431	C₂²	1	1	yes	characteristic
47	C₅×#408	—	2	1	no	—
48	C₅×#408	—	2	1	no	—
49	C₅×#407	—	2	1	no	—
50	C₂×C₅×C₂²⋊C₈	—	2	1	no	—
51	C₅×#335	C₂²	1	1	yes	characteristic, complemented
52	C₅×#335	C₂²	1	1	yes	characteristic, complemented
53	C₅×#334	C₂²	1	1	yes	characteristic, complemented
54	C₅×#334	C₂²	1	1	yes	characteristic, complemented
55	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic
56	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic
57	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic
58	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic
59	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
60	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
61	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
62	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
63	C₅×#322	C₂²	1	1	yes	characteristic, complemented
64	C₅×#322	C₂²	1	1	yes	characteristic, complemented
65	C₅×#322	C₂²	1	1	yes	characteristic, complemented
66	C₅×C₈²	C₂²	1	1	yes	characteristic, complemented
67	#18026	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
68	C₂×C₅×#41	—	2	1	no	—
69	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
70	C₂³×C₄×C₅	—	2	1	no	—
71	C₂×C₅×D₈	C₂×C₄	1	1	yes	characteristic
72	C₂×C₅×D₈	C₂×C₄	1	1	yes	characteristic
73	C₂×C₅×D₈	C₂×C₄	1	1	yes	characteristic
74	C₂×C₅×D₈	C₂×C₄	1	1	yes	characteristic
75	C₂×C₅×M₁₆	—	2	1	no	—
76	C₂×C₅×M₁₆	—	2	1	no	—
77	C₂×C₅×M₁₆	—	2	1	no	—
78	C₂×C₅×M₁₆	—	2	1	no	—
79	C₂²×C₅×C₈	—	2	1	no	—
80	C₂²×C₅×C₈	—	2	1	no	—
81	C₂²×C₅×C₈	—	2	1	no	—
82	C₂²×C₅×C₈	—	2	1	no	—
83	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
84	C₅×#127	C₂×C₄	1	1	yes	characteristic
85	C₅×#124	—	2	1	no	—
86	C₅×#121	—	2	1	no	—
87	C₅×#121	C₂×C₄	1	1	yes	characteristic
88	C₅×#121	C₂×C₄	1	1	yes	characteristic
89	C₄×C₅×D₄	—	2	1	no	—
90	C₄×C₅×D₄	—	2	1	no	—
91	C₄×C₅×D₄	—	2	1	no	—
92	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
93	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
94	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
95	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
96	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
97	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
98	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
99	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
100	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
101	C₅×#107	C₂×C₄	1	1	yes	characteristic
102	C₅×#107	C₂×C₄	1	1	yes	characteristic
103	C₅×#107	C₂×C₄	1	1	yes	characteristic
104	C₅×#107	C₂×C₄	1	1	yes	characteristic
105	C₅×C₄⋊C₈	—	2	1	no	—
106	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
107	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
108	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
109	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
110	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
111	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
112	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
113	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
114	C₅×#102	C₂×C₄	1	1	yes	characteristic
115	C₅×#102	C₂×C₄	1	1	yes	characteristic
116	C₅×#102	C₂×C₄	1	1	yes	characteristic
117	C₅×#102	C₂×C₄	1	1	yes	characteristic
118	C₅×#102	C₂×C₄	1	1	yes	characteristic
119	C₅×#102	C₂×C₄	1	1	yes	characteristic
120	C₅×#102	C₂×C₄	1	1	yes	characteristic
121	C₅×#102	C₂×C₄	1	1	yes	characteristic
122	C₅×C₂²⋊C₈	—	2	1	no	—
123	C₅×C₂²⋊C₈	—	2	1	no	—
124	C₅×C₂²⋊C₈	—	2	1	no	—
125	C₅×C₂²⋊C₈	—	2	1	no	—
126	C₅×C₂²⋊C₈	—	2	1	no	—
127	C₅×C₂²⋊C₈	—	2	1	no	—
128	C₅×C₂²⋊C₈	—	2	1	no	—
129	C₅×C₂²⋊C₈	—	2	1	no	—
130	C₅×C₂²⋊C₈	—	2	1	no	—
131	C₅×C₂²⋊C₈	—	2	1	no	—
132	C₅×C₂²⋊C₈	—	2	1	no	—
133	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
134	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
135	C₅×C₂²⋊C₈	D₄	1	1	yes	characteristic
136	C₅×C₂²⋊C₈	D₄	1	1	yes	characteristic
137	C₅×#97	—	2	1	no	—
138	C₄×C₅×C₈	—	2	1	no	—
139	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
140	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
141	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
142	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
143	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
144	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
145	#3100	C₂×C₅	1	1	yes	characteristic
146	#2979	C₂×C₅	1	1	yes	characteristic, complemented
147	#2974	C₂×C₅	1	1	yes	characteristic, complemented
148	#1594	C₂×C₅	1	1	yes	characteristic, complemented
149	#1589	C₂×C₅	1	1	yes	characteristic, complemented
150	#1586	C₂×C₅	1	1	yes	characteristic, complemented
151	#1586	C₂×C₅	1	1	yes	characteristic, complemented
152	#1581	C₂×C₅	1	1	yes	characteristic, complemented
153	#1581	C₂×C₅	1	1	yes	characteristic, complemented
154	#1580	C₂×C₅	1	1	yes	characteristic, complemented
155	C₈×D₈	C₂×C₅	1	1	yes	characteristic, complemented
156	#1572	C₂×C₅	1	1	yes	characteristic, complemented
157	#1496	C₂×C₅	1	1	yes	characteristic, complemented
158	#1478	C₂×C₅	1	1	yes	characteristic, complemented
159	#1454	C₂×C₅	1	1	yes	characteristic, complemented
160	C₂⁴×C₅	—	2	1	no	—
161	C₅×#41	—	8	1	no	—
162	C₅×#41	—	8	1	no	—
163	C₂×C₅×Q₈	—	2	1	no	—
164	C₂×C₅×D₄	—	2	2	no	—
165	C₂×C₅×D₄	—	2	1	no	—
166	C₂×C₅×D₄	—	2	1	no	—
167	C₂×C₅×D₄	—	2	1	no	—
168	C₂×C₅×D₄	—	2	1	no	—
169	C₂×C₅×D₄	—	2	1	no	—
170	C₂×C₅×D₄	—	4	1	no	—
171	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
172	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
173	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
174	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
175	C₂²×C₄×C₅	—	2	1	no	—
176	C₂²×C₄×C₅	—	2	1	no	—
177	C₂²×C₄×C₅	—	2	1	no	—
178	C₂²×C₄×C₅	—	2	1	no	—
179	C₂²×C₄×C₅	—	2	1	no	—
180	C₂²×C₄×C₅	—	2	1	no	—
181	C₂²×C₄×C₅	—	2	1	no	—
182	C₂²×C₄×C₅	—	8	1	no	—
183	C₂²×C₄×C₅	—	8	1	no	—
184	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
185	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
186	C₂²×C₄×C₅	#41	1	1	yes	characteristic
187	C₅×D₈	—	2	2	no	—
188	C₅×D₈	—	2	2	no	—
189	C₅×D₈	—	4	1	no	—
190	C₅×D₈	—	4	1	no	—
191	C₅×M₁₆	—	8	1	no	—
192	C₅×M₁₆	—	8	1	no	—
193	C₅×M₁₆	—	8	1	no	—
194	C₅×M₁₆	—	8	1	no	—
195	C₂×C₅×C₈	—	2	1	no	—
196	C₂×C₅×C₈	—	2	1	no	—
197	C₂×C₅×C₈	—	2	1	no	—
198	C₂×C₅×C₈	—	2	1	no	—
199	C₂×C₅×C₈	—	2	1	no	—
200	C₂×C₅×C₈	—	2	1	no	—
201	C₂×C₅×C₈	—	8	1	no	—
202	C₂×C₅×C₈	—	8	1	no	—
203	C₂×C₅×C₈	—	8	1	no	—
204	C₂×C₅×C₈	—	8	1	no	—
205	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
206	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
207	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
208	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
209	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
210	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
211	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
212	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
213	C₅×C₄⋊C₄	—	2	1	no	—
214	C₅×C₄⋊C₄	—	2	1	no	—
215	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
216	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
217	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
218	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
219	C₅×C₂²⋊C₄	—	2	1	no	—
220	C₅×C₂²⋊C₄	—	2	1	no	—
221	C₅×C₂²⋊C₄	—	2	1	no	—
222	C₅×C₂²⋊C₄	—	2	1	no	—
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	—	2	1	no	—
227	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
228	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
229	C₄²×C₅	#41	1	1	yes	characteristic
230	C₄²×C₅	C₂⁴	1	1	yes	characteristic
231	#532	C₂²×C₅	1	1	yes	characteristic
232	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
233	#480	C₄×C₅	1	1	yes	characteristic
234	#480	C₄×C₅	1	1	yes	characteristic
235	#474	C₄×C₅	1	1	yes	characteristic
236	#474	C₄×C₅	1	1	yes	characteristic
237	#459	C₄×C₅	1	1	yes	characteristic
238	#459	C₄×C₅	1	1	yes	characteristic
239	#447	C₄×C₅	1	1	yes	characteristic
240	#447	C₄×C₅	1	1	yes	characteristic
241	C₄×D₈	C₂²×C₅	1	1	yes	characteristic
242	C₄×D₈	C₂²×C₅	1	1	yes	characteristic
243	C₄×D₈	C₂²×C₅	1	1	yes	characteristic
244	C₄×D₈	C₂²×C₅	1	1	yes	characteristic
245	#436	—	2	1	no	—
246	#436	C₂²×C₅	1	1	yes	characteristic
247	#436	C₂²×C₅	1	1	yes	characteristic
248	#436	C₂²×C₅	1	1	yes	characteristic, complemented
249	#436	C₂²×C₅	1	1	yes	characteristic, complemented
250	#435	—	2	1	no	—
251	#435	—	2	1	no	—
252	C₈×D₄	—	2	1	no	—
253	C₈×D₄	C₂²×C₅	1	1	yes	characteristic
254	C₈×D₄	C₂²×C₅	1	1	yes	characteristic
255	C₈×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
256	C₈×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
257	#432	C₂²×C₅	1	1	yes	characteristic
258	#431	C₂²×C₅	1	1	yes	characteristic
259	#431	C₂²×C₅	1	1	yes	characteristic
260	#431	C₂²×C₅	1	1	yes	characteristic
261	#431	C₂²×C₅	1	1	yes	characteristic
262	#408	—	2	1	no	—
263	#408	—	2	1	no	—
264	#407	—	2	1	no	—
265	C₂×C₂²⋊C₈	—	2	1	no	—
266	#335	C₂²×C₅	1	1	yes	characteristic, complemented
267	#335	C₂²×C₅	1	1	yes	characteristic, complemented
268	#334	C₂²×C₅	1	1	yes	characteristic, complemented
269	#334	C₂²×C₅	1	1	yes	characteristic, complemented
270	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
271	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
272	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
273	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
274	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
275	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
276	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
277	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
278	#322	C₂²×C₅	1	1	yes	characteristic, complemented
279	#322	C₂²×C₅	1	1	yes	characteristic, complemented
280	#322	C₂²×C₅	1	1	yes	characteristic, complemented
281	C₈²	C₂²×C₅	1	1	yes	characteristic, complemented
282	C₂³×C₅	—	2	1	no	—
283	C₂³×C₅	—	2	1	no	—
284	C₂³×C₅	—	2	1	no	—
285	C₂³×C₅	—	2	1	no	—
286	C₂³×C₅	—	4	2	no	—
287	C₂³×C₅	—	4	2	no	—
288	C₂³×C₅	—	8	1	no	—
289	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
290	C₅×Q₈	—	8	1	no	—
291	C₅×D₄	—	2	1	no	—
292	C₅×D₄	—	2	1	no	—
293	C₅×D₄	—	2	1	no	—
294	C₅×D₄	—	2	1	no	—
295	C₅×D₄	—	2	1	no	—
296	C₅×D₄	—	2	1	no	—
297	C₅×D₄	—	2	1	no	—
298	C₅×D₄	—	4	2	no	—
299	C₅×D₄	—	4	2	no	—
300	C₅×D₄	—	8	1	no	—
301	C₅×D₄	—	8	1	no	—
302	C₅×D₄	—	8	1	no	—
303	C₅×D₄	#131	1	2	yes	—
304	C₂×C₄×C₅	—	2	1	no	—
305	C₂×C₄×C₅	—	2	1	no	—
306	C₂×C₄×C₅	—	2	1	no	—
307	C₂×C₄×C₅	—	2	1	no	—
308	C₂×C₄×C₅	—	2	1	no	—
309	C₂×C₄×C₅	—	2	1	no	—
310	C₂×C₄×C₅	—	2	1	no	—
311	C₂×C₄×C₅	—	2	1	no	—
312	C₂×C₄×C₅	—	4	1	no	—
313	C₂×C₄×C₅	—	4	1	no	—
314	C₂×C₄×C₅	—	4	1	no	—
315	C₂×C₄×C₅	—	4	1	no	—
316	C₂×C₄×C₅	—	4	1	no	—
317	C₂×C₄×C₅	—	4	1	no	—
318	C₂×C₄×C₅	—	4	1	no	—
319	C₂×C₄×C₅	—	4	1	no	—
320	C₂×C₄×C₅	—	4	1	no	—
321	C₂×C₄×C₅	—	8	1	no	—
322	C₂×C₄×C₅	—	8	1	no	—
323	C₂×C₄×C₅	—	8	1	no	—
324	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
325	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
326	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
327	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
328	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
329	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
330	C₅×C₈	—	2	1	no	—
331	C₅×C₈	—	2	1	no	—
332	C₅×C₈	—	2	1	no	—
333	C₅×C₈	—	2	1	no	—
334	C₅×C₈	—	2	1	no	—
335	C₅×C₈	—	2	1	no	—
336	C₅×C₈	—	2	1	no	—
337	C₅×C₈	—	2	1	no	—
338	C₅×C₈	—	4	1	no	—
339	C₅×C₈	—	4	1	no	—
340	C₅×C₈	—	4	1	no	—
341	C₅×C₈	—	4	1	no	—
342	C₅×C₈	—	4	1	no	—
343	C₅×C₈	—	4	1	no	—
344	C₂×#41	—	2	1	no	—
345	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
346	C₂³×C₄	—	2	1	no	—
347	C₂×D₈	C₂×C₄×C₅	1	1	yes	characteristic
348	C₂×D₈	C₂×C₄×C₅	1	1	yes	characteristic
349	C₂×D₈	C₂×C₄×C₅	1	1	yes	characteristic
350	C₂×D₈	C₂×C₄×C₅	1	1	yes	characteristic
351	C₂×M₁₆	—	2	1	no	—
352	C₂×M₁₆	—	2	1	no	—
353	C₂×M₁₆	—	2	1	no	—
354	C₂×M₁₆	—	2	1	no	—
355	C₂²×C₈	—	2	1	no	—
356	C₂²×C₈	—	2	1	no	—
357	C₂²×C₈	—	2	1	no	—
358	C₂²×C₈	—	2	1	no	—
359	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
360	#127	C₂×C₄×C₅	1	1	yes	characteristic
361	#124	—	2	1	no	—
362	#121	—	2	1	no	—
363	#121	C₂×C₄×C₅	1	1	yes	characteristic
364	#121	C₂×C₄×C₅	1	1	yes	characteristic
365	C₄×D₄	—	2	1	no	—
366	C₄×D₄	—	2	1	no	—
367	C₄×D₄	—	2	1	no	—
368	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
369	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
370	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
371	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
372	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
373	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
374	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
375	C₂×C₂²⋊C₄	—	2	1	no	—
376	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
377	#107	C₂×C₄×C₅	1	1	yes	characteristic
378	#107	C₂×C₄×C₅	1	1	yes	characteristic
379	#107	C₂×C₄×C₅	1	1	yes	characteristic
380	#107	C₂×C₄×C₅	1	1	yes	characteristic
381	C₄⋊C₈	—	2	1	no	—
382	C₄⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
383	C₄⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
384	C₄⋊C₈	C₅×D₄	1	1	yes	characteristic
385	C₄⋊C₈	C₅×D₄	1	1	yes	characteristic
386	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
387	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
388	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
389	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
390	#102	C₂×C₄×C₅	1	1	yes	characteristic
391	#102	C₂×C₄×C₅	1	1	yes	characteristic
392	#102	C₂×C₄×C₅	1	1	yes	characteristic
393	#102	C₂×C₄×C₅	1	1	yes	characteristic
394	#102	C₂×C₄×C₅	1	1	yes	characteristic
395	#102	C₂×C₄×C₅	1	1	yes	characteristic
396	#102	C₂×C₄×C₅	1	1	yes	characteristic
397	#102	C₂×C₄×C₅	1	1	yes	characteristic
398	C₂²⋊C₈	—	2	1	no	—
399	C₂²⋊C₈	—	2	1	no	—
400	C₂²⋊C₈	—	2	1	no	—
401	C₂²⋊C₈	—	2	1	no	—
402	C₂²⋊C₈	—	2	1	no	—
403	C₂²⋊C₈	—	2	1	no	—
404	C₂²⋊C₈	—	2	1	no	—
405	C₂²⋊C₈	—	2	1	no	—
406	C₂²⋊C₈	—	2	1	no	—
407	C₂²⋊C₈	—	2	1	no	—
408	C₂²⋊C₈	—	2	1	no	—
409	C₂²⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
410	C₂²⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
411	C₂²⋊C₈	C₅×D₄	1	1	yes	characteristic
412	C₂²⋊C₈	C₅×D₄	1	1	yes	characteristic
413	#97	—	2	1	no	—
414	C₄×C₈	—	2	1	no	—
415	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
416	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
417	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
418	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
419	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
420	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
421	C₂²×C₅	—	2	1	no	—
422	C₂²×C₅	—	2	2	no	—
423	C₂²×C₅	—	2	1	no	—
424	C₂²×C₅	—	2	1	no	—
425	C₂²×C₅	—	4	1	no	—
426	C₂²×C₅	—	4	1	no	—
427	C₂²×C₅	—	4	1	no	—
428	C₂²×C₅	—	4	1	no	—
429	C₂²×C₅	—	4	1	no	—
430	C₂²×C₅	—	4	1	no	—
431	C₂²×C₅	—	4	1	no	—
432	C₂²×C₅	—	4	1	no	—
433	C₂²×C₅	—	4	1	no	—
434	C₂²×C₅	—	4	1	no	—
435	C₂²×C₅	—	4	1	no	—
436	C₂²×C₅	—	8	4	no	—
437	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
438	C₄×C₅	—	2	1	no	—
439	C₄×C₅	—	2	1	no	—
440	C₄×C₅	—	2	1	no	—
441	C₄×C₅	—	2	1	no	—
442	C₄×C₅	—	4	1	no	—
443	C₄×C₅	—	4	1	no	—
444	C₄×C₅	—	4	1	no	—
445	C₄×C₅	—	4	1	no	—
446	C₄×C₅	C₂×#131	1	1	yes	characteristic
447	C₄×C₅	#568	1	1	yes	characteristic
448	C₄×C₅	#576	1	1	yes	characteristic
449	C₄×C₅	#576	1	1	yes	characteristic
450	C₂⁴	—	2	1	no	—
451	#41	—	8	1	no	—
452	#41	—	8	1	no	—
453	C₂×Q₈	—	2	1	no	—
454	C₂×D₄	—	2	2	no	—
455	C₂×D₄	—	2	1	no	—
456	C₂×D₄	—	2	1	no	—
457	C₂×D₄	—	2	1	no	—
458	C₂×D₄	—	2	1	no	—
459	C₂×D₄	—	2	1	no	—
460	C₂×D₄	—	4	1	no	—
461	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
462	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
463	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
464	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	2	1	no	—
472	C₂²×C₄	—	8	1	no	—
473	C₂²×C₄	—	8	1	no	—
474	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
475	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
476	C₂²×C₄	C₅×#41	1	1	yes	characteristic
477	D₈	—	2	2	no	—
478	D₈	—	2	2	no	—
479	D₈	—	4	1	no	—
480	D₈	—	4	1	no	—
481	M₁₆	—	8	1	no	—
482	M₁₆	—	8	1	no	—
483	M₁₆	—	8	1	no	—
484	M₁₆	—	8	1	no	—
485	C₂×C₈	—	2	1	no	—
486	C₂×C₈	—	2	1	no	—
487	C₂×C₈	—	2	1	no	—
488	C₂×C₈	—	2	1	no	—
489	C₂×C₈	—	2	1	no	—
490	C₂×C₈	—	2	1	no	—
491	C₂×C₈	—	8	1	no	—
492	C₂×C₈	—	8	1	no	—
493	C₂×C₈	—	8	1	no	—
494	C₂×C₈	—	8	1	no	—
495	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
496	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
497	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
498	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
499	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
500	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
501	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
502	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
503	C₄⋊C₄	—	2	1	no	—
504	C₄⋊C₄	—	2	1	no	—
505	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
506	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
507	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
508	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
509	C₂²⋊C₄	—	2	1	no	—
510	C₂²⋊C₄	—	2	1	no	—
511	C₂²⋊C₄	—	2	1	no	—
512	C₂²⋊C₄	—	2	1	no	—
513	C₂²⋊C₄	—	2	1	no	—
514	C₂²⋊C₄	—	2	1	no	—
515	C₂²⋊C₄	—	2	1	no	—
516	C₂²⋊C₄	—	2	1	no	—
517	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
518	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
519	C₄²	C₅×#41	1	1	yes	characteristic
520	C₄²	C₂⁴×C₅	1	1	yes	characteristic
521	C₂×C₅	—	4	1	no	—
522	C₂×C₅	—	4	2	no	—
523	C₂×C₅	—	8	1	no	—
524	C₂×C₅	—	8	1	no	—
525	C₂×C₅	—	8	1	no	—
526	C₂×C₅	#2933	1	1	yes	characteristic
527	C₂×C₅	#2948	1	1	yes	characteristic
528	C₂×C₅	#2955	1	1	yes	characteristic
529	C₂³	—	2	1	no	—
530	C₂³	—	2	1	no	—
531	C₂³	—	2	1	no	—
532	C₂³	—	2	1	no	—
533	C₂³	—	4	2	no	—
534	C₂³	—	4	2	no	—
535	C₂³	—	8	1	no	—
536	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
537	Q₈	—	8	1	no	—
538	D₄	—	2	1	no	—
539	D₄	—	2	1	no	—
540	D₄	—	2	1	no	—
541	D₄	—	2	1	no	—
542	D₄	—	2	1	no	—
543	D₄	—	2	1	no	—
544	D₄	—	2	1	no	—
545	D₄	—	4	2	no	—
546	D₄	—	4	2	no	—
547	D₄	—	8	1	no	—
548	D₄	—	8	1	no	—
549	D₄	—	8	1	no	—
550	D₄	C₅×#131	1	2	yes	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	—	4	1	no	—
563	C₂×C₄	—	4	1	no	—
564	C₂×C₄	—	4	1	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	8	1	no	—
569	C₂×C₄	—	8	1	no	—
570	C₂×C₄	—	8	1	no	—
571	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
572	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
573	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
574	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
575	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
576	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
577	C₈	—	2	1	no	—
578	C₈	—	2	1	no	—
579	C₈	—	2	1	no	—
580	C₈	—	2	1	no	—
581	C₈	—	2	1	no	—
582	C₈	—	2	1	no	—
583	C₈	—	2	1	no	—
584	C₈	—	2	1	no	—
585	C₈	—	4	1	no	—
586	C₈	—	4	1	no	—
587	C₈	—	4	1	no	—
588	C₈	—	4	1	no	—
589	C₈	—	4	1	no	—
590	C₈	—	4	1	no	—
591	C₅	#18026	1	1	yes	characteristic, direct product factor, Sylow
592	C₂²	—	2	1	no	—
593	C₂²	—	2	2	no	—
594	C₂²	—	2	1	no	—
595	C₂²	—	2	1	no	—
596	C₂²	—	4	1	no	—
597	C₂²	—	4	1	no	—
598	C₂²	—	4	1	no	—
599	C₂²	—	4	1	no	—
600	C₂²	—	4	1	no	—
601	C₂²	—	4	1	no	—
602	C₂²	—	4	1	no	—
603	C₂²	—	4	1	no	—
604	C₂²	—	4	1	no	—
605	C₂²	—	4	1	no	—
606	C₂²	—	4	1	no	—
607	C₂²	—	8	4	no	—
608	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
609	C₄	—	2	1	no	—
610	C₄	—	2	1	no	—
611	C₄	—	2	1	no	—
612	C₄	—	2	1	no	—
613	C₄	—	4	1	no	—
614	C₄	—	4	1	no	—
615	C₄	—	4	1	no	—
616	C₄	—	4	1	no	—
617	C₄	C₂×C₅×#131	1	1	yes	characteristic
618	C₄	C₅×#568	1	1	yes	characteristic
619	C₄	C₅×#576	1	1	yes	characteristic
620	C₄	C₅×#576	1	1	yes	characteristic
621	C₂	—	4	1	no	—
622	C₂	—	4	2	no	—
623	C₂	—	8	1	no	—
624	C₂	—	8	1	no	—
625	C₂	—	8	1	no	—
626	C₂	C₅×#2933	1	1	yes	characteristic
627	C₂	C₅×#2948	1	1	yes	characteristic
628	C₂	C₅×#2955	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₄²	C₂⁴×C₅
socle	C₂²×C₅	C₂×C₄×D₄
prime radical	C₅×#3100	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₅×#431 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#2979	C₂	semidirect
3. C₅×#2974	C₂	semidirect
4. C₅×#1594	C₂	semidirect
5. C₅×#1589	C₂	semidirect
6. C₅×#1586	C₂	semidirect
7. C₅×#1586	C₂	semidirect
8. C₅×#1581	C₂	semidirect
9. C₅×#1581	C₂	semidirect
10. C₅×#1580	C₂	semidirect
11. C₅×C₈×D₈	C₂	semidirect
12. C₅×#1572	C₂	semidirect
13. C₅×#1496	C₂	semidirect
14. C₅×#1478	C₂	semidirect
15. C₅×#1454	C₂	semidirect
33. C₅×#436	C₂²	semidirect
34. C₅×#436	C₂²	semidirect
40. C₅×C₈×D₄	C₂²	semidirect
41. C₅×C₈×D₄	C₂²	semidirect
51. C₅×#335	C₂²	semidirect
52. C₅×#335	C₂²	semidirect
53. C₅×#334	C₂²	semidirect
54. C₅×#334	C₂²	semidirect
59. C₅×D₄⋊C₈	C₂²	semidirect
60. C₅×D₄⋊C₈	C₂²	semidirect
61. C₅×D₄⋊C₈	C₂²	semidirect
62. C₅×D₄⋊C₈	C₂²	semidirect
63. C₅×#322	C₂²	semidirect
64. C₅×#322	C₂²	semidirect
65. C₅×#322	C₂²	semidirect
66. C₅×C₈²	C₂²	semidirect
67. #18026	C₅	direct (N × H)
146. #2979	C₂×C₅	semidirect
147. #2974	C₂×C₅	semidirect
148. #1594	C₂×C₅	semidirect
149. #1589	C₂×C₅	semidirect
150. #1586	C₂×C₅	semidirect
151. #1586	C₂×C₅	semidirect
152. #1581	C₂×C₅	semidirect
153. #1581	C₂×C₅	semidirect
154. #1580	C₂×C₅	semidirect
155. C₈×D₈	C₂×C₅	semidirect
156. #1572	C₂×C₅	semidirect
157. #1496	C₂×C₅	semidirect
158. #1478	C₂×C₅	semidirect
159. #1454	C₂×C₅	semidirect
248. #436	C₂²×C₅	semidirect
249. #436	C₂²×C₅	semidirect
255. C₈×D₄	C₂²×C₅	semidirect
256. C₈×D₄	C₂²×C₅	semidirect
266. #335	C₂²×C₅	semidirect
267. #335	C₂²×C₅	semidirect
268. #334	C₂²×C₅	semidirect
269. #334	C₂²×C₅	semidirect
274. D₄⋊C₈	C₂²×C₅	semidirect
275. D₄⋊C₈	C₂²×C₅	semidirect
276. D₄⋊C₈	C₂²×C₅	semidirect
277. D₄⋊C₈	C₂²×C₅	semidirect
278. #322	C₂²×C₅	semidirect
279. #322	C₂²×C₅	semidirect
280. #322	C₂²×C₅	semidirect
281. C₈²	C₂²×C₅	semidirect
591. C₅	#18026	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×#3100	2
C₅×#2979	2
C₅×#2974	2
C₅×#1594	2
C₅×#1589	2
C₅×#1586	2
C₅×#1581	2
C₅×#1580	2
C₅×C₈×D₈	2
C₅×#1572	2
C₅×#1496	2
C₅×#1478	2
C₅×#1454	2
#18026	5

Subgroups — C5×#18026 #11940746

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#18026 #11940746