Subgroups — C₅×#17950 #11940670

Order 1280.

646 conjugacy classes of subgroups.

The subgroup lattice has 410 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×#2981	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2975	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1594	C₂	1	2	yes	maximal, complemented
5	C₅×#1589	C₂	1	2	yes	maximal, complemented
6	C₅×#1586	C₂	1	2	yes	maximal, complemented
7	C₅×#1581	C₂	1	2	yes	maximal, complemented
8	C₅×#1572	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1490	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1484	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1453	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#532	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
14	C₅×#480	C₄	1	2	yes	—
15	C₅×#474	C₄	1	2	yes	—
16	C₅×#459	C₄	1	2	yes	—
17	C₅×#447	C₄	1	2	yes	—
18	C₄×C₅×D₈	C₂²	1	2	yes	—
19	C₄×C₅×D₈	C₂²	1	2	yes	—
20	C₅×#436	—	2	2	no	—
21	C₅×#436	C₂²	1	2	yes	—
22	C₅×#436	C₂²	1	2	yes	—
23	C₅×#436	C₂²	1	2	yes	complemented
24	C₅×#435	—	2	2	no	—
25	C₅×C₈×D₄	C₂²	1	2	yes	complemented
26	C₅×#432	C₂²	1	1	yes	characteristic
27	C₅×#431	C₂²	1	1	yes	characteristic
28	C₅×#431	C₂²	1	1	yes	characteristic
29	C₅×#431	C₂²	1	1	yes	characteristic
30	C₅×#408	—	2	2	no	—
31	C₅×#407	—	2	2	no	—
32	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
33	C₅×#335	C₂²	1	2	yes	complemented
34	C₅×#334	C₂²	1	2	yes	complemented
35	C₅×D₄⋊C₈	C₂²	1	2	yes	—
36	C₅×D₄⋊C₈	C₂²	1	2	yes	—
37	C₅×D₄⋊C₈	C₂²	1	2	yes	complemented
38	C₅×D₄⋊C₈	C₂²	1	2	yes	complemented
39	C₅×#322	C₂²	1	1	yes	characteristic, complemented
40	C₅×#322	C₂²	1	1	yes	characteristic, complemented
41	C₅×#322	C₂²	1	1	yes	characteristic, complemented
42	C₅×C₈²	C₂²	1	1	yes	characteristic, complemented
43	#17950	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂×C₅×#41	—	2	1	no	—
45	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
46	C₂³×C₄×C₅	—	2	1	no	—
47	C₂×C₅×D₈	C₂×C₄	1	2	yes	—
48	C₂×C₅×D₈	C₂×C₄	1	2	yes	—
49	C₂×C₅×M₁₆	—	2	1	no	—
50	C₂×C₅×M₁₆	—	2	2	no	—
51	C₂×C₅×M₁₆	—	2	2	no	—
52	C₂×C₅×M₁₆	—	2	2	no	—
53	C₂²×C₅×C₈	—	2	2	no	—
54	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
55	C₅×#127	C₂×C₄	1	1	yes	characteristic
56	C₅×#124	—	2	1	no	—
57	C₅×#121	—	2	1	no	—
58	C₅×#121	C₂×C₄	1	2	yes	—
59	C₄×C₅×D₄	—	2	1	no	—
60	C₄×C₅×D₄	—	2	1	no	—
61	C₄×C₅×D₄	—	2	1	no	—
62	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
63	C₄×C₅×D₄	C₂³	1	2	yes	—
64	C₄×C₅×D₄	C₂³	1	2	yes	—
65	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
66	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
67	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
68	C₅×#107	C₂×C₄	1	2	yes	—
69	C₅×#107	C₂×C₄	1	2	yes	—
70	C₅×C₄⋊C₈	C₂×C₄	1	2	yes	—
71	C₅×C₄⋊C₈	D₄	1	2	yes	—
72	C₅×C₄⋊C₈	C₂³	1	2	yes	—
73	C₅×C₄⋊C₈	C₂³	1	2	yes	—
74	C₅×#102	C₂×C₄	1	2	yes	—
75	C₅×#102	C₂×C₄	1	2	yes	—
76	C₅×#102	C₂×C₄	1	2	yes	—
77	C₅×#102	C₂×C₄	1	2	yes	—
78	C₅×C₂²⋊C₈	—	2	1	no	—
79	C₅×C₂²⋊C₈	—	2	1	no	—
80	C₅×C₂²⋊C₈	—	2	2	no	—
81	C₅×C₂²⋊C₈	—	2	2	no	—
82	C₅×C₂²⋊C₈	—	2	2	no	—
83	C₅×C₂²⋊C₈	—	2	2	no	—
84	C₅×C₂²⋊C₈	C₂×C₄	1	2	yes	—
85	C₅×C₂²⋊C₈	D₄	1	2	yes	—
86	C₅×#97	—	2	1	no	—
87	C₅×#97	—	2	1	no	—
88	C₄×C₅×C₈	—	2	1	no	—
89	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
90	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
91	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
92	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
93	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
94	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
95	#3100	C₂×C₅	1	1	yes	characteristic
96	#2981	C₂×C₅	1	1	yes	characteristic, complemented
97	#2975	C₂×C₅	1	1	yes	characteristic, complemented
98	#1594	C₂×C₅	1	2	yes	complemented
99	#1589	C₂×C₅	1	2	yes	complemented
100	#1586	C₂×C₅	1	2	yes	complemented
101	#1581	C₂×C₅	1	2	yes	complemented
102	#1572	C₂×C₅	1	1	yes	characteristic, complemented
103	#1490	C₂×C₅	1	1	yes	characteristic, complemented
104	#1484	C₂×C₅	1	1	yes	characteristic, complemented
105	#1453	C₂×C₅	1	1	yes	characteristic, complemented
106	C₂⁴×C₅	—	2	1	no	—
107	C₅×#41	—	8	2	no	—
108	C₂×C₅×Q₈	—	2	1	no	—
109	C₂×C₅×D₄	—	2	2	no	—
110	C₂×C₅×D₄	—	2	1	no	—
111	C₂×C₅×D₄	—	2	1	no	—
112	C₂×C₅×D₄	—	2	1	no	—
113	C₂×C₅×D₄	—	4	2	no	—
114	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
115	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
116	C₂²×C₄×C₅	—	2	1	no	—
117	C₂²×C₄×C₅	—	2	2	no	—
118	C₂²×C₄×C₅	—	2	2	no	—
119	C₂²×C₄×C₅	—	2	2	no	—
120	C₂²×C₄×C₅	—	8	2	no	—
121	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₅	#41	1	1	yes	characteristic
124	C₅×D₈	—	4	2	no	—
125	C₅×D₈	—	4	2	no	—
126	C₅×M₁₆	—	4	2	no	—
127	C₅×M₁₆	—	8	2	no	—
128	C₅×M₁₆	—	8	2	no	—
129	C₅×M₁₆	—	8	2	no	—
130	C₂×C₅×C₈	—	2	1	no	—
131	C₂×C₅×C₈	—	2	2	no	—
132	C₂×C₅×C₈	—	2	2	no	—
133	C₂×C₅×C₈	—	2	1	no	—
134	C₂×C₅×C₈	—	8	2	no	—
135	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
136	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
137	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
138	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
139	C₅×C₄⋊C₄	—	2	1	no	—
140	C₅×C₄⋊C₄	—	2	1	no	—
141	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
142	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
143	C₅×C₂²⋊C₄	—	2	2	no	—
144	C₅×C₂²⋊C₄	—	2	2	no	—
145	C₅×C₂²⋊C₄	—	2	2	no	—
146	C₅×C₂²⋊C₄	—	2	2	no	—
147	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
148	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
149	C₄²×C₅	#41	1	1	yes	characteristic
150	C₄²×C₅	C₂⁴	1	1	yes	characteristic
151	#532	C₂²×C₅	1	1	yes	characteristic
152	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
153	#480	C₄×C₅	1	2	yes	—
154	#474	C₄×C₅	1	2	yes	—
155	#459	C₄×C₅	1	2	yes	—
156	#447	C₄×C₅	1	2	yes	—
157	C₄×D₈	C₂²×C₅	1	2	yes	—
158	C₄×D₈	C₂²×C₅	1	2	yes	—
159	#436	—	2	2	no	—
160	#436	C₂²×C₅	1	2	yes	—
161	#436	C₂²×C₅	1	2	yes	—
162	#436	C₂²×C₅	1	2	yes	complemented
163	#435	—	2	2	no	—
164	C₈×D₄	C₂²×C₅	1	2	yes	complemented
165	#432	C₂²×C₅	1	1	yes	characteristic
166	#431	C₂²×C₅	1	1	yes	characteristic
167	#431	C₂²×C₅	1	1	yes	characteristic
168	#431	C₂²×C₅	1	1	yes	characteristic
169	#408	—	2	2	no	—
170	#407	—	2	2	no	—
171	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic
172	#335	C₂²×C₅	1	2	yes	complemented
173	#334	C₂²×C₅	1	2	yes	complemented
174	D₄⋊C₈	C₂²×C₅	1	2	yes	—
175	D₄⋊C₈	C₂²×C₅	1	2	yes	—
176	D₄⋊C₈	C₂²×C₅	1	2	yes	complemented
177	D₄⋊C₈	C₂²×C₅	1	2	yes	complemented
178	#322	C₂²×C₅	1	1	yes	characteristic, complemented
179	#322	C₂²×C₅	1	1	yes	characteristic, complemented
180	#322	C₂²×C₅	1	1	yes	characteristic, complemented
181	C₈²	C₂²×C₅	1	1	yes	characteristic, complemented
182	C₂³×C₅	—	2	2	no	—
183	C₂³×C₅	—	2	2	no	—
184	C₂³×C₅	—	4	2	no	—
185	C₂³×C₅	—	8	1	no	—
186	C₂³×C₅	—	8	1	no	—
187	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
188	C₅×Q₈	—	8	1	no	—
189	C₅×D₄	—	2	2	no	—
190	C₅×D₄	—	2	2	no	—
191	C₅×D₄	—	2	2	no	—
192	C₅×D₄	—	2	2	no	—
193	C₅×D₄	—	4	2	no	—
194	C₅×D₄	—	8	1	no	—
195	C₅×D₄	—	8	1	no	—
196	C₅×D₄	—	8	2	no	—
197	C₂×C₄×C₅	—	2	2	no	—
198	C₂×C₄×C₅	—	2	2	no	—
199	C₂×C₄×C₅	—	2	2	no	—
200	C₂×C₄×C₅	—	2	2	no	—
201	C₂×C₄×C₅	—	4	1	no	—
202	C₂×C₄×C₅	—	4	2	no	—
203	C₂×C₄×C₅	—	4	2	no	—
204	C₂×C₄×C₅	—	4	2	no	—
205	C₂×C₄×C₅	—	4	2	no	—
206	C₂×C₄×C₅	—	8	2	no	—
207	C₂×C₄×C₅	—	8	1	no	—
208	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
209	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
210	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
211	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
212	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
214	C₅×C₈	—	2	2	no	—
215	C₅×C₈	—	2	2	no	—
216	C₅×C₈	—	2	2	no	—
217	C₅×C₈	—	2	2	no	—
218	C₅×C₈	—	2	2	no	—
219	C₅×C₈	—	4	1	no	—
220	C₅×C₈	—	4	2	no	—
221	C₅×C₈	—	4	2	no	—
222	C₂×#41	—	2	1	no	—
223	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
224	C₂³×C₄	—	2	1	no	—
225	C₂×D₈	C₂×C₄×C₅	1	2	yes	—
226	C₂×D₈	C₂×C₄×C₅	1	2	yes	—
227	C₂×M₁₆	—	2	1	no	—
228	C₂×M₁₆	—	2	2	no	—
229	C₂×M₁₆	—	2	2	no	—
230	C₂×M₁₆	—	2	2	no	—
231	C₂²×C₈	—	2	2	no	—
232	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
233	#127	C₂×C₄×C₅	1	1	yes	characteristic
234	#124	—	2	1	no	—
235	#121	—	2	1	no	—
236	#121	C₂×C₄×C₅	1	2	yes	—
237	C₄×D₄	—	2	1	no	—
238	C₄×D₄	—	2	1	no	—
239	C₄×D₄	—	2	1	no	—
240	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
241	C₄×D₄	C₂³×C₅	1	2	yes	—
242	C₄×D₄	C₂³×C₅	1	2	yes	—
243	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
244	C₂×C₂²⋊C₄	—	2	1	no	—
245	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
246	#107	C₂×C₄×C₅	1	2	yes	—
247	#107	C₂×C₄×C₅	1	2	yes	—
248	C₄⋊C₈	C₂×C₄×C₅	1	2	yes	—
249	C₄⋊C₈	C₅×D₄	1	2	yes	—
250	C₄⋊C₈	C₂³×C₅	1	2	yes	—
251	C₄⋊C₈	C₂³×C₅	1	2	yes	—
252	#102	C₂×C₄×C₅	1	2	yes	—
253	#102	C₂×C₄×C₅	1	2	yes	—
254	#102	C₂×C₄×C₅	1	2	yes	—
255	#102	C₂×C₄×C₅	1	2	yes	—
256	C₂²⋊C₈	—	2	1	no	—
257	C₂²⋊C₈	—	2	1	no	—
258	C₂²⋊C₈	—	2	2	no	—
259	C₂²⋊C₈	—	2	2	no	—
260	C₂²⋊C₈	—	2	2	no	—
261	C₂²⋊C₈	—	2	2	no	—
262	C₂²⋊C₈	C₂×C₄×C₅	1	2	yes	—
263	C₂²⋊C₈	C₅×D₄	1	2	yes	—
264	#97	—	2	1	no	—
265	#97	—	2	1	no	—
266	C₄×C₈	—	2	1	no	—
267	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
268	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
269	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
270	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
271	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
272	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
273	C₂²×C₅	—	2	1	no	—
274	C₂²×C₅	—	2	1	no	—
275	C₂²×C₅	—	2	1	no	—
276	C₂²×C₅	—	4	2	no	—
277	C₂²×C₅	—	4	2	no	—
278	C₂²×C₅	—	4	2	no	—
279	C₂²×C₅	—	4	2	no	—
280	C₂²×C₅	—	4	2	no	—
281	C₂²×C₅	—	4	2	no	—
282	C₂²×C₅	—	8	4	no	—
283	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
284	C₄×C₅	—	2	1	no	—
285	C₄×C₅	—	2	1	no	—
286	C₄×C₅	—	2	1	no	—
287	C₄×C₅	—	2	1	no	—
288	C₄×C₅	—	4	2	no	—
289	C₄×C₅	—	4	2	no	—
290	C₄×C₅	#568	1	2	yes	—
291	C₄×C₅	#576	1	2	yes	—
292	C₂⁴	—	2	1	no	—
293	#41	—	8	2	no	—
294	C₂×Q₈	—	2	1	no	—
295	C₂×D₄	—	2	2	no	—
296	C₂×D₄	—	2	1	no	—
297	C₂×D₄	—	2	1	no	—
298	C₂×D₄	—	2	1	no	—
299	C₂×D₄	—	4	2	no	—
300	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
301	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
302	C₂²×C₄	—	2	1	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	8	2	no	—
307	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
308	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
309	C₂²×C₄	C₅×#41	1	1	yes	characteristic
310	D₈	—	4	2	no	—
311	D₈	—	4	2	no	—
312	M₁₆	—	4	2	no	—
313	M₁₆	—	8	2	no	—
314	M₁₆	—	8	2	no	—
315	M₁₆	—	8	2	no	—
316	C₂×C₈	—	2	1	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	1	no	—
320	C₂×C₈	—	8	2	no	—
321	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
322	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
323	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
324	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
325	C₄⋊C₄	—	2	1	no	—
326	C₄⋊C₄	—	2	1	no	—
327	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
328	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
329	C₂²⋊C₄	—	2	2	no	—
330	C₂²⋊C₄	—	2	2	no	—
331	C₂²⋊C₄	—	2	2	no	—
332	C₂²⋊C₄	—	2	2	no	—
333	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
334	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
335	C₄²	C₅×#41	1	1	yes	characteristic
336	C₄²	C₂⁴×C₅	1	1	yes	characteristic
337	C₂×C₅	—	4	1	no	—
338	C₂×C₅	—	8	2	no	—
339	C₂×C₅	—	8	2	no	—
340	C₂×C₅	#2930	1	1	yes	characteristic
341	C₂×C₅	#2948	1	1	yes	characteristic
342	C₂×C₅	#2956	1	1	yes	characteristic
343	C₂³	—	2	2	no	—
344	C₂³	—	2	2	no	—
345	C₂³	—	4	2	no	—
346	C₂³	—	8	1	no	—
347	C₂³	—	8	1	no	—
348	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
349	Q₈	—	8	1	no	—
350	D₄	—	2	2	no	—
351	D₄	—	2	2	no	—
352	D₄	—	2	2	no	—
353	D₄	—	2	2	no	—
354	D₄	—	4	2	no	—
355	D₄	—	8	1	no	—
356	D₄	—	8	1	no	—
357	D₄	—	8	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	8	2	no	—
368	C₂×C₄	—	8	1	no	—
369	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
370	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
371	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
372	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
373	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
374	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
375	C₈	—	2	2	no	—
376	C₈	—	2	2	no	—
377	C₈	—	2	2	no	—
378	C₈	—	2	2	no	—
379	C₈	—	2	2	no	—
380	C₈	—	4	1	no	—
381	C₈	—	4	2	no	—
382	C₈	—	4	2	no	—
383	C₅	#17950	1	1	yes	characteristic, direct product factor, Sylow
384	C₂²	—	2	1	no	—
385	C₂²	—	2	1	no	—
386	C₂²	—	2	1	no	—
387	C₂²	—	4	2	no	—
388	C₂²	—	4	2	no	—
389	C₂²	—	4	2	no	—
390	C₂²	—	4	2	no	—
391	C₂²	—	4	2	no	—
392	C₂²	—	4	2	no	—
393	C₂²	—	8	4	no	—
394	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
395	C₄	—	2	1	no	—
396	C₄	—	2	1	no	—
397	C₄	—	2	1	no	—
398	C₄	—	2	1	no	—
399	C₄	—	4	2	no	—
400	C₄	—	4	2	no	—
401	C₄	C₅×#568	1	2	yes	—
402	C₄	C₅×#576	1	2	yes	—
403	C₂	—	4	1	no	—
404	C₂	—	8	2	no	—
405	C₂	—	8	2	no	—
406	C₂	C₅×#2930	1	1	yes	characteristic
407	C₂	C₅×#2948	1	1	yes	characteristic
408	C₂	C₅×#2956	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×#2981	C₂	semidirect
3. C₅×#2975	C₂	semidirect
4. C₅×#1594	C₂	semidirect
5. C₅×#1589	C₂	semidirect
6. C₅×#1586	C₂	semidirect
7. C₅×#1581	C₂	semidirect
8. C₅×#1572	C₂	semidirect
9. C₅×#1490	C₂	semidirect
10. C₅×#1484	C₂	semidirect
11. C₅×#1453	C₂	semidirect
23. C₅×#436	C₂²	semidirect
25. C₅×C₈×D₄	C₂²	semidirect
33. C₅×#335	C₂²	semidirect
34. C₅×#334	C₂²	semidirect
37. C₅×D₄⋊C₈	C₂²	semidirect
38. C₅×D₄⋊C₈	C₂²	semidirect
39. C₅×#322	C₂²	semidirect
40. C₅×#322	C₂²	semidirect
41. C₅×#322	C₂²	semidirect
42. C₅×C₈²	C₂²	semidirect
43. #17950	C₅	direct (N × H)
96. #2981	C₂×C₅	semidirect
97. #2975	C₂×C₅	semidirect
98. #1594	C₂×C₅	semidirect
99. #1589	C₂×C₅	semidirect
100. #1586	C₂×C₅	semidirect
101. #1581	C₂×C₅	semidirect
102. #1572	C₂×C₅	semidirect
103. #1490	C₂×C₅	semidirect
104. #1484	C₂×C₅	semidirect
105. #1453	C₂×C₅	semidirect
162. #436	C₂²×C₅	semidirect
164. C₈×D₄	C₂²×C₅	semidirect
172. #335	C₂²×C₅	semidirect
173. #334	C₂²×C₅	semidirect
176. D₄⋊C₈	C₂²×C₅	semidirect
177. D₄⋊C₈	C₂²×C₅	semidirect
178. #322	C₂²×C₅	semidirect
179. #322	C₂²×C₅	semidirect
180. #322	C₂²×C₅	semidirect
181. C₈²	C₂²×C₅	semidirect
383. C₅	#17950	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×#2981	2
C₅×#2975	2
C₅×#1594	2
C₅×#1589	2
C₅×#1586	2
C₅×#1581	2
C₅×#1572	2
C₅×#1490	2
C₅×#1484	2
C₅×#1453	2
#17950	5

Subgroups — C5×#17950 #11940670

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#17950 #11940670