Subgroups — C₅×#33590 #11956310

Order 1280.

694 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#510	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#508	C₂	1	1	yes	maximal, characteristic
3	C₅×#3156	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2951	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2211	C₂	1	2	yes	maximal, complemented
6	C₅×#2210	C₂	1	2	yes	maximal, complemented
7	C₅×#2209	C₂	1	2	yes	maximal, complemented
8	C₅×#2208	C₂	1	2	yes	maximal, complemented
9	C₅×#2151	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#2139	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅×#358	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#137	—	2	1	no	—
13	C₂×C₅×#135	C₂²	1	1	yes	characteristic
14	C₂×C₅×#135	C₂²	1	1	yes	characteristic
15	C₂²×C₅×Q₁₆	C₂²	1	1	yes	characteristic
16	C₅×#536	—	2	1	no	—
17	C₅×#520	—	2	1	no	—
18	C₅×#510	—	2	4	no	—
19	C₅×#508	—	2	4	no	—
20	C₂×C₅×Q₃₂	C₂²	1	1	yes	characteristic
21	C₂×C₅×Q₃₂	C₂²	1	2	yes	—
22	C₂×C₅×SD₃₂	C₂²	1	1	yes	characteristic
23	C₂×C₅×SD₃₂	C₂²	1	1	yes	characteristic
24	C₂×C₅×SD₃₂	C₂²	1	2	yes	—
25	C₂×C₅×D₁₆	C₂²	1	1	yes	characteristic
26	C₂×C₅×M₃₂	C₂²	1	1	yes	characteristic
27	C₂²×C₅×C₁₆	C₂²	1	1	yes	characteristic
28	C₅×#497	—	2	2	no	—
29	C₅×#495	C₂²	1	2	yes	—
30	C₅×#494	C₂²	1	2	yes	—
31	C₅×#440	—	2	2	no	—
32	C₄×C₅×Q₁₆	C₂²	1	2	yes	—
33	C₄×C₅×D₈	C₂²	1	2	yes	—
34	C₂×C₅×#107	C₂²	1	1	yes	characteristic
35	C₅×#417	—	2	1	no	—
36	C₅×#405	C₂²	1	1	yes	characteristic
37	C₅×C₄⋊C₁₆	C₂²	1	2	yes	—
38	C₅×C₄⋊C₁₆	C₂²	1	2	yes	—
39	C₅×#358	C₂²	1	2	yes	—
40	C₅×#358	C₂²	1	2	yes	—
41	C₅×#358	C₂²	1	2	yes	—
42	C₅×#357	C₂²	1	2	yes	—
43	#33590	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂×C₅×#41	—	2	1	no	—
45	C₂×C₅×#41	—	2	1	no	—
46	C₂²×C₅×Q₈	—	2	1	no	—
47	C₅×#137	—	4	4	no	—
48	C₅×#135	—	2	2	no	—
49	C₅×#135	—	2	2	no	—
50	C₅×#135	—	2	2	no	—
51	C₅×#135	D₄	1	4	yes	—
52	C₂×C₅×Q₁₆	—	2	2	no	—
53	C₂×C₅×Q₁₆	—	2	2	no	—
54	C₂×C₅×Q₁₆	—	2	1	no	—
55	C₂×C₅×Q₁₆	—	2	2	no	—
56	C₂×C₅×Q₁₆	C₂³	1	1	yes	characteristic
57	C₂×C₅×Q₁₆	C₂³	1	2	yes	—
58	C₂×C₅×Q₁₆	C₂³	1	1	yes	characteristic
59	C₂×C₅×SD₁₆	—	2	1	no	—
60	C₂×C₅×SD₁₆	—	2	2	no	—
61	C₂×C₅×SD₁₆	—	2	1	no	—
62	C₂×C₅×D₈	C₂³	1	1	yes	characteristic
63	C₂×C₅×D₈	C₂³	1	1	yes	characteristic
64	C₂×C₅×M₁₆	D₄	1	1	yes	characteristic
65	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
66	C₅×C₄⋊Q₈	—	2	2	no	—
67	C₅×#124	—	2	2	no	—
68	C₅×#123	—	4	2	no	—
69	C₅×C₂²⋊Q₈	—	4	1	no	—
70	C₅×C₂²⋊Q₈	—	4	1	no	—
71	C₄×C₅×Q₈	—	2	2	no	—
72	C₄×C₅×D₄	—	2	2	no	—
73	C₄×C₅×D₄	—	4	2	no	—
74	C₅×#117	—	4	1	no	—
75	C₅×#117	D₄	1	1	yes	characteristic
76	C₂×C₅×C₄⋊C₄	—	2	1	no	—
77	C₂×C₅×C₄⋊C₄	—	4	1	no	—
78	C₅×Q₃₂	—	2	2	no	—
79	C₅×Q₃₂	—	2	4	no	—
80	C₅×SD₃₂	—	2	2	no	—
81	C₅×SD₃₂	—	2	2	no	—
82	C₅×SD₃₂	—	2	4	no	—
83	C₅×D₁₆	—	2	2	no	—
84	C₅×M₃₂	—	2	2	no	—
85	C₂×C₅×C₁₆	—	2	2	no	—
86	C₂×C₅×C₁₆	C₂³	1	2	yes	—
87	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
88	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
89	C₅×#107	—	2	1	no	—
90	C₅×#107	C₂³	1	2	yes	—
91	C₅×#103	—	2	2	no	—
92	C₅×#102	—	2	2	no	—
93	C₅×#97	D₄	1	2	yes	—
94	C₄×C₅×C₈	C₂³	1	2	yes	—
95	C₂×#510	C₂×C₅	1	1	yes	characteristic, complemented
96	C₂×#508	C₂×C₅	1	1	yes	characteristic
97	#3156	C₂×C₅	1	1	yes	characteristic, complemented
98	#2951	C₂×C₅	1	1	yes	characteristic, complemented
99	#2211	C₂×C₅	1	2	yes	complemented
100	#2210	C₂×C₅	1	2	yes	complemented
101	#2209	C₂×C₅	1	2	yes	complemented
102	#2208	C₂×C₅	1	2	yes	complemented
103	#2151	C₂×C₅	1	1	yes	characteristic, complemented
104	#2139	C₂×C₅	1	1	yes	characteristic, complemented
105	C₂×#358	C₂×C₅	1	1	yes	characteristic, complemented
106	C₅×#41	—	2	4	no	—
107	C₅×#41	—	4	2	no	—
108	C₅×#41	—	4	2	no	—
109	C₅×#41	—	4	2	no	—
110	C₂×C₅×Q₈	—	2	1	no	—
111	C₂×C₅×Q₈	—	2	2	no	—
112	C₂×C₅×Q₈	—	2	1	no	—
113	C₂×C₅×Q₈	—	4	1	no	—
114	C₂×C₅×Q₈	—	4	2	no	—
115	C₂×C₅×Q₈	—	4	2	no	—
116	C₂×C₅×D₄	—	2	1	no	—
117	C₂×C₅×D₄	—	2	1	no	—
118	C₂×C₅×D₄	—	4	1	no	—
119	C₂×C₅×D₄	—	4	1	no	—
120	C₂²×C₄×C₅	—	4	1	no	—
121	C₂²×C₄×C₅	—	4	1	no	—
122	C₂²×C₄×C₅	—	4	1	no	—
123	C₂²×C₄×C₅	—	4	1	no	—
124	C₂²×C₄×C₅	—	4	2	no	—
125	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
126	C₅×Q₁₆	—	2	2	no	—
127	C₅×Q₁₆	—	2	1	no	—
128	C₅×Q₁₆	—	2	1	no	—
129	C₅×Q₁₆	—	2	2	no	—
130	C₅×Q₁₆	—	2	1	no	—
131	C₅×Q₁₆	—	4	4	no	—
132	C₅×Q₁₆	—	4	2	no	—
133	C₅×Q₁₆	C₂×D₄	1	2	yes	—
134	C₅×SD₁₆	—	2	4	no	—
135	C₅×SD₁₆	—	4	4	no	—
136	C₅×SD₁₆	—	4	2	no	—
137	C₅×D₈	—	2	1	no	—
138	C₅×D₈	—	2	1	no	—
139	C₅×D₈	—	2	1	no	—
140	C₅×D₈	C₂×D₄	1	2	yes	—
141	C₅×M₁₆	—	2	2	no	—
142	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
143	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
144	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
145	C₂×C₅×C₈	#41	1	2	yes	—
146	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
147	C₅×C₄⋊C₄	—	2	2	no	—
148	C₅×C₄⋊C₄	—	4	1	no	—
149	C₅×C₄⋊C₄	—	4	2	no	—
150	C₅×C₄⋊C₄	—	4	2	no	—
151	C₅×C₄⋊C₄	—	4	2	no	—
152	C₅×C₄⋊C₄	D₈	1	1	yes	characteristic
153	C₅×C₄⋊C₄	D₈	1	1	yes	characteristic
154	C₅×C₂²⋊C₄	—	4	2	no	—
155	C₅×C₂²⋊C₄	—	4	2	no	—
156	C₅×C₂²⋊C₄	—	4	2	no	—
157	C₅×C₂²⋊C₄	D₈	1	2	yes	—
158	C₄²×C₅	—	4	2	no	—
159	C₄²×C₅	C₂×D₄	1	2	yes	—
160	C₅×C₁₆	—	2	1	no	—
161	C₅×C₁₆	—	2	1	no	—
162	C₅×C₁₆	—	2	2	no	—
163	C₂×#137	—	2	1	no	—
164	C₂×#135	C₂²×C₅	1	1	yes	characteristic
165	C₂×#135	C₂²×C₅	1	1	yes	characteristic
166	C₂²×Q₁₆	C₂²×C₅	1	1	yes	characteristic
167	#536	—	2	1	no	—
168	#520	—	2	1	no	—
169	#510	—	2	4	no	—
170	#508	—	2	4	no	—
171	C₂×Q₃₂	C₂²×C₅	1	1	yes	characteristic
172	C₂×Q₃₂	C₂²×C₅	1	2	yes	—
173	C₂×SD₃₂	C₂²×C₅	1	1	yes	characteristic
174	C₂×SD₃₂	C₂²×C₅	1	1	yes	characteristic
175	C₂×SD₃₂	C₂²×C₅	1	2	yes	—
176	C₂×D₁₆	C₂²×C₅	1	1	yes	characteristic
177	C₂×M₃₂	C₂²×C₅	1	1	yes	characteristic
178	C₂²×C₁₆	C₂²×C₅	1	1	yes	characteristic
179	#497	—	2	2	no	—
180	#495	C₂²×C₅	1	2	yes	—
181	#494	C₂²×C₅	1	2	yes	—
182	#440	—	2	2	no	—
183	C₄×Q₁₆	C₂²×C₅	1	2	yes	—
184	C₄×D₈	C₂²×C₅	1	2	yes	—
185	C₂×#107	C₂²×C₅	1	1	yes	characteristic
186	#417	—	2	1	no	—
187	#405	C₂²×C₅	1	1	yes	characteristic
188	C₄⋊C₁₆	C₂²×C₅	1	2	yes	—
189	C₄⋊C₁₆	C₂²×C₅	1	2	yes	—
190	#358	C₂²×C₅	1	2	yes	—
191	#358	C₂²×C₅	1	2	yes	—
192	#358	C₂²×C₅	1	2	yes	—
193	#357	C₂²×C₅	1	2	yes	—
194	C₂³×C₅	—	4	1	no	—
195	C₂³×C₅	—	4	1	no	—
196	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
197	C₅×Q₈	—	2	2	no	—
198	C₅×Q₈	—	4	1	no	—
199	C₅×Q₈	—	4	1	no	—
200	C₅×Q₈	—	4	2	no	—
201	C₅×Q₈	—	4	2	no	—
202	C₅×Q₈	—	4	1	no	—
203	C₅×Q₈	—	8	2	no	—
204	C₅×D₄	—	2	2	no	—
205	C₅×D₄	—	4	4	no	—
206	C₅×D₄	—	4	1	no	—
207	C₅×D₄	—	4	1	no	—
208	C₅×D₄	—	4	1	no	—
209	C₅×D₄	—	8	2	no	—
210	C₂×C₄×C₅	—	4	1	no	—
211	C₂×C₄×C₅	—	4	4	no	—
212	C₂×C₄×C₅	—	4	2	no	—
213	C₂×C₄×C₅	—	4	2	no	—
214	C₂×C₄×C₅	—	4	1	no	—
215	C₂×C₄×C₅	—	8	2	no	—
216	C₂×C₄×C₅	—	8	2	no	—
217	C₂×C₄×C₅	—	16	2	no	—
218	C₂×C₄×C₅	—	16	1	no	—
219	C₂×C₄×C₅	#121	1	2	yes	—
220	C₂×C₄×C₅	C₂×D₈	1	2	yes	—
221	C₂×C₄×C₅	C₂×D₈	1	2	yes	—
222	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
223	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
224	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
225	C₅×C₈	—	2	2	no	—
226	C₅×C₈	#121	1	2	yes	—
227	C₅×C₈	C₂²×D₄	1	1	yes	characteristic
228	C₅×C₈	C₂×#41	1	1	yes	characteristic
229	C₂×#41	—	2	1	no	—
230	C₂×#41	—	2	1	no	—
231	C₂²×Q₈	—	2	1	no	—
232	#137	—	4	4	no	—
233	#135	—	2	2	no	—
234	#135	—	2	2	no	—
235	#135	—	2	2	no	—
236	#135	C₅×D₄	1	4	yes	—
237	C₂×Q₁₆	—	2	2	no	—
238	C₂×Q₁₆	—	2	1	no	—
239	C₂×Q₁₆	—	2	2	no	—
240	C₂×Q₁₆	—	2	2	no	—
241	C₂×Q₁₆	C₂³×C₅	1	2	yes	—
242	C₂×Q₁₆	C₂³×C₅	1	1	yes	characteristic
243	C₂×Q₁₆	C₂³×C₅	1	1	yes	characteristic
244	C₂×SD₁₆	—	2	1	no	—
245	C₂×SD₁₆	—	2	1	no	—
246	C₂×SD₁₆	—	2	2	no	—
247	C₂×D₈	C₂³×C₅	1	1	yes	characteristic
248	C₂×D₈	C₂³×C₅	1	1	yes	characteristic
249	C₂×M₁₆	C₅×D₄	1	1	yes	characteristic
250	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
251	C₄⋊Q₈	—	2	2	no	—
252	#124	—	2	2	no	—
253	#123	—	4	2	no	—
254	C₂²⋊Q₈	—	4	1	no	—
255	C₂²⋊Q₈	—	4	1	no	—
256	C₄×Q₈	—	2	2	no	—
257	C₄×D₄	—	2	2	no	—
258	C₄×D₄	—	4	2	no	—
259	#117	—	4	1	no	—
260	#117	C₅×D₄	1	1	yes	characteristic
261	C₂×C₄⋊C₄	—	2	1	no	—
262	C₂×C₄⋊C₄	—	4	1	no	—
263	Q₃₂	—	2	2	no	—
264	Q₃₂	—	2	4	no	—
265	SD₃₂	—	2	2	no	—
266	SD₃₂	—	2	2	no	—
267	SD₃₂	—	2	4	no	—
268	D₁₆	—	2	2	no	—
269	M₃₂	—	2	2	no	—
270	C₂×C₁₆	—	2	2	no	—
271	C₂×C₁₆	C₂³×C₅	1	2	yes	—
272	C₂×C₁₆	C₂³×C₅	1	1	yes	characteristic
273	C₂×C₁₆	C₂³×C₅	1	1	yes	characteristic
274	#107	—	2	1	no	—
275	#107	C₂³×C₅	1	2	yes	—
276	#103	—	2	2	no	—
277	#102	—	2	2	no	—
278	#97	C₅×D₄	1	2	yes	—
279	C₄×C₈	C₂³×C₅	1	2	yes	—
280	C₂²×C₅	—	2	1	no	—
281	C₂²×C₅	—	2	1	no	—
282	C₂²×C₅	—	4	2	no	—
283	C₂²×C₅	—	8	1	no	—
284	C₂²×C₅	—	8	1	no	—
285	C₂²×C₅	—	8	1	no	—
286	C₂²×C₅	—	8	1	no	—
287	C₂²×C₅	—	8	1	no	—
288	C₂²×C₅	#459	1	2	yes	—
289	C₂²×C₅	C₂²×D₈	1	1	yes	characteristic
290	C₄×C₅	—	2	2	no	—
291	C₄×C₅	—	2	2	no	—
292	C₄×C₅	—	4	2	no	—
293	C₄×C₅	—	8	2	no	—
294	C₄×C₅	—	8	1	no	—
295	C₄×C₅	—	8	2	no	—
296	C₄×C₅	#459	1	2	yes	—
297	C₄×C₅	C₂×#121	1	1	yes	characteristic
298	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
299	#41	—	2	4	no	—
300	#41	—	4	2	no	—
301	#41	—	4	2	no	—
302	#41	—	4	2	no	—
303	C₂×Q₈	—	2	1	no	—
304	C₂×Q₈	—	2	2	no	—
305	C₂×Q₈	—	2	1	no	—
306	C₂×Q₈	—	4	1	no	—
307	C₂×Q₈	—	4	2	no	—
308	C₂×Q₈	—	4	2	no	—
309	C₂×D₄	—	2	1	no	—
310	C₂×D₄	—	2	1	no	—
311	C₂×D₄	—	4	1	no	—
312	C₂×D₄	—	4	1	no	—
313	C₂²×C₄	—	4	1	no	—
314	C₂²×C₄	—	4	1	no	—
315	C₂²×C₄	—	4	1	no	—
316	C₂²×C₄	—	4	1	no	—
317	C₂²×C₄	—	4	2	no	—
318	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
319	Q₁₆	—	2	2	no	—
320	Q₁₆	—	2	1	no	—
321	Q₁₆	—	2	1	no	—
322	Q₁₆	—	2	2	no	—
323	Q₁₆	—	2	1	no	—
324	Q₁₆	—	4	4	no	—
325	Q₁₆	—	4	2	no	—
326	Q₁₆	C₂×C₅×D₄	1	2	yes	—
327	SD₁₆	—	2	4	no	—
328	SD₁₆	—	4	4	no	—
329	SD₁₆	—	4	2	no	—
330	D₈	—	2	1	no	—
331	D₈	—	2	1	no	—
332	D₈	—	2	1	no	—
333	D₈	C₂×C₅×D₄	1	2	yes	—
334	M₁₆	—	2	2	no	—
335	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
336	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
337	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
338	C₂×C₈	C₅×#41	1	2	yes	—
339	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	4	1	no	—
342	C₄⋊C₄	—	4	2	no	—
343	C₄⋊C₄	—	4	2	no	—
344	C₄⋊C₄	—	4	2	no	—
345	C₄⋊C₄	C₅×D₈	1	1	yes	characteristic
346	C₄⋊C₄	C₅×D₈	1	1	yes	characteristic
347	C₂²⋊C₄	—	4	2	no	—
348	C₂²⋊C₄	—	4	2	no	—
349	C₂²⋊C₄	—	4	2	no	—
350	C₂²⋊C₄	C₅×D₈	1	2	yes	—
351	C₄²	—	4	2	no	—
352	C₄²	C₂×C₅×D₄	1	2	yes	—
353	C₁₆	—	2	1	no	—
354	C₁₆	—	2	1	no	—
355	C₁₆	—	2	2	no	—
356	C₂×C₅	—	2	2	no	—
357	C₂×C₅	—	8	2	no	—
358	C₂×C₅	—	16	1	no	—
359	C₂×C₅	C₂×#459	1	1	yes	characteristic
360	C₂×C₅	#3416	1	1	yes	characteristic
361	C₂×C₅	#3417	1	1	yes	characteristic
362	C₂³	—	4	1	no	—
363	C₂³	—	4	1	no	—
364	C₂³	C₂×C₅×D₈	1	1	yes	characteristic
365	Q₈	—	2	2	no	—
366	Q₈	—	4	1	no	—
367	Q₈	—	4	1	no	—
368	Q₈	—	4	2	no	—
369	Q₈	—	4	2	no	—
370	Q₈	—	4	1	no	—
371	Q₈	—	8	2	no	—
372	D₄	—	2	2	no	—
373	D₄	—	4	4	no	—
374	D₄	—	4	1	no	—
375	D₄	—	4	1	no	—
376	D₄	—	4	1	no	—
377	D₄	—	8	2	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	4	4	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	8	2	no	—
384	C₂×C₄	—	8	2	no	—
385	C₂×C₄	—	16	2	no	—
386	C₂×C₄	—	16	1	no	—
387	C₂×C₄	C₅×#121	1	2	yes	—
388	C₂×C₄	C₂×C₅×D₈	1	2	yes	—
389	C₂×C₄	C₂×C₅×D₈	1	2	yes	—
390	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
391	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
392	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
393	C₈	—	2	2	no	—
394	C₈	C₅×#121	1	2	yes	—
395	C₈	C₂²×C₅×D₄	1	1	yes	characteristic
396	C₈	C₂×C₅×#41	1	1	yes	characteristic
397	C₅	#33590	1	1	yes	characteristic, direct product factor, Sylow
398	C₂²	—	2	1	no	—
399	C₂²	—	2	1	no	—
400	C₂²	—	4	2	no	—
401	C₂²	—	8	1	no	—
402	C₂²	—	8	1	no	—
403	C₂²	—	8	1	no	—
404	C₂²	—	8	1	no	—
405	C₂²	—	8	1	no	—
406	C₂²	C₅×#459	1	2	yes	—
407	C₂²	C₂²×C₅×D₈	1	1	yes	characteristic
408	C₄	—	2	2	no	—
409	C₄	—	2	2	no	—
410	C₄	—	4	2	no	—
411	C₄	—	8	1	no	—
412	C₄	—	8	2	no	—
413	C₄	—	8	2	no	—
414	C₄	C₅×#459	1	2	yes	—
415	C₄	C₂×C₅×#121	1	1	yes	characteristic
416	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
417	C₂	—	2	2	no	—
418	C₂	—	8	2	no	—
419	C₂	—	16	1	no	—
420	C₂	C₂×C₅×#459	1	1	yes	characteristic
421	C₂	C₅×#3416	1	1	yes	characteristic
422	C₂	C₅×#3417	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₅
prime radical	C₂×C₅×#508	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₅×#117 ◁ C₅×#405 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#510	C₂	semidirect
3. C₅×#3156	C₂	semidirect
4. C₅×#2951	C₂	semidirect
5. C₅×#2211	C₂	semidirect
6. C₅×#2210	C₂	semidirect
7. C₅×#2209	C₂	semidirect
8. C₅×#2208	C₂	semidirect
9. C₅×#2151	C₂	semidirect
10. C₅×#2139	C₂	semidirect
11. C₂×C₅×#358	C₂	semidirect
43. #33590	C₅	direct (N × H)
95. C₂×#510	C₂×C₅	semidirect
97. #3156	C₂×C₅	semidirect
98. #2951	C₂×C₅	semidirect
99. #2211	C₂×C₅	semidirect
100. #2210	C₂×C₅	semidirect
101. #2209	C₂×C₅	semidirect
102. #2208	C₂×C₅	semidirect
103. #2151	C₂×C₅	semidirect
104. #2139	C₂×C₅	semidirect
105. C₂×#358	C₂×C₅	semidirect
397. C₅	#33590	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×#510	2
C₂×C₅×#508	2
C₅×#3156	2
C₅×#2951	2
C₅×#2211	2
C₅×#2210	2
C₅×#2209	2
C₅×#2208	2
C₅×#2151	2
C₅×#2139	2
C₂×C₅×#358	2
#33590	5

Subgroups — C5×#33590 #11956310

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#33590 #11956310