Subgroups — C₅×#21105 #11943825

Order 1280.

912 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#433	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×#97	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2290	C₂	1	1	yes	maximal, characteristic
4	C₅×#1924	C₂	1	2	yes	maximal, complemented
5	C₅×#1917	C₂	1	2	yes	maximal, complemented
6	C₅×#1869	C₂	1	2	yes	maximal
7	C₅×#1850	C₂	1	2	yes	maximal, complemented
8	C₅×#1768	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1750	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₅×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1746	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×C₅×C₈	C₂²	1	2	yes	—
13	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
14	C₂×C₅×#117	C₂²	1	1	yes	characteristic
15	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
16	C₅×#433	—	2	4	no	—
17	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
18	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
19	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
20	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
21	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
22	C₂×C₅×#97	—	2	4	no	—
23	C₂×C₅×#97	C₂²	1	1	yes	characteristic
24	C₂×C₅×#97	C₂²	1	2	yes	—
25	C₂×C₅×#97	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
28	C₅×#388	C₄	1	2	yes	—
29	C₅×#387	C₄	1	2	yes	—
30	C₅×#386	C₄	1	2	yes	—
31	C₅×#385	C₄	1	2	yes	—
32	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
34	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
35	C₅×#376	C₂²	1	1	yes	characteristic
36	C₅×#336	C₂²	1	2	yes	—
37	C₅×#336	C₂²	1	2	yes	—
38	C₅×#336	C₂²	1	2	yes	—
39	C₅×#336	C₂²	1	2	yes	—
40	C₅×#336	C₂²	1	2	yes	—
41	#21105	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
43	C₂³×C₄×C₅	C₂×C₄	1	2	yes	—
44	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
46	C₂²×C₅×C₈	—	2	4	no	—
47	C₂²×C₅×C₈	—	2	4	no	—
48	C₂²×C₅×C₈	—	2	4	no	—
49	C₂²×C₅×C₈	C₂³	1	2	yes	—
50	C₂²×C₅×C₈	C₂³	1	2	yes	—
51	C₂²×C₅×C₈	C₂³	1	2	yes	—
52	C₂²×C₅×C₈	C₂³	1	2	yes	—
53	C₄×C₅×D₄	—	2	4	no	—
54	C₅×#117	—	2	2	no	—
55	C₅×#117	—	2	2	no	—
56	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
57	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
58	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
59	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
60	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
61	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
62	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
63	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
64	C₂×C₄²×C₅	—	2	2	no	—
65	C₂×C₄²×C₅	—	2	2	no	—
66	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
67	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
71	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
72	C₅×C₄⋊C₈	—	2	4	no	—
73	C₅×C₄⋊C₈	—	2	4	no	—
74	C₅×C₂²⋊C₈	—	2	4	no	—
75	C₅×C₂²⋊C₈	—	2	4	no	—
76	C₅×C₂²⋊C₈	—	2	4	no	—
77	C₅×#97	—	2	4	no	—
78	C₅×#97	—	2	2	no	—
79	C₅×#97	D₄	1	4	yes	complemented
80	C₄×C₅×C₈	—	2	2	no	—
81	C₄×C₅×C₈	—	2	2	no	—
82	C₅×#95	C₂×C₄	1	2	yes	—
83	C₅×#95	C₂×C₄	1	2	yes	—
84	C₅×#95	C₂×C₄	1	2	yes	—
85	C₅×#95	C₂×C₄	1	2	yes	—
86	C₅×#95	C₂×C₄	1	2	yes	—
87	C₂×#433	C₂×C₅	1	1	yes	characteristic, complemented
88	C₂²×#97	C₂×C₅	1	1	yes	characteristic, complemented
89	#2290	C₂×C₅	1	1	yes	characteristic
90	#1924	C₂×C₅	1	2	yes	complemented
91	#1917	C₂×C₅	1	2	yes	complemented
92	#1869	C₂×C₅	1	2	yes	—
93	#1850	C₂×C₅	1	2	yes	complemented
94	#1768	C₂×C₅	1	1	yes	characteristic, complemented
95	#1750	C₂×C₅	1	1	yes	characteristic, complemented
96	C₄×C₂²⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
97	#1746	C₂×C₅	1	1	yes	characteristic, complemented
98	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
99	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
100	C₂×C₅×D₄	—	2	2	no	—
101	C₂×C₅×D₄	—	2	4	no	—
102	C₂²×C₄×C₅	—	2	1	no	—
103	C₂²×C₄×C₅	—	2	1	no	—
104	C₂²×C₄×C₅	—	2	2	no	—
105	C₂²×C₄×C₅	—	2	4	no	—
106	C₂²×C₄×C₅	—	2	4	no	—
107	C₂²×C₄×C₅	—	2	1	no	—
108	C₂²×C₄×C₅	—	2	1	no	—
109	C₂²×C₄×C₅	—	2	2	no	—
110	C₂²×C₄×C₅	—	2	2	no	—
111	C₂²×C₄×C₅	—	4	2	no	—
112	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
113	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
115	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
116	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
118	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
120	C₂²×C₄×C₅	#41	1	4	yes	—
121	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
122	C₂×C₅×C₈	—	2	16	no	—
123	C₂×C₅×C₈	—	2	2	no	—
124	C₂×C₅×C₈	—	2	2	no	—
125	C₂×C₅×C₈	—	2	2	no	—
126	C₂×C₅×C₈	—	2	2	no	—
127	C₂×C₅×C₈	—	2	2	no	—
128	C₂×C₅×C₈	—	2	2	no	—
129	C₂×C₅×C₈	—	2	2	no	—
130	C₂×C₅×C₈	—	2	2	no	—
131	C₂×C₅×C₈	—	2	2	no	—
132	C₂×C₅×C₈	—	2	2	no	—
133	C₂×C₅×C₈	C₂×D₄	1	4	yes	—
134	C₂×C₅×C₈	#41	1	4	yes	—
135	C₅×C₄⋊C₄	—	2	2	no	—
136	C₅×C₄⋊C₄	—	2	4	no	—
137	C₅×C₄⋊C₄	—	4	2	no	—
138	C₅×C₂²⋊C₄	—	2	2	no	—
139	C₅×C₂²⋊C₄	—	2	4	no	—
140	C₅×C₂²⋊C₄	—	2	2	no	—
141	C₅×C₂²⋊C₄	—	2	4	no	—
142	C₅×C₂²⋊C₄	—	4	2	no	—
143	C₄²×C₅	—	2	4	no	—
144	C₄²×C₅	—	2	1	no	—
145	C₄²×C₅	—	2	1	no	—
146	C₄²×C₅	—	2	1	no	—
147	C₄²×C₅	—	2	1	no	—
148	C₄²×C₅	—	2	2	no	—
149	C₄²×C₅	—	2	2	no	—
150	C₄²×C₅	C₂×D₄	1	2	yes	—
151	C₄²×C₅	#41	1	2	yes	—
152	C₂³×C₈	C₂²×C₅	1	2	yes	—
153	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
154	C₂×#117	C₂²×C₅	1	1	yes	characteristic
155	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
156	#433	—	2	4	no	—
157	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
158	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
159	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
160	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
161	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
162	C₂×#97	—	2	4	no	—
163	C₂×#97	C₂²×C₅	1	2	yes	—
164	C₂×#97	C₂²×C₅	1	1	yes	characteristic
165	C₂×#97	C₂²×C₅	1	1	yes	characteristic
166	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
167	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
168	#388	C₄×C₅	1	2	yes	—
169	#387	C₄×C₅	1	2	yes	—
170	#386	C₄×C₅	1	2	yes	—
171	#385	C₄×C₅	1	2	yes	—
172	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
173	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
174	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
175	#376	C₂²×C₅	1	1	yes	characteristic
176	#336	C₂²×C₅	1	2	yes	—
177	#336	C₂²×C₅	1	2	yes	—
178	#336	C₂²×C₅	1	2	yes	—
179	#336	C₂²×C₅	1	2	yes	—
180	#336	C₂²×C₅	1	2	yes	—
181	C₂³×C₅	—	2	1	no	—
182	C₂³×C₅	—	2	1	no	—
183	C₂³×C₅	—	2	2	no	—
184	C₂³×C₅	—	2	1	no	—
185	C₂³×C₅	—	2	1	no	—
186	C₂³×C₅	—	2	1	no	—
187	C₂³×C₅	—	2	2	no	—
188	C₂³×C₅	—	2	2	no	—
189	C₂³×C₅	#117	1	2	yes	—
190	C₂³×C₅	#131	1	4	yes	—
191	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
192	C₅×D₄	—	4	4	no	—
193	C₂×C₄×C₅	—	2	1	no	—
194	C₂×C₄×C₅	—	2	1	no	—
195	C₂×C₄×C₅	—	2	2	no	—
196	C₂×C₄×C₅	—	2	2	no	—
197	C₂×C₄×C₅	—	2	4	no	—
198	C₂×C₄×C₅	—	2	4	no	—
199	C₂×C₄×C₅	—	2	1	no	—
200	C₂×C₄×C₅	—	2	1	no	—
201	C₂×C₄×C₅	—	2	1	no	—
202	C₂×C₄×C₅	—	2	2	no	—
203	C₂×C₄×C₅	—	2	2	no	—
204	C₂×C₄×C₅	—	2	1	no	—
205	C₂×C₄×C₅	—	2	2	no	—
206	C₂×C₄×C₅	—	2	1	no	—
207	C₂×C₄×C₅	—	2	2	no	—
208	C₂×C₄×C₅	—	2	2	no	—
209	C₂×C₄×C₅	—	2	2	no	—
210	C₂×C₄×C₅	—	2	2	no	—
211	C₂×C₄×C₅	—	2	2	no	—
212	C₂×C₄×C₅	—	2	2	no	—
213	C₂×C₄×C₅	—	2	2	no	—
214	C₂×C₄×C₅	—	2	2	no	—
215	C₂×C₄×C₅	—	4	8	no	—
216	C₂×C₄×C₅	—	4	2	no	—
217	C₂×C₄×C₅	—	4	2	no	—
218	C₂×C₄×C₅	#117	1	2	yes	—
219	C₂×C₄×C₅	C₄×D₄	1	4	yes	—
220	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
221	C₂×C₄×C₅	C₂×#41	1	2	yes	—
222	C₂×C₄×C₅	C₂×#41	1	2	yes	—
223	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
224	C₅×C₈	—	2	4	no	—
225	C₅×C₈	—	2	4	no	—
226	C₅×C₈	—	4	2	no	—
227	C₅×C₈	—	4	2	no	—
228	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
229	C₂³×C₄	C₂×C₄×C₅	1	2	yes	—
230	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
231	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
232	C₂²×C₈	—	2	4	no	—
233	C₂²×C₈	—	2	4	no	—
234	C₂²×C₈	—	2	4	no	—
235	C₂²×C₈	C₂³×C₅	1	2	yes	—
236	C₂²×C₈	C₂³×C₅	1	2	yes	—
237	C₂²×C₈	C₂³×C₅	1	2	yes	—
238	C₂²×C₈	C₂³×C₅	1	2	yes	—
239	C₄×D₄	—	2	4	no	—
240	#117	—	2	2	no	—
241	#117	—	2	2	no	—
242	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
243	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
244	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
245	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
246	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
247	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
248	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
249	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
250	C₂×C₄²	—	2	2	no	—
251	C₂×C₄²	—	2	2	no	—
252	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
253	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
254	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
255	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
256	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
257	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
258	C₄⋊C₈	—	2	4	no	—
259	C₄⋊C₈	—	2	4	no	—
260	C₂²⋊C₈	—	2	4	no	—
261	C₂²⋊C₈	—	2	4	no	—
262	C₂²⋊C₈	—	2	4	no	—
263	#97	—	2	4	no	—
264	#97	—	2	2	no	—
265	#97	C₅×D₄	1	4	yes	complemented
266	C₄×C₈	—	2	2	no	—
267	C₄×C₈	—	2	2	no	—
268	#95	C₂×C₄×C₅	1	2	yes	—
269	#95	C₂×C₄×C₅	1	2	yes	—
270	#95	C₂×C₄×C₅	1	2	yes	—
271	#95	C₂×C₄×C₅	1	2	yes	—
272	#95	C₂×C₄×C₅	1	2	yes	—
273	C₂²×C₅	—	2	2	no	—
274	C₂²×C₅	—	2	4	no	—
275	C₂²×C₅	—	2	4	no	—
276	C₂²×C₅	—	2	2	no	—
277	C₂²×C₅	—	4	1	no	—
278	C₂²×C₅	—	4	1	no	—
279	C₂²×C₅	—	4	2	no	—
280	C₂²×C₅	—	4	2	no	—
281	C₂²×C₅	—	4	1	no	—
282	C₂²×C₅	#433	1	4	yes	complemented
283	C₂²×C₅	C₂×#117	1	1	yes	characteristic
284	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
285	C₂²×C₅	C₄×#41	1	1	yes	characteristic
286	C₂²×C₅	C₂×#131	1	2	yes	—
287	C₂²×C₅	#568	1	2	yes	—
288	C₄×C₅	—	2	4	no	—
289	C₄×C₅	—	2	2	no	—
290	C₄×C₅	—	4	1	no	—
291	C₄×C₅	—	4	1	no	—
292	C₄×C₅	—	4	2	no	—
293	C₄×C₅	—	4	2	no	—
294	C₄×C₅	—	4	2	no	—
295	C₄×C₅	—	4	1	no	—
296	C₄×C₅	#525	1	2	yes	—
297	C₄×C₅	#529	1	2	yes	—
298	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
299	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
300	C₂×D₄	—	2	2	no	—
301	C₂×D₄	—	2	4	no	—
302	C₂²×C₄	—	2	1	no	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	4	no	—
306	C₂²×C₄	—	2	4	no	—
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	4	2	no	—
312	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
313	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
314	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
315	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
316	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
317	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
318	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
319	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
320	C₂²×C₄	C₅×#41	1	4	yes	—
321	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
322	C₂×C₈	—	2	16	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	C₂×C₅×D₄	1	4	yes	—
334	C₂×C₈	C₅×#41	1	4	yes	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	4	no	—
337	C₄⋊C₄	—	4	2	no	—
338	C₂²⋊C₄	—	2	2	no	—
339	C₂²⋊C₄	—	2	4	no	—
340	C₂²⋊C₄	—	2	2	no	—
341	C₂²⋊C₄	—	2	4	no	—
342	C₂²⋊C₄	—	4	2	no	—
343	C₄²	—	2	4	no	—
344	C₄²	—	2	1	no	—
345	C₄²	—	2	1	no	—
346	C₄²	—	2	2	no	—
347	C₄²	—	2	1	no	—
348	C₄²	—	2	1	no	—
349	C₄²	—	2	2	no	—
350	C₄²	C₂×C₅×D₄	1	2	yes	—
351	C₄²	C₅×#41	1	2	yes	—
352	C₂×C₅	—	2	4	no	—
353	C₂×C₅	—	8	1	no	—
354	C₂×C₅	#2290	1	1	yes	characteristic
355	C₂×C₅	C₂×#433	1	1	yes	characteristic
356	C₂×C₅	#2923	1	1	yes	characteristic
357	C₂×C₅	#2933	1	2	yes	—
358	C₂×C₅	#2968	1	2	yes	—
359	C₂³	—	2	1	no	—
360	C₂³	—	2	1	no	—
361	C₂³	—	2	2	no	—
362	C₂³	—	2	1	no	—
363	C₂³	—	2	1	no	—
364	C₂³	—	2	1	no	—
365	C₂³	—	2	2	no	—
366	C₂³	—	2	2	no	—
367	C₂³	C₅×#117	1	2	yes	—
368	C₂³	C₅×#131	1	4	yes	—
369	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
370	D₄	—	4	4	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	4	no	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	4	8	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	C₅×#117	1	2	yes	—
397	C₂×C₄	C₄×C₅×D₄	1	4	yes	—
398	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
399	C₂×C₄	C₂×C₅×#41	1	2	yes	—
400	C₂×C₄	C₂×C₅×#41	1	2	yes	—
401	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
402	C₈	—	2	4	no	—
403	C₈	—	2	4	no	—
404	C₈	—	4	2	no	—
405	C₈	—	4	2	no	—
406	C₅	#21105	1	1	yes	characteristic, direct product factor, Sylow
407	C₂²	—	2	2	no	—
408	C₂²	—	2	2	no	—
409	C₂²	—	2	4	no	—
410	C₂²	—	2	4	no	—
411	C₂²	—	4	1	no	—
412	C₂²	—	4	1	no	—
413	C₂²	—	4	1	no	—
414	C₂²	—	4	2	no	—
415	C₂²	—	4	2	no	—
416	C₂²	C₅×#433	1	4	yes	complemented
417	C₂²	C₂×C₅×#117	1	1	yes	characteristic
418	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
419	C₂²	C₄×C₅×#41	1	1	yes	characteristic
420	C₂²	C₂×C₅×#131	1	2	yes	—
421	C₂²	C₅×#568	1	2	yes	—
422	C₄	—	2	2	no	—
423	C₄	—	2	4	no	—
424	C₄	—	4	1	no	—
425	C₄	—	4	1	no	—
426	C₄	—	4	1	no	—
427	C₄	—	4	2	no	—
428	C₄	—	4	2	no	—
429	C₄	—	4	2	no	—
430	C₄	C₅×#525	1	2	yes	—
431	C₄	C₅×#529	1	2	yes	—
432	C₂	—	2	4	no	—
433	C₂	—	8	1	no	—
434	C₂	C₅×#2290	1	1	yes	characteristic
435	C₂	C₂×C₅×#433	1	1	yes	characteristic
436	C₂	C₅×#2923	1	1	yes	characteristic
437	C₂	C₅×#2933	1	2	yes	—
438	C₂	C₅×#2968	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#433	C₂	semidirect
2. C₂²×C₅×#97	C₂	semidirect
4. C₅×#1924	C₂	semidirect
5. C₅×#1917	C₂	semidirect
7. C₅×#1850	C₂	semidirect
8. C₅×#1768	C₂	semidirect
9. C₅×#1750	C₂	semidirect
10. C₄×C₅×C₂²⋊C₈	C₂	semidirect
11. C₅×#1746	C₂	semidirect
41. #21105	C₅	direct (N × H)
79. C₅×#97	D₄	semidirect
87. C₂×#433	C₂×C₅	semidirect
88. C₂²×#97	C₂×C₅	semidirect
90. #1924	C₂×C₅	semidirect
91. #1917	C₂×C₅	semidirect
93. #1850	C₂×C₅	semidirect
94. #1768	C₂×C₅	semidirect
95. #1750	C₂×C₅	semidirect
96. C₄×C₂²⋊C₈	C₂×C₅	semidirect
97. #1746	C₂×C₅	semidirect
265. #97	C₅×D₄	semidirect
282. C₂²×C₅	#433	semidirect
406. C₅	#21105	direct (N × H)
416. C₂²	C₅×#433	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#433	2
C₂²×C₅×#97	2
C₅×#2290	2
C₅×#1924	2
C₅×#1917	2
C₅×#1869	2
C₅×#1850	2
C₅×#1768	2
C₅×#1750	2
C₄×C₅×C₂²⋊C₈	2
C₅×#1746	2
#21105	5

Subgroups — C5×#21105 #11943825

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#21105 #11943825