Subgroups — C₅×#21695 #11944415

Order 1280.

1126 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	C₂×C₅×#492	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#440	C₂	1	2	yes	maximal, complemented
3	C₂×C₄×C₅×SD₁₆	C₂	1	2	yes	maximal, complemented
4	C₅×#2328	C₂	1	1	yes	maximal, characteristic
5	C₅×#2327	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1973	C₂	1	2	yes	maximal, complemented
7	C₅×#1968	C₂	1	2	yes	maximal, complemented
8	C₅×#1961	C₂	1	1	yes	maximal, characteristic
9	C₅×#1960	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1846	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1726	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₅×SD₁₆	C₂²	1	2	yes	—
13	C₂²×C₅×SD₁₆	C₂²	1	2	yes	—
14	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₅×#127	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
17	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
18	C₅×#492	C₄	1	8	yes	complemented
19	C₅×#440	—	2	8	no	—
20	C₄×C₅×SD₁₆	—	2	8	no	—
21	C₂×C₅×#107	C₂²	1	2	yes	—
22	C₂×C₅×#106	C₂²	1	2	yes	—
23	C₂×C₅×#103	C₂²	1	2	yes	—
24	C₂×C₅×#103	C₂²	1	2	yes	—
25	C₂×C₅×#102	C₂²	1	2	yes	—
26	C₂×C₅×#102	C₂²	1	2	yes	—
27	C₂×C₅×#97	C₂²	1	1	yes	characteristic
28	C₂×C₅×#97	C₂²	1	1	yes	characteristic
29	C₂×C₅×#97	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
33	C₅×#391	C₂²	1	2	yes	—
34	C₅×#390	C₂²	1	2	yes	—
35	C₅×#387	—	2	4	no	—
36	C₅×#386	—	2	4	no	—
37	C₅×#382	C₂²	1	1	yes	characteristic
38	C₅×#382	C₂²	1	1	yes	characteristic
39	C₅×#376	C₂²	1	1	yes	characteristic
40	#21695	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
41	C₂²×C₅×Q₈	C₂³	1	2	yes	—
42	C₂²×C₅×D₄	—	2	2	no	—
43	C₂²×C₅×D₄	C₂³	1	2	yes	—
44	C₂³×C₄×C₅	—	2	2	no	—
45	C₂×C₅×SD₁₆	—	2	4	no	—
46	C₂×C₅×SD₁₆	—	2	4	no	—
47	C₂×C₅×SD₁₆	—	2	4	no	—
48	C₂×C₅×SD₁₆	—	2	4	no	—
49	C₂×C₅×SD₁₆	C₂×C₄	1	8	yes	complemented
50	C₂×C₅×SD₁₆	C₂×C₄	1	8	yes	complemented
51	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
52	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
53	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
54	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
55	C₅×C₄⋊Q₈	—	2	2	no	—
56	C₅×C₄⋊Q₈	C₂×C₄	1	4	yes	complemented
57	C₅×#127	—	2	2	no	—
58	C₅×#127	C₂×C₄	1	4	yes	—
59	C₄×C₅×Q₈	—	2	4	no	—
60	C₄×C₅×Q₈	—	2	4	no	—
61	C₄×C₅×D₄	—	2	4	no	—
62	C₄×C₅×D₄	—	2	4	no	—
63	C₂×C₅×C₄⋊C₄	—	2	2	no	—
64	C₂×C₅×C₄⋊C₄	—	2	2	no	—
65	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
66	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
67	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
68	C₂×C₅×C₂²⋊C₄	—	2	4	no	—
69	C₂×C₄²×C₅	—	2	2	no	—
70	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
71	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
73	C₅×#107	—	2	4	no	—
74	C₅×#106	—	2	4	no	—
75	C₅×#103	—	2	4	no	—
76	C₅×#103	—	2	4	no	—
77	C₅×#102	—	2	4	no	—
78	C₅×#102	—	2	4	no	—
79	C₅×#97	—	2	2	no	—
80	C₅×#97	—	2	2	no	—
81	C₅×#97	D₄	1	4	yes	complemented
82	C₄×C₅×C₈	—	2	2	no	—
83	C₄×C₅×C₈	C₂×C₄	1	4	yes	complemented
84	C₄×C₅×C₈	D₄	1	4	yes	complemented
85	C₅×#95	—	2	2	no	—
86	C₅×#95	—	2	2	no	—
87	C₅×#95	—	2	4	no	—
88	C₅×#95	D₄	1	4	yes	—
89	C₂×#492	C₂×C₅	1	1	yes	characteristic
90	C₂×#440	C₂×C₅	1	2	yes	complemented
91	C₂×C₄×SD₁₆	C₂×C₅	1	2	yes	complemented
92	#2328	C₂×C₅	1	1	yes	characteristic
93	#2327	C₂×C₅	1	1	yes	characteristic, complemented
94	#1973	C₂×C₅	1	2	yes	complemented
95	#1968	C₂×C₅	1	2	yes	complemented
96	#1961	C₂×C₅	1	1	yes	characteristic
97	#1960	C₂×C₅	1	1	yes	characteristic, complemented
98	#1846	C₂×C₅	1	1	yes	characteristic, complemented
99	#1726	C₂×C₅	1	1	yes	characteristic, complemented
100	C₂⁴×C₅	—	2	2	no	—
101	C₂×C₅×Q₈	—	2	2	no	—
102	C₂×C₅×Q₈	—	2	2	no	—
103	C₂×C₅×Q₈	—	2	2	no	—
104	C₂×C₅×Q₈	—	2	2	no	—
105	C₂×C₅×Q₈	—	2	2	no	—
106	C₂×C₅×Q₈	C₂²×C₄	1	4	yes	—
107	C₂×C₅×D₄	—	2	8	no	—
108	C₂×C₅×D₄	—	2	2	no	—
109	C₂×C₅×D₄	—	2	2	no	—
110	C₂×C₅×D₄	—	2	2	no	—
111	C₂×C₅×D₄	—	2	2	no	—
112	C₂×C₅×D₄	—	2	2	no	—
113	C₂×C₅×D₄	—	8	4	no	—
114	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
115	C₂²×C₄×C₅	—	2	2	no	—
116	C₂²×C₄×C₅	—	2	2	no	—
117	C₂²×C₄×C₅	—	2	2	no	—
118	C₂²×C₄×C₅	—	4	4	no	—
119	C₂²×C₄×C₅	—	8	4	no	—
120	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
124	C₅×SD₁₆	—	2	16	no	—
125	C₅×SD₁₆	—	2	16	no	—
126	C₂×C₅×C₈	—	2	1	no	—
127	C₂×C₅×C₈	—	2	1	no	—
128	C₂×C₅×C₈	—	2	1	no	—
129	C₂×C₅×C₈	—	2	1	no	—
130	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
131	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
132	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
133	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
134	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
135	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
136	C₂×C₅×C₈	#41	1	2	yes	—
137	C₂×C₅×C₈	#41	1	2	yes	—
138	C₅×C₄⋊C₄	—	2	8	no	—
139	C₅×C₄⋊C₄	—	2	2	no	—
140	C₅×C₄⋊C₄	—	2	2	no	—
141	C₅×C₄⋊C₄	—	2	2	no	—
142	C₅×C₄⋊C₄	—	2	2	no	—
143	C₅×C₄⋊C₄	—	4	4	no	—
144	C₅×C₂²⋊C₄	—	4	4	no	—
145	C₅×C₂²⋊C₄	—	8	4	no	—
146	C₄²×C₅	—	2	1	no	—
147	C₄²×C₅	—	2	1	no	—
148	C₄²×C₅	—	4	4	no	—
149	C₄²×C₅	C₂²×C₄	1	2	yes	—
150	C₄²×C₅	C₂×D₄	1	2	yes	—
151	C₄²×C₅	C₂×D₄	1	2	yes	—
152	C₄²×C₅	#41	1	2	yes	—
153	C₂²×SD₁₆	C₂²×C₅	1	2	yes	—
154	C₂²×SD₁₆	C₂²×C₅	1	2	yes	—
155	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
156	C₂×#127	C₂²×C₅	1	1	yes	characteristic
157	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
158	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
159	#492	C₄×C₅	1	8	yes	complemented
160	#440	—	2	8	no	—
161	C₄×SD₁₆	—	2	8	no	—
162	C₂×#107	C₂²×C₅	1	2	yes	—
163	C₂×#106	C₂²×C₅	1	2	yes	—
164	C₂×#103	C₂²×C₅	1	2	yes	—
165	C₂×#103	C₂²×C₅	1	2	yes	—
166	C₂×#102	C₂²×C₅	1	2	yes	—
167	C₂×#102	C₂²×C₅	1	2	yes	—
168	C₂×#97	C₂²×C₅	1	1	yes	characteristic
169	C₂×#97	C₂²×C₅	1	1	yes	characteristic
170	C₂×#97	C₂²×C₅	1	1	yes	characteristic
171	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
172	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
173	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
174	#391	C₂²×C₅	1	2	yes	—
175	#390	C₂²×C₅	1	2	yes	—
176	#387	—	2	4	no	—
177	#386	—	2	4	no	—
178	#382	C₂²×C₅	1	1	yes	characteristic
179	#382	C₂²×C₅	1	1	yes	characteristic
180	#376	C₂²×C₅	1	1	yes	characteristic
181	C₂³×C₅	—	2	4	no	—
182	C₂³×C₅	—	4	2	no	—
183	C₂³×C₅	—	4	2	no	—
184	C₂³×C₅	—	4	4	no	—
185	C₂³×C₅	—	4	4	no	—
186	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
187	C₅×Q₈	—	2	4	no	—
188	C₅×Q₈	—	2	4	no	—
189	C₅×Q₈	—	4	2	no	—
190	C₅×Q₈	—	4	2	no	—
191	C₅×D₄	—	2	4	no	—
192	C₅×D₄	—	2	4	no	—
193	C₅×D₄	—	4	2	no	—
194	C₅×D₄	—	4	2	no	—
195	C₅×D₄	—	8	8	no	—
196	C₂×C₄×C₅	—	2	4	no	—
197	C₂×C₄×C₅	—	2	4	no	—
198	C₂×C₄×C₅	—	2	4	no	—
199	C₂×C₄×C₅	—	2	2	no	—
200	C₂×C₄×C₅	—	2	4	no	—
201	C₂×C₄×C₅	—	4	2	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	4	no	—
206	C₂×C₄×C₅	—	4	4	no	—
207	C₂×C₄×C₅	—	8	8	no	—
208	C₂×C₄×C₅	C₄×D₄	1	4	yes	—
209	C₂×C₄×C₅	#127	1	4	yes	—
210	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
211	C₂×C₄×C₅	C₂²×D₄	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	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
215	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
216	C₅×C₈	—	2	2	no	—
217	C₅×C₈	—	2	2	no	—
218	C₅×C₈	C₄×D₄	1	4	yes	—
219	C₅×C₈	C₄×D₄	1	4	yes	—
220	C₂²×Q₈	C₂³×C₅	1	2	yes	—
221	C₂²×D₄	—	2	2	no	—
222	C₂²×D₄	C₂³×C₅	1	2	yes	—
223	C₂³×C₄	—	2	2	no	—
224	C₂×SD₁₆	—	2	4	no	—
225	C₂×SD₁₆	—	2	4	no	—
226	C₂×SD₁₆	—	2	4	no	—
227	C₂×SD₁₆	—	2	4	no	—
228	C₂×SD₁₆	C₂×C₄×C₅	1	8	yes	complemented
229	C₂×SD₁₆	C₂×C₄×C₅	1	8	yes	complemented
230	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
231	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
232	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
233	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
234	C₄⋊Q₈	—	2	2	no	—
235	C₄⋊Q₈	C₂×C₄×C₅	1	4	yes	complemented
236	#127	—	2	2	no	—
237	#127	C₂×C₄×C₅	1	4	yes	—
238	C₄×Q₈	—	2	4	no	—
239	C₄×Q₈	—	2	4	no	—
240	C₄×D₄	—	2	4	no	—
241	C₄×D₄	—	2	4	no	—
242	C₂×C₄⋊C₄	—	2	2	no	—
243	C₂×C₄⋊C₄	—	2	2	no	—
244	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
245	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
246	C₂×C₂²⋊C₄	—	2	2	no	—
247	C₂×C₂²⋊C₄	—	2	4	no	—
248	C₂×C₄²	—	2	2	no	—
249	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
250	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
251	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
252	#107	—	2	4	no	—
253	#106	—	2	4	no	—
254	#103	—	2	4	no	—
255	#103	—	2	4	no	—
256	#102	—	2	4	no	—
257	#102	—	2	4	no	—
258	#97	—	2	2	no	—
259	#97	—	2	2	no	—
260	#97	C₅×D₄	1	4	yes	complemented
261	C₄×C₈	—	2	2	no	—
262	C₄×C₈	C₂×C₄×C₅	1	4	yes	complemented
263	C₄×C₈	C₅×D₄	1	4	yes	complemented
264	#95	—	2	2	no	—
265	#95	—	2	2	no	—
266	#95	—	2	4	no	—
267	#95	C₅×D₄	1	4	yes	—
268	C₂²×C₅	—	4	4	no	—
269	C₂²×C₅	—	4	8	no	—
270	C₂²×C₅	—	8	2	no	—
271	C₂²×C₅	—	8	2	no	—
272	C₂²×C₅	—	8	4	no	—
273	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
274	C₂²×C₅	C₂×#127	1	1	yes	characteristic
275	C₂²×C₅	#532	1	1	yes	characteristic
276	C₂²×C₅	#577	1	4	yes	—
277	C₄×C₅	—	2	4	no	—
278	C₄×C₅	—	2	4	no	—
279	C₄×C₅	—	4	4	no	—
280	C₄×C₅	—	4	2	no	—
281	C₄×C₅	—	8	2	no	—
282	C₄×C₅	—	8	2	no	—
283	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
284	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
285	C₄×C₅	#532	1	1	yes	characteristic
286	C₄×C₅	#532	1	1	yes	characteristic
287	C₂⁴	—	2	2	no	—
288	C₂×Q₈	—	2	2	no	—
289	C₂×Q₈	—	2	2	no	—
290	C₂×Q₈	—	2	2	no	—
291	C₂×Q₈	—	2	2	no	—
292	C₂×Q₈	—	2	2	no	—
293	C₂×Q₈	C₂²×C₄×C₅	1	4	yes	—
294	C₂×D₄	—	2	8	no	—
295	C₂×D₄	—	2	2	no	—
296	C₂×D₄	—	2	2	no	—
297	C₂×D₄	—	2	2	no	—
298	C₂×D₄	—	2	2	no	—
299	C₂×D₄	—	2	2	no	—
300	C₂×D₄	—	8	4	no	—
301	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	4	4	no	—
306	C₂²×C₄	—	8	4	no	—
307	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
308	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
309	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
310	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
311	SD₁₆	—	2	16	no	—
312	SD₁₆	—	2	16	no	—
313	C₂×C₈	—	2	1	no	—
314	C₂×C₈	—	2	1	no	—
315	C₂×C₈	—	2	1	no	—
316	C₂×C₈	—	2	1	no	—
317	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
318	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
319	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
320	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
321	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
322	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
323	C₂×C₈	C₅×#41	1	2	yes	—
324	C₂×C₈	C₅×#41	1	2	yes	—
325	C₄⋊C₄	—	2	8	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	4	4	no	—
331	C₂²⋊C₄	—	4	4	no	—
332	C₂²⋊C₄	—	8	4	no	—
333	C₄²	—	2	1	no	—
334	C₄²	—	2	1	no	—
335	C₄²	—	4	4	no	—
336	C₄²	C₂²×C₄×C₅	1	2	yes	—
337	C₄²	C₂×C₅×D₄	1	2	yes	—
338	C₄²	C₂×C₅×D₄	1	2	yes	—
339	C₄²	C₅×#41	1	2	yes	—
340	C₂×C₅	—	8	4	no	—
341	C₂×C₅	C₄×#127	1	1	yes	characteristic
342	C₂×C₅	#2949	1	2	yes	—
343	C₂×C₅	#3154	1	2	yes	—
344	C₂×C₅	#3174	1	2	yes	—
345	C₂³	—	2	4	no	—
346	C₂³	—	4	2	no	—
347	C₂³	—	4	2	no	—
348	C₂³	—	4	4	no	—
349	C₂³	—	4	4	no	—
350	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
351	Q₈	—	2	4	no	—
352	Q₈	—	2	4	no	—
353	Q₈	—	4	2	no	—
354	Q₈	—	4	2	no	—
355	D₄	—	2	4	no	—
356	D₄	—	2	4	no	—
357	D₄	—	4	2	no	—
358	D₄	—	4	2	no	—
359	D₄	—	8	8	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	4	no	—
370	C₂×C₄	—	4	4	no	—
371	C₂×C₄	—	8	8	no	—
372	C₂×C₄	C₄×C₅×D₄	1	4	yes	—
373	C₂×C₄	C₅×#127	1	4	yes	—
374	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
375	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
376	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
377	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
378	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
379	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
380	C₈	—	2	2	no	—
381	C₈	—	2	2	no	—
382	C₈	C₄×C₅×D₄	1	4	yes	—
383	C₈	C₄×C₅×D₄	1	4	yes	—
384	C₅	#21695	1	1	yes	characteristic, direct product factor, Sylow
385	C₂²	—	4	4	no	—
386	C₂²	—	4	8	no	—
387	C₂²	—	8	2	no	—
388	C₂²	—	8	2	no	—
389	C₂²	—	8	4	no	—
390	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
391	C₂²	C₂×C₅×#127	1	1	yes	characteristic
392	C₂²	C₅×#532	1	1	yes	characteristic
393	C₂²	C₅×#577	1	4	yes	—
394	C₄	—	2	4	no	—
395	C₄	—	2	4	no	—
396	C₄	—	4	4	no	—
397	C₄	—	4	2	no	—
398	C₄	—	8	2	no	—
399	C₄	—	8	2	no	—
400	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
401	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
402	C₄	C₅×#532	1	1	yes	characteristic
403	C₄	C₅×#532	1	1	yes	characteristic
404	C₂	—	8	4	no	—
405	C₂	C₄×C₅×#127	1	1	yes	characteristic
406	C₂	C₅×#2949	1	2	yes	—
407	C₂	C₅×#3154	1	2	yes	—
408	C₂	C₅×#3174	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₅	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₂×C₅×#127	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₅×#376 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#440	C₂	semidirect
3. C₂×C₄×C₅×SD₁₆	C₂	semidirect
5. C₅×#2327	C₂	semidirect
6. C₅×#1973	C₂	semidirect
7. C₅×#1968	C₂	semidirect
9. C₅×#1960	C₂	semidirect
10. C₅×#1846	C₂	semidirect
11. C₅×#1726	C₂	semidirect
18. C₅×#492	C₄	semidirect
40. #21695	C₅	direct (N × H)
49. C₂×C₅×SD₁₆	C₂×C₄	semidirect
50. C₂×C₅×SD₁₆	C₂×C₄	semidirect
56. C₅×C₄⋊Q₈	C₂×C₄	semidirect
81. C₅×#97	D₄	semidirect
83. C₄×C₅×C₈	C₂×C₄	semidirect
84. C₄×C₅×C₈	D₄	semidirect
90. C₂×#440	C₂×C₅	semidirect
91. C₂×C₄×SD₁₆	C₂×C₅	semidirect
93. #2327	C₂×C₅	semidirect
94. #1973	C₂×C₅	semidirect
95. #1968	C₂×C₅	semidirect
97. #1960	C₂×C₅	semidirect
98. #1846	C₂×C₅	semidirect
99. #1726	C₂×C₅	semidirect
159. #492	C₄×C₅	semidirect
228. C₂×SD₁₆	C₂×C₄×C₅	semidirect
229. C₂×SD₁₆	C₂×C₄×C₅	semidirect
235. C₄⋊Q₈	C₂×C₄×C₅	semidirect
260. #97	C₅×D₄	semidirect
262. C₄×C₈	C₂×C₄×C₅	semidirect
263. C₄×C₈	C₅×D₄	semidirect
384. C₅	#21695	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×#492	2
C₂×C₅×#440	2
C₂×C₄×C₅×SD₁₆	2
C₅×#2328	2
C₅×#2327	2
C₅×#1973	2
C₅×#1968	2
C₅×#1961	2
C₅×#1960	2
C₅×#1846	2
C₅×#1726	2
#21695	5

Subgroups — C5×#21695 #11944415

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#21695 #11944415