Subgroups — C₅×#21873 #11944593

Order 1280.

1022 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#541	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#433	C₂	1	1	yes	maximal, characteristic
3	C₅×#2317	C₂	1	1	yes	maximal, characteristic
4	C₅×#1992	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1991	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1960	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1956	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1873	C₂	1	2	yes	maximal
9	C₅×#1872	C₂	1	2	yes	maximal
10	C₅×#1805	C₂	1	2	yes	maximal, complemented
11	C₅×#1803	C₂	1	2	yes	maximal, complemented
12	C₅×#541	—	2	4	no	—
13	C₅×#541	C₄	1	8	yes	complemented
14	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₅×#126	—	2	2	no	—
16	C₂×C₅×#125	—	2	2	no	—
17	C₂×C₅×#125	C₂²	1	1	yes	characteristic
18	C₂×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
19	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
20	C₂×C₅×#117	C₂²	1	1	yes	characteristic
21	C₂×C₅×#117	C₂²	1	1	yes	characteristic
22	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₅×#433	—	2	4	no	—
24	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
25	C₂×C₅×#103	C₂²	1	2	yes	—
26	C₂×C₅×#103	C₂²	1	2	yes	—
27	C₂×C₅×#103	C₂²	1	2	yes	—
28	C₂×C₅×#103	C₂²	1	2	yes	—
29	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
30	C₂×C₅×#97	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
32	C₅×#389	—	2	2	no	—
33	C₅×#385	—	2	2	no	—
34	C₅×#384	C₂²	1	1	yes	characteristic
35	C₅×#384	C₂²	1	1	yes	characteristic
36	C₅×#382	C₂²	1	1	yes	characteristic
37	C₅×#382	C₂²	1	1	yes	characteristic
38	C₅×#340	C₂²	1	2	yes	—
39	C₅×#340	C₂²	1	2	yes	—
40	C₅×#340	C₂²	1	2	yes	—
41	C₅×#340	C₂²	1	2	yes	—
42	#21873	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂²×C₅×Q₈	C₂³	1	2	yes	—
44	C₂³×C₄×C₅	—	2	1	no	—
45	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
46	C₂²×C₅×C₈	C₂³	1	2	yes	—
47	C₂²×C₅×C₈	C₂³	1	2	yes	—
48	C₅×C₄⋊Q₈	—	2	2	no	—
49	C₅×C₄⋊Q₈	C₂×C₄	1	4	yes	complemented
50	C₅×#126	—	2	16	no	—
51	C₅×#125	—	2	16	no	—
52	C₅×#125	—	2	2	no	—
53	C₅×#125	C₂×C₄	1	4	yes	complemented
54	C₅×C₂²⋊Q₈	—	2	4	no	—
55	C₅×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
56	C₄×C₅×Q₈	—	2	4	no	—
57	C₄×C₅×Q₈	C₂×C₄	1	8	yes	complemented
58	C₅×#117	—	4	2	no	—
59	C₅×#117	C₂×C₄	1	4	yes	—
60	C₅×#117	D₄	1	4	yes	—
61	C₂×C₅×C₄⋊C₄	—	2	2	no	—
62	C₂×C₅×C₄⋊C₄	—	2	2	no	—
63	C₂×C₅×C₄⋊C₄	—	2	2	no	—
64	C₂×C₅×C₄⋊C₄	—	2	2	no	—
65	C₂×C₅×C₄⋊C₄	—	2	1	no	—
66	C₂×C₅×C₄⋊C₄	—	2	2	no	—
67	C₂×C₅×C₄⋊C₄	—	2	2	no	—
68	C₂×C₅×C₄⋊C₄	—	4	2	no	—
69	C₂×C₅×C₄⋊C₄	D₄	1	2	yes	—
70	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
71	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
72	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
73	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
74	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
75	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
76	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
77	C₂×C₅×C₂²⋊C₄	D₄	1	2	yes	—
78	C₂×C₄²×C₅	—	2	2	no	—
79	C₂×C₄²×C₅	—	2	1	no	—
80	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
82	C₅×C₄⋊C₈	—	2	4	no	—
83	C₅×#103	—	4	2	no	—
84	C₅×#103	—	4	2	no	—
85	C₅×#103	—	4	2	no	—
86	C₅×#103	—	4	2	no	—
87	C₅×C₂²⋊C₈	—	2	4	no	—
88	C₅×#97	—	2	2	no	—
89	C₄×C₅×C₈	—	2	2	no	—
90	C₅×#95	—	2	2	no	—
91	C₅×#95	—	2	2	no	—
92	C₂×#541	C₂×C₅	1	1	yes	characteristic
93	C₂×#433	C₂×C₅	1	1	yes	characteristic
94	#2317	C₂×C₅	1	1	yes	characteristic
95	#1992	C₂×C₅	1	1	yes	characteristic, complemented
96	#1991	C₂×C₅	1	1	yes	characteristic, complemented
97	#1960	C₂×C₅	1	1	yes	characteristic, complemented
98	#1956	C₂×C₅	1	1	yes	characteristic, complemented
99	#1873	C₂×C₅	1	2	yes	—
100	#1872	C₂×C₅	1	2	yes	—
101	#1805	C₂×C₅	1	2	yes	complemented
102	#1803	C₂×C₅	1	2	yes	complemented
103	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
104	C₂×C₅×Q₈	—	2	2	no	—
105	C₂×C₅×Q₈	—	2	2	no	—
106	C₂×C₅×Q₈	—	2	2	no	—
107	C₂×C₅×Q₈	—	2	2	no	—
108	C₂×C₅×Q₈	—	2	2	no	—
109	C₂×C₅×Q₈	C₂²×C₄	1	4	yes	—
110	C₂²×C₄×C₅	—	2	2	no	—
111	C₂²×C₄×C₅	—	2	2	no	—
112	C₂²×C₄×C₅	—	2	2	no	—
113	C₂²×C₄×C₅	—	2	2	no	—
114	C₂²×C₄×C₅	—	2	1	no	—
115	C₂²×C₄×C₅	—	2	1	no	—
116	C₂²×C₄×C₅	—	2	1	no	—
117	C₂²×C₄×C₅	—	2	1	no	—
118	C₂²×C₄×C₅	—	4	2	no	—
119	C₂²×C₄×C₅	—	8	2	no	—
120	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
121	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
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	C₅×C₄⋊C₄	—	2	8	no	—
133	C₅×C₄⋊C₄	—	2	8	no	—
134	C₅×C₄⋊C₄	—	2	8	no	—
135	C₅×C₄⋊C₄	—	2	8	no	—
136	C₅×C₄⋊C₄	—	2	2	no	—
137	C₅×C₄⋊C₄	—	2	2	no	—
138	C₅×C₄⋊C₄	—	2	2	no	—
139	C₅×C₄⋊C₄	—	2	2	no	—
140	C₅×C₄⋊C₄	—	2	2	no	—
141	C₅×C₄⋊C₄	—	4	2	no	—
142	C₅×C₄⋊C₄	—	8	2	no	—
143	C₅×C₄⋊C₄	—	8	2	no	—
144	C₅×C₄⋊C₄	C₂²⋊C₄	1	8	yes	—
145	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
146	C₅×C₂²⋊C₄	—	2	8	no	—
147	C₅×C₂²⋊C₄	—	4	2	no	—
148	C₅×C₂²⋊C₄	C₂²⋊C₄	1	8	yes	—
149	C₄²×C₅	—	2	8	no	—
150	C₄²×C₅	—	4	2	no	—
151	C₄²×C₅	C₂²×C₄	1	2	yes	—
152	C₄²×C₅	C₂²×C₄	1	2	yes	—
153	C₄²×C₅	C₂×D₄	1	2	yes	—
154	C₄²×C₅	C₂×D₄	1	2	yes	—
155	#541	—	2	4	no	—
156	#541	C₄×C₅	1	8	yes	complemented
157	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
158	C₂×#126	—	2	2	no	—
159	C₂×#125	—	2	2	no	—
160	C₂×#125	C₂²×C₅	1	1	yes	characteristic
161	C₂×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
162	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
163	C₂×#117	C₂²×C₅	1	1	yes	characteristic
164	C₂×#117	C₂²×C₅	1	1	yes	characteristic
165	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
166	#433	—	2	4	no	—
167	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
168	C₂×#103	C₂²×C₅	1	2	yes	—
169	C₂×#103	C₂²×C₅	1	2	yes	—
170	C₂×#103	C₂²×C₅	1	2	yes	—
171	C₂×#103	C₂²×C₅	1	2	yes	—
172	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
173	C₂×#97	C₂²×C₅	1	1	yes	characteristic
174	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
175	#389	—	2	2	no	—
176	#385	—	2	2	no	—
177	#384	C₂²×C₅	1	1	yes	characteristic
178	#384	C₂²×C₅	1	1	yes	characteristic
179	#382	C₂²×C₅	1	1	yes	characteristic
180	#382	C₂²×C₅	1	1	yes	characteristic
181	#340	C₂²×C₅	1	2	yes	—
182	#340	C₂²×C₅	1	2	yes	—
183	#340	C₂²×C₅	1	2	yes	—
184	#340	C₂²×C₅	1	2	yes	—
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	C₂×C₂²⋊C₄	1	2	yes	—
190	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
191	C₅×Q₈	—	2	4	no	—
192	C₅×Q₈	—	2	4	no	—
193	C₅×Q₈	—	4	2	no	—
194	C₅×Q₈	—	4	2	no	—
195	C₂×C₄×C₅	—	2	1	no	—
196	C₂×C₄×C₅	—	2	1	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	—	2	4	no	—
202	C₂×C₄×C₅	—	2	4	no	—
203	C₂×C₄×C₅	—	2	4	no	—
204	C₂×C₄×C₅	—	2	4	no	—
205	C₂×C₄×C₅	—	4	2	no	—
206	C₂×C₄×C₅	—	4	2	no	—
207	C₂×C₄×C₅	—	4	2	no	—
208	C₂×C₄×C₅	—	4	2	no	—
209	C₂×C₄×C₅	—	4	1	no	—
210	C₂×C₄×C₅	—	4	1	no	—
211	C₂×C₄×C₅	—	4	1	no	—
212	C₂×C₄×C₅	—	4	1	no	—
213	C₂×C₄×C₅	—	4	2	no	—
214	C₂×C₄×C₅	—	4	2	no	—
215	C₂×C₄×C₅	—	4	2	no	—
216	C₂×C₄×C₅	—	4	2	no	—
217	C₂×C₄×C₅	—	8	4	no	—
218	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	4	yes	—
219	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	4	yes	—
220	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
221	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
222	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
223	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
224	C₂×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
225	C₅×C₈	—	4	2	no	—
226	C₅×C₈	—	4	2	no	—
227	C₂²×Q₈	C₂³×C₅	1	2	yes	—
228	C₂³×C₄	—	2	1	no	—
229	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
230	C₂²×C₈	C₂³×C₅	1	2	yes	—
231	C₂²×C₈	C₂³×C₅	1	2	yes	—
232	C₄⋊Q₈	—	2	2	no	—
233	C₄⋊Q₈	C₂×C₄×C₅	1	4	yes	complemented
234	#126	—	2	16	no	—
235	#125	—	2	16	no	—
236	#125	—	2	2	no	—
237	#125	C₂×C₄×C₅	1	4	yes	complemented
238	C₂²⋊Q₈	—	2	4	no	—
239	C₂²⋊Q₈	C₂×C₄×C₅	1	8	yes	—
240	C₄×Q₈	—	2	4	no	—
241	C₄×Q₈	C₂×C₄×C₅	1	8	yes	complemented
242	#117	—	4	2	no	—
243	#117	C₂×C₄×C₅	1	4	yes	—
244	#117	C₅×D₄	1	4	yes	—
245	C₂×C₄⋊C₄	—	2	2	no	—
246	C₂×C₄⋊C₄	—	2	2	no	—
247	C₂×C₄⋊C₄	—	2	2	no	—
248	C₂×C₄⋊C₄	—	2	2	no	—
249	C₂×C₄⋊C₄	—	2	1	no	—
250	C₂×C₄⋊C₄	—	2	2	no	—
251	C₂×C₄⋊C₄	—	2	2	no	—
252	C₂×C₄⋊C₄	—	4	2	no	—
253	C₂×C₄⋊C₄	C₅×D₄	1	2	yes	—
254	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
255	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
256	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
257	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
258	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
259	C₂×C₂²⋊C₄	—	2	2	no	—
260	C₂×C₂²⋊C₄	—	2	1	no	—
261	C₂×C₂²⋊C₄	C₅×D₄	1	2	yes	—
262	C₂×C₄²	—	2	2	no	—
263	C₂×C₄²	—	2	1	no	—
264	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
265	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
266	C₄⋊C₈	—	2	4	no	—
267	#103	—	4	2	no	—
268	#103	—	4	2	no	—
269	#103	—	4	2	no	—
270	#103	—	4	2	no	—
271	C₂²⋊C₈	—	2	4	no	—
272	#97	—	2	2	no	—
273	C₄×C₈	—	2	2	no	—
274	#95	—	2	2	no	—
275	#95	—	2	2	no	—
276	C₂²×C₅	—	2	2	no	—
277	C₂²×C₅	—	2	4	no	—
278	C₂²×C₅	—	4	1	no	—
279	C₂²×C₅	—	4	1	no	—
280	C₂²×C₅	—	4	2	no	—
281	C₂²×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
282	C₂²×C₅	#535	1	1	yes	characteristic
283	C₂²×C₅	#536	1	1	yes	characteristic
284	C₂²×C₅	#577	1	2	yes	—
285	C₂²×C₅	#578	1	2	yes	—
286	C₄×C₅	—	2	2	no	—
287	C₄×C₅	—	2	4	no	—
288	C₄×C₅	—	2	4	no	—
289	C₄×C₅	—	4	4	no	—
290	C₄×C₅	—	4	4	no	—
291	C₄×C₅	—	8	1	no	—
292	C₄×C₅	—	8	1	no	—
293	C₄×C₅	—	8	1	no	—
294	C₄×C₅	—	8	1	no	—
295	C₄×C₅	#520	1	2	yes	—
296	C₄×C₅	#537	1	2	yes	—
297	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
298	C₂×Q₈	—	2	2	no	—
299	C₂×Q₈	—	2	2	no	—
300	C₂×Q₈	—	2	2	no	—
301	C₂×Q₈	—	2	2	no	—
302	C₂×Q₈	—	2	2	no	—
303	C₂×Q₈	C₂²×C₄×C₅	1	4	yes	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	4	2	no	—
313	C₂²×C₄	—	8	2	no	—
314	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
315	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
316	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
317	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
318	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
319	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	2	no	—
326	C₄⋊C₄	—	2	8	no	—
327	C₄⋊C₄	—	2	8	no	—
328	C₄⋊C₄	—	2	8	no	—
329	C₄⋊C₄	—	2	8	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	4	2	no	—
336	C₄⋊C₄	—	8	2	no	—
337	C₄⋊C₄	—	8	2	no	—
338	C₄⋊C₄	C₅×C₂²⋊C₄	1	8	yes	—
339	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
340	C₂²⋊C₄	—	2	8	no	—
341	C₂²⋊C₄	—	4	2	no	—
342	C₂²⋊C₄	C₅×C₂²⋊C₄	1	8	yes	—
343	C₄²	—	2	8	no	—
344	C₄²	—	4	2	no	—
345	C₄²	C₂²×C₄×C₅	1	2	yes	—
346	C₄²	C₂²×C₄×C₅	1	2	yes	—
347	C₄²	C₂×C₅×D₄	1	2	yes	—
348	C₄²	C₂×C₅×D₄	1	2	yes	—
349	C₂×C₅	—	4	2	no	—
350	C₂×C₅	#2311	1	1	yes	characteristic
351	C₂×C₅	#2898	1	2	yes	—
352	C₂×C₅	#3222	1	1	yes	characteristic
353	C₂×C₅	#3223	1	1	yes	characteristic
354	C₂×C₅	#3242	1	2	yes	—
355	C₂³	—	2	1	no	—
356	C₂³	—	2	1	no	—
357	C₂³	—	2	2	no	—
358	C₂³	—	2	2	no	—
359	C₂³	C₂×C₅×C₂²⋊C₄	1	2	yes	—
360	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
361	Q₈	—	2	4	no	—
362	Q₈	—	2	4	no	—
363	Q₈	—	4	2	no	—
364	Q₈	—	4	2	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	4	no	—
372	C₂×C₄	—	2	4	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	8	4	no	—
388	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	4	yes	—
389	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	4	yes	—
390	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
391	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
392	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
393	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
394	C₂×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
395	C₈	—	4	2	no	—
396	C₈	—	4	2	no	—
397	C₅	#21873	1	1	yes	characteristic, direct product factor, Sylow
398	C₂²	—	2	2	no	—
399	C₂²	—	2	4	no	—
400	C₂²	—	4	2	no	—
401	C₂²	—	4	1	no	—
402	C₂²	—	4	1	no	—
403	C₂²	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
404	C₂²	C₅×#535	1	1	yes	characteristic
405	C₂²	C₅×#536	1	1	yes	characteristic
406	C₂²	C₅×#577	1	2	yes	—
407	C₂²	C₅×#578	1	2	yes	—
408	C₄	—	2	2	no	—
409	C₄	—	2	4	no	—
410	C₄	—	2	4	no	—
411	C₄	—	4	4	no	—
412	C₄	—	4	4	no	—
413	C₄	—	8	1	no	—
414	C₄	—	8	1	no	—
415	C₄	—	8	1	no	—
416	C₄	—	8	1	no	—
417	C₄	C₅×#520	1	2	yes	—
418	C₄	C₅×#537	1	2	yes	—
419	C₂	—	4	2	no	—
420	C₂	C₅×#2311	1	1	yes	characteristic
421	C₂	C₅×#2898	1	2	yes	—
422	C₂	C₅×#3222	1	1	yes	characteristic
423	C₂	C₅×#3223	1	1	yes	characteristic
424	C₂	C₅×#3242	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	C₂⁴×C₅	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₅×#117 ◁ G

Complements

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

N	H ≅ G/N	type
4. C₅×#1992	C₂	semidirect
5. C₅×#1991	C₂	semidirect
6. C₅×#1960	C₂	semidirect
7. C₅×#1956	C₂	semidirect
10. C₅×#1805	C₂	semidirect
11. C₅×#1803	C₂	semidirect
13. C₅×#541	C₄	semidirect
42. #21873	C₅	direct (N × H)
49. C₅×C₄⋊Q₈	C₂×C₄	semidirect
53. C₅×#125	C₂×C₄	semidirect
57. C₄×C₅×Q₈	C₂×C₄	semidirect
95. #1992	C₂×C₅	semidirect
96. #1991	C₂×C₅	semidirect
97. #1960	C₂×C₅	semidirect
98. #1956	C₂×C₅	semidirect
101. #1805	C₂×C₅	semidirect
102. #1803	C₂×C₅	semidirect
156. #541	C₄×C₅	semidirect
233. C₄⋊Q₈	C₂×C₄×C₅	semidirect
237. #125	C₂×C₄×C₅	semidirect
241. C₄×Q₈	C₂×C₄×C₅	semidirect
397. C₅	#21873	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×#541	2
C₂×C₅×#433	2
C₅×#2317	2
C₅×#1992	2
C₅×#1991	2
C₅×#1960	2
C₅×#1956	2
C₅×#1873	2
C₅×#1872	2
C₅×#1805	2
C₅×#1803	2
#21873	5

Subgroups — C5×#21873 #11944593

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#21873 #11944593