Subgroups — C₅×#10863 #11933583

Order 1280.

942 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×#107	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₅×#106	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₅×#97	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×#340	C₂	1	2	yes	maximal
5	C₅×C₄⋊#95	C₂	1	2	yes	maximal
6	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
7	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
8	C₂²×C₅×C₄⋊C₄	C₂²	1	2	yes	—
9	C₂²×C₅×C₄⋊C₄	C₂²	1	2	yes	—
10	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
11	C₂×C₅×#107	—	2	2	no	—
12	C₂×C₅×#107	—	2	2	no	—
13	C₂×C₅×#107	C₄	1	4	yes	complemented
14	C₂×C₅×#106	—	2	2	no	—
15	C₂×C₅×#106	—	2	2	no	—
16	C₂×C₅×#106	C₄	1	4	yes	complemented
17	C₂×C₅×#97	—	2	2	no	—
18	C₂×C₅×#97	—	2	2	no	—
19	C₂×C₅×#97	C₄	1	4	yes	complemented
20	C₂×C₅×#95	—	2	4	no	—
21	C₅×#340	—	2	4	no	—
22	#10863	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
23	C₂³×C₄×C₅	—	2	2	no	—
24	C₂³×C₄×C₅	—	2	2	no	—
25	C₂³×C₄×C₅	D₄	1	2	yes	—
26	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
27	C₂²×C₅×C₈	—	2	1	no	—
28	C₂²×C₅×C₈	—	2	1	no	—
29	C₂²×C₅×C₈	—	2	1	no	—
30	C₂²×C₅×C₈	—	2	1	no	—
31	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
32	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
33	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
34	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
35	C₂²×C₅×C₈	D₄	1	2	yes	—
36	C₂²×C₅×C₈	D₄	1	2	yes	—
37	C₂²×C₅×C₈	D₄	1	2	yes	—
38	C₂²×C₅×C₈	D₄	1	2	yes	—
39	C₂²×C₅×C₈	Q₈	1	2	yes	—
40	C₂²×C₅×C₈	Q₈	1	2	yes	—
41	C₂×C₅×C₄⋊C₄	—	2	2	no	—
42	C₂×C₅×C₄⋊C₄	—	2	2	no	—
43	C₂×C₅×C₄⋊C₄	—	2	2	no	—
44	C₂×C₅×C₄⋊C₄	—	2	2	no	—
45	C₂×C₅×C₄⋊C₄	—	2	2	no	—
46	C₂×C₅×C₄⋊C₄	—	2	2	no	—
47	C₂×C₅×C₄⋊C₄	—	2	2	no	—
48	C₂×C₅×C₄⋊C₄	—	2	2	no	—
49	C₂×C₅×C₄⋊C₄	—	2	2	no	—
50	C₂×C₅×C₄⋊C₄	—	2	2	no	—
51	C₂×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
52	C₂×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
53	C₂×C₄²×C₅	—	2	1	no	—
54	C₂×C₄²×C₅	—	2	1	no	—
55	C₂×C₄²×C₅	—	2	1	no	—
56	C₂×C₄²×C₅	—	2	1	no	—
57	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
58	C₂×C₄²×C₅	Q₈	1	2	yes	—
59	C₅×#107	—	2	8	no	—
60	C₅×#106	—	2	8	no	—
61	C₅×#97	—	2	8	no	—
62	C₅×#95	—	4	8	no	—
63	C₂²×#107	C₂×C₅	1	1	yes	characteristic
64	C₂²×#106	C₂×C₅	1	1	yes	characteristic
65	C₂²×#97	C₂×C₅	1	1	yes	characteristic
66	C₂×#340	C₂×C₅	1	2	yes	—
67	C₄⋊#95	C₂×C₅	1	2	yes	—
68	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
69	C₂²×C₄×C₅	—	2	2	no	—
70	C₂²×C₄×C₅	—	2	2	no	—
71	C₂²×C₄×C₅	—	2	4	no	—
72	C₂²×C₄×C₅	—	2	4	no	—
73	C₂²×C₄×C₅	—	2	4	no	—
74	C₂²×C₄×C₅	—	2	4	no	—
75	C₂²×C₄×C₅	—	4	2	no	—
76	C₂²×C₄×C₅	—	4	2	no	—
77	C₂²×C₄×C₅	—	4	2	no	—
78	C₂²×C₄×C₅	—	4	2	no	—
79	C₂²×C₄×C₅	—	4	4	no	—
80	C₂²×C₄×C₅	—	4	4	no	—
81	C₂²×C₄×C₅	—	4	4	no	—
82	C₂²×C₄×C₅	—	4	4	no	—
83	C₂²×C₄×C₅	C₄⋊C₄	1	4	yes	—
84	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
92	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
93	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
94	C₂²×C₄×C₅	#41	1	1	yes	characteristic
95	C₂²×C₄×C₅	#41	1	1	yes	characteristic
96	C₂²×C₄×C₅	#41	1	1	yes	characteristic
97	C₂²×C₄×C₅	#41	1	1	yes	characteristic
98	C₂×C₅×C₈	—	2	2	no	—
99	C₂×C₅×C₈	—	2	2	no	—
100	C₂×C₅×C₈	—	2	2	no	—
101	C₂×C₅×C₈	—	2	2	no	—
102	C₂×C₅×C₈	—	2	2	no	—
103	C₂×C₅×C₈	—	2	2	no	—
104	C₂×C₅×C₈	C₄²	1	4	yes	—
105	C₂×C₅×C₈	C₂²⋊C₄	1	4	yes	—
106	C₂×C₅×C₈	C₂²⋊C₄	1	4	yes	—
107	C₂×C₅×C₈	C₂²⋊C₄	1	4	yes	—
108	C₂×C₅×C₈	C₄⋊C₄	1	4	yes	—
109	C₂×C₅×C₈	C₄⋊C₄	1	4	yes	—
110	C₂×C₅×C₈	C₄⋊C₄	1	4	yes	—
111	C₂×C₅×C₈	C₄⋊C₄	1	4	yes	—
112	C₅×C₄⋊C₄	—	2	4	no	—
113	C₅×C₄⋊C₄	—	2	4	no	—
114	C₅×C₄⋊C₄	—	2	4	no	—
115	C₅×C₄⋊C₄	—	2	4	no	—
116	C₅×C₄⋊C₄	—	4	2	no	—
117	C₅×C₄⋊C₄	—	4	2	no	—
118	C₅×C₄⋊C₄	—	4	2	no	—
119	C₅×C₄⋊C₄	—	4	2	no	—
120	C₄²×C₅	—	2	2	no	—
121	C₄²×C₅	—	2	2	no	—
122	C₄²×C₅	—	2	2	no	—
123	C₄²×C₅	—	2	2	no	—
124	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
125	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
126	C₂²×C₄⋊C₄	C₂²×C₅	1	2	yes	—
127	C₂²×C₄⋊C₄	C₂²×C₅	1	2	yes	—
128	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
129	C₂×#107	—	2	2	no	—
130	C₂×#107	—	2	2	no	—
131	C₂×#107	C₄×C₅	1	4	yes	complemented
132	C₂×#106	—	2	2	no	—
133	C₂×#106	—	2	2	no	—
134	C₂×#106	C₄×C₅	1	4	yes	complemented
135	C₂×#97	—	2	2	no	—
136	C₂×#97	—	2	2	no	—
137	C₂×#97	C₄×C₅	1	4	yes	complemented
138	C₂×#95	—	2	4	no	—
139	#340	—	2	4	no	—
140	C₂³×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
141	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
142	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
143	C₂³×C₅	#121	1	1	yes	characteristic
144	C₂³×C₅	#121	1	1	yes	characteristic
145	C₂³×C₅	#127	1	1	yes	characteristic
146	C₂³×C₅	C₄⋊Q₈	1	1	yes	characteristic
147	C₂³×C₅	AGL(1,ℤ/8)	1	4	yes	—
148	C₂³×C₅	#137	1	4	yes	—
149	C₂×C₄×C₅	—	2	4	no	—
150	C₂×C₄×C₅	—	2	8	no	—
151	C₂×C₄×C₅	—	4	4	no	—
152	C₂×C₄×C₅	—	4	2	no	—
153	C₂×C₄×C₅	—	4	2	no	—
154	C₂×C₄×C₅	—	4	4	no	—
155	C₂×C₄×C₅	—	4	4	no	—
156	C₂×C₄×C₅	—	4	8	no	—
157	C₂×C₄×C₅	—	4	8	no	—
158	C₂×C₄×C₅	—	8	4	no	—
159	C₂×C₄×C₅	—	8	4	no	—
160	C₂×C₄×C₅	—	8	2	no	—
161	C₂×C₄×C₅	—	8	2	no	—
162	C₂×C₄×C₅	—	8	2	no	—
163	C₂×C₄×C₅	—	8	2	no	—
164	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
165	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
166	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
167	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
168	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
169	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
170	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
171	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₅	#117	1	1	yes	characteristic
173	C₂×C₄×C₅	#117	1	1	yes	characteristic
174	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
175	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
176	C₂×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
177	C₂×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
178	C₂×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
179	C₂×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
180	C₂×C₄×C₅	#121	1	1	yes	characteristic
181	C₂×C₄×C₅	#121	1	1	yes	characteristic
182	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
183	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
184	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
185	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
186	C₂×C₄×C₅	#124	1	1	yes	characteristic
187	C₂×C₄×C₅	#124	1	1	yes	characteristic
188	C₂×C₄×C₅	#125	1	1	yes	characteristic
189	C₂×C₄×C₅	#125	1	1	yes	characteristic
190	C₂×C₄×C₅	C₄⋊Q₈	1	1	yes	characteristic
191	C₂×C₄×C₅	C₄⋊Q₈	1	1	yes	characteristic
192	C₅×C₈	—	2	4	no	—
193	C₅×C₈	#95	1	8	yes	complemented
194	C₂³×C₄	—	2	2	no	—
195	C₂³×C₄	—	2	2	no	—
196	C₂³×C₄	C₅×D₄	1	2	yes	—
197	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
198	C₂²×C₈	—	2	1	no	—
199	C₂²×C₈	—	2	1	no	—
200	C₂²×C₈	—	2	1	no	—
201	C₂²×C₈	—	2	1	no	—
202	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
203	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
204	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
205	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
206	C₂²×C₈	C₅×D₄	1	2	yes	—
207	C₂²×C₈	C₅×D₄	1	2	yes	—
208	C₂²×C₈	C₅×D₄	1	2	yes	—
209	C₂²×C₈	C₅×D₄	1	2	yes	—
210	C₂²×C₈	C₅×Q₈	1	2	yes	—
211	C₂²×C₈	C₅×Q₈	1	2	yes	—
212	C₂×C₄⋊C₄	—	2	2	no	—
213	C₂×C₄⋊C₄	—	2	2	no	—
214	C₂×C₄⋊C₄	—	2	2	no	—
215	C₂×C₄⋊C₄	—	2	2	no	—
216	C₂×C₄⋊C₄	—	2	2	no	—
217	C₂×C₄⋊C₄	—	2	2	no	—
218	C₂×C₄⋊C₄	—	2	2	no	—
219	C₂×C₄⋊C₄	—	2	2	no	—
220	C₂×C₄⋊C₄	—	2	2	no	—
221	C₂×C₄⋊C₄	—	2	2	no	—
222	C₂×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	—
223	C₂×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	—
224	C₂×C₄²	—	2	1	no	—
225	C₂×C₄²	—	2	1	no	—
226	C₂×C₄²	—	2	1	no	—
227	C₂×C₄²	—	2	1	no	—
228	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
229	C₂×C₄²	C₅×Q₈	1	2	yes	—
230	#107	—	2	8	no	—
231	#106	—	2	8	no	—
232	#97	—	2	8	no	—
233	#95	—	4	8	no	—
234	C₂²×C₅	C₄×C₄⋊C₄	1	1	yes	characteristic
235	C₂²×C₅	#380	1	1	yes	characteristic
236	C₂²×C₅	#384	1	1	yes	characteristic
237	C₂²×C₅	#389	1	1	yes	characteristic
238	C₂²×C₅	#389	1	1	yes	characteristic
239	C₂²×C₅	#390	1	1	yes	characteristic
240	C₂²×C₅	#390	1	1	yes	characteristic
241	C₂²×C₅	#428	1	4	yes	—
242	C₂²×C₅	#440	1	4	yes	—
243	C₂²×C₅	#441	1	2	yes	—
244	C₂²×C₅	#442	1	2	yes	—
245	C₂²×C₅	#468	1	4	yes	—
246	C₂²×C₅	#469	1	2	yes	—
247	C₂²×C₅	#470	1	2	yes	—
248	C₂²×C₅	#496	1	2	yes	—
249	C₂²×C₅	#497	1	2	yes	—
250	C₂²×C₅	#501	1	4	yes	—
251	C₄×C₅	—	4	4	no	—
252	C₄×C₅	—	8	4	no	—
253	C₄×C₅	—	8	4	no	—
254	C₄×C₅	C₂×#95	1	1	yes	characteristic
255	C₄×C₅	C₄×C₄⋊C₄	1	1	yes	characteristic
256	C₄×C₅	#380	1	1	yes	characteristic
257	C₄×C₅	#382	1	1	yes	characteristic
258	C₄×C₅	#389	1	1	yes	characteristic
259	C₄×C₅	#389	1	1	yes	characteristic
260	C₄×C₅	#391	1	1	yes	characteristic
261	C₄×C₅	#391	1	1	yes	characteristic
262	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
263	C₂²×C₄	—	2	2	no	—
264	C₂²×C₄	—	2	2	no	—
265	C₂²×C₄	—	2	4	no	—
266	C₂²×C₄	—	2	4	no	—
267	C₂²×C₄	—	2	4	no	—
268	C₂²×C₄	—	2	4	no	—
269	C₂²×C₄	—	4	2	no	—
270	C₂²×C₄	—	4	2	no	—
271	C₂²×C₄	—	4	2	no	—
272	C₂²×C₄	—	4	2	no	—
273	C₂²×C₄	—	4	4	no	—
274	C₂²×C₄	—	4	4	no	—
275	C₂²×C₄	—	4	4	no	—
276	C₂²×C₄	—	4	4	no	—
277	C₂²×C₄	C₅×C₄⋊C₄	1	4	yes	—
278	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
279	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
280	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
281	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
282	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
283	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
284	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
285	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
286	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
287	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
288	C₂²×C₄	C₅×#41	1	1	yes	characteristic
289	C₂²×C₄	C₅×#41	1	1	yes	characteristic
290	C₂²×C₄	C₅×#41	1	1	yes	characteristic
291	C₂²×C₄	C₅×#41	1	1	yes	characteristic
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	C₄²×C₅	1	4	yes	—
299	C₂×C₈	C₅×C₂²⋊C₄	1	4	yes	—
300	C₂×C₈	C₅×C₂²⋊C₄	1	4	yes	—
301	C₂×C₈	C₅×C₂²⋊C₄	1	4	yes	—
302	C₂×C₈	C₅×C₄⋊C₄	1	4	yes	—
303	C₂×C₈	C₅×C₄⋊C₄	1	4	yes	—
304	C₂×C₈	C₅×C₄⋊C₄	1	4	yes	—
305	C₂×C₈	C₅×C₄⋊C₄	1	4	yes	—
306	C₄⋊C₄	—	2	4	no	—
307	C₄⋊C₄	—	2	4	no	—
308	C₄⋊C₄	—	2	4	no	—
309	C₄⋊C₄	—	2	4	no	—
310	C₄⋊C₄	—	4	2	no	—
311	C₄⋊C₄	—	4	2	no	—
312	C₄⋊C₄	—	4	2	no	—
313	C₄⋊C₄	—	4	2	no	—
314	C₄²	—	2	2	no	—
315	C₄²	—	2	2	no	—
316	C₄²	—	2	2	no	—
317	C₄²	—	2	2	no	—
318	C₂×C₅	C₄⋊#95	1	1	yes	characteristic
319	C₂×C₅	#1776	1	2	yes	—
320	C₂×C₅	#1809	1	2	yes	—
321	C₂×C₅	#1847	1	2	yes	—
322	C₂×C₅	#1943	1	2	yes	—
323	C₂×C₅	#1944	1	2	yes	—
324	C₂×C₅	#1971	1	1	yes	characteristic
325	C₂×C₅	#1972	1	1	yes	characteristic
326	C₂×C₅	#1973	1	2	yes	—
327	C₂³	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
328	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
329	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
330	C₂³	C₅×#121	1	1	yes	characteristic
331	C₂³	C₅×#121	1	1	yes	characteristic
332	C₂³	C₅×#127	1	1	yes	characteristic
333	C₂³	C₅×C₄⋊Q₈	1	1	yes	characteristic
334	C₂³	C₅×AGL(1,ℤ/8)	1	4	yes	—
335	C₂³	C₅×#137	1	4	yes	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	2	8	no	—
338	C₂×C₄	—	4	4	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	4	no	—
342	C₂×C₄	—	4	4	no	—
343	C₂×C₄	—	4	8	no	—
344	C₂×C₄	—	4	8	no	—
345	C₂×C₄	—	8	4	no	—
346	C₂×C₄	—	8	4	no	—
347	C₂×C₄	—	8	2	no	—
348	C₂×C₄	—	8	2	no	—
349	C₂×C₄	—	8	2	no	—
350	C₂×C₄	—	8	2	no	—
351	C₂×C₄	C₂×C₄²×C₅	1	1	yes	characteristic
352	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
353	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
354	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
355	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
356	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
357	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
358	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
359	C₂×C₄	C₅×#117	1	1	yes	characteristic
360	C₂×C₄	C₅×#117	1	1	yes	characteristic
361	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
362	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
363	C₂×C₄	C₄×C₅×Q₈	1	1	yes	characteristic
364	C₂×C₄	C₄×C₅×Q₈	1	1	yes	characteristic
365	C₂×C₄	C₄×C₅×Q₈	1	1	yes	characteristic
366	C₂×C₄	C₄×C₅×Q₈	1	1	yes	characteristic
367	C₂×C₄	C₅×#121	1	1	yes	characteristic
368	C₂×C₄	C₅×#121	1	1	yes	characteristic
369	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
370	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
371	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
372	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
373	C₂×C₄	C₅×#124	1	1	yes	characteristic
374	C₂×C₄	C₅×#124	1	1	yes	characteristic
375	C₂×C₄	C₅×#125	1	1	yes	characteristic
376	C₂×C₄	C₅×#125	1	1	yes	characteristic
377	C₂×C₄	C₅×C₄⋊Q₈	1	1	yes	characteristic
378	C₂×C₄	C₅×C₄⋊Q₈	1	1	yes	characteristic
379	C₈	—	2	4	no	—
380	C₈	C₅×#95	1	8	yes	complemented
381	C₅	#10863	1	1	yes	characteristic, direct product factor, Sylow
382	C₂²	C₄×C₅×C₄⋊C₄	1	1	yes	characteristic
383	C₂²	C₅×#380	1	1	yes	characteristic
384	C₂²	C₅×#384	1	1	yes	characteristic
385	C₂²	C₅×#389	1	1	yes	characteristic
386	C₂²	C₅×#389	1	1	yes	characteristic
387	C₂²	C₅×#390	1	1	yes	characteristic
388	C₂²	C₅×#390	1	1	yes	characteristic
389	C₂²	C₅×#428	1	4	yes	—
390	C₂²	C₅×#440	1	4	yes	—
391	C₂²	C₅×#441	1	2	yes	—
392	C₂²	C₅×#442	1	2	yes	—
393	C₂²	C₅×#468	1	4	yes	—
394	C₂²	C₅×#469	1	2	yes	—
395	C₂²	C₅×#470	1	2	yes	—
396	C₂²	C₅×#496	1	2	yes	—
397	C₂²	C₅×#497	1	2	yes	—
398	C₂²	C₅×#501	1	4	yes	—
399	C₄	—	4	4	no	—
400	C₄	—	8	4	no	—
401	C₄	—	8	4	no	—
402	C₄	C₂×C₅×#95	1	1	yes	characteristic
403	C₄	C₄×C₅×C₄⋊C₄	1	1	yes	characteristic
404	C₄	C₅×#380	1	1	yes	characteristic
405	C₄	C₅×#382	1	1	yes	characteristic
406	C₄	C₅×#389	1	1	yes	characteristic
407	C₄	C₅×#389	1	1	yes	characteristic
408	C₄	C₅×#391	1	1	yes	characteristic
409	C₄	C₅×#391	1	1	yes	characteristic
410	C₂	C₅×C₄⋊#95	1	1	yes	characteristic
411	C₂	C₅×#1776	1	2	yes	—
412	C₂	C₅×#1809	1	2	yes	—
413	C₂	C₅×#1847	1	2	yes	—
414	C₂	C₅×#1943	1	2	yes	—
415	C₂	C₅×#1944	1	2	yes	—
416	C₂	C₅×#1971	1	1	yes	characteristic
417	C₂	C₅×#1972	1	1	yes	characteristic
418	C₂	C₅×#1973	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₅	C₂×D₄
commutator	C₂×C₄	C₂×C₄²×C₅
Frattini, cosocle	C₂³×C₄	C₂³×C₅
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₅ ◁ C₂²×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
13. C₂×C₅×#107	C₄	semidirect
16. C₂×C₅×#106	C₄	semidirect
19. C₂×C₅×#97	C₄	semidirect
22. #10863	C₅	direct (N × H)
131. C₂×#107	C₄×C₅	semidirect
134. C₂×#106	C₄×C₅	semidirect
137. C₂×#97	C₄×C₅	semidirect
193. C₅×C₈	#95	semidirect
380. C₈	C₅×#95	semidirect
381. C₅	#10863	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₅×#107	2
C₂²×C₅×#106	2
C₂²×C₅×#97	2
C₂×C₅×#340	2
C₅×C₄⋊#95	2
#10863	5

Subgroups — C5×#10863 #11933583

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#10863 #11933583