Subgroups — C₅×#10849 #11933569

Order 1280.

1086 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×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#384	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×#340	C₂	1	4	yes	maximal
5	C₂³×C₅×C₈	C₂²	1	2	yes	—
6	C₂²×C₅×C₄⋊C₄	—	2	1	no	—
7	C₂²×C₅×C₄⋊C₄	—	2	1	no	—
8	C₂²×C₅×C₄⋊C₄	C₂²	1	2	yes	—
9	C₂²×C₅×C₄⋊C₄	C₂²	1	2	yes	—
10	C₂²×C₄²×C₅	—	2	1	no	—
11	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
12	C₂×C₅×C₄⋊C₈	—	2	2	no	—
13	C₂×C₅×C₄⋊C₈	—	2	2	no	—
14	C₂×C₅×C₄⋊C₈	C₄	1	4	yes	complemented
15	C₅×#384	—	2	2	no	—
16	C₅×#384	C₄	1	4	yes	complemented
17	C₄×C₅×C₄⋊C₄	—	2	2	no	—
18	C₄×C₅×C₄⋊C₄	C₄	1	4	yes	complemented
19	C₂×C₅×#95	—	2	1	no	—
20	C₅×#340	—	2	8	no	—
21	#10849	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
22	C₂³×C₄×C₅	—	2	2	no	—
23	C₂³×C₄×C₅	—	2	2	no	—
24	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
25	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
26	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
27	C₂²×C₅×C₈	—	2	4	no	—
28	C₂²×C₅×C₈	—	2	2	no	—
29	C₂²×C₅×C₈	—	2	2	no	—
30	C₂²×C₅×C₈	—	2	4	no	—
31	C₂²×C₅×C₈	C₂×C₄	1	4	yes	—
32	C₂×C₅×C₄⋊C₄	—	2	2	no	—
33	C₂×C₅×C₄⋊C₄	—	2	2	no	—
34	C₂×C₅×C₄⋊C₄	—	2	2	no	—
35	C₂×C₅×C₄⋊C₄	—	2	4	no	—
36	C₂×C₅×C₄⋊C₄	—	2	4	no	—
37	C₂×C₅×C₄⋊C₄	—	2	4	no	—
38	C₂×C₅×C₄⋊C₄	—	2	4	no	—
39	C₂×C₅×C₄⋊C₄	—	2	2	no	—
40	C₂×C₅×C₄⋊C₄	—	4	4	no	—
41	C₂×C₅×C₄⋊C₄	—	4	2	no	—
42	C₂×C₅×C₄⋊C₄	—	4	2	no	—
43	C₂×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
44	C₂×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
45	C₂×C₅×C₄⋊C₄	D₄	1	4	yes	—
46	C₂×C₅×C₄⋊C₄	Q₈	1	4	yes	—
47	C₂×C₄²×C₅	—	2	4	no	—
48	C₂×C₄²×C₅	—	4	2	no	—
49	C₂×C₄²×C₅	—	4	2	no	—
50	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
51	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
52	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
53	C₂×C₄²×C₅	D₄	1	2	yes	—
54	C₂×C₄²×C₅	D₄	1	2	yes	—
55	C₂×C₄²×C₅	Q₈	1	2	yes	—
56	C₅×C₄⋊C₈	—	2	8	no	—
57	C₅×#95	—	2	4	no	—
58	C₂²×C₄⋊C₈	C₂×C₅	1	1	yes	characteristic
59	C₂×#384	C₂×C₅	1	1	yes	characteristic
60	C₂×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
61	C₂×#340	C₂×C₅	1	4	yes	—
62	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
63	C₂²×C₄×C₅	—	2	2	no	—
64	C₂²×C₄×C₅	—	2	2	no	—
65	C₂²×C₄×C₅	—	2	4	no	—
66	C₂²×C₄×C₅	—	2	4	no	—
67	C₂²×C₄×C₅	—	2	4	no	—
68	C₂²×C₄×C₅	—	2	4	no	—
69	C₂²×C₄×C₅	—	4	2	no	—
70	C₂²×C₄×C₅	—	4	2	no	—
71	C₂²×C₄×C₅	—	4	2	no	—
72	C₂²×C₄×C₅	—	4	2	no	—
73	C₂²×C₄×C₅	—	4	4	no	—
74	C₂²×C₄×C₅	—	4	2	no	—
75	C₂²×C₄×C₅	—	4	2	no	—
76	C₂²×C₄×C₅	—	4	4	no	—
77	C₂²×C₄×C₅	C₂²⋊C₄	1	2	yes	—
78	C₂²×C₄×C₅	C₂²⋊C₄	1	2	yes	—
79	C₂²×C₄×C₅	C₂²⋊C₄	1	2	yes	—
80	C₂²×C₄×C₅	C₂²⋊C₄	1	2	yes	—
81	C₂²×C₄×C₅	C₄⋊C₄	1	2	yes	—
82	C₂²×C₄×C₅	C₄⋊C₄	1	2	yes	—
83	C₂²×C₄×C₅	D₈	1	2	yes	—
84	C₂²×C₄×C₅	SD₁₆	1	2	yes	—
85	C₂²×C₄×C₅	SD₁₆	1	2	yes	—
86	C₂²×C₄×C₅	Q₁₆	1	2	yes	—
87	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
93	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
94	C₂²×C₄×C₅	C₂×Q₈	1	2	yes	—
95	C₂²×C₄×C₅	#41	1	2	yes	—
96	C₂²×C₄×C₅	#41	1	2	yes	—
97	C₂×C₅×C₈	—	2	4	no	—
98	C₂×C₅×C₈	—	2	8	no	—
99	C₂×C₅×C₈	—	4	4	no	—
100	C₂×C₅×C₈	—	4	2	no	—
101	C₂×C₅×C₈	—	4	2	no	—
102	C₅×C₄⋊C₄	—	2	4	no	—
103	C₅×C₄⋊C₄	—	2	4	no	—
104	C₅×C₄⋊C₄	—	2	4	no	—
105	C₅×C₄⋊C₄	—	2	8	no	—
106	C₅×C₄⋊C₄	—	4	8	no	—
107	C₅×C₄⋊C₄	—	4	8	no	—
108	C₅×C₄⋊C₄	—	4	2	no	—
109	C₅×C₄⋊C₄	—	4	2	no	—
110	C₅×C₄⋊C₄	C₄⋊C₄	1	8	yes	complemented
111	C₄²×C₅	—	4	8	no	—
112	C₄²×C₅	C₄²	1	4	yes	—
113	C₄²×C₅	C₂²⋊C₄	1	4	yes	—
114	C₄²×C₅	C₄⋊C₄	1	4	yes	—
115	C₄²×C₅	C₄⋊C₄	1	4	yes	—
116	C₂³×C₈	C₂²×C₅	1	2	yes	—
117	C₂²×C₄⋊C₄	—	2	1	no	—
118	C₂²×C₄⋊C₄	—	2	1	no	—
119	C₂²×C₄⋊C₄	C₂²×C₅	1	2	yes	—
120	C₂²×C₄⋊C₄	C₂²×C₅	1	2	yes	—
121	C₂²×C₄²	—	2	1	no	—
122	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
123	C₂×C₄⋊C₈	—	2	2	no	—
124	C₂×C₄⋊C₈	—	2	2	no	—
125	C₂×C₄⋊C₈	C₄×C₅	1	4	yes	complemented
126	#384	—	2	2	no	—
127	#384	C₄×C₅	1	4	yes	complemented
128	C₄×C₄⋊C₄	—	2	2	no	—
129	C₄×C₄⋊C₄	C₄×C₅	1	4	yes	complemented
130	C₂×#95	—	2	1	no	—
131	#340	—	2	8	no	—
132	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
133	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
134	C₂³×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
135	C₂³×C₅	#121	1	2	yes	—
136	C₂³×C₅	C₂²⋊Q₈	1	2	yes	—
137	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
138	C₂³×C₅	C₂×SD₁₆	1	1	yes	characteristic
139	C₂³×C₅	C₂×SD₁₆	1	1	yes	characteristic
140	C₂³×C₅	C₂×Q₁₆	1	1	yes	characteristic
141	C₂³×C₅	AGL(1,ℤ/8)	1	2	yes	—
142	C₂³×C₅	#137	1	2	yes	—
143	C₂×C₄×C₅	—	2	4	no	—
144	C₂×C₄×C₅	—	2	2	no	—
145	C₂×C₄×C₅	—	2	2	no	—
146	C₂×C₄×C₅	—	2	4	no	—
147	C₂×C₄×C₅	—	2	8	no	—
148	C₂×C₄×C₅	—	4	4	no	—
149	C₂×C₄×C₅	—	4	4	no	—
150	C₂×C₄×C₅	—	4	4	no	—
151	C₂×C₄×C₅	—	4	4	no	—
152	C₂×C₄×C₅	—	4	4	no	—
153	C₂×C₄×C₅	—	4	4	no	—
154	C₂×C₄×C₅	—	4	4	no	—
155	C₂×C₄×C₅	—	4	4	no	—
156	C₂×C₄×C₅	—	4	4	no	—
157	C₂×C₄×C₅	—	8	4	no	—
158	C₂×C₄×C₅	—	8	4	no	—
159	C₂×C₄×C₅	#95	1	4	yes	—
160	C₂×C₄×C₅	#95	1	4	yes	—
161	C₂×C₄×C₅	#102	1	4	yes	—
162	C₂×C₄×C₅	#102	1	4	yes	—
163	C₂×C₄×C₅	#103	1	4	yes	—
164	C₂×C₄×C₅	#103	1	4	yes	—
165	C₂×C₄×C₅	#106	1	4	yes	—
166	C₂×C₄×C₅	#107	1	4	yes	—
167	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
168	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
169	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
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	2	yes	—
173	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
174	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
175	C₂×C₄×C₅	C₄×Q₈	1	2	yes	—
176	C₂×C₄×C₅	C₄×Q₈	1	2	yes	—
177	C₂×C₄×C₅	#121	1	2	yes	—
178	C₂×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
179	C₂×C₄×C₅	#124	1	1	yes	characteristic
180	C₂×C₄×C₅	#124	1	1	yes	characteristic
181	C₂×C₄×C₅	#125	1	2	yes	—
182	C₂×C₄×C₅	#127	1	1	yes	characteristic
183	C₂×C₄×C₅	C₄⋊Q₈	1	2	yes	—
184	C₂×C₄×C₅	C₄⋊Q₈	1	1	yes	characteristic
185	C₅×C₈	—	4	4	no	—
186	C₂³×C₄	—	2	2	no	—
187	C₂³×C₄	—	2	2	no	—
188	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
189	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
190	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
191	C₂²×C₈	—	2	4	no	—
192	C₂²×C₈	—	2	2	no	—
193	C₂²×C₈	—	2	2	no	—
194	C₂²×C₈	—	2	4	no	—
195	C₂²×C₈	C₂×C₄×C₅	1	4	yes	—
196	C₂×C₄⋊C₄	—	2	2	no	—
197	C₂×C₄⋊C₄	—	2	2	no	—
198	C₂×C₄⋊C₄	—	2	2	no	—
199	C₂×C₄⋊C₄	—	2	4	no	—
200	C₂×C₄⋊C₄	—	2	4	no	—
201	C₂×C₄⋊C₄	—	2	4	no	—
202	C₂×C₄⋊C₄	—	2	4	no	—
203	C₂×C₄⋊C₄	—	2	2	no	—
204	C₂×C₄⋊C₄	—	4	4	no	—
205	C₂×C₄⋊C₄	—	4	2	no	—
206	C₂×C₄⋊C₄	—	4	2	no	—
207	C₂×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	—
208	C₂×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	—
209	C₂×C₄⋊C₄	C₅×D₄	1	4	yes	—
210	C₂×C₄⋊C₄	C₅×Q₈	1	4	yes	—
211	C₂×C₄²	—	2	4	no	—
212	C₂×C₄²	—	4	2	no	—
213	C₂×C₄²	—	4	2	no	—
214	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
215	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
216	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
217	C₂×C₄²	C₅×D₄	1	2	yes	—
218	C₂×C₄²	C₅×D₄	1	2	yes	—
219	C₂×C₄²	C₅×Q₈	1	2	yes	—
220	C₄⋊C₈	—	2	8	no	—
221	#95	—	2	4	no	—
222	C₂²×C₅	C₂×#95	1	1	yes	characteristic
223	C₂²×C₅	#380	1	2	yes	—
224	C₂²×C₅	#389	1	2	yes	—
225	C₂²×C₅	#390	1	1	yes	characteristic
226	C₂²×C₅	#391	1	1	yes	characteristic
227	C₂²×C₅	C₂×#102	1	1	yes	characteristic
228	C₂²×C₅	C₂×#102	1	1	yes	characteristic
229	C₂²×C₅	C₂×#103	1	1	yes	characteristic
230	C₂²×C₅	C₂×#103	1	1	yes	characteristic
231	C₂²×C₅	#417	1	2	yes	—
232	C₂²×C₅	#418	1	1	yes	characteristic
233	C₂²×C₅	#419	1	1	yes	characteristic
234	C₂²×C₅	C₂×#106	1	1	yes	characteristic
235	C₂²×C₅	C₂×#107	1	1	yes	characteristic
236	C₂²×C₅	#428	1	2	yes	—
237	C₂²×C₅	#459	1	2	yes	—
238	C₂²×C₅	#460	1	2	yes	—
239	C₂²×C₅	#461	1	2	yes	—
240	C₂²×C₅	#462	1	2	yes	—
241	C₂²×C₅	#474	1	2	yes	—
242	C₂²×C₅	#475	1	2	yes	—
243	C₂²×C₅	#476	1	2	yes	—
244	C₂²×C₅	#477	1	2	yes	—
245	C₄×C₅	—	2	4	no	—
246	C₄×C₅	—	4	8	no	—
247	C₄×C₅	—	8	4	no	—
248	C₄×C₅	#340	1	8	yes	complemented
249	C₄×C₅	C₄×C₄⋊C₄	1	2	yes	—
250	C₄×C₅	#382	1	1	yes	characteristic
251	C₄×C₅	#384	1	1	yes	characteristic
252	C₄×C₅	#389	1	2	yes	—
253	C₄×C₅	#390	1	1	yes	characteristic
254	C₄×C₅	#391	1	1	yes	characteristic
255	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
256	C₂²×C₄	—	2	2	no	—
257	C₂²×C₄	—	2	2	no	—
258	C₂²×C₄	—	2	4	no	—
259	C₂²×C₄	—	2	4	no	—
260	C₂²×C₄	—	2	4	no	—
261	C₂²×C₄	—	2	4	no	—
262	C₂²×C₄	—	4	2	no	—
263	C₂²×C₄	—	4	2	no	—
264	C₂²×C₄	—	4	2	no	—
265	C₂²×C₄	—	4	2	no	—
266	C₂²×C₄	—	4	4	no	—
267	C₂²×C₄	—	4	2	no	—
268	C₂²×C₄	—	4	2	no	—
269	C₂²×C₄	—	4	4	no	—
270	C₂²×C₄	C₅×C₂²⋊C₄	1	2	yes	—
271	C₂²×C₄	C₅×C₂²⋊C₄	1	2	yes	—
272	C₂²×C₄	C₅×C₂²⋊C₄	1	2	yes	—
273	C₂²×C₄	C₅×C₂²⋊C₄	1	2	yes	—
274	C₂²×C₄	C₅×C₄⋊C₄	1	2	yes	—
275	C₂²×C₄	C₅×C₄⋊C₄	1	2	yes	—
276	C₂²×C₄	C₅×D₈	1	2	yes	—
277	C₂²×C₄	C₅×SD₁₆	1	2	yes	—
278	C₂²×C₄	C₅×SD₁₆	1	2	yes	—
279	C₂²×C₄	C₅×Q₁₆	1	2	yes	—
280	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
281	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
282	C₂²×C₄	C₂²×C₄×C₅	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×D₄	1	2	yes	—
286	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
287	C₂²×C₄	C₂×C₅×Q₈	1	2	yes	—
288	C₂²×C₄	C₅×#41	1	2	yes	—
289	C₂²×C₄	C₅×#41	1	2	yes	—
290	C₂×C₈	—	2	4	no	—
291	C₂×C₈	—	2	8	no	—
292	C₂×C₈	—	4	4	no	—
293	C₂×C₈	—	4	2	no	—
294	C₂×C₈	—	4	2	no	—
295	C₄⋊C₄	—	2	4	no	—
296	C₄⋊C₄	—	2	4	no	—
297	C₄⋊C₄	—	2	4	no	—
298	C₄⋊C₄	—	2	8	no	—
299	C₄⋊C₄	—	4	8	no	—
300	C₄⋊C₄	—	4	2	no	—
301	C₄⋊C₄	—	4	2	no	—
302	C₄⋊C₄	—	4	8	no	—
303	C₄⋊C₄	C₅×C₄⋊C₄	1	8	yes	complemented
304	C₄²	—	4	8	no	—
305	C₄²	C₄²×C₅	1	4	yes	—
306	C₄²	C₅×C₂²⋊C₄	1	4	yes	—
307	C₄²	C₅×C₄⋊C₄	1	4	yes	—
308	C₄²	C₅×C₄⋊C₄	1	4	yes	—
309	C₂×C₅	C₄⋊#95	1	1	yes	characteristic
310	C₂×C₅	C₂×#340	1	1	yes	characteristic
311	C₂×C₅	#1736	1	1	yes	characteristic
312	C₂×C₅	#1802	1	2	yes	—
313	C₂×C₅	#1803	1	2	yes	—
314	C₂×C₅	#1947	1	2	yes	—
315	C₂×C₅	#1948	1	2	yes	—
316	C₂×C₅	#1981	1	1	yes	characteristic
317	C₂×C₅	#1982	1	1	yes	characteristic
318	C₂×C₅	#1987	1	1	yes	characteristic
319	C₂×C₅	#1988	1	1	yes	characteristic
320	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
321	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
322	C₂³	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
323	C₂³	C₅×#121	1	2	yes	—
324	C₂³	C₅×C₂²⋊Q₈	1	2	yes	—
325	C₂³	C₂×C₅×D₈	1	1	yes	characteristic
326	C₂³	C₂×C₅×SD₁₆	1	1	yes	characteristic
327	C₂³	C₂×C₅×SD₁₆	1	1	yes	characteristic
328	C₂³	C₂×C₅×Q₁₆	1	1	yes	characteristic
329	C₂³	C₅×AGL(1,ℤ/8)	1	2	yes	—
330	C₂³	C₅×#137	1	2	yes	—
331	C₂×C₄	—	2	4	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	4	no	—
335	C₂×C₄	—	2	8	no	—
336	C₂×C₄	—	4	4	no	—
337	C₂×C₄	—	4	4	no	—
338	C₂×C₄	—	4	4	no	—
339	C₂×C₄	—	4	4	no	—
340	C₂×C₄	—	4	4	no	—
341	C₂×C₄	—	4	4	no	—
342	C₂×C₄	—	4	4	no	—
343	C₂×C₄	—	4	4	no	—
344	C₂×C₄	—	4	4	no	—
345	C₂×C₄	—	8	4	no	—
346	C₂×C₄	—	8	4	no	—
347	C₂×C₄	C₅×#95	1	4	yes	—
348	C₂×C₄	C₅×#95	1	4	yes	—
349	C₂×C₄	C₅×#102	1	4	yes	—
350	C₂×C₄	C₅×#102	1	4	yes	—
351	C₂×C₄	C₅×#103	1	4	yes	—
352	C₂×C₄	C₅×#103	1	4	yes	—
353	C₂×C₄	C₅×#106	1	4	yes	—
354	C₂×C₄	C₅×#107	1	4	yes	—
355	C₂×C₄	C₂×C₄²×C₅	1	1	yes	characteristic
356	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
357	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
358	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
359	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
360	C₂×C₄	C₅×#117	1	2	yes	—
361	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
362	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
363	C₂×C₄	C₄×C₅×Q₈	1	2	yes	—
364	C₂×C₄	C₄×C₅×Q₈	1	2	yes	—
365	C₂×C₄	C₅×#121	1	2	yes	—
366	C₂×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
367	C₂×C₄	C₅×#124	1	1	yes	characteristic
368	C₂×C₄	C₅×#124	1	1	yes	characteristic
369	C₂×C₄	C₅×#125	1	2	yes	—
370	C₂×C₄	C₅×#127	1	1	yes	characteristic
371	C₂×C₄	C₅×C₄⋊Q₈	1	2	yes	—
372	C₂×C₄	C₅×C₄⋊Q₈	1	1	yes	characteristic
373	C₈	—	4	4	no	—
374	C₅	#10849	1	1	yes	characteristic, direct product factor, Sylow
375	C₂²	C₂×C₅×#95	1	1	yes	characteristic
376	C₂²	C₅×#380	1	2	yes	—
377	C₂²	C₅×#389	1	2	yes	—
378	C₂²	C₅×#390	1	1	yes	characteristic
379	C₂²	C₅×#391	1	1	yes	characteristic
380	C₂²	C₂×C₅×#102	1	1	yes	characteristic
381	C₂²	C₂×C₅×#102	1	1	yes	characteristic
382	C₂²	C₂×C₅×#103	1	1	yes	characteristic
383	C₂²	C₂×C₅×#103	1	1	yes	characteristic
384	C₂²	C₅×#417	1	2	yes	—
385	C₂²	C₅×#418	1	1	yes	characteristic
386	C₂²	C₅×#419	1	1	yes	characteristic
387	C₂²	C₂×C₅×#106	1	1	yes	characteristic
388	C₂²	C₂×C₅×#107	1	1	yes	characteristic
389	C₂²	C₅×#428	1	2	yes	—
390	C₂²	C₅×#459	1	2	yes	—
391	C₂²	C₅×#460	1	2	yes	—
392	C₂²	C₅×#461	1	2	yes	—
393	C₂²	C₅×#462	1	2	yes	—
394	C₂²	C₅×#474	1	2	yes	—
395	C₂²	C₅×#475	1	2	yes	—
396	C₂²	C₅×#476	1	2	yes	—
397	C₂²	C₅×#477	1	2	yes	—
398	C₄	—	2	4	no	—
399	C₄	—	4	8	no	—
400	C₄	—	8	4	no	—
401	C₄	C₅×#340	1	8	yes	complemented
402	C₄	C₄×C₅×C₄⋊C₄	1	2	yes	—
403	C₄	C₅×#382	1	1	yes	characteristic
404	C₄	C₅×#384	1	1	yes	characteristic
405	C₄	C₅×#389	1	2	yes	—
406	C₄	C₅×#390	1	1	yes	characteristic
407	C₄	C₅×#391	1	1	yes	characteristic
408	C₂	C₅×C₄⋊#95	1	1	yes	characteristic
409	C₂	C₂×C₅×#340	1	1	yes	characteristic
410	C₂	C₅×#1736	1	1	yes	characteristic
411	C₂	C₅×#1802	1	2	yes	—
412	C₂	C₅×#1803	1	2	yes	—
413	C₂	C₅×#1947	1	2	yes	—
414	C₂	C₅×#1948	1	2	yes	—
415	C₂	C₅×#1981	1	1	yes	characteristic
416	C₂	C₅×#1982	1	1	yes	characteristic
417	C₂	C₅×#1987	1	1	yes	characteristic
418	C₂	C₅×#1988	1	1	yes	characteristic

	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
14. C₂×C₅×C₄⋊C₈	C₄	semidirect
16. C₅×#384	C₄	semidirect
18. C₄×C₅×C₄⋊C₄	C₄	semidirect
21. #10849	C₅	direct (N × H)
110. C₅×C₄⋊C₄	C₄⋊C₄	semidirect
125. C₂×C₄⋊C₈	C₄×C₅	semidirect
127. #384	C₄×C₅	semidirect
129. C₄×C₄⋊C₄	C₄×C₅	semidirect
248. C₄×C₅	#340	semidirect
303. C₄⋊C₄	C₅×C₄⋊C₄	semidirect
374. C₅	#10849	direct (N × H)
401. C₄	C₅×#340	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₅×C₄⋊C₈	2
C₂×C₅×#384	2
C₂×C₄×C₅×C₄⋊C₄	2
C₂×C₅×#340	2
#10849	5

Subgroups — C5×#10849 #11933569

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#10849 #11933569