Subgroups — C₅×#22309 #11945029

Order 1280.

686 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₅×#1985	C₂	1	2	yes	maximal
3	C₅×#1984	C₂	1	2	yes	maximal
4	C₅×#1939	C₂	1	1	yes	maximal, characteristic
5	C₅×#1939	C₂	1	1	yes	maximal, characteristic
6	C₅×#1917	C₂	1	2	yes	maximal
7	C₅×#1916	C₂	1	2	yes	maximal
8	C₅×#1831	C₂	1	1	yes	maximal, characteristic
9	C₅×#1770	C₂	1	1	yes	maximal, characteristic
10	C₅×C₈×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
11	C₅×#1744	C₂	1	1	yes	maximal, characteristic
12	C₂×C₅×C₄⋊Q₈	C₄	1	1	yes	characteristic
13	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
14	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
15	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
17	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
18	C₂×C₅×#97	C₂²	1	2	yes	—
19	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
21	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
22	C₅×#391	C₄	1	2	yes	—
23	C₅×#389	C₄	1	1	yes	characteristic
24	C₅×#389	C₄	1	2	yes	—
25	C₅×#389	C₄	1	1	yes	characteristic
26	C₅×#384	C₄	1	1	yes	characteristic
27	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
30	C₄³×C₅	C₂²	1	1	yes	characteristic
31	C₅×#336	C₂²	1	2	yes	—
32	C₅×#336	C₂²	1	2	yes	—
33	C₅×#336	C₂²	1	2	yes	—
34	C₅×#336	C₂²	1	2	yes	—
35	C₅×#336	C₂²	1	1	yes	characteristic
36	C₅×#336	C₂²	1	2	yes	—
37	C₅×#336	C₂²	1	1	yes	characteristic
38	C₅×#336	C₂²	1	2	yes	—
39	C₅×#336	C₂²	1	1	yes	characteristic
40	C₅×#336	C₂²	1	1	yes	characteristic
41	#22309	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂²×C₅×Q₈	C₂×C₄	1	2	yes	—
43	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
44	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
45	C₂²×C₅×C₈	C₂³	1	2	yes	—
46	C₂²×C₅×C₈	C₂³	1	2	yes	—
47	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
48	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
49	C₅×C₄⋊Q₈	—	2	4	no	—
50	C₄×C₅×Q₈	—	4	2	no	—
51	C₄×C₅×Q₈	—	4	2	no	—
52	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
53	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
54	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
55	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
56	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
57	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
58	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
59	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
60	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₅	C₂³	1	2	yes	—
68	C₂×C₄²×C₅	C₂³	1	2	yes	—
69	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
70	C₅×C₄⋊C₈	—	2	2	no	—
71	C₅×C₄⋊C₈	—	2	2	no	—
72	C₅×C₄⋊C₈	—	4	2	no	—
73	C₅×C₄⋊C₈	—	4	2	no	—
74	C₅×#97	—	4	2	no	—
75	C₄×C₅×C₈	—	2	2	no	—
76	C₄×C₅×C₈	—	4	2	no	—
77	C₄×C₅×C₈	Q₈	1	4	yes	complemented
78	C₅×#95	C₂×C₄	1	2	yes	—
79	C₅×#95	C₂×C₄	1	2	yes	—
80	C₅×#95	C₂×C₄	1	2	yes	—
81	C₅×#95	C₂×C₄	1	2	yes	—
82	C₄×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic
83	#1985	C₂×C₅	1	2	yes	—
84	#1984	C₂×C₅	1	2	yes	—
85	#1939	C₂×C₅	1	1	yes	characteristic
86	#1939	C₂×C₅	1	1	yes	characteristic
87	#1917	C₂×C₅	1	2	yes	—
88	#1916	C₂×C₅	1	2	yes	—
89	#1831	C₂×C₅	1	1	yes	characteristic
90	#1770	C₂×C₅	1	1	yes	characteristic
91	C₈×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
92	#1744	C₂×C₅	1	1	yes	characteristic
93	C₂×C₅×Q₈	—	2	4	no	—
94	C₂×C₅×Q₈	—	2	4	no	—
95	C₂×C₅×Q₈	—	4	2	no	—
96	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
101	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
103	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
107	C₂×C₅×C₈	—	2	1	no	—
108	C₂×C₅×C₈	—	2	1	no	—
109	C₂×C₅×C₈	—	2	1	no	—
110	C₂×C₅×C₈	—	2	1	no	—
111	C₂×C₅×C₈	—	2	1	no	—
112	C₂×C₅×C₈	—	2	1	no	—
113	C₂×C₅×C₈	—	2	2	no	—
114	C₂×C₅×C₈	—	2	2	no	—
115	C₂×C₅×C₈	—	2	2	no	—
116	C₂×C₅×C₈	—	2	2	no	—
117	C₂×C₅×C₈	—	2	1	no	—
118	C₂×C₅×C₈	—	2	1	no	—
119	C₂×C₅×C₈	—	2	1	no	—
120	C₂×C₅×C₈	—	2	1	no	—
121	C₂×C₅×C₈	—	2	2	no	—
122	C₂×C₅×C₈	—	2	2	no	—
123	C₂×C₅×C₈	C₂×Q₈	1	2	yes	—
124	C₂×C₅×C₈	C₂×Q₈	1	2	yes	—
125	C₅×C₄⋊C₄	—	2	4	no	—
126	C₅×C₄⋊C₄	—	2	2	no	—
127	C₅×C₄⋊C₄	—	2	4	no	—
128	C₅×C₄⋊C₄	—	2	2	no	—
129	C₅×C₄⋊C₄	—	2	2	no	—
130	C₅×C₄⋊C₄	—	4	2	no	—
131	C₅×C₄⋊C₄	—	4	2	no	—
132	C₅×C₄⋊C₄	—	4	2	no	—
133	C₅×C₄⋊C₄	M₁₆	1	4	yes	—
134	C₄²×C₅	—	2	2	no	—
135	C₄²×C₅	—	2	2	no	—
136	C₄²×C₅	—	2	2	no	—
137	C₄²×C₅	—	2	2	no	—
138	C₄²×C₅	—	2	1	no	—
139	C₄²×C₅	—	2	1	no	—
140	C₄²×C₅	—	2	2	no	—
141	C₄²×C₅	—	2	2	no	—
142	C₄²×C₅	—	2	2	no	—
143	C₄²×C₅	—	2	2	no	—
144	C₄²×C₅	—	2	1	no	—
145	C₄²×C₅	—	2	1	no	—
146	C₄²×C₅	C₂×Q₈	1	2	yes	—
147	C₄²×C₅	#41	1	2	yes	—
148	C₂×C₄⋊Q₈	C₄×C₅	1	1	yes	characteristic
149	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
150	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
151	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
152	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
153	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
154	C₂×#97	C₂²×C₅	1	2	yes	—
155	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
156	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
157	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
158	#391	C₄×C₅	1	2	yes	—
159	#389	C₄×C₅	1	1	yes	characteristic
160	#389	C₄×C₅	1	2	yes	—
161	#389	C₄×C₅	1	1	yes	characteristic
162	#384	C₄×C₅	1	1	yes	characteristic
163	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
164	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
165	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
166	C₄³	C₂²×C₅	1	1	yes	characteristic
167	#336	C₂²×C₅	1	2	yes	—
168	#336	C₂²×C₅	1	2	yes	—
169	#336	C₂²×C₅	1	1	yes	characteristic
170	#336	C₂²×C₅	1	2	yes	—
171	#336	C₂²×C₅	1	2	yes	—
172	#336	C₂²×C₅	1	1	yes	characteristic
173	#336	C₂²×C₅	1	2	yes	—
174	#336	C₂²×C₅	1	2	yes	—
175	#336	C₂²×C₅	1	1	yes	characteristic
176	#336	C₂²×C₅	1	1	yes	characteristic
177	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
178	C₅×Q₈	—	4	8	no	—
179	C₂×C₄×C₅	—	2	1	no	—
180	C₂×C₄×C₅	—	2	2	no	—
181	C₂×C₄×C₅	—	2	1	no	—
182	C₂×C₄×C₅	—	2	1	no	—
183	C₂×C₄×C₅	—	2	1	no	—
184	C₂×C₄×C₅	—	2	1	no	—
185	C₂×C₄×C₅	—	2	1	no	—
186	C₂×C₄×C₅	—	2	2	no	—
187	C₂×C₄×C₅	—	2	1	no	—
188	C₂×C₄×C₅	—	2	2	no	—
189	C₂×C₄×C₅	—	2	2	no	—
190	C₂×C₄×C₅	—	2	2	no	—
191	C₂×C₄×C₅	—	2	1	no	—
192	C₂×C₄×C₅	—	2	2	no	—
193	C₂×C₄×C₅	—	2	1	no	—
194	C₂×C₄×C₅	—	2	1	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	2	no	—
202	C₂×C₄×C₅	C₄×Q₈	1	2	yes	—
203	C₂×C₄×C₅	C₄×Q₈	1	2	yes	—
204	C₂×C₄×C₅	C₂×M₁₆	1	4	yes	—
205	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
206	C₂×C₄×C₅	#131	1	2	yes	—
207	C₂×C₄×C₅	#131	1	2	yes	—
208	C₂×C₄×C₅	#131	1	2	yes	—
209	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
210	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
211	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
212	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
213	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
214	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
215	C₅×C₈	—	2	2	no	—
216	C₅×C₈	—	2	2	no	—
217	C₅×C₈	—	4	1	no	—
218	C₅×C₈	—	4	1	no	—
219	C₅×C₈	—	4	2	no	—
220	C₅×C₈	—	4	2	no	—
221	C₂²×Q₈	C₂×C₄×C₅	1	2	yes	—
222	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
223	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
224	C₂²×C₈	C₂³×C₅	1	2	yes	—
225	C₂²×C₈	C₂³×C₅	1	2	yes	—
226	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
227	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
228	C₄⋊Q₈	—	2	4	no	—
229	C₄×Q₈	—	4	2	no	—
230	C₄×Q₈	—	4	2	no	—
231	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
232	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
233	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
234	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
235	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
236	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
237	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
238	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
239	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
240	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
241	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
242	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
243	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
244	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
245	C₂×C₄²	C₂³×C₅	1	2	yes	—
246	C₂×C₄²	C₂³×C₅	1	2	yes	—
247	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
248	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
249	C₄⋊C₈	—	2	2	no	—
250	C₄⋊C₈	—	2	2	no	—
251	C₄⋊C₈	—	4	2	no	—
252	C₄⋊C₈	—	4	2	no	—
253	#97	—	4	2	no	—
254	C₄×C₈	—	2	2	no	—
255	C₄×C₈	—	4	2	no	—
256	C₄×C₈	C₅×Q₈	1	4	yes	complemented
257	#95	C₂×C₄×C₅	1	2	yes	—
258	#95	C₂×C₄×C₅	1	2	yes	—
259	#95	C₂×C₄×C₅	1	2	yes	—
260	#95	C₂×C₄×C₅	1	2	yes	—
261	C₂²×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
262	C₂²×C₅	#518	1	1	yes	characteristic
263	C₂²×C₅	#519	1	1	yes	characteristic
264	C₂²×C₅	C₂²×M₁₆	1	1	yes	characteristic
265	C₂²×C₅	C₂×#131	1	1	yes	characteristic
266	C₂²×C₅	C₂×#131	1	1	yes	characteristic
267	C₂²×C₅	C₂×#131	1	1	yes	characteristic
268	C₄×C₅	—	2	2	no	—
269	C₄×C₅	—	2	4	no	—
270	C₄×C₅	—	2	2	no	—
271	C₄×C₅	—	2	2	no	—
272	C₄×C₅	—	4	2	no	—
273	C₄×C₅	—	4	1	no	—
274	C₄×C₅	—	4	2	no	—
275	C₄×C₅	—	4	2	no	—
276	C₄×C₅	—	4	1	no	—
277	C₄×C₅	#446	1	4	yes	—
278	C₄×C₅	#542	1	1	yes	characteristic
279	C₄×C₅	#542	1	1	yes	characteristic
280	C₄×C₅	#544	1	1	yes	characteristic
281	C₄×C₅	#544	1	1	yes	characteristic
282	C₂×Q₈	—	2	4	no	—
283	C₂×Q₈	—	2	4	no	—
284	C₂×Q₈	—	4	2	no	—
285	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
286	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
287	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
288	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
289	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
290	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
291	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
292	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
293	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
294	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
295	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
296	C₂×C₈	—	2	1	no	—
297	C₂×C₈	—	2	1	no	—
298	C₂×C₈	—	2	1	no	—
299	C₂×C₈	—	2	1	no	—
300	C₂×C₈	—	2	1	no	—
301	C₂×C₈	—	2	1	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	1	no	—
307	C₂×C₈	—	2	1	no	—
308	C₂×C₈	—	2	1	no	—
309	C₂×C₈	—	2	1	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	C₂×C₅×Q₈	1	2	yes	—
313	C₂×C₈	C₂×C₅×Q₈	1	2	yes	—
314	C₄⋊C₄	—	2	4	no	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	2	4	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	4	2	no	—
320	C₄⋊C₄	—	4	2	no	—
321	C₄⋊C₄	—	4	2	no	—
322	C₄⋊C₄	C₅×M₁₆	1	4	yes	—
323	C₄²	—	2	2	no	—
324	C₄²	—	2	2	no	—
325	C₄²	—	2	2	no	—
326	C₄²	—	2	2	no	—
327	C₄²	—	2	2	no	—
328	C₄²	—	2	2	no	—
329	C₄²	—	2	2	no	—
330	C₄²	—	2	2	no	—
331	C₄²	—	2	1	no	—
332	C₄²	—	2	1	no	—
333	C₄²	—	2	1	no	—
334	C₄²	—	2	1	no	—
335	C₄²	C₂×C₅×Q₈	1	2	yes	—
336	C₄²	C₅×#41	1	2	yes	—
337	C₂×C₅	#2331	1	1	yes	characteristic
338	C₂×C₅	C₂×#446	1	1	yes	characteristic
339	C₂×C₅	#2960	1	1	yes	characteristic
340	C₂×C₅	#2974	1	1	yes	characteristic
341	C₂×C₅	#2979	1	1	yes	characteristic
342	C₂×C₅	#2984	1	1	yes	characteristic
343	C₂×C₅	#2986	1	1	yes	characteristic
344	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
345	Q₈	—	4	8	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	C₄×C₅×Q₈	1	2	yes	—
370	C₂×C₄	C₄×C₅×Q₈	1	2	yes	—
371	C₂×C₄	C₂×C₅×M₁₆	1	4	yes	—
372	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
373	C₂×C₄	C₅×#131	1	2	yes	—
374	C₂×C₄	C₅×#131	1	2	yes	—
375	C₂×C₄	C₅×#131	1	2	yes	—
376	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
377	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
378	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
379	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
380	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
381	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
382	C₈	—	2	2	no	—
383	C₈	—	2	2	no	—
384	C₈	—	4	1	no	—
385	C₈	—	4	1	no	—
386	C₈	—	4	2	no	—
387	C₈	—	4	2	no	—
388	C₅	#22309	1	1	yes	characteristic, direct product factor, Sylow
389	C₂²	C₂×C₄×C₅×Q₈	1	1	yes	characteristic
390	C₂²	C₅×#518	1	1	yes	characteristic
391	C₂²	C₅×#519	1	1	yes	characteristic
392	C₂²	C₂²×C₅×M₁₆	1	1	yes	characteristic
393	C₂²	C₂×C₅×#131	1	1	yes	characteristic
394	C₂²	C₂×C₅×#131	1	1	yes	characteristic
395	C₂²	C₂×C₅×#131	1	1	yes	characteristic
396	C₄	—	2	2	no	—
397	C₄	—	2	2	no	—
398	C₄	—	2	4	no	—
399	C₄	—	2	2	no	—
400	C₄	—	4	1	no	—
401	C₄	—	4	2	no	—
402	C₄	—	4	1	no	—
403	C₄	—	4	2	no	—
404	C₄	—	4	2	no	—
405	C₄	C₅×#446	1	4	yes	—
406	C₄	C₅×#542	1	1	yes	characteristic
407	C₄	C₅×#542	1	1	yes	characteristic
408	C₄	C₅×#544	1	1	yes	characteristic
409	C₄	C₅×#544	1	1	yes	characteristic
410	C₂	C₅×#2331	1	1	yes	characteristic
411	C₂	C₂×C₅×#446	1	1	yes	characteristic
412	C₂	C₅×#2960	1	1	yes	characteristic
413	C₂	C₅×#2974	1	1	yes	characteristic
414	C₂	C₅×#2979	1	1	yes	characteristic
415	C₂	C₅×#2984	1	1	yes	characteristic
416	C₂	C₅×#2986	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₅	C₂⁴
commutator	C₂³	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
socle, prime radical	C₂³×C₅	C₂³×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
41. #22309	C₅	direct (N × H)
77. C₄×C₅×C₈	Q₈	semidirect
256. C₄×C₈	C₅×Q₈	semidirect
388. C₅	#22309	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₅×C₄⋊Q₈	2
C₅×#1985	2
C₅×#1984	2
C₅×#1939	2
C₅×#1917	2
C₅×#1916	2
C₅×#1831	2
C₅×#1770	2
C₅×C₈×C₄⋊C₄	2
C₅×#1744	2
#22309	5

Subgroups — C5×#22309 #11945029

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22309 #11945029