Subgroups — C₅×#22964 #11945684

Order 1280.

822 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#475	C₂	1	1	yes	maximal, characteristic
2	C₅×#2365	C₂	1	1	yes	maximal, characteristic
3	C₅×Q₈×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
4	C₅×#1990	C₂	1	1	yes	maximal, characteristic
5	C₅×#1948	C₂	1	1	yes	maximal, characteristic
6	C₅×#1941	C₂	1	2	yes	maximal
7	C₅×#1920	C₂	1	2	yes	maximal
8	C₅×#1865	C₂	1	2	yes	maximal
9	C₅×C₈×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
10	C₄×C₅×#103	C₂	1	2	yes	maximal
11	C₄×C₅×#103	C₂	1	1	yes	maximal, characteristic
12	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₅×Q₈	—	2	1	no	—
14	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
15	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
16	C₅×#475	C₄	1	8	yes	complemented
17	C₂×C₅×#106	C₂²	1	2	yes	—
18	C₂×C₅×#106	C₂²	1	2	yes	—
19	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₅×#103	C₂²	1	1	yes	characteristic
21	C₂×C₅×#103	C₂²	1	2	yes	—
22	C₂×C₅×#103	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
25	C₅×#391	—	2	1	no	—
26	C₅×#389	—	2	2	no	—
27	C₅×#389	C₂²	1	2	yes	—
28	C₅×#389	C₂²	1	2	yes	—
29	C₅×#387	—	2	2	no	—
30	C₅×#384	—	2	1	no	—
31	C₅×#384	C₂²	1	1	yes	characteristic
32	C₄×C₅×C₄⋊C₄	—	2	1	no	—
33	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
34	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₅×#340	C₂²	1	1	yes	characteristic
37	C₅×#340	C₂²	1	2	yes	—
38	C₅×#340	C₂²	1	1	yes	characteristic
39	C₅×#340	C₂²	1	2	yes	—
40	C₅×#340	C₂²	1	2	yes	—
41	C₅×#336	C₂²	1	2	yes	—
42	#22964	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂²×C₅×Q₈	—	2	1	no	—
44	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
45	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
46	C₂²×C₅×C₈	C₂³	1	2	yes	—
47	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
48	C₅×C₄⋊Q₈	—	2	2	no	—
49	C₅×C₄⋊Q₈	C₂×C₄	1	4	yes	—
50	C₄×C₅×Q₈	—	2	2	no	—
51	C₄×C₅×Q₈	—	2	4	no	—
52	C₄×C₅×Q₈	—	4	2	no	—
53	C₄×C₅×Q₈	—	4	4	no	—
54	C₄×C₅×Q₈	C₂×C₄	1	4	yes	—
55	C₂×C₅×C₄⋊C₄	—	2	1	no	—
56	C₂×C₅×C₄⋊C₄	—	2	1	no	—
57	C₂×C₅×C₄⋊C₄	—	2	1	no	—
58	C₂×C₅×C₄⋊C₄	—	2	2	no	—
59	C₂×C₅×C₄⋊C₄	—	2	2	no	—
60	C₂×C₅×C₄⋊C₄	—	2	2	no	—
61	C₂×C₅×C₄⋊C₄	—	2	1	no	—
62	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
63	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
64	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
65	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
66	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
67	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
68	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₅	—	2	1	no	—
70	C₂×C₄²×C₅	—	2	2	no	—
71	C₂×C₄²×C₅	—	2	2	no	—
72	C₂×C₄²×C₅	—	2	1	no	—
73	C₂×C₄²×C₅	C₂³	1	2	yes	—
74	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
75	C₅×#106	—	4	2	no	—
76	C₅×#106	C₂×C₄	1	8	yes	—
77	C₅×C₄⋊C₈	C₂×C₄	1	4	yes	—
78	C₅×#103	—	2	2	no	—
79	C₅×#103	C₂×C₄	1	8	yes	—
80	C₅×#103	Q₈	1	4	yes	complemented
81	C₄×C₅×C₈	—	2	2	no	—
82	C₄×C₅×C₈	—	4	2	no	—
83	C₅×#95	—	2	2	no	—
84	C₅×#95	—	2	1	no	—
85	C₅×#95	—	2	2	no	—
86	C₅×#95	—	2	2	no	—
87	C₅×#95	D₄	1	2	yes	—
88	C₂×#475	C₂×C₅	1	1	yes	characteristic
89	#2365	C₂×C₅	1	1	yes	characteristic
90	Q₈×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
91	#1990	C₂×C₅	1	1	yes	characteristic
92	#1948	C₂×C₅	1	1	yes	characteristic
93	#1941	C₂×C₅	1	2	yes	—
94	#1920	C₂×C₅	1	2	yes	—
95	#1865	C₂×C₅	1	2	yes	—
96	C₈×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
97	C₄×#103	C₂×C₅	1	2	yes	—
98	C₄×#103	C₂×C₅	1	1	yes	characteristic
99	C₂×C₅×Q₈	—	2	4	no	—
100	C₂×C₅×Q₈	—	2	1	no	—
101	C₂×C₅×Q₈	—	2	1	no	—
102	C₂×C₅×Q₈	—	2	1	no	—
103	C₂×C₅×Q₈	—	4	2	no	—
104	C₂×C₅×Q₈	—	4	2	no	—
105	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
106	C₂×C₅×Q₈	C₂×Q₈	1	2	yes	—
107	C₂×C₅×Q₈	#41	1	2	yes	—
108	C₂²×C₄×C₅	—	2	1	no	—
109	C₂²×C₄×C₅	—	2	1	no	—
110	C₂²×C₄×C₅	—	2	1	no	—
111	C₂²×C₄×C₅	—	2	2	no	—
112	C₂²×C₄×C₅	—	2	2	no	—
113	C₂²×C₄×C₅	—	2	1	no	—
114	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
124	C₂×C₅×C₈	—	2	1	no	—
125	C₂×C₅×C₈	—	2	1	no	—
126	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
127	C₂×C₅×C₈	C₂×Q₈	1	2	yes	—
128	C₅×C₄⋊C₄	—	2	4	no	—
129	C₅×C₄⋊C₄	—	2	4	no	—
130	C₅×C₄⋊C₄	—	2	2	no	—
131	C₅×C₄⋊C₄	—	2	1	no	—
132	C₅×C₄⋊C₄	—	2	2	no	—
133	C₅×C₄⋊C₄	—	2	1	no	—
134	C₅×C₄⋊C₄	—	2	2	no	—
135	C₅×C₄⋊C₄	—	2	1	no	—
136	C₅×C₄⋊C₄	—	2	2	no	—
137	C₅×C₄⋊C₄	—	2	1	no	—
138	C₅×C₄⋊C₄	—	4	4	no	—
139	C₅×C₄⋊C₄	—	4	4	no	—
140	C₅×C₄⋊C₄	—	4	2	no	—
141	C₅×C₄⋊C₄	—	8	1	no	—
142	C₅×C₄⋊C₄	—	8	2	no	—
143	C₅×C₄⋊C₄	SD₁₆	1	4	yes	—
144	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
145	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
146	C₅×C₄⋊C₄	C₂×Q₈	1	2	yes	—
147	C₄²×C₅	—	2	4	no	—
148	C₄²×C₅	—	2	2	no	—
149	C₄²×C₅	—	2	2	no	—
150	C₄²×C₅	—	4	4	no	—
151	C₄²×C₅	—	4	4	no	—
152	C₄²×C₅	—	4	2	no	—
153	C₄²×C₅	C₂²×C₄	1	2	yes	—
154	C₄²×C₅	#41	1	2	yes	—
155	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
156	C₂×C₄×Q₈	—	2	1	no	—
157	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
158	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
159	#475	C₄×C₅	1	8	yes	complemented
160	C₂×#106	C₂²×C₅	1	2	yes	—
161	C₂×#106	C₂²×C₅	1	2	yes	—
162	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
163	C₂×#103	C₂²×C₅	1	1	yes	characteristic
164	C₂×#103	C₂²×C₅	1	2	yes	—
165	C₂×#103	C₂²×C₅	1	1	yes	characteristic
166	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
167	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
168	#391	—	2	1	no	—
169	#389	—	2	2	no	—
170	#389	C₂²×C₅	1	2	yes	—
171	#389	C₂²×C₅	1	2	yes	—
172	#387	—	2	2	no	—
173	#384	—	2	1	no	—
174	#384	C₂²×C₅	1	1	yes	characteristic
175	C₄×C₄⋊C₄	—	2	1	no	—
176	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
177	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
178	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
179	#340	C₂²×C₅	1	2	yes	—
180	#340	C₂²×C₅	1	1	yes	characteristic
181	#340	C₂²×C₅	1	2	yes	—
182	#340	C₂²×C₅	1	1	yes	characteristic
183	#340	C₂²×C₅	1	2	yes	—
184	#336	C₂²×C₅	1	2	yes	—
185	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
186	C₅×Q₈	—	2	2	no	—
187	C₅×Q₈	—	2	2	no	—
188	C₅×Q₈	—	2	2	no	—
189	C₅×Q₈	—	4	8	no	—
190	C₅×Q₈	C₄×Q₈	1	4	yes	complemented
191	C₂×C₄×C₅	—	2	2	no	—
192	C₂×C₄×C₅	—	2	2	no	—
193	C₂×C₄×C₅	—	2	2	no	—
194	C₂×C₄×C₅	—	2	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	4	no	—
200	C₂×C₄×C₅	—	2	2	no	—
201	C₂×C₄×C₅	—	2	2	no	—
202	C₂×C₄×C₅	—	2	2	no	—
203	C₂×C₄×C₅	—	2	2	no	—
204	C₂×C₄×C₅	—	4	1	no	—
205	C₂×C₄×C₅	—	4	2	no	—
206	C₂×C₄×C₅	—	4	2	no	—
207	C₂×C₄×C₅	—	4	1	no	—
208	C₂×C₄×C₅	—	4	1	no	—
209	C₂×C₄×C₅	—	4	1	no	—
210	C₂×C₄×C₅	—	4	2	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	1	no	—
216	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
217	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
218	C₂×C₄×C₅	C₂×SD₁₆	1	4	yes	—
219	C₂×C₄×C₅	C₂×SD₁₆	1	2	yes	—
220	C₂×C₄×C₅	#135	1	2	yes	—
221	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
222	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
223	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
224	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
225	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
226	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
227	C₅×C₈	—	2	4	no	—
228	C₅×C₈	—	2	2	no	—
229	C₅×C₈	—	4	1	no	—
230	C₂²×Q₈	—	2	1	no	—
231	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
232	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
233	C₂²×C₈	C₂³×C₅	1	2	yes	—
234	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
235	C₄⋊Q₈	—	2	2	no	—
236	C₄⋊Q₈	C₂×C₄×C₅	1	4	yes	—
237	C₄×Q₈	—	2	2	no	—
238	C₄×Q₈	—	2	4	no	—
239	C₄×Q₈	—	4	2	no	—
240	C₄×Q₈	—	4	4	no	—
241	C₄×Q₈	C₂×C₄×C₅	1	4	yes	—
242	C₂×C₄⋊C₄	—	2	1	no	—
243	C₂×C₄⋊C₄	—	2	1	no	—
244	C₂×C₄⋊C₄	—	2	2	no	—
245	C₂×C₄⋊C₄	—	2	2	no	—
246	C₂×C₄⋊C₄	—	2	1	no	—
247	C₂×C₄⋊C₄	—	2	2	no	—
248	C₂×C₄⋊C₄	—	2	1	no	—
249	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
250	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
251	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
252	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
253	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
254	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
255	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
256	C₂×C₄²	—	2	1	no	—
257	C₂×C₄²	—	2	2	no	—
258	C₂×C₄²	—	2	1	no	—
259	C₂×C₄²	—	2	2	no	—
260	C₂×C₄²	C₂³×C₅	1	2	yes	—
261	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
262	#106	—	4	2	no	—
263	#106	C₂×C₄×C₅	1	8	yes	—
264	C₄⋊C₈	C₂×C₄×C₅	1	4	yes	—
265	#103	—	2	2	no	—
266	#103	C₂×C₄×C₅	1	8	yes	—
267	#103	C₅×Q₈	1	4	yes	complemented
268	C₄×C₈	—	2	2	no	—
269	C₄×C₈	—	4	2	no	—
270	#95	—	2	2	no	—
271	#95	—	2	1	no	—
272	#95	—	2	2	no	—
273	#95	—	2	2	no	—
274	#95	C₅×D₄	1	2	yes	—
275	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
276	C₂²×C₅	#546	1	1	yes	characteristic
277	C₂²×C₅	D₄×Q₈	1	1	yes	characteristic
278	C₂²×C₅	C₂²×SD₁₆	1	1	yes	characteristic
279	C₂²×C₅	C₂×#135	1	1	yes	characteristic
280	C₂²×C₅	#577	1	1	yes	characteristic
281	C₂²×C₅	#578	1	1	yes	characteristic
282	C₄×C₅	—	2	4	no	—
283	C₄×C₅	—	2	2	no	—
284	C₄×C₅	—	2	4	no	—
285	C₄×C₅	—	4	2	no	—
286	C₄×C₅	—	4	4	no	—
287	C₄×C₅	—	4	2	no	—
288	C₄×C₅	—	4	2	no	—
289	C₄×C₅	—	8	1	no	—
290	C₄×C₅	—	8	2	no	—
291	C₄×C₅	C₄×SD₁₆	1	4	yes	—
292	C₄×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
293	C₄×C₅	#520	1	1	yes	characteristic
294	C₄×C₅	#552	1	1	yes	characteristic
295	C₄×C₅	#554	1	1	yes	characteristic
296	C₂×Q₈	—	2	4	no	—
297	C₂×Q₈	—	2	1	no	—
298	C₂×Q₈	—	2	1	no	—
299	C₂×Q₈	—	2	1	no	—
300	C₂×Q₈	—	4	2	no	—
301	C₂×Q₈	—	4	2	no	—
302	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
303	C₂×Q₈	C₂×C₅×Q₈	1	2	yes	—
304	C₂×Q₈	C₅×#41	1	2	yes	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	2	1	no	—
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
312	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
313	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
314	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
315	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
316	C₂×C₈	—	2	1	no	—
317	C₂×C₈	—	2	1	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	1	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	C₂²×C₄×C₅	1	4	yes	—
324	C₂×C₈	C₂×C₅×Q₈	1	2	yes	—
325	C₄⋊C₄	—	2	4	no	—
326	C₄⋊C₄	—	2	4	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	1	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	1	no	—
331	C₄⋊C₄	—	2	1	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	2	1	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	4	4	no	—
336	C₄⋊C₄	—	4	4	no	—
337	C₄⋊C₄	—	4	2	no	—
338	C₄⋊C₄	—	8	1	no	—
339	C₄⋊C₄	—	8	2	no	—
340	C₄⋊C₄	C₅×SD₁₆	1	4	yes	—
341	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
342	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
343	C₄⋊C₄	C₂×C₅×Q₈	1	2	yes	—
344	C₄²	—	2	4	no	—
345	C₄²	—	2	2	no	—
346	C₄²	—	2	2	no	—
347	C₄²	—	4	4	no	—
348	C₄²	—	4	4	no	—
349	C₄²	—	4	2	no	—
350	C₄²	C₂²×C₄×C₅	1	2	yes	—
351	C₄²	C₅×#41	1	2	yes	—
352	C₂×C₅	#2360	1	1	yes	characteristic
353	C₂×C₅	C₂×C₄×SD₁₆	1	1	yes	characteristic
354	C₂×C₅	#2947	1	1	yes	characteristic
355	C₂×C₅	#3298	1	1	yes	characteristic
356	C₂×C₅	#3304	1	1	yes	characteristic
357	C₂×C₅	Q₈×SD₁₆	1	1	yes	characteristic
358	C₂×C₅	#3383	1	1	yes	characteristic
359	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
360	Q₈	—	2	2	no	—
361	Q₈	—	2	2	no	—
362	Q₈	—	2	2	no	—
363	Q₈	—	4	8	no	—
364	Q₈	C₄×C₅×Q₈	1	4	yes	complemented
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	—	2	1	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
391	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
392	C₂×C₄	C₂×C₅×SD₁₆	1	4	yes	—
393	C₂×C₄	C₂×C₅×SD₁₆	1	2	yes	—
394	C₂×C₄	C₅×#135	1	2	yes	—
395	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
396	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
397	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
398	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
399	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
400	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
401	C₈	—	2	4	no	—
402	C₈	—	2	2	no	—
403	C₈	—	4	1	no	—
404	C₅	#22964	1	1	yes	characteristic, direct product factor, Sylow
405	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
406	C₂²	C₅×#546	1	1	yes	characteristic
407	C₂²	C₅×D₄×Q₈	1	1	yes	characteristic
408	C₂²	C₂²×C₅×SD₁₆	1	1	yes	characteristic
409	C₂²	C₂×C₅×#135	1	1	yes	characteristic
410	C₂²	C₅×#577	1	1	yes	characteristic
411	C₂²	C₅×#578	1	1	yes	characteristic
412	C₄	—	2	4	no	—
413	C₄	—	2	4	no	—
414	C₄	—	2	2	no	—
415	C₄	—	4	2	no	—
416	C₄	—	4	2	no	—
417	C₄	—	4	4	no	—
418	C₄	—	4	2	no	—
419	C₄	—	8	1	no	—
420	C₄	—	8	2	no	—
421	C₄	C₄×C₅×SD₁₆	1	4	yes	—
422	C₄	C₂×C₄×C₅×Q₈	1	1	yes	characteristic
423	C₄	C₅×#520	1	1	yes	characteristic
424	C₄	C₅×#552	1	1	yes	characteristic
425	C₄	C₅×#554	1	1	yes	characteristic
426	C₂	C₅×#2360	1	1	yes	characteristic
427	C₂	C₂×C₄×C₅×SD₁₆	1	1	yes	characteristic
428	C₂	C₅×#2947	1	1	yes	characteristic
429	C₂	C₅×#3298	1	1	yes	characteristic
430	C₂	C₅×#3304	1	1	yes	characteristic
431	C₂	C₅×Q₈×SD₁₆	1	1	yes	characteristic
432	C₂	C₅×#3383	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
16. C₅×#475	C₄	semidirect
42. #22964	C₅	direct (N × H)
80. C₅×#103	Q₈	semidirect
159. #475	C₄×C₅	semidirect
190. C₅×Q₈	C₄×Q₈	semidirect
267. #103	C₅×Q₈	semidirect
364. Q₈	C₄×C₅×Q₈	semidirect
404. C₅	#22964	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×#475	2
C₅×#2365	2
C₅×Q₈×C₄⋊C₄	2
C₅×#1990	2
C₅×#1948	2
C₅×#1941	2
C₅×#1920	2
C₅×#1865	2
C₅×C₈×C₄⋊C₄	2
C₄×C₅×#103	2
#22964	5

Subgroups — C5×#22964 #11945684

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22964 #11945684