Subgroups — C₅×#8578 #11931298

Order 1280.

658 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₅×#1797	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#328	C₂	1	2	yes	maximal
4	C₅×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
5	C₅×#1294	C₂	1	2	yes	maximal
6	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₅×Q₈	C₄	1	1	yes	characteristic, complemented
8	C₂²×C₅×C₄⋊C₄	—	2	1	no	—
9	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
10	C₂×C₅×C₄⋊C₈	—	2	1	no	—
11	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
12	C₅×#391	C₄	1	1	yes	characteristic, complemented
13	C₅×#389	C₄	1	1	yes	characteristic, complemented
14	C₅×#387	—	2	1	no	—
15	C₅×#385	—	2	1	no	—
16	C₅×#380	C₂²	1	1	yes	characteristic
17	C₄×C₅×C₄⋊C₄	—	2	1	no	—
18	C₄×C₅×C₄⋊C₄	C₄	1	1	yes	characteristic, complemented
19	C₄×C₅×C₂²⋊C₄	—	2	1	no	—
20	C₂×C₅×#95	—	2	1	no	—
21	C₂×C₅×#95	C₂²	1	2	yes	—
22	C₅×#336	—	2	1	no	—
23	C₅×#328	—	2	4	no	—
24	#8578	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂²×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
26	C₂³×C₄×C₅	—	2	2	no	—
27	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
28	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
29	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
30	C₂²×C₅×C₈	—	2	2	no	—
31	C₅×C₂²⋊Q₈	—	2	1	no	—
32	C₅×C₂²⋊Q₈	—	2	1	no	—
33	C₅×C₂²⋊Q₈	D₄	1	2	yes	—
34	C₅×C₂²⋊Q₈	Q₈	1	2	yes	—
35	C₄×C₅×Q₈	—	4	2	no	—
36	C₂×C₅×C₄⋊C₄	—	2	1	no	—
37	C₂×C₅×C₄⋊C₄	—	2	4	no	—
38	C₂×C₅×C₄⋊C₄	—	2	1	no	—
39	C₂×C₅×C₄⋊C₄	—	2	1	no	—
40	C₂×C₅×C₄⋊C₄	—	4	2	no	—
41	C₂×C₅×C₄⋊C₄	—	4	2	no	—
42	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
43	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
44	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
45	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
46	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
47	C₂×C₄²×C₅	—	2	1	no	—
48	C₂×C₄²×C₅	—	2	1	no	—
49	C₂×C₄²×C₅	—	4	2	no	—
50	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
53	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
54	C₅×C₄⋊C₈	—	4	2	no	—
55	C₅×C₂²⋊C₈	—	2	2	no	—
56	C₅×C₂²⋊C₈	—	2	2	no	—
57	C₅×#95	—	2	1	no	—
58	C₅×#95	—	2	1	no	—
59	C₅×#95	—	2	1	no	—
60	C₅×#95	—	2	1	no	—
61	C₅×#95	—	2	1	no	—
62	C₅×#95	—	2	2	no	—
63	C₅×#95	—	2	2	no	—
64	C₅×#95	—	4	2	no	—
65	C₄×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic
66	#1797	C₂×C₅	1	1	yes	characteristic
67	C₂×#328	C₂×C₅	1	2	yes	—
68	C₄⋊#95	C₂×C₅	1	1	yes	characteristic
69	#1294	C₂×C₅	1	2	yes	—
70	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
71	C₂×C₅×Q₈	—	2	1	no	—
72	C₂×C₅×Q₈	—	4	1	no	—
73	C₂×C₅×Q₈	—	4	1	no	—
74	C₂×C₅×Q₈	C₄⋊C₄	1	2	yes	complemented
75	C₂²×C₄×C₅	—	2	1	no	—
76	C₂²×C₄×C₅	—	2	1	no	—
77	C₂²×C₄×C₅	—	2	2	no	—
78	C₂²×C₄×C₅	—	2	2	no	—
79	C₂²×C₄×C₅	—	2	1	no	—
80	C₂²×C₄×C₅	—	2	1	no	—
81	C₂²×C₄×C₅	—	2	4	no	—
82	C₂²×C₄×C₅	—	2	1	no	—
83	C₂²×C₄×C₅	—	2	1	no	—
84	C₂²×C₄×C₅	—	4	1	no	—
85	C₂²×C₄×C₅	—	4	1	no	—
86	C₂²×C₄×C₅	—	4	1	no	—
87	C₂²×C₄×C₅	—	4	1	no	—
88	C₂²×C₄×C₅	—	4	2	no	—
89	C₂²×C₄×C₅	—	4	2	no	—
90	C₂²×C₄×C₅	—	4	2	no	—
91	C₂²×C₄×C₅	—	4	2	no	—
92	C₂²×C₄×C₅	—	4	2	no	—
93	C₂²×C₄×C₅	—	4	2	no	—
94	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
95	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
96	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
97	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
98	C₂²×C₄×C₅	SD₁₆	1	2	yes	—
99	C₂²×C₄×C₅	Q₁₆	1	2	yes	—
100	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
104	C₂²×C₄×C₅	#41	1	1	yes	characteristic
105	C₂²×C₄×C₅	#41	1	1	yes	characteristic
106	C₂×C₅×C₈	—	4	2	no	—
107	C₂×C₅×C₈	—	4	2	no	—
108	C₂×C₅×C₈	—	4	2	no	—
109	C₅×C₄⋊C₄	—	2	1	no	—
110	C₅×C₄⋊C₄	—	2	2	no	—
111	C₅×C₄⋊C₄	—	2	2	no	—
112	C₅×C₄⋊C₄	—	4	1	no	—
113	C₅×C₄⋊C₄	—	4	1	no	—
114	C₅×C₄⋊C₄	—	4	8	no	—
115	C₅×C₄⋊C₄	—	4	2	no	—
116	C₅×C₄⋊C₄	—	4	2	no	—
117	C₅×C₄⋊C₄	C₄⋊C₄	1	2	yes	complemented
118	C₅×C₂²⋊C₄	—	2	2	no	—
119	C₅×C₂²⋊C₄	—	2	2	no	—
120	C₅×C₂²⋊C₄	—	4	1	no	—
121	C₅×C₂²⋊C₄	—	4	1	no	—
122	C₄²×C₅	—	2	2	no	—
123	C₄²×C₅	—	2	2	no	—
124	C₄²×C₅	—	4	1	no	—
125	C₄²×C₅	—	4	1	no	—
126	C₄²×C₅	—	4	2	no	—
127	C₄²×C₅	—	4	2	no	—
128	C₂×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
129	C₂×C₄×Q₈	C₄×C₅	1	1	yes	characteristic, complemented
130	C₂²×C₄⋊C₄	—	2	1	no	—
131	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
132	C₂×C₄⋊C₈	—	2	1	no	—
133	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
134	#391	C₄×C₅	1	1	yes	characteristic, complemented
135	#389	C₄×C₅	1	1	yes	characteristic, complemented
136	#387	—	2	1	no	—
137	#385	—	2	1	no	—
138	#380	C₂²×C₅	1	1	yes	characteristic
139	C₄×C₄⋊C₄	—	2	1	no	—
140	C₄×C₄⋊C₄	C₄×C₅	1	1	yes	characteristic, complemented
141	C₄×C₂²⋊C₄	—	2	1	no	—
142	C₂×#95	—	2	1	no	—
143	C₂×#95	C₂²×C₅	1	2	yes	—
144	#336	—	2	1	no	—
145	#328	—	2	4	no	—
146	C₂³×C₅	—	2	1	no	—
147	C₂³×C₅	—	2	1	no	—
148	C₂³×C₅	—	2	1	no	—
149	C₂³×C₅	—	2	1	no	—
150	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
151	C₂³×C₅	#121	1	1	yes	characteristic
152	C₂³×C₅	C₂²⋊Q₈	1	1	yes	characteristic
153	C₂³×C₅	C₂×SD₁₆	1	1	yes	characteristic
154	C₂³×C₅	C₂×Q₁₆	1	1	yes	characteristic
155	C₂³×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
156	C₂³×C₅	#137	1	1	yes	characteristic
157	C₅×Q₈	—	4	2	no	—
158	C₅×Q₈	—	4	2	no	—
159	C₂×C₄×C₅	—	2	4	no	—
160	C₂×C₄×C₅	—	2	4	no	—
161	C₂×C₄×C₅	—	2	1	no	—
162	C₂×C₄×C₅	—	2	1	no	—
163	C₂×C₄×C₅	—	2	1	no	—
164	C₂×C₄×C₅	—	2	1	no	—
165	C₂×C₄×C₅	—	2	1	no	—
166	C₂×C₄×C₅	—	2	1	no	—
167	C₂×C₄×C₅	—	2	1	no	—
168	C₂×C₄×C₅	—	2	1	no	—
169	C₂×C₄×C₅	—	2	1	no	—
170	C₂×C₄×C₅	—	2	1	no	—
171	C₂×C₄×C₅	—	2	1	no	—
172	C₂×C₄×C₅	—	2	1	no	—
173	C₂×C₄×C₅	—	2	2	no	—
174	C₂×C₄×C₅	—	2	2	no	—
175	C₂×C₄×C₅	—	4	2	no	—
176	C₂×C₄×C₅	—	4	2	no	—
177	C₂×C₄×C₅	—	4	1	no	—
178	C₂×C₄×C₅	—	4	1	no	—
179	C₂×C₄×C₅	—	4	1	no	—
180	C₂×C₄×C₅	—	4	1	no	—
181	C₂×C₄×C₅	—	4	1	no	—
182	C₂×C₄×C₅	—	4	1	no	—
183	C₂×C₄×C₅	—	4	1	no	—
184	C₂×C₄×C₅	—	4	1	no	—
185	C₂×C₄×C₅	—	4	4	no	—
186	C₂×C₄×C₅	—	4	4	no	—
187	C₂×C₄×C₅	—	4	4	no	—
188	C₂×C₄×C₅	—	4	1	no	—
189	C₂×C₄×C₅	—	4	1	no	—
190	C₂×C₄×C₅	—	4	1	no	—
191	C₂×C₄×C₅	—	4	1	no	—
192	C₂×C₄×C₅	—	4	1	no	—
193	C₂×C₄×C₅	—	4	1	no	—
194	C₂×C₄×C₅	—	8	2	no	—
195	C₂×C₄×C₅	—	8	2	no	—
196	C₂×C₄×C₅	—	8	2	no	—
197	C₂×C₄×C₅	—	8	2	no	—
198	C₂×C₄×C₅	#99	1	2	yes	—
199	C₂×C₄×C₅	#103	1	2	yes	—
200	C₂×C₄×C₅	#103	1	2	yes	—
201	C₂×C₄×C₅	#104	1	2	yes	—
202	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
203	C₂×C₄×C₅	#117	1	1	yes	characteristic
204	C₂×C₄×C₅	#121	1	1	yes	characteristic
205	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
206	C₅×C₈	—	8	2	no	—
207	C₂²×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
208	C₂³×C₄	—	2	2	no	—
209	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
210	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
211	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
212	C₂²×C₈	—	2	2	no	—
213	C₂²⋊Q₈	—	2	1	no	—
214	C₂²⋊Q₈	—	2	1	no	—
215	C₂²⋊Q₈	C₅×D₄	1	2	yes	—
216	C₂²⋊Q₈	C₅×Q₈	1	2	yes	—
217	C₄×Q₈	—	4	2	no	—
218	C₂×C₄⋊C₄	—	2	1	no	—
219	C₂×C₄⋊C₄	—	2	4	no	—
220	C₂×C₄⋊C₄	—	2	1	no	—
221	C₂×C₄⋊C₄	—	2	1	no	—
222	C₂×C₄⋊C₄	—	4	2	no	—
223	C₂×C₄⋊C₄	—	4	2	no	—
224	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
225	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
226	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
227	C₂×C₂²⋊C₄	—	2	1	no	—
228	C₂×C₂²⋊C₄	—	2	1	no	—
229	C₂×C₄²	—	2	1	no	—
230	C₂×C₄²	—	2	1	no	—
231	C₂×C₄²	—	4	2	no	—
232	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
233	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
234	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
235	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
236	C₄⋊C₈	—	4	2	no	—
237	C₂²⋊C₈	—	2	2	no	—
238	C₂²⋊C₈	—	2	2	no	—
239	#95	—	2	1	no	—
240	#95	—	2	1	no	—
241	#95	—	2	1	no	—
242	#95	—	2	1	no	—
243	#95	—	2	1	no	—
244	#95	—	2	2	no	—
245	#95	—	2	2	no	—
246	#95	—	4	2	no	—
247	C₂²×C₅	—	2	1	no	—
248	C₂²×C₅	—	2	1	no	—
249	C₂²×C₅	—	2	1	no	—
250	C₂²×C₅	—	2	1	no	—
251	C₂²×C₅	—	2	1	no	—
252	C₂²×C₅	—	2	1	no	—
253	C₂²×C₅	—	2	1	no	—
254	C₂²×C₅	—	2	1	no	—
255	C₂²×C₅	—	2	1	no	—
256	C₂²×C₅	—	2	1	no	—
257	C₂²×C₅	—	2	1	no	—
258	C₂²×C₅	—	2	1	no	—
259	C₂²×C₅	#380	1	1	yes	characteristic
260	C₂²×C₅	C₂×#99	1	1	yes	characteristic
261	C₂²×C₅	#410	1	1	yes	characteristic
262	C₂²×C₅	C₂×#103	1	1	yes	characteristic
263	C₂²×C₅	#417	1	1	yes	characteristic
264	C₂²×C₅	C₂×#104	1	1	yes	characteristic
265	C₂²×C₅	#421	1	1	yes	characteristic
266	C₂²×C₅	#460	1	1	yes	characteristic
267	C₂²×C₅	#462	1	1	yes	characteristic
268	C₂²×C₅	#475	1	1	yes	characteristic
269	C₂²×C₅	#477	1	1	yes	characteristic
270	C₄×C₅	—	2	1	no	—
271	C₄×C₅	—	2	1	no	—
272	C₄×C₅	—	2	1	no	—
273	C₄×C₅	—	2	1	no	—
274	C₄×C₅	—	2	2	no	—
275	C₄×C₅	—	2	2	no	—
276	C₄×C₅	—	2	2	no	—
277	C₄×C₅	—	2	2	no	—
278	C₄×C₅	—	4	2	no	—
279	C₄×C₅	—	4	2	no	—
280	C₄×C₅	—	8	4	no	—
281	C₄×C₅	—	8	1	no	—
282	C₄×C₅	—	8	1	no	—
283	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
284	C₂×Q₈	—	2	1	no	—
285	C₂×Q₈	—	4	1	no	—
286	C₂×Q₈	—	4	1	no	—
287	C₂×Q₈	C₅×C₄⋊C₄	1	2	yes	complemented
288	C₂²×C₄	—	2	1	no	—
289	C₂²×C₄	—	2	1	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	1	no	—
293	C₂²×C₄	—	2	1	no	—
294	C₂²×C₄	—	2	4	no	—
295	C₂²×C₄	—	2	1	no	—
296	C₂²×C₄	—	2	1	no	—
297	C₂²×C₄	—	4	1	no	—
298	C₂²×C₄	—	4	1	no	—
299	C₂²×C₄	—	4	1	no	—
300	C₂²×C₄	—	4	1	no	—
301	C₂²×C₄	—	4	2	no	—
302	C₂²×C₄	—	4	2	no	—
303	C₂²×C₄	—	4	2	no	—
304	C₂²×C₄	—	4	2	no	—
305	C₂²×C₄	—	4	2	no	—
306	C₂²×C₄	—	4	2	no	—
307	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
308	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
309	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
310	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
311	C₂²×C₄	C₅×SD₁₆	1	2	yes	—
312	C₂²×C₄	C₅×Q₁₆	1	2	yes	—
313	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
314	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
315	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
316	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
317	C₂²×C₄	C₅×#41	1	1	yes	characteristic
318	C₂²×C₄	C₅×#41	1	1	yes	characteristic
319	C₂×C₈	—	4	2	no	—
320	C₂×C₈	—	4	2	no	—
321	C₂×C₈	—	4	2	no	—
322	C₄⋊C₄	—	2	1	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	4	1	no	—
326	C₄⋊C₄	—	4	1	no	—
327	C₄⋊C₄	—	4	8	no	—
328	C₄⋊C₄	—	4	2	no	—
329	C₄⋊C₄	—	4	2	no	—
330	C₄⋊C₄	C₅×C₄⋊C₄	1	2	yes	complemented
331	C₂²⋊C₄	—	2	2	no	—
332	C₂²⋊C₄	—	2	2	no	—
333	C₂²⋊C₄	—	4	1	no	—
334	C₂²⋊C₄	—	4	1	no	—
335	C₄²	—	2	2	no	—
336	C₄²	—	2	2	no	—
337	C₄²	—	4	1	no	—
338	C₄²	—	4	1	no	—
339	C₄²	—	4	2	no	—
340	C₄²	—	4	2	no	—
341	C₂×C₅	—	2	1	no	—
342	C₂×C₅	—	2	1	no	—
343	C₂×C₅	—	2	1	no	—
344	C₂×C₅	—	2	1	no	—
345	C₂×C₅	#1503	1	1	yes	characteristic
346	C₂×C₅	#1504	1	1	yes	characteristic
347	C₂×C₅	#1512	1	1	yes	characteristic
348	C₂×C₅	#1520	1	1	yes	characteristic
349	C₂×C₅	#1799	1	1	yes	characteristic
350	C₂×C₅	#1803	1	1	yes	characteristic
351	C₂×C₅	#1806	1	1	yes	characteristic
352	C₂³	—	2	1	no	—
353	C₂³	—	2	1	no	—
354	C₂³	—	2	1	no	—
355	C₂³	—	2	1	no	—
356	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
357	C₂³	C₅×#121	1	1	yes	characteristic
358	C₂³	C₅×C₂²⋊Q₈	1	1	yes	characteristic
359	C₂³	C₂×C₅×SD₁₆	1	1	yes	characteristic
360	C₂³	C₂×C₅×Q₁₆	1	1	yes	characteristic
361	C₂³	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
362	C₂³	C₅×#137	1	1	yes	characteristic
363	Q₈	—	4	2	no	—
364	Q₈	—	4	2	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	4	no	—
392	C₂×C₄	—	4	4	no	—
393	C₂×C₄	—	4	4	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	8	2	no	—
401	C₂×C₄	—	8	2	no	—
402	C₂×C₄	—	8	2	no	—
403	C₂×C₄	—	8	2	no	—
404	C₂×C₄	C₅×#99	1	2	yes	—
405	C₂×C₄	C₅×#103	1	2	yes	—
406	C₂×C₄	C₅×#103	1	2	yes	—
407	C₂×C₄	C₅×#104	1	2	yes	—
408	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
409	C₂×C₄	C₅×#117	1	1	yes	characteristic
410	C₂×C₄	C₅×#121	1	1	yes	characteristic
411	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
412	C₈	—	8	2	no	—
413	C₅	#8578	1	1	yes	characteristic, direct product factor, Sylow
414	C₂²	—	2	1	no	—
415	C₂²	—	2	1	no	—
416	C₂²	—	2	1	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	2	1	no	—
422	C₂²	—	2	1	no	—
423	C₂²	—	2	1	no	—
424	C₂²	—	2	1	no	—
425	C₂²	—	2	1	no	—
426	C₂²	C₅×#380	1	1	yes	characteristic
427	C₂²	C₂×C₅×#99	1	1	yes	characteristic
428	C₂²	C₅×#410	1	1	yes	characteristic
429	C₂²	C₂×C₅×#103	1	1	yes	characteristic
430	C₂²	C₅×#417	1	1	yes	characteristic
431	C₂²	C₂×C₅×#104	1	1	yes	characteristic
432	C₂²	C₅×#421	1	1	yes	characteristic
433	C₂²	C₅×#460	1	1	yes	characteristic
434	C₂²	C₅×#462	1	1	yes	characteristic
435	C₂²	C₅×#475	1	1	yes	characteristic
436	C₂²	C₅×#477	1	1	yes	characteristic
437	C₄	—	2	2	no	—
438	C₄	—	2	2	no	—
439	C₄	—	2	2	no	—
440	C₄	—	2	2	no	—
441	C₄	—	2	1	no	—
442	C₄	—	2	1	no	—
443	C₄	—	2	1	no	—
444	C₄	—	2	1	no	—
445	C₄	—	4	2	no	—
446	C₄	—	4	2	no	—
447	C₄	—	8	4	no	—
448	C₄	—	8	1	no	—
449	C₄	—	8	1	no	—
450	C₂	—	2	1	no	—
451	C₂	—	2	1	no	—
452	C₂	—	2	1	no	—
453	C₂	—	2	1	no	—
454	C₂	C₅×#1503	1	1	yes	characteristic
455	C₂	C₅×#1504	1	1	yes	characteristic
456	C₂	C₅×#1512	1	1	yes	characteristic
457	C₂	C₅×#1520	1	1	yes	characteristic
458	C₂	C₅×#1799	1	1	yes	characteristic
459	C₂	C₅×#1803	1	1	yes	characteristic
460	C₂	C₅×#1806	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
7. C₂×C₄×C₅×Q₈	C₄	semidirect
12. C₅×#391	C₄	semidirect
13. C₅×#389	C₄	semidirect
18. C₄×C₅×C₄⋊C₄	C₄	semidirect
24. #8578	C₅	direct (N × H)
74. C₂×C₅×Q₈	C₄⋊C₄	semidirect
117. C₅×C₄⋊C₄	C₄⋊C₄	semidirect
129. C₂×C₄×Q₈	C₄×C₅	semidirect
134. #391	C₄×C₅	semidirect
135. #389	C₄×C₅	semidirect
140. C₄×C₄⋊C₄	C₄×C₅	semidirect
287. C₂×Q₈	C₅×C₄⋊C₄	semidirect
330. C₄⋊C₄	C₅×C₄⋊C₄	semidirect
413. C₅	#8578	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×C₂²⋊Q₈	2
C₅×#1797	2
C₂×C₅×#328	2
C₅×C₄⋊#95	2
C₅×#1294	2
#8578	5

Subgroups — C5×#8578 #11931298

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#8578 #11931298