Subgroups — C₅×#17892 #11940612

Order 1280.

648 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2965	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#446	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₅×#137	C₂	1	1	yes	maximal, characteristic
4	C₅×#1593	C₂	1	2	yes	maximal, complemented
5	C₅×#1592	C₂	1	2	yes	maximal, complemented
6	C₅×#1591	C₂	1	2	yes	maximal, complemented
7	C₅×#1590	C₂	1	2	yes	maximal, complemented
8	C₅×#1565	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1479	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1477	C₂	1	1	yes	maximal, characteristic
11	C₅×C₈×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#137	C₄	1	1	yes	characteristic
13	C₄×C₅×#41	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
15	C₅×#446	—	2	1	no	—
16	C₅×#446	—	2	1	no	—
17	C₅×#446	C₂²	1	2	yes	—
18	C₅×#446	C₂²	1	1	yes	characteristic
19	C₅×#446	C₂²	1	2	yes	—
20	C₅×#446	C₂²	1	1	yes	characteristic
21	C₅×#441	C₄	1	2	yes	—
22	C₅×#440	C₄	1	2	yes	—
23	C₄×C₅×Q₁₆	C₂²	1	2	yes	—
24	C₄×C₅×SD₁₆	C₂²	1	2	yes	—
25	C₅×#436	C₂²	1	1	yes	characteristic
26	C₅×#436	C₂²	1	1	yes	characteristic
27	C₅×#435	—	2	1	no	—
28	C₅×#435	—	2	1	no	—
29	C₅×#431	—	2	1	no	—
30	C₅×#431	C₂²	1	1	yes	characteristic
31	C₅×#431	C₂²	1	1	yes	characteristic
32	C₅×#428	C₄	1	1	yes	characteristic
33	C₂×C₅×C₄⋊C₈	—	2	1	no	—
34	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
35	C₅×#419	C₄	1	1	yes	characteristic
36	C₅×#417	C₄	1	1	yes	characteristic
37	C₄×C₅×M₁₆	—	2	1	no	—
38	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
39	C₂×C₅×#97	—	2	1	no	—
40	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
41	C₅×#335	C₂²	1	2	yes	—
42	C₅×#334	C₂²	1	2	yes	—
43	C₅×Q₈⋊C₈	C₂²	1	2	yes	—
44	C₅×Q₈⋊C₈	C₂²	1	2	yes	—
45	C₅×Q₈⋊C₈	C₂²	1	2	yes	—
46	C₅×D₄⋊C₈	C₂²	1	2	yes	—
47	C₅×#322	C₂²	1	2	yes	—
48	C₅×C₈²	C₂²	1	2	yes	—
49	#17892	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
50	C₂×C₅×#41	C₂×C₄	1	1	yes	characteristic
51	C₂²×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
52	C₅×#137	—	2	4	no	—
53	C₂×C₅×Q₁₆	C₂×C₄	1	2	yes	—
54	C₂×C₅×SD₁₆	C₂×C₄	1	2	yes	—
55	C₂×C₅×M₁₆	—	2	1	no	—
56	C₂×C₅×M₁₆	—	2	1	no	—
57	C₂×C₅×M₁₆	C₂×C₄	1	1	yes	characteristic
58	C₂×C₅×M₁₆	C₂×C₄	1	1	yes	characteristic
59	C₂²×C₅×C₈	—	2	1	no	—
60	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
61	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
62	C₄×C₅×Q₈	—	2	1	no	—
63	C₄×C₅×Q₈	—	2	1	no	—
64	C₄×C₅×Q₈	C₂×C₄	1	2	yes	—
65	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
66	C₄×C₅×Q₈	C₂³	1	2	yes	—
67	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
68	C₄×C₅×D₄	—	2	1	no	—
69	C₄×C₅×D₄	—	2	1	no	—
70	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
71	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
72	C₅×#117	—	2	1	no	—
73	C₅×#117	C₂×C₄	1	1	yes	characteristic
74	C₂×C₅×C₄⋊C₄	—	2	1	no	—
75	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄²×C₅	—	2	1	no	—
77	C₂×C₄²×C₅	—	2	1	no	—
78	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
79	C₅×#107	C₂×C₄	1	2	yes	—
80	C₅×#106	C₂×C₄	1	2	yes	—
81	C₅×C₄⋊C₈	—	2	2	no	—
82	C₅×C₄⋊C₈	—	2	2	no	—
83	C₅×C₄⋊C₈	—	2	1	no	—
84	C₅×C₄⋊C₈	—	2	1	no	—
85	C₅×C₄⋊C₈	—	2	1	no	—
86	C₅×C₄⋊C₈	—	2	1	no	—
87	C₅×C₄⋊C₈	C₂³	1	2	yes	—
88	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
89	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
90	C₅×#103	C₂×C₄	1	2	yes	—
91	C₅×#103	C₂×C₄	1	2	yes	—
92	C₅×#103	C₂×C₄	1	2	yes	—
93	C₅×#102	C₂×C₄	1	2	yes	—
94	C₅×C₂²⋊C₈	—	2	1	no	—
95	C₅×C₂²⋊C₈	—	2	1	no	—
96	C₅×C₂²⋊C₈	—	2	1	no	—
97	C₅×C₂²⋊C₈	—	2	1	no	—
98	C₅×#97	—	2	2	no	—
99	C₅×#97	—	2	2	no	—
100	C₅×#97	—	2	1	no	—
101	C₅×#97	—	2	1	no	—
102	C₅×#97	C₂×C₄	1	2	yes	—
103	C₄×C₅×C₈	—	2	1	no	—
104	C₄×C₅×C₈	D₄	1	1	yes	characteristic
105	C₄×C₅×C₈	D₄	1	1	yes	characteristic
106	C₄×C₅×C₈	C₂³	1	2	yes	—
107	C₄×C₅×C₈	C₂³	1	2	yes	—
108	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
109	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
110	#2965	C₂×C₅	1	1	yes	characteristic
111	C₂×#446	C₂×C₅	1	1	yes	characteristic, complemented
112	C₄×#137	C₂×C₅	1	1	yes	characteristic
113	#1593	C₂×C₅	1	2	yes	complemented
114	#1592	C₂×C₅	1	2	yes	complemented
115	#1591	C₂×C₅	1	2	yes	complemented
116	#1590	C₂×C₅	1	2	yes	complemented
117	#1565	C₂×C₅	1	1	yes	characteristic, complemented
118	#1479	C₂×C₅	1	1	yes	characteristic, complemented
119	#1477	C₂×C₅	1	1	yes	characteristic
120	C₈×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
121	C₅×#41	—	2	2	no	—
122	C₅×#41	—	2	2	no	—
123	C₂×C₅×Q₈	—	2	1	no	—
124	C₂×C₅×Q₈	—	2	2	no	—
125	C₂×C₅×Q₈	—	2	2	no	—
126	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
127	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₅×D₄	—	2	1	no	—
129	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₅	—	2	1	no	—
131	C₂²×C₄×C₅	—	2	1	no	—
132	C₂²×C₄×C₅	—	2	1	no	—
133	C₂²×C₄×C₅	—	2	1	no	—
134	C₂²×C₄×C₅	—	2	1	no	—
135	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₅	#41	1	1	yes	characteristic
138	C₅×Q₁₆	—	2	4	no	—
139	C₅×SD₁₆	—	2	4	no	—
140	C₅×M₁₆	—	2	2	no	—
141	C₅×M₁₆	—	4	2	no	—
142	C₅×M₁₆	—	4	2	no	—
143	C₅×M₁₆	M₁₆	1	4	yes	complemented
144	C₂×C₅×C₈	—	2	2	no	—
145	C₂×C₅×C₈	—	2	2	no	—
146	C₂×C₅×C₈	—	2	1	no	—
147	C₂×C₅×C₈	—	2	1	no	—
148	C₂×C₅×C₈	—	2	2	no	—
149	C₂×C₅×C₈	—	4	1	no	—
150	C₂×C₅×C₈	—	4	2	no	—
151	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
152	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
153	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
154	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
155	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
156	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
157	C₅×C₄⋊C₄	—	2	2	no	—
158	C₅×C₄⋊C₄	—	2	1	no	—
159	C₅×C₄⋊C₄	—	2	1	no	—
160	C₅×C₄⋊C₄	—	2	2	no	—
161	C₅×C₄⋊C₄	—	2	1	no	—
162	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
163	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
164	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
165	C₅×C₂²⋊C₄	—	2	1	no	—
166	C₅×C₂²⋊C₄	—	2	1	no	—
167	C₅×C₂²⋊C₄	—	2	1	no	—
168	C₄²×C₅	—	2	1	no	—
169	C₄²×C₅	—	2	1	no	—
170	C₄²×C₅	—	2	2	no	—
171	C₄²×C₅	—	2	1	no	—
172	C₄²×C₅	—	2	2	no	—
173	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
174	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
175	C₄²×C₅	#41	1	1	yes	characteristic
176	C₄²×C₅	C₂⁴	1	1	yes	characteristic
177	C₂×#137	C₄×C₅	1	1	yes	characteristic
178	C₄×#41	C₂²×C₅	1	1	yes	characteristic
179	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
180	#446	—	2	1	no	—
181	#446	—	2	1	no	—
182	#446	C₂²×C₅	1	2	yes	—
183	#446	C₂²×C₅	1	1	yes	characteristic
184	#446	C₂²×C₅	1	2	yes	—
185	#446	C₂²×C₅	1	1	yes	characteristic
186	#441	C₄×C₅	1	2	yes	—
187	#440	C₄×C₅	1	2	yes	—
188	C₄×Q₁₆	C₂²×C₅	1	2	yes	—
189	C₄×SD₁₆	C₂²×C₅	1	2	yes	—
190	#436	C₂²×C₅	1	1	yes	characteristic
191	#436	C₂²×C₅	1	1	yes	characteristic
192	#435	—	2	1	no	—
193	#435	—	2	1	no	—
194	#431	—	2	1	no	—
195	#431	C₂²×C₅	1	1	yes	characteristic
196	#431	C₂²×C₅	1	1	yes	characteristic
197	#428	C₄×C₅	1	1	yes	characteristic
198	C₂×C₄⋊C₈	—	2	1	no	—
199	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
200	#419	C₄×C₅	1	1	yes	characteristic
201	#417	C₄×C₅	1	1	yes	characteristic
202	C₄×M₁₆	—	2	1	no	—
203	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic
204	C₂×#97	—	2	1	no	—
205	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
206	#335	C₂²×C₅	1	2	yes	—
207	#334	C₂²×C₅	1	2	yes	—
208	Q₈⋊C₈	C₂²×C₅	1	2	yes	—
209	Q₈⋊C₈	C₂²×C₅	1	2	yes	—
210	Q₈⋊C₈	C₂²×C₅	1	2	yes	—
211	D₄⋊C₈	C₂²×C₅	1	2	yes	—
212	#322	C₂²×C₅	1	2	yes	—
213	C₈²	C₂²×C₅	1	2	yes	—
214	C₂³×C₅	—	2	1	no	—
215	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
216	C₅×Q₈	—	2	2	no	—
217	C₅×Q₈	—	2	1	no	—
218	C₅×Q₈	—	2	2	no	—
219	C₅×Q₈	—	2	1	no	—
220	C₅×Q₈	—	4	2	no	—
221	C₅×D₄	—	2	1	no	—
222	C₅×D₄	—	2	1	no	—
223	C₅×D₄	—	4	2	no	—
224	C₂×C₄×C₅	—	2	1	no	—
225	C₂×C₄×C₅	—	2	1	no	—
226	C₂×C₄×C₅	—	2	1	no	—
227	C₂×C₄×C₅	—	2	1	no	—
228	C₂×C₄×C₅	—	2	2	no	—
229	C₂×C₄×C₅	—	2	1	no	—
230	C₂×C₄×C₅	—	2	2	no	—
231	C₂×C₄×C₅	—	4	1	no	—
232	C₂×C₄×C₅	—	4	2	no	—
233	C₂×C₄×C₅	—	4	2	no	—
234	C₂×C₄×C₅	—	4	2	no	—
235	C₂×C₄×C₅	—	4	1	no	—
236	C₂×C₄×C₅	—	4	1	no	—
237	C₂×C₄×C₅	—	4	2	no	—
238	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
239	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
240	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
241	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
242	C₂×C₄×C₅	#131	1	2	yes	—
243	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
244	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
245	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
246	C₅×C₈	—	2	2	no	—
247	C₅×C₈	—	2	1	no	—
248	C₅×C₈	—	2	1	no	—
249	C₅×C₈	—	2	1	no	—
250	C₅×C₈	—	4	2	no	—
251	C₅×C₈	—	4	1	no	—
252	C₅×C₈	—	4	2	no	—
253	C₅×C₈	—	4	1	no	—
254	C₅×C₈	C₂×M₁₆	1	4	yes	—
255	C₅×C₈	#137	1	2	yes	complemented
256	C₂×#41	C₂×C₄×C₅	1	1	yes	characteristic
257	C₂²×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
258	#137	—	2	4	no	—
259	C₂×Q₁₆	C₂×C₄×C₅	1	2	yes	—
260	C₂×SD₁₆	C₂×C₄×C₅	1	2	yes	—
261	C₂×M₁₆	—	2	1	no	—
262	C₂×M₁₆	—	2	1	no	—
263	C₂×M₁₆	C₂×C₄×C₅	1	1	yes	characteristic
264	C₂×M₁₆	C₂×C₄×C₅	1	1	yes	characteristic
265	C₂²×C₈	—	2	1	no	—
266	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
267	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
268	C₄×Q₈	—	2	1	no	—
269	C₄×Q₈	—	2	1	no	—
270	C₄×Q₈	C₂×C₄×C₅	1	2	yes	—
271	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
272	C₄×Q₈	C₂³×C₅	1	2	yes	—
273	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
274	C₄×D₄	—	2	1	no	—
275	C₄×D₄	—	2	1	no	—
276	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
277	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
278	#117	—	2	1	no	—
279	#117	C₂×C₄×C₅	1	1	yes	characteristic
280	C₂×C₄⋊C₄	—	2	1	no	—
281	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
282	C₂×C₄²	—	2	1	no	—
283	C₂×C₄²	—	2	1	no	—
284	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
285	#107	C₂×C₄×C₅	1	2	yes	—
286	#106	C₂×C₄×C₅	1	2	yes	—
287	C₄⋊C₈	—	2	2	no	—
288	C₄⋊C₈	—	2	2	no	—
289	C₄⋊C₈	—	2	1	no	—
290	C₄⋊C₈	—	2	1	no	—
291	C₄⋊C₈	—	2	1	no	—
292	C₄⋊C₈	—	2	1	no	—
293	C₄⋊C₈	C₂³×C₅	1	2	yes	—
294	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
295	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
296	#103	C₂×C₄×C₅	1	2	yes	—
297	#103	C₂×C₄×C₅	1	2	yes	—
298	#103	C₂×C₄×C₅	1	2	yes	—
299	#102	C₂×C₄×C₅	1	2	yes	—
300	C₂²⋊C₈	—	2	1	no	—
301	C₂²⋊C₈	—	2	1	no	—
302	C₂²⋊C₈	—	2	1	no	—
303	C₂²⋊C₈	—	2	1	no	—
304	#97	—	2	2	no	—
305	#97	—	2	2	no	—
306	#97	—	2	1	no	—
307	#97	—	2	1	no	—
308	#97	C₂×C₄×C₅	1	2	yes	—
309	C₄×C₈	—	2	1	no	—
310	C₄×C₈	C₅×D₄	1	1	yes	characteristic
311	C₄×C₈	C₅×D₄	1	1	yes	characteristic
312	C₄×C₈	C₂³×C₅	1	2	yes	—
313	C₄×C₈	C₂³×C₅	1	2	yes	—
314	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
315	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
316	C₂²×C₅	—	2	1	no	—
317	C₂²×C₅	—	2	1	no	—
318	C₂²×C₅	—	4	1	no	—
319	C₂²×C₅	—	4	1	no	—
320	C₂²×C₅	—	4	1	no	—
321	C₂²×C₅	#436	1	2	yes	—
322	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
323	C₄×C₅	—	2	1	no	—
324	C₄×C₅	—	2	1	no	—
325	C₄×C₅	—	2	1	no	—
326	C₄×C₅	—	4	1	no	—
327	C₄×C₅	—	4	2	no	—
328	C₄×C₅	—	4	1	no	—
329	C₄×C₅	—	4	1	no	—
330	C₄×C₅	—	4	2	no	—
331	C₄×C₅	#436	1	2	yes	—
332	C₄×C₅	C₂²×M₁₆	1	1	yes	characteristic
333	C₄×C₅	C₂×#131	1	1	yes	characteristic
334	C₄×C₅	C₂×#137	1	1	yes	characteristic
335	C₄×C₅	#575	1	1	yes	characteristic
336	#41	—	2	2	no	—
337	#41	—	2	2	no	—
338	C₂×Q₈	—	2	1	no	—
339	C₂×Q₈	—	2	2	no	—
340	C₂×Q₈	—	2	2	no	—
341	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
342	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
343	C₂×D₄	—	2	1	no	—
344	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
351	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
352	C₂²×C₄	C₅×#41	1	1	yes	characteristic
353	Q₁₆	—	2	4	no	—
354	SD₁₆	—	2	4	no	—
355	M₁₆	—	2	2	no	—
356	M₁₆	—	4	2	no	—
357	M₁₆	—	4	2	no	—
358	M₁₆	C₅×M₁₆	1	4	yes	complemented
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	—	2	1	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	4	1	no	—
365	C₂×C₈	—	4	2	no	—
366	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
367	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
368	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
369	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
370	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
371	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	1	no	—
374	C₄⋊C₄	—	2	1	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
378	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
379	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
380	C₂²⋊C₄	—	2	1	no	—
381	C₂²⋊C₄	—	2	1	no	—
382	C₂²⋊C₄	—	2	1	no	—
383	C₄²	—	2	1	no	—
384	C₄²	—	2	1	no	—
385	C₄²	—	2	2	no	—
386	C₄²	—	2	1	no	—
387	C₄²	—	2	2	no	—
388	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
389	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
390	C₄²	C₅×#41	1	1	yes	characteristic
391	C₄²	C₂⁴×C₅	1	1	yes	characteristic
392	C₂×C₅	—	2	2	no	—
393	C₂×C₅	—	8	1	no	—
394	C₂×C₅	C₂×#436	1	1	yes	characteristic
395	C₂×C₅	C₄×#137	1	1	yes	characteristic
396	C₂×C₅	#2955	1	1	yes	characteristic
397	C₂³	—	2	1	no	—
398	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
399	Q₈	—	2	2	no	—
400	Q₈	—	2	1	no	—
401	Q₈	—	2	2	no	—
402	Q₈	—	2	1	no	—
403	Q₈	—	4	2	no	—
404	D₄	—	2	1	no	—
405	D₄	—	2	1	no	—
406	D₄	—	4	2	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
422	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
423	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
424	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
425	C₂×C₄	C₅×#131	1	2	yes	—
426	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
427	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
428	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
429	C₈	—	2	2	no	—
430	C₈	—	2	1	no	—
431	C₈	—	2	1	no	—
432	C₈	—	2	1	no	—
433	C₈	—	4	2	no	—
434	C₈	—	4	1	no	—
435	C₈	—	4	2	no	—
436	C₈	—	4	1	no	—
437	C₈	C₂×C₅×M₁₆	1	4	yes	—
438	C₈	C₅×#137	1	2	yes	complemented
439	C₅	#17892	1	1	yes	characteristic, direct product factor, Sylow
440	C₂²	—	2	1	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	4	1	no	—
443	C₂²	—	4	1	no	—
444	C₂²	—	4	1	no	—
445	C₂²	C₅×#436	1	2	yes	—
446	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
447	C₄	—	2	1	no	—
448	C₄	—	2	1	no	—
449	C₄	—	2	1	no	—
450	C₄	—	4	1	no	—
451	C₄	—	4	2	no	—
452	C₄	—	4	1	no	—
453	C₄	—	4	1	no	—
454	C₄	—	4	2	no	—
455	C₄	C₅×#436	1	2	yes	—
456	C₄	C₂²×C₅×M₁₆	1	1	yes	characteristic
457	C₄	C₂×C₅×#131	1	1	yes	characteristic
458	C₄	C₂×C₅×#137	1	1	yes	characteristic
459	C₄	C₅×#575	1	1	yes	characteristic
460	C₂	—	2	2	no	—
461	C₂	—	8	1	no	—
462	C₂	C₂×C₅×#436	1	1	yes	characteristic
463	C₂	C₄×C₅×#137	1	1	yes	characteristic
464	C₂	C₅×#2955	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₄²	C₂⁴×C₅
socle	C₂²×C₅	C₂×C₄×D₄
prime radical	C₂×C₅×#41	C₂×C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₄×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#446	C₂	semidirect
4. C₅×#1593	C₂	semidirect
5. C₅×#1592	C₂	semidirect
6. C₅×#1591	C₂	semidirect
7. C₅×#1590	C₂	semidirect
8. C₅×#1565	C₂	semidirect
9. C₅×#1479	C₂	semidirect
11. C₅×C₈×M₁₆	C₂	semidirect
49. #17892	C₅	direct (N × H)
111. C₂×#446	C₂×C₅	semidirect
113. #1593	C₂×C₅	semidirect
114. #1592	C₂×C₅	semidirect
115. #1591	C₂×C₅	semidirect
116. #1590	C₂×C₅	semidirect
117. #1565	C₂×C₅	semidirect
118. #1479	C₂×C₅	semidirect
120. C₈×M₁₆	C₂×C₅	semidirect
143. C₅×M₁₆	M₁₆	semidirect
255. C₅×C₈	#137	semidirect
358. M₁₆	C₅×M₁₆	semidirect
438. C₈	C₅×#137	semidirect
439. C₅	#17892	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#2965	2
C₂×C₅×#446	2
C₄×C₅×#137	2
C₅×#1593	2
C₅×#1592	2
C₅×#1591	2
C₅×#1590	2
C₅×#1565	2
C₅×#1479	2
C₅×#1477	2
C₅×C₈×M₁₆	2
#17892	5

Subgroups — C5×#17892 #11940612

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#17892 #11940612