Subgroups — C₅×#17919 #11940639

Order 1280.

596 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3108	C₂	1	1	yes	maximal, characteristic
2	C₅×#2993	C₂	1	1	yes	maximal, characteristic
3	C₅×#2982	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1588	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1587	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1584	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1583	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1579	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×SD₁₆⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×C₈×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×C₈×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1574	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1487	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1482	C₂	1	1	yes	maximal, characteristic
15	C₅×#1454	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#529	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
18	C₅×#483	C₄	1	1	yes	characteristic
19	C₅×#480	C₄	1	1	yes	characteristic
20	C₅×#479	C₄	1	1	yes	characteristic
21	C₅×#479	C₄	1	1	yes	characteristic
22	C₅×#464	C₄	1	1	yes	characteristic
23	C₅×#464	C₄	1	1	yes	characteristic
24	C₅×#451	C₄	1	1	yes	characteristic
25	C₅×#448	C₄	1	1	yes	characteristic
26	C₅×#446	C₂²	1	1	yes	characteristic
27	C₅×C₈×Q₈	—	2	1	no	—
28	C₅×C₈×Q₈	—	2	1	no	—
29	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic
30	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic
31	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic
32	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic
33	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic
34	C₄×C₅×Q₁₆	C₂²	1	1	yes	characteristic
35	C₄×C₅×Q₁₆	C₂²	1	1	yes	characteristic
36	C₄×C₅×SD₁₆	C₂²	1	1	yes	characteristic
37	C₄×C₅×SD₁₆	C₂²	1	1	yes	characteristic
38	C₅×#436	—	2	1	no	—
39	C₅×#436	C₂²	1	1	yes	characteristic
40	C₅×#435	—	2	1	no	—
41	C₅×C₈×D₄	C₂²	1	1	yes	characteristic
42	C₅×#433	—	2	1	no	—
43	C₅×#431	—	2	1	no	—
44	C₅×#431	—	2	1	no	—
45	C₅×#431	C₂²	1	1	yes	characteristic
46	C₅×#431	C₂²	1	1	yes	characteristic
47	C₅×#431	C₂²	1	1	yes	characteristic
48	C₅×#431	C₂²	1	1	yes	characteristic
49	C₅×#424	—	2	1	no	—
50	C₅×#423	C₂²	1	1	yes	characteristic
51	C₅×#335	C₂²	1	1	yes	characteristic
52	C₅×#335	C₂²	1	1	yes	characteristic
53	C₅×#334	C₂²	1	1	yes	characteristic
54	C₅×#334	C₂²	1	1	yes	characteristic
55	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic
56	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic
57	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic
58	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic
59	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic
60	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic
61	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic
62	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic
63	C₅×#322	C₂²	1	1	yes	characteristic
64	C₅×#322	C₂²	1	1	yes	characteristic
65	C₅×#322	C₂²	1	1	yes	characteristic
66	C₅×C₈²	C₂²	1	1	yes	characteristic
67	#17919	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
68	C₂²×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
69	C₂×C₅×Q₁₆	C₂×C₄	1	1	yes	characteristic
70	C₂×C₅×Q₁₆	C₂×C₄	1	1	yes	characteristic
71	C₂×C₅×SD₁₆	C₂×C₄	1	1	yes	characteristic
72	C₂×C₅×SD₁₆	C₂×C₄	1	1	yes	characteristic
73	C₂×C₅×M₁₆	—	2	1	no	—
74	C₂×C₅×M₁₆	—	2	1	no	—
75	C₂²×C₅×C₈	—	2	1	no	—
76	C₅×#126	—	2	1	no	—
77	C₅×#125	C₂×C₄	1	1	yes	characteristic
78	C₅×#124	C₂×C₄	1	1	yes	characteristic
79	C₅×#123	—	2	1	no	—
80	C₅×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
81	C₅×#121	C₂×C₄	1	1	yes	characteristic
82	C₄×C₅×Q₈	—	2	1	no	—
83	C₄×C₅×Q₈	—	2	1	no	—
84	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
85	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
86	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
87	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
88	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
89	C₄×C₅×D₄	—	2	1	no	—
90	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
91	C₅×#117	—	2	1	no	—
92	C₂×C₅×C₄⋊C₄	—	2	1	no	—
93	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄²×C₅	—	2	1	no	—
95	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
96	C₅×#107	C₂×C₄	1	1	yes	characteristic
97	C₅×#107	C₂×C₄	1	1	yes	characteristic
98	C₅×#106	C₂×C₄	1	1	yes	characteristic
99	C₅×#106	C₂×C₄	1	1	yes	characteristic
100	C₅×C₄⋊C₈	—	2	1	no	—
101	C₅×C₄⋊C₈	—	2	1	no	—
102	C₅×C₄⋊C₈	—	2	1	no	—
103	C₅×C₄⋊C₈	—	2	1	no	—
104	C₅×C₄⋊C₈	—	2	1	no	—
105	C₅×C₄⋊C₈	—	2	1	no	—
106	C₅×C₄⋊C₈	—	2	1	no	—
107	C₅×C₄⋊C₈	—	2	1	no	—
108	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
109	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
110	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
111	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
112	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
113	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
114	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
115	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
116	C₅×#103	C₂×C₄	1	1	yes	characteristic
117	C₅×#103	C₂×C₄	1	1	yes	characteristic
118	C₅×#103	C₂×C₄	1	1	yes	characteristic
119	C₅×#103	C₂×C₄	1	1	yes	characteristic
120	C₅×#103	C₂×C₄	1	1	yes	characteristic
121	C₅×#103	C₂×C₄	1	1	yes	characteristic
122	C₅×#102	C₂×C₄	1	1	yes	characteristic
123	C₅×#102	C₂×C₄	1	1	yes	characteristic
124	C₅×C₂²⋊C₈	—	2	1	no	—
125	C₅×C₂²⋊C₈	—	2	1	no	—
126	C₅×C₂²⋊C₈	—	2	1	no	—
127	C₅×C₂²⋊C₈	—	2	1	no	—
128	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
129	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
130	C₅×C₂²⋊C₈	D₄	1	1	yes	characteristic
131	C₅×C₂²⋊C₈	D₄	1	1	yes	characteristic
132	C₅×#97	—	2	1	no	—
133	C₄×C₅×C₈	—	2	1	no	—
134	C₄×C₅×C₈	—	2	1	no	—
135	C₄×C₅×C₈	—	2	1	no	—
136	C₄×C₅×C₈	—	2	1	no	—
137	C₄×C₅×C₈	—	2	1	no	—
138	C₄×C₅×C₈	—	2	1	no	—
139	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
140	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
141	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
142	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
143	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
144	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
145	#3108	C₂×C₅	1	1	yes	characteristic
146	#2993	C₂×C₅	1	1	yes	characteristic
147	#2982	C₂×C₅	1	1	yes	characteristic, complemented
148	#1588	C₂×C₅	1	1	yes	characteristic, complemented
149	#1587	C₂×C₅	1	1	yes	characteristic, complemented
150	#1584	C₂×C₅	1	1	yes	characteristic, complemented
151	#1583	C₂×C₅	1	1	yes	characteristic, complemented
152	#1579	C₂×C₅	1	1	yes	characteristic, complemented
153	SD₁₆⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
154	C₈×Q₁₆	C₂×C₅	1	1	yes	characteristic, complemented
155	C₈×SD₁₆	C₂×C₅	1	1	yes	characteristic, complemented
156	#1574	C₂×C₅	1	1	yes	characteristic, complemented
157	#1487	C₂×C₅	1	1	yes	characteristic, complemented
158	#1482	C₂×C₅	1	1	yes	characteristic
159	#1454	C₂×C₅	1	1	yes	characteristic, complemented
160	C₂×C₅×Q₈	—	2	2	no	—
161	C₂×C₅×Q₈	—	2	2	no	—
162	C₂×C₅×Q₈	—	2	1	no	—
163	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
164	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
165	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
166	C₂×C₅×D₄	—	2	1	no	—
167	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
168	C₂²×C₄×C₅	—	2	1	no	—
169	C₂²×C₄×C₅	—	2	1	no	—
170	C₂²×C₄×C₅	—	2	1	no	—
171	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
172	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₅	#41	1	1	yes	characteristic
174	C₅×Q₁₆	—	2	2	no	—
175	C₅×Q₁₆	—	2	2	no	—
176	C₅×SD₁₆	—	2	2	no	—
177	C₅×SD₁₆	—	2	2	no	—
178	C₅×M₁₆	—	8	1	no	—
179	C₅×M₁₆	—	8	1	no	—
180	C₂×C₅×C₈	—	2	1	no	—
181	C₂×C₅×C₈	—	2	1	no	—
182	C₂×C₅×C₈	—	2	1	no	—
183	C₂×C₅×C₈	—	2	1	no	—
184	C₂×C₅×C₈	—	2	1	no	—
185	C₂×C₅×C₈	—	2	1	no	—
186	C₂×C₅×C₈	—	8	1	no	—
187	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
188	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
189	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
190	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
191	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
192	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
193	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
194	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
195	C₅×C₄⋊C₄	—	2	1	no	—
196	C₅×C₄⋊C₄	—	2	1	no	—
197	C₅×C₄⋊C₄	—	2	1	no	—
198	C₅×C₄⋊C₄	—	2	1	no	—
199	C₅×C₄⋊C₄	—	2	1	no	—
200	C₅×C₄⋊C₄	—	2	1	no	—
201	C₅×C₄⋊C₄	—	2	1	no	—
202	C₅×C₄⋊C₄	—	2	1	no	—
203	C₅×C₄⋊C₄	—	2	1	no	—
204	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
205	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
206	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
207	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
208	C₅×C₂²⋊C₄	—	2	1	no	—
209	C₅×C₂²⋊C₄	—	2	1	no	—
210	C₅×C₂²⋊C₄	—	2	1	no	—
211	C₅×C₂²⋊C₄	—	2	1	no	—
212	C₅×C₂²⋊C₄	—	2	1	no	—
213	C₄²×C₅	—	2	1	no	—
214	C₄²×C₅	—	2	1	no	—
215	C₄²×C₅	—	2	1	no	—
216	C₄²×C₅	—	2	1	no	—
217	C₄²×C₅	—	2	1	no	—
218	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
219	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
220	C₄²×C₅	#41	1	1	yes	characteristic
221	C₄²×C₅	C₂⁴	1	1	yes	characteristic
222	#529	C₂²×C₅	1	1	yes	characteristic
223	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
224	#483	C₄×C₅	1	1	yes	characteristic
225	#480	C₄×C₅	1	1	yes	characteristic
226	#479	C₄×C₅	1	1	yes	characteristic
227	#479	C₄×C₅	1	1	yes	characteristic
228	#464	C₄×C₅	1	1	yes	characteristic
229	#464	C₄×C₅	1	1	yes	characteristic
230	#451	C₄×C₅	1	1	yes	characteristic
231	#448	C₄×C₅	1	1	yes	characteristic
232	#446	C₂²×C₅	1	1	yes	characteristic
233	C₈×Q₈	—	2	1	no	—
234	C₈×Q₈	—	2	1	no	—
235	C₈×Q₈	C₂²×C₅	1	1	yes	characteristic
236	C₈×Q₈	C₂²×C₅	1	1	yes	characteristic
237	C₈×Q₈	C₂²×C₅	1	1	yes	characteristic
238	C₈×Q₈	C₂²×C₅	1	1	yes	characteristic
239	C₈×Q₈	C₂²×C₅	1	1	yes	characteristic
240	C₄×Q₁₆	C₂²×C₅	1	1	yes	characteristic
241	C₄×Q₁₆	C₂²×C₅	1	1	yes	characteristic
242	C₄×SD₁₆	C₂²×C₅	1	1	yes	characteristic
243	C₄×SD₁₆	C₂²×C₅	1	1	yes	characteristic
244	#436	—	2	1	no	—
245	#436	C₂²×C₅	1	1	yes	characteristic
246	#435	—	2	1	no	—
247	C₈×D₄	C₂²×C₅	1	1	yes	characteristic
248	#433	—	2	1	no	—
249	#431	—	2	1	no	—
250	#431	—	2	1	no	—
251	#431	C₂²×C₅	1	1	yes	characteristic
252	#431	C₂²×C₅	1	1	yes	characteristic
253	#431	C₂²×C₅	1	1	yes	characteristic
254	#431	C₂²×C₅	1	1	yes	characteristic
255	#424	—	2	1	no	—
256	#423	C₂²×C₅	1	1	yes	characteristic
257	#335	C₂²×C₅	1	1	yes	characteristic
258	#335	C₂²×C₅	1	1	yes	characteristic
259	#334	C₂²×C₅	1	1	yes	characteristic
260	#334	C₂²×C₅	1	1	yes	characteristic
261	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
262	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
263	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
264	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
265	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
266	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
267	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
268	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
269	#322	C₂²×C₅	1	1	yes	characteristic
270	#322	C₂²×C₅	1	1	yes	characteristic
271	#322	C₂²×C₅	1	1	yes	characteristic
272	C₈²	C₂²×C₅	1	1	yes	characteristic
273	C₂³×C₅	—	2	1	no	—
274	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
275	C₅×Q₈	—	2	4	no	—
276	C₅×Q₈	—	2	1	no	—
277	C₅×Q₈	—	2	1	no	—
278	C₅×Q₈	—	2	1	no	—
279	C₅×Q₈	—	2	1	no	—
280	C₅×Q₈	#131	1	2	yes	—
281	C₅×Q₈	#131	1	2	yes	—
282	C₅×D₄	—	2	1	no	—
283	C₅×D₄	—	2	1	no	—
284	C₅×D₄	—	8	1	no	—
285	C₂×C₄×C₅	—	2	4	no	—
286	C₂×C₄×C₅	—	2	1	no	—
287	C₂×C₄×C₅	—	2	1	no	—
288	C₂×C₄×C₅	—	2	1	no	—
289	C₂×C₄×C₅	—	2	1	no	—
290	C₂×C₄×C₅	—	2	1	no	—
291	C₂×C₄×C₅	—	2	1	no	—
292	C₂×C₄×C₅	—	2	1	no	—
293	C₂×C₄×C₅	—	2	1	no	—
294	C₂×C₄×C₅	—	2	1	no	—
295	C₂×C₄×C₅	—	2	1	no	—
296	C₂×C₄×C₅	—	2	1	no	—
297	C₂×C₄×C₅	—	4	1	no	—
298	C₂×C₄×C₅	—	4	1	no	—
299	C₂×C₄×C₅	—	4	1	no	—
300	C₂×C₄×C₅	—	8	1	no	—
301	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
302	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
303	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
304	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
305	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
306	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
307	C₅×C₈	—	2	1	no	—
308	C₅×C₈	—	2	1	no	—
309	C₅×C₈	—	2	1	no	—
310	C₅×C₈	—	2	1	no	—
311	C₅×C₈	—	2	1	no	—
312	C₅×C₈	—	2	1	no	—
313	C₅×C₈	—	2	1	no	—
314	C₅×C₈	—	2	1	no	—
315	C₅×C₈	—	4	1	no	—
316	C₅×C₈	—	4	1	no	—
317	C₅×C₈	—	4	1	no	—
318	C₅×C₈	—	4	1	no	—
319	C₅×C₈	—	4	1	no	—
320	C₅×C₈	—	4	1	no	—
321	C₂²×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
322	C₂×Q₁₆	C₂×C₄×C₅	1	1	yes	characteristic
323	C₂×Q₁₆	C₂×C₄×C₅	1	1	yes	characteristic
324	C₂×SD₁₆	C₂×C₄×C₅	1	1	yes	characteristic
325	C₂×SD₁₆	C₂×C₄×C₅	1	1	yes	characteristic
326	C₂×M₁₆	—	2	1	no	—
327	C₂×M₁₆	—	2	1	no	—
328	C₂²×C₈	—	2	1	no	—
329	#126	—	2	1	no	—
330	#125	C₂×C₄×C₅	1	1	yes	characteristic
331	#124	C₂×C₄×C₅	1	1	yes	characteristic
332	#123	—	2	1	no	—
333	C₂²⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
334	#121	C₂×C₄×C₅	1	1	yes	characteristic
335	C₄×Q₈	—	2	1	no	—
336	C₄×Q₈	—	2	1	no	—
337	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
338	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
339	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
340	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
341	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
342	C₄×D₄	—	2	1	no	—
343	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
344	#117	—	2	1	no	—
345	C₂×C₄⋊C₄	—	2	1	no	—
346	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
347	C₂×C₄²	—	2	1	no	—
348	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
349	#107	C₂×C₄×C₅	1	1	yes	characteristic
350	#107	C₂×C₄×C₅	1	1	yes	characteristic
351	#106	C₂×C₄×C₅	1	1	yes	characteristic
352	#106	C₂×C₄×C₅	1	1	yes	characteristic
353	C₄⋊C₈	—	2	1	no	—
354	C₄⋊C₈	—	2	1	no	—
355	C₄⋊C₈	—	2	1	no	—
356	C₄⋊C₈	—	2	1	no	—
357	C₄⋊C₈	—	2	1	no	—
358	C₄⋊C₈	—	2	1	no	—
359	C₄⋊C₈	—	2	1	no	—
360	C₄⋊C₈	—	2	1	no	—
361	C₄⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
362	C₄⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
363	C₄⋊C₈	C₅×D₄	1	1	yes	characteristic
364	C₄⋊C₈	C₅×D₄	1	1	yes	characteristic
365	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
366	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
367	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
368	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
369	#103	C₂×C₄×C₅	1	1	yes	characteristic
370	#103	C₂×C₄×C₅	1	1	yes	characteristic
371	#103	C₂×C₄×C₅	1	1	yes	characteristic
372	#103	C₂×C₄×C₅	1	1	yes	characteristic
373	#103	C₂×C₄×C₅	1	1	yes	characteristic
374	#103	C₂×C₄×C₅	1	1	yes	characteristic
375	#102	C₂×C₄×C₅	1	1	yes	characteristic
376	#102	C₂×C₄×C₅	1	1	yes	characteristic
377	C₂²⋊C₈	—	2	1	no	—
378	C₂²⋊C₈	—	2	1	no	—
379	C₂²⋊C₈	—	2	1	no	—
380	C₂²⋊C₈	—	2	1	no	—
381	C₂²⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
382	C₂²⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
383	C₂²⋊C₈	C₅×D₄	1	1	yes	characteristic
384	C₂²⋊C₈	C₅×D₄	1	1	yes	characteristic
385	#97	—	2	1	no	—
386	C₄×C₈	—	2	1	no	—
387	C₄×C₈	—	2	1	no	—
388	C₄×C₈	—	2	1	no	—
389	C₄×C₈	—	2	1	no	—
390	C₄×C₈	—	2	1	no	—
391	C₄×C₈	—	2	1	no	—
392	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
393	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
394	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
395	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
396	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
397	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
398	C₂²×C₅	—	2	1	no	—
399	C₂²×C₅	—	2	1	no	—
400	C₂²×C₅	—	2	1	no	—
401	C₂²×C₅	—	4	1	no	—
402	C₂²×C₅	—	4	1	no	—
403	C₂²×C₅	—	4	1	no	—
404	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
405	C₄×C₅	—	2	2	no	—
406	C₄×C₅	—	2	2	no	—
407	C₄×C₅	—	2	1	no	—
408	C₄×C₅	—	2	1	no	—
409	C₄×C₅	—	2	1	no	—
410	C₄×C₅	—	2	1	no	—
411	C₄×C₅	—	4	1	no	—
412	C₄×C₅	—	4	1	no	—
413	C₄×C₅	—	4	1	no	—
414	C₄×C₅	—	4	1	no	—
415	C₄×C₅	—	4	1	no	—
416	C₄×C₅	C₂×#131	1	1	yes	characteristic
417	C₄×C₅	C₂×#131	1	1	yes	characteristic
418	C₄×C₅	#577	1	1	yes	characteristic
419	C₄×C₅	#578	1	1	yes	characteristic
420	C₂×Q₈	—	2	2	no	—
421	C₂×Q₈	—	2	2	no	—
422	C₂×Q₈	—	2	1	no	—
423	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
424	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
425	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
426	C₂×D₄	—	2	1	no	—
427	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
432	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
433	C₂²×C₄	C₅×#41	1	1	yes	characteristic
434	Q₁₆	—	2	2	no	—
435	Q₁₆	—	2	2	no	—
436	SD₁₆	—	2	2	no	—
437	SD₁₆	—	2	2	no	—
438	M₁₆	—	8	1	no	—
439	M₁₆	—	8	1	no	—
440	C₂×C₈	—	2	1	no	—
441	C₂×C₈	—	2	1	no	—
442	C₂×C₈	—	2	1	no	—
443	C₂×C₈	—	2	1	no	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	8	1	no	—
447	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
448	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
449	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
450	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
451	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
452	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
453	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
454	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
455	C₄⋊C₄	—	2	1	no	—
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
465	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
466	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
467	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
468	C₂²⋊C₄	—	2	1	no	—
469	C₂²⋊C₄	—	2	1	no	—
470	C₂²⋊C₄	—	2	1	no	—
471	C₂²⋊C₄	—	2	1	no	—
472	C₂²⋊C₄	—	2	1	no	—
473	C₄²	—	2	1	no	—
474	C₄²	—	2	1	no	—
475	C₄²	—	2	1	no	—
476	C₄²	—	2	1	no	—
477	C₄²	—	2	1	no	—
478	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
479	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
480	C₄²	C₅×#41	1	1	yes	characteristic
481	C₄²	C₂⁴×C₅	1	1	yes	characteristic
482	C₂×C₅	—	4	1	no	—
483	C₂×C₅	—	8	1	no	—
484	C₂×C₅	#2929	1	1	yes	characteristic
485	C₂×C₅	#2947	1	1	yes	characteristic
486	C₂×C₅	#2957	1	1	yes	characteristic
487	C₂³	—	2	1	no	—
488	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
489	Q₈	—	2	4	no	—
490	Q₈	—	2	1	no	—
491	Q₈	—	2	1	no	—
492	Q₈	—	2	1	no	—
493	Q₈	—	2	1	no	—
494	Q₈	C₅×#131	1	2	yes	—
495	Q₈	C₅×#131	1	2	yes	—
496	D₄	—	2	1	no	—
497	D₄	—	2	1	no	—
498	D₄	—	8	1	no	—
499	C₂×C₄	—	2	4	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	8	1	no	—
515	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
516	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
517	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
518	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
519	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
520	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
521	C₈	—	2	1	no	—
522	C₈	—	2	1	no	—
523	C₈	—	2	1	no	—
524	C₈	—	2	1	no	—
525	C₈	—	2	1	no	—
526	C₈	—	2	1	no	—
527	C₈	—	2	1	no	—
528	C₈	—	2	1	no	—
529	C₈	—	4	1	no	—
530	C₈	—	4	1	no	—
531	C₈	—	4	1	no	—
532	C₈	—	4	1	no	—
533	C₈	—	4	1	no	—
534	C₈	—	4	1	no	—
535	C₅	#17919	1	1	yes	characteristic, direct product factor, Sylow
536	C₂²	—	2	1	no	—
537	C₂²	—	2	1	no	—
538	C₂²	—	2	1	no	—
539	C₂²	—	4	1	no	—
540	C₂²	—	4	1	no	—
541	C₂²	—	4	1	no	—
542	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
543	C₄	—	2	2	no	—
544	C₄	—	2	2	no	—
545	C₄	—	2	1	no	—
546	C₄	—	2	1	no	—
547	C₄	—	2	1	no	—
548	C₄	—	2	1	no	—
549	C₄	—	4	1	no	—
550	C₄	—	4	1	no	—
551	C₄	—	4	1	no	—
552	C₄	—	4	1	no	—
553	C₄	—	4	1	no	—
554	C₄	C₂×C₅×#131	1	1	yes	characteristic
555	C₄	C₂×C₅×#131	1	1	yes	characteristic
556	C₄	C₅×#577	1	1	yes	characteristic
557	C₄	C₅×#578	1	1	yes	characteristic
558	C₂	—	4	1	no	—
559	C₂	—	8	1	no	—
560	C₂	C₅×#2929	1	1	yes	characteristic
561	C₂	C₅×#2947	1	1	yes	characteristic
562	C₂	C₅×#2957	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	C₅×#121	C₂×C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₅×#431 ◁ G

Complements

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

N	H ≅ G/N	type
3. C₅×#2982	C₂	semidirect
4. C₅×#1588	C₂	semidirect
5. C₅×#1587	C₂	semidirect
6. C₅×#1584	C₂	semidirect
7. C₅×#1583	C₂	semidirect
8. C₅×#1579	C₂	semidirect
9. C₅×SD₁₆⋊C₈	C₂	semidirect
10. C₅×C₈×Q₁₆	C₂	semidirect
11. C₅×C₈×SD₁₆	C₂	semidirect
12. C₅×#1574	C₂	semidirect
13. C₅×#1487	C₂	semidirect
15. C₅×#1454	C₂	semidirect
67. #17919	C₅	direct (N × H)
147. #2982	C₂×C₅	semidirect
148. #1588	C₂×C₅	semidirect
149. #1587	C₂×C₅	semidirect
150. #1584	C₂×C₅	semidirect
151. #1583	C₂×C₅	semidirect
152. #1579	C₂×C₅	semidirect
153. SD₁₆⋊C₈	C₂×C₅	semidirect
154. C₈×Q₁₆	C₂×C₅	semidirect
155. C₈×SD₁₆	C₂×C₅	semidirect
156. #1574	C₂×C₅	semidirect
157. #1487	C₂×C₅	semidirect
159. #1454	C₂×C₅	semidirect
535. C₅	#17919	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×#3108	2
C₅×#2993	2
C₅×#2982	2
C₅×#1588	2
C₅×#1587	2
C₅×#1584	2
C₅×#1583	2
C₅×#1579	2
C₅×SD₁₆⋊C₈	2
C₅×C₈×Q₁₆	2
C₅×C₈×SD₁₆	2
C₅×#1574	2
C₅×#1487	2
C₅×#1482	2
C₅×#1454	2
#17919	5

Subgroups — C5×#17919 #11940639

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#17919 #11940639