Subgroups — C₅×#17952 #11940672

Order 1280.

606 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3101	C₂	1	1	yes	maximal, characteristic
2	C₅×#2985	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2975	C₂	1	1	yes	maximal, characteristic
4	C₅×#1592	C₂	1	2	yes	maximal, complemented
5	C₅×#1590	C₂	1	2	yes	maximal, complemented
6	C₅×#1588	C₂	1	2	yes	maximal, complemented
7	C₅×#1583	C₂	1	2	yes	maximal, complemented
8	C₅×#1572	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1490	C₂	1	1	yes	maximal, characteristic
10	C₅×#1485	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1453	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#533	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
14	C₅×#483	C₄	1	2	yes	—
15	C₅×#476	C₄	1	2	yes	—
16	C₅×#461	C₄	1	2	yes	—
17	C₅×#450	C₄	1	2	yes	—
18	C₅×#446	—	2	2	no	—
19	C₅×#446	C₂²	1	2	yes	complemented
20	C₅×C₈×Q₈	C₂²	1	2	yes	complemented
21	C₄×C₅×SD₁₆	C₂²	1	2	yes	—
22	C₄×C₅×SD₁₆	C₂²	1	2	yes	—
23	C₅×#436	—	2	2	no	—
24	C₅×#436	C₂²	1	2	yes	—
25	C₅×#436	C₂²	1	2	yes	—
26	C₅×#433	—	2	2	no	—
27	C₅×#432	C₂²	1	1	yes	characteristic
28	C₅×#431	C₂²	1	1	yes	characteristic
29	C₅×#431	C₂²	1	1	yes	characteristic
30	C₅×#431	C₂²	1	1	yes	characteristic
31	C₅×#407	—	2	2	no	—
32	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
33	C₅×#335	C₂²	1	2	yes	complemented
34	C₅×#334	C₂²	1	2	yes	complemented
35	C₅×Q₈⋊C₈	C₂²	1	2	yes	complemented
36	C₅×Q₈⋊C₈	C₂²	1	2	yes	complemented
37	C₅×D₄⋊C₈	C₂²	1	2	yes	—
38	C₅×D₄⋊C₈	C₂²	1	2	yes	—
39	C₅×#322	C₂²	1	1	yes	characteristic, complemented
40	C₅×#322	C₂²	1	1	yes	characteristic, complemented
41	C₅×#322	C₂²	1	1	yes	characteristic, complemented
42	C₅×C₈²	C₂²	1	1	yes	characteristic, complemented
43	#17952	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×C₅	—	2	1	no	—
46	C₂×C₅×SD₁₆	C₂×C₄	1	2	yes	—
47	C₂×C₅×SD₁₆	C₂×C₄	1	2	yes	—
48	C₂×C₅×M₁₆	—	2	1	no	—
49	C₂×C₅×M₁₆	—	2	2	no	—
50	C₂×C₅×M₁₆	—	2	2	no	—
51	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
52	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
53	C₅×#125	—	2	1	no	—
54	C₅×C₂²⋊Q₈	—	2	1	no	—
55	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
56	C₄×C₅×Q₈	—	2	1	no	—
57	C₄×C₅×Q₈	C₂³	1	2	yes	—
58	C₄×C₅×D₄	—	2	1	no	—
59	C₄×C₅×D₄	—	2	1	no	—
60	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
61	C₄×C₅×D₄	C₂³	1	2	yes	—
62	C₅×#117	—	2	1	no	—
63	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
64	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
65	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
66	C₅×#106	C₂×C₄	1	2	yes	—
67	C₅×#106	C₂×C₄	1	2	yes	—
68	C₅×C₄⋊C₈	—	2	2	no	—
69	C₅×C₄⋊C₈	—	2	2	no	—
70	C₅×C₄⋊C₈	C₂×C₄	1	2	yes	—
71	C₅×C₄⋊C₈	D₄	1	2	yes	—
72	C₅×C₄⋊C₈	C₂³	1	2	yes	—
73	C₅×C₄⋊C₈	C₂³	1	2	yes	—
74	C₅×#103	C₂×C₄	1	2	yes	—
75	C₅×#103	C₂×C₄	1	2	yes	—
76	C₅×#102	C₂×C₄	1	2	yes	—
77	C₅×#102	C₂×C₄	1	2	yes	—
78	C₅×C₂²⋊C₈	—	2	1	no	—
79	C₅×C₂²⋊C₈	—	2	1	no	—
80	C₅×C₂²⋊C₈	—	2	2	no	—
81	C₅×C₂²⋊C₈	—	2	2	no	—
82	C₅×C₂²⋊C₈	C₂×C₄	1	2	yes	—
83	C₅×C₂²⋊C₈	D₄	1	2	yes	—
84	C₅×#97	—	2	2	no	—
85	C₅×#97	—	2	1	no	—
86	C₅×#97	—	2	1	no	—
87	C₄×C₅×C₈	—	2	2	no	—
88	C₄×C₅×C₈	—	2	1	no	—
89	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
90	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
91	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
92	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
93	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
94	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
95	#3101	C₂×C₅	1	1	yes	characteristic
96	#2985	C₂×C₅	1	1	yes	characteristic, complemented
97	#2975	C₂×C₅	1	1	yes	characteristic
98	#1592	C₂×C₅	1	2	yes	complemented
99	#1590	C₂×C₅	1	2	yes	complemented
100	#1588	C₂×C₅	1	2	yes	complemented
101	#1583	C₂×C₅	1	2	yes	complemented
102	#1572	C₂×C₅	1	1	yes	characteristic, complemented
103	#1490	C₂×C₅	1	1	yes	characteristic
104	#1485	C₂×C₅	1	1	yes	characteristic, complemented
105	#1453	C₂×C₅	1	1	yes	characteristic, complemented
106	C₂⁴×C₅	—	2	1	no	—
107	C₂×C₅×Q₈	—	2	1	no	—
108	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
109	C₂×C₅×D₄	—	2	1	no	—
110	C₂×C₅×D₄	—	4	2	no	—
111	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
112	C₂²×C₄×C₅	—	2	1	no	—
113	C₂²×C₄×C₅	—	2	2	no	—
114	C₂²×C₄×C₅	—	2	2	no	—
115	C₂²×C₄×C₅	—	8	2	no	—
116	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₅	#41	1	1	yes	characteristic
119	C₅×SD₁₆	—	4	2	no	—
120	C₅×SD₁₆	—	4	2	no	—
121	C₅×M₁₆	—	4	2	no	—
122	C₅×M₁₆	—	8	2	no	—
123	C₅×M₁₆	—	8	2	no	—
124	C₂×C₅×C₈	—	2	1	no	—
125	C₂×C₅×C₈	—	2	2	no	—
126	C₂×C₅×C₈	—	2	2	no	—
127	C₂×C₅×C₈	—	2	1	no	—
128	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
129	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
130	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
131	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
132	C₅×C₄⋊C₄	—	2	1	no	—
133	C₅×C₄⋊C₄	—	2	1	no	—
134	C₅×C₄⋊C₄	—	2	1	no	—
135	C₅×C₄⋊C₄	—	2	1	no	—
136	C₅×C₄⋊C₄	—	2	2	no	—
137	C₅×C₄⋊C₄	—	2	2	no	—
138	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
139	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
140	C₅×C₂²⋊C₄	—	2	2	no	—
141	C₅×C₂²⋊C₄	—	2	2	no	—
142	C₅×C₂²⋊C₄	—	2	2	no	—
143	C₄²×C₅	—	2	2	no	—
144	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
145	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
146	C₄²×C₅	#41	1	1	yes	characteristic
147	C₄²×C₅	C₂⁴	1	1	yes	characteristic
148	#533	C₂²×C₅	1	1	yes	characteristic
149	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
150	#483	C₄×C₅	1	2	yes	—
151	#476	C₄×C₅	1	2	yes	—
152	#461	C₄×C₅	1	2	yes	—
153	#450	C₄×C₅	1	2	yes	—
154	#446	—	2	2	no	—
155	#446	C₂²×C₅	1	2	yes	complemented
156	C₈×Q₈	C₂²×C₅	1	2	yes	complemented
157	C₄×SD₁₆	C₂²×C₅	1	2	yes	—
158	C₄×SD₁₆	C₂²×C₅	1	2	yes	—
159	#436	—	2	2	no	—
160	#436	C₂²×C₅	1	2	yes	—
161	#436	C₂²×C₅	1	2	yes	—
162	#433	—	2	2	no	—
163	#432	C₂²×C₅	1	1	yes	characteristic
164	#431	C₂²×C₅	1	1	yes	characteristic
165	#431	C₂²×C₅	1	1	yes	characteristic
166	#431	C₂²×C₅	1	1	yes	characteristic
167	#407	—	2	2	no	—
168	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic
169	#335	C₂²×C₅	1	2	yes	complemented
170	#334	C₂²×C₅	1	2	yes	complemented
171	Q₈⋊C₈	C₂²×C₅	1	2	yes	complemented
172	Q₈⋊C₈	C₂²×C₅	1	2	yes	complemented
173	D₄⋊C₈	C₂²×C₅	1	2	yes	—
174	D₄⋊C₈	C₂²×C₅	1	2	yes	—
175	#322	C₂²×C₅	1	1	yes	characteristic, complemented
176	#322	C₂²×C₅	1	1	yes	characteristic, complemented
177	#322	C₂²×C₅	1	1	yes	characteristic, complemented
178	C₈²	C₂²×C₅	1	1	yes	characteristic, complemented
179	C₂³×C₅	—	2	2	no	—
180	C₂³×C₅	—	4	2	no	—
181	C₂³×C₅	—	8	1	no	—
182	C₂³×C₅	—	8	1	no	—
183	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
184	C₅×Q₈	—	2	2	no	—
185	C₅×Q₈	—	2	2	no	—
186	C₅×Q₈	—	8	1	no	—
187	C₅×D₄	—	2	2	no	—
188	C₅×D₄	—	2	2	no	—
189	C₅×D₄	—	4	2	no	—
190	C₂×C₄×C₅	—	2	2	no	—
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	—	4	1	no	—
196	C₂×C₄×C₅	—	4	2	no	—
197	C₂×C₄×C₅	—	4	2	no	—
198	C₂×C₄×C₅	—	8	2	no	—
199	C₂×C₄×C₅	—	8	1	no	—
200	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
201	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
202	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
203	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
204	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
205	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
206	C₅×C₈	—	2	2	no	—
207	C₅×C₈	—	2	2	no	—
208	C₅×C₈	—	2	2	no	—
209	C₅×C₈	—	2	2	no	—
210	C₅×C₈	—	2	2	no	—
211	C₅×C₈	—	4	1	no	—
212	C₅×C₈	—	4	2	no	—
213	C₅×C₈	—	4	2	no	—
214	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
215	C₂³×C₄	—	2	1	no	—
216	C₂×SD₁₆	C₂×C₄×C₅	1	2	yes	—
217	C₂×SD₁₆	C₂×C₄×C₅	1	2	yes	—
218	C₂×M₁₆	—	2	1	no	—
219	C₂×M₁₆	—	2	2	no	—
220	C₂×M₁₆	—	2	2	no	—
221	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
222	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
223	#125	—	2	1	no	—
224	C₂²⋊Q₈	—	2	1	no	—
225	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
226	C₄×Q₈	—	2	1	no	—
227	C₄×Q₈	C₂³×C₅	1	2	yes	—
228	C₄×D₄	—	2	1	no	—
229	C₄×D₄	—	2	1	no	—
230	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
231	C₄×D₄	C₂³×C₅	1	2	yes	—
232	#117	—	2	1	no	—
233	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
234	C₂×C₂²⋊C₄	—	2	1	no	—
235	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
236	#106	C₂×C₄×C₅	1	2	yes	—
237	#106	C₂×C₄×C₅	1	2	yes	—
238	C₄⋊C₈	—	2	2	no	—
239	C₄⋊C₈	—	2	2	no	—
240	C₄⋊C₈	C₂×C₄×C₅	1	2	yes	—
241	C₄⋊C₈	C₅×D₄	1	2	yes	—
242	C₄⋊C₈	C₂³×C₅	1	2	yes	—
243	C₄⋊C₈	C₂³×C₅	1	2	yes	—
244	#103	C₂×C₄×C₅	1	2	yes	—
245	#103	C₂×C₄×C₅	1	2	yes	—
246	#102	C₂×C₄×C₅	1	2	yes	—
247	#102	C₂×C₄×C₅	1	2	yes	—
248	C₂²⋊C₈	—	2	1	no	—
249	C₂²⋊C₈	—	2	1	no	—
250	C₂²⋊C₈	—	2	2	no	—
251	C₂²⋊C₈	—	2	2	no	—
252	C₂²⋊C₈	C₂×C₄×C₅	1	2	yes	—
253	C₂²⋊C₈	C₅×D₄	1	2	yes	—
254	#97	—	2	2	no	—
255	#97	—	2	1	no	—
256	#97	—	2	1	no	—
257	C₄×C₈	—	2	2	no	—
258	C₄×C₈	—	2	1	no	—
259	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
260	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
261	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
262	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
263	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
264	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
265	C₂²×C₅	—	2	1	no	—
266	C₂²×C₅	—	2	1	no	—
267	C₂²×C₅	—	2	1	no	—
268	C₂²×C₅	—	4	2	no	—
269	C₂²×C₅	—	4	2	no	—
270	C₂²×C₅	—	4	2	no	—
271	C₂²×C₅	—	8	4	no	—
272	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
273	C₄×C₅	—	2	1	no	—
274	C₄×C₅	—	2	1	no	—
275	C₄×C₅	—	2	1	no	—
276	C₄×C₅	—	2	1	no	—
277	C₄×C₅	—	4	2	no	—
278	C₄×C₅	—	4	2	no	—
279	C₄×C₅	—	4	2	no	—
280	C₄×C₅	#568	1	2	yes	—
281	C₄×C₅	#577	1	2	yes	—
282	C₂⁴	—	2	1	no	—
283	C₂×Q₈	—	2	1	no	—
284	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
285	C₂×D₄	—	2	1	no	—
286	C₂×D₄	—	4	2	no	—
287	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
288	C₂²×C₄	—	2	1	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	8	2	no	—
292	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
293	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
294	C₂²×C₄	C₅×#41	1	1	yes	characteristic
295	SD₁₆	—	4	2	no	—
296	SD₁₆	—	4	2	no	—
297	M₁₆	—	4	2	no	—
298	M₁₆	—	8	2	no	—
299	M₁₆	—	8	2	no	—
300	C₂×C₈	—	2	1	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	2	1	no	—
304	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
305	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
306	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
307	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
308	C₄⋊C₄	—	2	1	no	—
309	C₄⋊C₄	—	2	1	no	—
310	C₄⋊C₄	—	2	1	no	—
311	C₄⋊C₄	—	2	1	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
315	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
316	C₂²⋊C₄	—	2	2	no	—
317	C₂²⋊C₄	—	2	2	no	—
318	C₂²⋊C₄	—	2	2	no	—
319	C₄²	—	2	2	no	—
320	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
321	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
322	C₄²	C₅×#41	1	1	yes	characteristic
323	C₄²	C₂⁴×C₅	1	1	yes	characteristic
324	C₂×C₅	—	4	1	no	—
325	C₂×C₅	—	8	2	no	—
326	C₂×C₅	#2930	1	1	yes	characteristic
327	C₂×C₅	#2949	1	1	yes	characteristic
328	C₂×C₅	#2956	1	1	yes	characteristic
329	C₂³	—	2	2	no	—
330	C₂³	—	4	2	no	—
331	C₂³	—	8	1	no	—
332	C₂³	—	8	1	no	—
333	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
334	Q₈	—	2	2	no	—
335	Q₈	—	2	2	no	—
336	Q₈	—	8	1	no	—
337	D₄	—	2	2	no	—
338	D₄	—	2	2	no	—
339	D₄	—	4	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	8	2	no	—
349	C₂×C₄	—	8	1	no	—
350	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
351	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
352	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
353	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
354	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
355	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
356	C₈	—	2	2	no	—
357	C₈	—	2	2	no	—
358	C₈	—	2	2	no	—
359	C₈	—	2	2	no	—
360	C₈	—	2	2	no	—
361	C₈	—	4	1	no	—
362	C₈	—	4	2	no	—
363	C₈	—	4	2	no	—
364	C₅	#17952	1	1	yes	characteristic, direct product factor, Sylow
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	2	1	no	—
368	C₂²	—	4	2	no	—
369	C₂²	—	4	2	no	—
370	C₂²	—	4	2	no	—
371	C₂²	—	8	4	no	—
372	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
373	C₄	—	2	1	no	—
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	—	4	2	no	—
378	C₄	—	4	2	no	—
379	C₄	—	4	2	no	—
380	C₄	C₅×#568	1	2	yes	—
381	C₄	C₅×#577	1	2	yes	—
382	C₂	—	4	1	no	—
383	C₂	—	8	2	no	—
384	C₂	C₅×#2930	1	1	yes	characteristic
385	C₂	C₅×#2949	1	1	yes	characteristic
386	C₂	C₅×#2956	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	C₂²×C₅×D₄	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
2. C₅×#2985	C₂	semidirect
4. C₅×#1592	C₂	semidirect
5. C₅×#1590	C₂	semidirect
6. C₅×#1588	C₂	semidirect
7. C₅×#1583	C₂	semidirect
8. C₅×#1572	C₂	semidirect
10. C₅×#1485	C₂	semidirect
11. C₅×#1453	C₂	semidirect
19. C₅×#446	C₂²	semidirect
20. C₅×C₈×Q₈	C₂²	semidirect
33. C₅×#335	C₂²	semidirect
34. C₅×#334	C₂²	semidirect
35. C₅×Q₈⋊C₈	C₂²	semidirect
36. C₅×Q₈⋊C₈	C₂²	semidirect
39. C₅×#322	C₂²	semidirect
40. C₅×#322	C₂²	semidirect
41. C₅×#322	C₂²	semidirect
42. C₅×C₈²	C₂²	semidirect
43. #17952	C₅	direct (N × H)
96. #2985	C₂×C₅	semidirect
98. #1592	C₂×C₅	semidirect
99. #1590	C₂×C₅	semidirect
100. #1588	C₂×C₅	semidirect
101. #1583	C₂×C₅	semidirect
102. #1572	C₂×C₅	semidirect
104. #1485	C₂×C₅	semidirect
105. #1453	C₂×C₅	semidirect
155. #446	C₂²×C₅	semidirect
156. C₈×Q₈	C₂²×C₅	semidirect
169. #335	C₂²×C₅	semidirect
170. #334	C₂²×C₅	semidirect
171. Q₈⋊C₈	C₂²×C₅	semidirect
172. Q₈⋊C₈	C₂²×C₅	semidirect
175. #322	C₂²×C₅	semidirect
176. #322	C₂²×C₅	semidirect
177. #322	C₂²×C₅	semidirect
178. C₈²	C₂²×C₅	semidirect
364. C₅	#17952	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×#3101	2
C₅×#2985	2
C₅×#2975	2
C₅×#1592	2
C₅×#1590	2
C₅×#1588	2
C₅×#1583	2
C₅×#1572	2
C₅×#1490	2
C₅×#1485	2
C₅×#1453	2
#17952	5

Subgroups — C5×#17952 #11940672

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#17952 #11940672