Subgroups — C₅×#19573 #11942293

Order 1280.

572 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3254	C₂	1	1	yes	maximal, characteristic
2	C₅×#3230	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#3226	C₂	1	1	yes	maximal, characteristic
4	C₅×#2986	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1698	C₂	1	2	yes	maximal, complemented
6	C₅×#1696	C₂	1	2	yes	maximal, complemented
7	C₅×#1678	C₂	1	2	yes	maximal, complemented
8	C₅×#1676	C₂	1	2	yes	maximal, complemented
9	C₅×#1574	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1548	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1543	C₂	1	1	yes	maximal, characteristic
12	C₅×#533	C₂²	1	1	yes	characteristic
13	C₅×#532	C₂²	1	1	yes	characteristic
14	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₅×#500	—	2	1	no	—
16	C₅×#500	C₂²	1	2	yes	—
17	C₅×#487	—	2	1	no	—
18	C₅×#486	C₂²	1	2	yes	—
19	C₅×#484	—	2	2	no	—
20	C₅×#480	—	2	2	no	—
21	C₅×#477	C₂²	1	2	yes	—
22	C₅×#477	C₂²	1	2	yes	—
23	C₅×#477	C₂²	1	2	yes	—
24	C₅×#474	—	2	1	no	—
25	C₅×#474	—	2	1	no	—
26	C₅×#474	—	2	1	no	—
27	C₅×#468	—	2	2	no	—
28	C₅×#461	—	2	1	no	—
29	C₅×#460	C₂²	1	2	yes	—
30	C₅×#446	—	2	1	no	—
31	C₅×#446	C₂²	1	2	yes	—
32	C₅×C₈×Q₈	—	2	1	no	—
33	C₅×C₈×Q₈	C₂²	1	2	yes	—
34	C₅×#433	—	2	2	no	—
35	C₅×#431	C₂²	1	1	yes	characteristic
36	C₅×#431	C₂²	1	1	yes	characteristic
37	C₅×#431	C₂²	1	1	yes	characteristic
38	C₅×#423	C₂²	1	1	yes	characteristic
39	C₅×#335	C₂²	1	2	yes	—
40	C₅×#334	C₂²	1	2	yes	—
41	C₅×#333	C₂²	1	1	yes	characteristic
42	C₅×#333	C₂²	1	1	yes	characteristic
43	C₅×#333	C₂²	1	2	yes	—
44	C₅×#333	C₂²	1	2	yes	—
45	C₅×#331	C₂²	1	1	yes	characteristic
46	C₅×#331	C₂²	1	1	yes	characteristic
47	#19573	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
48	C₂×C₅×#41	—	2	1	no	—
49	C₂²×C₅×Q₈	—	2	1	no	—
50	C₂×C₅×SD₁₆	—	2	2	no	—
51	C₂×C₅×M₁₆	—	2	1	no	—
52	C₅×C₄⋊Q₈	—	2	1	no	—
53	C₅×C₄⋊Q₈	—	2	1	no	—
54	C₅×C₄⋊Q₈	—	2	1	no	—
55	C₅×C₄⋊Q₈	D₄	1	1	yes	characteristic
56	C₅×C₄⋊Q₈	D₄	1	1	yes	characteristic
57	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
58	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
59	C₅×#127	C₂³	1	1	yes	characteristic
60	C₅×#125	—	2	1	no	—
61	C₅×#124	—	2	1	no	—
62	C₅×C₂²⋊Q₈	—	2	1	no	—
63	C₅×C₂²⋊Q₈	D₄	1	2	yes	—
64	C₅×#121	—	2	1	no	—
65	C₅×#121	—	2	1	no	—
66	C₄×C₅×Q₈	—	2	1	no	—
67	C₄×C₅×Q₈	C₂³	1	2	yes	—
68	C₄×C₅×D₄	—	2	1	no	—
69	C₄×C₅×D₄	—	2	1	no	—
70	C₅×#117	—	2	1	no	—
71	C₂×C₅×C₄⋊C₄	—	2	1	no	—
72	C₂×C₅×C₄⋊C₄	—	2	1	no	—
73	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
74	C₅×#107	—	2	2	no	—
75	C₅×#107	—	2	2	no	—
76	C₅×#107	—	2	2	no	—
77	C₅×#107	—	2	2	no	—
78	C₅×#107	—	2	2	no	—
79	C₅×C₄⋊C₈	—	2	2	no	—
80	C₅×C₄⋊C₈	—	2	2	no	—
81	C₅×C₄⋊C₈	—	2	1	no	—
82	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
83	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
84	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
85	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
86	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
87	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
88	C₅×C₄⋊C₈	C₂³	1	2	yes	—
89	C₅×#103	—	2	2	no	—
90	C₅×#103	—	2	2	no	—
91	C₅×#103	—	2	2	no	—
92	C₅×#102	—	2	2	no	—
93	C₅×#102	—	2	2	no	—
94	C₅×#102	—	2	2	no	—
95	C₅×C₂²⋊C₈	—	2	1	no	—
96	C₅×C₂²⋊C₈	—	2	1	no	—
97	C₅×C₂²⋊C₈	D₄	1	2	yes	—
98	C₅×#97	—	2	2	no	—
99	C₄×C₅×C₈	—	2	2	no	—
100	C₄×C₅×C₈	—	2	1	no	—
101	C₄×C₅×C₈	—	2	1	no	—
102	C₄×C₅×C₈	C₂³	1	2	yes	—
103	#3254	C₂×C₅	1	1	yes	characteristic
104	#3230	C₂×C₅	1	1	yes	characteristic, complemented
105	#3226	C₂×C₅	1	1	yes	characteristic
106	#2986	C₂×C₅	1	1	yes	characteristic, complemented
107	#1698	C₂×C₅	1	2	yes	complemented
108	#1696	C₂×C₅	1	2	yes	complemented
109	#1678	C₂×C₅	1	2	yes	complemented
110	#1676	C₂×C₅	1	2	yes	complemented
111	#1574	C₂×C₅	1	1	yes	characteristic, complemented
112	#1548	C₂×C₅	1	1	yes	characteristic, complemented
113	#1543	C₂×C₅	1	1	yes	characteristic
114	C₅×#41	—	8	2	no	—
115	C₂×C₅×Q₈	—	2	1	no	—
116	C₂×C₅×Q₈	—	2	1	no	—
117	C₂×C₅×Q₈	—	2	2	no	—
118	C₂×C₅×Q₈	—	4	1	no	—
119	C₂×C₅×Q₈	—	8	2	no	—
120	C₂×C₅×Q₈	C₂×D₄	1	2	yes	—
121	C₂×C₅×D₄	—	2	1	no	—
122	C₂×C₅×D₄	—	2	1	no	—
123	C₂×C₅×D₄	—	2	1	no	—
124	C₂×C₅×D₄	—	4	1	no	—
125	C₂²×C₄×C₅	—	4	1	no	—
126	C₂²×C₄×C₅	—	4	1	no	—
127	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₅	#41	1	1	yes	characteristic
130	C₅×SD₁₆	—	8	2	no	—
131	C₅×M₁₆	—	8	1	no	—
132	C₂×C₅×C₈	—	2	2	no	—
133	C₂×C₅×C₈	—	2	1	no	—
134	C₂×C₅×C₈	—	2	1	no	—
135	C₂×C₅×C₈	—	2	1	no	—
136	C₂×C₅×C₈	—	2	1	no	—
137	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
138	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
139	C₅×C₄⋊C₄	—	2	1	no	—
140	C₅×C₄⋊C₄	—	2	1	no	—
141	C₅×C₄⋊C₄	—	2	1	no	—
142	C₅×C₄⋊C₄	—	2	2	no	—
143	C₅×C₄⋊C₄	—	2	2	no	—
144	C₅×C₄⋊C₄	—	2	2	no	—
145	C₅×C₄⋊C₄	—	2	2	no	—
146	C₅×C₄⋊C₄	—	2	1	no	—
147	C₅×C₄⋊C₄	—	2	1	no	—
148	C₅×C₄⋊C₄	—	4	1	no	—
149	C₅×C₄⋊C₄	—	4	1	no	—
150	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
151	C₅×C₂²⋊C₄	—	2	2	no	—
152	C₅×C₂²⋊C₄	—	4	1	no	—
153	C₅×C₂²⋊C₄	—	4	1	no	—
154	C₄²×C₅	—	2	2	no	—
155	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
156	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
157	C₄²×C₅	#41	1	1	yes	characteristic
158	C₄²×C₅	C₂⁴	1	1	yes	characteristic
159	#533	C₂²×C₅	1	1	yes	characteristic
160	#532	C₂²×C₅	1	1	yes	characteristic
161	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
162	#500	—	2	1	no	—
163	#500	C₂²×C₅	1	2	yes	—
164	#487	—	2	1	no	—
165	#486	C₂²×C₅	1	2	yes	—
166	#484	—	2	2	no	—
167	#480	—	2	2	no	—
168	#477	C₂²×C₅	1	2	yes	—
169	#477	C₂²×C₅	1	2	yes	—
170	#477	C₂²×C₅	1	2	yes	—
171	#474	—	2	1	no	—
172	#474	—	2	1	no	—
173	#474	—	2	1	no	—
174	#468	—	2	2	no	—
175	#461	—	2	1	no	—
176	#460	C₂²×C₅	1	2	yes	—
177	#446	—	2	1	no	—
178	#446	C₂²×C₅	1	2	yes	—
179	C₈×Q₈	—	2	1	no	—
180	C₈×Q₈	C₂²×C₅	1	2	yes	—
181	#433	—	2	2	no	—
182	#431	C₂²×C₅	1	1	yes	characteristic
183	#431	C₂²×C₅	1	1	yes	characteristic
184	#431	C₂²×C₅	1	1	yes	characteristic
185	#423	C₂²×C₅	1	1	yes	characteristic
186	#335	C₂²×C₅	1	2	yes	—
187	#334	C₂²×C₅	1	2	yes	—
188	#333	C₂²×C₅	1	1	yes	characteristic
189	#333	C₂²×C₅	1	1	yes	characteristic
190	#333	C₂²×C₅	1	2	yes	—
191	#333	C₂²×C₅	1	2	yes	—
192	#331	C₂²×C₅	1	1	yes	characteristic
193	#331	C₂²×C₅	1	1	yes	characteristic
194	C₂³×C₅	—	4	1	no	—
195	C₂³×C₅	#121	1	1	yes	characteristic
196	C₅×Q₈	—	2	2	no	—
197	C₅×Q₈	—	2	2	no	—
198	C₅×Q₈	—	4	2	no	—
199	C₅×Q₈	—	8	2	no	—
200	C₅×Q₈	—	8	1	no	—
201	C₅×Q₈	—	8	2	no	—
202	C₅×D₄	—	4	1	no	—
203	C₅×D₄	—	4	1	no	—
204	C₅×D₄	—	4	1	no	—
205	C₅×D₄	—	4	1	no	—
206	C₅×D₄	—	8	1	no	—
207	C₅×D₄	—	8	2	no	—
208	C₂×C₄×C₅	—	2	1	no	—
209	C₂×C₄×C₅	—	2	1	no	—
210	C₂×C₄×C₅	—	2	1	no	—
211	C₂×C₄×C₅	—	2	1	no	—
212	C₂×C₄×C₅	—	2	2	no	—
213	C₂×C₄×C₅	—	2	2	no	—
214	C₂×C₄×C₅	—	2	2	no	—
215	C₂×C₄×C₅	—	4	1	no	—
216	C₂×C₄×C₅	—	4	2	no	—
217	C₂×C₄×C₅	—	8	2	no	—
218	C₂×C₄×C₅	—	8	2	no	—
219	C₂×C₄×C₅	#121	1	1	yes	characteristic
220	C₂×C₄×C₅	#121	1	1	yes	characteristic
221	C₂×C₄×C₅	#121	1	1	yes	characteristic
222	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
223	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
224	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
225	C₅×C₈	—	2	2	no	—
226	C₅×C₈	—	2	2	no	—
227	C₅×C₈	—	4	1	no	—
228	C₅×C₈	—	4	2	no	—
229	C₅×C₈	—	4	1	no	—
230	C₅×C₈	—	4	1	no	—
231	C₅×C₈	—	4	1	no	—
232	C₂×#41	—	2	1	no	—
233	C₂²×Q₈	—	2	1	no	—
234	C₂×SD₁₆	—	2	2	no	—
235	C₂×M₁₆	—	2	1	no	—
236	C₄⋊Q₈	—	2	1	no	—
237	C₄⋊Q₈	—	2	1	no	—
238	C₄⋊Q₈	—	2	1	no	—
239	C₄⋊Q₈	C₅×D₄	1	1	yes	characteristic
240	C₄⋊Q₈	C₅×D₄	1	1	yes	characteristic
241	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
242	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
243	#127	C₂³×C₅	1	1	yes	characteristic
244	#125	—	2	1	no	—
245	#124	—	2	1	no	—
246	C₂²⋊Q₈	—	2	1	no	—
247	C₂²⋊Q₈	C₅×D₄	1	2	yes	—
248	#121	—	2	1	no	—
249	#121	—	2	1	no	—
250	C₄×Q₈	—	2	1	no	—
251	C₄×Q₈	C₂³×C₅	1	2	yes	—
252	C₄×D₄	—	2	1	no	—
253	C₄×D₄	—	2	1	no	—
254	#117	—	2	1	no	—
255	C₂×C₄⋊C₄	—	2	1	no	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
258	#107	—	2	2	no	—
259	#107	—	2	2	no	—
260	#107	—	2	2	no	—
261	#107	—	2	2	no	—
262	#107	—	2	2	no	—
263	C₄⋊C₈	—	2	2	no	—
264	C₄⋊C₈	—	2	2	no	—
265	C₄⋊C₈	—	2	1	no	—
266	C₄⋊C₈	C₅×D₄	1	1	yes	characteristic
267	C₄⋊C₈	C₅×D₄	1	1	yes	characteristic
268	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
269	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
270	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
271	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
272	C₄⋊C₈	C₂³×C₅	1	2	yes	—
273	#103	—	2	2	no	—
274	#103	—	2	2	no	—
275	#103	—	2	2	no	—
276	#102	—	2	2	no	—
277	#102	—	2	2	no	—
278	#102	—	2	2	no	—
279	C₂²⋊C₈	—	2	1	no	—
280	C₂²⋊C₈	—	2	1	no	—
281	C₂²⋊C₈	C₅×D₄	1	2	yes	—
282	#97	—	2	2	no	—
283	C₄×C₈	—	2	2	no	—
284	C₄×C₈	—	2	1	no	—
285	C₄×C₈	—	2	1	no	—
286	C₄×C₈	C₂³×C₅	1	2	yes	—
287	C₂²×C₅	—	2	1	no	—
288	C₂²×C₅	—	2	1	no	—
289	C₂²×C₅	—	2	1	no	—
290	C₂²×C₅	—	8	1	no	—
291	C₂²×C₅	—	8	1	no	—
292	C₂²×C₅	—	8	1	no	—
293	C₂²×C₅	C₂×#121	1	1	yes	characteristic
294	C₄×C₅	—	2	1	no	—
295	C₄×C₅	—	2	1	no	—
296	C₄×C₅	—	2	1	no	—
297	C₄×C₅	—	4	2	no	—
298	C₄×C₅	—	4	2	no	—
299	C₄×C₅	—	8	1	no	—
300	C₄×C₅	—	8	2	no	—
301	C₄×C₅	#472	1	2	yes	—
302	C₄×C₅	#577	1	1	yes	characteristic
303	C₄×C₅	#578	1	1	yes	characteristic
304	C₄×C₅	#578	1	1	yes	characteristic
305	C₄×C₅	#578	1	1	yes	characteristic
306	#41	—	8	2	no	—
307	C₂×Q₈	—	2	1	no	—
308	C₂×Q₈	—	2	1	no	—
309	C₂×Q₈	—	2	2	no	—
310	C₂×Q₈	—	4	1	no	—
311	C₂×Q₈	—	8	2	no	—
312	C₂×Q₈	C₂×C₅×D₄	1	2	yes	—
313	C₂×D₄	—	2	1	no	—
314	C₂×D₄	—	2	1	no	—
315	C₂×D₄	—	2	1	no	—
316	C₂×D₄	—	4	1	no	—
317	C₂²×C₄	—	4	1	no	—
318	C₂²×C₄	—	4	1	no	—
319	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
320	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
321	C₂²×C₄	C₅×#41	1	1	yes	characteristic
322	SD₁₆	—	8	2	no	—
323	M₁₆	—	8	1	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
330	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
331	C₄⋊C₄	—	2	1	no	—
332	C₄⋊C₄	—	2	1	no	—
333	C₄⋊C₄	—	2	1	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	2	2	no	—
338	C₄⋊C₄	—	2	1	no	—
339	C₄⋊C₄	—	2	1	no	—
340	C₄⋊C₄	—	4	1	no	—
341	C₄⋊C₄	—	4	1	no	—
342	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
343	C₂²⋊C₄	—	2	2	no	—
344	C₂²⋊C₄	—	4	1	no	—
345	C₂²⋊C₄	—	4	1	no	—
346	C₄²	—	2	2	no	—
347	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
348	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
349	C₄²	C₅×#41	1	1	yes	characteristic
350	C₄²	C₂⁴×C₅	1	1	yes	characteristic
351	C₂×C₅	—	4	1	no	—
352	C₂×C₅	—	16	1	no	—
353	C₂×C₅	#3044	1	1	yes	characteristic
354	C₂×C₅	#3063	1	1	yes	characteristic
355	C₂×C₅	C₂×#472	1	1	yes	characteristic
356	C₂³	—	4	1	no	—
357	C₂³	C₅×#121	1	1	yes	characteristic
358	Q₈	—	2	2	no	—
359	Q₈	—	2	2	no	—
360	Q₈	—	4	2	no	—
361	Q₈	—	8	2	no	—
362	Q₈	—	8	1	no	—
363	Q₈	—	8	2	no	—
364	D₄	—	4	1	no	—
365	D₄	—	4	1	no	—
366	D₄	—	4	1	no	—
367	D₄	—	4	1	no	—
368	D₄	—	8	1	no	—
369	D₄	—	8	2	no	—
370	C₂×C₄	—	2	2	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	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	8	2	no	—
380	C₂×C₄	—	8	2	no	—
381	C₂×C₄	C₅×#121	1	1	yes	characteristic
382	C₂×C₄	C₅×#121	1	1	yes	characteristic
383	C₂×C₄	C₅×#121	1	1	yes	characteristic
384	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
385	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
386	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
387	C₈	—	2	2	no	—
388	C₈	—	2	2	no	—
389	C₈	—	4	2	no	—
390	C₈	—	4	1	no	—
391	C₈	—	4	1	no	—
392	C₈	—	4	1	no	—
393	C₈	—	4	1	no	—
394	C₅	#19573	1	1	yes	characteristic, direct product factor, Sylow
395	C₂²	—	2	1	no	—
396	C₂²	—	2	1	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	8	1	no	—
399	C₂²	—	8	1	no	—
400	C₂²	—	8	1	no	—
401	C₂²	C₂×C₅×#121	1	1	yes	characteristic
402	C₄	—	2	1	no	—
403	C₄	—	2	1	no	—
404	C₄	—	2	1	no	—
405	C₄	—	4	2	no	—
406	C₄	—	4	2	no	—
407	C₄	—	8	1	no	—
408	C₄	—	8	2	no	—
409	C₄	C₅×#472	1	2	yes	—
410	C₄	C₅×#577	1	1	yes	characteristic
411	C₄	C₅×#578	1	1	yes	characteristic
412	C₄	C₅×#578	1	1	yes	characteristic
413	C₄	C₅×#578	1	1	yes	characteristic
414	C₂	—	4	1	no	—
415	C₂	—	16	1	no	—
416	C₂	C₅×#3044	1	1	yes	characteristic
417	C₂	C₅×#3063	1	1	yes	characteristic
418	C₂	C₂×C₅×#472	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅
prime radical	C₅×#532	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#3230	C₂	semidirect
4. C₅×#2986	C₂	semidirect
5. C₅×#1698	C₂	semidirect
6. C₅×#1696	C₂	semidirect
7. C₅×#1678	C₂	semidirect
8. C₅×#1676	C₂	semidirect
9. C₅×#1574	C₂	semidirect
10. C₅×#1548	C₂	semidirect
47. #19573	C₅	direct (N × H)
104. #3230	C₂×C₅	semidirect
106. #2986	C₂×C₅	semidirect
107. #1698	C₂×C₅	semidirect
108. #1696	C₂×C₅	semidirect
109. #1678	C₂×C₅	semidirect
110. #1676	C₂×C₅	semidirect
111. #1574	C₂×C₅	semidirect
112. #1548	C₂×C₅	semidirect
394. C₅	#19573	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×#3254	2
C₅×#3230	2
C₅×#3226	2
C₅×#2986	2
C₅×#1698	2
C₅×#1696	2
C₅×#1678	2
C₅×#1676	2
C₅×#1574	2
C₅×#1548	2
C₅×#1543	2
#19573	5

Subgroups — C5×#19573 #11942293

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19573 #11942293