Subgroups — C₅×#19277 #11941997

Order 1280.

638 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#487	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3079	C₂	1	1	yes	maximal, characteristic
3	C₅×#3079	C₂	1	1	yes	maximal, characteristic
4	C₅×C₈×#41	C₂	1	1	yes	maximal, characteristic
5	C₅×#1684	C₂	1	4	yes	maximal, complemented
6	C₅×#1683	C₂	1	4	yes	maximal, complemented
7	C₅×#1567	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1549	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1548	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
11	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
12	C₄×C₅×#41	C₂²	1	1	yes	characteristic
13	C₅×#487	—	2	1	no	—
14	C₅×#487	—	2	1	no	—
15	C₅×#487	C₂²	1	4	yes	—
16	C₅×#477	—	2	1	no	—
17	C₅×#477	C₂²	1	2	yes	—
18	C₅×#476	—	2	1	no	—
19	C₅×#476	C₂²	1	2	yes	—
20	C₅×#475	—	2	1	no	—
21	C₅×#475	C₂²	1	2	yes	—
22	C₅×#474	—	2	1	no	—
23	C₅×#474	C₂²	1	2	yes	—
24	C₅×C₈×Q₈	C₂²	1	2	yes	—
25	C₅×C₈×D₄	—	2	2	no	—
26	C₅×C₈×D₄	C₂²	1	2	yes	—
27	C₅×#431	—	2	1	no	—
28	C₅×#431	C₂²	1	1	yes	characteristic
29	C₅×#428	—	2	1	no	—
30	C₅×#428	—	2	1	no	—
31	C₅×#423	C₂²	1	1	yes	characteristic
32	C₅×#423	C₂²	1	1	yes	characteristic
33	C₅×#417	—	2	1	no	—
34	C₅×#417	—	2	1	no	—
35	C₂×C₅×#103	—	2	2	no	—
36	C₂×C₄×C₅×C₈	—	2	1	no	—
37	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
38	C₅×#335	C₂²	1	4	yes	—
39	C₅×#333	C₂²	1	4	yes	—
40	C₅×#332	C₂²	1	4	yes	—
41	#19277	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂×C₅×#41	D₄	1	1	yes	characteristic
43	C₂²×C₅×Q₈	—	2	1	no	—
44	C₂²×C₅×Q₈	—	2	1	no	—
45	C₂×C₅×M₁₆	—	2	1	no	—
46	C₂×C₅×M₁₆	—	2	1	no	—
47	C₂²×C₅×C₈	—	2	2	no	—
48	C₂²×C₅×C₈	D₄	1	2	yes	—
49	C₅×C₄⋊Q₈	—	2	1	no	—
50	C₅×C₄⋊Q₈	—	2	1	no	—
51	C₅×C₄⋊Q₈	—	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	C₂³	1	2	yes	—
56	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
57	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
58	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
59	C₄×C₅×D₄	—	2	1	no	—
60	C₄×C₅×D₄	—	2	1	no	—
61	C₄×C₅×D₄	D₄	1	1	yes	characteristic
62	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
63	C₅×#117	—	2	1	no	—
64	C₅×#117	D₄	1	1	yes	characteristic
65	C₂×C₅×C₄⋊C₄	—	2	1	no	—
66	C₂×C₅×C₄⋊C₄	—	2	1	no	—
67	C₂×C₅×C₄⋊C₄	—	2	1	no	—
68	C₂×C₅×C₄⋊C₄	—	2	1	no	—
69	C₂×C₄²×C₅	—	2	1	no	—
70	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
71	C₅×#107	—	2	2	no	—
72	C₅×#107	—	2	2	no	—
73	C₅×#106	—	2	2	no	—
74	C₅×#106	—	2	2	no	—
75	C₅×C₄⋊C₈	—	2	2	no	—
76	C₅×C₄⋊C₈	—	2	1	no	—
77	C₅×C₄⋊C₈	—	2	1	no	—
78	C₅×C₄⋊C₈	C₂³	1	2	yes	—
79	C₅×C₄⋊C₈	C₂³	1	2	yes	—
80	C₅×C₄⋊C₈	C₂³	1	2	yes	—
81	C₅×#103	—	2	2	no	—
82	C₅×#103	—	2	2	no	—
83	C₅×#103	—	2	4	no	—
84	C₅×#103	—	2	4	no	—
85	C₅×#102	—	2	2	no	—
86	C₅×#102	—	2	2	no	—
87	C₅×C₂²⋊C₈	—	2	1	no	—
88	C₅×C₂²⋊C₈	—	2	2	no	—
89	C₄×C₅×C₈	—	2	2	no	—
90	C₄×C₅×C₈	—	2	1	no	—
91	C₄×C₅×C₈	D₄	1	1	yes	characteristic
92	C₄×C₅×C₈	D₄	1	1	yes	characteristic
93	C₄×C₅×C₈	C₂³	1	2	yes	—
94	C₂×#487	C₂×C₅	1	1	yes	characteristic, complemented
95	#3079	C₂×C₅	1	1	yes	characteristic
96	#3079	C₂×C₅	1	1	yes	characteristic
97	C₈×#41	C₂×C₅	1	1	yes	characteristic
98	#1684	C₂×C₅	1	4	yes	complemented
99	#1683	C₂×C₅	1	4	yes	complemented
100	#1567	C₂×C₅	1	1	yes	characteristic, complemented
101	#1549	C₂×C₅	1	1	yes	characteristic, complemented
102	#1548	C₂×C₅	1	1	yes	characteristic, complemented
103	C₅×#41	—	2	2	no	—
104	C₅×#41	Q₁₆	1	4	yes	—
105	C₂×C₅×Q₈	—	2	2	no	—
106	C₂×C₅×Q₈	—	2	2	no	—
107	C₂×C₅×Q₈	—	4	4	no	—
108	C₂×C₅×Q₈	—	4	1	no	—
109	C₂×C₅×Q₈	—	4	1	no	—
110	C₂×C₅×Q₈	—	8	2	no	—
111	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
112	C₂×C₅×D₄	—	2	1	no	—
113	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₅	—	2	1	no	—
115	C₂²×C₄×C₅	—	2	1	no	—
116	C₂²×C₄×C₅	—	2	1	no	—
117	C₂²×C₄×C₅	—	4	1	no	—
118	C₂²×C₄×C₅	—	4	1	no	—
119	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₅	#41	1	1	yes	characteristic
122	C₅×M₁₆	—	4	2	no	—
123	C₅×M₁₆	—	4	2	no	—
124	C₂×C₅×C₈	—	2	2	no	—
125	C₂×C₅×C₈	—	2	2	no	—
126	C₂×C₅×C₈	—	2	2	no	—
127	C₂×C₅×C₈	—	4	2	no	—
128	C₂×C₅×C₈	—	4	4	no	—
129	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
130	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
131	C₅×C₄⋊C₄	—	2	1	no	—
132	C₅×C₄⋊C₄	—	2	1	no	—
133	C₅×C₄⋊C₄	—	2	2	no	—
134	C₅×C₄⋊C₄	—	2	2	no	—
135	C₅×C₄⋊C₄	—	2	2	no	—
136	C₅×C₄⋊C₄	—	2	2	no	—
137	C₅×C₄⋊C₄	—	4	1	no	—
138	C₅×C₄⋊C₄	—	4	1	no	—
139	C₅×C₄⋊C₄	—	4	1	no	—
140	C₅×C₄⋊C₄	—	4	1	no	—
141	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
142	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
143	C₅×C₂²⋊C₄	—	2	1	no	—
144	C₅×C₂²⋊C₄	—	2	1	no	—
145	C₅×C₂²⋊C₄	—	2	1	no	—
146	C₄²×C₅	—	2	1	no	—
147	C₄²×C₅	—	2	1	no	—
148	C₄²×C₅	—	2	1	no	—
149	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
150	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
151	C₄²×C₅	#41	1	1	yes	characteristic
152	C₄²×C₅	C₂⁴	1	1	yes	characteristic
153	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
154	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
155	C₄×#41	C₂²×C₅	1	1	yes	characteristic
156	#487	—	2	1	no	—
157	#487	—	2	1	no	—
158	#487	C₂²×C₅	1	4	yes	—
159	#477	—	2	1	no	—
160	#477	C₂²×C₅	1	2	yes	—
161	#476	—	2	1	no	—
162	#476	C₂²×C₅	1	2	yes	—
163	#475	—	2	1	no	—
164	#475	C₂²×C₅	1	2	yes	—
165	#474	—	2	1	no	—
166	#474	C₂²×C₅	1	2	yes	—
167	C₈×Q₈	C₂²×C₅	1	2	yes	—
168	C₈×D₄	—	2	2	no	—
169	C₈×D₄	C₂²×C₅	1	2	yes	—
170	#431	—	2	1	no	—
171	#431	C₂²×C₅	1	1	yes	characteristic
172	#428	—	2	1	no	—
173	#428	—	2	1	no	—
174	#423	C₂²×C₅	1	1	yes	characteristic
175	#423	C₂²×C₅	1	1	yes	characteristic
176	#417	—	2	1	no	—
177	#417	—	2	1	no	—
178	C₂×#103	—	2	2	no	—
179	C₂×C₄×C₈	—	2	1	no	—
180	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
181	#335	C₂²×C₅	1	4	yes	—
182	#333	C₂²×C₅	1	4	yes	—
183	#332	C₂²×C₅	1	4	yes	—
184	C₂³×C₅	—	2	1	no	—
185	C₂³×C₅	#121	1	1	yes	characteristic
186	C₅×Q₈	—	2	1	no	—
187	C₅×Q₈	—	4	4	no	—
188	C₅×Q₈	—	8	2	no	—
189	C₅×Q₈	—	8	2	no	—
190	C₅×Q₈	—	8	2	no	—
191	C₅×Q₈	C₂×Q₁₆	1	2	yes	—
192	C₅×D₄	—	2	4	no	—
193	C₅×D₄	—	2	1	no	—
194	C₅×D₄	C₂×Q₁₆	1	2	yes	—
195	C₂×C₄×C₅	—	2	1	no	—
196	C₂×C₄×C₅	—	2	2	no	—
197	C₂×C₄×C₅	—	2	4	no	—
198	C₂×C₄×C₅	—	2	2	no	—
199	C₂×C₄×C₅	—	2	1	no	—
200	C₂×C₄×C₅	—	2	1	no	—
201	C₂×C₄×C₅	—	4	2	no	—
202	C₂×C₄×C₅	—	4	2	no	—
203	C₂×C₄×C₅	—	4	2	no	—
204	C₂×C₄×C₅	—	4	2	no	—
205	C₂×C₄×C₅	—	8	2	no	—
206	C₂×C₄×C₅	—	8	2	no	—
207	C₂×C₄×C₅	#121	1	1	yes	characteristic
208	C₂×C₄×C₅	#121	1	1	yes	characteristic
209	C₂×C₄×C₅	#121	1	1	yes	characteristic
210	C₂×C₄×C₅	C₂×Q₁₆	1	2	yes	—
211	C₂×C₄×C₅	#135	1	2	yes	—
212	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
215	C₅×C₈	—	2	2	no	—
216	C₅×C₈	—	2	2	no	—
217	C₅×C₈	—	4	2	no	—
218	C₅×C₈	—	4	2	no	—
219	C₅×C₈	—	4	2	no	—
220	C₂×#41	C₅×D₄	1	1	yes	characteristic
221	C₂²×Q₈	—	2	1	no	—
222	C₂²×Q₈	—	2	1	no	—
223	C₂×M₁₆	—	2	1	no	—
224	C₂×M₁₆	—	2	1	no	—
225	C₂²×C₈	—	2	2	no	—
226	C₂²×C₈	C₅×D₄	1	2	yes	—
227	C₄⋊Q₈	—	2	1	no	—
228	C₄⋊Q₈	—	2	1	no	—
229	C₄⋊Q₈	—	2	1	no	—
230	C₄⋊Q₈	—	2	1	no	—
231	C₄⋊Q₈	—	2	1	no	—
232	C₄⋊Q₈	—	2	1	no	—
233	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
234	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
235	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
236	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
237	C₄×D₄	—	2	1	no	—
238	C₄×D₄	—	2	1	no	—
239	C₄×D₄	C₅×D₄	1	1	yes	characteristic
240	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
241	#117	—	2	1	no	—
242	#117	C₅×D₄	1	1	yes	characteristic
243	C₂×C₄⋊C₄	—	2	1	no	—
244	C₂×C₄⋊C₄	—	2	1	no	—
245	C₂×C₄⋊C₄	—	2	1	no	—
246	C₂×C₄⋊C₄	—	2	1	no	—
247	C₂×C₄²	—	2	1	no	—
248	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
249	#107	—	2	2	no	—
250	#107	—	2	2	no	—
251	#106	—	2	2	no	—
252	#106	—	2	2	no	—
253	C₄⋊C₈	—	2	2	no	—
254	C₄⋊C₈	—	2	1	no	—
255	C₄⋊C₈	—	2	1	no	—
256	C₄⋊C₈	C₂³×C₅	1	2	yes	—
257	C₄⋊C₈	C₂³×C₅	1	2	yes	—
258	C₄⋊C₈	C₂³×C₅	1	2	yes	—
259	#103	—	2	2	no	—
260	#103	—	2	2	no	—
261	#103	—	2	4	no	—
262	#103	—	2	4	no	—
263	#102	—	2	2	no	—
264	#102	—	2	2	no	—
265	C₂²⋊C₈	—	2	1	no	—
266	C₂²⋊C₈	—	2	2	no	—
267	C₄×C₈	—	2	2	no	—
268	C₄×C₈	—	2	1	no	—
269	C₄×C₈	C₅×D₄	1	1	yes	characteristic
270	C₄×C₈	C₅×D₄	1	1	yes	characteristic
271	C₄×C₈	C₂³×C₅	1	2	yes	—
272	C₂²×C₅	—	2	1	no	—
273	C₂²×C₅	—	2	1	no	—
274	C₂²×C₅	—	2	2	no	—
275	C₂²×C₅	—	4	1	no	—
276	C₂²×C₅	—	4	1	no	—
277	C₂²×C₅	#467	1	2	yes	—
278	C₂²×C₅	C₂×#121	1	1	yes	characteristic
279	C₄×C₅	—	2	1	no	—
280	C₄×C₅	—	2	2	no	—
281	C₄×C₅	—	2	1	no	—
282	C₄×C₅	—	4	1	no	—
283	C₄×C₅	—	4	1	no	—
284	C₄×C₅	—	8	2	no	—
285	C₄×C₅	—	8	2	no	—
286	C₄×C₅	#467	1	2	yes	—
287	C₄×C₅	#471	1	2	yes	—
288	C₄×C₅	C₂²×Q₁₆	1	1	yes	characteristic
289	C₄×C₅	C₂×#135	1	1	yes	characteristic
290	C₄×C₅	#575	1	2	yes	—
291	#41	—	2	2	no	—
292	#41	C₅×Q₁₆	1	4	yes	—
293	C₂×Q₈	—	2	2	no	—
294	C₂×Q₈	—	2	2	no	—
295	C₂×Q₈	—	4	4	no	—
296	C₂×Q₈	—	4	1	no	—
297	C₂×Q₈	—	4	1	no	—
298	C₂×Q₈	—	8	2	no	—
299	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
300	C₂×D₄	—	2	1	no	—
301	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
302	C₂²×C₄	—	2	1	no	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	4	1	no	—
306	C₂²×C₄	—	4	1	no	—
307	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
308	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
309	C₂²×C₄	C₅×#41	1	1	yes	characteristic
310	M₁₆	—	4	2	no	—
311	M₁₆	—	4	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	4	2	no	—
316	C₂×C₈	—	4	4	no	—
317	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
318	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
319	C₄⋊C₄	—	2	1	no	—
320	C₄⋊C₄	—	2	1	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	2	2	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	1	no	—
328	C₄⋊C₄	—	4	1	no	—
329	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
330	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
331	C₂²⋊C₄	—	2	1	no	—
332	C₂²⋊C₄	—	2	1	no	—
333	C₂²⋊C₄	—	2	1	no	—
334	C₄²	—	2	1	no	—
335	C₄²	—	2	1	no	—
336	C₄²	—	2	1	no	—
337	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
338	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
339	C₄²	C₅×#41	1	1	yes	characteristic
340	C₄²	C₂⁴×C₅	1	1	yes	characteristic
341	C₂×C₅	—	2	2	no	—
342	C₂×C₅	—	4	2	no	—
343	C₂×C₅	#3040	1	1	yes	characteristic
344	C₂×C₅	C₂×#467	1	1	yes	characteristic
345	C₂×C₅	C₂×#471	1	1	yes	characteristic
346	C₂³	—	2	1	no	—
347	C₂³	C₅×#121	1	1	yes	characteristic
348	Q₈	—	2	1	no	—
349	Q₈	—	4	4	no	—
350	Q₈	—	8	2	no	—
351	Q₈	—	8	2	no	—
352	Q₈	—	8	2	no	—
353	Q₈	C₂×C₅×Q₁₆	1	2	yes	—
354	D₄	—	2	4	no	—
355	D₄	—	2	1	no	—
356	D₄	C₂×C₅×Q₁₆	1	2	yes	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	8	2	no	—
368	C₂×C₄	—	8	2	no	—
369	C₂×C₄	C₅×#121	1	1	yes	characteristic
370	C₂×C₄	C₅×#121	1	1	yes	characteristic
371	C₂×C₄	C₅×#121	1	1	yes	characteristic
372	C₂×C₄	C₂×C₅×Q₁₆	1	2	yes	—
373	C₂×C₄	C₅×#135	1	2	yes	—
374	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
375	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
376	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
377	C₈	—	2	2	no	—
378	C₈	—	2	2	no	—
379	C₈	—	4	2	no	—
380	C₈	—	4	2	no	—
381	C₈	—	4	2	no	—
382	C₅	#19277	1	1	yes	characteristic, direct product factor, Sylow
383	C₂²	—	2	1	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	2	no	—
386	C₂²	—	4	1	no	—
387	C₂²	—	4	1	no	—
388	C₂²	C₅×#467	1	2	yes	—
389	C₂²	C₂×C₅×#121	1	1	yes	characteristic
390	C₄	—	2	1	no	—
391	C₄	—	2	2	no	—
392	C₄	—	2	1	no	—
393	C₄	—	4	1	no	—
394	C₄	—	4	1	no	—
395	C₄	—	8	2	no	—
396	C₄	—	8	2	no	—
397	C₄	C₅×#467	1	2	yes	—
398	C₄	C₅×#471	1	2	yes	—
399	C₄	C₂²×C₅×Q₁₆	1	1	yes	characteristic
400	C₄	C₂×C₅×#135	1	1	yes	characteristic
401	C₄	C₅×#575	1	2	yes	—
402	C₂	—	2	2	no	—
403	C₂	—	4	2	no	—
404	C₂	C₅×#3040	1	1	yes	characteristic
405	C₂	C₂×C₅×#467	1	1	yes	characteristic
406	C₂	C₂×C₅×#471	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅
prime radical	C₂×C₅×#41	D₄
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
1. C₂×C₅×#487	C₂	semidirect
5. C₅×#1684	C₂	semidirect
6. C₅×#1683	C₂	semidirect
7. C₅×#1567	C₂	semidirect
8. C₅×#1549	C₂	semidirect
9. C₅×#1548	C₂	semidirect
41. #19277	C₅	direct (N × H)
94. C₂×#487	C₂×C₅	semidirect
98. #1684	C₂×C₅	semidirect
99. #1683	C₂×C₅	semidirect
100. #1567	C₂×C₅	semidirect
101. #1549	C₂×C₅	semidirect
102. #1548	C₂×C₅	semidirect
382. C₅	#19277	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×#487	2
C₅×#3079	2
C₅×C₈×#41	2
C₅×#1684	2
C₅×#1683	2
C₅×#1567	2
C₅×#1549	2
C₅×#1548	2
#19277	5

Subgroups — C5×#19277 #11941997

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19277 #11941997