Subgroups — C₅×#29821 #11952541

Order 1280.

800 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#495	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3040	C₂	1	2	yes	maximal, complemented
3	C₅×#2922	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2047	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2046	C₂	1	2	yes	maximal, complemented
6	C₅×#2045	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2020	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2019	C₂	1	2	yes	maximal, complemented
9	C₅×#2018	C₂	1	1	yes	maximal, characteristic
10	C₅×#1967	C₂	1	2	yes	maximal, complemented
11	C₅×#1837	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#137	C₂²	1	2	yes	—
13	C₂×C₅×AGL(1,ℤ/8)	C₂²	1	2	yes	—
14	C₂²×C₅×Q₁₆	C₂²	1	1	yes	characteristic
15	C₂²×C₅×SD₁₆	C₂²	1	2	yes	—
16	C₂²×C₅×D₈	C₂²	1	1	yes	characteristic
17	C₂×C₅×#124	C₂²	1	2	yes	—
18	C₄×C₅×#41	C₂²	1	1	yes	characteristic
19	C₅×#495	—	2	2	no	—
20	C₅×#495	—	2	2	no	—
21	C₅×#464	—	2	4	no	—
22	C₅×#463	—	2	4	no	—
23	C₅×#433	—	2	2	no	—
24	C₅×#431	—	2	2	no	—
25	C₅×#424	C₂²	1	1	yes	characteristic
26	C₅×#424	C₂²	1	1	yes	characteristic
27	C₅×#423	C₂²	1	2	yes	—
28	C₅×#419	C₂²	1	2	yes	—
29	C₅×#418	C₂²	1	2	yes	—
30	C₂×C₅×#101	C₂²	1	2	yes	—
31	C₂×C₅×#101	C₂²	1	2	yes	—
32	C₂×C₅×#100	C₂²	1	2	yes	—
33	C₂×C₅×#100	C₂²	1	2	yes	—
34	C₅×#408	C₂²	1	1	yes	characteristic
35	C₅×#408	C₂²	1	1	yes	characteristic
36	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
38	C₅×#341	C₂²	1	1	yes	characteristic
39	C₅×#341	C₂²	1	2	yes	—
40	C₅×#341	C₂²	1	1	yes	characteristic
41	#29821	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂×C₅×#41	C₂³	1	1	yes	characteristic
43	C₂²×C₅×Q₈	C₂³	1	2	yes	—
44	C₂²×C₅×D₄	C₂³	1	2	yes	—
45	C₅×#137	—	4	2	no	—
46	C₅×#137	—	4	2	no	—
47	C₅×AGL(1,ℤ/8)	—	4	2	no	—
48	C₅×AGL(1,ℤ/8)	—	4	2	no	—
49	C₂×C₅×Q₁₆	—	2	2	no	—
50	C₂×C₅×Q₁₆	—	2	2	no	—
51	C₂×C₅×Q₁₆	—	4	2	no	—
52	C₂×C₅×SD₁₆	—	2	2	no	—
53	C₂×C₅×SD₁₆	—	2	2	no	—
54	C₂×C₅×SD₁₆	—	2	4	no	—
55	C₂×C₅×SD₁₆	—	4	2	no	—
56	C₂×C₅×SD₁₆	—	4	2	no	—
57	C₂×C₅×D₈	—	2	2	no	—
58	C₂×C₅×D₈	—	2	2	no	—
59	C₂×C₅×D₈	—	4	2	no	—
60	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
61	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
62	C₂×C₅×M₁₆	C₂³	1	2	yes	—
63	C₂×C₅×M₁₆	C₂³	1	2	yes	—
64	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
65	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
66	C₅×#124	—	2	4	no	—
67	C₅×#124	—	2	2	no	—
68	C₅×#124	—	2	2	no	—
69	C₄×C₅×Q₈	D₄	1	2	yes	—
70	C₄×C₅×D₄	—	2	2	no	—
71	C₄×C₅×D₄	D₄	1	2	yes	—
72	C₅×#117	—	2	1	no	—
73	C₅×#117	C₂³	1	1	yes	characteristic
74	C₂×C₅×C₂²⋊C₄	—	2	4	no	—
75	C₂×C₄²×C₅	—	2	1	no	—
76	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
77	C₅×C₄⋊C₈	—	2	2	no	—
78	C₅×C₄⋊C₈	—	2	2	no	—
79	C₅×C₄⋊C₈	—	2	4	no	—
80	C₅×#103	—	2	4	no	—
81	C₅×#102	—	2	4	no	—
82	C₅×#101	—	4	2	no	—
83	C₅×#101	—	4	2	no	—
84	C₅×#100	—	4	2	no	—
85	C₅×#100	—	4	2	no	—
86	C₅×C₂²⋊C₈	—	2	2	no	—
87	C₅×C₂²⋊C₈	—	2	2	no	—
88	C₅×#97	—	2	1	no	—
89	C₄×C₅×C₈	—	2	1	no	—
90	C₄×C₅×C₈	D₄	1	2	yes	—
91	C₄×C₅×C₈	D₄	1	2	yes	—
92	C₂×#495	C₂×C₅	1	1	yes	characteristic, complemented
93	#3040	C₂×C₅	1	2	yes	complemented
94	#2922	C₂×C₅	1	1	yes	characteristic, complemented
95	#2047	C₂×C₅	1	1	yes	characteristic, complemented
96	#2046	C₂×C₅	1	2	yes	complemented
97	#2045	C₂×C₅	1	1	yes	characteristic, complemented
98	#2020	C₂×C₅	1	1	yes	characteristic, complemented
99	#2019	C₂×C₅	1	2	yes	complemented
100	#2018	C₂×C₅	1	1	yes	characteristic
101	#1967	C₂×C₅	1	2	yes	complemented
102	#1837	C₂×C₅	1	1	yes	characteristic, complemented
103	C₂⁴×C₅	—	2	2	no	—
104	C₅×#41	—	2	2	no	—
105	C₅×#41	—	2	2	no	—
106	C₂×C₅×Q₈	—	2	2	no	—
107	C₂×C₅×Q₈	—	2	2	no	—
108	C₂×C₅×Q₈	—	2	2	no	—
109	C₂×C₅×Q₈	—	2	2	no	—
110	C₂×C₅×Q₈	—	2	2	no	—
111	C₂×C₅×Q₈	—	2	2	no	—
112	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
113	C₂×C₅×D₄	—	2	1	no	—
114	C₂×C₅×D₄	—	2	2	no	—
115	C₂×C₅×D₄	—	2	2	no	—
116	C₂×C₅×D₄	—	2	2	no	—
117	C₂×C₅×D₄	—	2	2	no	—
118	C₂×C₅×D₄	—	2	2	no	—
119	C₂×C₅×D₄	—	2	2	no	—
120	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₅	—	2	2	no	—
122	C₂²×C₄×C₅	—	2	1	no	—
123	C₂²×C₄×C₅	—	2	2	no	—
124	C₂²×C₄×C₅	#41	1	2	yes	—
125	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
126	C₅×Q₁₆	—	4	4	no	—
127	C₅×Q₁₆	—	4	4	no	—
128	C₅×SD₁₆	—	4	8	no	—
129	C₅×SD₁₆	—	4	4	no	—
130	C₅×SD₁₆	—	4	4	no	—
131	C₅×D₈	—	4	4	no	—
132	C₅×D₈	—	4	4	no	—
133	C₅×M₁₆	—	2	2	no	—
134	C₅×M₁₆	—	2	2	no	—
135	C₅×M₁₆	—	2	2	no	—
136	C₅×M₁₆	—	2	2	no	—
137	C₅×M₁₆	—	2	2	no	—
138	C₅×M₁₆	—	2	2	no	—
139	C₂×C₅×C₈	—	2	2	no	—
140	C₂×C₅×C₈	—	2	2	no	—
141	C₂×C₅×C₈	—	2	2	no	—
142	C₂×C₅×C₈	—	2	2	no	—
143	C₂×C₅×C₈	—	2	1	no	—
144	C₂×C₅×C₈	—	2	1	no	—
145	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
146	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
147	C₅×C₄⋊C₄	—	2	2	no	—
148	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
149	C₅×C₂²⋊C₄	—	2	1	no	—
150	C₅×C₂²⋊C₄	—	2	2	no	—
151	C₅×C₂²⋊C₄	—	4	4	no	—
152	C₅×C₂²⋊C₄	—	4	4	no	—
153	C₄²×C₅	—	2	2	no	—
154	C₄²×C₅	—	2	1	no	—
155	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
156	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
157	C₄²×C₅	C₂×D₄	1	2	yes	—
158	C₂×#137	C₂²×C₅	1	2	yes	—
159	C₂×AGL(1,ℤ/8)	C₂²×C₅	1	2	yes	—
160	C₂²×Q₁₆	C₂²×C₅	1	1	yes	characteristic
161	C₂²×SD₁₆	C₂²×C₅	1	2	yes	—
162	C₂²×D₈	C₂²×C₅	1	1	yes	characteristic
163	C₂×#124	C₂²×C₅	1	2	yes	—
164	C₄×#41	C₂²×C₅	1	1	yes	characteristic
165	#495	—	2	2	no	—
166	#495	—	2	2	no	—
167	#464	—	2	4	no	—
168	#463	—	2	4	no	—
169	#433	—	2	2	no	—
170	#431	—	2	2	no	—
171	#424	C₂²×C₅	1	1	yes	characteristic
172	#424	C₂²×C₅	1	1	yes	characteristic
173	#423	C₂²×C₅	1	2	yes	—
174	#419	C₂²×C₅	1	2	yes	—
175	#418	C₂²×C₅	1	2	yes	—
176	C₂×#101	C₂²×C₅	1	2	yes	—
177	C₂×#101	C₂²×C₅	1	2	yes	—
178	C₂×#100	C₂²×C₅	1	2	yes	—
179	C₂×#100	C₂²×C₅	1	2	yes	—
180	#408	C₂²×C₅	1	1	yes	characteristic
181	#408	C₂²×C₅	1	1	yes	characteristic
182	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic
183	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
184	#341	C₂²×C₅	1	1	yes	characteristic
185	#341	C₂²×C₅	1	2	yes	—
186	#341	C₂²×C₅	1	1	yes	characteristic
187	C₂³×C₅	—	2	1	no	—
188	C₂³×C₅	—	4	2	no	—
189	C₂³×C₅	—	4	2	no	—
190	C₂³×C₅	—	4	2	no	—
191	C₂³×C₅	—	8	4	no	—
192	C₂³×C₅	C₂×#41	1	1	yes	characteristic
193	C₅×Q₈	—	2	2	no	—
194	C₅×Q₈	—	4	2	no	—
195	C₅×Q₈	—	4	2	no	—
196	C₅×Q₈	—	4	2	no	—
197	C₅×Q₈	—	4	2	no	—
198	C₅×D₄	—	2	2	no	—
199	C₅×D₄	—	4	2	no	—
200	C₅×D₄	—	4	2	no	—
201	C₅×D₄	—	4	2	no	—
202	C₅×D₄	—	4	2	no	—
203	C₅×D₄	—	4	2	no	—
204	C₂×C₄×C₅	—	2	2	no	—
205	C₂×C₄×C₅	—	2	1	no	—
206	C₂×C₄×C₅	—	4	2	no	—
207	C₂×C₄×C₅	—	4	4	no	—
208	C₂×C₄×C₅	—	4	1	no	—
209	C₂×C₄×C₅	—	4	1	no	—
210	C₂×C₄×C₅	—	4	2	no	—
211	C₂×C₄×C₅	—	4	2	no	—
212	C₂×C₄×C₅	—	4	2	no	—
213	C₂×C₄×C₅	#121	1	2	yes	—
214	C₂×C₄×C₅	#121	1	2	yes	—
215	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
216	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
217	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
218	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
219	C₅×C₈	—	2	2	no	—
220	C₅×C₈	—	2	2	no	—
221	C₅×C₈	—	4	1	no	—
222	C₅×C₈	—	4	1	no	—
223	C₅×C₈	—	4	2	no	—
224	C₅×C₈	—	4	2	no	—
225	C₂×#41	C₂³×C₅	1	1	yes	characteristic
226	C₂²×Q₈	C₂³×C₅	1	2	yes	—
227	C₂²×D₄	C₂³×C₅	1	2	yes	—
228	#137	—	4	2	no	—
229	#137	—	4	2	no	—
230	AGL(1,ℤ/8)	—	4	2	no	—
231	AGL(1,ℤ/8)	—	4	2	no	—
232	C₂×Q₁₆	—	2	2	no	—
233	C₂×Q₁₆	—	2	2	no	—
234	C₂×Q₁₆	—	4	2	no	—
235	C₂×SD₁₆	—	2	2	no	—
236	C₂×SD₁₆	—	2	2	no	—
237	C₂×SD₁₆	—	2	4	no	—
238	C₂×SD₁₆	—	4	2	no	—
239	C₂×SD₁₆	—	4	2	no	—
240	C₂×D₈	—	2	2	no	—
241	C₂×D₈	—	2	2	no	—
242	C₂×D₈	—	4	2	no	—
243	C₂×M₁₆	C₂³×C₅	1	2	yes	—
244	C₂×M₁₆	C₂³×C₅	1	2	yes	—
245	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
246	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
247	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
248	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
249	#124	—	2	4	no	—
250	#124	—	2	2	no	—
251	#124	—	2	2	no	—
252	C₄×Q₈	C₅×D₄	1	2	yes	—
253	C₄×D₄	—	2	2	no	—
254	C₄×D₄	C₅×D₄	1	2	yes	—
255	#117	—	2	1	no	—
256	#117	C₂³×C₅	1	1	yes	characteristic
257	C₂×C₂²⋊C₄	—	2	4	no	—
258	C₂×C₄²	—	2	1	no	—
259	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
260	C₄⋊C₈	—	2	2	no	—
261	C₄⋊C₈	—	2	2	no	—
262	C₄⋊C₈	—	2	4	no	—
263	#103	—	2	4	no	—
264	#102	—	2	4	no	—
265	#101	—	4	2	no	—
266	#101	—	4	2	no	—
267	#100	—	4	2	no	—
268	#100	—	4	2	no	—
269	C₂²⋊C₈	—	2	2	no	—
270	C₂²⋊C₈	—	2	2	no	—
271	#97	—	2	1	no	—
272	C₄×C₈	—	2	1	no	—
273	C₄×C₈	C₅×D₄	1	2	yes	—
274	C₄×C₈	C₅×D₄	1	2	yes	—
275	C₂²×C₅	—	2	2	no	—
276	C₂²×C₅	—	4	1	no	—
277	C₂²×C₅	—	4	2	no	—
278	C₂²×C₅	—	8	2	no	—
279	C₂²×C₅	—	8	4	no	—
280	C₂²×C₅	—	16	2	no	—
281	C₂²×C₅	—	16	2	no	—
282	C₂²×C₅	C₂×#121	1	1	yes	characteristic
283	C₂²×C₅	#540	1	2	yes	—
284	C₄×C₅	—	2	2	no	—
285	C₄×C₅	—	2	2	no	—
286	C₄×C₅	—	4	1	no	—
287	C₄×C₅	—	4	2	no	—
288	C₄×C₅	—	8	2	no	—
289	C₄×C₅	#535	1	1	yes	characteristic
290	C₄×C₅	#535	1	1	yes	characteristic
291	C₄×C₅	#535	1	2	yes	—
292	C₂⁴	—	2	2	no	—
293	#41	—	2	2	no	—
294	#41	—	2	2	no	—
295	C₂×Q₈	—	2	2	no	—
296	C₂×Q₈	—	2	2	no	—
297	C₂×Q₈	—	2	2	no	—
298	C₂×Q₈	—	2	2	no	—
299	C₂×Q₈	—	2	2	no	—
300	C₂×Q₈	—	2	2	no	—
301	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
302	C₂×D₄	—	2	1	no	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	2	2	no	—
305	C₂×D₄	—	2	2	no	—
306	C₂×D₄	—	2	2	no	—
307	C₂×D₄	—	2	2	no	—
308	C₂×D₄	—	2	2	no	—
309	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	C₅×#41	1	2	yes	—
314	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
315	Q₁₆	—	4	4	no	—
316	Q₁₆	—	4	4	no	—
317	SD₁₆	—	4	8	no	—
318	SD₁₆	—	4	4	no	—
319	SD₁₆	—	4	4	no	—
320	D₈	—	4	4	no	—
321	D₈	—	4	4	no	—
322	M₁₆	—	2	2	no	—
323	M₁₆	—	2	2	no	—
324	M₁₆	—	2	2	no	—
325	M₁₆	—	2	2	no	—
326	M₁₆	—	2	2	no	—
327	M₁₆	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	—	2	1	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
335	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
338	C₂²⋊C₄	—	2	1	no	—
339	C₂²⋊C₄	—	2	2	no	—
340	C₂²⋊C₄	—	4	4	no	—
341	C₂²⋊C₄	—	4	4	no	—
342	C₄²	—	2	2	no	—
343	C₄²	—	2	1	no	—
344	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
345	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
346	C₄²	C₂×C₅×D₄	1	2	yes	—
347	C₂×C₅	—	2	2	no	—
348	C₂×C₅	—	8	1	no	—
349	C₂×C₅	—	16	2	no	—
350	C₂×C₅	#2619	1	1	yes	characteristic
351	C₂×C₅	#3067	1	2	yes	—
352	C₂³	—	2	1	no	—
353	C₂³	—	4	2	no	—
354	C₂³	—	4	2	no	—
355	C₂³	—	4	2	no	—
356	C₂³	—	8	4	no	—
357	C₂³	C₂×C₅×#41	1	1	yes	characteristic
358	Q₈	—	2	2	no	—
359	Q₈	—	4	2	no	—
360	Q₈	—	4	2	no	—
361	Q₈	—	4	2	no	—
362	Q₈	—	4	2	no	—
363	D₄	—	2	2	no	—
364	D₄	—	4	2	no	—
365	D₄	—	4	2	no	—
366	D₄	—	4	2	no	—
367	D₄	—	4	2	no	—
368	D₄	—	4	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	4	no	—
373	C₂×C₄	—	4	1	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	C₅×#121	1	2	yes	—
379	C₂×C₄	C₅×#121	1	2	yes	—
380	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
381	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
382	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
383	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
384	C₈	—	2	2	no	—
385	C₈	—	2	2	no	—
386	C₈	—	4	2	no	—
387	C₈	—	4	2	no	—
388	C₈	—	4	1	no	—
389	C₈	—	4	1	no	—
390	C₅	#29821	1	1	yes	characteristic, direct product factor, Sylow
391	C₂²	—	2	2	no	—
392	C₂²	—	4	2	no	—
393	C₂²	—	4	1	no	—
394	C₂²	—	8	4	no	—
395	C₂²	—	8	2	no	—
396	C₂²	—	16	2	no	—
397	C₂²	—	16	2	no	—
398	C₂²	C₂×C₅×#121	1	1	yes	characteristic
399	C₂²	C₅×#540	1	2	yes	—
400	C₄	—	2	2	no	—
401	C₄	—	2	2	no	—
402	C₄	—	4	2	no	—
403	C₄	—	4	1	no	—
404	C₄	—	8	2	no	—
405	C₄	C₅×#535	1	1	yes	characteristic
406	C₄	C₅×#535	1	1	yes	characteristic
407	C₄	C₅×#535	1	2	yes	—
408	C₂	—	2	2	no	—
409	C₂	—	8	1	no	—
410	C₂	—	16	2	no	—
411	C₂	C₅×#2619	1	1	yes	characteristic
412	C₂	C₅×#3067	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₅	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₅×#2018	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ 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×#495	C₂	semidirect
2. C₅×#3040	C₂	semidirect
3. C₅×#2922	C₂	semidirect
4. C₅×#2047	C₂	semidirect
5. C₅×#2046	C₂	semidirect
6. C₅×#2045	C₂	semidirect
7. C₅×#2020	C₂	semidirect
8. C₅×#2019	C₂	semidirect
10. C₅×#1967	C₂	semidirect
11. C₅×#1837	C₂	semidirect
41. #29821	C₅	direct (N × H)
92. C₂×#495	C₂×C₅	semidirect
93. #3040	C₂×C₅	semidirect
94. #2922	C₂×C₅	semidirect
95. #2047	C₂×C₅	semidirect
96. #2046	C₂×C₅	semidirect
97. #2045	C₂×C₅	semidirect
98. #2020	C₂×C₅	semidirect
99. #2019	C₂×C₅	semidirect
101. #1967	C₂×C₅	semidirect
102. #1837	C₂×C₅	semidirect
390. C₅	#29821	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×#495	2
C₅×#3040	2
C₅×#2922	2
C₅×#2047	2
C₅×#2046	2
C₅×#2045	2
C₅×#2020	2
C₅×#2019	2
C₅×#2018	2
C₅×#1967	2
C₅×#1837	2
#29821	5

Subgroups — C5×#29821 #11952541

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#29821 #11952541