Subgroups — C₅×#33580 #11956300

Order 1280.

770 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#509	C₂	1	2	yes	maximal, complemented
2	C₅×#3147	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₅×D₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2210	C₂	1	4	yes	maximal, complemented
5	C₅×#2208	C₂	1	2	yes	maximal, complemented
6	C₅×#2206	C₂	1	2	yes	maximal, complemented
7	C₅×#2150	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2139	C₂	1	2	yes	maximal, complemented
9	C₂×C₅×#135	—	2	1	no	—
10	C₂×C₅×#135	C₂²	1	2	yes	—
11	C₂²×C₅×D₈	C₂²	1	1	yes	characteristic
12	C₅×#532	—	2	1	no	—
13	C₂×C₄×C₅×D₄	—	2	1	no	—
14	C₅×#509	—	2	8	no	—
15	C₂×C₅×SD₃₂	C₂²	1	4	yes	—
16	C₂×C₅×D₁₆	C₂²	1	4	yes	—
17	C₂×C₅×M₃₂	C₂²	1	2	yes	—
18	C₅×#495	—	2	1	no	—
19	C₅×#495	C₂²	1	2	yes	complemented
20	C₅×#494	C₂²	1	1	yes	characteristic, complemented
21	C₅×#493	C₂²	1	1	yes	characteristic, complemented
22	C₅×#492	—	2	1	no	—
23	C₄×C₅×D₈	—	2	1	no	—
24	C₄×C₅×D₈	—	2	1	no	—
25	C₄×C₅×D₈	C₂²	1	2	yes	—
26	C₄×C₅×D₈	C₂²	1	2	yes	—
27	C₂×C₅×#107	C₂²	1	1	yes	characteristic
28	C₂×C₅×#102	—	2	1	no	—
29	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
30	C₅×C₄⋊C₁₆	C₂²	1	2	yes	complemented
31	C₅×C₄⋊C₁₆	C₂²	1	2	yes	complemented
32	C₅×#358	C₂²	1	4	yes	complemented
33	C₅×#357	C₂²	1	4	yes	complemented
34	#33580	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
35	C₂×C₅×#41	—	2	2	no	—
36	C₂²×C₅×D₄	—	2	1	no	—
37	C₂³×C₄×C₅	—	4	1	no	—
38	C₅×#135	—	2	4	no	—
39	C₅×#135	—	2	4	no	—
40	C₅×#135	—	4	4	no	—
41	C₂×C₅×Q₁₆	—	2	1	no	—
42	C₂×C₅×Q₁₆	C₂³	1	2	yes	—
43	C₂×C₅×SD₁₆	—	2	2	no	—
44	C₂×C₅×SD₁₆	—	2	2	no	—
45	C₂×C₅×D₈	—	2	1	no	—
46	C₂×C₅×D₈	—	2	1	no	—
47	C₂×C₅×D₈	—	2	2	no	—
48	C₂×C₅×D₈	D₄	1	4	yes	complemented
49	C₂×C₅×D₈	C₂³	1	2	yes	—
50	C₂×C₅×D₈	C₂³	1	2	yes	—
51	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
52	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
53	C₅×C₄⋊Q₈	—	2	1	no	—
54	C₅×#127	—	2	1	no	—
55	C₅×#124	—	2	2	no	—
56	C₅×#121	—	4	1	no	—
57	C₅×#121	—	4	1	no	—
58	C₄×C₅×D₄	—	2	2	no	—
59	C₄×C₅×D₄	—	2	2	no	—
60	C₄×C₅×D₄	—	4	1	no	—
61	C₄×C₅×D₄	—	4	1	no	—
62	C₄×C₅×D₄	—	4	1	no	—
63	C₄×C₅×D₄	—	4	1	no	—
64	C₂×C₅×C₄⋊C₄	—	2	1	no	—
65	C₂×C₅×C₂²⋊C₄	—	4	1	no	—
66	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
67	C₅×SD₃₂	—	2	8	no	—
68	C₅×D₁₆	—	2	8	no	—
69	C₅×M₃₂	—	2	4	no	—
70	C₂×C₅×C₁₆	C₂³	1	4	yes	—
71	C₅×#107	—	2	1	no	—
72	C₅×#107	C₂³	1	2	yes	—
73	C₅×#102	—	2	2	no	—
74	C₅×#102	—	2	2	no	—
75	C₄×C₅×C₈	D₄	1	1	yes	characteristic
76	C₄×C₅×C₈	D₄	1	1	yes	characteristic
77	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
78	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
79	C₂×#509	C₂×C₅	1	2	yes	complemented
80	#3147	C₂×C₅	1	1	yes	characteristic, complemented
81	C₂×C₄×D₈	C₂×C₅	1	1	yes	characteristic, complemented
82	#2210	C₂×C₅	1	4	yes	complemented
83	#2208	C₂×C₅	1	2	yes	complemented
84	#2206	C₂×C₅	1	2	yes	complemented
85	#2150	C₂×C₅	1	1	yes	characteristic, complemented
86	#2139	C₂×C₅	1	2	yes	complemented
87	C₂⁴×C₅	—	4	1	no	—
88	C₅×#41	—	4	4	no	—
89	C₅×#41	—	4	4	no	—
90	C₂×C₅×Q₈	—	2	2	no	—
91	C₂×C₅×D₄	—	2	4	no	—
92	C₂×C₅×D₄	—	2	2	no	—
93	C₂×C₅×D₄	—	2	2	no	—
94	C₂×C₅×D₄	—	4	2	no	—
95	C₂×C₅×D₄	—	4	1	no	—
96	C₂×C₅×D₄	—	4	1	no	—
97	C₂×C₅×D₄	—	4	1	no	—
98	C₂×C₅×D₄	—	4	2	no	—
99	C₂²×C₄×C₅	—	4	1	no	—
100	C₂²×C₄×C₅	—	4	2	no	—
101	C₂²×C₄×C₅	—	4	2	no	—
102	C₂²×C₄×C₅	—	4	2	no	—
103	C₂²×C₄×C₅	—	8	4	no	—
104	C₂²×C₄×C₅	D₈	1	1	yes	characteristic
105	C₂²×C₄×C₅	D₈	1	1	yes	characteristic
106	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
107	C₅×Q₁₆	—	2	2	no	—
108	C₅×Q₁₆	—	2	2	no	—
109	C₅×Q₁₆	—	4	2	no	—
110	C₅×SD₁₆	—	4	4	no	—
111	C₅×SD₁₆	—	4	4	no	—
112	C₅×D₈	—	2	4	no	—
113	C₅×D₈	—	2	2	no	—
114	C₅×D₈	—	2	2	no	—
115	C₅×D₈	—	2	2	no	—
116	C₅×D₈	—	4	2	no	—
117	C₅×D₈	C₂×D₄	1	4	yes	—
118	C₂×C₅×C₈	—	2	2	no	—
119	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
120	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
121	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
122	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
123	C₂×C₅×C₈	#41	1	2	yes	—
124	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
125	C₅×C₄⋊C₄	—	2	2	no	—
126	C₅×C₄⋊C₄	—	4	1	no	—
127	C₅×C₄⋊C₄	—	4	1	no	—
128	C₅×C₄⋊C₄	—	4	1	no	—
129	C₅×C₂²⋊C₄	—	4	2	no	—
130	C₅×C₂²⋊C₄	—	4	2	no	—
131	C₅×C₂²⋊C₄	—	4	2	no	—
132	C₅×C₂²⋊C₄	—	4	2	no	—
133	C₄²×C₅	D₈	1	1	yes	characteristic
134	C₄²×C₅	D₈	1	1	yes	characteristic
135	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
136	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
137	C₅×C₁₆	—	2	4	no	—
138	C₂×#135	—	2	1	no	—
139	C₂×#135	C₂²×C₅	1	2	yes	—
140	C₂²×D₈	C₂²×C₅	1	1	yes	characteristic
141	#532	—	2	1	no	—
142	C₂×C₄×D₄	—	2	1	no	—
143	#509	—	2	8	no	—
144	C₂×SD₃₂	C₂²×C₅	1	4	yes	—
145	C₂×D₁₆	C₂²×C₅	1	4	yes	—
146	C₂×M₃₂	C₂²×C₅	1	2	yes	—
147	#495	—	2	1	no	—
148	#495	C₂²×C₅	1	2	yes	complemented
149	#494	C₂²×C₅	1	1	yes	characteristic, complemented
150	#493	C₂²×C₅	1	1	yes	characteristic, complemented
151	#492	—	2	1	no	—
152	C₄×D₈	—	2	1	no	—
153	C₄×D₈	—	2	1	no	—
154	C₄×D₈	C₂²×C₅	1	2	yes	—
155	C₄×D₈	C₂²×C₅	1	2	yes	—
156	C₂×#107	C₂²×C₅	1	1	yes	characteristic
157	C₂×#102	—	2	1	no	—
158	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
159	C₄⋊C₁₆	C₂²×C₅	1	2	yes	complemented
160	C₄⋊C₁₆	C₂²×C₅	1	2	yes	complemented
161	#358	C₂²×C₅	1	4	yes	complemented
162	#357	C₂²×C₅	1	4	yes	complemented
163	C₂³×C₅	—	4	2	no	—
164	C₂³×C₅	—	4	4	no	—
165	C₂³×C₅	—	4	2	no	—
166	C₂³×C₅	—	8	2	no	—
167	C₂³×C₅	—	8	2	no	—
168	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
169	C₅×Q₈	—	4	2	no	—
170	C₅×Q₈	—	4	2	no	—
171	C₅×D₄	—	2	4	no	—
172	C₅×D₄	—	4	2	no	—
173	C₅×D₄	—	4	2	no	—
174	C₅×D₄	—	4	2	no	—
175	C₅×D₄	—	4	4	no	—
176	C₅×D₄	—	8	2	no	—
177	C₅×D₄	—	8	4	no	—
178	C₅×D₄	—	8	2	no	—
179	C₂×C₄×C₅	—	2	2	no	—
180	C₂×C₄×C₅	—	4	1	no	—
181	C₂×C₄×C₅	—	4	2	no	—
182	C₂×C₄×C₅	—	4	2	no	—
183	C₂×C₄×C₅	—	8	4	no	—
184	C₂×C₄×C₅	—	8	2	no	—
185	C₂×C₄×C₅	—	8	4	no	—
186	C₂×C₄×C₅	—	8	4	no	—
187	C₂×C₄×C₅	#121	1	2	yes	—
188	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
189	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
190	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
191	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
192	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
193	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
194	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
195	C₅×C₈	—	2	1	no	—
196	C₅×C₈	—	2	1	no	—
197	C₅×C₈	#121	1	2	yes	—
198	C₅×C₈	C₂²×D₄	1	1	yes	characteristic
199	C₅×C₈	C₂×#41	1	1	yes	characteristic
200	C₂×#41	—	2	2	no	—
201	C₂²×D₄	—	2	1	no	—
202	C₂³×C₄	—	4	1	no	—
203	#135	—	2	4	no	—
204	#135	—	2	4	no	—
205	#135	—	4	4	no	—
206	C₂×Q₁₆	—	2	1	no	—
207	C₂×Q₁₆	C₂³×C₅	1	2	yes	—
208	C₂×SD₁₆	—	2	2	no	—
209	C₂×SD₁₆	—	2	2	no	—
210	C₂×D₈	—	2	1	no	—
211	C₂×D₈	—	2	1	no	—
212	C₂×D₈	—	2	2	no	—
213	C₂×D₈	C₅×D₄	1	4	yes	complemented
214	C₂×D₈	C₂³×C₅	1	2	yes	—
215	C₂×D₈	C₂³×C₅	1	2	yes	—
216	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
217	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
218	C₄⋊Q₈	—	2	1	no	—
219	#127	—	2	1	no	—
220	#124	—	2	2	no	—
221	#121	—	4	1	no	—
222	#121	—	4	1	no	—
223	C₄×D₄	—	2	2	no	—
224	C₄×D₄	—	2	2	no	—
225	C₄×D₄	—	4	1	no	—
226	C₄×D₄	—	4	1	no	—
227	C₄×D₄	—	4	1	no	—
228	C₄×D₄	—	4	1	no	—
229	C₂×C₄⋊C₄	—	2	1	no	—
230	C₂×C₂²⋊C₄	—	4	1	no	—
231	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
232	SD₃₂	—	2	8	no	—
233	D₁₆	—	2	8	no	—
234	M₃₂	—	2	4	no	—
235	C₂×C₁₆	C₂³×C₅	1	4	yes	—
236	#107	—	2	1	no	—
237	#107	C₂³×C₅	1	2	yes	—
238	#102	—	2	2	no	—
239	#102	—	2	2	no	—
240	C₄×C₈	C₅×D₄	1	1	yes	characteristic
241	C₄×C₈	C₅×D₄	1	1	yes	characteristic
242	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
243	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
244	C₂²×C₅	—	2	1	no	—
245	C₂²×C₅	—	2	1	no	—
246	C₂²×C₅	—	4	4	no	—
247	C₂²×C₅	—	8	8	no	—
248	C₂²×C₅	—	8	2	no	—
249	C₂²×C₅	—	8	2	no	—
250	C₂²×C₅	—	8	2	no	—
251	C₂²×C₅	—	8	2	no	—
252	C₂²×C₅	—	8	2	no	—
253	C₂²×C₅	#459	1	2	yes	—
254	C₂²×C₅	C₂²×D₈	1	1	yes	characteristic
255	C₄×C₅	—	2	1	no	—
256	C₄×C₅	—	2	1	no	—
257	C₄×C₅	—	2	1	no	—
258	C₄×C₅	—	8	2	no	—
259	C₄×C₅	—	8	2	no	—
260	C₄×C₅	#459	1	2	yes	—
261	C₄×C₅	#509	1	2	yes	complemented
262	C₄×C₅	C₂×#121	1	1	yes	characteristic
263	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
264	C₂⁴	—	4	1	no	—
265	#41	—	4	4	no	—
266	#41	—	4	4	no	—
267	C₂×Q₈	—	2	2	no	—
268	C₂×D₄	—	2	4	no	—
269	C₂×D₄	—	2	2	no	—
270	C₂×D₄	—	2	2	no	—
271	C₂×D₄	—	4	2	no	—
272	C₂×D₄	—	4	1	no	—
273	C₂×D₄	—	4	1	no	—
274	C₂×D₄	—	4	1	no	—
275	C₂×D₄	—	4	2	no	—
276	C₂²×C₄	—	4	1	no	—
277	C₂²×C₄	—	4	2	no	—
278	C₂²×C₄	—	4	2	no	—
279	C₂²×C₄	—	4	2	no	—
280	C₂²×C₄	—	8	4	no	—
281	C₂²×C₄	C₅×D₈	1	1	yes	characteristic
282	C₂²×C₄	C₅×D₈	1	1	yes	characteristic
283	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
284	Q₁₆	—	2	2	no	—
285	Q₁₆	—	2	2	no	—
286	Q₁₆	—	4	2	no	—
287	SD₁₆	—	4	4	no	—
288	SD₁₆	—	4	4	no	—
289	D₈	—	2	4	no	—
290	D₈	—	2	2	no	—
291	D₈	—	2	2	no	—
292	D₈	—	2	2	no	—
293	D₈	—	4	2	no	—
294	D₈	C₂×C₅×D₄	1	4	yes	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
297	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
298	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
299	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
300	C₂×C₈	C₅×#41	1	2	yes	—
301	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
302	C₄⋊C₄	—	2	2	no	—
303	C₄⋊C₄	—	4	1	no	—
304	C₄⋊C₄	—	4	1	no	—
305	C₄⋊C₄	—	4	1	no	—
306	C₂²⋊C₄	—	4	2	no	—
307	C₂²⋊C₄	—	4	2	no	—
308	C₂²⋊C₄	—	4	2	no	—
309	C₂²⋊C₄	—	4	2	no	—
310	C₄²	C₅×D₈	1	1	yes	characteristic
311	C₄²	C₅×D₈	1	1	yes	characteristic
312	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
313	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
314	C₁₆	—	2	4	no	—
315	C₂×C₅	—	2	2	no	—
316	C₂×C₅	—	8	4	no	—
317	C₂×C₅	—	16	2	no	—
318	C₂×C₅	C₂×#459	1	1	yes	characteristic
319	C₂×C₅	C₂×#509	1	1	yes	characteristic
320	C₂×C₅	#3414	1	1	yes	characteristic
321	C₂³	—	4	4	no	—
322	C₂³	—	4	2	no	—
323	C₂³	—	4	2	no	—
324	C₂³	—	8	2	no	—
325	C₂³	—	8	2	no	—
326	C₂³	C₂×C₅×D₈	1	1	yes	characteristic
327	Q₈	—	4	2	no	—
328	Q₈	—	4	2	no	—
329	D₄	—	2	4	no	—
330	D₄	—	4	4	no	—
331	D₄	—	4	2	no	—
332	D₄	—	4	2	no	—
333	D₄	—	4	2	no	—
334	D₄	—	8	2	no	—
335	D₄	—	8	4	no	—
336	D₄	—	8	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	8	4	no	—
342	C₂×C₄	—	8	2	no	—
343	C₂×C₄	—	8	4	no	—
344	C₂×C₄	—	8	4	no	—
345	C₂×C₄	C₅×#121	1	2	yes	—
346	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
347	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
348	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
349	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
350	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
351	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
352	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
353	C₈	—	2	1	no	—
354	C₈	—	2	1	no	—
355	C₈	C₅×#121	1	2	yes	—
356	C₈	C₂²×C₅×D₄	1	1	yes	characteristic
357	C₈	C₂×C₅×#41	1	1	yes	characteristic
358	C₅	#33580	1	1	yes	characteristic, direct product factor, Sylow
359	C₂²	—	2	1	no	—
360	C₂²	—	2	1	no	—
361	C₂²	—	4	4	no	—
362	C₂²	—	8	8	no	—
363	C₂²	—	8	2	no	—
364	C₂²	—	8	2	no	—
365	C₂²	—	8	2	no	—
366	C₂²	—	8	2	no	—
367	C₂²	—	8	2	no	—
368	C₂²	C₅×#459	1	2	yes	—
369	C₂²	C₂²×C₅×D₈	1	1	yes	characteristic
370	C₄	—	2	1	no	—
371	C₄	—	2	1	no	—
372	C₄	—	2	1	no	—
373	C₄	—	8	2	no	—
374	C₄	—	8	2	no	—
375	C₄	C₅×#459	1	2	yes	—
376	C₄	C₅×#509	1	2	yes	complemented
377	C₄	C₂×C₅×#121	1	1	yes	characteristic
378	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
379	C₂	—	2	2	no	—
380	C₂	—	8	4	no	—
381	C₂	—	16	2	no	—
382	C₂	C₂×C₅×#459	1	1	yes	characteristic
383	C₂	C₂×C₅×#509	1	1	yes	characteristic
384	C₂	C₅×#3414	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₅
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄²×C₅ ◁ C₂×C₄×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#509	C₂	semidirect
2. C₅×#3147	C₂	semidirect
3. C₂×C₄×C₅×D₈	C₂	semidirect
4. C₅×#2210	C₂	semidirect
5. C₅×#2208	C₂	semidirect
6. C₅×#2206	C₂	semidirect
7. C₅×#2150	C₂	semidirect
8. C₅×#2139	C₂	semidirect
19. C₅×#495	C₂²	semidirect
20. C₅×#494	C₂²	semidirect
21. C₅×#493	C₂²	semidirect
30. C₅×C₄⋊C₁₆	C₂²	semidirect
31. C₅×C₄⋊C₁₆	C₂²	semidirect
32. C₅×#358	C₂²	semidirect
33. C₅×#357	C₂²	semidirect
34. #33580	C₅	direct (N × H)
48. C₂×C₅×D₈	D₄	semidirect
79. C₂×#509	C₂×C₅	semidirect
80. #3147	C₂×C₅	semidirect
81. C₂×C₄×D₈	C₂×C₅	semidirect
82. #2210	C₂×C₅	semidirect
83. #2208	C₂×C₅	semidirect
84. #2206	C₂×C₅	semidirect
85. #2150	C₂×C₅	semidirect
86. #2139	C₂×C₅	semidirect
148. #495	C₂²×C₅	semidirect
149. #494	C₂²×C₅	semidirect
150. #493	C₂²×C₅	semidirect
159. C₄⋊C₁₆	C₂²×C₅	semidirect
160. C₄⋊C₁₆	C₂²×C₅	semidirect
161. #358	C₂²×C₅	semidirect
162. #357	C₂²×C₅	semidirect
213. C₂×D₈	C₅×D₄	semidirect
261. C₄×C₅	#509	semidirect
358. C₅	#33580	direct (N × H)
376. C₄	C₅×#509	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#509	2
C₅×#3147	2
C₂×C₄×C₅×D₈	2
C₅×#2210	2
C₅×#2208	2
C₅×#2206	2
C₅×#2150	2
C₅×#2139	2
#33580	5

Subgroups — C5×#33580 #11956300

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#33580 #11956300