Subgroups — C₅×#33667 #11956387

Order 1280.

552 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3170	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₅×#135	C₂	1	1	yes	maximal, characteristic
3	C₅×#2237	C₂	1	2	yes	maximal, complemented
4	C₅×#2225	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2224	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2209	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2208	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2189	C₂	1	2	yes	maximal
9	C₄×C₅×Q₃₂	C₂	1	2	yes	maximal, complemented
10	C₄×C₅×SD₃₂	C₂	1	2	yes	maximal, complemented
11	C₅×#2162	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#135	C₂²	1	1	yes	characteristic
13	C₅×#533	—	2	1	no	—
14	C₄×C₅×#41	—	2	1	no	—
15	C₂×C₅×Q₃₂	C₂²	1	2	yes	—
16	C₂×C₅×SD₃₂	C₂²	1	2	yes	—
17	C₅×#500	C₂²	1	1	yes	characteristic
18	C₅×#494	C₂²	1	1	yes	characteristic
19	C₅×#487	—	2	1	no	—
20	C₅×#467	—	2	1	no	—
21	C₅×#467	C₂²	1	2	yes	—
22	C₄×C₅×Q₁₆	—	2	1	no	—
23	C₄×C₅×Q₁₆	C₂²	1	2	yes	—
24	C₄×C₅×Q₁₆	C₂²	1	1	yes	characteristic
25	C₄×C₅×Q₁₆	C₂²	1	1	yes	characteristic
26	C₄×C₅×SD₁₆	—	2	1	no	—
27	C₄×C₅×SD₁₆	—	2	1	no	—
28	C₄×C₅×D₈	C₂²	1	1	yes	characteristic
29	C₄×C₅×D₈	C₂²	1	1	yes	characteristic
30	C₅×#427	C₂²	1	1	yes	characteristic
31	C₅×#416	—	2	1	no	—
32	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
33	C₅×#367	C₂²	1	2	yes	—
34	C₅×#366	C₂²	1	2	yes	—
35	C₅×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
36	C₅×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
37	C₅×#358	C₂²	1	2	yes	—
38	C₅×#358	C₂²	1	2	yes	—
39	C₅×#358	C₂²	1	2	yes	—
40	C₅×#357	C₂²	1	2	yes	—
41	C₅×C₂²⋊C₁₆	C₂²	1	2	yes	—
42	C₄×C₅×C₁₆	C₂²	1	2	yes	—
43	#33667	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂×C₅×#41	—	2	1	no	—
45	C₅×#135	—	2	2	no	—
46	C₅×#135	—	2	2	no	—
47	C₂×C₅×Q₁₆	—	2	1	no	—
48	C₂×C₅×Q₁₆	C₂³	1	2	yes	—
49	C₂×C₅×Q₁₆	C₂³	1	1	yes	characteristic
50	C₂×C₅×SD₁₆	—	2	1	no	—
51	C₂×C₅×D₈	C₂³	1	1	yes	characteristic
52	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
53	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
54	C₅×C₄⋊Q₈	—	2	1	no	—
55	C₅×C₄⋊Q₈	—	2	1	no	—
56	C₅×#125	—	4	1	no	—
57	C₅×C₂²⋊Q₈	—	2	2	no	—
58	C₅×C₂²⋊Q₈	—	4	1	no	—
59	C₄×C₅×Q₈	—	2	1	no	—
60	C₄×C₅×Q₈	—	2	1	no	—
61	C₄×C₅×Q₈	—	2	2	no	—
62	C₄×C₅×Q₈	—	4	1	no	—
63	C₄×C₅×D₄	—	2	1	no	—
64	C₄×C₅×D₄	—	2	1	no	—
65	C₄×C₅×D₄	—	4	1	no	—
66	C₄×C₅×D₄	—	4	1	no	—
67	C₅×#117	—	2	1	no	—
68	C₅×#117	—	4	1	no	—
69	C₅×#117	—	4	1	no	—
70	C₂×C₄²×C₅	—	4	1	no	—
71	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
72	C₅×Q₃₂	—	2	4	no	—
73	C₅×SD₃₂	—	2	4	no	—
74	C₂×C₅×C₁₆	C₂³	1	2	yes	—
75	C₂×C₅×C₁₆	C₂³	1	2	yes	—
76	C₅×#107	—	2	1	no	—
77	C₅×#107	C₂³	1	1	yes	characteristic
78	C₅×#107	C₂³	1	1	yes	characteristic
79	C₅×#107	C₂³	1	2	yes	—
80	C₅×#106	—	2	1	no	—
81	C₅×#103	—	2	1	no	—
82	C₅×#103	—	2	1	no	—
83	C₅×#103	—	2	2	no	—
84	C₅×#103	—	2	2	no	—
85	C₅×#102	—	2	1	no	—
86	C₅×#102	—	2	1	no	—
87	C₄×C₅×C₈	D₄	1	1	yes	characteristic
88	C₄×C₅×C₈	D₄	1	1	yes	characteristic
89	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
90	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
91	#3170	C₂×C₅	1	1	yes	characteristic, complemented
92	C₄×#135	C₂×C₅	1	1	yes	characteristic
93	#2237	C₂×C₅	1	2	yes	complemented
94	#2225	C₂×C₅	1	1	yes	characteristic, complemented
95	#2224	C₂×C₅	1	1	yes	characteristic, complemented
96	#2209	C₂×C₅	1	1	yes	characteristic, complemented
97	#2208	C₂×C₅	1	1	yes	characteristic, complemented
98	#2189	C₂×C₅	1	2	yes	—
99	C₄×Q₃₂	C₂×C₅	1	2	yes	complemented
100	C₄×SD₃₂	C₂×C₅	1	2	yes	complemented
101	#2162	C₂×C₅	1	1	yes	characteristic, complemented
102	C₅×#41	—	2	4	no	—
103	C₅×#41	—	4	2	no	—
104	C₂×C₅×Q₈	—	2	1	no	—
105	C₂×C₅×Q₈	—	2	2	no	—
106	C₂×C₅×Q₈	—	4	1	no	—
107	C₂×C₅×D₄	—	2	1	no	—
108	C₂×C₅×D₄	—	4	1	no	—
109	C₂²×C₄×C₅	—	4	1	no	—
110	C₂²×C₄×C₅	—	4	1	no	—
111	C₂²×C₄×C₅	—	4	1	no	—
112	C₂²×C₄×C₅	D₈	1	1	yes	characteristic
113	C₂²×C₄×C₅	D₈	1	1	yes	characteristic
114	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
115	C₅×Q₁₆	—	2	1	no	—
116	C₅×Q₁₆	—	2	2	no	—
117	C₅×Q₁₆	—	2	2	no	—
118	C₅×Q₁₆	—	4	2	no	—
119	C₅×Q₁₆	#41	1	2	yes	—
120	C₅×SD₁₆	—	2	4	no	—
121	C₅×D₈	—	2	1	no	—
122	C₅×D₈	#41	1	2	yes	—
123	C₂×C₅×C₈	—	2	1	no	—
124	C₂×C₅×C₈	—	2	1	no	—
125	C₂×C₅×C₈	—	4	1	no	—
126	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
127	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
128	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
129	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
130	C₅×C₄⋊C₄	—	2	1	no	—
131	C₅×C₄⋊C₄	—	2	1	no	—
132	C₅×C₄⋊C₄	—	2	2	no	—
133	C₅×C₄⋊C₄	—	4	1	no	—
134	C₅×C₄⋊C₄	—	4	1	no	—
135	C₅×C₄⋊C₄	—	4	1	no	—
136	C₅×C₄⋊C₄	—	4	1	no	—
137	C₅×C₄⋊C₄	—	4	2	no	—
138	C₅×C₄⋊C₄	—	4	2	no	—
139	C₅×C₄⋊C₄	—	4	1	no	—
140	C₅×C₂²⋊C₄	—	4	1	no	—
141	C₅×C₂²⋊C₄	—	4	2	no	—
142	C₅×C₂²⋊C₄	—	4	1	no	—
143	C₅×C₂²⋊C₄	—	4	1	no	—
144	C₄²×C₅	—	4	1	no	—
145	C₄²×C₅	—	4	1	no	—
146	C₄²×C₅	—	4	1	no	—
147	C₄²×C₅	—	4	2	no	—
148	C₄²×C₅	D₈	1	1	yes	characteristic
149	C₄²×C₅	D₈	1	1	yes	characteristic
150	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
151	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
152	C₅×C₁₆	—	2	2	no	—
153	C₅×C₁₆	—	2	2	no	—
154	C₂×#135	C₂²×C₅	1	1	yes	characteristic
155	#533	—	2	1	no	—
156	C₄×#41	—	2	1	no	—
157	C₂×Q₃₂	C₂²×C₅	1	2	yes	—
158	C₂×SD₃₂	C₂²×C₅	1	2	yes	—
159	#500	C₂²×C₅	1	1	yes	characteristic
160	#494	C₂²×C₅	1	1	yes	characteristic
161	#487	—	2	1	no	—
162	#467	—	2	1	no	—
163	#467	C₂²×C₅	1	2	yes	—
164	C₄×Q₁₆	—	2	1	no	—
165	C₄×Q₁₆	C₂²×C₅	1	2	yes	—
166	C₄×Q₁₆	C₂²×C₅	1	1	yes	characteristic
167	C₄×Q₁₆	C₂²×C₅	1	1	yes	characteristic
168	C₄×SD₁₆	—	2	1	no	—
169	C₄×SD₁₆	—	2	1	no	—
170	C₄×D₈	C₂²×C₅	1	1	yes	characteristic
171	C₄×D₈	C₂²×C₅	1	1	yes	characteristic
172	#427	C₂²×C₅	1	1	yes	characteristic
173	#416	—	2	1	no	—
174	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
175	#367	C₂²×C₅	1	2	yes	—
176	#366	C₂²×C₅	1	2	yes	—
177	C₄⋊C₁₆	C₂²×C₅	1	1	yes	characteristic
178	C₄⋊C₁₆	C₂²×C₅	1	1	yes	characteristic
179	#358	C₂²×C₅	1	2	yes	—
180	#358	C₂²×C₅	1	2	yes	—
181	#358	C₂²×C₅	1	2	yes	—
182	#357	C₂²×C₅	1	2	yes	—
183	C₂²⋊C₁₆	C₂²×C₅	1	2	yes	—
184	C₄×C₁₆	C₂²×C₅	1	2	yes	—
185	C₂³×C₅	—	4	1	no	—
186	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
187	C₅×Q₈	—	2	2	no	—
188	C₅×Q₈	—	4	1	no	—
189	C₅×Q₈	—	4	2	no	—
190	C₅×Q₈	—	4	2	no	—
191	C₅×Q₈	—	8	2	no	—
192	C₅×D₄	—	2	2	no	—
193	C₅×D₄	—	4	4	no	—
194	C₅×D₄	—	4	1	no	—
195	C₂×C₄×C₅	—	2	1	no	—
196	C₂×C₄×C₅	—	2	1	no	—
197	C₂×C₄×C₅	—	2	2	no	—
198	C₂×C₄×C₅	—	2	2	no	—
199	C₂×C₄×C₅	—	4	4	no	—
200	C₂×C₄×C₅	—	4	1	no	—
201	C₂×C₄×C₅	—	4	1	no	—
202	C₂×C₄×C₅	—	4	1	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	C₂×D₈	1	1	yes	characteristic
208	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
209	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
210	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
211	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
212	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
213	C₅×C₈	—	2	1	no	—
214	C₅×C₈	—	2	1	no	—
215	C₅×C₈	—	2	1	no	—
216	C₅×C₈	C₂×#41	1	1	yes	characteristic
217	C₅×C₈	C₂×#41	1	1	yes	characteristic
218	C₂×#41	—	2	1	no	—
219	#135	—	2	2	no	—
220	#135	—	2	2	no	—
221	C₂×Q₁₆	—	2	1	no	—
222	C₂×Q₁₆	C₂³×C₅	1	2	yes	—
223	C₂×Q₁₆	C₂³×C₅	1	1	yes	characteristic
224	C₂×SD₁₆	—	2	1	no	—
225	C₂×D₈	C₂³×C₅	1	1	yes	characteristic
226	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
227	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
228	C₄⋊Q₈	—	2	1	no	—
229	C₄⋊Q₈	—	2	1	no	—
230	#125	—	4	1	no	—
231	C₂²⋊Q₈	—	2	2	no	—
232	C₂²⋊Q₈	—	4	1	no	—
233	C₄×Q₈	—	2	1	no	—
234	C₄×Q₈	—	2	1	no	—
235	C₄×Q₈	—	2	2	no	—
236	C₄×Q₈	—	4	1	no	—
237	C₄×D₄	—	2	1	no	—
238	C₄×D₄	—	2	1	no	—
239	C₄×D₄	—	4	1	no	—
240	C₄×D₄	—	4	1	no	—
241	#117	—	2	1	no	—
242	#117	—	4	1	no	—
243	#117	—	4	1	no	—
244	C₂×C₄²	—	4	1	no	—
245	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
246	Q₃₂	—	2	4	no	—
247	SD₃₂	—	2	4	no	—
248	C₂×C₁₆	C₂³×C₅	1	2	yes	—
249	C₂×C₁₆	C₂³×C₅	1	2	yes	—
250	#107	—	2	1	no	—
251	#107	C₂³×C₅	1	2	yes	—
252	#107	C₂³×C₅	1	1	yes	characteristic
253	#107	C₂³×C₅	1	1	yes	characteristic
254	#106	—	2	1	no	—
255	#103	—	2	1	no	—
256	#103	—	2	1	no	—
257	#103	—	2	2	no	—
258	#103	—	2	2	no	—
259	#102	—	2	1	no	—
260	#102	—	2	1	no	—
261	C₄×C₈	C₅×D₄	1	1	yes	characteristic
262	C₄×C₈	C₅×D₄	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	—	8	1	no	—
270	C₂²×C₅	—	8	1	no	—
271	C₂²×C₅	C₂²×D₈	1	1	yes	characteristic
272	C₄×C₅	—	2	1	no	—
273	C₄×C₅	—	2	1	no	—
274	C₄×C₅	—	2	1	no	—
275	C₄×C₅	—	4	2	no	—
276	C₄×C₅	—	8	2	no	—
277	C₄×C₅	—	8	1	no	—
278	C₄×C₅	—	8	2	no	—
279	C₄×C₅	—	8	1	no	—
280	C₄×C₅	#508	1	2	yes	—
281	C₄×C₅	#510	1	2	yes	—
282	C₄×C₅	#525	1	1	yes	characteristic
283	C₄×C₅	#575	1	1	yes	characteristic
284	#41	—	2	4	no	—
285	#41	—	4	2	no	—
286	C₂×Q₈	—	2	1	no	—
287	C₂×Q₈	—	2	2	no	—
288	C₂×Q₈	—	4	1	no	—
289	C₂×D₄	—	2	1	no	—
290	C₂×D₄	—	4	1	no	—
291	C₂²×C₄	—	4	1	no	—
292	C₂²×C₄	—	4	1	no	—
293	C₂²×C₄	—	4	1	no	—
294	C₂²×C₄	C₅×D₈	1	1	yes	characteristic
295	C₂²×C₄	C₅×D₈	1	1	yes	characteristic
296	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
297	Q₁₆	—	2	1	no	—
298	Q₁₆	—	2	2	no	—
299	Q₁₆	—	2	2	no	—
300	Q₁₆	—	4	2	no	—
301	Q₁₆	C₅×#41	1	2	yes	—
302	SD₁₆	—	2	4	no	—
303	D₈	—	2	1	no	—
304	D₈	C₅×#41	1	2	yes	—
305	C₂×C₈	—	2	1	no	—
306	C₂×C₈	—	2	1	no	—
307	C₂×C₈	—	4	1	no	—
308	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
309	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
310	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
311	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
312	C₄⋊C₄	—	2	1	no	—
313	C₄⋊C₄	—	2	1	no	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	4	1	no	—
316	C₄⋊C₄	—	4	1	no	—
317	C₄⋊C₄	—	4	1	no	—
318	C₄⋊C₄	—	4	1	no	—
319	C₄⋊C₄	—	4	2	no	—
320	C₄⋊C₄	—	4	2	no	—
321	C₄⋊C₄	—	4	1	no	—
322	C₂²⋊C₄	—	4	1	no	—
323	C₂²⋊C₄	—	4	2	no	—
324	C₂²⋊C₄	—	4	1	no	—
325	C₂²⋊C₄	—	4	1	no	—
326	C₄²	—	4	1	no	—
327	C₄²	—	4	1	no	—
328	C₄²	—	4	1	no	—
329	C₄²	—	4	2	no	—
330	C₄²	C₅×D₈	1	1	yes	characteristic
331	C₄²	C₅×D₈	1	1	yes	characteristic
332	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
333	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
334	C₁₆	—	2	2	no	—
335	C₁₆	—	2	2	no	—
336	C₂×C₅	—	4	1	no	—
337	C₂×C₅	—	8	2	no	—
338	C₂×C₅	#3100	1	1	yes	characteristic
339	C₂×C₅	C₂×#508	1	1	yes	characteristic
340	C₂×C₅	C₂×#510	1	1	yes	characteristic
341	C₂³	—	4	1	no	—
342	C₂³	C₂×C₅×D₈	1	1	yes	characteristic
343	Q₈	—	2	2	no	—
344	Q₈	—	4	1	no	—
345	Q₈	—	4	2	no	—
346	Q₈	—	4	2	no	—
347	Q₈	—	8	2	no	—
348	D₄	—	2	2	no	—
349	D₄	—	4	4	no	—
350	D₄	—	4	1	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	4	4	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	8	2	no	—
362	C₂×C₄	—	8	2	no	—
363	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
364	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
365	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
366	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
367	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
368	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
369	C₈	—	2	1	no	—
370	C₈	—	2	1	no	—
371	C₈	—	2	1	no	—
372	C₈	C₂×C₅×#41	1	1	yes	characteristic
373	C₈	C₂×C₅×#41	1	1	yes	characteristic
374	C₅	#33667	1	1	yes	characteristic, direct product factor, Sylow
375	C₂²	—	2	1	no	—
376	C₂²	—	2	1	no	—
377	C₂²	—	2	1	no	—
378	C₂²	—	4	2	no	—
379	C₂²	—	8	1	no	—
380	C₂²	—	8	1	no	—
381	C₂²	C₂²×C₅×D₈	1	1	yes	characteristic
382	C₄	—	2	1	no	—
383	C₄	—	2	1	no	—
384	C₄	—	2	1	no	—
385	C₄	—	4	2	no	—
386	C₄	—	8	2	no	—
387	C₄	—	8	1	no	—
388	C₄	—	8	2	no	—
389	C₄	—	8	1	no	—
390	C₄	C₅×#508	1	2	yes	—
391	C₄	C₅×#510	1	2	yes	—
392	C₄	C₅×#525	1	1	yes	characteristic
393	C₄	C₅×#575	1	1	yes	characteristic
394	C₂	—	4	1	no	—
395	C₂	—	8	2	no	—
396	C₂	C₅×#3100	1	1	yes	characteristic
397	C₂	C₂×C₅×#508	1	1	yes	characteristic
398	C₂	C₂×C₅×#510	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₅
socle	C₂²×C₅	C₂²×D₈
prime radical	C₂×C₅×#135	C₂²
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×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. C₅×#3170	C₂	semidirect
3. C₅×#2237	C₂	semidirect
4. C₅×#2225	C₂	semidirect
5. C₅×#2224	C₂	semidirect
6. C₅×#2209	C₂	semidirect
7. C₅×#2208	C₂	semidirect
9. C₄×C₅×Q₃₂	C₂	semidirect
10. C₄×C₅×SD₃₂	C₂	semidirect
11. C₅×#2162	C₂	semidirect
43. #33667	C₅	direct (N × H)
91. #3170	C₂×C₅	semidirect
93. #2237	C₂×C₅	semidirect
94. #2225	C₂×C₅	semidirect
95. #2224	C₂×C₅	semidirect
96. #2209	C₂×C₅	semidirect
97. #2208	C₂×C₅	semidirect
99. C₄×Q₃₂	C₂×C₅	semidirect
100. C₄×SD₃₂	C₂×C₅	semidirect
101. #2162	C₂×C₅	semidirect
374. C₅	#33667	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×#3170	2
C₄×C₅×#135	2
C₅×#2237	2
C₅×#2225	2
C₅×#2224	2
C₅×#2209	2
C₅×#2208	2
C₅×#2189	2
C₄×C₅×Q₃₂	2
C₄×C₅×SD₃₂	2
C₅×#2162	2
#33667	5

Subgroups — C5×#33667 #11956387

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#33667 #11956387