Subgroups — C₅×#33842 #11956562

Order 1280.

664 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×#510	C₂	1	2	yes	maximal, complemented
2	C₅×D₄×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#3283	C₂	1	1	yes	maximal, characteristic
4	C₅×#2247	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2219	C₂	1	2	yes	maximal, 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, complemented
9	C₅×#2188	C₂	1	2	yes	maximal, complemented
10	C₄×C₅×SD₃₂	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#2169	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#135	C₂²	1	2	yes	—
13	C₂²×C₅×Q₁₆	C₂²	1	2	yes	—
14	C₅×D₄×Q₈	—	2	1	no	—
15	C₅×#547	—	2	1	no	—
16	C₅×#510	—	2	8	no	—
17	C₂×C₅×Q₃₂	C₂²	1	2	yes	—
18	C₂×C₅×Q₃₂	C₂²	1	2	yes	—
19	C₂×C₅×Q₃₂	C₂²	1	2	yes	—
20	C₂×C₅×SD₃₂	C₂²	1	2	yes	—
21	C₂×C₅×SD₃₂	C₂²	1	1	yes	characteristic
22	C₂×C₅×M₃₂	C₂²	1	2	yes	—
23	C₅×#494	C₂²	1	1	yes	characteristic
24	C₅×#494	C₂²	1	1	yes	characteristic
25	C₅×#467	C₂²	1	2	yes	—
26	C₅×#467	C₂²	1	2	yes	—
27	C₅×#462	—	2	1	no	—
28	C₅×#461	—	2	1	no	—
29	C₅×#452	—	2	2	no	—
30	C₅×#451	—	2	2	no	—
31	C₄×C₅×Q₁₆	C₂²	1	1	yes	characteristic
32	C₄×C₅×D₈	C₂²	1	1	yes	characteristic
33	C₅×C₈×D₄	C₂²	1	1	yes	characteristic
34	C₅×#367	C₂²	1	1	yes	characteristic
35	C₅×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
36	C₅×#358	C₂²	1	1	yes	characteristic
37	C₅×#358	C₂²	1	2	yes	—
38	C₅×#358	C₂²	1	2	yes	—
39	C₅×#357	C₂²	1	1	yes	characteristic
40	C₅×C₂²⋊C₁₆	C₂²	1	2	yes	—
41	C₄×C₅×C₁₆	C₂²	1	1	yes	characteristic
42	#33842	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂×C₅×#41	—	2	2	no	—
44	C₂²×C₅×Q₈	—	2	2	no	—
45	C₅×#135	—	2	4	no	—
46	C₅×#135	—	4	2	no	—
47	C₂×C₅×Q₁₆	—	2	4	no	—
48	C₂×C₅×Q₁₆	—	2	2	no	—
49	C₂×C₅×Q₁₆	—	2	1	no	—
50	C₂×C₅×Q₁₆	—	2	1	no	—
51	C₂×C₅×Q₁₆	—	4	2	no	—
52	C₂×C₅×Q₁₆	C₂³	1	2	yes	—
53	C₂×C₅×Q₁₆	C₂³	1	2	yes	—
54	C₂×C₅×Q₁₆	C₂³	1	1	yes	characteristic
55	C₂×C₅×SD₁₆	—	2	2	no	—
56	C₂×C₅×D₈	C₂³	1	1	yes	characteristic
57	C₂²×C₅×C₈	C₂³	1	2	yes	—
58	C₅×C₄⋊Q₈	—	2	1	no	—
59	C₅×C₄⋊Q₈	—	2	1	no	—
60	C₅×C₄⋊Q₈	—	4	1	no	—
61	C₅×#123	—	4	2	no	—
62	C₅×C₂²⋊Q₈	—	2	2	no	—
63	C₅×C₂²⋊Q₈	—	2	2	no	—
64	C₅×C₂²⋊Q₈	—	4	2	no	—
65	C₅×#121	—	4	1	no	—
66	C₄×C₅×Q₈	—	2	1	no	—
67	C₄×C₅×D₄	—	2	1	no	—
68	C₄×C₅×D₄	—	4	1	no	—
69	C₄×C₅×D₄	D₄	1	1	yes	characteristic
70	C₂×C₅×C₄⋊C₄	—	4	1	no	—
71	C₅×Q₃₂	—	2	4	no	—
72	C₅×Q₃₂	—	2	4	no	—
73	C₅×Q₃₂	—	4	2	no	—
74	C₅×SD₃₂	—	2	4	no	—
75	C₅×SD₃₂	D₄	1	4	yes	complemented
76	C₅×M₃₂	—	2	4	no	—
77	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
78	C₂×C₅×C₁₆	C₂³	1	2	yes	—
79	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
80	C₅×#107	C₂³	1	1	yes	characteristic
81	C₅×#107	C₂³	1	1	yes	characteristic
82	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
83	C₅×#103	—	2	1	no	—
84	C₅×#103	—	2	2	no	—
85	C₅×#103	—	2	2	no	—
86	C₅×#102	—	2	1	no	—
87	C₅×C₂²⋊C₈	D₄	1	2	yes	—
88	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
89	C₂×#510	C₂×C₅	1	2	yes	complemented
90	D₄×Q₁₆	C₂×C₅	1	1	yes	characteristic, complemented
91	#3283	C₂×C₅	1	1	yes	characteristic
92	#2247	C₂×C₅	1	1	yes	characteristic, complemented
93	#2219	C₂×C₅	1	2	yes	complemented
94	#2209	C₂×C₅	1	1	yes	characteristic, complemented
95	#2208	C₂×C₅	1	1	yes	characteristic, complemented
96	#2189	C₂×C₅	1	2	yes	complemented
97	#2188	C₂×C₅	1	2	yes	complemented
98	C₄×SD₃₂	C₂×C₅	1	1	yes	characteristic, complemented
99	#2169	C₂×C₅	1	1	yes	characteristic, complemented
100	C₅×#41	—	4	4	no	—
101	C₅×#41	—	8	2	no	—
102	C₂×C₅×Q₈	—	2	1	no	—
103	C₂×C₅×Q₈	—	2	2	no	—
104	C₂×C₅×Q₈	—	2	2	no	—
105	C₂×C₅×Q₈	—	4	4	no	—
106	C₂×C₅×Q₈	—	4	2	no	—
107	C₂×C₅×Q₈	—	8	2	no	—
108	C₂×C₅×D₄	—	2	1	no	—
109	C₂×C₅×D₄	—	4	2	no	—
110	C₂×C₅×D₄	D₈	1	1	yes	characteristic
111	C₂²×C₄×C₅	—	4	2	no	—
112	C₂²×C₄×C₅	—	4	1	no	—
113	C₂²×C₄×C₅	—	4	2	no	—
114	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
115	C₅×Q₁₆	—	2	2	no	—
116	C₅×Q₁₆	—	2	2	no	—
117	C₅×Q₁₆	—	2	1	no	—
118	C₅×Q₁₆	—	2	2	no	—
119	C₅×Q₁₆	—	2	2	no	—
120	C₅×Q₁₆	—	4	4	no	—
121	C₅×Q₁₆	—	8	1	no	—
122	C₅×Q₁₆	—	8	1	no	—
123	C₅×Q₁₆	C₂×D₄	1	2	yes	—
124	C₅×SD₁₆	—	4	4	no	—
125	C₅×D₈	—	2	1	no	—
126	C₅×D₈	C₂×D₄	1	2	yes	—
127	C₂×C₅×C₈	—	2	2	no	—
128	C₂×C₅×C₈	—	2	2	no	—
129	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
130	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
131	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
132	C₅×C₄⋊C₄	—	2	1	no	—
133	C₅×C₄⋊C₄	—	2	1	no	—
134	C₅×C₄⋊C₄	—	4	1	no	—
135	C₅×C₄⋊C₄	—	4	2	no	—
136	C₅×C₄⋊C₄	—	4	1	no	—
137	C₅×C₄⋊C₄	—	4	1	no	—
138	C₅×C₄⋊C₄	—	4	2	no	—
139	C₅×C₄⋊C₄	—	4	1	no	—
140	C₅×C₄⋊C₄	—	4	1	no	—
141	C₅×C₄⋊C₄	D₈	1	1	yes	characteristic
142	C₅×C₂²⋊C₄	—	4	2	no	—
143	C₅×C₂²⋊C₄	—	4	2	no	—
144	C₅×C₂²⋊C₄	—	4	1	no	—
145	C₅×C₂²⋊C₄	D₈	1	2	yes	—
146	C₄²×C₅	—	4	1	no	—
147	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
148	C₅×C₁₆	—	2	2	no	—
149	C₅×C₁₆	—	2	1	no	—
150	C₅×C₁₆	C₂×D₄	1	2	yes	—
151	C₂×#135	C₂²×C₅	1	2	yes	—
152	C₂²×Q₁₆	C₂²×C₅	1	2	yes	—
153	D₄×Q₈	—	2	1	no	—
154	#547	—	2	1	no	—
155	#510	—	2	8	no	—
156	C₂×Q₃₂	C₂²×C₅	1	2	yes	—
157	C₂×Q₃₂	C₂²×C₅	1	2	yes	—
158	C₂×Q₃₂	C₂²×C₅	1	2	yes	—
159	C₂×SD₃₂	C₂²×C₅	1	2	yes	—
160	C₂×SD₃₂	C₂²×C₅	1	1	yes	characteristic
161	C₂×M₃₂	C₂²×C₅	1	2	yes	—
162	#494	C₂²×C₅	1	1	yes	characteristic
163	#494	C₂²×C₅	1	1	yes	characteristic
164	#467	C₂²×C₅	1	2	yes	—
165	#467	C₂²×C₅	1	2	yes	—
166	#462	—	2	1	no	—
167	#461	—	2	1	no	—
168	#452	—	2	2	no	—
169	#451	—	2	2	no	—
170	C₄×Q₁₆	C₂²×C₅	1	1	yes	characteristic
171	C₄×D₈	C₂²×C₅	1	1	yes	characteristic
172	C₈×D₄	C₂²×C₅	1	1	yes	characteristic
173	#367	C₂²×C₅	1	1	yes	characteristic
174	C₄⋊C₁₆	C₂²×C₅	1	1	yes	characteristic
175	#358	C₂²×C₅	1	1	yes	characteristic
176	#358	C₂²×C₅	1	2	yes	—
177	#358	C₂²×C₅	1	2	yes	—
178	#357	C₂²×C₅	1	1	yes	characteristic
179	C₂²⋊C₁₆	C₂²×C₅	1	2	yes	—
180	C₄×C₁₆	C₂²×C₅	1	1	yes	characteristic
181	C₂³×C₅	—	4	1	no	—
182	C₂³×C₅	C₂×D₈	1	2	yes	—
183	C₅×Q₈	—	2	2	no	—
184	C₅×Q₈	—	4	1	no	—
185	C₅×Q₈	—	4	2	no	—
186	C₅×Q₈	—	4	2	no	—
187	C₅×Q₈	—	4	2	no	—
188	C₅×Q₈	—	4	2	no	—
189	C₅×Q₈	—	8	4	no	—
190	C₅×D₄	—	2	2	no	—
191	C₅×D₄	—	2	2	no	—
192	C₅×D₄	—	4	1	no	—
193	C₅×D₄	—	8	4	no	—
194	C₂×C₄×C₅	—	2	2	no	—
195	C₂×C₄×C₅	—	2	2	no	—
196	C₂×C₄×C₅	—	4	1	no	—
197	C₂×C₄×C₅	—	4	1	no	—
198	C₂×C₄×C₅	—	4	1	no	—
199	C₂×C₄×C₅	—	4	2	no	—
200	C₂×C₄×C₅	—	4	2	no	—
201	C₂×C₄×C₅	—	8	4	no	—
202	C₂×C₄×C₅	—	8	4	no	—
203	C₂×C₄×C₅	—	8	2	no	—
204	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
205	C₂×C₄×C₅	C₂×D₈	1	2	yes	—
206	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
207	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
208	C₅×C₈	—	2	2	no	—
209	C₅×C₈	—	2	1	no	—
210	C₅×C₈	C₂²×D₄	1	1	yes	characteristic
211	C₅×C₈	H(5,𝔽₂)	1	1	yes	characteristic
212	C₂×#41	—	2	2	no	—
213	C₂²×Q₈	—	2	2	no	—
214	#135	—	2	4	no	—
215	#135	—	4	2	no	—
216	C₂×Q₁₆	—	2	4	no	—
217	C₂×Q₁₆	—	2	2	no	—
218	C₂×Q₁₆	—	2	1	no	—
219	C₂×Q₁₆	—	2	1	no	—
220	C₂×Q₁₆	—	4	2	no	—
221	C₂×Q₁₆	C₂³×C₅	1	2	yes	—
222	C₂×Q₁₆	C₂³×C₅	1	2	yes	—
223	C₂×Q₁₆	C₂³×C₅	1	1	yes	characteristic
224	C₂×SD₁₆	—	2	2	no	—
225	C₂×D₈	C₂³×C₅	1	1	yes	characteristic
226	C₂²×C₈	C₂³×C₅	1	2	yes	—
227	C₄⋊Q₈	—	2	1	no	—
228	C₄⋊Q₈	—	2	1	no	—
229	C₄⋊Q₈	—	4	1	no	—
230	#123	—	4	2	no	—
231	C₂²⋊Q₈	—	2	2	no	—
232	C₂²⋊Q₈	—	2	2	no	—
233	C₂²⋊Q₈	—	4	2	no	—
234	#121	—	4	1	no	—
235	C₄×Q₈	—	2	1	no	—
236	C₄×D₄	—	2	1	no	—
237	C₄×D₄	—	4	1	no	—
238	C₄×D₄	C₅×D₄	1	1	yes	characteristic
239	C₂×C₄⋊C₄	—	4	1	no	—
240	Q₃₂	—	2	4	no	—
241	Q₃₂	—	2	4	no	—
242	Q₃₂	—	4	2	no	—
243	SD₃₂	—	2	4	no	—
244	SD₃₂	C₅×D₄	1	4	yes	complemented
245	M₃₂	—	2	4	no	—
246	C₂×C₁₆	C₂³×C₅	1	1	yes	characteristic
247	C₂×C₁₆	C₂³×C₅	1	2	yes	—
248	C₂×C₁₆	C₂³×C₅	1	1	yes	characteristic
249	#107	C₂³×C₅	1	1	yes	characteristic
250	#107	C₂³×C₅	1	1	yes	characteristic
251	C₄⋊C₈	C₅×D₄	1	1	yes	characteristic
252	#103	—	2	1	no	—
253	#103	—	2	2	no	—
254	#103	—	2	2	no	—
255	#102	—	2	1	no	—
256	C₂²⋊C₈	C₅×D₄	1	2	yes	—
257	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
258	C₂²×C₅	—	2	2	no	—
259	C₂²×C₅	—	2	2	no	—
260	C₂²×C₅	—	2	2	no	—
261	C₂²×C₅	—	4	2	no	—
262	C₂²×C₅	—	8	1	no	—
263	C₂²×C₅	—	8	1	no	—
264	C₂²×C₅	C₂²×D₈	1	1	yes	characteristic
265	C₄×C₅	—	2	1	no	—
266	C₄×C₅	—	2	2	no	—
267	C₄×C₅	—	4	2	no	—
268	C₄×C₅	—	8	1	no	—
269	C₄×C₅	—	8	1	no	—
270	C₄×C₅	—	8	2	no	—
271	C₄×C₅	—	8	2	no	—
272	C₄×C₅	#510	1	2	yes	complemented
273	C₄×C₅	D₄²	1	1	yes	characteristic
274	C₄×C₅	#576	1	1	yes	characteristic
275	#41	—	4	4	no	—
276	#41	—	8	2	no	—
277	C₂×Q₈	—	2	1	no	—
278	C₂×Q₈	—	2	2	no	—
279	C₂×Q₈	—	2	2	no	—
280	C₂×Q₈	—	4	4	no	—
281	C₂×Q₈	—	4	2	no	—
282	C₂×Q₈	—	8	2	no	—
283	C₂×D₄	—	2	1	no	—
284	C₂×D₄	—	4	2	no	—
285	C₂×D₄	C₅×D₈	1	1	yes	characteristic
286	C₂²×C₄	—	4	2	no	—
287	C₂²×C₄	—	4	1	no	—
288	C₂²×C₄	—	4	2	no	—
289	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
290	Q₁₆	—	2	2	no	—
291	Q₁₆	—	2	2	no	—
292	Q₁₆	—	2	1	no	—
293	Q₁₆	—	2	2	no	—
294	Q₁₆	—	2	2	no	—
295	Q₁₆	—	4	4	no	—
296	Q₁₆	—	8	1	no	—
297	Q₁₆	—	8	1	no	—
298	Q₁₆	C₂×C₅×D₄	1	2	yes	—
299	SD₁₆	—	4	4	no	—
300	D₈	—	2	1	no	—
301	D₈	C₂×C₅×D₄	1	2	yes	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
305	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
306	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
307	C₄⋊C₄	—	2	1	no	—
308	C₄⋊C₄	—	2	1	no	—
309	C₄⋊C₄	—	4	1	no	—
310	C₄⋊C₄	—	4	2	no	—
311	C₄⋊C₄	—	4	1	no	—
312	C₄⋊C₄	—	4	1	no	—
313	C₄⋊C₄	—	4	2	no	—
314	C₄⋊C₄	—	4	1	no	—
315	C₄⋊C₄	—	4	1	no	—
316	C₄⋊C₄	C₅×D₈	1	1	yes	characteristic
317	C₂²⋊C₄	—	4	2	no	—
318	C₂²⋊C₄	—	4	2	no	—
319	C₂²⋊C₄	—	4	1	no	—
320	C₂²⋊C₄	C₅×D₈	1	2	yes	—
321	C₄²	—	4	1	no	—
322	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
323	C₁₆	—	2	2	no	—
324	C₁₆	—	2	1	no	—
325	C₁₆	C₂×C₅×D₄	1	2	yes	—
326	C₂×C₅	—	4	2	no	—
327	C₂×C₅	—	8	2	no	—
328	C₂×C₅	D₄×D₈	1	1	yes	characteristic
329	C₂×C₅	C₂×#510	1	1	yes	characteristic
330	C₂×C₅	#3417	1	1	yes	characteristic
331	C₂³	—	4	1	no	—
332	C₂³	C₂×C₅×D₈	1	2	yes	—
333	Q₈	—	2	2	no	—
334	Q₈	—	4	1	no	—
335	Q₈	—	4	2	no	—
336	Q₈	—	4	2	no	—
337	Q₈	—	4	2	no	—
338	Q₈	—	4	2	no	—
339	Q₈	—	8	4	no	—
340	D₄	—	2	2	no	—
341	D₄	—	2	2	no	—
342	D₄	—	4	1	no	—
343	D₄	—	8	4	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	4	1	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	8	4	no	—
352	C₂×C₄	—	8	4	no	—
353	C₂×C₄	—	8	2	no	—
354	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
355	C₂×C₄	C₂×C₅×D₈	1	2	yes	—
356	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
357	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
358	C₈	—	2	2	no	—
359	C₈	—	2	1	no	—
360	C₈	C₂²×C₅×D₄	1	1	yes	characteristic
361	C₈	C₅×H(5,𝔽₂)	1	1	yes	characteristic
362	C₅	#33842	1	1	yes	characteristic, direct product factor, Sylow
363	C₂²	—	2	2	no	—
364	C₂²	—	2	2	no	—
365	C₂²	—	2	2	no	—
366	C₂²	—	4	2	no	—
367	C₂²	—	8	1	no	—
368	C₂²	—	8	1	no	—
369	C₂²	C₂²×C₅×D₈	1	1	yes	characteristic
370	C₄	—	2	2	no	—
371	C₄	—	2	1	no	—
372	C₄	—	4	2	no	—
373	C₄	—	8	2	no	—
374	C₄	—	8	2	no	—
375	C₄	—	8	1	no	—
376	C₄	—	8	1	no	—
377	C₄	C₅×#510	1	2	yes	complemented
378	C₄	C₅×D₄²	1	1	yes	characteristic
379	C₄	C₅×#576	1	1	yes	characteristic
380	C₂	—	4	2	no	—
381	C₂	—	8	2	no	—
382	C₂	C₅×D₄×D₈	1	1	yes	characteristic
383	C₂	C₂×C₅×#510	1	1	yes	characteristic
384	C₂	C₅×#3417	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₅
prime radical	C₅×#3283	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₄×C₅×D₄ ◁ C₅×C₈×D₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#510	C₂	semidirect
2. C₅×D₄×Q₁₆	C₂	semidirect
4. C₅×#2247	C₂	semidirect
5. C₅×#2219	C₂	semidirect
6. C₅×#2209	C₂	semidirect
7. C₅×#2208	C₂	semidirect
8. C₅×#2189	C₂	semidirect
9. C₅×#2188	C₂	semidirect
10. C₄×C₅×SD₃₂	C₂	semidirect
11. C₅×#2169	C₂	semidirect
42. #33842	C₅	direct (N × H)
75. C₅×SD₃₂	D₄	semidirect
89. C₂×#510	C₂×C₅	semidirect
90. D₄×Q₁₆	C₂×C₅	semidirect
92. #2247	C₂×C₅	semidirect
93. #2219	C₂×C₅	semidirect
94. #2209	C₂×C₅	semidirect
95. #2208	C₂×C₅	semidirect
96. #2189	C₂×C₅	semidirect
97. #2188	C₂×C₅	semidirect
98. C₄×SD₃₂	C₂×C₅	semidirect
99. #2169	C₂×C₅	semidirect
244. SD₃₂	C₅×D₄	semidirect
272. C₄×C₅	#510	semidirect
362. C₅	#33842	direct (N × H)
377. C₄	C₅×#510	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#510	2
C₅×D₄×Q₁₆	2
C₅×#3283	2
C₅×#2247	2
C₅×#2219	2
C₅×#2209	2
C₅×#2208	2
C₅×#2189	2
C₅×#2188	2
C₄×C₅×SD₃₂	2
C₅×#2169	2
#33842	5

Subgroups — C5×#33842 #11956562

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#33842 #11956562