Subgroups — C₅×#33766 #11956486

Order 1280.

584 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3059	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3058	C₂	1	1	yes	maximal, characteristic
3	C₅×#2237	C₂	1	2	yes	maximal, complemented
4	C₅×#2234	C₂	1	2	yes	maximal, complemented
5	C₅×#2220	C₂	1	2	yes	maximal, complemented
6	C₅×#2217	C₂	1	2	yes	maximal, complemented
7	C₅×#2187	C₂	1	2	yes	maximal, complemented
8	C₅×#2185	C₂	1	2	yes	maximal, complemented
9	C₅×#2113	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₅×Q₁₆	C₂²	1	1	yes	characteristic, complemented
11	C₂²×C₅×D₈	C₂²	1	1	yes	characteristic
12	C₂×C₅×#131	C₂²	1	1	yes	characteristic
13	C₅×#536	—	2	1	no	—
14	C₅×#535	—	2	1	no	—
15	C₂×C₅×SD₃₂	C₂²	1	2	yes	—
16	C₂×C₅×SD₃₂	C₂²	1	2	yes	—
17	C₂×C₅×M₃₂	C₂²	1	1	yes	characteristic, complemented
18	C₂²×C₅×C₁₆	C₂²	1	1	yes	characteristic, complemented
19	C₅×#470	—	2	1	no	—
20	C₅×#470	—	2	1	no	—
21	C₅×#469	—	2	1	no	—
22	C₅×#469	—	2	1	no	—
23	C₅×#467	C₂²	1	2	yes	—
24	C₅×#467	C₂²	1	2	yes	complemented
25	C₅×#466	C₂²	1	2	yes	—
26	C₅×#466	C₂²	1	2	yes	—
27	C₅×#427	C₂²	1	1	yes	characteristic
28	C₅×#427	C₂²	1	1	yes	characteristic, complemented
29	C₅×#419	—	2	1	no	—
30	C₅×#418	—	2	1	no	—
31	C₅×#367	C₂²	1	2	yes	complemented
32	C₅×#366	C₂²	1	2	yes	complemented
33	C₅×#358	C₂²	1	2	yes	complemented
34	C₅×#358	C₂²	1	2	yes	complemented
35	C₅×#357	C₂²	1	2	yes	—
36	C₅×#357	C₂²	1	2	yes	—
37	C₅×C₂²⋊C₁₆	C₂²	1	2	yes	—
38	C₅×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
39	#33766	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
40	C₂×C₅×#41	D₄	1	1	yes	characteristic
41	C₂²×C₅×Q₈	—	2	1	no	—
42	C₂²×C₅×D₄	—	2	1	no	—
43	C₂×C₅×Q₁₆	—	2	1	no	—
44	C₂×C₅×Q₁₆	—	4	1	no	—
45	C₂×C₅×Q₁₆	—	4	1	no	—
46	C₂×C₅×Q₁₆	C₂³	1	2	yes	—
47	C₂×C₅×D₈	—	2	1	no	—
48	C₂×C₅×D₈	—	4	1	no	—
49	C₂×C₅×D₈	—	4	1	no	—
50	C₂×C₅×D₈	C₂³	1	2	yes	—
51	C₅×#131	—	4	1	no	—
52	C₅×#131	—	4	1	no	—
53	C₂×C₅×M₁₆	D₄	1	1	yes	characteristic
54	C₂×C₅×M₁₆	D₄	1	1	yes	characteristic
55	C₂×C₅×M₁₆	D₄	1	1	yes	characteristic
56	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
57	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
58	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
59	C₅×C₄⋊Q₈	—	4	1	no	—
60	C₅×#127	—	4	1	no	—
61	C₅×#124	—	4	1	no	—
62	C₅×#124	—	4	1	no	—
63	C₅×#123	—	4	1	no	—
64	C₅×#123	—	4	1	no	—
65	C₅×C₂²⋊Q₈	—	2	2	no	—
66	C₅×C₂²⋊Q₈	—	2	2	no	—
67	C₅×#121	—	2	2	no	—
68	C₅×#121	—	2	2	no	—
69	C₅×#120	—	4	1	no	—
70	C₅×#120	—	4	1	no	—
71	C₅×#117	—	2	1	no	—
72	C₅×#117	—	2	1	no	—
73	C₅×SD₃₂	—	4	2	no	—
74	C₅×SD₃₂	—	4	2	no	—
75	C₅×M₃₂	—	4	1	no	—
76	C₂×C₅×C₁₆	—	4	1	no	—
77	C₂×C₅×C₁₆	C₂³	1	2	yes	—
78	C₂×C₅×C₁₆	C₂³	1	2	yes	—
79	C₅×#107	C₂³	1	2	yes	—
80	C₅×#107	C₂³	1	2	yes	—
81	C₅×#106	—	2	1	no	—
82	C₅×#106	—	2	1	no	—
83	C₅×#103	—	2	2	no	—
84	C₅×#103	—	2	2	no	—
85	C₅×#102	—	2	2	no	—
86	C₅×#102	—	2	2	no	—
87	#3059	C₂×C₅	1	1	yes	characteristic, complemented
88	#3058	C₂×C₅	1	1	yes	characteristic
89	#2237	C₂×C₅	1	2	yes	complemented
90	#2234	C₂×C₅	1	2	yes	complemented
91	#2220	C₂×C₅	1	2	yes	complemented
92	#2217	C₂×C₅	1	2	yes	complemented
93	#2187	C₂×C₅	1	2	yes	complemented
94	#2185	C₂×C₅	1	2	yes	complemented
95	#2113	C₂×C₅	1	1	yes	characteristic, complemented
96	C₂⁴×C₅	—	4	1	no	—
97	C₅×#41	—	4	1	no	—
98	C₅×#41	—	4	1	no	—
99	C₂×C₅×Q₈	—	2	2	no	—
100	C₂×C₅×Q₈	—	4	2	no	—
101	C₂×C₅×Q₈	—	4	2	no	—
102	C₂×C₅×Q₈	—	4	1	no	—
103	C₂×C₅×Q₈	D₈	1	1	yes	characteristic
104	C₂×C₅×D₄	—	2	2	no	—
105	C₂×C₅×D₄	—	4	2	no	—
106	C₂×C₅×D₄	—	4	2	no	—
107	C₂×C₅×D₄	—	4	2	no	—
108	C₂×C₅×D₄	—	4	2	no	—
109	C₂×C₅×D₄	—	4	1	no	—
110	C₂×C₅×D₄	D₈	1	1	yes	characteristic
111	C₂×C₅×D₄	D₈	1	1	yes	characteristic
112	C₂×C₅×D₄	D₈	1	1	yes	characteristic
113	C₂²×C₄×C₅	—	4	1	no	—
114	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
117	C₅×Q₁₆	—	2	2	no	—
118	C₅×Q₁₆	—	2	2	no	—
119	C₅×Q₁₆	—	4	2	no	—
120	C₅×D₈	—	2	2	no	—
121	C₅×D₈	—	2	2	no	—
122	C₅×D₈	—	4	2	no	—
123	C₅×M₁₆	—	4	1	no	—
124	C₅×M₁₆	—	4	1	no	—
125	C₅×M₁₆	—	4	1	no	—
126	C₂×C₅×C₈	—	2	1	no	—
127	C₂×C₅×C₈	—	2	1	no	—
128	C₂×C₅×C₈	—	2	1	no	—
129	C₂×C₅×C₈	—	2	1	no	—
130	C₂×C₅×C₈	—	2	1	no	—
131	C₂×C₅×C₈	—	2	1	no	—
132	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
133	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
134	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
135	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
136	C₅×C₄⋊C₄	—	2	2	no	—
137	C₅×C₄⋊C₄	—	2	2	no	—
138	C₅×C₄⋊C₄	—	4	2	no	—
139	C₅×C₄⋊C₄	—	4	2	no	—
140	C₅×C₂²⋊C₄	—	4	1	no	—
141	C₅×C₂²⋊C₄	—	4	1	no	—
142	C₅×C₂²⋊C₄	—	4	2	no	—
143	C₅×C₂²⋊C₄	—	4	2	no	—
144	C₅×C₂²⋊C₄	—	4	2	no	—
145	C₅×C₂²⋊C₄	—	4	2	no	—
146	C₄²×C₅	—	4	1	no	—
147	C₄²×C₅	—	4	1	no	—
148	C₅×C₁₆	—	2	2	no	—
149	C₅×C₁₆	—	2	2	no	—
150	C₂²×Q₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
151	C₂²×D₈	C₂²×C₅	1	1	yes	characteristic
152	C₂×#131	C₂²×C₅	1	1	yes	characteristic
153	#536	—	2	1	no	—
154	#535	—	2	1	no	—
155	C₂×SD₃₂	C₂²×C₅	1	2	yes	—
156	C₂×SD₃₂	C₂²×C₅	1	2	yes	—
157	C₂×M₃₂	C₂²×C₅	1	1	yes	characteristic, complemented
158	C₂²×C₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
159	#470	—	2	1	no	—
160	#470	—	2	1	no	—
161	#469	—	2	1	no	—
162	#469	—	2	1	no	—
163	#467	C₂²×C₅	1	2	yes	—
164	#467	C₂²×C₅	1	2	yes	complemented
165	#466	C₂²×C₅	1	2	yes	—
166	#466	C₂²×C₅	1	2	yes	—
167	#427	C₂²×C₅	1	1	yes	characteristic
168	#427	C₂²×C₅	1	1	yes	characteristic, complemented
169	#419	—	2	1	no	—
170	#418	—	2	1	no	—
171	#367	C₂²×C₅	1	2	yes	complemented
172	#366	C₂²×C₅	1	2	yes	complemented
173	#358	C₂²×C₅	1	2	yes	complemented
174	#358	C₂²×C₅	1	2	yes	complemented
175	#357	C₂²×C₅	1	2	yes	—
176	#357	C₂²×C₅	1	2	yes	—
177	C₂²⋊C₁₆	C₂²×C₅	1	2	yes	—
178	C₂²⋊C₁₆	C₂²×C₅	1	2	yes	complemented
179	C₂³×C₅	—	4	2	no	—
180	C₂³×C₅	—	8	2	no	—
181	C₂³×C₅	—	16	2	no	—
182	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
183	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
184	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
185	C₅×Q₈	—	4	1	no	—
186	C₅×Q₈	—	4	2	no	—
187	C₅×Q₈	—	4	2	no	—
188	C₅×Q₈	—	8	2	no	—
189	C₅×D₄	—	4	1	no	—
190	C₅×D₄	—	4	1	no	—
191	C₅×D₄	—	4	1	no	—
192	C₅×D₄	—	4	2	no	—
193	C₅×D₄	—	4	2	no	—
194	C₅×D₄	—	8	2	no	—
195	C₅×D₄	—	16	2	no	—
196	C₅×D₄	—	16	2	no	—
197	C₂×C₄×C₅	—	2	1	no	—
198	C₂×C₄×C₅	—	2	1	no	—
199	C₂×C₄×C₅	—	2	1	no	—
200	C₂×C₄×C₅	—	2	1	no	—
201	C₂×C₄×C₅	—	2	1	no	—
202	C₂×C₄×C₅	—	2	1	no	—
203	C₂×C₄×C₅	—	4	2	no	—
204	C₂×C₄×C₅	—	4	2	no	—
205	C₂×C₄×C₅	—	4	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	C₂²×D₄	1	1	yes	characteristic
211	C₅×C₈	—	2	1	no	—
212	C₅×C₈	—	2	1	no	—
213	C₅×C₈	—	2	1	no	—
214	C₅×C₈	H(5,𝔽₂)	1	1	yes	characteristic
215	C₅×C₈	H(5,𝔽₂)	1	1	yes	characteristic
216	C₂×#41	C₅×D₄	1	1	yes	characteristic
217	C₂²×Q₈	—	2	1	no	—
218	C₂²×D₄	—	2	1	no	—
219	C₂×Q₁₆	—	2	1	no	—
220	C₂×Q₁₆	—	4	1	no	—
221	C₂×Q₁₆	—	4	1	no	—
222	C₂×Q₁₆	C₂³×C₅	1	2	yes	—
223	C₂×D₈	—	2	1	no	—
224	C₂×D₈	—	4	1	no	—
225	C₂×D₈	—	4	1	no	—
226	C₂×D₈	C₂³×C₅	1	2	yes	—
227	#131	—	4	1	no	—
228	#131	—	4	1	no	—
229	C₂×M₁₆	C₅×D₄	1	1	yes	characteristic
230	C₂×M₁₆	C₅×D₄	1	1	yes	characteristic
231	C₂×M₁₆	C₅×D₄	1	1	yes	characteristic
232	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
233	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
234	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
235	C₄⋊Q₈	—	4	1	no	—
236	#127	—	4	1	no	—
237	#124	—	4	1	no	—
238	#124	—	4	1	no	—
239	#123	—	4	1	no	—
240	#123	—	4	1	no	—
241	C₂²⋊Q₈	—	2	2	no	—
242	C₂²⋊Q₈	—	2	2	no	—
243	#121	—	2	2	no	—
244	#121	—	2	2	no	—
245	#120	—	4	1	no	—
246	#120	—	4	1	no	—
247	#117	—	2	1	no	—
248	#117	—	2	1	no	—
249	SD₃₂	—	4	2	no	—
250	SD₃₂	—	4	2	no	—
251	M₃₂	—	4	1	no	—
252	C₂×C₁₆	—	4	1	no	—
253	C₂×C₁₆	C₂³×C₅	1	2	yes	—
254	C₂×C₁₆	C₂³×C₅	1	2	yes	—
255	#107	C₂³×C₅	1	2	yes	—
256	#107	C₂³×C₅	1	2	yes	—
257	#106	—	2	1	no	—
258	#106	—	2	1	no	—
259	#103	—	2	2	no	—
260	#103	—	2	2	no	—
261	#102	—	2	2	no	—
262	#102	—	2	2	no	—
263	C₂²×C₅	—	2	2	no	—
264	C₂²×C₅	—	2	2	no	—
265	C₂²×C₅	—	2	2	no	—
266	C₂²×C₅	—	2	1	no	—
267	C₂²×C₅	—	2	1	no	—
268	C₂²×C₅	—	2	1	no	—
269	C₂²×C₅	—	8	2	no	—
270	C₂²×C₅	—	8	2	no	—
271	C₂²×C₅	—	8	2	no	—
272	C₂²×C₅	—	16	4	no	—
273	C₂²×C₅	C₂²×D₈	1	1	yes	characteristic
274	C₄×C₅	—	2	1	no	—
275	C₄×C₅	—	2	1	no	—
276	C₄×C₅	—	2	1	no	—
277	C₄×C₅	—	8	2	no	—
278	C₄×C₅	—	8	2	no	—
279	C₄×C₅	—	8	2	no	—
280	C₄×C₅	#534	1	1	yes	characteristic
281	C₄×C₅	#575	1	1	yes	characteristic
282	C₂⁴	—	4	1	no	—
283	#41	—	4	1	no	—
284	#41	—	4	1	no	—
285	C₂×Q₈	—	2	2	no	—
286	C₂×Q₈	—	4	2	no	—
287	C₂×Q₈	—	4	2	no	—
288	C₂×Q₈	—	4	1	no	—
289	C₂×Q₈	C₅×D₈	1	1	yes	characteristic
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	4	2	no	—
292	C₂×D₄	—	4	2	no	—
293	C₂×D₄	—	4	2	no	—
294	C₂×D₄	—	4	2	no	—
295	C₂×D₄	—	4	1	no	—
296	C₂×D₄	C₅×D₈	1	1	yes	characteristic
297	C₂×D₄	C₅×D₈	1	1	yes	characteristic
298	C₂×D₄	C₅×D₈	1	1	yes	characteristic
299	C₂²×C₄	—	4	1	no	—
300	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
301	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
302	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
303	Q₁₆	—	2	2	no	—
304	Q₁₆	—	2	2	no	—
305	Q₁₆	—	4	2	no	—
306	D₈	—	2	2	no	—
307	D₈	—	2	2	no	—
308	D₈	—	4	2	no	—
309	M₁₆	—	4	1	no	—
310	M₁₆	—	4	1	no	—
311	M₁₆	—	4	1	no	—
312	C₂×C₈	—	2	1	no	—
313	C₂×C₈	—	2	1	no	—
314	C₂×C₈	—	2	1	no	—
315	C₂×C₈	—	2	1	no	—
316	C₂×C₈	—	2	1	no	—
317	C₂×C₈	—	2	1	no	—
318	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
319	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
320	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
321	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	4	2	no	—
325	C₄⋊C₄	—	4	2	no	—
326	C₂²⋊C₄	—	4	1	no	—
327	C₂²⋊C₄	—	4	1	no	—
328	C₂²⋊C₄	—	4	2	no	—
329	C₂²⋊C₄	—	4	2	no	—
330	C₂²⋊C₄	—	4	2	no	—
331	C₂²⋊C₄	—	4	2	no	—
332	C₄²	—	4	1	no	—
333	C₄²	—	4	1	no	—
334	C₁₆	—	2	2	no	—
335	C₁₆	—	2	2	no	—
336	C₂×C₅	—	4	1	no	—
337	C₂×C₅	—	4	1	no	—
338	C₂×C₅	—	4	1	no	—
339	C₂×C₅	—	16	2	no	—
340	C₂×C₅	#3186	1	1	yes	characteristic
341	C₂×C₅	#3416	1	2	yes	—
342	C₂³	—	4	2	no	—
343	C₂³	—	8	2	no	—
344	C₂³	—	16	2	no	—
345	C₂³	C₂×C₅×D₈	1	1	yes	characteristic
346	C₂³	C₂×C₅×D₈	1	1	yes	characteristic
347	C₂³	C₂×C₅×D₈	1	1	yes	characteristic
348	Q₈	—	4	1	no	—
349	Q₈	—	4	2	no	—
350	Q₈	—	4	2	no	—
351	Q₈	—	8	2	no	—
352	D₄	—	4	1	no	—
353	D₄	—	4	1	no	—
354	D₄	—	4	1	no	—
355	D₄	—	4	2	no	—
356	D₄	—	4	2	no	—
357	D₄	—	8	2	no	—
358	D₄	—	16	2	no	—
359	D₄	—	16	2	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	8	2	no	—
370	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
371	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
372	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
373	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
374	C₈	—	2	1	no	—
375	C₈	—	2	1	no	—
376	C₈	—	2	1	no	—
377	C₈	C₅×H(5,𝔽₂)	1	1	yes	characteristic
378	C₈	C₅×H(5,𝔽₂)	1	1	yes	characteristic
379	C₅	#33766	1	1	yes	characteristic, direct product factor, Sylow
380	C₂²	—	2	2	no	—
381	C₂²	—	2	2	no	—
382	C₂²	—	2	2	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	1	no	—
386	C₂²	—	8	2	no	—
387	C₂²	—	8	2	no	—
388	C₂²	—	8	2	no	—
389	C₂²	—	16	4	no	—
390	C₂²	C₂²×C₅×D₈	1	1	yes	characteristic
391	C₄	—	2	1	no	—
392	C₄	—	2	1	no	—
393	C₄	—	2	1	no	—
394	C₄	—	8	2	no	—
395	C₄	—	8	2	no	—
396	C₄	—	8	2	no	—
397	C₄	C₅×#534	1	1	yes	characteristic
398	C₄	C₅×#575	1	1	yes	characteristic
399	C₂	—	4	1	no	—
400	C₂	—	4	1	no	—
401	C₂	—	4	1	no	—
402	C₂	—	16	2	no	—
403	C₂	C₅×#3186	1	1	yes	characteristic
404	C₂	C₅×#3416	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₅	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₅
prime radical	C₅×#3058	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₅×#41 ◁ C₂×C₅×#131 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#3059	C₂	semidirect
3. C₅×#2237	C₂	semidirect
4. C₅×#2234	C₂	semidirect
5. C₅×#2220	C₂	semidirect
6. C₅×#2217	C₂	semidirect
7. C₅×#2187	C₂	semidirect
8. C₅×#2185	C₂	semidirect
9. C₅×#2113	C₂	semidirect
10. C₂²×C₅×Q₁₆	C₂²	semidirect
17. C₂×C₅×M₃₂	C₂²	semidirect
18. C₂²×C₅×C₁₆	C₂²	semidirect
24. C₅×#467	C₂²	semidirect
28. C₅×#427	C₂²	semidirect
31. C₅×#367	C₂²	semidirect
32. C₅×#366	C₂²	semidirect
33. C₅×#358	C₂²	semidirect
34. C₅×#358	C₂²	semidirect
38. C₅×C₂²⋊C₁₆	C₂²	semidirect
39. #33766	C₅	direct (N × H)
87. #3059	C₂×C₅	semidirect
89. #2237	C₂×C₅	semidirect
90. #2234	C₂×C₅	semidirect
91. #2220	C₂×C₅	semidirect
92. #2217	C₂×C₅	semidirect
93. #2187	C₂×C₅	semidirect
94. #2185	C₂×C₅	semidirect
95. #2113	C₂×C₅	semidirect
150. C₂²×Q₁₆	C₂²×C₅	semidirect
157. C₂×M₃₂	C₂²×C₅	semidirect
158. C₂²×C₁₆	C₂²×C₅	semidirect
164. #467	C₂²×C₅	semidirect
168. #427	C₂²×C₅	semidirect
171. #367	C₂²×C₅	semidirect
172. #366	C₂²×C₅	semidirect
173. #358	C₂²×C₅	semidirect
174. #358	C₂²×C₅	semidirect
178. C₂²⋊C₁₆	C₂²×C₅	semidirect
379. C₅	#33766	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×#3059	2
C₅×#3058	2
C₅×#2237	2
C₅×#2234	2
C₅×#2220	2
C₅×#2217	2
C₅×#2187	2
C₅×#2185	2
C₅×#2113	2
#33766	5

Subgroups — C5×#33766 #11956486

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#33766 #11956486