Subgroups — C₅×#33846 #11956566

Order 1280.

718 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#508	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×D₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#3280	C₂	1	2	yes	maximal, complemented
4	C₅×#2249	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2216	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2215	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2210	C₂	1	2	yes	maximal, complemented
8	C₅×#2187	C₂	1	2	yes	maximal, complemented
9	C₅×#2186	C₂	1	2	yes	maximal, complemented
10	C₄×C₅×D₁₆	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×D₄×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#135	C₂²	1	2	yes	complemented
13	C₂²×C₅×D₈	C₂²	1	2	yes	—
14	C₅×#546	—	2	2	no	—
15	C₅×#508	—	2	4	no	—
16	C₂×C₅×Q₃₂	C₂²	1	1	yes	characteristic, complemented
17	C₂×C₅×SD₃₂	C₂²	1	2	yes	complemented
18	C₂×C₅×SD₃₂	C₂²	1	2	yes	complemented
19	C₂×C₅×D₁₆	—	2	4	no	—
20	C₂×C₅×D₁₆	C₂²	1	2	yes	—
21	C₂×C₅×D₁₆	C₂²	1	1	yes	characteristic
22	C₂×C₅×D₁₆	C₂²	1	1	yes	characteristic
23	C₂²×C₅×C₁₆	C₂²	1	1	yes	characteristic
24	C₂²×C₅×C₁₆	C₂²	1	1	yes	characteristic, complemented
25	C₅×#495	C₂²	1	2	yes	complemented
26	C₅×#467	C₂²	1	2	yes	—
27	C₅×#466	C₂²	1	2	yes	complemented
28	C₅×#463	—	2	2	no	—
29	C₅×#450	—	2	2	no	—
30	C₅×#449	—	2	2	no	—
31	C₄×C₅×D₈	C₂²	1	2	yes	complemented
32	C₅×C₈×D₄	C₂²	1	1	yes	characteristic
33	C₅×#366	C₂²	1	1	yes	characteristic, complemented
34	C₅×C₄⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
35	C₅×#358	C₂²	1	2	yes	complemented
36	C₅×#357	C₂²	1	2	yes	complemented
37	C₅×#357	C₂²	1	2	yes	complemented
38	C₅×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
39	C₅×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
40	C₄×C₅×C₁₆	C₂²	1	1	yes	characteristic, complemented
41	#33846	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂×C₅×#41	—	2	2	no	—
43	C₂²×C₅×D₄	—	2	2	no	—
44	C₅×#135	—	2	4	no	—
45	C₅×#135	—	4	2	no	—
46	C₂×C₅×Q₁₆	C₂³	1	2	yes	—
47	C₂×C₅×SD₁₆	—	2	2	no	—
48	C₂×C₅×SD₁₆	—	2	2	no	—
49	C₂×C₅×D₈	—	2	4	no	—
50	C₂×C₅×D₈	—	2	2	no	—
51	C₂×C₅×D₈	—	4	2	no	—
52	C₂×C₅×D₈	C₂³	1	2	yes	—
53	C₂×C₅×D₈	C₂³	1	2	yes	—
54	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
55	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
56	C₅×#124	—	2	2	no	—
57	C₅×#123	—	4	2	no	—
58	C₅×C₂²⋊Q₈	—	2	2	no	—
59	C₅×#121	—	2	2	no	—
60	C₅×#121	—	4	2	no	—
61	C₅×#120	—	4	2	no	—
62	C₄×C₅×D₄	—	2	2	no	—
63	C₄×C₅×D₄	D₄	1	1	yes	characteristic
64	C₂×C₅×C₂²⋊C₄	—	4	2	no	—
65	C₅×Q₃₂	—	2	2	no	—
66	C₅×SD₃₂	—	2	4	no	—
67	C₅×SD₃₂	—	4	2	no	—
68	C₅×D₁₆	—	2	4	no	—
69	C₅×D₁₆	—	2	2	no	—
70	C₅×D₁₆	D₄	1	4	yes	complemented
71	C₂×C₅×C₁₆	—	2	2	no	—
72	C₂×C₅×C₁₆	—	2	2	no	—
73	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
74	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
75	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
76	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
77	C₅×#107	C₂³	1	2	yes	—
78	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
79	C₅×#103	—	2	2	no	—
80	C₅×#102	—	2	2	no	—
81	C₅×#102	—	2	2	no	—
82	C₅×C₂²⋊C₈	D₄	1	1	yes	characteristic
83	C₅×C₂²⋊C₈	D₄	1	1	yes	characteristic
84	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
85	C₂×#508	C₂×C₅	1	1	yes	characteristic, complemented
86	C₂²×D₁₆	C₂×C₅	1	1	yes	characteristic, complemented
87	#3280	C₂×C₅	1	2	yes	complemented
88	#2249	C₂×C₅	1	1	yes	characteristic, complemented
89	#2216	C₂×C₅	1	1	yes	characteristic, complemented
90	#2215	C₂×C₅	1	1	yes	characteristic, complemented
91	#2210	C₂×C₅	1	2	yes	complemented
92	#2187	C₂×C₅	1	2	yes	complemented
93	#2186	C₂×C₅	1	2	yes	complemented
94	C₄×D₁₆	C₂×C₅	1	1	yes	characteristic, complemented
95	D₄×C₁₆	C₂×C₅	1	1	yes	characteristic, complemented
96	C₂⁴×C₅	—	4	2	no	—
97	C₅×#41	—	4	4	no	—
98	C₅×#41	—	8	2	no	—
99	C₂×C₅×Q₈	—	2	2	no	—
100	C₂×C₅×D₄	—	2	2	no	—
101	C₂×C₅×D₄	—	2	2	no	—
102	C₂×C₅×D₄	—	4	4	no	—
103	C₂×C₅×D₄	—	4	2	no	—
104	C₂×C₅×D₄	—	4	2	no	—
105	C₂×C₅×D₄	—	4	2	no	—
106	C₂×C₅×D₄	—	8	2	no	—
107	C₂×C₅×D₄	D₈	1	1	yes	characteristic
108	C₂²×C₄×C₅	—	4	2	no	—
109	C₂²×C₄×C₅	—	4	2	no	—
110	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
112	C₅×Q₁₆	—	2	2	no	—
113	C₅×Q₁₆	—	2	2	no	—
114	C₅×SD₁₆	—	4	4	no	—
115	C₅×SD₁₆	—	8	2	no	—
116	C₅×D₈	—	2	2	no	—
117	C₅×D₈	—	2	2	no	—
118	C₅×D₈	—	2	2	no	—
119	C₅×D₈	—	4	4	no	—
120	C₅×D₈	C₂×D₄	1	4	yes	—
121	C₂×C₅×C₈	—	2	1	no	—
122	C₂×C₅×C₈	—	2	1	no	—
123	C₂×C₅×C₈	—	2	1	no	—
124	C₂×C₅×C₈	—	2	1	no	—
125	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
126	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
127	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
128	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
129	C₅×C₄⋊C₄	—	2	2	no	—
130	C₅×C₄⋊C₄	—	4	2	no	—
131	C₅×C₄⋊C₄	D₈	1	1	yes	characteristic
132	C₅×C₂²⋊C₄	—	4	2	no	—
133	C₅×C₂²⋊C₄	—	4	2	no	—
134	C₅×C₂²⋊C₄	—	4	2	no	—
135	C₅×C₂²⋊C₄	—	4	2	no	—
136	C₅×C₂²⋊C₄	—	4	2	no	—
137	C₅×C₂²⋊C₄	D₈	1	1	yes	characteristic
138	C₅×C₂²⋊C₄	D₈	1	1	yes	characteristic
139	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
140	C₅×C₁₆	—	2	1	no	—
141	C₅×C₁₆	—	2	1	no	—
142	C₅×C₁₆	—	2	1	no	—
143	C₅×C₁₆	C₂×D₄	1	2	yes	—
144	C₂×#135	C₂²×C₅	1	2	yes	complemented
145	C₂²×D₈	C₂²×C₅	1	2	yes	—
146	#546	—	2	2	no	—
147	#508	—	2	4	no	—
148	C₂×Q₃₂	C₂²×C₅	1	1	yes	characteristic, complemented
149	C₂×SD₃₂	C₂²×C₅	1	2	yes	complemented
150	C₂×SD₃₂	C₂²×C₅	1	2	yes	complemented
151	C₂×D₁₆	—	2	4	no	—
152	C₂×D₁₆	C₂²×C₅	1	2	yes	—
153	C₂×D₁₆	C₂²×C₅	1	1	yes	characteristic
154	C₂×D₁₆	C₂²×C₅	1	1	yes	characteristic
155	C₂²×C₁₆	C₂²×C₅	1	1	yes	characteristic
156	C₂²×C₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
157	#495	C₂²×C₅	1	2	yes	complemented
158	#467	C₂²×C₅	1	2	yes	—
159	#466	C₂²×C₅	1	2	yes	complemented
160	#463	—	2	2	no	—
161	#450	—	2	2	no	—
162	#449	—	2	2	no	—
163	C₄×D₈	C₂²×C₅	1	2	yes	complemented
164	C₈×D₄	C₂²×C₅	1	1	yes	characteristic
165	#366	C₂²×C₅	1	1	yes	characteristic, complemented
166	C₄⋊C₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
167	#358	C₂²×C₅	1	2	yes	complemented
168	#357	C₂²×C₅	1	2	yes	complemented
169	#357	C₂²×C₅	1	2	yes	complemented
170	C₂²⋊C₁₆	C₂²×C₅	1	1	yes	characteristic
171	C₂²⋊C₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
172	C₄×C₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
173	C₂³×C₅	—	4	2	no	—
174	C₂³×C₅	—	4	2	no	—
175	C₂³×C₅	—	8	4	no	—
176	C₂³×C₅	—	8	4	no	—
177	C₂³×C₅	—	16	2	no	—
178	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
179	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
180	C₅×Q₈	—	4	2	no	—
181	C₅×Q₈	—	4	2	no	—
182	C₅×D₄	—	2	2	no	—
183	C₅×D₄	—	2	4	no	—
184	C₅×D₄	—	4	2	no	—
185	C₅×D₄	—	4	2	no	—
186	C₅×D₄	—	4	2	no	—
187	C₅×D₄	—	8	4	no	—
188	C₅×D₄	—	8	4	no	—
189	C₅×D₄	—	16	2	no	—
190	C₂×C₄×C₅	—	2	1	no	—
191	C₂×C₄×C₅	—	2	1	no	—
192	C₂×C₄×C₅	—	2	1	no	—
193	C₂×C₄×C₅	—	2	1	no	—
194	C₂×C₄×C₅	—	4	2	no	—
195	C₂×C₄×C₅	—	4	2	no	—
196	C₂×C₄×C₅	—	8	4	no	—
197	C₂×C₄×C₅	—	16	2	no	—
198	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
199	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
200	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
201	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
202	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
203	C₅×C₈	—	2	1	no	—
204	C₅×C₈	—	2	1	no	—
205	C₅×C₈	—	2	1	no	—
206	C₅×C₈	C₂²×D₄	1	1	yes	characteristic
207	C₅×C₈	H(5,𝔽₂)	1	1	yes	characteristic
208	C₂×#41	—	2	2	no	—
209	C₂²×D₄	—	2	2	no	—
210	#135	—	2	4	no	—
211	#135	—	4	2	no	—
212	C₂×Q₁₆	C₂³×C₅	1	2	yes	—
213	C₂×SD₁₆	—	2	2	no	—
214	C₂×SD₁₆	—	2	2	no	—
215	C₂×D₈	—	2	4	no	—
216	C₂×D₈	—	2	2	no	—
217	C₂×D₈	—	4	2	no	—
218	C₂×D₈	C₂³×C₅	1	2	yes	—
219	C₂×D₈	C₂³×C₅	1	2	yes	—
220	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
221	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
222	#124	—	2	2	no	—
223	#123	—	4	2	no	—
224	C₂²⋊Q₈	—	2	2	no	—
225	#121	—	2	2	no	—
226	#121	—	4	2	no	—
227	#120	—	4	2	no	—
228	C₄×D₄	—	2	2	no	—
229	C₄×D₄	C₅×D₄	1	1	yes	characteristic
230	C₂×C₂²⋊C₄	—	4	2	no	—
231	Q₃₂	—	2	2	no	—
232	SD₃₂	—	2	4	no	—
233	SD₃₂	—	4	2	no	—
234	D₁₆	—	2	4	no	—
235	D₁₆	—	2	2	no	—
236	D₁₆	C₅×D₄	1	4	yes	complemented
237	C₂×C₁₆	—	2	2	no	—
238	C₂×C₁₆	—	2	2	no	—
239	C₂×C₁₆	C₂³×C₅	1	1	yes	characteristic
240	C₂×C₁₆	C₂³×C₅	1	1	yes	characteristic
241	C₂×C₁₆	C₂³×C₅	1	1	yes	characteristic
242	C₂×C₁₆	C₂³×C₅	1	1	yes	characteristic
243	#107	C₂³×C₅	1	2	yes	—
244	C₄⋊C₈	C₅×D₄	1	1	yes	characteristic
245	#103	—	2	2	no	—
246	#102	—	2	2	no	—
247	#102	—	2	2	no	—
248	C₂²⋊C₈	C₅×D₄	1	1	yes	characteristic
249	C₂²⋊C₈	C₅×D₄	1	1	yes	characteristic
250	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
251	C₂²×C₅	—	2	1	no	—
252	C₂²×C₅	—	2	1	no	—
253	C₂²×C₅	—	2	1	no	—
254	C₂²×C₅	—	2	1	no	—
255	C₂²×C₅	—	2	1	no	—
256	C₂²×C₅	—	4	4	no	—
257	C₂²×C₅	—	8	2	no	—
258	C₂²×C₅	—	8	2	no	—
259	C₂²×C₅	—	8	2	no	—
260	C₂²×C₅	—	8	2	no	—
261	C₂²×C₅	—	8	2	no	—
262	C₂²×C₅	—	16	8	no	—
263	C₂²×C₅	#508	1	2	yes	complemented
264	C₂²×C₅	C₂²×D₈	1	1	yes	characteristic
265	C₄×C₅	—	2	1	no	—
266	C₄×C₅	—	2	1	no	—
267	C₄×C₅	—	2	1	no	—
268	C₄×C₅	—	2	1	no	—
269	C₄×C₅	—	8	2	no	—
270	C₄×C₅	—	8	2	no	—
271	C₄×C₅	D₄²	1	1	yes	characteristic
272	C₄×C₅	#576	1	1	yes	characteristic
273	C₂⁴	—	4	2	no	—
274	#41	—	4	4	no	—
275	#41	—	8	2	no	—
276	C₂×Q₈	—	2	2	no	—
277	C₂×D₄	—	2	2	no	—
278	C₂×D₄	—	2	2	no	—
279	C₂×D₄	—	4	4	no	—
280	C₂×D₄	—	4	2	no	—
281	C₂×D₄	—	4	2	no	—
282	C₂×D₄	—	4	2	no	—
283	C₂×D₄	—	8	2	no	—
284	C₂×D₄	C₅×D₈	1	1	yes	characteristic
285	C₂²×C₄	—	4	2	no	—
286	C₂²×C₄	—	4	2	no	—
287	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
288	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
289	Q₁₆	—	2	2	no	—
290	Q₁₆	—	2	2	no	—
291	SD₁₆	—	4	4	no	—
292	SD₁₆	—	8	2	no	—
293	D₈	—	2	2	no	—
294	D₈	—	2	2	no	—
295	D₈	—	2	2	no	—
296	D₈	—	4	4	no	—
297	D₈	C₂×C₅×D₄	1	4	yes	—
298	C₂×C₈	—	2	1	no	—
299	C₂×C₈	—	2	1	no	—
300	C₂×C₈	—	2	1	no	—
301	C₂×C₈	—	2	1	no	—
302	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
303	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
304	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
305	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	4	2	no	—
308	C₄⋊C₄	C₅×D₈	1	1	yes	characteristic
309	C₂²⋊C₄	—	4	2	no	—
310	C₂²⋊C₄	—	4	2	no	—
311	C₂²⋊C₄	—	4	2	no	—
312	C₂²⋊C₄	—	4	2	no	—
313	C₂²⋊C₄	—	4	2	no	—
314	C₂²⋊C₄	C₅×D₈	1	1	yes	characteristic
315	C₂²⋊C₄	C₅×D₈	1	1	yes	characteristic
316	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
317	C₁₆	—	2	1	no	—
318	C₁₆	—	2	1	no	—
319	C₁₆	—	2	1	no	—
320	C₁₆	C₂×C₅×D₄	1	2	yes	—
321	C₂×C₅	—	2	2	no	—
322	C₂×C₅	—	4	1	no	—
323	C₂×C₅	—	8	4	no	—
324	C₂×C₅	—	16	2	no	—
325	C₂×C₅	D₄×D₈	1	1	yes	characteristic
326	C₂×C₅	C₂×#508	1	1	yes	characteristic
327	C₂×C₅	#3415	1	1	yes	characteristic
328	C₂³	—	4	2	no	—
329	C₂³	—	4	2	no	—
330	C₂³	—	8	4	no	—
331	C₂³	—	8	4	no	—
332	C₂³	—	16	2	no	—
333	C₂³	C₂×C₅×D₈	1	1	yes	characteristic
334	C₂³	C₂×C₅×D₈	1	1	yes	characteristic
335	Q₈	—	4	2	no	—
336	Q₈	—	4	2	no	—
337	D₄	—	2	2	no	—
338	D₄	—	2	4	no	—
339	D₄	—	4	2	no	—
340	D₄	—	4	2	no	—
341	D₄	—	4	2	no	—
342	D₄	—	8	4	no	—
343	D₄	—	8	4	no	—
344	D₄	—	16	2	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	8	4	no	—
352	C₂×C₄	—	16	2	no	—
353	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
354	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
355	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
356	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
357	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
358	C₈	—	2	1	no	—
359	C₈	—	2	1	no	—
360	C₈	—	2	1	no	—
361	C₈	C₂²×C₅×D₄	1	1	yes	characteristic
362	C₈	C₅×H(5,𝔽₂)	1	1	yes	characteristic
363	C₅	#33846	1	1	yes	characteristic, direct product factor, Sylow
364	C₂²	—	2	1	no	—
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	2	1	no	—
368	C₂²	—	2	1	no	—
369	C₂²	—	4	4	no	—
370	C₂²	—	8	2	no	—
371	C₂²	—	8	2	no	—
372	C₂²	—	8	2	no	—
373	C₂²	—	8	2	no	—
374	C₂²	—	8	2	no	—
375	C₂²	—	16	8	no	—
376	C₂²	C₅×#508	1	2	yes	complemented
377	C₂²	C₂²×C₅×D₈	1	1	yes	characteristic
378	C₄	—	2	1	no	—
379	C₄	—	2	1	no	—
380	C₄	—	2	1	no	—
381	C₄	—	2	1	no	—
382	C₄	—	8	2	no	—
383	C₄	—	8	2	no	—
384	C₄	C₅×D₄²	1	1	yes	characteristic
385	C₄	C₅×#576	1	1	yes	characteristic
386	C₂	—	2	2	no	—
387	C₂	—	4	1	no	—
388	C₂	—	8	4	no	—
389	C₂	—	16	2	no	—
390	C₂	C₅×D₄×D₈	1	1	yes	characteristic
391	C₂	C₂×C₅×#508	1	1	yes	characteristic
392	C₂	C₅×#3415	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 ◁ 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×#508	C₂	semidirect
2. C₂²×C₅×D₁₆	C₂	semidirect
3. C₅×#3280	C₂	semidirect
4. C₅×#2249	C₂	semidirect
5. C₅×#2216	C₂	semidirect
6. C₅×#2215	C₂	semidirect
7. C₅×#2210	C₂	semidirect
8. C₅×#2187	C₂	semidirect
9. C₅×#2186	C₂	semidirect
10. C₄×C₅×D₁₆	C₂	semidirect
11. C₅×D₄×C₁₆	C₂	semidirect
12. C₂×C₅×#135	C₂²	semidirect
16. C₂×C₅×Q₃₂	C₂²	semidirect
17. C₂×C₅×SD₃₂	C₂²	semidirect
18. C₂×C₅×SD₃₂	C₂²	semidirect
24. C₂²×C₅×C₁₆	C₂²	semidirect
25. C₅×#495	C₂²	semidirect
27. C₅×#466	C₂²	semidirect
31. C₄×C₅×D₈	C₂²	semidirect
33. C₅×#366	C₂²	semidirect
34. C₅×C₄⋊C₁₆	C₂²	semidirect
35. C₅×#358	C₂²	semidirect
36. C₅×#357	C₂²	semidirect
37. C₅×#357	C₂²	semidirect
39. C₅×C₂²⋊C₁₆	C₂²	semidirect
40. C₄×C₅×C₁₆	C₂²	semidirect
41. #33846	C₅	direct (N × H)
70. C₅×D₁₆	D₄	semidirect
85. C₂×#508	C₂×C₅	semidirect
86. C₂²×D₁₆	C₂×C₅	semidirect
87. #3280	C₂×C₅	semidirect
88. #2249	C₂×C₅	semidirect
89. #2216	C₂×C₅	semidirect
90. #2215	C₂×C₅	semidirect
91. #2210	C₂×C₅	semidirect
92. #2187	C₂×C₅	semidirect
93. #2186	C₂×C₅	semidirect
94. C₄×D₁₆	C₂×C₅	semidirect
95. D₄×C₁₆	C₂×C₅	semidirect
144. C₂×#135	C₂²×C₅	semidirect
148. C₂×Q₃₂	C₂²×C₅	semidirect
149. C₂×SD₃₂	C₂²×C₅	semidirect
150. C₂×SD₃₂	C₂²×C₅	semidirect
156. C₂²×C₁₆	C₂²×C₅	semidirect
157. #495	C₂²×C₅	semidirect
159. #466	C₂²×C₅	semidirect
163. C₄×D₈	C₂²×C₅	semidirect
165. #366	C₂²×C₅	semidirect
166. C₄⋊C₁₆	C₂²×C₅	semidirect
167. #358	C₂²×C₅	semidirect
168. #357	C₂²×C₅	semidirect
169. #357	C₂²×C₅	semidirect
171. C₂²⋊C₁₆	C₂²×C₅	semidirect
172. C₄×C₁₆	C₂²×C₅	semidirect
236. D₁₆	C₅×D₄	semidirect
263. C₂²×C₅	#508	semidirect
363. C₅	#33846	direct (N × H)
376. C₂²	C₅×#508	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#508	2
C₂²×C₅×D₁₆	2
C₅×#3280	2
C₅×#2249	2
C₅×#2216	2
C₅×#2215	2
C₅×#2210	2
C₅×#2187	2
C₅×#2186	2
C₄×C₅×D₁₆	2
C₅×D₄×C₁₆	2
#33846	5

Subgroups — C5×#33846 #11956566

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#33846 #11956566