Subgroups — C₅×#33759 #11956479

Order 1280.

636 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#467	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#466	C₂	1	1	yes	maximal, characteristic
3	C₅×#2236	C₂	1	2	yes	maximal, complemented
4	C₅×#2232	C₂	1	2	yes	maximal, complemented
5	C₅×#2220	C₂	1	4	yes	maximal, complemented
6	C₅×#2187	C₂	1	2	yes	maximal, complemented
7	C₅×#2185	C₂	1	2	yes	maximal, complemented
8	C₅×#2112	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₅×Q₁₆	C₂²	1	1	yes	characteristic, complemented
10	C₂²×C₅×D₈	C₂²	1	1	yes	characteristic
11	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₂×C₅×C₂²⋊Q₈	—	2	1	no	—
13	C₂×C₅×#121	—	2	1	no	—
14	C₂×C₅×SD₃₂	C₂²	1	4	yes	complemented
15	C₂×C₅×M₃₂	C₂²	1	2	yes	complemented
16	C₅×#467	—	2	1	no	—
17	C₅×#467	—	2	1	no	—
18	C₅×#467	C₂²	1	2	yes	—
19	C₅×#467	C₂²	1	2	yes	complemented
20	C₅×#466	—	2	1	no	—
21	C₅×#466	—	2	1	no	—
22	C₅×#466	C₂²	1	2	yes	—
23	C₅×#466	C₂²	1	2	yes	—
24	C₂×C₅×#107	C₂²	1	1	yes	characteristic
25	C₂×C₅×#107	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₅×#103	—	2	1	no	—
27	C₂×C₅×#102	—	2	1	no	—
28	C₅×#366	C₂²	1	4	yes	complemented
29	C₅×#358	C₂²	1	4	yes	complemented
30	C₅×#357	C₂²	1	4	yes	complemented
31	C₅×C₂²⋊C₁₆	C₂²	1	2	yes	—
32	C₅×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
33	#33759	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
34	C₂²×C₅×Q₈	—	2	1	no	—
35	C₂²×C₅×D₄	—	2	1	no	—
36	C₂²×C₅×D₄	—	4	1	no	—
37	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
38	C₂×C₅×Q₁₆	—	2	1	no	—
39	C₂×C₅×Q₁₆	—	4	2	no	—
40	C₂×C₅×Q₁₆	C₂³	1	2	yes	—
41	C₂×C₅×D₈	—	2	1	no	—
42	C₂×C₅×D₈	—	4	2	no	—
43	C₂×C₅×D₈	C₂³	1	2	yes	—
44	C₂²×C₅×C₈	—	4	2	no	—
45	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
46	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
47	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
48	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
49	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
50	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
51	C₅×C₂²⋊Q₈	—	2	2	no	—
52	C₅×C₂²⋊Q₈	—	2	2	no	—
53	C₅×C₂²⋊Q₈	—	4	1	no	—
54	C₅×C₂²⋊Q₈	—	4	1	no	—
55	C₅×#121	—	2	2	no	—
56	C₅×#121	—	2	2	no	—
57	C₅×#121	—	4	1	no	—
58	C₅×#121	—	4	1	no	—
59	C₂×C₅×C₄⋊C₄	—	2	1	no	—
60	C₂×C₅×C₄⋊C₄	—	2	1	no	—
61	C₂×C₅×C₄⋊C₄	—	4	1	no	—
62	C₂×C₅×C₂²⋊C₄	—	4	1	no	—
63	C₂×C₅×C₂²⋊C₄	—	4	1	no	—
64	C₅×SD₃₂	—	4	4	no	—
65	C₅×M₃₂	—	4	2	no	—
66	C₂×C₅×C₁₆	C₂³	1	4	yes	—
67	C₅×#107	—	2	1	no	—
68	C₅×#107	—	2	1	no	—
69	C₅×#107	C₂³	1	2	yes	—
70	C₅×#107	C₂³	1	2	yes	—
71	C₅×#103	—	2	2	no	—
72	C₅×#103	—	2	2	no	—
73	C₅×#102	—	2	2	no	—
74	C₅×#102	—	2	2	no	—
75	C₂×#467	C₂×C₅	1	1	yes	characteristic, complemented
76	C₂×#466	C₂×C₅	1	1	yes	characteristic
77	#2236	C₂×C₅	1	2	yes	complemented
78	#2232	C₂×C₅	1	2	yes	complemented
79	#2220	C₂×C₅	1	4	yes	complemented
80	#2187	C₂×C₅	1	2	yes	complemented
81	#2185	C₂×C₅	1	2	yes	complemented
82	#2112	C₂×C₅	1	1	yes	characteristic, complemented
83	C₂⁴×C₅	—	4	1	no	—
84	C₂⁴×C₅	D₈	1	1	yes	characteristic
85	C₂×C₅×Q₈	—	2	2	no	—
86	C₂×C₅×Q₈	—	4	2	no	—
87	C₂×C₅×Q₈	—	4	2	no	—
88	C₂×C₅×Q₈	—	4	1	no	—
89	C₂×C₅×D₄	—	2	2	no	—
90	C₂×C₅×D₄	—	4	2	no	—
91	C₂×C₅×D₄	—	4	2	no	—
92	C₂×C₅×D₄	—	4	2	no	—
93	C₂×C₅×D₄	—	4	2	no	—
94	C₂×C₅×D₄	—	4	1	no	—
95	C₂×C₅×D₄	—	8	4	no	—
96	C₂²×C₄×C₅	—	4	1	no	—
97	C₂²×C₄×C₅	—	4	1	no	—
98	C₂²×C₄×C₅	—	4	1	no	—
99	C₂²×C₄×C₅	—	4	1	no	—
100	C₂²×C₄×C₅	—	4	1	no	—
101	C₂²×C₄×C₅	D₈	1	1	yes	characteristic
102	C₂²×C₄×C₅	D₈	1	1	yes	characteristic
103	C₂²×C₄×C₅	D₈	1	1	yes	characteristic
104	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
107	C₅×Q₁₆	—	2	4	no	—
108	C₅×Q₁₆	—	4	2	no	—
109	C₅×D₈	—	2	4	no	—
110	C₅×D₈	—	4	2	no	—
111	C₂×C₅×C₈	—	2	2	no	—
112	C₂×C₅×C₈	—	2	2	no	—
113	C₂×C₅×C₈	—	2	2	no	—
114	C₂×C₅×C₈	—	4	1	no	—
115	C₂×C₅×C₈	—	4	1	no	—
116	C₂×C₅×C₈	—	4	1	no	—
117	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
118	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
119	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
120	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
121	C₅×C₄⋊C₄	—	2	2	no	—
122	C₅×C₄⋊C₄	—	2	2	no	—
123	C₅×C₄⋊C₄	—	4	1	no	—
124	C₅×C₄⋊C₄	—	4	1	no	—
125	C₅×C₄⋊C₄	—	4	2	no	—
126	C₅×C₄⋊C₄	—	4	2	no	—
127	C₅×C₂²⋊C₄	—	4	2	no	—
128	C₅×C₂²⋊C₄	—	4	2	no	—
129	C₅×C₂²⋊C₄	—	4	2	no	—
130	C₅×C₂²⋊C₄	—	4	2	no	—
131	C₅×C₁₆	—	2	4	no	—
132	C₂²×Q₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
133	C₂²×D₈	C₂²×C₅	1	1	yes	characteristic
134	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
135	C₂×C₂²⋊Q₈	—	2	1	no	—
136	C₂×#121	—	2	1	no	—
137	C₂×SD₃₂	C₂²×C₅	1	4	yes	complemented
138	C₂×M₃₂	C₂²×C₅	1	2	yes	complemented
139	#467	—	2	1	no	—
140	#467	—	2	1	no	—
141	#467	C₂²×C₅	1	2	yes	—
142	#467	C₂²×C₅	1	2	yes	complemented
143	#466	—	2	1	no	—
144	#466	—	2	1	no	—
145	#466	C₂²×C₅	1	2	yes	—
146	#466	C₂²×C₅	1	2	yes	—
147	C₂×#107	C₂²×C₅	1	1	yes	characteristic
148	C₂×#107	C₂²×C₅	1	1	yes	characteristic, complemented
149	C₂×#103	—	2	1	no	—
150	C₂×#102	—	2	1	no	—
151	#366	C₂²×C₅	1	4	yes	complemented
152	#358	C₂²×C₅	1	4	yes	complemented
153	#357	C₂²×C₅	1	4	yes	complemented
154	C₂²⋊C₁₆	C₂²×C₅	1	2	yes	—
155	C₂²⋊C₁₆	C₂²×C₅	1	2	yes	complemented
156	C₂³×C₅	—	2	2	no	—
157	C₂³×C₅	—	2	2	no	—
158	C₂³×C₅	—	4	1	no	—
159	C₂³×C₅	—	4	2	no	—
160	C₂³×C₅	—	8	2	no	—
161	C₂³×C₅	—	8	2	no	—
162	C₂³×C₅	—	8	2	no	—
163	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
164	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
165	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
166	C₅×Q₈	—	4	2	no	—
167	C₅×Q₈	—	4	2	no	—
168	C₅×Q₈	—	8	2	no	—
169	C₅×D₄	—	4	2	no	—
170	C₅×D₄	—	4	2	no	—
171	C₅×D₄	—	8	2	no	—
172	C₅×D₄	—	8	4	no	—
173	C₅×D₄	—	8	4	no	—
174	C₂×C₄×C₅	—	2	1	no	—
175	C₂×C₄×C₅	—	2	1	no	—
176	C₂×C₄×C₅	—	2	1	no	—
177	C₂×C₄×C₅	—	2	1	no	—
178	C₂×C₄×C₅	—	2	1	no	—
179	C₂×C₄×C₅	—	2	1	no	—
180	C₂×C₄×C₅	—	4	1	no	—
181	C₂×C₄×C₅	—	4	1	no	—
182	C₂×C₄×C₅	—	4	1	no	—
183	C₂×C₄×C₅	—	4	2	no	—
184	C₂×C₄×C₅	—	4	2	no	—
185	C₂×C₄×C₅	—	4	2	no	—
186	C₂×C₄×C₅	—	8	2	no	—
187	C₂×C₄×C₅	—	8	2	no	—
188	C₂×C₄×C₅	—	8	2	no	—
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	C₂²×D₄	1	1	yes	characteristic
193	C₅×C₈	—	2	1	no	—
194	C₅×C₈	—	2	1	no	—
195	C₅×C₈	—	2	1	no	—
196	C₅×C₈	H(5,𝔽₂)	1	2	yes	—
197	C₂²×Q₈	—	2	1	no	—
198	C₂²×D₄	—	2	1	no	—
199	C₂²×D₄	—	4	1	no	—
200	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
201	C₂×Q₁₆	—	2	1	no	—
202	C₂×Q₁₆	—	4	2	no	—
203	C₂×Q₁₆	C₂³×C₅	1	2	yes	—
204	C₂×D₈	—	2	1	no	—
205	C₂×D₈	—	4	2	no	—
206	C₂×D₈	C₂³×C₅	1	2	yes	—
207	C₂²×C₈	—	4	2	no	—
208	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
209	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
210	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
211	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
212	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
213	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
214	C₂²⋊Q₈	—	2	2	no	—
215	C₂²⋊Q₈	—	2	2	no	—
216	C₂²⋊Q₈	—	4	1	no	—
217	C₂²⋊Q₈	—	4	1	no	—
218	#121	—	2	2	no	—
219	#121	—	2	2	no	—
220	#121	—	4	1	no	—
221	#121	—	4	1	no	—
222	C₂×C₄⋊C₄	—	2	1	no	—
223	C₂×C₄⋊C₄	—	2	1	no	—
224	C₂×C₄⋊C₄	—	4	1	no	—
225	C₂×C₂²⋊C₄	—	4	1	no	—
226	C₂×C₂²⋊C₄	—	4	1	no	—
227	SD₃₂	—	4	4	no	—
228	M₃₂	—	4	2	no	—
229	C₂×C₁₆	C₂³×C₅	1	4	yes	—
230	#107	—	2	1	no	—
231	#107	—	2	1	no	—
232	#107	C₂³×C₅	1	2	yes	—
233	#107	C₂³×C₅	1	2	yes	—
234	#103	—	2	2	no	—
235	#103	—	2	2	no	—
236	#102	—	2	2	no	—
237	#102	—	2	2	no	—
238	C₂²×C₅	—	2	1	no	—
239	C₂²×C₅	—	2	1	no	—
240	C₂²×C₅	—	2	1	no	—
241	C₂²×C₅	—	2	1	no	—
242	C₂²×C₅	—	2	1	no	—
243	C₂²×C₅	—	2	1	no	—
244	C₂²×C₅	—	2	1	no	—
245	C₂²×C₅	—	4	4	no	—
246	C₂²×C₅	—	8	2	no	—
247	C₂²×C₅	—	8	2	no	—
248	C₂²×C₅	—	8	2	no	—
249	C₂²×C₅	—	16	4	no	—
250	C₂²×C₅	#509	1	2	yes	—
251	C₂²×C₅	#510	1	2	yes	—
252	C₂²×C₅	C₂²×D₈	1	1	yes	characteristic
253	C₄×C₅	—	2	1	no	—
254	C₄×C₅	—	2	1	no	—
255	C₄×C₅	—	2	1	no	—
256	C₄×C₅	—	8	2	no	—
257	C₄×C₅	—	8	2	no	—
258	C₄×C₅	—	8	2	no	—
259	C₄×C₅	#534	1	1	yes	characteristic
260	C₄×C₅	#575	1	1	yes	characteristic
261	C₂⁴	—	4	1	no	—
262	C₂⁴	C₅×D₈	1	1	yes	characteristic
263	C₂×Q₈	—	2	2	no	—
264	C₂×Q₈	—	4	2	no	—
265	C₂×Q₈	—	4	2	no	—
266	C₂×Q₈	—	4	1	no	—
267	C₂×D₄	—	2	2	no	—
268	C₂×D₄	—	4	2	no	—
269	C₂×D₄	—	4	2	no	—
270	C₂×D₄	—	4	2	no	—
271	C₂×D₄	—	4	2	no	—
272	C₂×D₄	—	4	1	no	—
273	C₂×D₄	—	8	4	no	—
274	C₂²×C₄	—	4	1	no	—
275	C₂²×C₄	—	4	1	no	—
276	C₂²×C₄	—	4	1	no	—
277	C₂²×C₄	—	4	1	no	—
278	C₂²×C₄	—	4	1	no	—
279	C₂²×C₄	C₅×D₈	1	1	yes	characteristic
280	C₂²×C₄	C₅×D₈	1	1	yes	characteristic
281	C₂²×C₄	C₅×D₈	1	1	yes	characteristic
282	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
283	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
284	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
285	Q₁₆	—	2	4	no	—
286	Q₁₆	—	4	2	no	—
287	D₈	—	2	4	no	—
288	D₈	—	4	2	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	—	4	1	no	—
293	C₂×C₈	—	4	1	no	—
294	C₂×C₈	—	4	1	no	—
295	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
296	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
297	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
298	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	—	2	2	no	—
301	C₄⋊C₄	—	4	1	no	—
302	C₄⋊C₄	—	4	1	no	—
303	C₄⋊C₄	—	4	2	no	—
304	C₄⋊C₄	—	4	2	no	—
305	C₂²⋊C₄	—	4	2	no	—
306	C₂²⋊C₄	—	4	2	no	—
307	C₂²⋊C₄	—	4	2	no	—
308	C₂²⋊C₄	—	4	2	no	—
309	C₁₆	—	2	4	no	—
310	C₂×C₅	—	2	2	no	—
311	C₂×C₅	—	2	2	no	—
312	C₂×C₅	—	4	1	no	—
313	C₂×C₅	—	16	2	no	—
314	C₂×C₅	#3186	1	1	yes	characteristic
315	C₂×C₅	C₂×#509	1	1	yes	characteristic
316	C₂×C₅	C₂×#510	1	1	yes	characteristic
317	C₂³	—	2	2	no	—
318	C₂³	—	2	2	no	—
319	C₂³	—	4	1	no	—
320	C₂³	—	4	2	no	—
321	C₂³	—	8	2	no	—
322	C₂³	—	8	2	no	—
323	C₂³	—	8	2	no	—
324	C₂³	C₂×C₅×D₈	1	1	yes	characteristic
325	C₂³	C₂×C₅×D₈	1	1	yes	characteristic
326	C₂³	C₂×C₅×D₈	1	1	yes	characteristic
327	Q₈	—	4	2	no	—
328	Q₈	—	4	2	no	—
329	Q₈	—	8	2	no	—
330	D₄	—	4	2	no	—
331	D₄	—	4	2	no	—
332	D₄	—	8	2	no	—
333	D₄	—	8	4	no	—
334	D₄	—	8	4	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	8	2	no	—
348	C₂×C₄	—	8	2	no	—
349	C₂×C₄	—	8	2	no	—
350	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
351	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
352	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
353	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
354	C₈	—	2	1	no	—
355	C₈	—	2	1	no	—
356	C₈	—	2	1	no	—
357	C₈	C₅×H(5,𝔽₂)	1	2	yes	—
358	C₅	#33759	1	1	yes	characteristic, direct product factor, Sylow
359	C₂²	—	2	1	no	—
360	C₂²	—	2	1	no	—
361	C₂²	—	2	1	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	2	1	no	—
364	C₂²	—	2	1	no	—
365	C₂²	—	2	1	no	—
366	C₂²	—	4	4	no	—
367	C₂²	—	8	2	no	—
368	C₂²	—	8	2	no	—
369	C₂²	—	8	2	no	—
370	C₂²	—	16	4	no	—
371	C₂²	C₅×#509	1	2	yes	—
372	C₂²	C₅×#510	1	2	yes	—
373	C₂²	C₂²×C₅×D₈	1	1	yes	characteristic
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	—	8	2	no	—
378	C₄	—	8	2	no	—
379	C₄	—	8	2	no	—
380	C₄	C₅×#534	1	1	yes	characteristic
381	C₄	C₅×#575	1	1	yes	characteristic
382	C₂	—	2	2	no	—
383	C₂	—	2	2	no	—
384	C₂	—	4	1	no	—
385	C₂	—	16	2	no	—
386	C₂	C₅×#3186	1	1	yes	characteristic
387	C₂	C₂×C₅×#509	1	1	yes	characteristic
388	C₂	C₂×C₅×#510	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₅
prime radical	C₂×C₅×#466	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂³×C₄×C₅ ◁ C₂³×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#467	C₂	semidirect
3. C₅×#2236	C₂	semidirect
4. C₅×#2232	C₂	semidirect
5. C₅×#2220	C₂	semidirect
6. C₅×#2187	C₂	semidirect
7. C₅×#2185	C₂	semidirect
8. C₅×#2112	C₂	semidirect
9. C₂²×C₅×Q₁₆	C₂²	semidirect
14. C₂×C₅×SD₃₂	C₂²	semidirect
15. C₂×C₅×M₃₂	C₂²	semidirect
19. C₅×#467	C₂²	semidirect
25. C₂×C₅×#107	C₂²	semidirect
28. C₅×#366	C₂²	semidirect
29. C₅×#358	C₂²	semidirect
30. C₅×#357	C₂²	semidirect
32. C₅×C₂²⋊C₁₆	C₂²	semidirect
33. #33759	C₅	direct (N × H)
75. C₂×#467	C₂×C₅	semidirect
77. #2236	C₂×C₅	semidirect
78. #2232	C₂×C₅	semidirect
79. #2220	C₂×C₅	semidirect
80. #2187	C₂×C₅	semidirect
81. #2185	C₂×C₅	semidirect
82. #2112	C₂×C₅	semidirect
132. C₂²×Q₁₆	C₂²×C₅	semidirect
137. C₂×SD₃₂	C₂²×C₅	semidirect
138. C₂×M₃₂	C₂²×C₅	semidirect
142. #467	C₂²×C₅	semidirect
148. C₂×#107	C₂²×C₅	semidirect
151. #366	C₂²×C₅	semidirect
152. #358	C₂²×C₅	semidirect
153. #357	C₂²×C₅	semidirect
155. C₂²⋊C₁₆	C₂²×C₅	semidirect
358. C₅	#33759	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×#467	2
C₂×C₅×#466	2
C₅×#2236	2
C₅×#2232	2
C₅×#2220	2
C₅×#2187	2
C₅×#2185	2
C₅×#2112	2
#33759	5

Subgroups — C5×#33759 #11956479

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#33759 #11956479