Subgroups — C₅×#3012 #10616607

Order 640.

764 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#135	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#537	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#452	C₂	1	2	yes	maximal, complemented
6	C₅×#450	C₂	1	2	yes	maximal, complemented
7	C₅×#449	C₂	1	2	yes	maximal, complemented
8	C₅×#447	C₂	1	2	yes	maximal, complemented
9	C₅×#417	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅×#102	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#408	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×H(5,𝔽₂)	—	2	4	no	—
13	C₅×H(5,𝔽₂)	—	2	4	no	—
14	C₂×C₅×#41	—	2	1	no	—
15	C₂×C₅×#41	C₂²	1	2	yes	—
16	C₂×C₅×#41	C₂²	1	1	yes	characteristic
17	C₂×C₅×#41	C₂²	1	1	yes	characteristic
18	C₂×C₅×#41	C₂²	1	1	yes	characteristic, complemented
19	C₂²×C₅×D₄	—	2	2	no	—
20	C₂²×C₅×D₄	—	2	1	no	—
21	C₂²×C₅×D₄	C₂²	1	2	yes	—
22	C₂²×C₅×D₄	C₂²	1	1	yes	characteristic
23	C₅×AGL(1,ℤ/8)	—	2	4	no	—
24	C₅×#135	—	2	4	no	—
25	C₂×C₅×Q₁₆	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₅×SD₁₆	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₅×SD₁₆	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₅×SD₁₆	C₂²	1	2	yes	complemented
29	C₂×C₅×D₈	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₅×D₈	C₂²	1	2	yes	complemented
31	C₂×C₅×M₁₆	C₂²	1	1	yes	characteristic, complemented
32	C₂²×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
33	C₅×C₂²⋊Q₈	—	2	1	no	—
34	C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
35	C₅×#121	—	2	1	no	—
36	C₅×#121	—	2	2	no	—
37	C₅×#121	C₂²	1	2	yes	complemented
38	C₂×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
39	C₅×#103	C₂²	1	2	yes	complemented
40	C₅×#102	C₂²	1	2	yes	complemented
41	C₅×#102	C₂²	1	2	yes	complemented
42	C₅×#102	C₂²	1	2	yes	complemented
43	C₅×C₂²⋊C₈	C₂²	1	2	yes	complemented
44	C₅×C₂²⋊C₈	C₂²	1	2	yes	complemented
45	#3012	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
46	C₂⁴×C₅	—	2	2	no	—
47	C₂⁴×C₅	—	2	1	no	—
48	C₅×#41	—	2	8	no	—
49	C₅×#41	—	2	4	no	—
50	C₅×#41	—	2	4	no	—
51	C₅×#41	—	2	2	no	—
52	C₅×#41	—	2	2	no	—
53	C₅×#41	—	2	2	no	—
54	C₅×#41	—	2	2	no	—
55	C₅×#41	—	2	2	no	—
56	C₅×#41	D₄	1	4	yes	complemented
57	C₂×C₅×Q₈	D₄	1	1	yes	characteristic
58	C₂×C₅×Q₈	C₂³	1	1	yes	characteristic
59	C₂×C₅×Q₈	C₂³	1	1	yes	characteristic
60	C₂×C₅×D₄	—	2	16	no	—
61	C₂×C₅×D₄	—	2	8	no	—
62	C₂×C₅×D₄	—	2	2	no	—
63	C₂×C₅×D₄	—	2	1	no	—
64	C₂×C₅×D₄	—	2	4	no	—
65	C₂×C₅×D₄	—	2	4	no	—
66	C₂×C₅×D₄	—	2	1	no	—
67	C₂×C₅×D₄	—	2	2	no	—
68	C₂×C₅×D₄	—	2	2	no	—
69	C₂×C₅×D₄	—	2	1	no	—
70	C₂×C₅×D₄	—	2	2	no	—
71	C₂×C₅×D₄	D₄	1	2	yes	—
72	C₂×C₅×D₄	D₄	1	1	yes	characteristic
73	C₂×C₅×D₄	D₄	1	4	yes	complemented
74	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
75	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
76	C₂×C₅×D₄	C₂³	1	2	yes	—
77	C₂²×C₄×C₅	—	2	2	no	—
78	C₂²×C₄×C₅	—	2	1	no	—
79	C₂²×C₄×C₅	—	2	1	no	—
80	C₂²×C₄×C₅	—	2	1	no	—
81	C₂²×C₄×C₅	C₂³	1	2	yes	—
82	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
83	C₅×Q₁₆	—	2	2	no	—
84	C₅×SD₁₆	—	2	2	no	—
85	C₅×SD₁₆	—	2	2	no	—
86	C₅×SD₁₆	—	2	4	no	—
87	C₅×D₈	—	2	2	no	—
88	C₅×D₈	—	2	4	no	—
89	C₅×M₁₆	—	2	2	no	—
90	C₂×C₅×C₈	—	2	2	no	—
91	C₂×C₅×C₈	C₂³	1	1	yes	characteristic
92	C₂×C₅×C₈	C₂³	1	1	yes	characteristic
93	C₂×C₅×C₈	C₂³	1	2	yes	—
94	C₅×C₄⋊C₄	—	2	1	no	—
95	C₅×C₄⋊C₄	—	2	2	no	—
96	C₅×C₄⋊C₄	C₂³	1	2	yes	—
97	C₅×C₂²⋊C₄	—	2	2	no	—
98	C₅×C₂²⋊C₄	—	2	2	no	—
99	C₂×H(5,𝔽₂)	C₂×C₅	1	1	yes	characteristic, complemented
100	C₂×AGL(1,ℤ/8)	C₂×C₅	1	1	yes	characteristic, complemented
101	C₂×#135	C₂×C₅	1	1	yes	characteristic, complemented
102	#537	C₂×C₅	1	1	yes	characteristic, complemented
103	#452	C₂×C₅	1	2	yes	complemented
104	#450	C₂×C₅	1	2	yes	complemented
105	#449	C₂×C₅	1	2	yes	complemented
106	#447	C₂×C₅	1	2	yes	complemented
107	#417	C₂×C₅	1	1	yes	characteristic, complemented
108	C₂×#102	C₂×C₅	1	1	yes	characteristic, complemented
109	#408	C₂×C₅	1	1	yes	characteristic, complemented
110	C₂³×C₅	—	2	8	no	—
111	C₂³×C₅	—	2	2	no	—
112	C₂³×C₅	—	2	1	no	—
113	C₂³×C₅	—	2	4	no	—
114	C₂³×C₅	—	2	1	no	—
115	C₂³×C₅	—	8	1	no	—
116	C₂³×C₅	—	8	1	no	—
117	C₂³×C₅	—	8	2	no	—
118	C₂³×C₅	—	8	2	no	—
119	C₂³×C₅	C₂×D₄	1	2	yes	—
120	C₂³×C₅	C₂×D₄	1	1	yes	characteristic
121	C₅×Q₈	—	2	2	no	—
122	C₅×Q₈	—	2	1	no	—
123	C₅×Q₈	—	2	1	no	—
124	C₅×Q₈	—	2	1	no	—
125	C₅×Q₈	C₂×D₄	1	2	yes	—
126	C₅×D₄	—	2	8	no	—
127	C₅×D₄	—	2	8	no	—
128	C₅×D₄	—	2	4	no	—
129	C₅×D₄	—	2	4	no	—
130	C₅×D₄	—	2	2	no	—
131	C₅×D₄	—	2	4	no	—
132	C₅×D₄	—	2	2	no	—
133	C₅×D₄	—	2	1	no	—
134	C₅×D₄	—	2	1	no	—
135	C₅×D₄	—	2	1	no	—
136	C₅×D₄	—	4	2	no	—
137	C₅×D₄	—	8	2	no	—
138	C₅×D₄	C₂×D₄	1	2	yes	—
139	C₅×D₄	C₂×D₄	1	4	yes	—
140	C₂×C₄×C₅	—	2	8	no	—
141	C₂×C₄×C₅	—	2	1	no	—
142	C₂×C₄×C₅	—	2	4	no	—
143	C₂×C₄×C₅	—	2	2	no	—
144	C₂×C₄×C₅	—	2	2	no	—
145	C₂×C₄×C₅	—	2	2	no	—
146	C₂×C₄×C₅	—	2	1	no	—
147	C₂×C₄×C₅	—	4	2	no	—
148	C₂×C₄×C₅	—	8	1	no	—
149	C₂×C₄×C₅	C₂×D₄	1	2	yes	—
150	C₂×C₄×C₅	C₂×D₄	1	1	yes	characteristic
151	C₂×C₄×C₅	C₂×D₄	1	2	yes	—
152	C₂×C₄×C₅	C₂×D₄	1	2	yes	—
153	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
154	C₅×C₈	—	2	1	no	—
155	C₅×C₈	—	2	1	no	—
156	C₅×C₈	—	2	2	no	—
157	H(5,𝔽₂)	—	2	4	no	—
158	H(5,𝔽₂)	—	2	4	no	—
159	C₂×#41	—	2	1	no	—
160	C₂×#41	C₂²×C₅	1	2	yes	—
161	C₂×#41	C₂²×C₅	1	1	yes	characteristic
162	C₂×#41	C₂²×C₅	1	1	yes	characteristic
163	C₂×#41	C₂²×C₅	1	1	yes	characteristic, complemented
164	C₂²×D₄	—	2	2	no	—
165	C₂²×D₄	—	2	1	no	—
166	C₂²×D₄	C₂²×C₅	1	2	yes	—
167	C₂²×D₄	C₂²×C₅	1	1	yes	characteristic
168	AGL(1,ℤ/8)	—	2	4	no	—
169	#135	—	2	4	no	—
170	C₂×Q₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
171	C₂×SD₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
172	C₂×SD₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
173	C₂×SD₁₆	C₂²×C₅	1	2	yes	complemented
174	C₂×D₈	C₂²×C₅	1	1	yes	characteristic, complemented
175	C₂×D₈	C₂²×C₅	1	2	yes	complemented
176	C₂×M₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
177	C₂²×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
178	C₂²⋊Q₈	—	2	1	no	—
179	C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
180	#121	—	2	1	no	—
181	#121	—	2	2	no	—
182	#121	C₂²×C₅	1	2	yes	complemented
183	C₂×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
184	#103	C₂²×C₅	1	2	yes	complemented
185	#102	C₂²×C₅	1	2	yes	complemented
186	#102	C₂²×C₅	1	2	yes	complemented
187	#102	C₂²×C₅	1	2	yes	complemented
188	C₂²⋊C₈	C₂²×C₅	1	2	yes	complemented
189	C₂²⋊C₈	C₂²×C₅	1	2	yes	complemented
190	C₂²×C₅	—	2	1	no	—
191	C₂²×C₅	—	2	1	no	—
192	C₂²×C₅	—	2	2	no	—
193	C₂²×C₅	—	2	4	no	—
194	C₂²×C₅	—	2	2	no	—
195	C₂²×C₅	—	2	2	no	—
196	C₂²×C₅	—	2	2	no	—
197	C₂²×C₅	—	4	2	no	—
198	C₂²×C₅	—	4	1	no	—
199	C₂²×C₅	—	4	2	no	—
200	C₂²×C₅	—	4	1	no	—
201	C₂²×C₅	—	4	1	no	—
202	C₂²×C₅	—	4	1	no	—
203	C₂²×C₅	—	4	1	no	—
204	C₂²×C₅	—	8	4	no	—
205	C₂²×C₅	—	8	8	no	—
206	C₂²×C₅	#120	1	2	yes	—
207	C₂²×C₅	C₂²×D₄	1	1	yes	characteristic
208	C₄×C₅	—	2	2	no	—
209	C₄×C₅	—	2	2	no	—
210	C₄×C₅	—	4	1	no	—
211	C₄×C₅	—	4	2	no	—
212	C₄×C₅	#120	1	2	yes	—
213	C₄×C₅	C₂²×D₄	1	1	yes	characteristic
214	C₄×C₅	C₂²×D₄	1	1	yes	characteristic
215	C₂⁴	—	2	2	no	—
216	C₂⁴	—	2	1	no	—
217	#41	—	2	8	no	—
218	#41	—	2	4	no	—
219	#41	—	2	4	no	—
220	#41	—	2	2	no	—
221	#41	—	2	2	no	—
222	#41	—	2	2	no	—
223	#41	—	2	2	no	—
224	#41	—	2	2	no	—
225	#41	C₅×D₄	1	4	yes	complemented
226	C₂×Q₈	C₅×D₄	1	1	yes	characteristic
227	C₂×Q₈	C₂³×C₅	1	1	yes	characteristic
228	C₂×Q₈	C₂³×C₅	1	1	yes	characteristic
229	C₂×D₄	—	2	16	no	—
230	C₂×D₄	—	2	8	no	—
231	C₂×D₄	—	2	2	no	—
232	C₂×D₄	—	2	1	no	—
233	C₂×D₄	—	2	4	no	—
234	C₂×D₄	—	2	4	no	—
235	C₂×D₄	—	2	1	no	—
236	C₂×D₄	—	2	2	no	—
237	C₂×D₄	—	2	2	no	—
238	C₂×D₄	—	2	1	no	—
239	C₂×D₄	—	2	2	no	—
240	C₂×D₄	C₅×D₄	1	2	yes	—
241	C₂×D₄	C₅×D₄	1	1	yes	characteristic
242	C₂×D₄	C₅×D₄	1	4	yes	complemented
243	C₂×D₄	C₂³×C₅	1	1	yes	characteristic
244	C₂×D₄	C₂³×C₅	1	1	yes	characteristic
245	C₂×D₄	C₂³×C₅	1	2	yes	—
246	C₂²×C₄	—	2	2	no	—
247	C₂²×C₄	—	2	1	no	—
248	C₂²×C₄	—	2	1	no	—
249	C₂²×C₄	—	2	1	no	—
250	C₂²×C₄	C₂³×C₅	1	2	yes	—
251	C₂²×C₄	C₂³×C₅	1	1	yes	characteristic
252	Q₁₆	—	2	2	no	—
253	SD₁₆	—	2	2	no	—
254	SD₁₆	—	2	2	no	—
255	SD₁₆	—	2	4	no	—
256	D₈	—	2	2	no	—
257	D₈	—	2	4	no	—
258	M₁₆	—	2	2	no	—
259	C₂×C₈	—	2	2	no	—
260	C₂×C₈	C₂³×C₅	1	1	yes	characteristic
261	C₂×C₈	C₂³×C₅	1	1	yes	characteristic
262	C₂×C₈	C₂³×C₅	1	2	yes	—
263	C₄⋊C₄	—	2	1	no	—
264	C₄⋊C₄	—	2	2	no	—
265	C₄⋊C₄	C₂³×C₅	1	2	yes	—
266	C₂²⋊C₄	—	2	2	no	—
267	C₂²⋊C₄	—	2	2	no	—
268	C₂×C₅	—	2	2	no	—
269	C₂×C₅	—	4	2	no	—
270	C₂×C₅	—	4	4	no	—
271	C₂×C₅	—	4	2	no	—
272	C₂×C₅	—	8	1	no	—
273	C₂×C₅	C₂×#120	1	1	yes	characteristic
274	C₂×C₅	#576	1	1	yes	characteristic
275	C₂×C₅	#577	1	1	yes	characteristic
276	C₂³	—	2	8	no	—
277	C₂³	—	2	2	no	—
278	C₂³	—	2	1	no	—
279	C₂³	—	2	4	no	—
280	C₂³	—	2	1	no	—
281	C₂³	—	8	1	no	—
282	C₂³	—	8	1	no	—
283	C₂³	—	8	2	no	—
284	C₂³	—	8	2	no	—
285	C₂³	C₂×C₅×D₄	1	2	yes	—
286	C₂³	C₂×C₅×D₄	1	1	yes	characteristic
287	Q₈	—	2	2	no	—
288	Q₈	—	2	1	no	—
289	Q₈	—	2	1	no	—
290	Q₈	—	2	1	no	—
291	Q₈	C₂×C₅×D₄	1	2	yes	—
292	D₄	—	2	8	no	—
293	D₄	—	2	8	no	—
294	D₄	—	2	4	no	—
295	D₄	—	2	4	no	—
296	D₄	—	2	2	no	—
297	D₄	—	2	4	no	—
298	D₄	—	2	2	no	—
299	D₄	—	2	1	no	—
300	D₄	—	2	1	no	—
301	D₄	—	2	1	no	—
302	D₄	—	4	2	no	—
303	D₄	—	8	2	no	—
304	D₄	C₂×C₅×D₄	1	2	yes	—
305	D₄	C₂×C₅×D₄	1	4	yes	—
306	C₂×C₄	—	2	8	no	—
307	C₂×C₄	—	2	1	no	—
308	C₂×C₄	—	2	4	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	1	no	—
313	C₂×C₄	—	4	2	no	—
314	C₂×C₄	—	8	1	no	—
315	C₂×C₄	C₂×C₅×D₄	1	2	yes	—
316	C₂×C₄	C₂×C₅×D₄	1	1	yes	characteristic
317	C₂×C₄	C₂×C₅×D₄	1	2	yes	—
318	C₂×C₄	C₂×C₅×D₄	1	2	yes	—
319	C₂×C₄	C₂⁴×C₅	1	1	yes	characteristic
320	C₈	—	2	1	no	—
321	C₈	—	2	1	no	—
322	C₈	—	2	2	no	—
323	C₅	#3012	1	1	yes	characteristic, direct product factor, Sylow
324	C₂²	—	2	1	no	—
325	C₂²	—	2	1	no	—
326	C₂²	—	2	2	no	—
327	C₂²	—	2	4	no	—
328	C₂²	—	2	2	no	—
329	C₂²	—	2	2	no	—
330	C₂²	—	2	2	no	—
331	C₂²	—	4	2	no	—
332	C₂²	—	4	1	no	—
333	C₂²	—	4	2	no	—
334	C₂²	—	4	1	no	—
335	C₂²	—	4	1	no	—
336	C₂²	—	4	1	no	—
337	C₂²	—	4	1	no	—
338	C₂²	—	8	4	no	—
339	C₂²	—	8	8	no	—
340	C₂²	C₅×#120	1	2	yes	—
341	C₂²	C₂²×C₅×D₄	1	1	yes	characteristic
342	C₄	—	2	2	no	—
343	C₄	—	2	2	no	—
344	C₄	—	4	1	no	—
345	C₄	—	4	2	no	—
346	C₄	C₅×#120	1	2	yes	—
347	C₄	C₂²×C₅×D₄	1	1	yes	characteristic
348	C₄	C₂²×C₅×D₄	1	1	yes	characteristic
349	C₂	—	2	2	no	—
350	C₂	—	4	2	no	—
351	C₂	—	4	4	no	—
352	C₂	—	4	2	no	—
353	C₂	—	8	1	no	—
354	C₂	C₂×C₅×#120	1	1	yes	characteristic
355	C₂	C₅×#576	1	1	yes	characteristic
356	C₂	C₅×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₅
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₅×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×H(5,𝔽₂)	C₂	semidirect
2. C₂×C₅×AGL(1,ℤ/8)	C₂	semidirect
3. C₂×C₅×#135	C₂	semidirect
4. C₅×#537	C₂	semidirect
5. C₅×#452	C₂	semidirect
6. C₅×#450	C₂	semidirect
7. C₅×#449	C₂	semidirect
8. C₅×#447	C₂	semidirect
9. C₅×#417	C₂	semidirect
10. C₂×C₅×#102	C₂	semidirect
11. C₅×#408	C₂	semidirect
18. C₂×C₅×#41	C₂²	semidirect
25. C₂×C₅×Q₁₆	C₂²	semidirect
26. C₂×C₅×SD₁₆	C₂²	semidirect
27. C₂×C₅×SD₁₆	C₂²	semidirect
28. C₂×C₅×SD₁₆	C₂²	semidirect
29. C₂×C₅×D₈	C₂²	semidirect
30. C₂×C₅×D₈	C₂²	semidirect
31. C₂×C₅×M₁₆	C₂²	semidirect
32. C₂²×C₅×C₈	C₂²	semidirect
34. C₅×C₂²⋊Q₈	C₂²	semidirect
37. C₅×#121	C₂²	semidirect
38. C₂×C₅×C₄⋊C₄	C₂²	semidirect
39. C₅×#103	C₂²	semidirect
40. C₅×#102	C₂²	semidirect
41. C₅×#102	C₂²	semidirect
42. C₅×#102	C₂²	semidirect
43. C₅×C₂²⋊C₈	C₂²	semidirect
44. C₅×C₂²⋊C₈	C₂²	semidirect
45. #3012	C₅	direct (N × H)
56. C₅×#41	D₄	semidirect
73. C₂×C₅×D₄	D₄	semidirect
99. C₂×H(5,𝔽₂)	C₂×C₅	semidirect
100. C₂×AGL(1,ℤ/8)	C₂×C₅	semidirect
101. C₂×#135	C₂×C₅	semidirect
102. #537	C₂×C₅	semidirect
103. #452	C₂×C₅	semidirect
104. #450	C₂×C₅	semidirect
105. #449	C₂×C₅	semidirect
106. #447	C₂×C₅	semidirect
107. #417	C₂×C₅	semidirect
108. C₂×#102	C₂×C₅	semidirect
109. #408	C₂×C₅	semidirect
163. C₂×#41	C₂²×C₅	semidirect
170. C₂×Q₁₆	C₂²×C₅	semidirect
171. C₂×SD₁₆	C₂²×C₅	semidirect
172. C₂×SD₁₆	C₂²×C₅	semidirect
173. C₂×SD₁₆	C₂²×C₅	semidirect
174. C₂×D₈	C₂²×C₅	semidirect
175. C₂×D₈	C₂²×C₅	semidirect
176. C₂×M₁₆	C₂²×C₅	semidirect
177. C₂²×C₈	C₂²×C₅	semidirect
179. C₂²⋊Q₈	C₂²×C₅	semidirect
182. #121	C₂²×C₅	semidirect
183. C₂×C₄⋊C₄	C₂²×C₅	semidirect
184. #103	C₂²×C₅	semidirect
185. #102	C₂²×C₅	semidirect
186. #102	C₂²×C₅	semidirect
187. #102	C₂²×C₅	semidirect
188. C₂²⋊C₈	C₂²×C₅	semidirect
189. C₂²⋊C₈	C₂²×C₅	semidirect
225. #41	C₅×D₄	semidirect
242. C₂×D₄	C₅×D₄	semidirect
323. C₅	#3012	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×H(5,𝔽₂)	2
C₂×C₅×AGL(1,ℤ/8)	2
C₂×C₅×#135	2
C₅×#537	2
C₅×#452	2
C₅×#450	2
C₅×#449	2
C₅×#447	2
C₅×#417	2
C₂×C₅×#102	2
C₅×#408	2
#3012	5

Subgroups — C5×#3012 #10616607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#3012 #10616607