Subgroups — C₂×C₅×#3416 #11985353

Order 1280.

2074 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#578	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#576	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#3416	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₅×#510	C₂	1	3	yes	maximal, complemented
5	C₂×C₅×#509	C₂	1	3	yes	maximal, complemented
6	C₂×C₅×#508	C₂	1	3	yes	maximal, complemented
7	C₂²×C₅×SD₃₂	C₂	1	3	yes	maximal, complemented
8	C₂×C₅×#504	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×2₋¹⁺⁴	—	2	1	no	—
10	C₂×C₅×H(5,𝔽₂)	—	2	1	no	—
11	C₅×#578	—	2	4	no	—
12	C₅×#578	C₂²	1	8	yes	complemented
13	C₅×#576	—	2	4	no	—
14	C₅×#576	C₂²	1	8	yes	complemented
15	C₂×C₅×#137	—	2	3	no	—
16	C₂×C₅×AGL(1,ℤ/8)	—	2	3	no	—
17	C₂×C₅×#135	C₂²	1	3	yes	—
18	C₂×C₅×#135	C₂²	1	3	yes	complemented
19	C₂²×C₅×Q₁₆	C₂²	1	3	yes	complemented
20	C₂²×C₅×D₈	C₂²	1	3	yes	—
21	C₂×C₅×#131	C₂²	1	1	yes	characteristic
22	C₅×#510	C₂²	1	24	yes	complemented
23	C₅×#509	C₂²	1	24	yes	complemented
24	C₅×#508	C₂²	1	24	yes	complemented
25	C₂×C₅×Q₃₂	C₂²	1	3	yes	complemented
26	C₂×C₅×SD₃₂	C₂²	1	3	yes	complemented
27	C₂×C₅×SD₃₂	C₂²	1	6	yes	complemented
28	C₂×C₅×SD₃₂	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₅×SD₃₂	C₂²	1	24	yes	complemented
30	C₂×C₅×D₁₆	C₂²	1	3	yes	complemented
31	C₅×#504	C₂²	1	8	yes	complemented
32	C₂×C₅×M₃₂	C₂²	1	3	yes	complemented
33	C₂²×C₅×C₁₆	C₂²	1	3	yes	complemented
34	C₂×#3416	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
35	C₅×2₋¹⁺⁴	—	2	8	no	—
36	C₅×2₋¹⁺⁴	—	4	4	no	—
37	C₅×H(5,𝔽₂)	—	2	8	no	—
38	C₅×H(5,𝔽₂)	—	4	4	no	—
39	C₂×C₅×#41	—	2	3	no	—
40	C₂×C₅×#41	—	2	3	no	—
41	C₂×C₅×#41	—	4	1	no	—
42	C₂×C₅×#41	—	4	3	no	—
43	C₂×C₅×#41	D₄	1	1	yes	characteristic
44	C₂²×C₅×Q₈	—	2	3	no	—
45	C₂²×C₅×Q₈	—	4	1	no	—
46	C₂²×C₅×D₄	—	2	3	no	—
47	C₂²×C₅×D₄	—	4	3	no	—
48	C₅×#137	—	2	24	no	—
49	C₅×AGL(1,ℤ/8)	—	2	24	no	—
50	C₅×#135	—	2	6	no	—
51	C₅×#135	—	2	6	no	—
52	C₅×#135	C₂³	1	12	yes	—
53	C₅×#135	C₂³	1	12	yes	complemented
54	C₂×C₅×Q₁₆	—	2	3	no	—
55	C₂×C₅×Q₁₆	—	2	6	no	—
56	C₂×C₅×Q₁₆	C₂³	1	3	yes	—
57	C₂×C₅×Q₁₆	C₂³	1	1	yes	characteristic
58	C₂×C₅×Q₁₆	C₂³	1	12	yes	complemented
59	C₂×C₅×SD₁₆	—	2	3	no	—
60	C₂×C₅×SD₁₆	—	2	3	no	—
61	C₂×C₅×D₈	—	2	3	no	—
62	C₂×C₅×D₈	—	2	6	no	—
63	C₂×C₅×D₈	C₂³	1	1	yes	characteristic
64	C₂×C₅×D₈	C₂³	1	3	yes	—
65	C₂×C₅×D₈	C₂³	1	12	yes	—
66	C₅×#131	D₄	1	4	yes	—
67	C₅×#131	C₂³	1	4	yes	—
68	C₂×C₅×M₁₆	D₄	1	3	yes	—
69	C₂²×C₅×C₈	C₂³	1	3	yes	—
70	C₅×Q₃₂	C₂³	1	12	yes	complemented
71	C₅×SD₃₂	C₂³	1	12	yes	complemented
72	C₅×SD₃₂	C₂³	1	24	yes	complemented
73	C₅×SD₃₂	C₂³	1	4	yes	complemented
74	C₅×D₁₆	C₂³	1	12	yes	complemented
75	C₅×M₃₂	C₂³	1	12	yes	complemented
76	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
77	C₂×C₅×C₁₆	C₂³	1	3	yes	—
78	C₂×C₅×C₁₆	C₂³	1	12	yes	complemented
79	C₂×#578	C₂×C₅	1	1	yes	characteristic, complemented
80	C₂×#576	C₂×C₅	1	1	yes	characteristic, complemented
81	#3416	C₂×C₅	1	16	yes	direct product factor
82	C₂×#510	C₂×C₅	1	3	yes	complemented
83	C₂×#509	C₂×C₅	1	3	yes	complemented
84	C₂×#508	C₂×C₅	1	3	yes	complemented
85	C₂²×SD₃₂	C₂×C₅	1	3	yes	complemented
86	C₂×#504	C₂×C₅	1	1	yes	characteristic, complemented
87	C₂⁴×C₅	—	4	3	no	—
88	C₅×#41	—	2	12	no	—
89	C₅×#41	—	2	12	no	—
90	C₅×#41	—	4	8	no	—
91	C₅×#41	—	4	24	no	—
92	C₅×#41	—	4	6	no	—
93	C₅×#41	—	4	6	no	—
94	C₅×#41	D₈	1	4	yes	—
95	C₅×#41	C₂×D₄	1	4	yes	—
96	C₂×C₅×Q₈	—	2	1	no	—
97	C₂×C₅×Q₈	—	2	3	no	—
98	C₂×C₅×Q₈	—	2	12	no	—
99	C₂×C₅×Q₈	—	4	8	no	—
100	C₂×C₅×Q₈	—	4	3	no	—
101	C₂×C₅×Q₈	—	4	6	no	—
102	C₂×C₅×Q₈	D₈	1	1	yes	characteristic
103	C₂×C₅×D₄	—	2	3	no	—
104	C₂×C₅×D₄	—	2	12	no	—
105	C₂×C₅×D₄	—	2	1	no	—
106	C₂×C₅×D₄	—	4	3	no	—
107	C₂×C₅×D₄	—	4	3	no	—
108	C₂×C₅×D₄	—	4	24	no	—
109	C₂×C₅×D₄	—	4	3	no	—
110	C₂×C₅×D₄	—	4	6	no	—
111	C₂×C₅×D₄	D₈	1	3	yes	—
112	C₂²×C₄×C₅	—	4	3	no	—
113	C₂²×C₄×C₅	—	4	3	no	—
114	C₂²×C₄×C₅	—	4	3	no	—
115	C₂²×C₄×C₅	C₂×D₄	1	3	yes	—
116	C₅×Q₁₆	—	2	3	no	—
117	C₅×Q₁₆	—	2	12	no	—
118	C₅×Q₁₆	—	2	1	no	—
119	C₅×Q₁₆	C₂⁴	1	6	yes	—
120	C₅×Q₁₆	C₂⁴	1	2	yes	—
121	C₅×SD₁₆	—	2	12	no	—
122	C₅×SD₁₆	—	2	12	no	—
123	C₅×D₈	—	2	3	no	—
124	C₅×D₈	—	2	12	no	—
125	C₅×D₈	—	2	1	no	—
126	C₅×D₈	C₂⁴	1	6	yes	—
127	C₅×D₈	C₂⁴	1	2	yes	—
128	C₅×M₁₆	C₂×D₄	1	12	yes	—
129	C₂×C₅×C₈	C₂×D₄	1	3	yes	—
130	C₂×C₅×C₈	C₂×D₄	1	6	yes	—
131	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
132	C₂×C₅×C₈	C₂⁴	1	6	yes	—
133	C₅×C₁₆	C₂⁴	1	2	yes	—
134	C₅×C₁₆	C₂⁴	1	6	yes	—
135	C₂×2₋¹⁺⁴	—	2	1	no	—
136	C₂×H(5,𝔽₂)	—	2	1	no	—
137	#578	—	2	4	no	—
138	#578	C₂²×C₅	1	8	yes	complemented
139	#576	—	2	4	no	—
140	#576	C₂²×C₅	1	8	yes	complemented
141	C₂×#137	—	2	3	no	—
142	C₂×AGL(1,ℤ/8)	—	2	3	no	—
143	C₂×#135	C₂²×C₅	1	3	yes	—
144	C₂×#135	C₂²×C₅	1	3	yes	complemented
145	C₂²×Q₁₆	C₂²×C₅	1	3	yes	complemented
146	C₂²×D₈	C₂²×C₅	1	3	yes	—
147	C₂×#131	C₂²×C₅	1	1	yes	characteristic
148	#510	C₂²×C₅	1	24	yes	complemented
149	#509	C₂²×C₅	1	24	yes	complemented
150	#508	C₂²×C₅	1	24	yes	complemented
151	C₂×Q₃₂	C₂²×C₅	1	3	yes	complemented
152	C₂×SD₃₂	C₂²×C₅	1	3	yes	complemented
153	C₂×SD₃₂	C₂²×C₅	1	6	yes	complemented
154	C₂×SD₃₂	C₂²×C₅	1	1	yes	characteristic, complemented
155	C₂×SD₃₂	C₂²×C₅	1	24	yes	complemented
156	C₂×D₁₆	C₂²×C₅	1	3	yes	complemented
157	#504	C₂²×C₅	1	8	yes	complemented
158	C₂×M₃₂	C₂²×C₅	1	3	yes	complemented
159	C₂²×C₁₆	C₂²×C₅	1	3	yes	complemented
160	C₂³×C₅	—	4	1	no	—
161	C₂³×C₅	—	4	3	no	—
162	C₂³×C₅	—	4	12	no	—
163	C₂³×C₅	—	16	6	no	—
164	C₂³×C₅	C₂×D₈	1	3	yes	—
165	C₅×Q₈	—	2	2	no	—
166	C₅×Q₈	—	2	6	no	—
167	C₅×Q₈	—	4	12	no	—
168	C₅×Q₈	—	4	3	no	—
169	C₅×Q₈	—	4	1	no	—
170	C₅×Q₈	C₂×D₈	1	4	yes	—
171	C₅×D₄	—	2	6	no	—
172	C₅×D₄	—	2	2	no	—
173	C₅×D₄	—	4	12	no	—
174	C₅×D₄	—	4	12	no	—
175	C₅×D₄	—	4	12	no	—
176	C₅×D₄	—	4	3	no	—
177	C₅×D₄	—	4	1	no	—
178	C₅×D₄	C₂×D₈	1	12	yes	—
179	C₂×C₄×C₅	—	4	12	no	—
180	C₂×C₄×C₅	—	4	1	no	—
181	C₂×C₄×C₅	—	4	3	no	—
182	C₂×C₄×C₅	—	4	12	no	—
183	C₂×C₄×C₅	—	4	12	no	—
184	C₂×C₄×C₅	C₂×D₈	1	6	yes	—
185	C₂×C₄×C₅	C₂×D₈	1	3	yes	—
186	C₂×C₄×C₅	C₂²×D₄	1	6	yes	—
187	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
188	C₅×C₈	C₂²×D₄	1	1	yes	characteristic
189	C₅×C₈	C₂²×D₄	1	6	yes	—
190	C₅×C₈	C₂⁵	1	1	yes	characteristic
191	2₋¹⁺⁴	—	2	8	no	—
192	2₋¹⁺⁴	—	4	4	no	—
193	H(5,𝔽₂)	—	2	8	no	—
194	H(5,𝔽₂)	—	4	4	no	—
195	C₂×#41	—	2	3	no	—
196	C₂×#41	—	2	3	no	—
197	C₂×#41	—	4	1	no	—
198	C₂×#41	—	4	3	no	—
199	C₂×#41	C₅×D₄	1	1	yes	characteristic
200	C₂²×Q₈	—	2	3	no	—
201	C₂²×Q₈	—	4	1	no	—
202	C₂²×D₄	—	2	3	no	—
203	C₂²×D₄	—	4	3	no	—
204	#137	—	2	24	no	—
205	AGL(1,ℤ/8)	—	2	24	no	—
206	#135	—	2	6	no	—
207	#135	—	2	6	no	—
208	#135	C₂³×C₅	1	12	yes	—
209	#135	C₂³×C₅	1	12	yes	complemented
210	C₂×Q₁₆	—	2	3	no	—
211	C₂×Q₁₆	—	2	6	no	—
212	C₂×Q₁₆	C₂³×C₅	1	3	yes	—
213	C₂×Q₁₆	C₂³×C₅	1	1	yes	characteristic
214	C₂×Q₁₆	C₂³×C₅	1	12	yes	complemented
215	C₂×SD₁₆	—	2	3	no	—
216	C₂×SD₁₆	—	2	3	no	—
217	C₂×D₈	—	2	3	no	—
218	C₂×D₈	—	2	6	no	—
219	C₂×D₈	C₂³×C₅	1	3	yes	—
220	C₂×D₈	C₂³×C₅	1	12	yes	—
221	C₂×D₈	C₂³×C₅	1	1	yes	characteristic
222	#131	C₅×D₄	1	4	yes	—
223	#131	C₂³×C₅	1	4	yes	—
224	C₂×M₁₆	C₅×D₄	1	3	yes	—
225	C₂²×C₈	C₂³×C₅	1	3	yes	—
226	Q₃₂	C₂³×C₅	1	12	yes	complemented
227	SD₃₂	C₂³×C₅	1	12	yes	complemented
228	SD₃₂	C₂³×C₅	1	24	yes	complemented
229	SD₃₂	C₂³×C₅	1	4	yes	complemented
230	D₁₆	C₂³×C₅	1	12	yes	complemented
231	M₃₂	C₂³×C₅	1	12	yes	complemented
232	C₂×C₁₆	C₂³×C₅	1	1	yes	characteristic
233	C₂×C₁₆	C₂³×C₅	1	3	yes	—
234	C₂×C₁₆	C₂³×C₅	1	12	yes	complemented
235	C₂²×C₅	—	2	6	no	—
236	C₂²×C₅	—	4	2	no	—
237	C₂²×C₅	—	4	6	no	—
238	C₂²×C₅	—	8	2	no	—
239	C₂²×C₅	—	8	6	no	—
240	C₂²×C₅	—	16	12	no	—
241	C₂²×C₅	C₂²×D₈	1	6	yes	—
242	C₂²×C₅	C₂²×D₈	1	1	yes	characteristic
243	C₄×C₅	—	4	2	no	—
244	C₄×C₅	—	4	6	no	—
245	C₄×C₅	C₂²×D₈	1	6	yes	—
246	C₄×C₅	C₂²×D₈	1	1	yes	characteristic
247	C₄×C₅	C₂³×D₄	1	1	yes	characteristic
248	C₂⁴	—	4	3	no	—
249	#41	—	2	12	no	—
250	#41	—	2	12	no	—
251	#41	—	4	8	no	—
252	#41	—	4	24	no	—
253	#41	—	4	6	no	—
254	#41	—	4	6	no	—
255	#41	C₅×D₈	1	4	yes	—
256	#41	C₂×C₅×D₄	1	4	yes	—
257	C₂×Q₈	—	2	1	no	—
258	C₂×Q₈	—	2	3	no	—
259	C₂×Q₈	—	2	12	no	—
260	C₂×Q₈	—	4	8	no	—
261	C₂×Q₈	—	4	3	no	—
262	C₂×Q₈	—	4	6	no	—
263	C₂×Q₈	C₅×D₈	1	1	yes	characteristic
264	C₂×D₄	—	2	3	no	—
265	C₂×D₄	—	2	12	no	—
266	C₂×D₄	—	2	1	no	—
267	C₂×D₄	—	4	3	no	—
268	C₂×D₄	—	4	3	no	—
269	C₂×D₄	—	4	24	no	—
270	C₂×D₄	—	4	3	no	—
271	C₂×D₄	—	4	6	no	—
272	C₂×D₄	C₅×D₈	1	3	yes	—
273	C₂²×C₄	—	4	3	no	—
274	C₂²×C₄	—	4	3	no	—
275	C₂²×C₄	—	4	3	no	—
276	C₂²×C₄	C₂×C₅×D₄	1	3	yes	—
277	Q₁₆	—	2	3	no	—
278	Q₁₆	—	2	12	no	—
279	Q₁₆	—	2	1	no	—
280	Q₁₆	C₂⁴×C₅	1	6	yes	—
281	Q₁₆	C₂⁴×C₅	1	2	yes	—
282	SD₁₆	—	2	12	no	—
283	SD₁₆	—	2	12	no	—
284	D₈	—	2	3	no	—
285	D₈	—	2	12	no	—
286	D₈	—	2	1	no	—
287	D₈	C₂⁴×C₅	1	2	yes	—
288	D₈	C₂⁴×C₅	1	6	yes	—
289	M₁₆	C₂×C₅×D₄	1	12	yes	—
290	C₂×C₈	C₂×C₅×D₄	1	3	yes	—
291	C₂×C₈	C₂×C₅×D₄	1	6	yes	—
292	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
293	C₂×C₈	C₂⁴×C₅	1	6	yes	—
294	C₁₆	C₂⁴×C₅	1	2	yes	—
295	C₁₆	C₂⁴×C₅	1	6	yes	—
296	C₂×C₅	—	2	6	no	—
297	C₂×C₅	—	8	2	no	—
298	C₂×C₅	—	8	6	no	—
299	C₂×C₅	#3416	1	2	yes	direct product factor
300	C₂×C₅	C₂³×D₈	1	1	yes	characteristic
301	C₂³	—	4	1	no	—
302	C₂³	—	4	3	no	—
303	C₂³	—	4	12	no	—
304	C₂³	—	16	6	no	—
305	C₂³	C₂×C₅×D₈	1	3	yes	—
306	Q₈	—	2	2	no	—
307	Q₈	—	2	6	no	—
308	Q₈	—	4	12	no	—
309	Q₈	—	4	3	no	—
310	Q₈	—	4	1	no	—
311	Q₈	C₂×C₅×D₈	1	4	yes	—
312	D₄	—	2	6	no	—
313	D₄	—	2	2	no	—
314	D₄	—	4	12	no	—
315	D₄	—	4	12	no	—
316	D₄	—	4	12	no	—
317	D₄	—	4	3	no	—
318	D₄	—	4	1	no	—
319	D₄	C₂×C₅×D₈	1	12	yes	—
320	C₂×C₄	—	4	1	no	—
321	C₂×C₄	—	4	3	no	—
322	C₂×C₄	—	4	12	no	—
323	C₂×C₄	—	4	12	no	—
324	C₂×C₄	—	4	12	no	—
325	C₂×C₄	C₂×C₅×D₈	1	3	yes	—
326	C₂×C₄	C₂×C₅×D₈	1	6	yes	—
327	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
328	C₂×C₄	C₂²×C₅×D₄	1	6	yes	—
329	C₈	C₂²×C₅×D₄	1	1	yes	characteristic
330	C₈	C₂²×C₅×D₄	1	6	yes	—
331	C₈	C₂⁵×C₅	1	1	yes	characteristic
332	C₅	C₂×#3416	1	1	yes	characteristic, direct product factor, Sylow
333	C₂²	—	2	6	no	—
334	C₂²	—	4	2	no	—
335	C₂²	—	4	6	no	—
336	C₂²	—	8	6	no	—
337	C₂²	—	8	2	no	—
338	C₂²	—	16	12	no	—
339	C₂²	C₂²×C₅×D₈	1	6	yes	—
340	C₂²	C₂²×C₅×D₈	1	1	yes	characteristic
341	C₄	—	4	2	no	—
342	C₄	—	4	6	no	—
343	C₄	C₂²×C₅×D₈	1	6	yes	—
344	C₄	C₂²×C₅×D₈	1	1	yes	characteristic
345	C₄	C₂³×C₅×D₄	1	1	yes	characteristic
346	C₂	—	2	6	no	—
347	C₂	—	8	6	no	—
348	C₂	—	8	2	no	—
349	C₂	C₅×#3416	1	2	yes	direct product factor
350	C₂	C₂³×C₅×D₈	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂²×D₈
commutator, Frattini, cosocle	C₈	C₂⁵×C₅
LCS	G ▷ 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. C₂×C₅×#578	C₂	semidirect
2. C₂×C₅×#576	C₂	semidirect
3. C₅×#3416	C₂	direct (N × H)
4. C₂×C₅×#510	C₂	semidirect
5. C₂×C₅×#509	C₂	semidirect
6. C₂×C₅×#508	C₂	semidirect
7. C₂²×C₅×SD₃₂	C₂	semidirect
8. C₂×C₅×#504	C₂	semidirect
12. C₅×#578	C₂²	semidirect
14. C₅×#576	C₂²	semidirect
18. C₂×C₅×#135	C₂²	semidirect
19. C₂²×C₅×Q₁₆	C₂²	semidirect
22. C₅×#510	C₂²	semidirect
23. C₅×#509	C₂²	semidirect
24. C₅×#508	C₂²	semidirect
25. C₂×C₅×Q₃₂	C₂²	semidirect
26. C₂×C₅×SD₃₂	C₂²	semidirect
27. C₂×C₅×SD₃₂	C₂²	semidirect
28. C₂×C₅×SD₃₂	C₂²	semidirect
29. C₂×C₅×SD₃₂	C₂²	semidirect
30. C₂×C₅×D₁₆	C₂²	semidirect
31. C₅×#504	C₂²	semidirect
32. C₂×C₅×M₃₂	C₂²	semidirect
33. C₂²×C₅×C₁₆	C₂²	semidirect
34. C₂×#3416	C₅	direct (N × H)
53. C₅×#135	C₂³	semidirect
58. C₂×C₅×Q₁₆	C₂³	semidirect
70. C₅×Q₃₂	C₂³	semidirect
71. C₅×SD₃₂	C₂³	semidirect
72. C₅×SD₃₂	C₂³	semidirect
73. C₅×SD₃₂	C₂³	semidirect
74. C₅×D₁₆	C₂³	semidirect
75. C₅×M₃₂	C₂³	semidirect
78. C₂×C₅×C₁₆	C₂³	semidirect
79. C₂×#578	C₂×C₅	semidirect
80. C₂×#576	C₂×C₅	semidirect
81. #3416	C₂×C₅	direct (N × H)
82. C₂×#510	C₂×C₅	semidirect
83. C₂×#509	C₂×C₅	semidirect
84. C₂×#508	C₂×C₅	semidirect
85. C₂²×SD₃₂	C₂×C₅	semidirect
86. C₂×#504	C₂×C₅	semidirect
138. #578	C₂²×C₅	semidirect
140. #576	C₂²×C₅	semidirect
144. C₂×#135	C₂²×C₅	semidirect
145. C₂²×Q₁₆	C₂²×C₅	semidirect
148. #510	C₂²×C₅	semidirect
149. #509	C₂²×C₅	semidirect
150. #508	C₂²×C₅	semidirect
151. C₂×Q₃₂	C₂²×C₅	semidirect
152. C₂×SD₃₂	C₂²×C₅	semidirect
153. C₂×SD₃₂	C₂²×C₅	semidirect
154. C₂×SD₃₂	C₂²×C₅	semidirect
155. C₂×SD₃₂	C₂²×C₅	semidirect
156. C₂×D₁₆	C₂²×C₅	semidirect
157. #504	C₂²×C₅	semidirect
158. C₂×M₃₂	C₂²×C₅	semidirect
159. C₂²×C₁₆	C₂²×C₅	semidirect
209. #135	C₂³×C₅	semidirect
214. C₂×Q₁₆	C₂³×C₅	semidirect
226. Q₃₂	C₂³×C₅	semidirect
227. SD₃₂	C₂³×C₅	semidirect
228. SD₃₂	C₂³×C₅	semidirect
229. SD₃₂	C₂³×C₅	semidirect
230. D₁₆	C₂³×C₅	semidirect
231. M₃₂	C₂³×C₅	semidirect
234. C₂×C₁₆	C₂³×C₅	semidirect
299. C₂×C₅	#3416	direct (N × H)
332. C₅	C₂×#3416	direct (N × H)
349. C₂	C₅×#3416	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×#578	2
C₂×C₅×#576	2
C₅×#3416	2
C₂×C₅×#510	2
C₂×C₅×#509	2
C₂×C₅×#508	2
C₂²×C₅×SD₃₂	2
C₂×C₅×#504	2
C₂×#3416	5

Subgroups — C2×C5×#3416 #11985353

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#3416 #11985353