Subgroups — C₂×#11717472 #13107813

Order 1600.

1960 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×#87900	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#709	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₅×D₂₀	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₅×C₂²⋊D₅	C₂	1	4	yes	maximal, complemented
5	#11717472	C₂	1	16	yes	maximal, direct product factor
6	C₂×#87877	C₂	1	2	yes	maximal, complemented
7	C₂×D₅×D₂₀	C₂	1	2	yes	maximal, complemented
8	C₂×#87871	C₂	1	2	yes	maximal, complemented
9	C₂×#87870	C₂	1	2	yes	maximal, complemented
10	C₂³×C₅×D₅	C₂²	1	2	yes	complemented
11	C₂²×D₅²	C₂²	1	4	yes	complemented
12	C₂²×C₄×C₅²	C₂²	1	1	yes	characteristic, complemented
13	C₂×C₂²⋊(C₅⋊D₅)	C₂²	1	2	yes	complemented
14	#87900	C₂²	1	8	yes	complemented
15	C₂×C₄⋊(C₅⋊D₅)	C₂²	1	1	yes	characteristic, complemented
16	C₂×C₄×C₅⋊D₅	C₂²	1	2	yes	complemented
17	C₂×#6045	C₂²	1	1	yes	characteristic, complemented
18	C₂×C₅×C₂²⋊D₅	C₂²	1	2	yes	complemented
19	C₅×#709	C₂²	1	8	yes	complemented
20	C₂×C₅×D₂₀	C₂²	1	2	yes	complemented
21	C₂×C₅×D₂₀	C₂²	1	2	yes	complemented
22	C₂×C₅×D₂₀	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₅×D₂₀	C₂²	1	8	yes	complemented
24	C₂×C₄×C₅×D₅	C₂²	1	2	yes	complemented
25	C₂×C₅×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
26	D₅×C₂²⋊D₅	C₂²	1	32	yes	complemented
27	C₂×#6038	C₂²	1	4	yes	complemented
28	C₂×#6037	C₂²	1	4	yes	complemented
29	C₂×D₅×Dic₅	C₂²	1	4	yes	complemented
30	#87877	C₂²	1	16	yes	complemented
31	D₅×D₂₀	C₂²	1	16	yes	complemented
32	#87871	C₂²	1	16	yes	complemented
33	#87870	C₂²	1	16	yes	complemented
34	C₂×#4149	—	5	1	no	maximal
35	C₂×#4144	—	5	1	no	maximal
36	C₂³×C₅²	C₂³	1	1	yes	characteristic
37	C₂²×C₅⋊D₅	C₂³	1	2	yes	—
38	C₂²×C₅×D₅	—	4	4	no	—
39	C₂²×C₅×D₅	C₂³	1	4	yes	—
40	C₂²×C₅×D₅	C₂³	1	2	yes	—
41	C₂²×C₅×D₅	C₂³	1	8	yes	complemented
42	C₂×D₅²	—	4	8	no	—
43	C₂×D₅²	C₂³	1	16	yes	complemented
44	C₂×C₄×C₅²	C₂³	1	1	yes	characteristic
45	C₂×C₄×C₅²	C₂³	1	1	yes	characteristic
46	C₂×C₄×C₅²	C₂³	1	4	yes	complemented
47	C₂²⋊(C₅⋊D₅)	C₂³	1	8	yes	complemented
48	C₂×#1039	C₂³	1	2	yes	—
49	C₄⋊(C₅⋊D₅)	C₂³	1	4	yes	complemented
50	C₄×C₅⋊D₅	C₂³	1	8	yes	complemented
51	#6045	C₂³	1	4	yes	complemented
52	C₅×C₂²⋊D₅	C₂³	1	8	yes	complemented
53	C₂×C₅×Dic₅	C₂³	1	2	yes	—
54	C₅×D₂₀	C₂³	1	8	yes	complemented
55	C₅×D₂₀	C₂³	1	8	yes	complemented
56	C₅×D₂₀	C₂³	1	4	yes	complemented
57	C₄×C₅×D₅	C₂³	1	8	yes	complemented
58	C₅×Dic₁₀	C₂³	1	4	yes	complemented
59	#6038	C₂³	1	16	yes	complemented
60	#6037	C₂³	1	16	yes	complemented
61	D₅×Dic₅	C₂³	1	16	yes	complemented
62	C₂×C₅×#41	—	5	1	no	—
63	C₂²×C₅×D₄	—	5	1	no	—
64	C₂²×C₂²⋊D₅	—	5	4	no	—
65	#4149	—	5	16	no	—
66	C₂×#713	—	5	2	no	—
67	#4144	—	5	16	no	—
68	C₂×#711	—	5	2	no	—
69	C₂×#711	—	5	2	no	—
70	C₂×D₄×D₅	—	5	4	no	—
71	C₂×D₄×D₅	—	5	2	no	—
72	C₂×D₄×D₅	—	5	2	no	—
73	C₂×D₄×D₅	—	5	2	no	—
74	C₂×#709	—	5	1	no	—
75	C₂×#709	—	5	1	no	—
76	C₂×#709	—	5	2	no	—
77	C₂×#709	—	10	2	no	—
78	C₂×#709	D₅	1	1	yes	characteristic, complemented
79	C₂²×D₂₀	—	5	2	no	—
80	C₂²×D₂₀	D₅	1	1	yes	characteristic, complemented
81	C₂²×C₅²	—	2	2	no	—
82	C₂²×C₅²	C₂⁴	1	2	yes	—
83	C₂²×C₅²	C₂⁴	1	1	yes	characteristic
84	C₂×C₅⋊D₅	—	2	4	no	—
85	C₂×C₅⋊D₅	C₂⁴	1	4	yes	—
86	C₂×C₅×D₅	—	2	4	no	—
87	C₂×C₅×D₅	—	2	8	no	—
88	C₂×C₅×D₅	—	4	8	no	—
89	C₂×C₅×D₅	C₂⁴	1	8	yes	—
90	C₂×C₅×D₅	C₂⁴	1	4	yes	—
91	D₅²	—	4	16	no	—
92	C₄×C₅²	C₂⁴	1	2	yes	—
93	C₄×C₅²	C₂⁴	1	2	yes	—
94	#1039	C₂⁴	1	4	yes	—
95	C₅×Dic₅	C₂⁴	1	4	yes	—
96	C₂⁴×C₅	—	5	2	no	—
97	C₂³×D₅	—	5	4	no	—
98	C₂³×D₅	—	5	4	no	—
99	C₂³×D₅	C₂×D₅	1	2	yes	complemented
100	C₅×#41	—	5	8	no	—
101	C₂×C₅×Q₈	—	5	1	no	—
102	C₂×C₅×D₄	—	5	2	no	—
103	C₂×C₅×D₄	—	5	1	no	—
104	C₂×C₅×D₄	—	5	2	no	—
105	C₂×C₅×D₄	—	5	2	no	—
106	C₂×C₅×D₄	—	5	8	no	—
107	C₂²×C₄×C₅	—	2	2	no	—
108	C₂²×C₄×C₅	—	5	2	no	—
109	C₂²×C₄×C₅	C₂×D₅	1	1	yes	characteristic, complemented
110	C₂²×C₄×C₅	C₂×D₅	1	1	yes	characteristic, complemented
111	C₂×C₂²⋊D₅	—	5	2	no	—
112	C₂×C₂²⋊D₅	—	5	2	no	—
113	C₂×C₂²⋊D₅	—	5	4	no	—
114	C₂×C₂²⋊D₅	—	5	4	no	—
115	C₂×C₂²⋊D₅	—	5	32	no	—
116	C₂×C₂²⋊D₅	—	5	4	no	—
117	C₂×C₂²⋊D₅	—	10	4	no	—
118	C₂×C₂²⋊D₅	C₂×D₅	1	2	yes	complemented
119	C₂²×Dic₅	—	5	4	no	—
120	#713	—	5	16	no	—
121	#711	—	5	16	no	—
122	#711	—	5	16	no	—
123	D₄×D₅	—	5	32	no	—
124	D₄×D₅	—	5	16	no	—
125	D₄×D₅	—	5	16	no	—
126	D₄×D₅	—	5	16	no	—
127	#709	—	5	8	no	—
128	#709	—	5	8	no	—
129	#709	—	5	16	no	—
130	#709	—	10	16	no	—
131	#709	C₂×D₅	1	8	yes	complemented
132	C₂×D₂₀	—	5	4	no	—
133	C₂×D₂₀	—	5	1	no	—
134	C₂×D₂₀	—	5	1	no	—
135	C₂×D₂₀	—	5	16	no	—
136	C₂×D₂₀	—	10	2	no	—
137	C₂×D₂₀	C₂×D₅	1	2	yes	complemented
138	C₂×D₂₀	C₂×D₅	1	2	yes	complemented
139	C₂×D₂₀	C₂×D₅	1	1	yes	characteristic, complemented
140	C₂×D₂₀	C₂×D₅	1	8	yes	complemented
141	C₂×C₄×D₅	—	5	4	no	—
142	C₂×C₄×D₅	—	5	2	no	—
143	C₂×C₄×D₅	—	5	2	no	—
144	C₂×C₄×D₅	—	10	4	no	—
145	C₂×C₄×D₅	C₂×D₅	1	2	yes	complemented
146	C₂×Dic₁₀	—	5	1	no	—
147	C₂×Dic₁₀	—	5	1	no	—
148	C₂×Dic₁₀	—	10	2	no	—
149	C₂×Dic₁₀	C₂×D₅	1	1	yes	characteristic, complemented
150	C₂×H(5,𝔽₂)	—	25	1	no	Sylow
151	C₂×C₅²	—	2	2	no	—
152	C₂×C₅²	H(5,𝔽₂)	1	2	yes	complemented
153	C₂×C₅²	C₂⁵	1	1	yes	characteristic
154	C₅⋊D₅	—	2	4	no	—
155	C₅×D₅	—	2	4	no	—
156	C₅×D₅	—	2	8	no	—
157	C₂³×C₅	—	2	2	no	—
158	C₂³×C₅	—	5	4	no	—
159	C₂³×C₅	—	5	2	no	—
160	C₂³×C₅	—	5	8	no	—
161	C₂³×C₅	—	20	4	no	—
162	C₂³×C₅	C₂²×D₅	1	1	yes	characteristic
163	C₂³×C₅	C₂²×D₅	1	1	yes	characteristic
164	C₂²×D₅	—	4	4	no	—
165	C₂²×D₅	—	5	2	no	—
166	C₂²×D₅	—	5	2	no	—
167	C₂²×D₅	—	5	16	no	—
168	C₂²×D₅	—	5	16	no	—
169	C₂²×D₅	—	10	4	no	—
170	C₂²×D₅	—	20	8	no	—
171	C₂²×D₅	—	20	8	no	—
172	C₂²×D₅	C₂²×D₅	1	4	yes	—
173	C₂²×D₅	C₂²×D₅	1	2	yes	—
174	C₂²×D₅	C₂²×D₅	1	8	yes	complemented
175	C₅×Q₈	—	5	4	no	—
176	C₅×D₄	—	5	8	no	—
177	C₅×D₄	—	5	4	no	—
178	C₅×D₄	—	5	8	no	—
179	C₅×D₄	—	5	8	no	—
180	C₂×C₄×C₅	—	2	2	no	—
181	C₂×C₄×C₅	—	2	2	no	—
182	C₂×C₄×C₅	—	2	8	no	—
183	C₂×C₄×C₅	—	5	2	no	—
184	C₂×C₄×C₅	—	5	8	no	—
185	C₂×C₄×C₅	C₂²×D₅	1	1	yes	characteristic
186	C₂×C₄×C₅	C₂²×D₅	1	1	yes	characteristic
187	C₂×C₄×C₅	C₂²×D₅	1	1	yes	characteristic
188	C₂×C₄×C₅	C₂²×D₅	1	1	yes	characteristic
189	C₂×C₄×C₅	C₂²×D₅	1	4	yes	complemented
190	C₂×C₄×C₅	C₂²×D₅	1	4	yes	complemented
191	C₂²⋊D₅	—	5	8	no	—
192	C₂²⋊D₅	—	5	8	no	—
193	C₂²⋊D₅	—	5	16	no	—
194	C₂²⋊D₅	—	5	16	no	—
195	C₂²⋊D₅	—	5	16	no	—
196	C₂²⋊D₅	—	10	16	no	—
197	C₂²⋊D₅	C₂²×D₅	1	8	yes	complemented
198	C₂×Dic₅	—	5	2	no	—
199	C₂×Dic₅	—	5	2	no	—
200	C₂×Dic₅	—	5	16	no	—
201	C₂×Dic₅	—	10	4	no	—
202	C₂×Dic₅	C₂²×D₅	1	2	yes	—
203	D₂₀	—	5	16	no	—
204	D₂₀	—	5	4	no	—
205	D₂₀	—	5	4	no	—
206	D₂₀	—	10	8	no	—
207	D₂₀	C₂²×D₅	1	8	yes	complemented
208	D₂₀	C₂²×D₅	1	8	yes	complemented
209	D₂₀	C₂²×D₅	1	4	yes	complemented
210	C₄×D₅	—	5	16	no	—
211	C₄×D₅	—	5	8	no	—
212	C₄×D₅	—	5	8	no	—
213	C₄×D₅	—	10	16	no	—
214	C₄×D₅	C₂²×D₅	1	8	yes	complemented
215	Dic₁₀	—	5	4	no	—
216	Dic₁₀	—	5	4	no	—
217	Dic₁₀	—	10	8	no	—
218	Dic₁₀	C₂²×D₅	1	4	yes	complemented
219	H(5,𝔽₂)	—	25	16	no	—
220	C₂×#41	—	5	1	no	—
221	C₂×#41	—	25	2	no	—
222	C₂×#41	—	25	2	no	—
223	C₂×#41	—	25	1	no	—
224	C₂²×D₄	—	5	1	no	—
225	C₂²×D₄	—	25	2	no	—
226	C₂²×D₄	—	25	2	no	—
227	C₂²×D₄	—	25	4	no	—
228	C₅²	C₂×H(5,𝔽₂)	1	1	yes	characteristic, complemented, Sylow
229	C₂²×C₅	—	2	2	no	—
230	C₂²×C₅	—	2	2	no	—
231	C₂²×C₅	—	2	4	no	—
232	C₂²×C₅	—	2	2	no	—
233	C₂²×C₅	—	4	4	no	—
234	C₂²×C₅	—	5	8	no	—
235	C₂²×C₅	—	5	4	no	—
236	C₂²×C₅	—	10	4	no	—
237	C₂²×C₅	—	10	8	no	—
238	C₂²×C₅	—	20	8	no	—
239	C₂²×C₅	C₂³×D₅	1	2	yes	—
240	C₂²×C₅	C₂³×D₅	1	2	yes	—
241	C₂²×C₅	C₂³×D₅	1	1	yes	characteristic
242	C₂²×C₅	C₂³×D₅	1	1	yes	characteristic
243	C₂×D₅	—	2	8	no	—
244	C₂×D₅	—	2	4	no	—
245	C₂×D₅	—	4	8	no	—
246	C₂×D₅	—	5	4	no	—
247	C₂×D₅	—	5	4	no	—
248	C₂×D₅	—	10	8	no	—
249	C₂×D₅	—	10	4	no	—
250	C₂×D₅	—	10	4	no	—
251	C₂×D₅	—	20	8	no	—
252	C₂×D₅	—	20	16	no	—
253	C₂×D₅	—	20	16	no	—
254	C₂×D₅	C₂³×D₅	1	8	yes	—
255	C₂×D₅	C₂³×D₅	1	4	yes	—
256	C₄×C₅	—	2	4	no	—
257	C₄×C₅	—	2	4	no	—
258	C₄×C₅	—	5	4	no	—
259	C₄×C₅	C₂³×D₅	1	2	yes	—
260	C₄×C₅	C₂³×D₅	1	2	yes	—
261	C₄×C₅	C₂³×D₅	1	2	yes	—
262	C₄×C₅	C₂³×D₅	1	2	yes	—
263	Dic₅	—	5	4	no	—
264	Dic₅	—	5	4	no	—
265	Dic₅	—	10	8	no	—
266	Dic₅	C₂³×D₅	1	4	yes	—
267	C₂⁴	—	5	2	no	—
268	C₂⁴	—	25	4	no	—
269	#41	—	5	8	no	—
270	#41	—	25	16	no	—
271	#41	—	25	16	no	—
272	#41	—	25	8	no	—
273	C₂×Q₈	—	5	1	no	—
274	C₂×Q₈	—	25	1	no	—
275	C₂×D₄	—	5	2	no	—
276	C₂×D₄	—	5	2	no	—
277	C₂×D₄	—	5	2	no	—
278	C₂×D₄	—	5	1	no	—
279	C₂×D₄	—	5	8	no	—
280	C₂×D₄	—	25	16	no	—
281	C₂×D₄	—	25	4	no	—
282	C₂×D₄	—	25	16	no	—
283	C₂×D₄	—	25	32	no	—
284	C₂×D₄	—	25	4	no	—
285	C₂×D₄	—	25	2	no	—
286	C₂×D₄	—	25	1	no	—
287	C₂²×C₄	—	5	2	no	—
288	C₂²×C₄	—	25	4	no	—
289	C₂²×C₄	—	25	2	no	—
290	C₂²×C₄	D₅²	1	1	yes	characteristic, complemented
291	C₂×C₅	—	2	2	no	—
292	C₂×C₅	—	2	2	no	—
293	C₂×C₅	—	2	4	no	—
294	C₂×C₅	—	2	2	no	—
295	C₂×C₅	—	4	4	no	—
296	C₂×C₅	—	10	4	no	—
297	C₂×C₅	—	10	8	no	—
298	C₂×C₅	#4144	1	2	yes	complemented
299	C₂×C₅	#4149	1	2	yes	complemented
300	C₂×C₅	C₂⁴×D₅	1	1	yes	characteristic
301	C₂×C₅	C₂⁴×D₅	1	1	yes	characteristic
302	D₅	—	2	8	no	—
303	D₅	—	2	4	no	—
304	D₅	—	10	4	no	—
305	D₅	—	10	4	no	—
306	D₅	—	20	8	no	—
307	C₂³	—	5	2	no	—
308	C₂³	—	5	4	no	—
309	C₂³	—	5	8	no	—
310	C₂³	—	20	4	no	—
311	C₂³	—	25	16	no	—
312	C₂³	—	25	2	no	—
313	C₂³	—	100	8	no	—
314	C₂³	C₂×D₅²	1	1	yes	characteristic
315	Q₈	—	5	4	no	—
316	Q₈	—	25	4	no	—
317	D₄	—	5	8	no	—
318	D₄	—	5	8	no	—
319	D₄	—	5	8	no	—
320	D₄	—	5	4	no	—
321	D₄	—	25	16	no	—
322	D₄	—	25	16	no	—
323	D₄	—	25	8	no	—
324	D₄	—	25	4	no	—
325	C₂×C₄	—	5	2	no	—
326	C₂×C₄	—	5	8	no	—
327	C₂×C₄	—	25	16	no	—
328	C₂×C₄	—	25	2	no	—
329	C₂×C₄	—	25	8	no	—
330	C₂×C₄	C₂×D₅²	1	1	yes	characteristic
331	C₂×C₄	C₂×D₅²	1	1	yes	characteristic
332	C₂×C₄	C₂×D₅²	1	4	yes	complemented
333	C₅	—	2	2	no	—
334	C₅	C₂×#4144	1	1	yes	characteristic, complemented
335	C₅	C₂×#4149	1	1	yes	characteristic, complemented
336	C₂²	—	2	2	no	—
337	C₂²	—	5	4	no	—
338	C₂²	—	5	8	no	—
339	C₂²	—	10	8	no	—
340	C₂²	—	10	4	no	—
341	C₂²	—	20	8	no	—
342	C₂²	—	25	4	no	—
343	C₂²	—	50	4	no	—
344	C₂²	—	100	16	no	—
345	C₂²	C₂²×D₅²	1	2	yes	—
346	C₂²	C₂²×D₅²	1	1	yes	characteristic
347	C₄	—	5	4	no	—
348	C₄	—	25	4	no	—
349	C₄	C₂²×D₅²	1	2	yes	—
350	C₄	C₂²×D₅²	1	2	yes	—
351	C₂	—	2	2	no	—
352	C₂	—	10	8	no	—
353	C₂	—	10	4	no	—
354	C₂	—	50	4	no	—
355	C₂	#11717472	1	2	yes	direct product factor
356	C₂	C₂³×D₅²	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₅²
commutator, cosocle	C₂×C₅²	C₂⁵
Frattini	C₂	C₂³×D₅²
Fitting	C₂²×C₄×C₅²	C₂²
socle	C₂²×C₅²	C₂⁴
hypercenter	C₂²×C₄	D₅²
hypocenter	C₅²	C₂×H(5,𝔽₂)
LCS	G ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂² ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
1. C₂×#87900	C₂	semidirect
2. C₂×C₅×#709	C₂	semidirect
3. C₂²×C₅×D₂₀	C₂	semidirect
4. C₂×D₅×C₂²⋊D₅	C₂	semidirect
5. #11717472	C₂	direct (N × H)
6. C₂×#87877	C₂	semidirect
7. C₂×D₅×D₂₀	C₂	semidirect
8. C₂×#87871	C₂	semidirect
9. C₂×#87870	C₂	semidirect
10. C₂³×C₅×D₅	C₂²	semidirect
11. C₂²×D₅²	C₂²	semidirect
12. C₂²×C₄×C₅²	C₂²	semidirect
13. C₂×C₂²⋊(C₅⋊D₅)	C₂²	semidirect
14. #87900	C₂²	semidirect
15. C₂×C₄⋊(C₅⋊D₅)	C₂²	semidirect
16. C₂×C₄×C₅⋊D₅	C₂²	semidirect
17. C₂×#6045	C₂²	semidirect
18. C₂×C₅×C₂²⋊D₅	C₂²	semidirect
19. C₅×#709	C₂²	semidirect
20. C₂×C₅×D₂₀	C₂²	semidirect
21. C₂×C₅×D₂₀	C₂²	semidirect
22. C₂×C₅×D₂₀	C₂²	semidirect
23. C₂×C₅×D₂₀	C₂²	semidirect
24. C₂×C₄×C₅×D₅	C₂²	semidirect
25. C₂×C₅×Dic₁₀	C₂²	semidirect
26. D₅×C₂²⋊D₅	C₂²	semidirect
27. C₂×#6038	C₂²	semidirect
28. C₂×#6037	C₂²	semidirect
29. C₂×D₅×Dic₅	C₂²	semidirect
30. #87877	C₂²	semidirect
31. D₅×D₂₀	C₂²	semidirect
32. #87871	C₂²	semidirect
33. #87870	C₂²	semidirect
41. C₂²×C₅×D₅	C₂³	semidirect
43. C₂×D₅²	C₂³	semidirect
46. C₂×C₄×C₅²	C₂³	semidirect
47. C₂²⋊(C₅⋊D₅)	C₂³	semidirect
49. C₄⋊(C₅⋊D₅)	C₂³	semidirect
50. C₄×C₅⋊D₅	C₂³	semidirect
51. #6045	C₂³	semidirect
52. C₅×C₂²⋊D₅	C₂³	semidirect
54. C₅×D₂₀	C₂³	semidirect
55. C₅×D₂₀	C₂³	semidirect
56. C₅×D₂₀	C₂³	semidirect
57. C₄×C₅×D₅	C₂³	semidirect
58. C₅×Dic₁₀	C₂³	semidirect
59. #6038	C₂³	semidirect
60. #6037	C₂³	semidirect
61. D₅×Dic₅	C₂³	semidirect
78. C₂×#709	D₅	semidirect
80. C₂²×D₂₀	D₅	semidirect
99. C₂³×D₅	C₂×D₅	semidirect
109. C₂²×C₄×C₅	C₂×D₅	semidirect
110. C₂²×C₄×C₅	C₂×D₅	semidirect
118. C₂×C₂²⋊D₅	C₂×D₅	semidirect
131. #709	C₂×D₅	semidirect
137. C₂×D₂₀	C₂×D₅	semidirect
138. C₂×D₂₀	C₂×D₅	semidirect
139. C₂×D₂₀	C₂×D₅	semidirect
140. C₂×D₂₀	C₂×D₅	semidirect
145. C₂×C₄×D₅	C₂×D₅	semidirect
149. C₂×Dic₁₀	C₂×D₅	semidirect
152. C₂×C₅²	H(5,𝔽₂)	semidirect
174. C₂²×D₅	C₂²×D₅	semidirect
189. C₂×C₄×C₅	C₂²×D₅	semidirect
190. C₂×C₄×C₅	C₂²×D₅	semidirect
197. C₂²⋊D₅	C₂²×D₅	semidirect
207. D₂₀	C₂²×D₅	semidirect
208. D₂₀	C₂²×D₅	semidirect
209. D₂₀	C₂²×D₅	semidirect
214. C₄×D₅	C₂²×D₅	semidirect
218. Dic₁₀	C₂²×D₅	semidirect
228. C₅²	C₂×H(5,𝔽₂)	semidirect
290. C₂²×C₄	D₅²	semidirect
298. C₂×C₅	#4144	semidirect
299. C₂×C₅	#4149	semidirect
332. C₂×C₄	C₂×D₅²	semidirect
334. C₅	C₂×#4144	semidirect
335. C₅	C₂×#4149	semidirect
355. C₂	#11717472	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×#87900	2
C₂×C₅×#709	2
C₂²×C₅×D₂₀	2
C₂×D₅×C₂²⋊D₅	2
#11717472	2
C₂×#87877	2
C₂×D₅×D₂₀	2
C₂×#87871	2
C₂×#87870	2
C₂×#4149	5
C₂×#4144	5

Subgroups — C2×#11717472 #13107813

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11717472 #13107813