Subgroups — C₂×#10618142 #13007189

Order 1280.

12378 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#4149	C₂	1	2	yes	maximal, complemented
2	C₂×C₅×#532	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#66167	C₂	1	2	yes	maximal, complemented
4	#10618142	C₂	1	32	yes	maximal, direct product factor
5	C₂×#66060	C₂	1	2	yes	maximal, complemented
6	C₂×#66051	C₂	1	2	yes	maximal, complemented
7	C₂×#66010	C₂	1	4	yes	maximal, complemented
8	C₂×#65939	C₂	1	4	yes	maximal, complemented
9	C₂×D₅×#121	C₂	1	4	yes	maximal, complemented
10	C₂×#65885	C₂	1	2	yes	maximal, complemented
11	C₂×#65884	C₂	1	4	yes	maximal, complemented
12	C₂×D₄×D₂₀	C₂	1	2	yes	maximal, complemented
13	C₂×#65811	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×C₄×D₂₀	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×C₅×#41	C₂²	1	2	yes	complemented
16	C₂×#4149	—	2	32	no	—
17	C₂×#4149	C₂²	1	32	yes	complemented
18	C₂²×#713	C₂²	1	4	yes	complemented
19	C₂²×D₄×D₅	C₂²	1	4	yes	complemented
20	C₂²×D₄×D₅	C₂²	1	8	yes	complemented
21	C₂²×D₄×D₅	C₂²	1	4	yes	complemented
22	C₂²×#709	C₂²	1	2	yes	complemented
23	C₂²×#709	C₂²	1	4	yes	complemented
24	C₂³×D₂₀	C₂²	1	1	yes	characteristic
25	C₂³×D₂₀	C₂²	1	4	yes	complemented
26	C₂³×C₄×D₅	C₂²	1	2	yes	complemented
27	C₅×#532	C₂²	1	16	yes	complemented
28	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₅×#127	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₅×#124	C₂²	1	2	yes	complemented
31	C₂×C₅×#121	C₂²	1	2	yes	complemented
32	C₂×C₅×#121	C₂²	1	2	yes	complemented
33	C₂×C₄×C₅×D₄	C₂²	1	2	yes	complemented
34	C₂×C₄×C₅×D₄	C₂²	1	2	yes	complemented
35	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
36	#66167	C₂²	1	32	yes	complemented
37	C₂×#4092	C₂²	1	4	yes	complemented
38	C₂×#4085	C₂²	1	8	yes	complemented
39	C₂×#4084	C₂²	1	4	yes	complemented
40	C₂×#4084	C₂²	1	4	yes	complemented
41	C₂×#4083	C₂²	1	8	yes	complemented
42	C₂×#4076	C₂²	1	4	yes	complemented
43	C₂×#4076	C₂²	1	2	yes	complemented
44	C₂×#4076	C₂²	1	2	yes	complemented
45	C₂²×#685	C₂²	1	2	yes	complemented
46	C₂²×C₄⋊Dic₅	C₂²	1	1	yes	characteristic, complemented
47	C₂×#4070	C₂²	1	4	yes	complemented
48	#66060	C₂²	1	32	yes	complemented
49	#66051	C₂²	1	32	yes	complemented
50	#66010	C₂²	1	64	yes	complemented
51	#65939	C₂²	1	64	yes	complemented
52	D₅×#121	C₂²	1	64	yes	complemented
53	#65885	C₂²	1	32	yes	complemented
54	#65884	C₂²	1	64	yes	complemented
55	D₄×D₂₀	C₂²	1	32	yes	complemented
56	C₂×#4041	C₂²	1	4	yes	complemented
57	C₂×#4040	C₂²	1	8	yes	complemented
58	C₂×D₅×C₄⋊C₄	C₂²	1	4	yes	complemented
59	C₂×#4030	C₂²	1	8	yes	complemented
60	C₂×#4029	C₂²	1	8	yes	complemented
61	C₂×#4028	C₂²	1	8	yes	complemented
62	C₂×D₅×C₂²⋊C₄	C₂²	1	8	yes	complemented
63	#65811	C₂²	1	16	yes	complemented
64	C₂×#4021	C₂²	1	2	yes	complemented
65	C₂×#4020	C₂²	1	1	yes	characteristic, complemented
66	C₂×C₄×D₂₀	C₂²	1	2	yes	complemented
67	C₂×C₄×D₂₀	C₂²	1	2	yes	complemented
68	C₂×C₄×D₂₀	C₂²	1	2	yes	complemented
69	C₂×C₄×D₂₀	C₂²	1	2	yes	complemented
70	C₂×C₄×D₂₀	C₂²	1	2	yes	complemented
71	C₂×C₄×D₂₀	C₂²	1	2	yes	complemented
72	C₂×C₄×D₂₀	C₂²	1	16	yes	complemented
73	C₂×#4015	C₂²	1	1	yes	characteristic, complemented
74	C₂×#3496	—	5	1	no	maximal, Sylow
75	C₂⁴×D₅	C₂³	1	8	yes	—
76	C₂⁴×D₅	C₂³	1	2	yes	—
77	C₂×C₅×#41	—	2	16	no	—
78	C₂×C₅×#41	C₂³	1	16	yes	complemented
79	C₂²×C₅×Q₈	C₂³	1	2	yes	—
80	C₂²×C₅×D₄	C₂³	1	2	yes	—
81	C₂²×C₅×D₄	C₂³	1	2	yes	—
82	C₂²×C₅×D₄	C₂³	1	4	yes	—
83	C₂²×C₅×D₄	C₂³	1	2	yes	—
84	C₂³×C₄×C₅	C₂³	1	4	yes	—
85	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
88	C₂²×C₂²⋊D₅	C₂³	1	8	yes	—
89	C₂²×C₂²⋊D₅	C₂³	1	4	yes	—
90	C₂²×C₂²⋊D₅	C₂³	1	8	yes	—
91	C₂³×Dic₅	C₂³	1	2	yes	—
92	#4149	—	2	256	no	—
93	C₂×#713	—	2	32	no	—
94	C₂×#713	C₂³	1	32	yes	complemented
95	C₂×D₄×D₅	—	2	64	no	—
96	C₂×D₄×D₅	—	2	32	no	—
97	C₂×D₄×D₅	—	4	16	no	—
98	C₂×D₄×D₅	C₂³	1	32	yes	complemented
99	C₂×D₄×D₅	C₂³	1	64	yes	complemented
100	C₂×D₄×D₅	C₂³	1	32	yes	complemented
101	C₂×#709	—	2	16	no	—
102	C₂×#709	—	2	32	no	—
103	C₂×#709	C₂³	1	16	yes	complemented
104	C₂×#709	C₂³	1	32	yes	complemented
105	C₂²×D₂₀	—	2	32	no	—
106	C₂²×D₂₀	D₄	1	16	yes	complemented
107	C₂²×D₂₀	C₂³	1	2	yes	—
108	C₂²×D₂₀	C₂³	1	2	yes	—
109	C₂²×D₂₀	C₂³	1	8	yes	—
110	C₂²×D₂₀	C₂³	1	2	yes	—
111	C₂²×D₂₀	C₂³	1	2	yes	—
112	C₂²×D₂₀	C₂³	1	2	yes	—
113	C₂²×D₂₀	C₂³	1	8	yes	—
114	C₂²×D₂₀	C₂³	1	32	yes	complemented
115	C₂²×C₄×D₅	—	4	8	no	—
116	C₂²×C₄×D₅	C₂³	1	4	yes	—
117	C₂²×C₄×D₅	C₂³	1	4	yes	—
118	C₂²×C₄×D₅	C₂³	1	8	yes	—
119	C₂²×C₄×D₅	C₂³	1	4	yes	—
120	C₂²×C₄×D₅	C₂³	1	16	yes	complemented
121	C₂²×Dic₁₀	C₂³	1	2	yes	—
122	C₅×C₄⋊Q₈	C₂³	1	8	yes	complemented
123	C₅×#127	C₂³	1	8	yes	complemented
124	C₅×#124	C₂³	1	16	yes	complemented
125	C₅×#121	C₂³	1	16	yes	complemented
126	C₅×#121	C₂³	1	16	yes	complemented
127	C₄×C₅×D₄	C₂³	1	16	yes	complemented
128	C₄×C₅×D₄	C₂³	1	16	yes	complemented
129	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
130	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
131	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
132	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
133	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
134	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
135	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
136	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
137	C₂×C₄²×C₅	C₂³	1	8	yes	complemented
138	C₂×C₂²⋊Dic₅	C₂³	1	8	yes	—
139	#4092	C₂³	1	32	yes	complemented
140	#4085	C₂³	1	64	yes	complemented
141	#4084	C₂³	1	32	yes	complemented
142	#4084	C₂³	1	32	yes	complemented
143	#4083	C₂³	1	64	yes	complemented
144	#4076	C₂³	1	16	yes	complemented
145	#4076	C₂³	1	16	yes	complemented
146	#4076	C₂³	1	32	yes	complemented
147	C₂×#685	C₂³	1	4	yes	—
148	C₂×#685	C₂³	1	4	yes	—
149	C₂×#685	C₂³	1	4	yes	—
150	C₂×#685	C₂³	1	4	yes	—
151	C₂×#685	C₂³	1	8	yes	—
152	C₂×#685	C₂³	1	16	yes	complemented
153	C₂×C₄⋊Dic₅	C₂³	1	2	yes	—
154	C₂×C₄⋊Dic₅	C₂³	1	2	yes	—
155	C₂×C₄⋊Dic₅	C₂³	1	2	yes	—
156	C₂×C₄⋊Dic₅	C₂³	1	2	yes	—
157	C₂×C₄⋊Dic₅	C₂³	1	8	yes	complemented
158	#4070	C₂³	1	32	yes	complemented
159	C₂×#683	C₂³	1	8	yes	—
160	#4041	C₂³	1	32	yes	complemented
161	#4040	C₂³	1	64	yes	complemented
162	D₅×C₄⋊C₄	C₂³	1	32	yes	complemented
163	#4030	C₂³	1	64	yes	complemented
164	#4029	C₂³	1	64	yes	complemented
165	#4028	C₂³	1	64	yes	complemented
166	D₅×C₂²⋊C₄	C₂³	1	64	yes	complemented
167	#4021	C₂³	1	16	yes	complemented
168	#4020	C₂³	1	8	yes	complemented
169	C₄×D₂₀	C₂³	1	16	yes	complemented
170	C₄×D₂₀	C₂³	1	16	yes	complemented
171	C₄×D₂₀	C₂³	1	16	yes	complemented
172	C₄×D₂₀	C₂³	1	16	yes	complemented
173	C₄×D₂₀	C₂³	1	16	yes	complemented
174	C₄×D₂₀	C₂³	1	16	yes	complemented
175	#4015	C₂³	1	8	yes	complemented
176	C₂²×H(5,𝔽₂)	—	5	2	no	—
177	#3496	—	5	32	no	—
178	C₂×#547	—	5	2	no	—
179	C₂×#547	—	5	2	no	—
180	C₂×#546	—	5	4	no	—
181	C₂×#546	—	5	4	no	—
182	C₂×D₄²	—	5	2	no	—
183	C₂×D₄²	—	5	2	no	—
184	C₂×#537	—	5	2	no	—
185	C₂×#534	—	5	4	no	—
186	C₂×#532	—	5	1	no	—
187	C₂×#532	D₅	1	1	yes	characteristic, complemented
188	C₂²×#121	—	5	4	no	—
189	C₂²×C₄×D₄	—	5	1	no	—
190	C₂⁴×C₅	C₂⁴	1	4	yes	—
191	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
192	C₂³×D₅	—	2	32	no	—
193	C₂³×D₅	—	4	4	no	—
194	C₂³×D₅	—	4	4	no	—
195	C₂³×D₅	—	4	16	no	—
196	C₂³×D₅	—	4	16	no	—
197	C₂³×D₅	C₂×D₄	1	16	yes	complemented
198	C₂³×D₅	C₂⁴	1	4	yes	—
199	C₂³×D₅	C₂⁴	1	4	yes	—
200	C₂³×D₅	C₂⁴	1	32	yes	—
201	C₂³×D₅	C₂⁴	1	8	yes	—
202	C₅×#41	—	2	64	no	—
203	C₂×C₅×Q₈	—	2	8	no	—
204	C₂×C₅×Q₈	C₂⁴	1	8	yes	—
205	C₂×C₅×D₄	—	2	16	no	—
206	C₂×C₅×D₄	—	2	8	no	—
207	C₂×C₅×D₄	—	2	8	no	—
208	C₂×C₅×D₄	—	4	4	no	—
209	C₂×C₅×D₄	C₂⁴	1	8	yes	—
210	C₂×C₅×D₄	C₂⁴	1	16	yes	—
211	C₂×C₅×D₄	C₂⁴	1	8	yes	—
212	C₂×C₅×D₄	C₂⁴	1	8	yes	—
213	C₂²×C₄×C₅	—	2	16	no	—
214	C₂²×C₄×C₅	—	2	4	no	—
215	C₂²×C₄×C₅	—	4	2	no	—
216	C₂²×C₄×C₅	C₂×D₄	1	8	yes	complemented
217	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
218	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
219	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
220	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
221	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
222	C₂²×C₄×C₅	C₂⁴	1	16	yes	—
223	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
224	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
225	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
226	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
227	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
228	C₂×C₂²⋊D₅	—	2	16	no	—
229	C₂×C₂²⋊D₅	—	2	32	no	—
230	C₂×C₂²⋊D₅	—	4	16	no	—
231	C₂×C₂²⋊D₅	C₂⁴	1	32	yes	—
232	C₂×C₂²⋊D₅	C₂⁴	1	16	yes	—
233	C₂×C₂²⋊D₅	C₂⁴	1	32	yes	—
234	C₂²×Dic₅	—	4	4	no	—
235	C₂²×Dic₅	C₂⁴	1	4	yes	—
236	C₂²×Dic₅	C₂⁴	1	4	yes	—
237	C₂²×Dic₅	C₂⁴	1	8	yes	—
238	#713	—	2	128	no	—
239	D₄×D₅	—	2	256	no	—
240	D₄×D₅	—	2	128	no	—
241	D₄×D₅	—	4	64	no	—
242	#709	—	2	64	no	—
243	#709	—	2	128	no	—
244	C₂×D₂₀	—	2	32	no	—
245	C₂×D₂₀	—	2	8	no	—
246	C₂×D₂₀	—	2	8	no	—
247	C₂×D₂₀	—	2	128	no	—
248	C₂×D₂₀	—	4	4	no	—
249	C₂×D₂₀	C₂×D₄	1	16	yes	complemented
250	C₂×D₂₀	C₂×D₄	1	16	yes	complemented
251	C₂×D₂₀	C₂×D₄	1	64	yes	complemented
252	C₂×D₂₀	C₂⁴	1	8	yes	—
253	C₂×D₂₀	C₂⁴	1	32	yes	—
254	C₂×D₂₀	C₂⁴	1	8	yes	—
255	C₂×D₂₀	C₂⁴	1	8	yes	—
256	C₂×D₂₀	C₂⁴	1	8	yes	—
257	C₂×D₂₀	C₂⁴	1	8	yes	—
258	C₂×C₄×D₅	—	2	32	no	—
259	C₂×C₄×D₅	—	2	16	no	—
260	C₂×C₄×D₅	—	2	16	no	—
261	C₂×C₄×D₅	—	4	32	no	—
262	C₂×C₄×D₅	—	4	8	no	—
263	C₂×C₄×D₅	C₂⁴	1	16	yes	—
264	C₂×C₄×D₅	C₂⁴	1	16	yes	—
265	C₂×C₄×D₅	C₂⁴	1	32	yes	—
266	C₂×C₄×D₅	C₂⁴	1	16	yes	—
267	C₂×Dic₁₀	—	2	8	no	—
268	C₂×Dic₁₀	C₂⁴	1	8	yes	—
269	C₅×C₄⋊C₄	C₂⁴	1	8	yes	—
270	C₅×C₄⋊C₄	C₂⁴	1	8	yes	—
271	C₅×C₂²⋊C₄	C₂⁴	1	16	yes	—
272	C₅×C₂²⋊C₄	C₂⁴	1	16	yes	—
273	C₄²×C₅	C₂⁴	1	4	yes	—
274	C₄²×C₅	C₂⁴	1	4	yes	—
275	C₄²×C₅	C₂⁴	1	4	yes	—
276	C₄²×C₅	C₂⁴	1	4	yes	—
277	C₂²⋊Dic₅	C₂⁴	1	32	yes	—
278	#685	C₂⁴	1	16	yes	—
279	#685	C₂⁴	1	16	yes	—
280	#685	C₂⁴	1	16	yes	—
281	#685	C₂⁴	1	16	yes	—
282	#685	C₂⁴	1	32	yes	—
283	C₄⋊Dic₅	C₂⁴	1	8	yes	—
284	C₄⋊Dic₅	C₂⁴	1	8	yes	—
285	C₄⋊Dic₅	C₂⁴	1	8	yes	—
286	C₄⋊Dic₅	C₂⁴	1	8	yes	—
287	#683	C₂⁴	1	32	yes	—
288	C₂×H(5,𝔽₂)	—	5	32	no	—
289	C₂×H(5,𝔽₂)	—	10	32	no	—
290	C₂²×#41	—	5	4	no	—
291	C₂²×#41	—	5	2	no	—
292	C₂²×#41	—	5	4	no	—
293	C₂²×#41	C₂×D₅	1	2	yes	complemented
294	C₂³×D₄	—	5	8	no	—
295	C₂³×D₄	—	5	4	no	—
296	C₂³×D₄	—	5	4	no	—
297	C₂³×D₄	—	5	1	no	—
298	C₂³×D₄	—	5	4	no	—
299	C₂⁴×C₄	—	5	2	no	—
300	#547	—	5	32	no	—
301	#547	—	5	32	no	—
302	#546	—	5	64	no	—
303	#546	—	5	64	no	—
304	D₄²	—	5	32	no	—
305	D₄²	—	5	32	no	—
306	#537	—	5	32	no	—
307	#534	—	5	64	no	—
308	#532	—	5	16	no	—
309	#532	C₂×D₅	1	16	yes	complemented
310	C₂×C₄⋊Q₈	—	5	1	no	—
311	C₂×C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
312	C₂×#127	—	5	1	no	—
313	C₂×#127	C₂×D₅	1	1	yes	characteristic, complemented
314	C₂×#124	—	5	2	no	—
315	C₂×#124	C₂×D₅	1	2	yes	complemented
316	C₂×#123	—	5	8	no	—
317	C₂×#123	—	5	8	no	—
318	C₂×C₂²⋊Q₈	—	5	4	no	—
319	C₂×C₂²⋊Q₈	—	5	4	no	—
320	C₂×#121	—	5	4	no	—
321	C₂×#121	—	5	4	no	—
322	C₂×#121	—	5	8	no	—
323	C₂×#121	—	5	2	no	—
324	C₂×#121	—	5	2	no	—
325	C₂×#121	—	5	4	no	—
326	C₂×#121	—	5	64	no	—
327	C₂×#121	—	5	4	no	—
328	C₂×#121	—	5	8	no	—
329	C₂×#121	C₂×D₅	1	2	yes	complemented
330	C₂×#121	C₂×D₅	1	2	yes	complemented
331	C₂×#120	—	5	8	no	—
332	C₂×#120	—	5	8	no	—
333	C₂×C₄×D₄	—	5	2	no	—
334	C₂×C₄×D₄	—	5	2	no	—
335	C₂×C₄×D₄	—	5	2	no	—
336	C₂×C₄×D₄	—	5	2	no	—
337	C₂×C₄×D₄	—	5	2	no	—
338	C₂×C₄×D₄	—	5	2	no	—
339	C₂×C₄×D₄	—	5	16	no	—
340	C₂×C₄×D₄	C₂×D₅	1	2	yes	complemented
341	C₂×C₄×D₄	C₂×D₅	1	2	yes	complemented
342	C₂²×C₄⋊C₄	—	5	1	no	—
343	C₂²×C₄⋊C₄	—	5	4	no	—
344	C₂²×C₂²⋊C₄	—	5	2	no	—
345	C₂²×C₂²⋊C₄	—	5	8	no	—
346	C₂²×C₄²	C₂×D₅	1	1	yes	characteristic, complemented
347	C₂³×C₅	—	2	2	no	—
348	C₂³×C₅	—	2	2	no	—
349	C₂³×C₅	—	2	8	no	—
350	C₂³×C₅	—	2	8	no	—
351	C₂³×C₅	—	2	8	no	—
352	C₂³×C₅	C₂²×D₄	1	4	yes	—
353	C₂³×C₅	C₂⁵	1	8	yes	—
354	C₂³×C₅	C₂⁵	1	2	yes	—
355	C₂³×C₅	C₂⁵	1	1	yes	characteristic
356	C₂²×D₅	—	2	8	no	—
357	C₂²×D₅	—	2	8	no	—
358	C₂²×D₅	—	2	8	no	—
359	C₂²×D₅	—	2	8	no	—
360	C₂²×D₅	—	2	8	no	—
361	C₂²×D₅	—	2	64	no	—
362	C₂²×D₅	—	4	8	no	—
363	C₂²×D₅	—	4	32	no	—
364	C₂²×D₅	—	4	8	no	—
365	C₂²×D₅	—	4	32	no	—
366	C₂²×D₅	—	4	32	no	—
367	C₂²×D₅	—	8	64	no	—
368	C₂²×D₅	C₂²×D₄	1	16	yes	—
369	C₂²×D₅	C₂²×D₄	1	32	yes	complemented
370	C₂²×D₅	C₂⁵	1	8	yes	—
371	C₂²×D₅	C₂⁵	1	8	yes	—
372	C₅×Q₈	—	2	16	no	—
373	C₅×D₄	—	2	32	no	—
374	C₅×D₄	—	2	16	no	—
375	C₅×D₄	—	2	16	no	—
376	C₅×D₄	—	4	8	no	—
377	C₂×C₄×C₅	—	2	8	no	—
378	C₂×C₄×C₅	—	2	2	no	—
379	C₂×C₄×C₅	—	2	2	no	—
380	C₂×C₄×C₅	—	2	2	no	—
381	C₂×C₄×C₅	—	2	32	no	—
382	C₂×C₄×C₅	—	2	8	no	—
383	C₂×C₄×C₅	—	4	4	no	—
384	C₂×C₄×C₅	C₂²×D₄	1	4	yes	—
385	C₂×C₄×C₅	C₂²×D₄	1	4	yes	—
386	C₂×C₄×C₅	C₂²×D₄	1	16	yes	complemented
387	C₂×C₄×C₅	H(5,𝔽₂)	1	4	yes	complemented
388	C₂×C₄×C₅	C₂⁵	1	8	yes	—
389	C₂×C₄×C₅	C₂⁵	1	2	yes	—
390	C₂×C₄×C₅	C₂⁵	1	2	yes	—
391	C₂×C₄×C₅	C₂⁵	1	2	yes	—
392	C₂×C₄×C₅	C₂⁵	1	2	yes	—
393	C₂×C₄×C₅	C₂⁵	1	2	yes	—
394	C₂×C₄×C₅	C₂⁵	1	2	yes	—
395	C₂²⋊D₅	—	2	32	no	—
396	C₂²⋊D₅	—	2	64	no	—
397	C₂²⋊D₅	—	4	32	no	—
398	C₂×Dic₅	—	2	8	no	—
399	C₂×Dic₅	—	2	8	no	—
400	C₂×Dic₅	—	4	8	no	—
401	C₂×Dic₅	C₂⁵	1	8	yes	—
402	C₂×Dic₅	C₂⁵	1	8	yes	—
403	D₂₀	—	2	64	no	—
404	D₂₀	—	2	16	no	—
405	D₂₀	—	2	16	no	—
406	D₂₀	—	4	8	no	—
407	D₂₀	C₂²×D₄	1	32	yes	complemented
408	D₂₀	C₂²×D₄	1	32	yes	complemented
409	C₄×D₅	—	2	64	no	—
410	C₄×D₅	—	2	32	no	—
411	C₄×D₅	—	2	32	no	—
412	C₄×D₅	—	4	16	no	—
413	Dic₁₀	—	2	16	no	—
414	C₂⁵	—	5	2	no	—
415	C₂⁵	—	5	8	no	—
416	H(5,𝔽₂)	—	10	256	no	—
417	C₂×#41	—	2	16	no	—
418	C₂×#41	—	5	32	no	—
419	C₂×#41	—	5	16	no	—
420	C₂×#41	—	5	32	no	—
421	C₂×#41	—	10	32	no	—
422	C₂×#41	—	10	32	no	—
423	C₂×#41	—	10	16	no	—
424	C₂×#41	C₂²×D₅	1	16	yes	complemented
425	C₂²×Q₈	—	5	2	no	—
426	C₂²×Q₈	C₂²×D₅	1	2	yes	—
427	C₂²×D₄	—	5	8	no	—
428	C₂²×D₄	—	5	4	no	—
429	C₂²×D₄	—	5	8	no	—
430	C₂²×D₄	—	5	64	no	—
431	C₂²×D₄	—	5	32	no	—
432	C₂²×D₄	—	5	32	no	—
433	C₂²×D₄	—	5	16	no	—
434	C₂²×D₄	—	5	2	no	—
435	C₂²×D₄	—	5	2	no	—
436	C₂²×D₄	—	5	8	no	—
437	C₂²×D₄	—	5	2	no	—
438	C₂²×D₄	—	5	8	no	—
439	C₂²×D₄	—	5	2	no	—
440	C₂²×D₄	—	5	32	no	—
441	C₂²×D₄	—	5	2	no	—
442	C₂²×D₄	—	10	32	no	—
443	C₂²×D₄	—	10	32	no	—
444	C₂²×D₄	—	10	64	no	—
445	C₂²×D₄	—	20	16	no	—
446	C₂²×D₄	C₂²×D₅	1	2	yes	—
447	C₂²×D₄	C₂²×D₅	1	4	yes	—
448	C₂²×D₄	C₂²×D₅	1	2	yes	—
449	C₂²×D₄	C₂²×D₅	1	2	yes	—
450	C₂³×C₄	—	5	2	no	—
451	C₂³×C₄	—	5	8	no	—
452	C₂³×C₄	—	5	4	no	—
453	C₂³×C₄	—	5	4	no	—
454	C₂³×C₄	—	5	4	no	—
455	C₂³×C₄	—	5	16	no	—
456	C₂³×C₄	—	20	8	no	—
457	C₂³×C₄	C₂²×D₅	1	4	yes	—
458	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
459	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
460	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
461	C₄⋊Q₈	—	5	8	no	—
462	C₄⋊Q₈	C₂²×D₅	1	8	yes	complemented
463	#127	—	5	8	no	—
464	#127	C₂²×D₅	1	8	yes	complemented
465	#124	—	5	16	no	—
466	#124	C₂²×D₅	1	16	yes	complemented
467	#123	—	5	64	no	—
468	#123	—	5	64	no	—
469	C₂²⋊Q₈	—	5	32	no	—
470	C₂²⋊Q₈	—	5	32	no	—
471	#121	—	5	64	no	—
472	#121	—	5	32	no	—
473	#121	—	5	32	no	—
474	#121	—	5	16	no	—
475	#121	—	5	16	no	—
476	#121	—	5	32	no	—
477	#121	—	5	32	no	—
478	#121	—	5	64	no	—
479	#121	C₂²×D₅	1	16	yes	complemented
480	#121	C₂²×D₅	1	16	yes	complemented
481	#120	—	5	64	no	—
482	#120	—	5	64	no	—
483	C₄×D₄	—	5	16	no	—
484	C₄×D₄	—	5	16	no	—
485	C₄×D₄	—	5	16	no	—
486	C₄×D₄	—	5	16	no	—
487	C₄×D₄	—	5	16	no	—
488	C₄×D₄	—	5	16	no	—
489	C₄×D₄	C₂²×D₅	1	16	yes	complemented
490	C₄×D₄	C₂²×D₅	1	16	yes	complemented
491	C₂×C₄⋊C₄	—	5	2	no	—
492	C₂×C₄⋊C₄	—	5	2	no	—
493	C₂×C₄⋊C₄	—	5	2	no	—
494	C₂×C₄⋊C₄	—	5	8	no	—
495	C₂×C₄⋊C₄	—	5	8	no	—
496	C₂×C₄⋊C₄	—	5	2	no	—
497	C₂×C₄⋊C₄	—	5	32	no	—
498	C₂×C₄⋊C₄	C₂²×D₅	1	2	yes	—
499	C₂×C₄⋊C₄	C₂²×D₅	1	2	yes	—
500	C₂×C₂²⋊C₄	—	5	8	no	—
501	C₂×C₂²⋊C₄	—	5	4	no	—
502	C₂×C₂²⋊C₄	—	5	4	no	—
503	C₂×C₂²⋊C₄	—	5	4	no	—
504	C₂×C₂²⋊C₄	—	5	16	no	—
505	C₂×C₂²⋊C₄	—	5	8	no	—
506	C₂×C₂²⋊C₄	—	5	4	no	—
507	C₂×C₂²⋊C₄	—	5	64	no	—
508	C₂×C₂²⋊C₄	C₂²×D₅	1	4	yes	—
509	C₂×C₂²⋊C₄	C₂²×D₅	1	4	yes	—
510	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
511	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
512	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
513	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
514	C₂×C₄²	C₂²×D₅	1	8	yes	complemented
515	C₂²×C₅	—	2	2	no	—
516	C₂²×C₅	—	2	2	no	—
517	C₂²×C₅	—	2	8	no	—
518	C₂²×C₅	—	2	8	no	—
519	C₂²×C₅	—	2	8	no	—
520	C₂²×C₅	—	2	8	no	—
521	C₂²×C₅	—	4	16	no	—
522	C₂²×C₅	C₂³×D₄	1	4	yes	—
523	C₂²×C₅	C₂³×D₄	1	2	yes	—
524	C₂²×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
525	C₂²×C₅	#585	1	2	yes	—
526	C₂²×C₅	C₂⁶	1	1	yes	characteristic
527	C₂×D₅	—	2	8	no	—
528	C₂×D₅	—	2	8	no	—
529	C₂×D₅	—	2	32	no	—
530	C₂×D₅	—	2	8	no	—
531	C₂×D₅	—	2	8	no	—
532	C₂×D₅	—	2	8	no	—
533	C₂×D₅	—	4	32	no	—
534	C₂×D₅	—	4	16	no	—
535	C₂×D₅	—	8	64	no	—
536	C₂×D₅	C₂³×D₄	1	16	yes	—
537	C₄×C₅	—	2	8	no	—
538	C₄×C₅	—	2	2	no	—
539	C₄×C₅	—	2	2	no	—
540	C₄×C₅	—	2	2	no	—
541	C₄×C₅	C₂³×D₄	1	4	yes	—
542	C₄×C₅	C₂³×D₄	1	4	yes	—
543	C₄×C₅	C₂×H(5,𝔽₂)	1	4	yes	complemented
544	Dic₅	—	2	8	no	—
545	Dic₅	—	2	8	no	—
546	C₂⁴	—	5	4	no	—
547	C₂⁴	—	5	16	no	—
548	C₂⁴	—	5	8	no	—
549	C₂⁴	—	5	4	no	—
550	C₂⁴	—	5	32	no	—
551	C₂⁴	—	10	32	no	—
552	C₂⁴	—	20	4	no	—
553	C₂⁴	—	20	4	no	—
554	C₂⁴	—	20	16	no	—
555	C₂⁴	—	20	16	no	—
556	C₂⁴	C₂³×D₅	1	4	yes	—
557	C₂⁴	C₂³×D₅	1	1	yes	characteristic
558	#41	—	2	64	no	—
559	#41	—	10	128	no	—
560	#41	—	10	128	no	—
561	#41	—	10	64	no	—
562	C₂×Q₈	—	2	8	no	—
563	C₂×Q₈	—	5	8	no	—
564	C₂×Q₈	—	10	8	no	—
565	C₂×Q₈	C₂³×D₅	1	8	yes	—
566	C₂×D₄	—	2	16	no	—
567	C₂×D₄	—	2	8	no	—
568	C₂×D₄	—	2	8	no	—
569	C₂×D₄	—	4	4	no	—
570	C₂×D₄	—	5	32	no	—
571	C₂×D₄	—	5	16	no	—
572	C₂×D₄	—	5	32	no	—
573	C₂×D₄	—	5	16	no	—
574	C₂×D₄	—	5	16	no	—
575	C₂×D₄	—	5	64	no	—
576	C₂×D₄	—	5	8	no	—
577	C₂×D₄	—	5	8	no	—
578	C₂×D₄	—	5	8	no	—
579	C₂×D₄	—	5	32	no	—
580	C₂×D₄	—	5	8	no	—
581	C₂×D₄	—	5	8	no	—
582	C₂×D₄	—	10	128	no	—
583	C₂×D₄	—	10	32	no	—
584	C₂×D₄	—	10	128	no	—
585	C₂×D₄	—	10	256	no	—
586	C₂×D₄	—	10	32	no	—
587	C₂×D₄	—	10	16	no	—
588	C₂×D₄	—	10	8	no	—
589	C₂×D₄	—	10	8	no	—
590	C₂×D₄	—	20	4	no	—
591	C₂×D₄	—	20	64	no	—
592	C₂×D₄	—	20	16	no	—
593	C₂×D₄	C₂³×D₅	1	8	yes	—
594	C₂×D₄	C₂³×D₅	1	16	yes	—
595	C₂×D₄	C₂³×D₅	1	8	yes	—
596	C₂×D₄	C₂³×D₅	1	8	yes	—
597	C₂²×C₄	—	2	16	no	—
598	C₂²×C₄	—	2	4	no	—
599	C₂²×C₄	—	4	2	no	—
600	C₂²×C₄	—	5	4	no	—
601	C₂²×C₄	—	5	4	no	—
602	C₂²×C₄	—	5	8	no	—
603	C₂²×C₄	—	5	32	no	—
604	C₂²×C₄	—	5	16	no	—
605	C₂²×C₄	—	5	16	no	—
606	C₂²×C₄	—	5	16	no	—
607	C₂²×C₄	—	10	32	no	—
608	C₂²×C₄	—	10	16	no	—
609	C₂²×C₄	—	10	16	no	—
610	C₂²×C₄	—	20	32	no	—
611	C₂²×C₄	—	20	8	no	—
612	C₂²×C₄	—	20	4	no	—
613	C₂²×C₄	D₄×D₅	1	8	yes	complemented
614	C₂²×C₄	C₂³×D₅	1	4	yes	—
615	C₂²×C₄	C₂³×D₅	1	16	yes	—
616	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
617	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
618	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
619	C₂²×C₄	C₂³×D₅	1	4	yes	—
620	C₂²×C₄	C₂³×D₅	1	4	yes	—
621	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
622	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
623	C₂²×C₄	C₂³×D₅	1	4	yes	—
624	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
625	C₄⋊C₄	—	5	8	no	—
626	C₄⋊C₄	—	5	8	no	—
627	C₄⋊C₄	—	5	8	no	—
628	C₄⋊C₄	—	5	32	no	—
629	C₄⋊C₄	—	5	8	no	—
630	C₄⋊C₄	C₂³×D₅	1	8	yes	—
631	C₄⋊C₄	C₂³×D₅	1	8	yes	—
632	C₂²⋊C₄	—	5	32	no	—
633	C₂²⋊C₄	—	5	16	no	—
634	C₂²⋊C₄	—	5	16	no	—
635	C₂²⋊C₄	—	5	16	no	—
636	C₂²⋊C₄	—	5	32	no	—
637	C₂²⋊C₄	—	5	16	no	—
638	C₂²⋊C₄	C₂³×D₅	1	16	yes	—
639	C₂²⋊C₄	C₂³×D₅	1	16	yes	—
640	C₄²	C₂³×D₅	1	4	yes	—
641	C₄²	C₂³×D₅	1	4	yes	—
642	C₄²	C₂³×D₅	1	4	yes	—
643	C₄²	C₂³×D₅	1	4	yes	—
644	C₂×C₅	—	2	4	no	—
645	C₂×C₅	—	4	8	no	—
646	C₂×C₅	#3496	1	4	yes	complemented
647	C₂×C₅	C₂⁴×D₄	1	1	yes	characteristic
648	C₂×C₅	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
649	C₂×C₅	C₂×#585	1	1	yes	characteristic
650	D₅	—	2	16	no	—
651	D₅	—	4	8	no	—
652	C₂³	—	2	2	no	—
653	C₂³	—	2	2	no	—
654	C₂³	—	2	8	no	—
655	C₂³	—	2	8	no	—
656	C₂³	—	2	8	no	—
657	C₂³	—	5	16	no	—
658	C₂³	—	5	8	no	—
659	C₂³	—	5	32	no	—
660	C₂³	—	5	8	no	—
661	C₂³	—	10	64	no	—
662	C₂³	—	10	8	no	—
663	C₂³	—	10	8	no	—
664	C₂³	—	10	8	no	—
665	C₂³	—	10	8	no	—
666	C₂³	—	10	8	no	—
667	C₂³	—	20	8	no	—
668	C₂³	—	20	32	no	—
669	C₂³	—	20	8	no	—
670	C₂³	—	20	32	no	—
671	C₂³	—	20	32	no	—
672	C₂³	—	40	64	no	—
673	C₂³	C₂×D₄×D₅	1	4	yes	—
674	C₂³	C₂⁴×D₅	1	8	yes	—
675	C₂³	C₂⁴×D₅	1	2	yes	—
676	C₂³	C₂⁴×D₅	1	1	yes	characteristic
677	Q₈	—	2	16	no	—
678	Q₈	—	10	16	no	—
679	D₄	—	2	32	no	—
680	D₄	—	2	16	no	—
681	D₄	—	2	16	no	—
682	D₄	—	4	8	no	—
683	D₄	—	5	32	no	—
684	D₄	—	5	32	no	—
685	D₄	—	10	64	no	—
686	D₄	—	10	64	no	—
687	D₄	—	10	32	no	—
688	D₄	—	10	16	no	—
689	D₄	—	10	16	no	—
690	D₄	—	20	8	no	—
691	D₄	—	20	32	no	—
692	C₂×C₄	—	2	8	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	32	no	—
697	C₂×C₄	—	2	8	no	—
698	C₂×C₄	—	4	4	no	—
699	C₂×C₄	—	5	8	no	—
700	C₂×C₄	—	5	8	no	—
701	C₂×C₄	—	10	64	no	—
702	C₂×C₄	—	10	8	no	—
703	C₂×C₄	—	10	8	no	—
704	C₂×C₄	—	10	32	no	—
705	C₂×C₄	—	10	32	no	—
706	C₂×C₄	—	20	16	no	—
707	C₂×C₄	—	20	8	no	—
708	C₂×C₄	C₂×D₄×D₅	1	4	yes	—
709	C₂×C₄	C₂×D₄×D₅	1	4	yes	—
710	C₂×C₄	C₂×D₄×D₅	1	16	yes	complemented
711	C₂×C₄	#4149	1	4	yes	complemented
712	C₂×C₄	C₂⁴×D₅	1	2	yes	—
713	C₂×C₄	C₂⁴×D₅	1	2	yes	—
714	C₂×C₄	C₂⁴×D₅	1	2	yes	—
715	C₂×C₄	C₂⁴×D₅	1	8	yes	—
716	C₂×C₄	C₂⁴×D₅	1	2	yes	—
717	C₂×C₄	C₂⁴×D₅	1	2	yes	—
718	C₂×C₄	C₂⁴×D₅	1	2	yes	—
719	C₅	C₂×#3496	1	1	yes	characteristic, complemented, Sylow
720	C₂²	—	2	8	no	—
721	C₂²	—	2	2	no	—
722	C₂²	—	2	2	no	—
723	C₂²	—	2	8	no	—
724	C₂²	—	2	8	no	—
725	C₂²	—	2	8	no	—
726	C₂²	—	4	16	no	—
727	C₂²	—	5	16	no	—
728	C₂²	—	10	32	no	—
729	C₂²	—	10	8	no	—
730	C₂²	—	10	8	no	—
731	C₂²	—	10	8	no	—
732	C₂²	—	10	8	no	—
733	C₂²	—	10	8	no	—
734	C₂²	—	20	32	no	—
735	C₂²	—	20	16	no	—
736	C₂²	—	40	64	no	—
737	C₂²	C₂²×D₄×D₅	1	4	yes	—
738	C₂²	C₂²×D₄×D₅	1	2	yes	—
739	C₂²	C₂×#4149	1	2	yes	—
740	C₂²	#66283	1	2	yes	—
741	C₂²	C₂⁵×D₅	1	1	yes	characteristic
742	C₄	—	2	8	no	—
743	C₄	—	2	2	no	—
744	C₄	—	2	2	no	—
745	C₄	—	2	2	no	—
746	C₄	—	10	8	no	—
747	C₄	—	10	8	no	—
748	C₄	C₂²×D₄×D₅	1	4	yes	—
749	C₄	C₂²×D₄×D₅	1	4	yes	—
750	C₄	C₂×#4149	1	4	yes	complemented
751	C₂	—	2	4	no	—
752	C₂	—	4	8	no	—
753	C₂	—	10	16	no	—
754	C₂	—	20	8	no	—
755	C₂	#10618142	1	4	yes	direct product factor
756	C₂	C₂³×D₄×D₅	1	1	yes	characteristic
757	C₂	C₂²×#4149	1	1	yes	characteristic
758	C₂	C₂×#66283	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₅
commutator, cosocle	C₂²×C₅	C₂⁶
Frattini	C₂²	C₂⁵×D₅
Fitting	C₂×C₅×#532	C₂
socle	C₂³×C₅	C₂⁵
hypercenter	C₂×#532	D₅
hypocenter	C₅	C₂×#3496
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³ ◁ C₂×#532

Complements

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

N	H ≅ G/N	type
1. C₂²×#4149	C₂	semidirect
2. C₂×C₅×#532	C₂	semidirect
3. C₂×#66167	C₂	semidirect
4. #10618142	C₂	direct (N × H)
5. C₂×#66060	C₂	semidirect
6. C₂×#66051	C₂	semidirect
7. C₂×#66010	C₂	semidirect
8. C₂×#65939	C₂	semidirect
9. C₂×D₅×#121	C₂	semidirect
10. C₂×#65885	C₂	semidirect
11. C₂×#65884	C₂	semidirect
12. C₂×D₄×D₂₀	C₂	semidirect
13. C₂×#65811	C₂	semidirect
14. C₂²×C₄×D₂₀	C₂	semidirect
15. C₂²×C₅×#41	C₂²	semidirect
17. C₂×#4149	C₂²	semidirect
18. C₂²×#713	C₂²	semidirect
19. C₂²×D₄×D₅	C₂²	semidirect
20. C₂²×D₄×D₅	C₂²	semidirect
21. C₂²×D₄×D₅	C₂²	semidirect
22. C₂²×#709	C₂²	semidirect
23. C₂²×#709	C₂²	semidirect
25. C₂³×D₂₀	C₂²	semidirect
26. C₂³×C₄×D₅	C₂²	semidirect
27. C₅×#532	C₂²	semidirect
28. C₂×C₅×C₄⋊Q₈	C₂²	semidirect
29. C₂×C₅×#127	C₂²	semidirect
30. C₂×C₅×#124	C₂²	semidirect
31. C₂×C₅×#121	C₂²	semidirect
32. C₂×C₅×#121	C₂²	semidirect
33. C₂×C₄×C₅×D₄	C₂²	semidirect
34. C₂×C₄×C₅×D₄	C₂²	semidirect
35. C₂²×C₄²×C₅	C₂²	semidirect
36. #66167	C₂²	semidirect
37. C₂×#4092	C₂²	semidirect
38. C₂×#4085	C₂²	semidirect
39. C₂×#4084	C₂²	semidirect
40. C₂×#4084	C₂²	semidirect
41. C₂×#4083	C₂²	semidirect
42. C₂×#4076	C₂²	semidirect
43. C₂×#4076	C₂²	semidirect
44. C₂×#4076	C₂²	semidirect
45. C₂²×#685	C₂²	semidirect
46. C₂²×C₄⋊Dic₅	C₂²	semidirect
47. C₂×#4070	C₂²	semidirect
48. #66060	C₂²	semidirect
49. #66051	C₂²	semidirect
50. #66010	C₂²	semidirect
51. #65939	C₂²	semidirect
52. D₅×#121	C₂²	semidirect
53. #65885	C₂²	semidirect
54. #65884	C₂²	semidirect
55. D₄×D₂₀	C₂²	semidirect
56. C₂×#4041	C₂²	semidirect
57. C₂×#4040	C₂²	semidirect
58. C₂×D₅×C₄⋊C₄	C₂²	semidirect
59. C₂×#4030	C₂²	semidirect
60. C₂×#4029	C₂²	semidirect
61. C₂×#4028	C₂²	semidirect
62. C₂×D₅×C₂²⋊C₄	C₂²	semidirect
63. #65811	C₂²	semidirect
64. C₂×#4021	C₂²	semidirect
65. C₂×#4020	C₂²	semidirect
66. C₂×C₄×D₂₀	C₂²	semidirect
67. C₂×C₄×D₂₀	C₂²	semidirect
68. C₂×C₄×D₂₀	C₂²	semidirect
69. C₂×C₄×D₂₀	C₂²	semidirect
70. C₂×C₄×D₂₀	C₂²	semidirect
71. C₂×C₄×D₂₀	C₂²	semidirect
72. C₂×C₄×D₂₀	C₂²	semidirect
73. C₂×#4015	C₂²	semidirect
78. C₂×C₅×#41	C₂³	semidirect
94. C₂×#713	C₂³	semidirect
98. C₂×D₄×D₅	C₂³	semidirect
99. C₂×D₄×D₅	C₂³	semidirect
100. C₂×D₄×D₅	C₂³	semidirect
103. C₂×#709	C₂³	semidirect
104. C₂×#709	C₂³	semidirect
106. C₂²×D₂₀	D₄	semidirect
114. C₂²×D₂₀	C₂³	semidirect
120. C₂²×C₄×D₅	C₂³	semidirect
122. C₅×C₄⋊Q₈	C₂³	semidirect
123. C₅×#127	C₂³	semidirect
124. C₅×#124	C₂³	semidirect
125. C₅×#121	C₂³	semidirect
126. C₅×#121	C₂³	semidirect
127. C₄×C₅×D₄	C₂³	semidirect
128. C₄×C₅×D₄	C₂³	semidirect
137. C₂×C₄²×C₅	C₂³	semidirect
139. #4092	C₂³	semidirect
140. #4085	C₂³	semidirect
141. #4084	C₂³	semidirect
142. #4084	C₂³	semidirect
143. #4083	C₂³	semidirect
144. #4076	C₂³	semidirect
145. #4076	C₂³	semidirect
146. #4076	C₂³	semidirect
152. C₂×#685	C₂³	semidirect
157. C₂×C₄⋊Dic₅	C₂³	semidirect
158. #4070	C₂³	semidirect
160. #4041	C₂³	semidirect
161. #4040	C₂³	semidirect
162. D₅×C₄⋊C₄	C₂³	semidirect
163. #4030	C₂³	semidirect
164. #4029	C₂³	semidirect
165. #4028	C₂³	semidirect
166. D₅×C₂²⋊C₄	C₂³	semidirect
167. #4021	C₂³	semidirect
168. #4020	C₂³	semidirect
169. C₄×D₂₀	C₂³	semidirect
170. C₄×D₂₀	C₂³	semidirect
171. C₄×D₂₀	C₂³	semidirect
172. C₄×D₂₀	C₂³	semidirect
173. C₄×D₂₀	C₂³	semidirect
174. C₄×D₂₀	C₂³	semidirect
175. #4015	C₂³	semidirect
187. C₂×#532	D₅	semidirect
197. C₂³×D₅	C₂×D₄	semidirect
216. C₂²×C₄×C₅	C₂×D₄	semidirect
249. C₂×D₂₀	C₂×D₄	semidirect
250. C₂×D₂₀	C₂×D₄	semidirect
251. C₂×D₂₀	C₂×D₄	semidirect
293. C₂²×#41	C₂×D₅	semidirect
309. #532	C₂×D₅	semidirect
311. C₂×C₄⋊Q₈	C₂×D₅	semidirect
313. C₂×#127	C₂×D₅	semidirect
315. C₂×#124	C₂×D₅	semidirect
329. C₂×#121	C₂×D₅	semidirect
330. C₂×#121	C₂×D₅	semidirect
340. C₂×C₄×D₄	C₂×D₅	semidirect
341. C₂×C₄×D₄	C₂×D₅	semidirect
346. C₂²×C₄²	C₂×D₅	semidirect
369. C₂²×D₅	C₂²×D₄	semidirect
386. C₂×C₄×C₅	C₂²×D₄	semidirect
387. C₂×C₄×C₅	H(5,𝔽₂)	semidirect
407. D₂₀	C₂²×D₄	semidirect
408. D₂₀	C₂²×D₄	semidirect
424. C₂×#41	C₂²×D₅	semidirect
462. C₄⋊Q₈	C₂²×D₅	semidirect
464. #127	C₂²×D₅	semidirect
466. #124	C₂²×D₅	semidirect
479. #121	C₂²×D₅	semidirect
480. #121	C₂²×D₅	semidirect
489. C₄×D₄	C₂²×D₅	semidirect
490. C₄×D₄	C₂²×D₅	semidirect
514. C₂×C₄²	C₂²×D₅	semidirect
543. C₄×C₅	C₂×H(5,𝔽₂)	semidirect
613. C₂²×C₄	D₄×D₅	semidirect
646. C₂×C₅	#3496	semidirect
710. C₂×C₄	C₂×D₄×D₅	semidirect
711. C₂×C₄	#4149	semidirect
719. C₅	C₂×#3496	semidirect
750. C₄	C₂×#4149	semidirect
755. C₂	#10618142	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#4149	2
C₂×C₅×#532	2
C₂×#66167	2
#10618142	2
C₂×#66060	2
C₂×#66051	2
C₂×#66010	2
C₂×#65939	2
C₂×D₅×#121	2
C₂×#65885	2
C₂×#65884	2
C₂×D₄×D₂₀	2
C₂×#65811	2
C₂²×C₄×D₂₀	2
C₂×#3496	5

Subgroups — C2×#10618142 #13007189

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10618142 #13007189