Subgroups — C₂×D₄²×D₅ #13006206

Order 1280.

20038 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₄×D₅	C₂	1	4	yes	maximal, complemented
2	C₂×C₅×D₄²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₄×C₂²⋊D₅	C₂	1	4	yes	maximal, complemented
4	D₄²×D₅	C₂	1	32	yes	maximal, direct product factor
5	C₂×#66051	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₅×#127	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#65943	C₂	1	4	yes	maximal, complemented
8	C₂×D₅×#121	C₂	1	4	yes	maximal, complemented
9	C₂×#65924	C₂	1	4	yes	maximal, complemented
10	C₂×D₅×#120	C₂	1	4	yes	maximal, complemented
11	C₂×D₄×D₂₀	C₂	1	2	yes	maximal, complemented
12	C₂×C₄×D₄×D₅	C₂	1	2	yes	maximal, complemented
13	C₂⁵×D₅	C₂²	1	4	yes	complemented
14	C₂³×C₅×D₄	C₂²	1	4	yes	complemented
15	C₂³×C₂²⋊D₅	C₂²	1	8	yes	complemented
16	C₂²×D₄×D₅	—	2	64	no	—
17	C₂²×D₄×D₅	C₂²	1	2	yes	—
18	C₂²×D₄×D₅	C₂²	1	8	yes	complemented
19	C₂²×D₄×D₅	C₂²	1	4	yes	complemented
20	C₂²×D₄×D₅	C₂²	1	2	yes	complemented
21	C₂²×D₄×D₅	C₂²	1	4	yes	complemented
22	C₂²×D₄×D₅	C₂²	1	64	yes	complemented
23	C₂²×D₄×D₅	C₂²	1	8	yes	complemented
24	C₂²×D₄×D₅	C₂²	1	4	yes	complemented
25	C₂³×D₂₀	C₂²	1	4	yes	complemented
26	C₂³×C₄×D₅	C₂²	1	4	yes	complemented
27	C₅×D₄²	C₂²	1	16	yes	complemented
28	C₂×C₅×#127	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₅×#121	C₂²	1	4	yes	complemented
30	C₂×C₅×#120	C₂²	1	4	yes	complemented
31	C₂×C₄×C₅×D₄	C₂²	1	2	yes	complemented
32	C₂×#4099	C₂²	1	4	yes	complemented
33	C₂×#4086	C₂²	1	4	yes	complemented
34	C₂×#4086	C₂²	1	2	yes	complemented
35	C₂×#4085	C₂²	1	8	yes	complemented
36	D₄×C₂²⋊D₅	C₂²	1	64	yes	complemented
37	C₂×#4084	C₂²	1	4	yes	complemented
38	C₂×#4083	C₂²	1	8	yes	complemented
39	C₂×#4083	C₂²	1	4	yes	complemented
40	C₂×D₄×Dic₅	C₂²	1	2	yes	complemented
41	C₂×#4076	C₂²	1	4	yes	complemented
42	C₂×C₄×C₂²⋊D₅	C₂²	1	4	yes	complemented
43	#66051	C₂²	1	16	yes	complemented
44	D₅×#127	C₂²	1	16	yes	complemented
45	#65943	C₂²	1	64	yes	complemented
46	D₅×#121	C₂²	1	64	yes	complemented
47	#65924	C₂²	1	64	yes	complemented
48	D₅×#120	C₂²	1	64	yes	complemented
49	D₄×D₂₀	C₂²	1	32	yes	complemented
50	C₄×D₄×D₅	C₂²	1	32	yes	complemented
51	C₂×#4041	C₂²	1	4	yes	complemented
52	C₂×#4039	C₂²	1	2	yes	complemented
53	C₂×D₅×C₄⋊C₄	C₂²	1	2	yes	complemented
54	C₂×#4030	C₂²	1	8	yes	complemented
55	C₂×#4028	C₂²	1	8	yes	complemented
56	C₂×#4028	C₂²	1	4	yes	complemented
57	C₂×#4027	C₂²	1	4	yes	complemented
58	C₂×D₅×C₂²⋊C₄	C₂²	1	4	yes	complemented
59	C₂×D₅×C₂²⋊C₄	C₂²	1	4	yes	complemented
60	C₂×#4020	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₄×D₂₀	C₂²	1	2	yes	complemented
62	C₂×C₄²×D₅	C₂²	1	1	yes	characteristic, complemented
63	C₂²×D₄²	—	5	1	no	maximal, Sylow
64	C₂⁵×C₅	C₂³	1	4	yes	complemented
65	C₂⁴×D₅	—	2	64	no	—
66	C₂⁴×D₅	—	4	16	no	—
67	C₂⁴×D₅	C₂³	1	4	yes	—
68	C₂⁴×D₅	C₂³	1	4	yes	—
69	C₂⁴×D₅	C₂³	1	32	yes	complemented
70	C₂⁴×D₅	C₂³	1	8	yes	complemented
71	C₂⁴×D₅	C₂³	1	4	yes	complemented
72	C₂²×C₅×D₄	—	2	32	no	—
73	C₂²×C₅×D₄	C₂³	1	2	yes	—
74	C₂²×C₅×D₄	C₂³	1	8	yes	complemented
75	C₂²×C₅×D₄	C₂³	1	4	yes	complemented
76	C₂²×C₅×D₄	C₂³	1	2	yes	complemented
77	C₂²×C₅×D₄	C₂³	1	32	yes	complemented
78	C₂³×C₄×C₅	C₂³	1	4	yes	complemented
79	C₂²×C₂²⋊D₅	—	2	64	no	—
80	C₂²×C₂²⋊D₅	C₂³	1	4	yes	—
81	C₂²×C₂²⋊D₅	C₂³	1	8	yes	complemented
82	C₂²×C₂²⋊D₅	C₂³	1	8	yes	complemented
83	C₂²×C₂²⋊D₅	C₂³	1	8	yes	complemented
84	C₂²×C₂²⋊D₅	C₂³	1	4	yes	complemented
85	C₂²×C₂²⋊D₅	C₂³	1	64	yes	complemented
86	C₂³×Dic₅	C₂³	1	4	yes	complemented
87	C₂×D₄×D₅	—	2	64	no	—
88	C₂×D₄×D₅	—	2	32	no	—
89	C₂×D₄×D₅	—	2	64	no	—
90	C₂×D₄×D₅	—	2	512	no	—
91	C₂×D₄×D₅	—	2	32	no	—
92	C₂×D₄×D₅	—	2	32	no	—
93	C₂×D₄×D₅	—	4	8	no	—
94	C₂×D₄×D₅	D₄	1	32	yes	direct product factor
95	C₂×D₄×D₅	C₂³	1	16	yes	—
96	C₂×D₄×D₅	C₂³	1	32	yes	complemented
97	C₂×D₄×D₅	C₂³	1	64	yes	complemented
98	C₂×D₄×D₅	C₂³	1	16	yes	complemented
99	C₂×D₄×D₅	C₂³	1	32	yes	complemented
100	C₂×D₄×D₅	C₂³	1	64	yes	complemented
101	C₂×D₄×D₅	C₂³	1	32	yes	complemented
102	C₂²×D₂₀	—	2	32	no	—
103	C₂²×D₂₀	C₂³	1	2	yes	—
104	C₂²×D₂₀	C₂³	1	32	yes	complemented
105	C₂²×D₂₀	C₂³	1	4	yes	complemented
106	C₂²×D₂₀	C₂³	1	8	yes	complemented
107	C₂²×D₂₀	C₂³	1	2	yes	complemented
108	C₂²×C₄×D₅	—	2	32	no	—
109	C₂²×C₄×D₅	C₂³	1	1	yes	characteristic
110	C₂²×C₄×D₅	C₂³	1	4	yes	—
111	C₂²×C₄×D₅	C₂³	1	2	yes	—
112	C₂²×C₄×D₅	C₂³	1	32	yes	complemented
113	C₂²×C₄×D₅	C₂³	1	4	yes	complemented
114	C₂²×C₄×D₅	C₂³	1	4	yes	complemented
115	C₅×#127	C₂³	1	8	yes	complemented
116	C₅×#121	C₂³	1	32	yes	complemented
117	C₅×#120	C₂³	1	32	yes	complemented
118	C₄×C₅×D₄	C₂³	1	16	yes	complemented
119	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	complemented
120	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	complemented
121	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	complemented
122	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic, complemented
123	#4099	C₂³	1	32	yes	complemented
124	C₂×C₂²⋊Dic₅	C₂³	1	4	yes	complemented
125	C₂×C₂²⋊Dic₅	C₂³	1	4	yes	complemented
126	#4086	C₂³	1	32	yes	complemented
127	#4086	C₂³	1	16	yes	complemented
128	#4085	C₂³	1	64	yes	complemented
129	#4084	C₂³	1	32	yes	complemented
130	#4083	C₂³	1	32	yes	complemented
131	#4083	C₂³	1	64	yes	complemented
132	D₄×Dic₅	C₂³	1	16	yes	complemented
133	#4076	C₂³	1	32	yes	complemented
134	C₄×C₂²⋊D₅	C₂³	1	32	yes	complemented
135	C₂×#685	C₂³	1	4	yes	complemented
136	C₂×#685	C₂³	1	4	yes	complemented
137	C₂×#685	C₂³	1	8	yes	complemented
138	C₂×C₄⋊Dic₅	C₂³	1	2	yes	complemented
139	C₂×#683	C₂³	1	4	yes	complemented
140	C₂×C₄×Dic₅	C₂³	1	1	yes	characteristic, complemented
141	C₂×C₄×Dic₅	C₂³	1	2	yes	complemented
142	#4041	C₂³	1	32	yes	complemented
143	#4039	C₂³	1	16	yes	complemented
144	D₅×C₄⋊C₄	C₂³	1	16	yes	complemented
145	#4030	C₂³	1	64	yes	complemented
146	#4028	C₂³	1	64	yes	complemented
147	#4028	C₂³	1	32	yes	complemented
148	#4027	C₂³	1	32	yes	complemented
149	D₅×C₂²⋊C₄	C₂³	1	32	yes	complemented
150	D₅×C₂²⋊C₄	C₂³	1	32	yes	complemented
151	#4020	C₂³	1	8	yes	complemented
152	C₄×D₂₀	C₂³	1	16	yes	complemented
153	C₄²×D₅	C₂³	1	8	yes	complemented
154	C₂⁴×D₄	—	5	4	no	—
155	C₂×D₄²	—	5	4	no	—
156	C₂×D₄²	—	5	32	no	—
157	C₂×D₄²	—	5	1	no	—
158	C₂×D₄²	—	5	4	no	—
159	C₂×D₄²	—	5	4	no	—
160	C₂×D₄²	—	5	2	no	—
161	C₂×D₄²	D₅	1	1	yes	characteristic, direct product factor
162	C₂²×#127	—	5	1	no	—
163	C₂²×#121	—	5	4	no	—
164	C₂²×#120	—	5	4	no	—
165	C₂²×C₄×D₄	—	5	2	no	—
166	C₂⁴×C₅	—	2	32	no	—
167	C₂⁴×C₅	—	4	8	no	—
168	C₂⁴×C₅	C₂⁴	1	4	yes	—
169	C₂⁴×C₅	C₂⁴	1	4	yes	—
170	C₂⁴×C₅	C₂⁴	1	16	yes	complemented
171	C₂³×D₅	—	2	16	no	—
172	C₂³×D₅	—	2	16	no	—
173	C₂³×D₅	—	2	32	no	—
174	C₂³×D₅	—	2	32	no	—
175	C₂³×D₅	—	2	32	no	—
176	C₂³×D₅	—	2	32	no	—
177	C₂³×D₅	—	2	256	no	—
178	C₂³×D₅	—	2	16	no	—
179	C₂³×D₅	—	4	64	no	—
180	C₂³×D₅	—	4	8	no	—
181	C₂³×D₅	—	4	16	no	—
182	C₂³×D₅	—	4	256	no	—
183	C₂³×D₅	C₂×D₄	1	32	yes	complemented
184	C₂³×D₅	C₂⁴	1	4	yes	—
185	C₂³×D₅	C₂⁴	1	16	yes	—
186	C₂³×D₅	C₂⁴	1	4	yes	—
187	C₂³×D₅	C₂⁴	1	16	yes	—
188	C₂³×D₅	C₂⁴	1	1	yes	characteristic
189	C₂³×D₅	C₂⁴	1	32	yes	complemented
190	C₂³×D₅	C₂⁴	1	16	yes	complemented
191	C₂×C₅×D₄	—	2	32	no	—
192	C₂×C₅×D₄	—	2	128	no	—
193	C₂×C₅×D₄	—	2	16	no	—
194	C₂×C₅×D₄	—	4	4	no	—
195	C₂×C₅×D₄	C₂×D₄	1	16	yes	complemented
196	C₂×C₅×D₄	C₂⁴	1	8	yes	—
197	C₂×C₅×D₄	C₂⁴	1	32	yes	complemented
198	C₂×C₅×D₄	C₂⁴	1	16	yes	complemented
199	C₂×C₅×D₄	C₂⁴	1	8	yes	complemented
200	C₂²×C₄×C₅	—	2	16	no	—
201	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
202	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
203	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
204	C₂²×C₄×C₅	C₂⁴	1	16	yes	complemented
205	C₂×C₂²⋊D₅	—	2	32	no	—
206	C₂×C₂²⋊D₅	—	2	32	no	—
207	C₂×C₂²⋊D₅	—	2	256	no	—
208	C₂×C₂²⋊D₅	—	2	32	no	—
209	C₂×C₂²⋊D₅	—	4	8	no	—
210	C₂×C₂²⋊D₅	C₂×D₄	1	32	yes	complemented
211	C₂×C₂²⋊D₅	C₂⁴	1	16	yes	—
212	C₂×C₂²⋊D₅	C₂⁴	1	32	yes	complemented
213	C₂×C₂²⋊D₅	C₂⁴	1	32	yes	complemented
214	C₂×C₂²⋊D₅	C₂⁴	1	32	yes	complemented
215	C₂×C₂²⋊D₅	C₂⁴	1	16	yes	complemented
216	C₂²×Dic₅	—	2	16	no	—
217	C₂²×Dic₅	C₂⁴	1	1	yes	characteristic
218	C₂²×Dic₅	C₂⁴	1	4	yes	—
219	C₂²×Dic₅	C₂⁴	1	2	yes	—
220	C₂²×Dic₅	C₂⁴	1	16	yes	complemented
221	D₄×D₅	—	2	256	no	—
222	D₄×D₅	—	2	128	no	—
223	D₄×D₅	—	2	256	no	—
224	D₄×D₅	—	2	128	no	—
225	D₄×D₅	—	2	128	no	—
226	D₄×D₅	—	4	32	no	—
227	D₄×D₅	C₂×D₄	1	128	yes	direct product factor
228	C₂×D₂₀	—	2	32	no	—
229	C₂×D₂₀	—	2	16	no	—
230	C₂×D₂₀	—	2	128	no	—
231	C₂×D₂₀	—	4	4	no	—
232	C₂×D₂₀	C₂×D₄	1	16	yes	complemented
233	C₂×D₂₀	C₂⁴	1	8	yes	—
234	C₂×D₂₀	C₂⁴	1	16	yes	complemented
235	C₂×D₂₀	C₂⁴	1	32	yes	complemented
236	C₂×D₂₀	C₂⁴	1	8	yes	complemented
237	C₂×C₄×D₅	—	2	16	no	—
238	C₂×C₄×D₅	—	2	4	no	—
239	C₂×C₄×D₅	—	2	16	no	—
240	C₂×C₄×D₅	—	2	16	no	—
241	C₂×C₄×D₅	—	2	128	no	—
242	C₂×C₄×D₅	C₂×D₄	1	16	yes	complemented
243	C₂×C₄×D₅	C₂⁴	1	16	yes	—
244	C₂×C₄×D₅	C₂⁴	1	4	yes	—
245	C₂×C₄×D₅	C₂⁴	1	8	yes	—
246	C₂×C₄×D₅	C₂⁴	1	16	yes	complemented
247	C₂×C₄×D₅	C₂⁴	1	16	yes	complemented
248	C₅×C₄⋊C₄	C₂⁴	1	8	yes	complemented
249	C₅×C₂²⋊C₄	C₂⁴	1	16	yes	complemented
250	C₅×C₂²⋊C₄	C₂⁴	1	16	yes	complemented
251	C₄²×C₅	C₂⁴	1	4	yes	complemented
252	C₂²⋊Dic₅	C₂⁴	1	16	yes	complemented
253	C₂²⋊Dic₅	C₂⁴	1	16	yes	complemented
254	#685	C₂⁴	1	16	yes	complemented
255	#685	C₂⁴	1	16	yes	complemented
256	#685	C₂⁴	1	32	yes	complemented
257	C₄⋊Dic₅	C₂⁴	1	8	yes	complemented
258	#683	C₂⁴	1	16	yes	complemented
259	C₄×Dic₅	C₂⁴	1	4	yes	complemented
260	C₄×Dic₅	C₂⁴	1	8	yes	complemented
261	C₂⁶	—	5	4	no	—
262	C₂³×D₄	—	5	2	no	—
263	C₂³×D₄	—	5	8	no	—
264	C₂³×D₄	—	5	4	no	—
265	C₂³×D₄	—	5	8	no	—
266	C₂³×D₄	—	5	4	no	—
267	C₂³×D₄	—	5	8	no	—
268	C₂³×D₄	—	5	4	no	—
269	C₂³×D₄	—	5	64	no	—
270	C₂³×D₄	—	5	2	no	—
271	C₂³×D₄	—	5	4	no	—
272	C₂³×D₄	—	10	64	no	—
273	C₂³×D₄	C₂×D₅	1	4	yes	complemented
274	C₂⁴×C₄	—	5	4	no	—
275	D₄²	—	5	64	no	—
276	D₄²	—	5	16	no	—
277	D₄²	—	5	64	no	—
278	D₄²	—	5	64	no	—
279	D₄²	—	5	32	no	—
280	D₄²	C₂×D₅	1	16	yes	direct product factor
281	C₂×#127	—	5	2	no	—
282	C₂×#127	—	5	4	no	—
283	C₂×#127	—	5	16	no	—
284	C₂×#127	—	5	1	no	—
285	C₂×#127	C₂×D₅	1	1	yes	characteristic, complemented
286	C₂×#121	—	5	4	no	—
287	C₂×#121	—	5	8	no	—
288	C₂×#121	—	5	4	no	—
289	C₂×#121	—	5	64	no	—
290	C₂×#121	—	5	4	no	—
291	C₂×#121	—	5	8	no	—
292	C₂×#121	C₂×D₅	1	4	yes	complemented
293	C₂×#120	—	5	4	no	—
294	C₂×#120	—	5	8	no	—
295	C₂×#120	—	5	4	no	—
296	C₂×#120	—	5	64	no	—
297	C₂×#120	—	5	4	no	—
298	C₂×#120	—	5	8	no	—
299	C₂×#120	C₂×D₅	1	4	yes	complemented
300	C₂×C₄×D₄	—	5	2	no	—
301	C₂×C₄×D₄	—	5	4	no	—
302	C₂×C₄×D₄	—	5	32	no	—
303	C₂×C₄×D₄	—	5	2	no	—
304	C₂×C₄×D₄	—	5	4	no	—
305	C₂×C₄×D₄	—	5	2	no	—
306	C₂×C₄×D₄	C₂×D₅	1	2	yes	complemented
307	C₂²×C₄⋊C₄	—	5	2	no	—
308	C₂²×C₂²⋊C₄	—	5	4	no	—
309	C₂²×C₂²⋊C₄	—	5	4	no	—
310	C₂²×C₄²	—	5	1	no	—
311	C₂³×C₅	—	2	8	no	—
312	C₂³×C₅	—	2	8	no	—
313	C₂³×C₅	—	2	16	no	—
314	C₂³×C₅	—	2	64	no	—
315	C₂³×C₅	—	2	8	no	—
316	C₂³×C₅	—	4	16	no	—
317	C₂³×C₅	—	4	64	no	—
318	C₂³×C₅	C₂²×D₄	1	16	yes	complemented
319	C₂³×C₅	C₂⁵	1	8	yes	—
320	C₂³×C₅	C₂⁵	1	8	yes	—
321	C₂³×C₅	C₂⁵	1	1	yes	characteristic
322	C₂²×D₅	—	2	8	no	—
323	C₂²×D₅	—	2	8	no	—
324	C₂²×D₅	—	2	128	no	—
325	C₂²×D₅	—	2	32	no	—
326	C₂²×D₅	—	2	32	no	—
327	C₂²×D₅	—	2	16	no	—
328	C₂²×D₅	—	2	64	no	—
329	C₂²×D₅	—	2	8	no	—
330	C₂²×D₅	—	2	64	no	—
331	C₂²×D₅	—	2	64	no	—
332	C₂²×D₅	—	2	64	no	—
333	C₂²×D₅	—	2	32	no	—
334	C₂²×D₅	—	4	16	no	—
335	C₂²×D₅	—	4	32	no	—
336	C₂²×D₅	—	4	64	no	—
337	C₂²×D₅	—	4	512	no	—
338	C₂²×D₅	—	4	128	no	—
339	C₂²×D₅	—	4	64	no	—
340	C₂²×D₅	C₂²×D₄	1	8	yes	—
341	C₂²×D₅	C₂²×D₄	1	64	yes	complemented
342	C₂²×D₅	C₂²×D₄	1	16	yes	complemented
343	C₂²×D₅	H(5,𝔽₂)	1	4	yes	—
344	C₂²×D₅	C₂⁵	1	8	yes	—
345	C₂²×D₅	C₂⁵	1	8	yes	—
346	C₂²×D₅	C₂⁵	1	2	yes	—
347	C₅×D₄	—	2	64	no	—
348	C₅×D₄	—	2	32	no	—
349	C₅×D₄	—	4	8	no	—
350	C₅×D₄	C₂²×D₄	1	32	yes	complemented
351	C₂×C₄×C₅	—	2	8	no	—
352	C₂×C₄×C₅	—	2	2	no	—
353	C₂×C₄×C₅	—	2	32	no	—
354	C₂×C₄×C₅	C₂²×D₄	1	8	yes	complemented
355	C₂×C₄×C₅	C₂⁵	1	2	yes	—
356	C₂×C₄×C₅	C₂⁵	1	8	yes	—
357	C₂×C₄×C₅	C₂⁵	1	4	yes	—
358	C₂²⋊D₅	—	2	64	no	—
359	C₂²⋊D₅	—	2	64	no	—
360	C₂²⋊D₅	—	2	64	no	—
361	C₂²⋊D₅	—	4	16	no	—
362	C₂²⋊D₅	C₂²×D₄	1	64	yes	complemented
363	C₂×Dic₅	—	2	8	no	—
364	C₂×Dic₅	—	2	2	no	—
365	C₂×Dic₅	—	2	32	no	—
366	C₂×Dic₅	C₂²×D₄	1	8	yes	complemented
367	C₂×Dic₅	C₂⁵	1	2	yes	—
368	C₂×Dic₅	C₂⁵	1	8	yes	—
369	C₂×Dic₅	C₂⁵	1	4	yes	—
370	D₂₀	—	2	64	no	—
371	D₂₀	—	2	32	no	—
372	D₂₀	—	4	8	no	—
373	D₂₀	C₂²×D₄	1	32	yes	complemented
374	C₄×D₅	—	2	32	no	—
375	C₄×D₅	—	2	8	no	—
376	C₄×D₅	—	2	32	no	—
377	C₄×D₅	—	2	32	no	—
378	C₄×D₅	C₂²×D₄	1	32	yes	complemented
379	C₂⁵	—	5	4	no	—
380	C₂⁵	—	5	4	no	—
381	C₂⁵	—	5	4	no	—
382	C₂⁵	—	5	8	no	—
383	C₂⁵	—	5	32	no	—
384	C₂⁵	—	10	64	no	—
385	C₂⁵	—	20	16	no	—
386	C₂⁵	C₂²×D₅	1	4	yes	complemented
387	C₂²×D₄	—	2	32	no	—
388	C₂²×D₄	—	5	4	no	—
389	C₂²×D₄	—	5	32	no	—
390	C₂²×D₄	—	5	16	no	—
391	C₂²×D₄	—	5	8	no	—
392	C₂²×D₄	—	5	8	no	—
393	C₂²×D₄	—	5	8	no	—
394	C₂²×D₄	—	5	64	no	—
395	C₂²×D₄	—	5	4	no	—
396	C₂²×D₄	—	5	32	no	—
397	C₂²×D₄	—	5	64	no	—
398	C₂²×D₄	—	5	32	no	—
399	C₂²×D₄	—	5	64	no	—
400	C₂²×D₄	—	5	32	no	—
401	C₂²×D₄	—	5	16	no	—
402	C₂²×D₄	—	5	2	no	—
403	C₂²×D₄	—	5	8	no	—
404	C₂²×D₄	—	5	4	no	—
405	C₂²×D₄	—	5	2	no	—
406	C₂²×D₄	—	5	32	no	—
407	C₂²×D₄	—	10	32	no	—
408	C₂²×D₄	—	10	32	no	—
409	C₂²×D₄	—	10	64	no	—
410	C₂²×D₄	—	10	512	no	—
411	C₂²×D₄	—	10	32	no	—
412	C₂²×D₄	—	10	64	no	—
413	C₂²×D₄	—	10	64	no	—
414	C₂²×D₄	—	10	32	no	—
415	C₂²×D₄	—	20	8	no	—
416	C₂²×D₄	C₂²×D₅	1	2	yes	—
417	C₂²×D₄	C₂²×D₅	1	8	yes	complemented
418	C₂²×D₄	C₂²×D₅	1	4	yes	complemented
419	C₂²×D₄	C₂²×D₅	1	2	yes	complemented
420	C₂²×D₄	C₂²×D₅	1	32	yes	complemented
421	C₂³×C₄	—	5	2	no	—
422	C₂³×C₄	—	5	4	no	—
423	C₂³×C₄	—	5	1	no	—
424	C₂³×C₄	—	5	4	no	—
425	C₂³×C₄	—	5	4	no	—
426	C₂³×C₄	—	5	4	no	—
427	C₂³×C₄	—	5	32	no	—
428	C₂³×C₄	—	10	32	no	—
429	C₂³×C₄	C₂²×D₅	1	4	yes	complemented
430	#127	—	5	16	no	—
431	#127	—	5	32	no	—
432	#127	—	5	8	no	—
433	#127	C₂²×D₅	1	8	yes	complemented
434	#121	—	5	32	no	—
435	#121	—	5	64	no	—
436	#121	—	5	32	no	—
437	#121	—	5	32	no	—
438	#121	—	5	64	no	—
439	#121	C₂²×D₅	1	32	yes	complemented
440	#120	—	5	32	no	—
441	#120	—	5	64	no	—
442	#120	—	5	32	no	—
443	#120	—	5	32	no	—
444	#120	—	5	64	no	—
445	#120	C₂²×D₅	1	32	yes	complemented
446	C₄×D₄	—	5	16	no	—
447	C₄×D₄	—	5	32	no	—
448	C₄×D₄	—	5	16	no	—
449	C₄×D₄	—	5	32	no	—
450	C₄×D₄	—	5	16	no	—
451	C₄×D₄	C₂²×D₅	1	16	yes	complemented
452	C₂×C₄⋊C₄	—	5	4	no	—
453	C₂×C₄⋊C₄	—	5	2	no	—
454	C₂×C₄⋊C₄	—	5	16	no	—
455	C₂×C₄⋊C₄	C₂²×D₅	1	2	yes	complemented
456	C₂×C₂²⋊C₄	—	5	4	no	—
457	C₂×C₂²⋊C₄	—	5	4	no	—
458	C₂×C₂²⋊C₄	—	5	4	no	—
459	C₂×C₂²⋊C₄	—	5	4	no	—
460	C₂×C₂²⋊C₄	—	5	8	no	—
461	C₂×C₂²⋊C₄	—	5	32	no	—
462	C₂×C₂²⋊C₄	—	5	32	no	—
463	C₂×C₂²⋊C₄	C₂²×D₅	1	4	yes	complemented
464	C₂×C₂²⋊C₄	C₂²×D₅	1	4	yes	complemented
465	C₂×C₄²	—	5	1	no	—
466	C₂×C₄²	—	5	2	no	—
467	C₂×C₄²	—	5	8	no	—
468	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic, complemented
469	C₂²×C₅	—	2	8	no	—
470	C₂²×C₅	—	2	8	no	—
471	C₂²×C₅	—	2	32	no	—
472	C₂²×C₅	—	2	16	no	—
473	C₂²×C₅	—	2	8	no	—
474	C₂²×C₅	—	4	64	no	—
475	C₂²×C₅	—	4	16	no	—
476	C₂²×C₅	C₂³×D₄	1	4	yes	—
477	C₂²×C₅	C₂³×D₄	1	16	yes	complemented
478	C₂²×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
479	C₂²×C₅	C₂⁶	1	1	yes	characteristic
480	C₂×D₅	—	2	8	no	—
481	C₂×D₅	—	2	8	no	—
482	C₂×D₅	—	2	32	no	—
483	C₂×D₅	—	2	128	no	—
484	C₂×D₅	—	2	16	no	—
485	C₂×D₅	—	2	8	no	—
486	C₂×D₅	—	4	64	no	—
487	C₂×D₅	—	4	128	no	—
488	C₂×D₅	—	4	16	no	—
489	C₂×D₅	—	4	64	no	—
490	C₂×D₅	D₄²	1	16	yes	direct product factor
491	C₂×D₅	C₂³×D₄	1	8	yes	—
492	C₂×D₅	C₂³×D₄	1	16	yes	complemented
493	C₂×D₅	C₂×H(5,𝔽₂)	1	4	yes	—
494	C₄×C₅	—	2	8	no	—
495	C₄×C₅	—	2	2	no	—
496	C₄×C₅	C₂³×D₄	1	8	yes	complemented
497	Dic₅	—	2	8	no	—
498	Dic₅	—	2	2	no	—
499	Dic₅	C₂³×D₄	1	8	yes	complemented
500	C₂⁴	—	2	32	no	—
501	C₂⁴	—	4	8	no	—
502	C₂⁴	—	5	1	no	—
503	C₂⁴	—	5	32	no	—
504	C₂⁴	—	5	16	no	—
505	C₂⁴	—	5	4	no	—
506	C₂⁴	—	5	16	no	—
507	C₂⁴	—	5	4	no	—
508	C₂⁴	—	5	16	no	—
509	C₂⁴	—	5	32	no	—
510	C₂⁴	—	10	16	no	—
511	C₂⁴	—	10	16	no	—
512	C₂⁴	—	10	32	no	—
513	C₂⁴	—	10	32	no	—
514	C₂⁴	—	10	32	no	—
515	C₂⁴	—	10	256	no	—
516	C₂⁴	—	10	16	no	—
517	C₂⁴	—	10	32	no	—
518	C₂⁴	—	20	16	no	—
519	C₂⁴	—	20	8	no	—
520	C₂⁴	—	20	64	no	—
521	C₂⁴	—	20	256	no	—
522	C₂⁴	C₂³×D₅	1	4	yes	—
523	C₂⁴	C₂³×D₅	1	4	yes	—
524	C₂⁴	C₂³×D₅	1	16	yes	complemented
525	C₂×D₄	—	2	32	no	—
526	C₂×D₄	—	2	128	no	—
527	C₂×D₄	—	2	16	no	—
528	C₂×D₄	—	4	4	no	—
529	C₂×D₄	—	5	32	no	—
530	C₂×D₄	—	5	16	no	—
531	C₂×D₄	—	5	128	no	—
532	C₂×D₄	—	5	32	no	—
533	C₂×D₄	—	5	32	no	—
534	C₂×D₄	—	5	32	no	—
535	C₂×D₄	—	5	16	no	—
536	C₂×D₄	—	5	16	no	—
537	C₂×D₄	—	5	8	no	—
538	C₂×D₄	—	5	32	no	—
539	C₂×D₄	—	5	16	no	—
540	C₂×D₄	—	5	8	no	—
541	C₂×D₄	—	10	128	no	—
542	C₂×D₄	—	10	32	no	—
543	C₂×D₄	—	10	128	no	—
544	C₂×D₄	—	10	32	no	—
545	C₂×D₄	—	10	256	no	—
546	C₂×D₄	—	10	128	no	—
547	C₂×D₄	—	10	256	no	—
548	C₂×D₄	—	10	256	no	—
549	C₂×D₄	—	10	32	no	—
550	C₂×D₄	—	10	32	no	—
551	C₂×D₄	—	10	128	no	—
552	C₂×D₄	—	10	16	no	—
553	C₂×D₄	—	20	4	no	—
554	C₂×D₄	—	20	32	no	—
555	C₂×D₄	—	20	8	no	—
556	C₂×D₄	D₄×D₅	1	16	yes	direct product factor
557	C₂×D₄	C₂³×D₅	1	8	yes	—
558	C₂×D₄	C₂³×D₅	1	32	yes	complemented
559	C₂×D₄	C₂³×D₅	1	16	yes	complemented
560	C₂×D₄	C₂³×D₅	1	8	yes	complemented
561	C₂²×C₄	—	2	16	no	—
562	C₂²×C₄	—	5	2	no	—
563	C₂²×C₄	—	5	16	no	—
564	C₂²×C₄	—	5	8	no	—
565	C₂²×C₄	—	5	16	no	—
566	C₂²×C₄	—	5	1	no	—
567	C₂²×C₄	—	5	4	no	—
568	C₂²×C₄	—	5	4	no	—
569	C₂²×C₄	—	5	16	no	—
570	C₂²×C₄	—	5	16	no	—
571	C₂²×C₄	—	5	16	no	—
572	C₂²×C₄	—	10	16	no	—
573	C₂²×C₄	—	10	128	no	—
574	C₂²×C₄	—	10	16	no	—
575	C₂²×C₄	—	10	4	no	—
576	C₂²×C₄	—	10	16	no	—
577	C₂²×C₄	—	10	16	no	—
578	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
579	C₂²×C₄	C₂³×D₅	1	4	yes	—
580	C₂²×C₄	C₂³×D₅	1	2	yes	—
581	C₂²×C₄	C₂³×D₅	1	16	yes	complemented
582	C₄⋊C₄	—	5	16	no	—
583	C₄⋊C₄	—	5	8	no	—
584	C₄⋊C₄	C₂³×D₅	1	8	yes	complemented
585	C₂²⋊C₄	—	5	16	no	—
586	C₂²⋊C₄	—	5	16	no	—
587	C₂²⋊C₄	—	5	16	no	—
588	C₂²⋊C₄	—	5	16	no	—
589	C₂²⋊C₄	—	5	32	no	—
590	C₂²⋊C₄	C₂³×D₅	1	16	yes	complemented
591	C₂²⋊C₄	C₂³×D₅	1	16	yes	complemented
592	C₄²	—	5	4	no	—
593	C₄²	—	5	8	no	—
594	C₄²	C₂³×D₅	1	4	yes	complemented
595	C₂×C₅	—	2	16	no	—
596	C₂×C₅	—	4	8	no	—
597	C₂×C₅	C₂×D₄²	1	4	yes	complemented
598	C₂×C₅	C₂⁴×D₄	1	2	yes	—
599	C₂×C₅	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
600	D₅	—	2	16	no	—
601	D₅	—	4	8	no	—
602	D₅	C₂×D₄²	1	8	yes	direct product factor
603	C₂³	—	2	8	no	—
604	C₂³	—	2	8	no	—
605	C₂³	—	2	16	no	—
606	C₂³	—	2	64	no	—
607	C₂³	—	2	8	no	—
608	C₂³	—	4	16	no	—
609	C₂³	—	4	64	no	—
610	C₂³	—	5	8	no	—
611	C₂³	—	5	4	no	—
612	C₂³	—	5	2	no	—
613	C₂³	—	5	16	no	—
614	C₂³	—	5	64	no	—
615	C₂³	—	5	8	no	—
616	C₂³	—	5	8	no	—
617	C₂³	—	10	32	no	—
618	C₂³	—	10	32	no	—
619	C₂³	—	10	128	no	—
620	C₂³	—	10	64	no	—
621	C₂³	—	10	64	no	—
622	C₂³	—	10	64	no	—
623	C₂³	—	10	32	no	—
624	C₂³	—	10	8	no	—
625	C₂³	—	10	8	no	—
626	C₂³	—	10	16	no	—
627	C₂³	—	10	64	no	—
628	C₂³	—	10	8	no	—
629	C₂³	—	20	32	no	—
630	C₂³	—	20	16	no	—
631	C₂³	—	20	128	no	—
632	C₂³	—	20	64	no	—
633	C₂³	—	20	512	no	—
634	C₂³	—	20	64	no	—
635	C₂³	C₂×D₄×D₅	1	16	yes	complemented
636	C₂³	C₂⁴×D₅	1	8	yes	—
637	C₂³	C₂⁴×D₅	1	8	yes	—
638	C₂³	C₂⁴×D₅	1	1	yes	characteristic
639	D₄	—	2	64	no	—
640	D₄	—	2	32	no	—
641	D₄	—	4	8	no	—
642	D₄	—	5	64	no	—
643	D₄	—	5	32	no	—
644	D₄	—	10	64	no	—
645	D₄	—	10	64	no	—
646	D₄	—	10	64	no	—
647	D₄	—	10	64	no	—
648	D₄	—	10	32	no	—
649	D₄	—	20	8	no	—
650	D₄	—	20	16	no	—
651	D₄	C₂×D₄×D₅	1	32	yes	direct product factor
652	C₂×C₄	—	2	8	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	32	no	—
655	C₂×C₄	—	5	8	no	—
656	C₂×C₄	—	5	4	no	—
657	C₂×C₄	—	5	32	no	—
658	C₂×C₄	—	5	2	no	—
659	C₂×C₄	—	5	8	no	—
660	C₂×C₄	—	10	32	no	—
661	C₂×C₄	—	10	32	no	—
662	C₂×C₄	—	10	8	no	—
663	C₂×C₄	—	10	32	no	—
664	C₂×C₄	—	10	8	no	—
665	C₂×C₄	—	10	2	no	—
666	C₂×C₄	—	10	32	no	—
667	C₂×C₄	C₂×D₄×D₅	1	8	yes	complemented
668	C₂×C₄	C₂⁴×D₅	1	2	yes	—
669	C₂×C₄	C₂⁴×D₅	1	8	yes	—
670	C₂×C₄	C₂⁴×D₅	1	4	yes	—
671	C₅	C₂²×D₄²	1	1	yes	characteristic, complemented, Sylow
672	C₂²	—	2	8	no	—
673	C₂²	—	2	8	no	—
674	C₂²	—	2	32	no	—
675	C₂²	—	2	16	no	—
676	C₂²	—	2	8	no	—
677	C₂²	—	4	64	no	—
678	C₂²	—	4	16	no	—
679	C₂²	—	5	8	no	—
680	C₂²	—	5	4	no	—
681	C₂²	—	5	16	no	—
682	C₂²	—	5	16	no	—
683	C₂²	—	10	128	no	—
684	C₂²	—	10	8	no	—
685	C₂²	—	10	8	no	—
686	C₂²	—	10	32	no	—
687	C₂²	—	10	16	no	—
688	C₂²	—	10	8	no	—
689	C₂²	—	20	128	no	—
690	C₂²	—	20	64	no	—
691	C₂²	—	20	64	no	—
692	C₂²	—	20	16	no	—
693	C₂²	C₂²×D₄×D₅	1	4	yes	—
694	C₂²	C₂²×D₄×D₅	1	16	yes	complemented
695	C₂²	D₅×H(5,𝔽₂)	1	2	yes	—
696	C₂²	C₂⁵×D₅	1	1	yes	characteristic
697	C₄	—	2	8	no	—
698	C₄	—	2	2	no	—
699	C₄	—	5	8	no	—
700	C₄	—	10	8	no	—
701	C₄	—	10	2	no	—
702	C₄	C₂²×D₄×D₅	1	8	yes	complemented
703	C₂	—	2	16	no	—
704	C₂	—	4	8	no	—
705	C₂	—	5	8	no	—
706	C₂	—	10	16	no	—
707	C₂	—	20	8	no	—
708	C₂	D₄²×D₅	1	4	yes	direct product factor
709	C₂	C₂³×D₄×D₅	1	2	yes	—
710	C₂	C₂×D₅×H(5,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₅
commutator, cosocle	C₂²×C₅	C₂⁶
Frattini	C₂²	C₂⁵×D₅
Fitting	C₂×C₅×D₄²	C₂
socle	C₂³×C₅	C₂⁵
hypercenter	C₂×D₄²	D₅
hypocenter	C₅	C₂²×D₄²
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³ ◁ C₂×D₄²

Complements

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

N	H ≅ G/N	type
1. C₂³×D₄×D₅	C₂	semidirect
2. C₂×C₅×D₄²	C₂	semidirect
3. C₂×D₄×C₂²⋊D₅	C₂	semidirect
4. D₄²×D₅	C₂	direct (N × H)
5. C₂×#66051	C₂	semidirect
6. C₂×D₅×#127	C₂	semidirect
7. C₂×#65943	C₂	semidirect
8. C₂×D₅×#121	C₂	semidirect
9. C₂×#65924	C₂	semidirect
10. C₂×D₅×#120	C₂	semidirect
11. C₂×D₄×D₂₀	C₂	semidirect
12. C₂×C₄×D₄×D₅	C₂	semidirect
13. C₂⁵×D₅	C₂²	semidirect
14. C₂³×C₅×D₄	C₂²	semidirect
15. C₂³×C₂²⋊D₅	C₂²	semidirect
18. C₂²×D₄×D₅	C₂²	semidirect
19. C₂²×D₄×D₅	C₂²	semidirect
20. C₂²×D₄×D₅	C₂²	semidirect
21. C₂²×D₄×D₅	C₂²	semidirect
22. C₂²×D₄×D₅	C₂²	semidirect
23. C₂²×D₄×D₅	C₂²	semidirect
24. C₂²×D₄×D₅	C₂²	semidirect
25. C₂³×D₂₀	C₂²	semidirect
26. C₂³×C₄×D₅	C₂²	semidirect
27. C₅×D₄²	C₂²	semidirect
28. C₂×C₅×#127	C₂²	semidirect
29. C₂×C₅×#121	C₂²	semidirect
30. C₂×C₅×#120	C₂²	semidirect
31. C₂×C₄×C₅×D₄	C₂²	semidirect
32. C₂×#4099	C₂²	semidirect
33. C₂×#4086	C₂²	semidirect
34. C₂×#4086	C₂²	semidirect
35. C₂×#4085	C₂²	semidirect
36. D₄×C₂²⋊D₅	C₂²	semidirect
37. C₂×#4084	C₂²	semidirect
38. C₂×#4083	C₂²	semidirect
39. C₂×#4083	C₂²	semidirect
40. C₂×D₄×Dic₅	C₂²	semidirect
41. C₂×#4076	C₂²	semidirect
42. C₂×C₄×C₂²⋊D₅	C₂²	semidirect
43. #66051	C₂²	semidirect
44. D₅×#127	C₂²	semidirect
45. #65943	C₂²	semidirect
46. D₅×#121	C₂²	semidirect
47. #65924	C₂²	semidirect
48. D₅×#120	C₂²	semidirect
49. D₄×D₂₀	C₂²	semidirect
50. C₄×D₄×D₅	C₂²	semidirect
51. C₂×#4041	C₂²	semidirect
52. C₂×#4039	C₂²	semidirect
53. C₂×D₅×C₄⋊C₄	C₂²	semidirect
54. C₂×#4030	C₂²	semidirect
55. C₂×#4028	C₂²	semidirect
56. C₂×#4028	C₂²	semidirect
57. C₂×#4027	C₂²	semidirect
58. C₂×D₅×C₂²⋊C₄	C₂²	semidirect
59. C₂×D₅×C₂²⋊C₄	C₂²	semidirect
60. C₂×#4020	C₂²	semidirect
61. C₂×C₄×D₂₀	C₂²	semidirect
62. C₂×C₄²×D₅	C₂²	semidirect
64. C₂⁵×C₅	C₂³	semidirect
69. C₂⁴×D₅	C₂³	semidirect
70. C₂⁴×D₅	C₂³	semidirect
71. C₂⁴×D₅	C₂³	semidirect
74. C₂²×C₅×D₄	C₂³	semidirect
75. C₂²×C₅×D₄	C₂³	semidirect
76. C₂²×C₅×D₄	C₂³	semidirect
77. C₂²×C₅×D₄	C₂³	semidirect
78. C₂³×C₄×C₅	C₂³	semidirect
81. C₂²×C₂²⋊D₅	C₂³	semidirect
82. C₂²×C₂²⋊D₅	C₂³	semidirect
83. C₂²×C₂²⋊D₅	C₂³	semidirect
84. C₂²×C₂²⋊D₅	C₂³	semidirect
85. C₂²×C₂²⋊D₅	C₂³	semidirect
86. C₂³×Dic₅	C₂³	semidirect
94. C₂×D₄×D₅	D₄	direct (N × H)
96. C₂×D₄×D₅	C₂³	semidirect
97. C₂×D₄×D₅	C₂³	semidirect
98. C₂×D₄×D₅	C₂³	semidirect
99. C₂×D₄×D₅	C₂³	semidirect
100. C₂×D₄×D₅	C₂³	semidirect
101. C₂×D₄×D₅	C₂³	semidirect
104. C₂²×D₂₀	C₂³	semidirect
105. C₂²×D₂₀	C₂³	semidirect
106. C₂²×D₂₀	C₂³	semidirect
107. C₂²×D₂₀	C₂³	semidirect
112. C₂²×C₄×D₅	C₂³	semidirect
113. C₂²×C₄×D₅	C₂³	semidirect
114. C₂²×C₄×D₅	C₂³	semidirect
115. C₅×#127	C₂³	semidirect
116. C₅×#121	C₂³	semidirect
117. C₅×#120	C₂³	semidirect
118. C₄×C₅×D₄	C₂³	semidirect
119. C₂×C₅×C₄⋊C₄	C₂³	semidirect
120. C₂×C₅×C₂²⋊C₄	C₂³	semidirect
121. C₂×C₅×C₂²⋊C₄	C₂³	semidirect
122. C₂×C₄²×C₅	C₂³	semidirect
123. #4099	C₂³	semidirect
124. C₂×C₂²⋊Dic₅	C₂³	semidirect
125. C₂×C₂²⋊Dic₅	C₂³	semidirect
126. #4086	C₂³	semidirect
127. #4086	C₂³	semidirect
128. #4085	C₂³	semidirect
129. #4084	C₂³	semidirect
130. #4083	C₂³	semidirect
131. #4083	C₂³	semidirect
132. D₄×Dic₅	C₂³	semidirect
133. #4076	C₂³	semidirect
134. C₄×C₂²⋊D₅	C₂³	semidirect
135. C₂×#685	C₂³	semidirect
136. C₂×#685	C₂³	semidirect
137. C₂×#685	C₂³	semidirect
138. C₂×C₄⋊Dic₅	C₂³	semidirect
139. C₂×#683	C₂³	semidirect
140. C₂×C₄×Dic₅	C₂³	semidirect
141. C₂×C₄×Dic₅	C₂³	semidirect
142. #4041	C₂³	semidirect
143. #4039	C₂³	semidirect
144. D₅×C₄⋊C₄	C₂³	semidirect
145. #4030	C₂³	semidirect
146. #4028	C₂³	semidirect
147. #4028	C₂³	semidirect
148. #4027	C₂³	semidirect
149. D₅×C₂²⋊C₄	C₂³	semidirect
150. D₅×C₂²⋊C₄	C₂³	semidirect
151. #4020	C₂³	semidirect
152. C₄×D₂₀	C₂³	semidirect
153. C₄²×D₅	C₂³	semidirect
161. C₂×D₄²	D₅	direct (N × H)
170. C₂⁴×C₅	C₂⁴	semidirect
183. C₂³×D₅	C₂×D₄	semidirect
189. C₂³×D₅	C₂⁴	semidirect
190. C₂³×D₅	C₂⁴	semidirect
195. C₂×C₅×D₄	C₂×D₄	semidirect
197. C₂×C₅×D₄	C₂⁴	semidirect
198. C₂×C₅×D₄	C₂⁴	semidirect
199. C₂×C₅×D₄	C₂⁴	semidirect
204. C₂²×C₄×C₅	C₂⁴	semidirect
210. C₂×C₂²⋊D₅	C₂×D₄	semidirect
212. C₂×C₂²⋊D₅	C₂⁴	semidirect
213. C₂×C₂²⋊D₅	C₂⁴	semidirect
214. C₂×C₂²⋊D₅	C₂⁴	semidirect
215. C₂×C₂²⋊D₅	C₂⁴	semidirect
220. C₂²×Dic₅	C₂⁴	semidirect
227. D₄×D₅	C₂×D₄	direct (N × H)
232. C₂×D₂₀	C₂×D₄	semidirect
234. C₂×D₂₀	C₂⁴	semidirect
235. C₂×D₂₀	C₂⁴	semidirect
236. C₂×D₂₀	C₂⁴	semidirect
242. C₂×C₄×D₅	C₂×D₄	semidirect
246. C₂×C₄×D₅	C₂⁴	semidirect
247. C₂×C₄×D₅	C₂⁴	semidirect
248. C₅×C₄⋊C₄	C₂⁴	semidirect
249. C₅×C₂²⋊C₄	C₂⁴	semidirect
250. C₅×C₂²⋊C₄	C₂⁴	semidirect
251. C₄²×C₅	C₂⁴	semidirect
252. C₂²⋊Dic₅	C₂⁴	semidirect
253. C₂²⋊Dic₅	C₂⁴	semidirect
254. #685	C₂⁴	semidirect
255. #685	C₂⁴	semidirect
256. #685	C₂⁴	semidirect
257. C₄⋊Dic₅	C₂⁴	semidirect
258. #683	C₂⁴	semidirect
259. C₄×Dic₅	C₂⁴	semidirect
260. C₄×Dic₅	C₂⁴	semidirect
273. C₂³×D₄	C₂×D₅	semidirect
280. D₄²	C₂×D₅	direct (N × H)
285. C₂×#127	C₂×D₅	semidirect
292. C₂×#121	C₂×D₅	semidirect
299. C₂×#120	C₂×D₅	semidirect
306. C₂×C₄×D₄	C₂×D₅	semidirect
318. C₂³×C₅	C₂²×D₄	semidirect
341. C₂²×D₅	C₂²×D₄	semidirect
342. C₂²×D₅	C₂²×D₄	semidirect
350. C₅×D₄	C₂²×D₄	semidirect
354. C₂×C₄×C₅	C₂²×D₄	semidirect
362. C₂²⋊D₅	C₂²×D₄	semidirect
366. C₂×Dic₅	C₂²×D₄	semidirect
373. D₂₀	C₂²×D₄	semidirect
378. C₄×D₅	C₂²×D₄	semidirect
386. C₂⁵	C₂²×D₅	semidirect
417. C₂²×D₄	C₂²×D₅	semidirect
418. C₂²×D₄	C₂²×D₅	semidirect
419. C₂²×D₄	C₂²×D₅	semidirect
420. C₂²×D₄	C₂²×D₅	semidirect
429. C₂³×C₄	C₂²×D₅	semidirect
433. #127	C₂²×D₅	semidirect
439. #121	C₂²×D₅	semidirect
445. #120	C₂²×D₅	semidirect
451. C₄×D₄	C₂²×D₅	semidirect
455. C₂×C₄⋊C₄	C₂²×D₅	semidirect
463. C₂×C₂²⋊C₄	C₂²×D₅	semidirect
464. C₂×C₂²⋊C₄	C₂²×D₅	semidirect
468. C₂×C₄²	C₂²×D₅	semidirect
477. C₂²×C₅	C₂³×D₄	semidirect
490. C₂×D₅	D₄²	direct (N × H)
492. C₂×D₅	C₂³×D₄	semidirect
496. C₄×C₅	C₂³×D₄	semidirect
499. Dic₅	C₂³×D₄	semidirect
524. C₂⁴	C₂³×D₅	semidirect
556. C₂×D₄	D₄×D₅	direct (N × H)
558. C₂×D₄	C₂³×D₅	semidirect
559. C₂×D₄	C₂³×D₅	semidirect
560. C₂×D₄	C₂³×D₅	semidirect
581. C₂²×C₄	C₂³×D₅	semidirect
584. C₄⋊C₄	C₂³×D₅	semidirect
590. C₂²⋊C₄	C₂³×D₅	semidirect
591. C₂²⋊C₄	C₂³×D₅	semidirect
594. C₄²	C₂³×D₅	semidirect
597. C₂×C₅	C₂×D₄²	semidirect
602. D₅	C₂×D₄²	direct (N × H)
635. C₂³	C₂×D₄×D₅	semidirect
651. D₄	C₂×D₄×D₅	direct (N × H)
667. C₂×C₄	C₂×D₄×D₅	semidirect
671. C₅	C₂²×D₄²	semidirect
694. C₂²	C₂²×D₄×D₅	semidirect
702. C₄	C₂²×D₄×D₅	semidirect
708. C₂	D₄²×D₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×D₄×D₅	2
C₂×C₅×D₄²	2
C₂×D₄×C₂²⋊D₅	2
D₄²×D₅	2
C₂×#66051	2
C₂×D₅×#127	2
C₂×#65943	2
C₂×D₅×#121	2
C₂×#65924	2
C₂×D₅×#120	2
C₂×D₄×D₂₀	2
C₂×C₄×D₄×D₅	2
C₂²×D₄²	5

Subgroups — C2×D42×D5 #13006206

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₄²×D₅ #13006206