Subgroups — C₂²×#65824 #13006222

Order 1280.

14462 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₂²⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×#709	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂³×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#4099	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×#4075	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#4076	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₄×C₂²⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#65824	C₂	1	48	yes	maximal, direct product factor
9	C₂²×#4029	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#4030	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×#4030	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#4028	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×D₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×#4031	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#4024	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#4027	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂⁶×C₅	C₂²	1	1	yes	characteristic
18	C₂⁵×D₅	C₂²	1	1	yes	characteristic
19	C₂⁴×C₄×C₅	C₂²	1	1	yes	characteristic, complemented
20	C₂⁴×C₄×C₅	C₂²	1	1	yes	characteristic, complemented
21	C₂³×C₂²⋊D₅	—	2	16	no	—
22	C₂³×C₂²⋊D₅	C₂²	1	1	yes	characteristic
23	C₂³×C₂²⋊D₅	C₂²	1	1	yes	characteristic
24	C₂³×C₂²⋊D₅	C₂²	1	1	yes	characteristic
25	C₂³×C₂²⋊D₅	C₂²	1	1	yes	characteristic
26	C₂³×C₂²⋊D₅	C₂²	1	1	yes	characteristic
27	C₂³×C₂²⋊D₅	C₂²	1	24	yes	complemented
28	C₂³×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
29	C₂³×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
30	C₂⁴×Dic₅	C₂²	1	1	yes	characteristic
31	C₂²×#709	—	2	16	no	—
32	C₂²×#709	C₂²	1	24	yes	complemented
33	C₂³×D₂₀	C₂²	1	1	yes	characteristic, complemented
34	C₂³×D₂₀	C₂²	1	1	yes	characteristic, complemented
35	C₂³×C₄×D₅	C₂²	1	1	yes	characteristic, complemented
36	C₂³×C₄×D₅	C₂²	1	1	yes	characteristic, complemented
37	C₂³×C₄×D₅	C₂²	1	1	yes	characteristic, complemented
38	C₂³×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
39	C₂²×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
40	C₂²×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
41	C₂²×C₅×C₂²⋊C₄	C₂²	1	24	yes	complemented
42	C₂²×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
43	C₂²×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
44	C₂×#4099	C₂²	1	24	yes	complemented
45	C₂²×C₂²⋊Dic₅	C₂²	1	1	yes	characteristic
46	C₂²×C₂²⋊Dic₅	C₂²	1	1	yes	characteristic, complemented
47	C₂²×C₂²⋊Dic₅	C₂²	1	1	yes	characteristic, complemented
48	C₂×#4076	C₂²	1	24	yes	complemented
49	C₂×#4075	C₂²	1	24	yes	complemented
50	C₂×C₄×C₂²⋊D₅	C₂²	1	24	yes	complemented
51	C₂²×#685	C₂²	1	1	yes	characteristic, complemented
52	C₂²×#685	C₂²	1	1	yes	characteristic, complemented
53	C₂²×#685	C₂²	1	1	yes	characteristic, complemented
54	C₂²×#685	C₂²	1	1	yes	characteristic, complemented
55	C₂²×#685	C₂²	1	1	yes	characteristic, complemented
56	C₂²×C₄⋊Dic₅	C₂²	1	1	yes	characteristic, complemented
57	C₂²×#683	C₂²	1	1	yes	characteristic, complemented
58	C₂²×#683	C₂²	1	1	yes	characteristic, complemented
59	C₂²×#683	C₂²	1	1	yes	characteristic, complemented
60	C₂²×C₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
61	C₂×#4031	C₂²	1	24	yes	complemented
62	#65824	C₂²	1	256	yes	direct product factor
63	C₂×#4030	C₂²	1	24	yes	complemented
64	C₂×#4030	C₂²	1	24	yes	complemented
65	C₂×#4029	C₂²	1	24	yes	complemented
66	C₂×#4028	C₂²	1	24	yes	complemented
67	C₂×#4027	C₂²	1	24	yes	complemented
68	C₂×D₅×C₂²⋊C₄	C₂²	1	24	yes	complemented
69	C₂×#4024	C₂²	1	24	yes	complemented
70	C₂²×#546	—	5	1	no	maximal, Sylow
71	C₂⁵×C₅	—	2	8	no	—
72	C₂⁵×C₅	—	2	8	no	—
73	C₂⁵×C₅	—	4	4	no	—
74	C₂⁵×C₅	C₂³	1	1	yes	characteristic
75	C₂⁵×C₅	C₂³	1	12	yes	—
76	C₂⁵×C₅	C₂³	1	1	yes	characteristic
77	C₂⁵×C₅	C₂³	1	1	yes	characteristic
78	C₂⁴×D₅	—	2	8	no	—
79	C₂⁴×D₅	—	2	8	no	—
80	C₂⁴×D₅	—	4	4	no	—
81	C₂⁴×D₅	C₂³	1	1	yes	characteristic
82	C₂⁴×D₅	C₂³	1	1	yes	characteristic
83	C₂⁴×D₅	C₂³	1	12	yes	—
84	C₂⁴×D₅	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₅	—	2	8	no	—
86	C₂³×C₄×C₅	—	4	4	no	—
87	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₅	C₂³	1	12	yes	complemented
92	C₂³×C₄×C₅	C₂³	1	12	yes	complemented
93	C₂²×C₂²⋊D₅	—	2	8	no	—
94	C₂²×C₂²⋊D₅	—	2	8	no	—
95	C₂²×C₂²⋊D₅	—	2	8	no	—
96	C₂²×C₂²⋊D₅	—	2	8	no	—
97	C₂²×C₂²⋊D₅	—	2	192	no	—
98	C₂²×C₂²⋊D₅	—	2	8	no	—
99	C₂²×C₂²⋊D₅	—	4	4	no	—
100	C₂²×C₂²⋊D₅	D₄	1	16	yes	complemented
101	C₂²×C₂²⋊D₅	C₂³	1	12	yes	—
102	C₂²×C₂²⋊D₅	C₂³	1	12	yes	—
103	C₂²×C₂²⋊D₅	C₂³	1	12	yes	—
104	C₂²×C₂²⋊D₅	C₂³	1	12	yes	—
105	C₂²×C₂²⋊D₅	C₂³	1	12	yes	—
106	C₂²×C₂²⋊D₅	C₂³	1	64	yes	complemented
107	C₂²×C₂²⋊D₅	C₂³	1	12	yes	complemented
108	C₂²×C₂²⋊D₅	C₂³	1	12	yes	complemented
109	C₂³×Dic₅	—	2	8	no	—
110	C₂³×Dic₅	C₂³	1	12	yes	—
111	C₂³×Dic₅	C₂³	1	1	yes	characteristic
112	C₂³×Dic₅	C₂³	1	1	yes	characteristic
113	C₂³×Dic₅	C₂³	1	1	yes	characteristic
114	C₂³×Dic₅	C₂³	1	1	yes	characteristic
115	C₂³×Dic₅	C₂³	1	1	yes	characteristic
116	C₂×#709	—	2	192	no	—
117	C₂×#709	C₂³	1	64	yes	complemented
118	C₂²×D₂₀	—	2	8	no	—
119	C₂²×D₂₀	—	4	4	no	—
120	C₂²×D₂₀	C₂³	1	12	yes	complemented
121	C₂²×D₂₀	C₂³	1	12	yes	complemented
122	C₂²×C₄×D₅	—	2	8	no	—
123	C₂²×C₄×D₅	—	2	8	no	—
124	C₂²×C₄×D₅	—	4	4	no	—
125	C₂²×C₄×D₅	C₂³	1	12	yes	complemented
126	C₂²×C₄×D₅	C₂³	1	12	yes	complemented
127	C₂²×C₄×D₅	C₂³	1	12	yes	complemented
128	C₂²×Dic₁₀	—	2	8	no	—
129	C₂²×Dic₁₀	C₂³	1	12	yes	complemented
130	C₂×C₅×C₂²⋊C₄	C₂³	1	12	yes	—
131	C₂×C₅×C₂²⋊C₄	C₂³	1	12	yes	—
132	C₂×C₅×C₂²⋊C₄	C₂³	1	64	yes	complemented
133	C₂×C₅×C₂²⋊C₄	C₂³	1	12	yes	complemented
134	C₂×C₅×C₂²⋊C₄	C₂³	1	12	yes	complemented
135	#4099	C₂³	1	64	yes	complemented
136	C₂×C₂²⋊Dic₅	C₂³	1	12	yes	—
137	C₂×C₂²⋊Dic₅	C₂³	1	12	yes	complemented
138	C₂×C₂²⋊Dic₅	C₂³	1	12	yes	complemented
139	#4076	C₂³	1	64	yes	complemented
140	#4075	C₂³	1	64	yes	complemented
141	C₄×C₂²⋊D₅	C₂³	1	64	yes	complemented
142	C₂×#685	C₂³	1	12	yes	complemented
143	C₂×#685	C₂³	1	12	yes	complemented
144	C₂×#685	C₂³	1	12	yes	complemented
145	C₂×#685	C₂³	1	12	yes	complemented
146	C₂×#685	C₂³	1	12	yes	complemented
147	C₂×C₄⋊Dic₅	C₂³	1	12	yes	complemented
148	C₂×#683	C₂³	1	12	yes	complemented
149	C₂×#683	C₂³	1	12	yes	complemented
150	C₂×#683	C₂³	1	12	yes	complemented
151	C₂×C₄×Dic₅	C₂³	1	12	yes	complemented
152	#4031	C₂³	1	64	yes	complemented
153	#4030	C₂³	1	64	yes	complemented
154	#4030	C₂³	1	64	yes	complemented
155	#4029	C₂³	1	64	yes	complemented
156	#4028	C₂³	1	64	yes	complemented
157	#4027	C₂³	1	64	yes	complemented
158	D₅×C₂²⋊C₄	C₂³	1	64	yes	complemented
159	#4024	C₂³	1	64	yes	complemented
160	C₂³×#41	—	5	1	no	—
161	C₂⁴×D₄	—	5	1	no	—
162	C₂×#546	—	5	48	no	—
163	C₂²×#124	—	5	1	no	—
164	C₂²×#123	—	5	1	no	—
165	C₂²×#123	—	5	1	no	—
166	C₂²×C₂²⋊Q₈	—	5	1	no	—
167	C₂²×#121	—	5	1	no	—
168	C₂²×#121	—	5	1	no	—
169	C₂²×#121	—	5	1	no	—
170	C₂²×#120	—	5	1	no	—
171	C₂²×#120	—	5	1	no	—
172	C₂²×C₄×D₄	—	5	1	no	—
173	C₂²×C₄×D₄	—	5	1	no	—
174	C₂³×C₂²⋊C₄	—	5	1	no	—
175	C₂³×C₂²⋊C₄	D₅	1	1	yes	characteristic, complemented
176	C₂⁴×C₅	—	2	4	no	—
177	C₂⁴×C₅	—	2	4	no	—
178	C₂⁴×C₅	—	2	4	no	—
179	C₂⁴×C₅	—	2	4	no	—
180	C₂⁴×C₅	—	2	48	no	—
181	C₂⁴×C₅	—	2	4	no	—
182	C₂⁴×C₅	—	2	4	no	—
183	C₂⁴×C₅	—	2	48	no	—
184	C₂⁴×C₅	—	2	4	no	—
185	C₂⁴×C₅	—	4	24	no	—
186	C₂⁴×C₅	—	4	64	no	—
187	C₂⁴×C₅	C₂×D₄	1	8	yes	—
188	C₂⁴×C₅	#41	1	8	yes	complemented
189	C₂⁴×C₅	C₂⁴	1	6	yes	—
190	C₂⁴×C₅	C₂⁴	1	16	yes	—
191	C₂⁴×C₅	C₂⁴	1	6	yes	—
192	C₂⁴×C₅	C₂⁴	1	6	yes	—
193	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
194	C₂³×D₅	—	2	4	no	—
195	C₂³×D₅	—	2	4	no	—
196	C₂³×D₅	—	2	4	no	—
197	C₂³×D₅	—	2	4	no	—
198	C₂³×D₅	—	2	4	no	—
199	C₂³×D₅	—	2	4	no	—
200	C₂³×D₅	—	2	48	no	—
201	C₂³×D₅	—	2	4	no	—
202	C₂³×D₅	—	2	4	no	—
203	C₂³×D₅	—	2	48	no	—
204	C₂³×D₅	—	4	24	no	—
205	C₂³×D₅	—	4	64	no	—
206	C₂³×D₅	C₂×D₄	1	8	yes	—
207	C₂³×D₅	C₂⁴	1	6	yes	—
208	C₂³×D₅	C₂⁴	1	6	yes	—
209	C₂³×D₅	C₂⁴	1	16	yes	—
210	C₂³×D₅	C₂⁴	1	6	yes	—
211	C₂²×C₄×C₅	—	2	4	no	—
212	C₂²×C₄×C₅	—	2	4	no	—
213	C₂²×C₄×C₅	—	2	48	no	—
214	C₂²×C₄×C₅	—	2	4	no	—
215	C₂²×C₄×C₅	—	2	4	no	—
216	C₂²×C₄×C₅	—	4	24	no	—
217	C₂²×C₄×C₅	C₂⁴	1	6	yes	—
218	C₂²×C₄×C₅	C₂⁴	1	6	yes	—
219	C₂²×C₄×C₅	C₂⁴	1	6	yes	—
220	C₂²×C₄×C₅	C₂⁴	1	6	yes	—
221	C₂²×C₄×C₅	C₂⁴	1	16	yes	complemented
222	C₂²×C₄×C₅	C₂⁴	1	16	yes	complemented
223	C₂×C₂²⋊D₅	—	2	48	no	—
224	C₂×C₂²⋊D₅	—	2	48	no	—
225	C₂×C₂²⋊D₅	—	2	48	no	—
226	C₂×C₂²⋊D₅	—	2	48	no	—
227	C₂×C₂²⋊D₅	—	2	256	no	—
228	C₂×C₂²⋊D₅	—	2	48	no	—
229	C₂×C₂²⋊D₅	—	4	24	no	—
230	C₂×C₂²⋊D₅	C₂×D₄	1	96	yes	complemented
231	C₂×C₂²⋊D₅	C₂⁴	1	16	yes	—
232	C₂×C₂²⋊D₅	C₂⁴	1	16	yes	—
233	C₂×C₂²⋊D₅	C₂⁴	1	16	yes	—
234	C₂×C₂²⋊D₅	C₂⁴	1	16	yes	—
235	C₂×C₂²⋊D₅	C₂⁴	1	16	yes	—
236	C₂×C₂²⋊D₅	C₂⁴	1	16	yes	complemented
237	C₂×C₂²⋊D₅	C₂⁴	1	16	yes	complemented
238	C₂²×Dic₅	—	2	4	no	—
239	C₂²×Dic₅	—	2	4	no	—
240	C₂²×Dic₅	—	2	4	no	—
241	C₂²×Dic₅	—	2	4	no	—
242	C₂²×Dic₅	—	2	48	no	—
243	C₂²×Dic₅	C₂×D₄	1	8	yes	—
244	C₂²×Dic₅	C₂⁴	1	6	yes	—
245	C₂²×Dic₅	C₂⁴	1	6	yes	—
246	C₂²×Dic₅	C₂⁴	1	6	yes	—
247	C₂²×Dic₅	C₂⁴	1	6	yes	—
248	C₂²×Dic₅	C₂⁴	1	16	yes	—
249	C₂²×Dic₅	C₂⁴	1	6	yes	—
250	#709	—	2	256	no	—
251	C₂×D₂₀	—	2	48	no	—
252	C₂×D₂₀	—	4	24	no	—
253	C₂×D₂₀	C₂⁴	1	16	yes	complemented
254	C₂×D₂₀	C₂⁴	1	16	yes	complemented
255	C₂×C₄×D₅	—	2	48	no	—
256	C₂×C₄×D₅	—	2	48	no	—
257	C₂×C₄×D₅	—	4	24	no	—
258	C₂×C₄×D₅	C₂⁴	1	16	yes	complemented
259	C₂×C₄×D₅	C₂⁴	1	16	yes	complemented
260	C₂×C₄×D₅	C₂⁴	1	16	yes	complemented
261	C₂×Dic₁₀	—	2	48	no	—
262	C₂×Dic₁₀	C₂⁴	1	16	yes	complemented
263	C₅×C₂²⋊C₄	C₂⁴	1	16	yes	—
264	C₅×C₂²⋊C₄	C₂⁴	1	16	yes	—
265	C₅×C₂²⋊C₄	C₂⁴	1	16	yes	complemented
266	C₅×C₂²⋊C₄	C₂⁴	1	16	yes	complemented
267	C₂²⋊Dic₅	C₂⁴	1	16	yes	—
268	C₂²⋊Dic₅	C₂⁴	1	16	yes	complemented
269	C₂²⋊Dic₅	C₂⁴	1	16	yes	complemented
270	#685	C₂⁴	1	16	yes	complemented
271	#685	C₂⁴	1	16	yes	complemented
272	#685	C₂⁴	1	16	yes	complemented
273	#685	C₂⁴	1	16	yes	complemented
274	#685	C₂⁴	1	16	yes	complemented
275	C₄⋊Dic₅	C₂⁴	1	16	yes	complemented
276	#683	C₂⁴	1	16	yes	complemented
277	#683	C₂⁴	1	16	yes	complemented
278	#683	C₂⁴	1	16	yes	complemented
279	C₄×Dic₅	C₂⁴	1	16	yes	complemented
280	C₂⁶	—	5	1	no	—
281	C₂⁶	C₂×D₅	1	1	yes	characteristic
282	C₂²×#41	—	5	24	no	—
283	C₂²×#41	—	10	16	no	—
284	C₂³×Q₈	—	5	1	no	—
285	C₂³×D₄	—	5	1	no	—
286	C₂³×D₄	—	5	1	no	—
287	C₂³×D₄	—	5	1	no	—
288	C₂³×D₄	—	5	1	no	—
289	C₂³×D₄	—	5	24	no	—
290	C₂³×D₄	—	5	1	no	—
291	C₂³×D₄	—	5	1	no	—
292	C₂³×D₄	—	5	1	no	—
293	C₂³×D₄	—	5	1	no	—
294	C₂³×D₄	—	5	1	no	—
295	C₂³×D₄	—	10	16	no	—
296	C₂⁴×C₄	—	5	1	no	—
297	C₂⁴×C₄	—	5	1	no	—
298	C₂⁴×C₄	—	5	1	no	—
299	C₂⁴×C₄	—	5	1	no	—
300	C₂⁴×C₄	C₂×D₅	1	1	yes	characteristic, complemented
301	C₂⁴×C₄	C₂×D₅	1	1	yes	characteristic, complemented
302	#546	—	5	256	no	—
303	C₂×#124	—	5	24	no	—
304	C₂×#123	—	5	24	no	—
305	C₂×#123	—	5	24	no	—
306	C₂×C₂²⋊Q₈	—	5	24	no	—
307	C₂×#121	—	5	24	no	—
308	C₂×#121	—	5	24	no	—
309	C₂×#121	—	5	24	no	—
310	C₂×#120	—	5	24	no	—
311	C₂×#120	—	5	24	no	—
312	C₂×C₄×D₄	—	5	24	no	—
313	C₂×C₄×D₄	—	5	24	no	—
314	C₂²×C₄⋊C₄	—	5	1	no	—
315	C₂²×C₄⋊C₄	—	5	1	no	—
316	C₂²×C₄⋊C₄	—	5	1	no	—
317	C₂²×C₄⋊C₄	—	5	1	no	—
318	C₂²×C₂²⋊C₄	—	5	1	no	—
319	C₂²×C₂²⋊C₄	—	5	1	no	—
320	C₂²×C₂²⋊C₄	—	5	1	no	—
321	C₂²×C₂²⋊C₄	—	5	1	no	—
322	C₂²×C₂²⋊C₄	—	5	1	no	—
323	C₂²×C₂²⋊C₄	—	5	1	no	—
324	C₂²×C₂²⋊C₄	—	5	1	no	—
325	C₂²×C₂²⋊C₄	—	5	1	no	—
326	C₂²×C₂²⋊C₄	—	5	24	no	—
327	C₂²×C₂²⋊C₄	C₂×D₅	1	1	yes	characteristic
328	C₂²×C₂²⋊C₄	C₂×D₅	1	1	yes	characteristic
329	C₂²×C₂²⋊C₄	C₂×D₅	1	24	yes	complemented
330	C₂²×C₂²⋊C₄	C₂×D₅	1	1	yes	characteristic, complemented
331	C₂²×C₂²⋊C₄	C₂×D₅	1	1	yes	characteristic, complemented
332	C₂²×C₄²	—	5	1	no	—
333	C₂³×C₅	—	2	32	no	—
334	C₂³×C₅	—	2	32	no	—
335	C₂³×C₅	—	2	12	no	—
336	C₂³×C₅	—	2	12	no	—
337	C₂³×C₅	—	2	12	no	—
338	C₂³×C₅	—	2	12	no	—
339	C₂³×C₅	—	2	32	no	—
340	C₂³×C₅	—	2	12	no	—
341	C₂³×C₅	—	2	12	no	—
342	C₂³×C₅	—	2	32	no	—
343	C₂³×C₅	—	2	12	no	—
344	C₂³×C₅	—	4	16	no	—
345	C₂³×C₅	—	4	192	no	—
346	C₂³×C₅	—	4	16	no	—
347	C₂³×C₅	C₂²×D₄	1	24	yes	—
348	C₂³×C₅	C₂²×D₄	1	4	yes	—
349	C₂³×C₅	C₂×#41	1	4	yes	—
350	C₂³×C₅	C₂×#41	1	24	yes	complemented
351	C₂³×C₅	H(5,𝔽₂)	1	4	yes	—
352	C₂³×C₅	C₂⁵	1	4	yes	—
353	C₂³×C₅	C₂⁵	1	4	yes	—
354	C₂³×C₅	C₂⁵	1	4	yes	—
355	C₂³×C₅	C₂⁵	1	3	yes	—
356	C₂²×D₅	—	2	32	no	—
357	C₂²×D₅	—	2	12	no	—
358	C₂²×D₅	—	2	12	no	—
359	C₂²×D₅	—	2	12	no	—
360	C₂²×D₅	—	2	12	no	—
361	C₂²×D₅	—	2	12	no	—
362	C₂²×D₅	—	2	12	no	—
363	C₂²×D₅	—	2	32	no	—
364	C₂²×D₅	—	2	12	no	—
365	C₂²×D₅	—	2	12	no	—
366	C₂²×D₅	—	2	32	no	—
367	C₂²×D₅	—	4	16	no	—
368	C₂²×D₅	—	4	192	no	—
369	C₂²×D₅	—	4	16	no	—
370	C₂²×D₅	—	4	16	no	—
371	C₂²×D₅	C₂²×D₄	1	24	yes	—
372	C₂²×D₅	C₂⁵	1	4	yes	—
373	C₂²×D₅	C₂⁵	1	4	yes	—
374	C₂²×D₅	C₂⁵	1	4	yes	—
375	C₂×C₄×C₅	—	2	12	no	—
376	C₂×C₄×C₅	—	2	12	no	—
377	C₂×C₄×C₅	—	2	32	no	—
378	C₂×C₄×C₅	—	2	12	no	—
379	C₂×C₄×C₅	—	2	12	no	—
380	C₂×C₄×C₅	—	4	16	no	—
381	C₂×C₄×C₅	C₂⁵	1	4	yes	—
382	C₂×C₄×C₅	C₂⁵	1	4	yes	—
383	C₂×C₄×C₅	C₂⁵	1	4	yes	—
384	C₂×C₄×C₅	C₂⁵	1	4	yes	—
385	C₂²⋊D₅	—	2	32	no	—
386	C₂²⋊D₅	—	2	32	no	—
387	C₂²⋊D₅	—	2	32	no	—
388	C₂²⋊D₅	—	2	32	no	—
389	C₂²⋊D₅	—	2	32	no	—
390	C₂²⋊D₅	—	4	16	no	—
391	C₂²⋊D₅	C₂²×D₄	1	64	yes	complemented
392	C₂×Dic₅	—	2	12	no	—
393	C₂×Dic₅	—	2	12	no	—
394	C₂×Dic₅	—	2	12	no	—
395	C₂×Dic₅	—	2	12	no	—
396	C₂×Dic₅	—	2	32	no	—
397	C₂×Dic₅	C₂²×D₄	1	24	yes	—
398	C₂×Dic₅	C₂⁵	1	4	yes	—
399	C₂×Dic₅	C₂⁵	1	4	yes	—
400	C₂×Dic₅	C₂⁵	1	4	yes	—
401	C₂×Dic₅	C₂⁵	1	4	yes	—
402	C₂×Dic₅	C₂⁵	1	4	yes	—
403	D₂₀	—	2	32	no	—
404	D₂₀	—	4	16	no	—
405	C₄×D₅	—	2	32	no	—
406	C₄×D₅	—	2	32	no	—
407	C₄×D₅	—	4	16	no	—
408	Dic₁₀	—	2	32	no	—
409	C₂⁵	—	2	8	no	—
410	C₂⁵	—	2	8	no	—
411	C₂⁵	—	4	4	no	—
412	C₂⁵	—	5	1	no	—
413	C₂⁵	—	5	1	no	—
414	C₂⁵	—	5	1	no	—
415	C₂⁵	—	5	12	no	—
416	C₂⁵	—	10	8	no	—
417	C₂⁵	—	10	8	no	—
418	C₂⁵	—	20	4	no	—
419	C₂⁵	C₂²×D₅	1	1	yes	characteristic
420	C₂⁵	C₂²×D₅	1	12	yes	—
421	C₂⁵	C₂²×D₅	1	1	yes	characteristic
422	C₂⁵	C₂²×D₅	1	1	yes	characteristic
423	C₂×#41	—	5	64	no	—
424	C₂×#41	—	10	192	no	—
425	C₂²×Q₈	—	5	12	no	—
426	C₂²×Q₈	—	10	8	no	—
427	C₂²×D₄	—	5	16	no	—
428	C₂²×D₄	—	5	12	no	—
429	C₂²×D₄	—	5	12	no	—
430	C₂²×D₄	—	5	12	no	—
431	C₂²×D₄	—	5	12	no	—
432	C₂²×D₄	—	5	12	no	—
433	C₂²×D₄	—	5	12	no	—
434	C₂²×D₄	—	5	64	no	—
435	C₂²×D₄	—	5	12	no	—
436	C₂²×D₄	—	5	12	no	—
437	C₂²×D₄	—	5	12	no	—
438	C₂²×D₄	—	10	8	no	—
439	C₂²×D₄	—	10	8	no	—
440	C₂²×D₄	—	10	192	no	—
441	C₂²×D₄	—	10	8	no	—
442	C₂²×D₄	—	10	8	no	—
443	C₂²×D₄	—	10	8	no	—
444	C₂²×D₄	—	10	8	no	—
445	C₂²×D₄	—	20	4	no	—
446	C₂²×D₄	—	20	4	no	—
447	C₂³×C₄	—	2	8	no	—
448	C₂³×C₄	—	4	4	no	—
449	C₂³×C₄	—	5	1	no	—
450	C₂³×C₄	—	5	12	no	—
451	C₂³×C₄	—	5	1	no	—
452	C₂³×C₄	—	5	1	no	—
453	C₂³×C₄	—	5	1	no	—
454	C₂³×C₄	—	5	1	no	—
455	C₂³×C₄	—	5	12	no	—
456	C₂³×C₄	—	5	12	no	—
457	C₂³×C₄	—	5	12	no	—
458	C₂³×C₄	—	10	8	no	—
459	C₂³×C₄	—	10	8	no	—
460	C₂³×C₄	—	10	8	no	—
461	C₂³×C₄	—	20	4	no	—
462	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
463	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
464	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
465	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
466	C₂³×C₄	C₂²×D₅	1	12	yes	complemented
467	C₂³×C₄	C₂²×D₅	1	12	yes	complemented
468	#124	—	5	64	no	—
469	#123	—	5	64	no	—
470	#123	—	5	64	no	—
471	C₂²⋊Q₈	—	5	64	no	—
472	#121	—	5	64	no	—
473	#121	—	5	64	no	—
474	#121	—	5	64	no	—
475	#120	—	5	64	no	—
476	#120	—	5	64	no	—
477	C₄×D₄	—	5	64	no	—
478	C₄×D₄	—	5	64	no	—
479	C₂×C₄⋊C₄	—	5	12	no	—
480	C₂×C₄⋊C₄	—	5	12	no	—
481	C₂×C₄⋊C₄	—	5	12	no	—
482	C₂×C₄⋊C₄	—	5	12	no	—
483	C₂×C₂²⋊C₄	—	5	12	no	—
484	C₂×C₂²⋊C₄	—	5	12	no	—
485	C₂×C₂²⋊C₄	—	5	12	no	—
486	C₂×C₂²⋊C₄	—	5	12	no	—
487	C₂×C₂²⋊C₄	—	5	12	no	—
488	C₂×C₂²⋊C₄	—	5	12	no	—
489	C₂×C₂²⋊C₄	—	5	12	no	—
490	C₂×C₂²⋊C₄	—	5	12	no	—
491	C₂×C₂²⋊C₄	—	5	64	no	—
492	C₂×C₂²⋊C₄	C₂²×D₅	1	12	yes	—
493	C₂×C₂²⋊C₄	C₂²×D₅	1	12	yes	—
494	C₂×C₂²⋊C₄	C₂²×D₅	1	64	yes	complemented
495	C₂×C₂²⋊C₄	C₂²×D₅	1	12	yes	complemented
496	C₂×C₂²⋊C₄	C₂²×D₅	1	12	yes	complemented
497	C₂×C₄²	—	5	12	no	—
498	C₂²×C₅	—	2	4	no	—
499	C₂²×C₅	—	2	4	no	—
500	C₂²×C₅	—	2	4	no	—
501	C₂²×C₅	—	2	4	no	—
502	C₂²×C₅	—	2	48	no	—
503	C₂²×C₅	—	2	48	no	—
504	C₂²×C₅	—	2	4	no	—
505	C₂²×C₅	—	2	4	no	—
506	C₂²×C₅	—	2	4	no	—
507	C₂²×C₅	—	4	64	no	—
508	C₂²×C₅	—	4	24	no	—
509	C₂²×C₅	#546	1	16	yes	complemented
510	C₂²×C₅	C₂³×D₄	1	8	yes	—
511	C₂²×C₅	C₂³×D₄	1	6	yes	—
512	C₂²×C₅	C₂²×#41	1	6	yes	—
513	C₂²×C₅	C₂²×#41	1	8	yes	complemented
514	C₂²×C₅	C₂×H(5,𝔽₂)	1	6	yes	—
515	C₂²×C₅	C₂⁶	1	1	yes	characteristic
516	C₂×D₅	—	2	4	no	—
517	C₂×D₅	—	2	4	no	—
518	C₂×D₅	—	2	48	no	—
519	C₂×D₅	—	2	4	no	—
520	C₂×D₅	—	2	4	no	—
521	C₂×D₅	—	2	4	no	—
522	C₂×D₅	—	2	4	no	—
523	C₂×D₅	—	2	4	no	—
524	C₂×D₅	—	2	4	no	—
525	C₂×D₅	—	4	64	no	—
526	C₂×D₅	—	4	24	no	—
527	C₂×D₅	—	4	24	no	—
528	C₂×D₅	C₂³×D₄	1	8	yes	—
529	C₄×C₅	—	2	4	no	—
530	C₄×C₅	—	2	4	no	—
531	C₄×C₅	—	2	4	no	—
532	C₄×C₅	—	2	4	no	—
533	Dic₅	—	2	4	no	—
534	Dic₅	—	2	4	no	—
535	Dic₅	—	2	4	no	—
536	Dic₅	—	2	4	no	—
537	Dic₅	C₂³×D₄	1	8	yes	—
538	C₂⁴	—	2	4	no	—
539	C₂⁴	—	2	4	no	—
540	C₂⁴	—	2	4	no	—
541	C₂⁴	—	2	4	no	—
542	C₂⁴	—	2	4	no	—
543	C₂⁴	—	2	48	no	—
544	C₂⁴	—	2	48	no	—
545	C₂⁴	—	2	4	no	—
546	C₂⁴	—	2	4	no	—
547	C₂⁴	—	4	24	no	—
548	C₂⁴	—	4	64	no	—
549	C₂⁴	—	5	8	no	—
550	C₂⁴	—	5	6	no	—
551	C₂⁴	—	5	6	no	—
552	C₂⁴	—	5	6	no	—
553	C₂⁴	—	5	16	no	—
554	C₂⁴	—	10	48	no	—
555	C₂⁴	—	10	4	no	—
556	C₂⁴	—	10	4	no	—
557	C₂⁴	—	10	4	no	—
558	C₂⁴	—	10	4	no	—
559	C₂⁴	—	10	48	no	—
560	C₂⁴	—	10	4	no	—
561	C₂⁴	—	10	4	no	—
562	C₂⁴	—	10	4	no	—
563	C₂⁴	—	10	4	no	—
564	C₂⁴	—	20	24	no	—
565	C₂⁴	—	20	64	no	—
566	C₂⁴	#709	1	8	yes	complemented
567	C₂⁴	D₄×D₅	1	8	yes	—
568	C₂⁴	C₂³×D₅	1	6	yes	—
569	C₂⁴	C₂³×D₅	1	16	yes	—
570	C₂⁴	C₂³×D₅	1	6	yes	—
571	C₂⁴	C₂³×D₅	1	6	yes	—
572	C₂⁴	C₂³×D₅	1	1	yes	characteristic
573	#41	—	10	256	no	—
574	C₂×Q₈	—	5	16	no	—
575	C₂×Q₈	—	10	48	no	—
576	C₂×D₄	—	5	96	no	—
577	C₂×D₄	—	5	16	no	—
578	C₂×D₄	—	5	16	no	—
579	C₂×D₄	—	5	16	no	—
580	C₂×D₄	—	5	16	no	—
581	C₂×D₄	—	5	16	no	—
582	C₂×D₄	—	5	16	no	—
583	C₂×D₄	—	5	16	no	—
584	C₂×D₄	—	5	16	no	—
585	C₂×D₄	—	5	16	no	—
586	C₂×D₄	—	10	48	no	—
587	C₂×D₄	—	10	48	no	—
588	C₂×D₄	—	10	256	no	—
589	C₂×D₄	—	10	48	no	—
590	C₂×D₄	—	10	48	no	—
591	C₂×D₄	—	10	48	no	—
592	C₂×D₄	—	10	48	no	—
593	C₂×D₄	—	20	24	no	—
594	C₂×D₄	—	20	24	no	—
595	C₂²×C₄	—	2	4	no	—
596	C₂²×C₄	—	2	4	no	—
597	C₂²×C₄	—	2	48	no	—
598	C₂²×C₄	—	2	4	no	—
599	C₂²×C₄	—	2	4	no	—
600	C₂²×C₄	—	4	24	no	—
601	C₂²×C₄	—	5	8	no	—
602	C₂²×C₄	—	5	6	no	—
603	C₂²×C₄	—	5	6	no	—
604	C₂²×C₄	—	5	6	no	—
605	C₂²×C₄	—	5	6	no	—
606	C₂²×C₄	—	5	6	no	—
607	C₂²×C₄	—	5	16	no	—
608	C₂²×C₄	—	5	16	no	—
609	C₂²×C₄	—	5	16	no	—
610	C₂²×C₄	—	5	16	no	—
611	C₂²×C₄	—	10	48	no	—
612	C₂²×C₄	—	10	48	no	—
613	C₂²×C₄	—	10	48	no	—
614	C₂²×C₄	—	10	4	no	—
615	C₂²×C₄	—	10	4	no	—
616	C₂²×C₄	—	10	4	no	—
617	C₂²×C₄	—	10	4	no	—
618	C₂²×C₄	—	20	24	no	—
619	C₂²×C₄	C₂³×D₅	1	6	yes	—
620	C₂²×C₄	C₂³×D₅	1	6	yes	—
621	C₂²×C₄	C₂³×D₅	1	6	yes	—
622	C₂²×C₄	C₂³×D₅	1	6	yes	—
623	C₂²×C₄	C₂³×D₅	1	16	yes	complemented
624	C₂²×C₄	C₂³×D₅	1	16	yes	complemented
625	C₄⋊C₄	—	5	16	no	—
626	C₄⋊C₄	—	5	16	no	—
627	C₄⋊C₄	—	5	16	no	—
628	C₄⋊C₄	—	5	16	no	—
629	C₂²⋊C₄	—	5	16	no	—
630	C₂²⋊C₄	—	5	16	no	—
631	C₂²⋊C₄	—	5	16	no	—
632	C₂²⋊C₄	—	5	16	no	—
633	C₂²⋊C₄	—	5	16	no	—
634	C₂²⋊C₄	—	5	16	no	—
635	C₂²⋊C₄	—	5	16	no	—
636	C₂²⋊C₄	—	5	16	no	—
637	C₂²⋊C₄	C₂³×D₅	1	16	yes	—
638	C₂²⋊C₄	C₂³×D₅	1	16	yes	—
639	C₂²⋊C₄	C₂³×D₅	1	16	yes	complemented
640	C₂²⋊C₄	C₂³×D₅	1	16	yes	complemented
641	C₄²	—	5	16	no	—
642	C₂×C₅	—	2	8	no	—
643	C₂×C₅	—	2	8	no	—
644	C₂×C₅	—	4	4	no	—
645	C₂×C₅	C₂×#546	1	12	yes	complemented
646	C₂×C₅	C₂⁴×D₄	1	1	yes	characteristic
647	C₂×C₅	C₂³×#41	1	1	yes	characteristic
648	C₂×C₅	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
649	D₅	—	2	8	no	—
650	D₅	—	4	4	no	—
651	D₅	—	4	4	no	—
652	C₂³	—	2	32	no	—
653	C₂³	—	2	32	no	—
654	C₂³	—	2	12	no	—
655	C₂³	—	2	12	no	—
656	C₂³	—	2	12	no	—
657	C₂³	—	2	12	no	—
658	C₂³	—	2	12	no	—
659	C₂³	—	2	32	no	—
660	C₂³	—	2	32	no	—
661	C₂³	—	2	12	no	—
662	C₂³	—	2	12	no	—
663	C₂³	—	4	16	no	—
664	C₂³	—	4	192	no	—
665	C₂³	—	4	16	no	—
666	C₂³	—	5	24	no	—
667	C₂³	—	5	4	no	—
668	C₂³	—	5	4	no	—
669	C₂³	—	5	4	no	—
670	C₂³	—	10	32	no	—
671	C₂³	—	10	32	no	—
672	C₂³	—	10	12	no	—
673	C₂³	—	10	12	no	—
674	C₂³	—	10	12	no	—
675	C₂³	—	10	12	no	—
676	C₂³	—	10	32	no	—
677	C₂³	—	10	12	no	—
678	C₂³	—	10	12	no	—
679	C₂³	—	10	12	no	—
680	C₂³	—	10	12	no	—
681	C₂³	—	20	16	no	—
682	C₂³	—	20	192	no	—
683	C₂³	—	20	16	no	—
684	C₂³	—	20	16	no	—
685	C₂³	C₂×#709	1	4	yes	—
686	C₂³	C₂×#709	1	24	yes	complemented
687	C₂³	C₂×D₄×D₅	1	24	yes	—
688	C₂³	C₂×D₄×D₅	1	4	yes	—
689	C₂³	#4144	1	4	yes	—
690	C₂³	C₂⁴×D₅	1	4	yes	—
691	C₂³	C₂⁴×D₅	1	4	yes	—
692	C₂³	C₂⁴×D₅	1	4	yes	—
693	C₂³	C₂⁴×D₅	1	3	yes	—
694	Q₈	—	10	32	no	—
695	D₄	—	5	64	no	—
696	D₄	—	10	32	no	—
697	D₄	—	10	32	no	—
698	D₄	—	10	32	no	—
699	D₄	—	10	32	no	—
700	D₄	—	10	32	no	—
701	D₄	—	10	32	no	—
702	D₄	—	20	16	no	—
703	D₄	—	20	16	no	—
704	C₂×C₄	—	2	12	no	—
705	C₂×C₄	—	2	12	no	—
706	C₂×C₄	—	2	32	no	—
707	C₂×C₄	—	2	12	no	—
708	C₂×C₄	—	2	12	no	—
709	C₂×C₄	—	4	16	no	—
710	C₂×C₄	—	5	24	no	—
711	C₂×C₄	—	5	4	no	—
712	C₂×C₄	—	5	4	no	—
713	C₂×C₄	—	5	4	no	—
714	C₂×C₄	—	5	4	no	—
715	C₂×C₄	—	5	4	no	—
716	C₂×C₄	—	10	32	no	—
717	C₂×C₄	—	10	32	no	—
718	C₂×C₄	—	10	32	no	—
719	C₂×C₄	—	10	12	no	—
720	C₂×C₄	—	10	12	no	—
721	C₂×C₄	—	10	12	no	—
722	C₂×C₄	—	10	12	no	—
723	C₂×C₄	—	20	16	no	—
724	C₂×C₄	C₂⁴×D₅	1	4	yes	—
725	C₂×C₄	C₂⁴×D₅	1	4	yes	—
726	C₂×C₄	C₂⁴×D₅	1	4	yes	—
727	C₂×C₄	C₂⁴×D₅	1	4	yes	—
728	C₅	C₂²×#546	1	1	yes	characteristic, complemented, Sylow
729	C₂²	—	2	4	no	—
730	C₂²	—	2	4	no	—
731	C₂²	—	2	4	no	—
732	C₂²	—	2	4	no	—
733	C₂²	—	2	48	no	—
734	C₂²	—	2	48	no	—
735	C₂²	—	2	4	no	—
736	C₂²	—	2	4	no	—
737	C₂²	—	2	4	no	—
738	C₂²	—	4	64	no	—
739	C₂²	—	4	24	no	—
740	C₂²	—	5	8	no	—
741	C₂²	—	10	4	no	—
742	C₂²	—	10	4	no	—
743	C₂²	—	10	48	no	—
744	C₂²	—	10	4	no	—
745	C₂²	—	10	4	no	—
746	C₂²	—	10	4	no	—
747	C₂²	—	10	4	no	—
748	C₂²	—	10	4	no	—
749	C₂²	—	10	4	no	—
750	C₂²	—	20	64	no	—
751	C₂²	—	20	24	no	—
752	C₂²	—	20	24	no	—
753	C₂²	#65824	1	16	yes	direct product factor
754	C₂²	C₂²×#709	1	6	yes	—
755	C₂²	C₂²×#709	1	8	yes	complemented
756	C₂²	C₂²×D₄×D₅	1	8	yes	—
757	C₂²	C₂²×D₄×D₅	1	6	yes	—
758	C₂²	C₂×#4144	1	6	yes	—
759	C₂²	C₂⁵×D₅	1	1	yes	characteristic
760	C₄	—	2	4	no	—
761	C₄	—	2	4	no	—
762	C₄	—	2	4	no	—
763	C₄	—	2	4	no	—
764	C₄	—	5	8	no	—
765	C₄	—	10	4	no	—
766	C₄	—	10	4	no	—
767	C₄	—	10	4	no	—
768	C₄	—	10	4	no	—
769	C₂	—	2	8	no	—
770	C₂	—	2	8	no	—
771	C₂	—	4	4	no	—
772	C₂	—	10	8	no	—
773	C₂	—	20	4	no	—
774	C₂	—	20	4	no	—
775	C₂	C₂×#65824	1	12	yes	direct product factor
776	C₂	C₂³×#709	1	1	yes	characteristic
777	C₂	C₂³×D₄×D₅	1	1	yes	characteristic
778	C₂	C₂²×#4144	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂³×D₅
commutator, cosocle	C₂²×C₅	C₂⁶
Frattini	C₂²	C₂⁵×D₅
Fitting	C₂³×C₅×C₂²⋊C₄	C₂
socle	C₂⁴×C₅	C₂⁴
hypercenter	C₂³×C₂²⋊C₄	D₅
hypocenter	C₅	C₂²×#546
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
1. C₂⁴×C₂²⋊D₅	C₂	semidirect
2. C₂³×#709	C₂	semidirect
3. C₂³×C₅×C₂²⋊C₄	C₂	semidirect
4. C₂²×#4099	C₂	semidirect
5. C₂²×#4075	C₂	semidirect
6. C₂²×#4076	C₂	semidirect
7. C₂²×C₄×C₂²⋊D₅	C₂	semidirect
8. C₂×#65824	C₂	direct (N × H)
9. C₂²×#4029	C₂	semidirect
10. C₂²×#4030	C₂	semidirect
11. C₂²×#4030	C₂	semidirect
12. C₂²×#4028	C₂	semidirect
13. C₂²×D₅×C₂²⋊C₄	C₂	semidirect
14. C₂²×#4031	C₂	semidirect
15. C₂²×#4024	C₂	semidirect
16. C₂²×#4027	C₂	semidirect
19. C₂⁴×C₄×C₅	C₂²	semidirect
20. C₂⁴×C₄×C₅	C₂²	semidirect
27. C₂³×C₂²⋊D₅	C₂²	semidirect
28. C₂³×C₂²⋊D₅	C₂²	semidirect
29. C₂³×C₂²⋊D₅	C₂²	semidirect
32. C₂²×#709	C₂²	semidirect
33. C₂³×D₂₀	C₂²	semidirect
34. C₂³×D₂₀	C₂²	semidirect
35. C₂³×C₄×D₅	C₂²	semidirect
36. C₂³×C₄×D₅	C₂²	semidirect
37. C₂³×C₄×D₅	C₂²	semidirect
38. C₂³×Dic₁₀	C₂²	semidirect
41. C₂²×C₅×C₂²⋊C₄	C₂²	semidirect
42. C₂²×C₅×C₂²⋊C₄	C₂²	semidirect
43. C₂²×C₅×C₂²⋊C₄	C₂²	semidirect
44. C₂×#4099	C₂²	semidirect
46. C₂²×C₂²⋊Dic₅	C₂²	semidirect
47. C₂²×C₂²⋊Dic₅	C₂²	semidirect
48. C₂×#4076	C₂²	semidirect
49. C₂×#4075	C₂²	semidirect
50. C₂×C₄×C₂²⋊D₅	C₂²	semidirect
51. C₂²×#685	C₂²	semidirect
52. C₂²×#685	C₂²	semidirect
53. C₂²×#685	C₂²	semidirect
54. C₂²×#685	C₂²	semidirect
55. C₂²×#685	C₂²	semidirect
56. C₂²×C₄⋊Dic₅	C₂²	semidirect
57. C₂²×#683	C₂²	semidirect
58. C₂²×#683	C₂²	semidirect
59. C₂²×#683	C₂²	semidirect
60. C₂²×C₄×Dic₅	C₂²	semidirect
61. C₂×#4031	C₂²	semidirect
62. #65824	C₂²	direct (N × H)
63. C₂×#4030	C₂²	semidirect
64. C₂×#4030	C₂²	semidirect
65. C₂×#4029	C₂²	semidirect
66. C₂×#4028	C₂²	semidirect
67. C₂×#4027	C₂²	semidirect
68. C₂×D₅×C₂²⋊C₄	C₂²	semidirect
69. C₂×#4024	C₂²	semidirect
91. C₂³×C₄×C₅	C₂³	semidirect
92. C₂³×C₄×C₅	C₂³	semidirect
100. C₂²×C₂²⋊D₅	D₄	semidirect
106. C₂²×C₂²⋊D₅	C₂³	semidirect
107. C₂²×C₂²⋊D₅	C₂³	semidirect
108. C₂²×C₂²⋊D₅	C₂³	semidirect
117. C₂×#709	C₂³	semidirect
120. C₂²×D₂₀	C₂³	semidirect
121. C₂²×D₂₀	C₂³	semidirect
125. C₂²×C₄×D₅	C₂³	semidirect
126. C₂²×C₄×D₅	C₂³	semidirect
127. C₂²×C₄×D₅	C₂³	semidirect
129. C₂²×Dic₁₀	C₂³	semidirect
132. C₂×C₅×C₂²⋊C₄	C₂³	semidirect
133. C₂×C₅×C₂²⋊C₄	C₂³	semidirect
134. C₂×C₅×C₂²⋊C₄	C₂³	semidirect
135. #4099	C₂³	semidirect
137. C₂×C₂²⋊Dic₅	C₂³	semidirect
138. C₂×C₂²⋊Dic₅	C₂³	semidirect
139. #4076	C₂³	semidirect
140. #4075	C₂³	semidirect
141. C₄×C₂²⋊D₅	C₂³	semidirect
142. C₂×#685	C₂³	semidirect
143. C₂×#685	C₂³	semidirect
144. C₂×#685	C₂³	semidirect
145. C₂×#685	C₂³	semidirect
146. C₂×#685	C₂³	semidirect
147. C₂×C₄⋊Dic₅	C₂³	semidirect
148. C₂×#683	C₂³	semidirect
149. C₂×#683	C₂³	semidirect
150. C₂×#683	C₂³	semidirect
151. C₂×C₄×Dic₅	C₂³	semidirect
152. #4031	C₂³	semidirect
153. #4030	C₂³	semidirect
154. #4030	C₂³	semidirect
155. #4029	C₂³	semidirect
156. #4028	C₂³	semidirect
157. #4027	C₂³	semidirect
158. D₅×C₂²⋊C₄	C₂³	semidirect
159. #4024	C₂³	semidirect
175. C₂³×C₂²⋊C₄	D₅	semidirect
188. C₂⁴×C₅	#41	semidirect
221. C₂²×C₄×C₅	C₂⁴	semidirect
222. C₂²×C₄×C₅	C₂⁴	semidirect
230. C₂×C₂²⋊D₅	C₂×D₄	semidirect
236. C₂×C₂²⋊D₅	C₂⁴	semidirect
237. C₂×C₂²⋊D₅	C₂⁴	semidirect
253. C₂×D₂₀	C₂⁴	semidirect
254. C₂×D₂₀	C₂⁴	semidirect
258. C₂×C₄×D₅	C₂⁴	semidirect
259. C₂×C₄×D₅	C₂⁴	semidirect
260. C₂×C₄×D₅	C₂⁴	semidirect
262. C₂×Dic₁₀	C₂⁴	semidirect
265. C₅×C₂²⋊C₄	C₂⁴	semidirect
266. C₅×C₂²⋊C₄	C₂⁴	semidirect
268. C₂²⋊Dic₅	C₂⁴	semidirect
269. C₂²⋊Dic₅	C₂⁴	semidirect
270. #685	C₂⁴	semidirect
271. #685	C₂⁴	semidirect
272. #685	C₂⁴	semidirect
273. #685	C₂⁴	semidirect
274. #685	C₂⁴	semidirect
275. C₄⋊Dic₅	C₂⁴	semidirect
276. #683	C₂⁴	semidirect
277. #683	C₂⁴	semidirect
278. #683	C₂⁴	semidirect
279. C₄×Dic₅	C₂⁴	semidirect
300. C₂⁴×C₄	C₂×D₅	semidirect
301. C₂⁴×C₄	C₂×D₅	semidirect
329. C₂²×C₂²⋊C₄	C₂×D₅	semidirect
330. C₂²×C₂²⋊C₄	C₂×D₅	semidirect
331. C₂²×C₂²⋊C₄	C₂×D₅	semidirect
350. C₂³×C₅	C₂×#41	semidirect
391. C₂²⋊D₅	C₂²×D₄	semidirect
466. C₂³×C₄	C₂²×D₅	semidirect
467. C₂³×C₄	C₂²×D₅	semidirect
494. C₂×C₂²⋊C₄	C₂²×D₅	semidirect
495. C₂×C₂²⋊C₄	C₂²×D₅	semidirect
496. C₂×C₂²⋊C₄	C₂²×D₅	semidirect
509. C₂²×C₅	#546	semidirect
513. C₂²×C₅	C₂²×#41	semidirect
566. C₂⁴	#709	semidirect
623. C₂²×C₄	C₂³×D₅	semidirect
624. C₂²×C₄	C₂³×D₅	semidirect
639. C₂²⋊C₄	C₂³×D₅	semidirect
640. C₂²⋊C₄	C₂³×D₅	semidirect
645. C₂×C₅	C₂×#546	semidirect
686. C₂³	C₂×#709	semidirect
728. C₅	C₂²×#546	semidirect
753. C₂²	#65824	direct (N × H)
755. C₂²	C₂²×#709	semidirect
775. C₂	C₂×#65824	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×C₂²⋊D₅	2
C₂³×#709	2
C₂³×C₅×C₂²⋊C₄	2
C₂²×#4099	2
C₂²×#4075	2
C₂²×#4076	2
C₂²×C₄×C₂²⋊D₅	2
C₂×#65824	2
C₂²×#4029	2
C₂²×#4030	2
C₂²×#4028	2
C₂²×D₅×C₂²⋊C₄	2
C₂²×#4031	2
C₂²×#4024	2
C₂²×#4027	2
C₂²×#546	5

Subgroups — C22×#65824 #13006222

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#65824 #13006222