Subgroups — #10618521

Order 640.

1900 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#4144	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×D₄×D₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×D₄²	C₂	1	1	yes	maximal, characteristic, complemented
4	#66140	C₂	1	1	yes	maximal, characteristic, complemented
5	D₄×C₂²⋊D₅	C₂	1	2	yes	maximal, complemented
6	D₄×C₂²⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#4083	C₂	1	2	yes	maximal, complemented
8	#66051	C₂	1	1	yes	maximal, characteristic, complemented
9	#66049	C₂	1	1	yes	maximal, characteristic, complemented
10	#65946	C₂	1	1	yes	maximal, characteristic, complemented
11	#65944	C₂	1	2	yes	maximal, complemented
12	#65943	C₂	1	1	yes	maximal, characteristic, complemented
13	#65941	C₂	1	1	yes	maximal, characteristic, complemented
14	#65940	C₂	1	1	yes	maximal, characteristic, complemented
15	#65939	C₂	1	2	yes	maximal, complemented
16	#65925	C₂	1	2	yes	maximal, complemented
17	#65924	C₂	1	2	yes	maximal, complemented
18	#65923	C₂	1	2	yes	maximal, complemented
19	D₅×#120	C₂	1	2	yes	maximal, complemented
20	#65888	C₂	1	1	yes	maximal, characteristic, complemented
21	#65884	C₂	1	1	yes	maximal, characteristic, complemented
22	#65881	C₂	1	1	yes	maximal, characteristic, complemented
23	#65879	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂⁴×D₅	C₂²	1	2	yes	complemented
25	C₂²×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
26	C₂²×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
27	C₂²×C₅×D₄	C₂²	1	2	yes	complemented
28	C₂²×C₂²⋊D₅	C₂²	1	2	yes	complemented
29	C₂²×C₂²⋊D₅	C₂²	1	2	yes	complemented
30	C₂²×C₂²⋊D₅	C₂²	1	2	yes	complemented
31	C₂²×C₂²⋊D₅	C₂²	1	2	yes	complemented
32	#4144	—	2	8	no	—
33	C₂×#711	C₂²	1	1	yes	characteristic, complemented
34	C₂×#711	C₂²	1	2	yes	complemented
35	C₂×#711	C₂²	1	1	yes	characteristic, complemented
36	C₂×D₄×D₅	—	2	8	no	—
37	C₂×D₄×D₅	C₂²	1	1	yes	characteristic
38	C₂×D₄×D₅	C₂²	1	1	yes	characteristic, complemented
39	C₂×D₄×D₅	C₂²	1	1	yes	characteristic, complemented
40	C₂×D₄×D₅	C₂²	1	1	yes	characteristic, complemented
41	C₂×D₄×D₅	C₂²	1	2	yes	complemented
42	C₂×D₄×D₅	C₂²	1	2	yes	complemented
43	C₂×D₄×D₅	C₂²	1	2	yes	complemented
44	C₂×D₄×D₅	C₂²	1	1	yes	characteristic, complemented
45	C₂×D₄×D₅	C₂²	1	2	yes	complemented
46	C₂×D₄×D₅	C₂²	1	2	yes	complemented
47	C₂×#709	C₂²	1	1	yes	characteristic, complemented
48	C₂×#709	C₂²	1	1	yes	characteristic, complemented
49	C₂²×D₂₀	C₂²	1	1	yes	characteristic, complemented
50	C₂²×C₄×D₅	C₂²	1	1	yes	characteristic, complemented
51	C₅×#127	C₂²	1	1	yes	characteristic, complemented
52	C₅×#121	C₂²	1	1	yes	characteristic, complemented
53	C₅×#121	C₂²	1	2	yes	complemented
54	C₅×#121	C₂²	1	1	yes	characteristic, complemented
55	C₅×#120	C₂²	1	2	yes	complemented
56	C₅×#120	C₂²	1	2	yes	complemented
57	C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
58	C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
59	#4099	C₂²	1	2	yes	complemented
60	#4099	C₂²	1	2	yes	complemented
61	C₂×C₂²⋊Dic₅	C₂²	1	2	yes	complemented
62	#4086	C₂²	1	1	yes	characteristic, complemented
63	#4086	C₂²	1	2	yes	complemented
64	#4085	C₂²	1	1	yes	characteristic, complemented
65	#4085	C₂²	1	2	yes	complemented
66	#4085	C₂²	1	2	yes	complemented
67	#4085	C₂²	1	2	yes	complemented
68	#4085	C₂²	1	2	yes	complemented
69	#4084	C₂²	1	1	yes	characteristic, complemented
70	#4084	C₂²	1	2	yes	complemented
71	#4084	C₂²	1	2	yes	complemented
72	#4084	C₂²	1	1	yes	characteristic, complemented
73	#4083	C₂²	1	1	yes	characteristic, complemented
74	#4083	C₂²	1	2	yes	complemented
75	#4083	C₂²	1	2	yes	complemented
76	#4083	C₂²	1	2	yes	complemented
77	#4083	C₂²	1	2	yes	complemented
78	#4083	C₂²	1	2	yes	complemented
79	#4083	C₂²	1	2	yes	complemented
80	#4083	C₂²	1	2	yes	complemented
81	#4083	C₂²	1	2	yes	complemented
82	#4083	C₂²	1	2	yes	complemented
83	#4083	C₂²	1	2	yes	complemented
84	#4082	C₂²	1	1	yes	characteristic, complemented
85	#4081	C₂²	1	2	yes	complemented
86	D₄×Dic₅	C₂²	1	2	yes	complemented
87	D₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
88	#4076	C₂²	1	1	yes	characteristic, complemented
89	#4076	C₂²	1	2	yes	complemented
90	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
91	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
92	C₄×C₂²⋊D₅	C₂²	1	2	yes	complemented
93	C₂×#685	C₂²	1	2	yes	complemented
94	C₂×#685	C₂²	1	2	yes	complemented
95	#4070	C₂²	1	1	yes	characteristic, complemented
96	#4043	C₂²	1	1	yes	characteristic, complemented
97	#4042	C₂²	1	1	yes	characteristic, complemented
98	#4041	C₂²	1	1	yes	characteristic, complemented
99	#4040	C₂²	1	1	yes	characteristic, complemented
100	#4040	C₂²	1	2	yes	complemented
101	#4039	C₂²	1	1	yes	characteristic, complemented
102	#4038	C₂²	1	1	yes	characteristic, complemented
103	#4032	C₂²	1	2	yes	complemented
104	#4031	C₂²	1	2	yes	complemented
105	#4030	C₂²	1	1	yes	characteristic, complemented
106	#4030	C₂²	1	2	yes	complemented
107	#4030	C₂²	1	2	yes	complemented
108	#4029	C₂²	1	1	yes	characteristic, complemented
109	#4029	C₂²	1	2	yes	complemented
110	#4029	C₂²	1	2	yes	complemented
111	#4028	C₂²	1	1	yes	characteristic, complemented
112	#4028	C₂²	1	2	yes	complemented
113	#4028	C₂²	1	2	yes	complemented
114	#4028	C₂²	1	2	yes	complemented
115	#4027	C₂²	1	2	yes	complemented
116	#4027	C₂²	1	2	yes	complemented
117	D₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
118	D₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
119	D₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
120	#4024	C₂²	1	1	yes	characteristic, complemented
121	#4021	C₂²	1	1	yes	characteristic, complemented
122	C₄×D₂₀	C₂²	1	1	yes	characteristic, complemented
123	C₄×D₂₀	C₂²	1	1	yes	characteristic, complemented
124	#4018	C₂²	1	1	yes	characteristic, complemented
125	#3484	—	5	1	no	maximal, Sylow
126	C₂⁴×C₅	C₂³	1	2	yes	—
127	C₂⁴×C₅	C₂³	1	2	yes	complemented
128	C₂³×D₅	—	2	8	no	—
129	C₂³×D₅	—	4	4	no	—
130	C₂³×D₅	—	4	4	no	—
131	C₂³×D₅	C₂³	1	1	yes	characteristic
132	C₂³×D₅	C₂³	1	2	yes	—
133	C₂³×D₅	C₂³	1	2	yes	—
134	C₂³×D₅	C₂³	1	2	yes	—
135	C₂³×D₅	C₂³	1	2	yes	—
136	C₂³×D₅	C₂³	1	2	yes	—
137	C₂³×D₅	C₂³	1	2	yes	complemented
138	C₂×C₅×D₄	—	2	4	no	—
139	C₂×C₅×D₄	—	2	4	no	—
140	C₂×C₅×D₄	—	4	4	no	—
141	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
142	C₂×C₅×D₄	C₂³	1	2	yes	—
143	C₂×C₅×D₄	C₂³	1	2	yes	—
144	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
145	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
146	C₂×C₅×D₄	C₂³	1	2	yes	complemented
147	C₂×C₅×D₄	C₂³	1	1	yes	characteristic, complemented
148	C₂×C₅×D₄	C₂³	1	2	yes	complemented
149	C₂×C₅×D₄	C₂³	1	2	yes	complemented
150	C₂×C₅×D₄	C₂³	1	2	yes	complemented
151	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
152	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic, complemented
153	C₂²×C₄×C₅	C₂³	1	2	yes	complemented
154	C₂×C₂²⋊D₅	—	2	8	no	—
155	C₂×C₂²⋊D₅	—	2	8	no	—
156	C₂×C₂²⋊D₅	—	2	8	no	—
157	C₂×C₂²⋊D₅	—	4	4	no	—
158	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
159	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
160	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
161	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
162	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
163	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
164	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
165	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
166	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
167	C₂×C₂²⋊D₅	C₂³	1	2	yes	complemented
168	C₂×C₂²⋊D₅	C₂³	1	2	yes	complemented
169	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic, complemented
170	C₂×C₂²⋊D₅	C₂³	1	2	yes	complemented
171	C₂×C₂²⋊D₅	C₂³	1	2	yes	complemented
172	C₂×C₂²⋊D₅	C₂³	1	2	yes	complemented
173	C₂×C₂²⋊D₅	C₂³	1	2	yes	complemented
174	C₂×C₂²⋊D₅	C₂³	1	2	yes	complemented
175	C₂²×Dic₅	C₂³	1	1	yes	characteristic
176	C₂²×Dic₅	C₂³	1	2	yes	complemented
177	C₂²×Dic₅	C₂³	1	2	yes	complemented
178	C₂²×Dic₅	C₂³	1	2	yes	complemented
179	#711	—	2	4	no	—
180	#711	—	2	8	no	—
181	#711	—	2	4	no	—
182	D₄×D₅	—	2	8	no	—
183	D₄×D₅	—	2	8	no	—
184	D₄×D₅	—	2	4	no	—
185	D₄×D₅	—	2	8	no	—
186	D₄×D₅	—	2	4	no	—
187	D₄×D₅	—	2	4	no	—
188	D₄×D₅	—	2	4	no	—
189	D₄×D₅	—	4	4	no	—
190	D₄×D₅	—	4	4	no	—
191	D₄×D₅	D₄	1	8	yes	complemented
192	#709	—	2	4	no	—
193	#709	—	2	4	no	—
194	C₂×D₂₀	—	2	4	no	—
195	C₂×D₂₀	C₂³	1	1	yes	characteristic
196	C₂×D₂₀	C₂³	1	2	yes	—
197	C₂×D₂₀	C₂³	1	1	yes	characteristic
198	C₂×D₂₀	C₂³	1	1	yes	characteristic
199	C₂×D₂₀	C₂³	1	1	yes	characteristic
200	C₂×D₂₀	C₂³	1	2	yes	complemented
201	C₂×C₄×D₅	—	2	4	no	—
202	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
203	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
204	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
205	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
206	C₂×C₄×D₅	C₂³	1	1	yes	characteristic, complemented
207	C₂×C₄×D₅	C₂³	1	2	yes	complemented
208	C₂×C₄×D₅	C₂³	1	2	yes	complemented
209	C₂×C₄×D₅	C₂³	1	2	yes	complemented
210	C₂×Dic₁₀	C₂³	1	1	yes	characteristic, complemented
211	C₂×Dic₁₀	C₂³	1	1	yes	characteristic, complemented
212	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic, complemented
213	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic, complemented
214	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
215	C₅×C₂²⋊C₄	C₂³	1	2	yes	complemented
216	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic, complemented
217	C₅×C₂²⋊C₄	C₂³	1	2	yes	complemented
218	C₅×C₂²⋊C₄	C₂³	1	2	yes	complemented
219	C₄²×C₅	C₂³	1	1	yes	characteristic, complemented
220	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
221	C₂²⋊Dic₅	C₂³	1	2	yes	—
222	C₂²⋊Dic₅	C₂³	1	2	yes	complemented
223	C₂²⋊Dic₅	C₂³	1	2	yes	complemented
224	C₂²⋊Dic₅	C₂³	1	2	yes	complemented
225	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic, complemented
226	C₂²⋊Dic₅	C₂³	1	2	yes	complemented
227	C₂²⋊Dic₅	C₂³	1	2	yes	complemented
228	#685	C₂³	1	1	yes	characteristic
229	#685	C₂³	1	1	yes	characteristic
230	#685	C₂³	1	1	yes	characteristic
231	#685	C₂³	1	1	yes	characteristic
232	#685	C₂³	1	2	yes	—
233	#685	C₂³	1	2	yes	—
234	#685	C₂³	1	2	yes	complemented
235	#685	C₂³	1	1	yes	characteristic, complemented
236	#685	C₂³	1	2	yes	complemented
237	#685	C₂³	1	2	yes	complemented
238	#685	C₂³	1	2	yes	complemented
239	#685	C₂³	1	2	yes	complemented
240	#685	C₂³	1	1	yes	characteristic, complemented
241	#685	C₂³	1	2	yes	complemented
242	C₄⋊Dic₅	C₂³	1	1	yes	characteristic, complemented
243	C₄⋊Dic₅	C₂³	1	1	yes	characteristic, complemented
244	C₄⋊Dic₅	C₂³	1	2	yes	complemented
245	#683	C₂³	1	1	yes	characteristic, complemented
246	#683	C₂³	1	1	yes	characteristic, complemented
247	#683	C₂³	1	1	yes	characteristic, complemented
248	#683	C₂³	1	2	yes	complemented
249	#683	C₂³	1	1	yes	characteristic, complemented
250	C₄×Dic₅	C₂³	1	1	yes	characteristic, complemented
251	C₄×Dic₅	C₂³	1	2	yes	complemented
252	C₂×H(5,𝔽₂)	—	5	1	no	—
253	C₂³×D₄	—	5	1	no	—
254	#546	—	5	1	no	—
255	#546	—	5	2	no	—
256	#546	—	5	1	no	—
257	#546	—	5	2	no	—
258	#546	—	5	1	no	—
259	#546	—	5	1	no	—
260	D₄²	—	5	1	no	—
261	D₄²	—	5	2	no	—
262	D₄²	—	5	1	no	—
263	D₄²	—	5	1	no	—
264	D₄²	—	5	2	no	—
265	D₄²	D₅	1	1	yes	characteristic, complemented
266	#535	—	5	1	no	—
267	#535	—	5	1	no	—
268	#534	—	5	2	no	—
269	#534	—	5	2	no	—
270	#525	—	5	1	no	—
271	#525	—	5	1	no	—
272	C₂×#120	—	5	2	no	—
273	C₂×#120	—	5	2	no	—
274	#518	—	5	1	no	—
275	C₂³×C₅	—	2	4	no	—
276	C₂³×C₅	—	2	4	no	—
277	C₂³×C₅	—	2	4	no	—
278	C₂³×C₅	—	4	2	no	—
279	C₂³×C₅	—	4	2	no	—
280	C₂³×C₅	—	4	2	no	—
281	C₂³×C₅	C₂⁴	1	2	yes	—
282	C₂³×C₅	C₂⁴	1	2	yes	—
283	C₂³×C₅	C₂⁴	1	1	yes	characteristic
284	C₂³×C₅	C₂⁴	1	2	yes	—
285	C₂³×C₅	C₂⁴	1	1	yes	characteristic
286	C₂²×D₅	—	2	2	no	—
287	C₂²×D₅	—	2	2	no	—
288	C₂²×D₅	—	2	2	no	—
289	C₂²×D₅	—	2	4	no	—
290	C₂²×D₅	—	2	4	no	—
291	C₂²×D₅	—	2	4	no	—
292	C₂²×D₅	—	2	4	no	—
293	C₂²×D₅	—	2	4	no	—
294	C₂²×D₅	—	2	4	no	—
295	C₂²×D₅	—	2	4	no	—
296	C₂²×D₅	—	2	4	no	—
297	C₂²×D₅	—	4	2	no	—
298	C₂²×D₅	—	4	2	no	—
299	C₂²×D₅	—	4	2	no	—
300	C₂²×D₅	—	4	2	no	—
301	C₂²×D₅	—	4	2	no	—
302	C₂²×D₅	—	4	2	no	—
303	C₂²×D₅	—	4	2	no	—
304	C₂²×D₅	—	4	2	no	—
305	C₂²×D₅	—	4	2	no	—
306	C₂²×D₅	—	4	32	no	—
307	C₂²×D₅	C₂×D₄	1	8	yes	complemented
308	C₂²×D₅	C₂⁴	1	2	yes	—
309	C₂²×D₅	C₂⁴	1	1	yes	characteristic
310	C₂²×D₅	C₂⁴	1	1	yes	characteristic
311	C₂²×D₅	C₂⁴	1	2	yes	—
312	C₂²×D₅	C₂⁴	1	1	yes	characteristic
313	C₅×D₄	—	2	4	no	—
314	C₅×D₄	—	2	4	no	—
315	C₅×D₄	—	2	4	no	—
316	C₅×D₄	—	2	2	no	—
317	C₅×D₄	—	2	2	no	—
318	C₅×D₄	—	2	2	no	—
319	C₅×D₄	—	4	2	no	—
320	C₅×D₄	—	4	2	no	—
321	C₅×D₄	—	4	2	no	—
322	C₅×D₄	C₂×D₄	1	4	yes	complemented
323	C₂×C₄×C₅	—	2	2	no	—
324	C₂×C₄×C₅	—	2	2	no	—
325	C₂×C₄×C₅	—	4	2	no	—
326	C₂×C₄×C₅	C₂⁴	1	2	yes	—
327	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
328	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
329	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
330	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
331	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
332	C₂²⋊D₅	—	2	4	no	—
333	C₂²⋊D₅	—	2	4	no	—
334	C₂²⋊D₅	—	2	2	no	—
335	C₂²⋊D₅	—	2	2	no	—
336	C₂²⋊D₅	—	2	4	no	—
337	C₂²⋊D₅	—	2	4	no	—
338	C₂²⋊D₅	—	2	4	no	—
339	C₂²⋊D₅	—	2	4	no	—
340	C₂²⋊D₅	—	2	4	no	—
341	C₂²⋊D₅	—	2	2	no	—
342	C₂²⋊D₅	—	2	2	no	—
343	C₂²⋊D₅	—	2	4	no	—
344	C₂²⋊D₅	—	4	2	no	—
345	C₂²⋊D₅	—	4	2	no	—
346	C₂²⋊D₅	—	4	2	no	—
347	C₂²⋊D₅	—	4	2	no	—
348	C₂²⋊D₅	C₂×D₄	1	8	yes	complemented
349	C₂×Dic₅	—	2	4	no	—
350	C₂×Dic₅	—	2	2	no	—
351	C₂×Dic₅	—	2	4	no	—
352	C₂×Dic₅	—	4	2	no	—
353	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
354	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
355	C₂×Dic₅	C₂⁴	1	2	yes	—
356	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
357	C₂×Dic₅	C₂⁴	1	2	yes	—
358	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
359	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
360	D₂₀	—	2	4	no	—
361	D₂₀	—	2	2	no	—
362	D₂₀	—	2	2	no	—
363	D₂₀	—	2	2	no	—
364	D₂₀	—	4	2	no	—
365	D₂₀	C₂×D₄	1	4	yes	complemented
366	C₄×D₅	—	2	2	no	—
367	C₄×D₅	—	2	4	no	—
368	C₄×D₅	—	2	2	no	—
369	C₄×D₅	—	2	2	no	—
370	C₄×D₅	—	2	2	no	—
371	C₄×D₅	—	4	2	no	—
372	C₄×D₅	—	4	2	no	—
373	C₄×D₅	C₂×D₄	1	4	yes	complemented
374	Dic₁₀	—	2	2	no	—
375	Dic₁₀	—	2	2	no	—
376	C₂⁵	—	5	2	no	—
377	H(5,𝔽₂)	—	10	8	no	—
378	C₂×#41	—	5	1	no	—
379	C₂×#41	—	5	1	no	—
380	C₂×#41	—	5	2	no	—
381	C₂×#41	—	5	1	no	—
382	C₂×#41	—	5	1	no	—
383	C₂²×D₄	—	5	1	no	—
384	C₂²×D₄	—	5	2	no	—
385	C₂²×D₄	—	5	2	no	—
386	C₂²×D₄	—	5	2	no	—
387	C₂²×D₄	—	5	2	no	—
388	C₂²×D₄	—	5	2	no	—
389	C₂²×D₄	—	5	1	no	—
390	C₂²×D₄	—	5	2	no	—
391	C₂²×D₄	—	5	1	no	—
392	C₂²×D₄	—	5	1	no	—
393	C₂²×D₄	—	5	2	no	—
394	C₂²×D₄	—	5	1	no	—
395	C₂²×D₄	—	5	2	no	—
396	C₂²×D₄	—	5	2	no	—
397	C₂²×D₄	—	5	1	no	—
398	C₂²×D₄	—	10	8	no	—
399	C₂²×D₄	C₂×D₅	1	1	yes	characteristic, complemented
400	C₂²×D₄	C₂×D₅	1	1	yes	characteristic, complemented
401	C₂²×D₄	C₂×D₅	1	2	yes	complemented
402	C₂³×C₄	—	5	1	no	—
403	#127	—	5	2	no	—
404	#127	—	5	1	no	—
405	#127	C₂×D₅	1	1	yes	characteristic, complemented
406	#124	—	5	1	no	—
407	#124	—	5	2	no	—
408	#124	—	5	1	no	—
409	#123	—	5	2	no	—
410	#123	—	5	1	no	—
411	#123	—	5	2	no	—
412	#123	—	5	2	no	—
413	#123	—	5	1	no	—
414	#123	—	5	2	no	—
415	#123	—	5	2	no	—
416	C₂²⋊Q₈	—	5	1	no	—
417	C₂²⋊Q₈	—	5	1	no	—
418	C₂²⋊Q₈	—	5	1	no	—
419	C₂²⋊Q₈	—	5	1	no	—
420	#121	—	5	1	no	—
421	#121	—	5	2	no	—
422	#121	—	5	1	no	—
423	#121	—	5	1	no	—
424	#121	—	5	2	no	—
425	#121	—	5	2	no	—
426	#121	—	5	2	no	—
427	#121	—	5	2	no	—
428	#121	—	5	2	no	—
429	#121	—	5	2	no	—
430	#121	—	5	1	no	—
431	#121	—	5	1	no	—
432	#121	—	5	1	no	—
433	#121	—	5	2	no	—
434	#121	—	5	2	no	—
435	#121	C₂×D₅	1	1	yes	characteristic, complemented
436	#121	C₂×D₅	1	2	yes	complemented
437	#121	C₂×D₅	1	1	yes	characteristic, complemented
438	#120	—	5	2	no	—
439	#120	—	5	2	no	—
440	#120	—	5	2	no	—
441	#120	—	5	1	no	—
442	#120	—	5	2	no	—
443	#120	—	5	2	no	—
444	#120	—	5	2	no	—
445	#120	—	5	2	no	—
446	#120	—	5	2	no	—
447	#120	—	5	2	no	—
448	#120	—	5	2	no	—
449	#120	—	5	2	no	—
450	#120	—	5	2	no	—
451	#120	—	5	1	no	—
452	#120	—	5	2	no	—
453	#120	—	5	2	no	—
454	#120	—	5	2	no	—
455	#120	C₂×D₅	1	2	yes	complemented
456	#120	C₂×D₅	1	2	yes	complemented
457	C₄×D₄	—	5	1	no	—
458	C₄×D₄	—	5	2	no	—
459	C₄×D₄	—	5	1	no	—
460	C₄×D₄	—	5	2	no	—
461	C₄×D₄	—	5	1	no	—
462	C₄×D₄	—	5	1	no	—
463	C₄×D₄	—	5	2	no	—
464	C₄×D₄	—	5	2	no	—
465	C₄×D₄	—	5	1	no	—
466	C₄×D₄	—	5	1	no	—
467	C₄×D₄	C₂×D₅	1	1	yes	characteristic, complemented
468	C₄×D₄	C₂×D₅	1	1	yes	characteristic, complemented
469	#117	—	5	1	no	—
470	#117	—	5	1	no	—
471	C₂×C₂²⋊C₄	—	5	2	no	—
472	C₂×C₂²⋊C₄	—	5	2	no	—
473	C₂×C₂²⋊C₄	—	5	2	no	—
474	C₂×C₂²⋊C₄	—	5	2	no	—
475	C₂×C₂²⋊C₄	—	5	2	no	—
476	C₂×C₂²⋊C₄	—	5	2	no	—
477	C₂²×C₅	—	2	1	no	—
478	C₂²×C₅	—	2	2	no	—
479	C₂²×C₅	—	2	2	no	—
480	C₂²×C₅	—	2	1	no	—
481	C₂²×C₅	—	2	2	no	—
482	C₂²×C₅	—	2	1	no	—
483	C₂²×C₅	—	2	2	no	—
484	C₂²×C₅	—	2	1	no	—
485	C₂²×C₅	—	2	2	no	—
486	C₂²×C₅	—	2	2	no	—
487	C₂²×C₅	—	2	2	no	—
488	C₂²×C₅	—	2	1	no	—
489	C₂²×C₅	—	2	2	no	—
490	C₂²×C₅	—	4	8	no	—
491	C₂²×C₅	—	8	4	no	—
492	C₂²×C₅	C₂²×D₄	1	4	yes	—
493	C₂²×C₅	H(5,𝔽₂)	1	2	yes	complemented
494	C₂²×C₅	C₂⁵	1	1	yes	characteristic
495	C₂×D₅	—	2	8	no	—
496	C₂×D₅	—	2	1	no	—
497	C₂×D₅	—	2	2	no	—
498	C₂×D₅	—	2	2	no	—
499	C₂×D₅	—	2	1	no	—
500	C₂×D₅	—	2	1	no	—
501	C₂×D₅	—	2	1	no	—
502	C₂×D₅	—	2	1	no	—
503	C₂×D₅	—	2	2	no	—
504	C₂×D₅	—	2	1	no	—
505	C₂×D₅	—	2	1	no	—
506	C₂×D₅	—	2	2	no	—
507	C₂×D₅	—	2	2	no	—
508	C₂×D₅	—	4	8	no	—
509	C₂×D₅	—	4	8	no	—
510	C₂×D₅	—	4	8	no	—
511	C₂×D₅	—	4	8	no	—
512	C₂×D₅	—	4	8	no	—
513	C₂×D₅	—	8	4	no	—
514	C₂×D₅	C₂²×D₄	1	2	yes	—
515	C₂×D₅	C₂²×D₄	1	4	yes	—
516	C₂×D₅	H(5,𝔽₂)	1	2	yes	complemented
517	C₄×C₅	—	2	1	no	—
518	C₄×C₅	—	2	1	no	—
519	C₄×C₅	—	2	1	no	—
520	C₄×C₅	—	2	2	no	—
521	C₄×C₅	—	2	1	no	—
522	C₄×C₅	C₂²×D₄	1	2	yes	—
523	Dic₅	—	2	2	no	—
524	Dic₅	—	2	1	no	—
525	Dic₅	—	2	1	no	—
526	Dic₅	—	2	1	no	—
527	Dic₅	—	2	2	no	—
528	Dic₅	—	2	1	no	—
529	Dic₅	C₂²×D₄	1	2	yes	—
530	C₂⁴	—	5	2	no	—
531	C₂⁴	—	5	1	no	—
532	C₂⁴	—	5	2	no	—
533	C₂⁴	—	5	2	no	—
534	C₂⁴	—	5	2	no	—
535	C₂⁴	—	5	2	no	—
536	C₂⁴	—	5	2	no	—
537	C₂⁴	—	10	8	no	—
538	C₂⁴	—	20	4	no	—
539	C₂⁴	—	20	4	no	—
540	C₂⁴	C₂²×D₅	1	2	yes	—
541	C₂⁴	C₂²×D₅	1	2	yes	complemented
542	#41	—	10	4	no	—
543	#41	—	10	4	no	—
544	#41	—	10	4	no	—
545	#41	—	10	8	no	—
546	#41	—	10	4	no	—
547	C₂×Q₈	—	5	1	no	—
548	C₂×Q₈	—	5	1	no	—
549	C₂×D₄	—	2	4	no	—
550	C₂×D₄	—	2	4	no	—
551	C₂×D₄	—	4	4	no	—
552	C₂×D₄	—	5	2	no	—
553	C₂×D₄	—	5	8	no	—
554	C₂×D₄	—	5	2	no	—
555	C₂×D₄	—	5	1	no	—
556	C₂×D₄	—	5	1	no	—
557	C₂×D₄	—	5	2	no	—
558	C₂×D₄	—	5	1	no	—
559	C₂×D₄	—	5	2	no	—
560	C₂×D₄	—	5	2	no	—
561	C₂×D₄	—	5	2	no	—
562	C₂×D₄	—	5	2	no	—
563	C₂×D₄	—	5	2	no	—
564	C₂×D₄	—	5	2	no	—
565	C₂×D₄	—	5	1	no	—
566	C₂×D₄	—	5	2	no	—
567	C₂×D₄	—	5	2	no	—
568	C₂×D₄	—	5	2	no	—
569	C₂×D₄	—	5	2	no	—
570	C₂×D₄	—	5	1	no	—
571	C₂×D₄	—	5	1	no	—
572	C₂×D₄	—	5	1	no	—
573	C₂×D₄	—	5	2	no	—
574	C₂×D₄	—	5	1	no	—
575	C₂×D₄	—	5	2	no	—
576	C₂×D₄	—	10	4	no	—
577	C₂×D₄	—	10	4	no	—
578	C₂×D₄	—	10	8	no	—
579	C₂×D₄	—	10	4	no	—
580	C₂×D₄	—	10	4	no	—
581	C₂×D₄	—	10	8	no	—
582	C₂×D₄	—	10	8	no	—
583	C₂×D₄	—	10	8	no	—
584	C₂×D₄	—	10	8	no	—
585	C₂×D₄	—	10	8	no	—
586	C₂×D₄	—	10	4	no	—
587	C₂×D₄	—	20	4	no	—
588	C₂×D₄	—	20	4	no	—
589	C₂×D₄	—	20	4	no	—
590	C₂×D₄	C₂²×D₅	1	2	yes	—
591	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
592	C₂×D₄	C₂²×D₅	1	2	yes	—
593	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
594	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
595	C₂×D₄	C₂²×D₅	1	2	yes	complemented
596	C₂×D₄	C₂²×D₅	1	1	yes	characteristic, complemented
597	C₂×D₄	C₂²×D₅	1	2	yes	complemented
598	C₂×D₄	C₂²×D₅	1	2	yes	complemented
599	C₂×D₄	C₂²×D₅	1	2	yes	complemented
600	C₂²×C₄	—	5	1	no	—
601	C₂²×C₄	—	5	2	no	—
602	C₂²×C₄	—	5	2	no	—
603	C₂²×C₄	—	5	1	no	—
604	C₂²×C₄	—	5	2	no	—
605	C₂²×C₄	—	5	2	no	—
606	C₂²×C₄	—	5	1	no	—
607	C₂²×C₄	—	5	1	no	—
608	C₂²×C₄	—	5	1	no	—
609	C₂²×C₄	—	5	1	no	—
610	C₂²×C₄	—	5	2	no	—
611	C₂²×C₄	—	5	2	no	—
612	C₂²×C₄	—	10	4	no	—
613	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
614	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic, complemented
615	C₂²×C₄	C₂²×D₅	1	2	yes	complemented
616	C₄⋊C₄	—	5	1	no	—
617	C₄⋊C₄	—	5	1	no	—
618	C₄⋊C₄	—	5	1	no	—
619	C₄⋊C₄	—	5	1	no	—
620	C₄⋊C₄	—	5	2	no	—
621	C₄⋊C₄	—	5	1	no	—
622	C₄⋊C₄	—	5	2	no	—
623	C₄⋊C₄	—	5	1	no	—
624	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic, complemented
625	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic, complemented
626	C₂²⋊C₄	—	5	1	no	—
627	C₂²⋊C₄	—	5	2	no	—
628	C₂²⋊C₄	—	5	2	no	—
629	C₂²⋊C₄	—	5	2	no	—
630	C₂²⋊C₄	—	5	2	no	—
631	C₂²⋊C₄	—	5	2	no	—
632	C₂²⋊C₄	—	5	2	no	—
633	C₂²⋊C₄	—	5	1	no	—
634	C₂²⋊C₄	—	5	2	no	—
635	C₂²⋊C₄	—	5	1	no	—
636	C₂²⋊C₄	—	5	1	no	—
637	C₂²⋊C₄	—	5	1	no	—
638	C₂²⋊C₄	—	5	2	no	—
639	C₂²⋊C₄	—	5	1	no	—
640	C₂²⋊C₄	—	5	2	no	—
641	C₂²⋊C₄	—	5	2	no	—
642	C₂²⋊C₄	—	5	2	no	—
643	C₂²⋊C₄	—	5	2	no	—
644	C₂²⋊C₄	—	5	2	no	—
645	C₂²⋊C₄	—	5	2	no	—
646	C₂²⋊C₄	—	5	1	no	—
647	C₂²⋊C₄	—	5	1	no	—
648	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
649	C₂²⋊C₄	C₂²×D₅	1	2	yes	complemented
650	C₂²⋊C₄	C₂²×D₅	1	2	yes	complemented
651	C₂²⋊C₄	C₂²×D₅	1	2	yes	complemented
652	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic, complemented
653	C₄²	—	5	2	no	—
654	C₄²	—	5	1	no	—
655	C₄²	C₂²×D₅	1	1	yes	characteristic, complemented
656	C₂×C₅	—	2	2	no	—
657	C₂×C₅	—	2	4	no	—
658	C₂×C₅	—	4	2	no	—
659	C₂×C₅	—	4	2	no	—
660	C₂×C₅	—	4	1	no	—
661	C₂×C₅	C₂³×D₄	1	1	yes	characteristic
662	C₂×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
663	C₂×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
664	D₅	—	2	2	no	—
665	D₅	—	2	2	no	—
666	D₅	—	2	4	no	—
667	D₅	—	4	2	no	—
668	D₅	—	4	1	no	—
669	C₂³	—	2	4	no	—
670	C₂³	—	2	4	no	—
671	C₂³	—	2	4	no	—
672	C₂³	—	4	2	no	—
673	C₂³	—	4	2	no	—
674	C₂³	—	4	2	no	—
675	C₂³	—	5	1	no	—
676	C₂³	—	5	1	no	—
677	C₂³	—	5	2	no	—
678	C₂³	—	5	8	no	—
679	C₂³	—	5	2	no	—
680	C₂³	—	5	1	no	—
681	C₂³	—	10	2	no	—
682	C₂³	—	10	2	no	—
683	C₂³	—	10	4	no	—
684	C₂³	—	10	4	no	—
685	C₂³	—	10	4	no	—
686	C₂³	—	10	4	no	—
687	C₂³	—	10	4	no	—
688	C₂³	—	10	4	no	—
689	C₂³	—	10	2	no	—
690	C₂³	—	10	4	no	—
691	C₂³	—	10	4	no	—
692	C₂³	—	20	2	no	—
693	C₂³	—	20	2	no	—
694	C₂³	—	20	2	no	—
695	C₂³	—	20	2	no	—
696	C₂³	—	20	2	no	—
697	C₂³	—	20	2	no	—
698	C₂³	—	20	2	no	—
699	C₂³	—	20	2	no	—
700	C₂³	—	20	2	no	—
701	C₂³	—	20	32	no	—
702	C₂³	C₂³×D₅	1	2	yes	—
703	C₂³	C₂³×D₅	1	2	yes	—
704	C₂³	C₂³×D₅	1	1	yes	characteristic
705	C₂³	C₂³×D₅	1	2	yes	—
706	C₂³	C₂³×D₅	1	1	yes	characteristic
707	Q₈	—	10	2	no	—
708	Q₈	—	10	2	no	—
709	D₄	—	2	4	no	—
710	D₄	—	2	4	no	—
711	D₄	—	2	2	no	—
712	D₄	—	2	4	no	—
713	D₄	—	2	2	no	—
714	D₄	—	2	2	no	—
715	D₄	—	4	2	no	—
716	D₄	—	4	2	no	—
717	D₄	—	4	2	no	—
718	D₄	—	5	8	no	—
719	D₄	—	5	4	no	—
720	D₄	—	10	4	no	—
721	D₄	—	10	2	no	—
722	D₄	—	10	2	no	—
723	D₄	—	10	4	no	—
724	D₄	—	10	2	no	—
725	D₄	—	10	4	no	—
726	D₄	—	10	2	no	—
727	D₄	—	10	4	no	—
728	D₄	—	10	4	no	—
729	D₄	—	10	4	no	—
730	D₄	—	10	4	no	—
731	D₄	—	10	2	no	—
732	D₄	—	10	4	no	—
733	D₄	—	10	4	no	—
734	D₄	—	10	2	no	—
735	D₄	—	10	2	no	—
736	D₄	—	20	2	no	—
737	D₄	—	20	2	no	—
738	D₄	—	20	2	no	—
739	D₄	—	20	2	no	—
740	D₄	—	20	2	no	—
741	D₄	D₄×D₅	1	4	yes	complemented
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	4	2	no	—
745	C₂×C₄	—	5	1	no	—
746	C₂×C₄	—	5	4	no	—
747	C₂×C₄	—	5	1	no	—
748	C₂×C₄	—	5	2	no	—
749	C₂×C₄	—	5	1	no	—
750	C₂×C₄	—	5	1	no	—
751	C₂×C₄	—	5	2	no	—
752	C₂×C₄	—	5	1	no	—
753	C₂×C₄	—	10	2	no	—
754	C₂×C₄	—	10	2	no	—
755	C₂×C₄	—	10	4	no	—
756	C₂×C₄	—	10	2	no	—
757	C₂×C₄	—	10	4	no	—
758	C₂×C₄	—	10	4	no	—
759	C₂×C₄	—	10	2	no	—
760	C₂×C₄	—	10	2	no	—
761	C₂×C₄	—	20	2	no	—
762	C₂×C₄	—	20	2	no	—
763	C₂×C₄	—	20	2	no	—
764	C₂×C₄	C₂³×D₅	1	2	yes	—
765	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
766	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
767	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
768	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
769	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
770	C₅	#3484	1	1	yes	characteristic, complemented, Sylow
771	C₂²	—	2	1	no	—
772	C₂²	—	2	2	no	—
773	C₂²	—	2	2	no	—
774	C₂²	—	2	1	no	—
775	C₂²	—	2	1	no	—
776	C₂²	—	2	2	no	—
777	C₂²	—	2	2	no	—
778	C₂²	—	2	1	no	—
779	C₂²	—	2	2	no	—
780	C₂²	—	2	2	no	—
781	C₂²	—	2	2	no	—
782	C₂²	—	2	2	no	—
783	C₂²	—	2	1	no	—
784	C₂²	—	4	8	no	—
785	C₂²	—	5	2	no	—
786	C₂²	—	5	4	no	—
787	C₂²	—	5	2	no	—
788	C₂²	—	8	4	no	—
789	C₂²	—	10	8	no	—
790	C₂²	—	10	1	no	—
791	C₂²	—	10	2	no	—
792	C₂²	—	10	1	no	—
793	C₂²	—	10	1	no	—
794	C₂²	—	10	2	no	—
795	C₂²	—	10	1	no	—
796	C₂²	—	10	1	no	—
797	C₂²	—	10	2	no	—
798	C₂²	—	10	1	no	—
799	C₂²	—	10	2	no	—
800	C₂²	—	10	1	no	—
801	C₂²	—	10	2	no	—
802	C₂²	—	20	8	no	—
803	C₂²	—	20	8	no	—
804	C₂²	—	20	8	no	—
805	C₂²	—	20	8	no	—
806	C₂²	—	20	8	no	—
807	C₂²	—	40	4	no	—
808	C₂²	C₂×D₄×D₅	1	4	yes	—
809	C₂²	#4144	1	2	yes	complemented
810	C₂²	C₂⁴×D₅	1	1	yes	characteristic
811	C₄	—	2	1	no	—
812	C₄	—	2	1	no	—
813	C₄	—	2	1	no	—
814	C₄	—	2	2	no	—
815	C₄	—	2	1	no	—
816	C₄	—	5	2	no	—
817	C₄	—	10	1	no	—
818	C₄	—	10	2	no	—
819	C₄	—	10	1	no	—
820	C₄	—	10	1	no	—
821	C₄	—	10	2	no	—
822	C₄	—	10	1	no	—
823	C₄	C₂×D₄×D₅	1	2	yes	—
824	C₂	—	2	2	no	—
825	C₂	—	2	4	no	—
826	C₂	—	4	2	no	—
827	C₂	—	4	1	no	—
828	C₂	—	4	2	no	—
829	C₂	—	10	2	no	—
830	C₂	—	10	2	no	—
831	C₂	—	10	4	no	—
832	C₂	—	20	2	no	—
833	C₂	—	20	1	no	—
834	C₂	C₂²×D₄×D₅	1	1	yes	characteristic
835	C₂	C₂×#4144	1	1	yes	characteristic
836	C₂	D₅×H(5,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅
commutator, socle, cosocle	C₂²×C₅	C₂⁵
Fitting	C₅×D₄²	C₂
hypercenter	D₄²	D₅
hypocenter	C₅	#3484
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ D₄²

Complements

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

N	H ≅ G/N	type
1. C₂×#4144	C₂	semidirect
2. C₂²×D₄×D₅	C₂	semidirect
3. C₅×D₄²	C₂	semidirect
4. #66140	C₂	semidirect
5. D₄×C₂²⋊D₅	C₂	semidirect
6. D₄×C₂²⋊D₅	C₂	semidirect
7. C₂×#4083	C₂	semidirect
8. #66051	C₂	semidirect
9. #66049	C₂	semidirect
10. #65946	C₂	semidirect
11. #65944	C₂	semidirect
12. #65943	C₂	semidirect
13. #65941	C₂	semidirect
14. #65940	C₂	semidirect
15. #65939	C₂	semidirect
16. #65925	C₂	semidirect
17. #65924	C₂	semidirect
18. #65923	C₂	semidirect
19. D₅×#120	C₂	semidirect
20. #65888	C₂	semidirect
21. #65884	C₂	semidirect
22. #65881	C₂	semidirect
23. #65879	C₂	semidirect
24. C₂⁴×D₅	C₂²	semidirect
25. C₂²×C₅×D₄	C₂²	semidirect
26. C₂²×C₅×D₄	C₂²	semidirect
27. C₂²×C₅×D₄	C₂²	semidirect
28. C₂²×C₂²⋊D₅	C₂²	semidirect
29. C₂²×C₂²⋊D₅	C₂²	semidirect
30. C₂²×C₂²⋊D₅	C₂²	semidirect
31. C₂²×C₂²⋊D₅	C₂²	semidirect
33. C₂×#711	C₂²	semidirect
34. C₂×#711	C₂²	semidirect
35. C₂×#711	C₂²	semidirect
38. C₂×D₄×D₅	C₂²	semidirect
39. C₂×D₄×D₅	C₂²	semidirect
40. C₂×D₄×D₅	C₂²	semidirect
41. C₂×D₄×D₅	C₂²	semidirect
42. C₂×D₄×D₅	C₂²	semidirect
43. C₂×D₄×D₅	C₂²	semidirect
44. C₂×D₄×D₅	C₂²	semidirect
45. C₂×D₄×D₅	C₂²	semidirect
46. C₂×D₄×D₅	C₂²	semidirect
47. C₂×#709	C₂²	semidirect
48. C₂×#709	C₂²	semidirect
49. C₂²×D₂₀	C₂²	semidirect
50. C₂²×C₄×D₅	C₂²	semidirect
51. C₅×#127	C₂²	semidirect
52. C₅×#121	C₂²	semidirect
53. C₅×#121	C₂²	semidirect
54. C₅×#121	C₂²	semidirect
55. C₅×#120	C₂²	semidirect
56. C₅×#120	C₂²	semidirect
57. C₄×C₅×D₄	C₂²	semidirect
58. C₄×C₅×D₄	C₂²	semidirect
59. #4099	C₂²	semidirect
60. #4099	C₂²	semidirect
61. C₂×C₂²⋊Dic₅	C₂²	semidirect
62. #4086	C₂²	semidirect
63. #4086	C₂²	semidirect
64. #4085	C₂²	semidirect
65. #4085	C₂²	semidirect
66. #4085	C₂²	semidirect
67. #4085	C₂²	semidirect
68. #4085	C₂²	semidirect
69. #4084	C₂²	semidirect
70. #4084	C₂²	semidirect
71. #4084	C₂²	semidirect
72. #4084	C₂²	semidirect
73. #4083	C₂²	semidirect
74. #4083	C₂²	semidirect
75. #4083	C₂²	semidirect
76. #4083	C₂²	semidirect
77. #4083	C₂²	semidirect
78. #4083	C₂²	semidirect
79. #4083	C₂²	semidirect
80. #4083	C₂²	semidirect
81. #4083	C₂²	semidirect
82. #4083	C₂²	semidirect
83. #4083	C₂²	semidirect
84. #4082	C₂²	semidirect
85. #4081	C₂²	semidirect
86. D₄×Dic₅	C₂²	semidirect
87. D₄×Dic₅	C₂²	semidirect
88. #4076	C₂²	semidirect
89. #4076	C₂²	semidirect
90. C₄×C₂²⋊D₅	C₂²	semidirect
91. C₄×C₂²⋊D₅	C₂²	semidirect
92. C₄×C₂²⋊D₅	C₂²	semidirect
93. C₂×#685	C₂²	semidirect
94. C₂×#685	C₂²	semidirect
95. #4070	C₂²	semidirect
96. #4043	C₂²	semidirect
97. #4042	C₂²	semidirect
98. #4041	C₂²	semidirect
99. #4040	C₂²	semidirect
100. #4040	C₂²	semidirect
101. #4039	C₂²	semidirect
102. #4038	C₂²	semidirect
103. #4032	C₂²	semidirect
104. #4031	C₂²	semidirect
105. #4030	C₂²	semidirect
106. #4030	C₂²	semidirect
107. #4030	C₂²	semidirect
108. #4029	C₂²	semidirect
109. #4029	C₂²	semidirect
110. #4029	C₂²	semidirect
111. #4028	C₂²	semidirect
112. #4028	C₂²	semidirect
113. #4028	C₂²	semidirect
114. #4028	C₂²	semidirect
115. #4027	C₂²	semidirect
116. #4027	C₂²	semidirect
117. D₅×C₂²⋊C₄	C₂²	semidirect
118. D₅×C₂²⋊C₄	C₂²	semidirect
119. D₅×C₂²⋊C₄	C₂²	semidirect
120. #4024	C₂²	semidirect
121. #4021	C₂²	semidirect
122. C₄×D₂₀	C₂²	semidirect
123. C₄×D₂₀	C₂²	semidirect
124. #4018	C₂²	semidirect
127. C₂⁴×C₅	C₂³	semidirect
137. C₂³×D₅	C₂³	semidirect
146. C₂×C₅×D₄	C₂³	semidirect
147. C₂×C₅×D₄	C₂³	semidirect
148. C₂×C₅×D₄	C₂³	semidirect
149. C₂×C₅×D₄	C₂³	semidirect
150. C₂×C₅×D₄	C₂³	semidirect
152. C₂²×C₄×C₅	C₂³	semidirect
153. C₂²×C₄×C₅	C₂³	semidirect
167. C₂×C₂²⋊D₅	C₂³	semidirect
168. C₂×C₂²⋊D₅	C₂³	semidirect
169. C₂×C₂²⋊D₅	C₂³	semidirect
170. C₂×C₂²⋊D₅	C₂³	semidirect
171. C₂×C₂²⋊D₅	C₂³	semidirect
172. C₂×C₂²⋊D₅	C₂³	semidirect
173. C₂×C₂²⋊D₅	C₂³	semidirect
174. C₂×C₂²⋊D₅	C₂³	semidirect
176. C₂²×Dic₅	C₂³	semidirect
177. C₂²×Dic₅	C₂³	semidirect
178. C₂²×Dic₅	C₂³	semidirect
191. D₄×D₅	D₄	semidirect
200. C₂×D₂₀	C₂³	semidirect
206. C₂×C₄×D₅	C₂³	semidirect
207. C₂×C₄×D₅	C₂³	semidirect
208. C₂×C₄×D₅	C₂³	semidirect
209. C₂×C₄×D₅	C₂³	semidirect
210. C₂×Dic₁₀	C₂³	semidirect
211. C₂×Dic₁₀	C₂³	semidirect
212. C₅×C₄⋊C₄	C₂³	semidirect
213. C₅×C₄⋊C₄	C₂³	semidirect
215. C₅×C₂²⋊C₄	C₂³	semidirect
216. C₅×C₂²⋊C₄	C₂³	semidirect
217. C₅×C₂²⋊C₄	C₂³	semidirect
218. C₅×C₂²⋊C₄	C₂³	semidirect
219. C₄²×C₅	C₂³	semidirect
222. C₂²⋊Dic₅	C₂³	semidirect
223. C₂²⋊Dic₅	C₂³	semidirect
224. C₂²⋊Dic₅	C₂³	semidirect
225. C₂²⋊Dic₅	C₂³	semidirect
226. C₂²⋊Dic₅	C₂³	semidirect
227. C₂²⋊Dic₅	C₂³	semidirect
234. #685	C₂³	semidirect
235. #685	C₂³	semidirect
236. #685	C₂³	semidirect
237. #685	C₂³	semidirect
238. #685	C₂³	semidirect
239. #685	C₂³	semidirect
240. #685	C₂³	semidirect
241. #685	C₂³	semidirect
242. C₄⋊Dic₅	C₂³	semidirect
243. C₄⋊Dic₅	C₂³	semidirect
244. C₄⋊Dic₅	C₂³	semidirect
245. #683	C₂³	semidirect
246. #683	C₂³	semidirect
247. #683	C₂³	semidirect
248. #683	C₂³	semidirect
249. #683	C₂³	semidirect
250. C₄×Dic₅	C₂³	semidirect
251. C₄×Dic₅	C₂³	semidirect
265. D₄²	D₅	semidirect
307. C₂²×D₅	C₂×D₄	semidirect
322. C₅×D₄	C₂×D₄	semidirect
348. C₂²⋊D₅	C₂×D₄	semidirect
365. D₂₀	C₂×D₄	semidirect
373. C₄×D₅	C₂×D₄	semidirect
399. C₂²×D₄	C₂×D₅	semidirect
400. C₂²×D₄	C₂×D₅	semidirect
401. C₂²×D₄	C₂×D₅	semidirect
405. #127	C₂×D₅	semidirect
435. #121	C₂×D₅	semidirect
436. #121	C₂×D₅	semidirect
437. #121	C₂×D₅	semidirect
455. #120	C₂×D₅	semidirect
456. #120	C₂×D₅	semidirect
467. C₄×D₄	C₂×D₅	semidirect
468. C₄×D₄	C₂×D₅	semidirect
493. C₂²×C₅	H(5,𝔽₂)	semidirect
516. C₂×D₅	H(5,𝔽₂)	semidirect
541. C₂⁴	C₂²×D₅	semidirect
595. C₂×D₄	C₂²×D₅	semidirect
596. C₂×D₄	C₂²×D₅	semidirect
597. C₂×D₄	C₂²×D₅	semidirect
598. C₂×D₄	C₂²×D₅	semidirect
599. C₂×D₄	C₂²×D₅	semidirect
614. C₂²×C₄	C₂²×D₅	semidirect
615. C₂²×C₄	C₂²×D₅	semidirect
624. C₄⋊C₄	C₂²×D₅	semidirect
625. C₄⋊C₄	C₂²×D₅	semidirect
649. C₂²⋊C₄	C₂²×D₅	semidirect
650. C₂²⋊C₄	C₂²×D₅	semidirect
651. C₂²⋊C₄	C₂²×D₅	semidirect
652. C₂²⋊C₄	C₂²×D₅	semidirect
655. C₄²	C₂²×D₅	semidirect
741. D₄	D₄×D₅	semidirect
770. C₅	#3484	semidirect
809. C₂²	#4144	semidirect

Maximal subgroups

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

subgroup	index
C₂×#4144	2
C₂²×D₄×D₅	2
C₅×D₄²	2
#66140	2
D₄×C₂²⋊D₅	2
C₂×#4083	2
#66051	2
#66049	2
#65946	2
#65944	2
#65943	2
#65941	2
#65940	2
#65939	2
#65925	2
#65924	2
#65923	2
D₅×#120	2
#65888	2
#65884	2
#65881	2
#65879	2
#3484	5