Subgroups — #10611213

Order 640.

502 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₅×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#4047	C₂	1	1	yes	maximal, characteristic, complemented
3	#65881	C₂	1	1	yes	maximal, characteristic
4	C₅×#435	C₂	1	1	yes	maximal, characteristic, complemented
5	#65417	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈×C₂²⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
7	#65301	C₂	1	1	yes	maximal, characteristic, complemented
8	#65128	C₂	1	1	yes	maximal, characteristic, complemented
9	#65123	C₂	1	1	yes	maximal, characteristic, complemented
10	#65017	C₂	1	1	yes	maximal, characteristic, complemented
11	#65017	C₂	1	1	yes	maximal, characteristic, complemented
12	#65016	C₂	1	1	yes	maximal, characteristic, complemented
13	D₅×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
14	#64997	C₂	1	1	yes	maximal, characteristic, complemented
15	#64995	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#709	C₂²	1	1	yes	characteristic
17	C₂²×C₄×D₅	C₂²	1	1	yes	characteristic
18	C₂×C₅×M₁₆	C₂²	1	1	yes	characteristic
19	C₂²×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
20	C₄×C₅×D₄	C₂²	1	1	yes	characteristic
21	#4085	C₄	1	1	yes	characteristic
22	#4083	C₄	1	1	yes	characteristic
23	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
24	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
25	C₂×#681	C₂²	1	1	yes	characteristic
26	C₂×#681	C₂²	1	1	yes	characteristic, complemented
27	D₅×M₁₆	—	2	4	no	—
28	#4047	—	2	4	no	—
29	C₂×#676	C₂²	1	1	yes	characteristic
30	C₂×#676	C₂²	1	1	yes	characteristic
31	C₂×#676	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₈×D₅	C₂²	1	1	yes	characteristic
33	C₂×C₈×D₅	C₂²	1	1	yes	characteristic
34	C₂×C₈×D₅	C₂²	1	1	yes	characteristic
35	C₂×C₈×D₅	C₂²	1	1	yes	characteristic
36	C₂×C₈×D₅	C₂²	1	1	yes	characteristic, complemented
37	#4042	C₄	1	1	yes	characteristic
38	#4040	C₄	1	1	yes	characteristic
39	#4030	C₄	1	1	yes	characteristic
40	#4029	C₄	1	1	yes	characteristic
41	#4028	C₄	1	1	yes	characteristic
42	#4024	C₄	1	1	yes	characteristic
43	C₄×D₂₀	C₂²	1	1	yes	characteristic
44	#4018	C₂²	1	1	yes	characteristic
45	C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
46	C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
47	C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
48	C₅×#97	C₂²	1	1	yes	characteristic, complemented
49	C₂²⋊#168	C₂²	1	1	yes	characteristic
50	C₂²⋊#168	C₂²	1	1	yes	characteristic, complemented
51	#3952	C₂²	1	1	yes	characteristic
52	#3952	C₂²	1	1	yes	characteristic
53	#3952	C₂²	1	1	yes	characteristic, complemented
54	#3952	C₂²	1	1	yes	characteristic, complemented
55	#3947	C₂²	1	1	yes	characteristic, complemented
56	#3946	C₂²	1	1	yes	characteristic, complemented
57	#3946	C₂²	1	1	yes	characteristic, complemented
58	C₈×Dic₅	C₂²	1	1	yes	characteristic, complemented
59	C₄⋊#168	C₂²	1	1	yes	characteristic, complemented
60	C₄×#168	C₂²	1	1	yes	characteristic, complemented
61	#2933	—	5	1	no	maximal, Sylow
62	C₂³×D₅	C₂×C₄	1	1	yes	characteristic
63	C₂×C₅×D₄	C₂×C₄	1	1	yes	characteristic
64	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
65	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
66	C₂×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
67	C₂×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
68	C₂×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
69	C₂×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
70	C₂²×Dic₅	C₂×C₄	1	1	yes	characteristic
71	#709	—	2	2	no	—
72	#709	—	2	2	no	—
73	C₂×D₂₀	C₂×C₄	1	1	yes	characteristic
74	C₂×D₂₀	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄×D₅	—	2	2	no	—
76	C₂×C₄×D₅	—	2	2	no	—
77	C₂×C₄×D₅	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄×D₅	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
80	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
81	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
82	C₂×Dic₁₀	C₂×C₄	1	1	yes	characteristic
83	C₅×M₁₆	—	2	2	no	—
84	C₂×C₅×C₈	—	2	2	no	—
85	C₂×C₅×C₈	C₂³	1	1	yes	characteristic
86	C₂×C₅×C₈	C₂³	1	1	yes	characteristic
87	C₂×C₅×C₈	C₂³	1	1	yes	characteristic
88	C₂×C₅×C₈	C₂³	1	1	yes	characteristic
89	C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
90	C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
91	C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
92	C₄²×C₅	C₂³	1	1	yes	characteristic
93	C₂²⋊Dic₅	C₂×C₄	1	1	yes	characteristic
94	C₂²⋊Dic₅	C₂×C₄	1	1	yes	characteristic
95	#685	C₂×C₄	1	1	yes	characteristic
96	#685	C₂×C₄	1	1	yes	characteristic
97	#685	C₂×C₄	1	1	yes	characteristic
98	#685	C₂×C₄	1	1	yes	characteristic
99	#685	C₂×C₄	1	1	yes	characteristic
100	#685	C₂×C₄	1	1	yes	characteristic
101	C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
102	#683	C₂×C₄	1	1	yes	characteristic
103	#683	C₂×C₄	1	1	yes	characteristic
104	#683	C₂×C₄	1	1	yes	characteristic
105	#683	C₂×C₄	1	1	yes	characteristic
106	C₄×Dic₅	C₂³	1	1	yes	characteristic
107	#681	—	2	2	no	—
108	#681	—	2	2	no	—
109	C₂×#168	C₂³	1	1	yes	characteristic
110	C₂×#168	C₂³	1	1	yes	characteristic
111	C₂×#168	C₂³	1	1	yes	characteristic
112	C₂×#168	C₂³	1	1	yes	characteristic
113	#676	—	2	2	no	—
114	#676	—	2	2	no	—
115	#676	D₄	1	4	yes	complemented
116	C₈×D₅	—	2	2	no	—
117	C₈×D₅	—	2	2	no	—
118	C₈×D₅	—	2	2	no	—
119	C₈×D₅	—	2	2	no	—
120	C₈×D₅	—	2	2	no	—
121	C₂×#131	—	5	1	no	—
122	C₂²×M₁₆	—	5	1	no	—
123	#525	—	5	1	no	—
124	#436	—	5	1	no	—
125	#436	—	5	1	no	—
126	#435	—	5	1	no	—
127	#435	—	5	1	no	—
128	#435	—	5	1	no	—
129	#435	D₅	1	1	yes	characteristic, complemented
130	C₈×D₄	—	5	1	no	—
131	C₈×D₄	—	5	1	no	—
132	#424	—	5	1	no	—
133	#408	—	5	1	no	—
134	C₂×C₂²⋊C₈	—	5	1	no	—
135	#405	—	5	1	no	—
136	C₂³×C₅	C₂²×C₄	1	1	yes	characteristic
137	C₂³×C₅	C₂²×C₄	1	1	yes	characteristic
138	C₂²×D₅	—	2	2	no	—
139	C₂²×D₅	—	2	2	no	—
140	C₂²×D₅	—	4	1	no	—
141	C₂²×D₅	C₂²×C₄	1	1	yes	characteristic
142	C₂²×D₅	C₂²×C₄	1	1	yes	characteristic
143	C₂²×D₅	C₂²×C₄	1	1	yes	characteristic
144	C₅×D₄	—	4	1	no	—
145	C₂×C₄×C₅	—	2	1	no	—
146	C₂×C₄×C₅	—	2	1	no	—
147	C₂×C₄×C₅	—	2	1	no	—
148	C₂×C₄×C₅	—	2	1	no	—
149	C₂×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
153	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
154	C₂²⋊D₅	—	2	2	no	—
155	C₂²⋊D₅	—	2	2	no	—
156	C₂²⋊D₅	—	2	2	no	—
157	C₂²⋊D₅	—	4	1	no	—
158	C₂×Dic₅	—	2	2	no	—
159	C₂×Dic₅	C₂²×C₄	1	1	yes	characteristic
160	C₂×Dic₅	C₂²×C₄	1	1	yes	characteristic
161	C₂×Dic₅	C₂²×C₄	1	1	yes	characteristic
162	C₂×Dic₅	C₂²×C₄	1	1	yes	characteristic
163	C₂×Dic₅	C₂²×C₄	1	1	yes	characteristic
164	D₂₀	—	2	2	no	—
165	D₂₀	—	2	2	no	—
166	C₄×D₅	—	2	2	no	—
167	C₄×D₅	—	2	1	no	—
168	C₄×D₅	—	2	1	no	—
169	C₄×D₅	—	2	1	no	—
170	C₄×D₅	—	2	1	no	—
171	C₄×D₅	—	2	2	no	—
172	C₄×D₅	C₂×D₄	1	2	yes	—
173	C₄×D₅	#41	1	2	yes	—
174	Dic₁₀	—	2	2	no	—
175	C₅×C₈	—	2	1	no	—
176	C₅×C₈	—	2	1	no	—
177	C₅×C₈	—	2	1	no	—
178	C₅×C₈	C₂×D₄	1	2	yes	—
179	#168	—	2	1	no	—
180	#168	—	2	1	no	—
181	#168	—	2	1	no	—
182	#168	C₂×D₄	1	2	yes	—
183	C₂×#41	—	5	1	no	—
184	C₂³×C₄	—	5	1	no	—
185	#131	—	10	4	no	—
186	C₂×M₁₆	—	5	1	no	—
187	C₂×M₁₆	—	5	1	no	—
188	C₂×M₁₆	—	5	1	no	—
189	C₂×M₁₆	—	5	1	no	—
190	C₂×M₁₆	—	5	1	no	—
191	C₂×M₁₆	—	10	4	no	—
192	C₂×M₁₆	C₂×D₅	1	1	yes	characteristic
193	C₂²×C₈	—	5	1	no	—
194	C₂²×C₈	—	5	1	no	—
195	C₂²×C₈	—	5	1	no	—
196	C₂²×C₈	—	5	1	no	—
197	C₂²×C₈	—	5	1	no	—
198	C₂²×C₈	C₂×D₅	1	1	yes	characteristic, complemented
199	#123	—	5	1	no	—
200	#123	—	5	1	no	—
201	C₂²⋊Q₈	—	5	1	no	—
202	C₂²⋊Q₈	—	5	1	no	—
203	#121	—	5	1	no	—
204	#121	—	5	1	no	—
205	#120	—	5	1	no	—
206	#120	—	5	1	no	—
207	C₄×D₄	—	5	1	no	—
208	C₄×D₄	—	5	1	no	—
209	C₄×D₄	—	5	1	no	—
210	C₄×D₄	C₂×D₅	1	1	yes	characteristic
211	#117	—	5	1	no	—
212	C₄⋊C₈	—	5	1	no	—
213	C₄⋊C₈	—	5	1	no	—
214	C₄⋊C₈	—	5	1	no	—
215	C₄⋊C₈	C₂×D₅	1	1	yes	characteristic, complemented
216	C₂²⋊C₈	—	5	1	no	—
217	C₂²⋊C₈	—	5	1	no	—
218	C₂²⋊C₈	—	5	1	no	—
219	C₂²⋊C₈	—	5	1	no	—
220	C₂²⋊C₈	—	5	1	no	—
221	C₂²⋊C₈	—	5	1	no	—
222	C₂²⋊C₈	C₂×D₅	1	1	yes	characteristic
223	C₂²⋊C₈	C₂×D₅	1	1	yes	characteristic, complemented
224	#97	—	5	1	no	—
225	#97	C₂×D₅	1	1	yes	characteristic, complemented
226	C₄×C₈	—	5	1	no	—
227	C₄×C₈	—	5	1	no	—
228	C₂²×C₅	—	2	1	no	—
229	C₂²×C₅	—	2	1	no	—
230	C₂²×C₅	—	2	1	no	—
231	C₂²×C₅	—	2	1	no	—
232	C₂²×C₅	—	2	1	no	—
233	C₂²×C₅	—	2	1	no	—
234	C₂²×C₅	C₂³×C₄	1	1	yes	characteristic
235	C₂×D₅	—	2	1	no	—
236	C₂×D₅	—	2	1	no	—
237	C₂×D₅	—	2	1	no	—
238	C₂×D₅	—	2	1	no	—
239	C₂×D₅	—	2	1	no	—
240	C₂×D₅	—	2	1	no	—
241	C₂×D₅	—	2	1	no	—
242	C₂×D₅	—	4	4	no	—
243	C₂×D₅	C₄×D₄	1	2	yes	—
244	C₂×D₅	#131	1	2	yes	complemented
245	C₄×C₅	—	2	1	no	—
246	C₄×C₅	—	2	1	no	—
247	C₄×C₅	—	2	1	no	—
248	C₄×C₅	—	2	1	no	—
249	C₄×C₅	C₂²×D₄	1	1	yes	characteristic
250	C₄×C₅	C₂×#41	1	1	yes	characteristic
251	Dic₅	—	2	1	no	—
252	Dic₅	—	2	1	no	—
253	Dic₅	—	2	1	no	—
254	Dic₅	—	2	1	no	—
255	Dic₅	C₄×D₄	1	2	yes	—
256	C₂⁴	—	5	1	no	—
257	#41	—	10	2	no	—
258	#41	—	10	2	no	—
259	C₂×Q₈	—	5	1	no	—
260	C₂×D₄	—	5	1	no	—
261	C₂×D₄	—	5	1	no	—
262	C₂×D₄	—	5	1	no	—
263	C₂×D₄	—	5	1	no	—
264	C₂×D₄	—	5	1	no	—
265	C₂×D₄	—	5	1	no	—
266	C₂×D₄	C₄×D₅	1	1	yes	characteristic
267	C₂²×C₄	—	5	1	no	—
268	C₂²×C₄	—	5	1	no	—
269	C₂²×C₄	—	5	1	no	—
270	C₂²×C₄	—	5	1	no	—
271	C₂²×C₄	—	5	1	no	—
272	C₂²×C₄	—	5	1	no	—
273	C₂²×C₄	—	10	2	no	—
274	C₂²×C₄	—	10	2	no	—
275	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
276	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
277	M₁₆	—	2	2	no	—
278	M₁₆	—	5	4	no	—
279	M₁₆	—	10	2	no	—
280	M₁₆	—	10	2	no	—
281	M₁₆	—	10	2	no	—
282	M₁₆	—	10	2	no	—
283	C₂×C₈	—	2	2	no	—
284	C₂×C₈	—	5	1	no	—
285	C₂×C₈	—	5	1	no	—
286	C₂×C₈	—	5	1	no	—
287	C₂×C₈	—	5	1	no	—
288	C₂×C₈	—	10	2	no	—
289	C₂×C₈	—	10	2	no	—
290	C₂×C₈	—	10	2	no	—
291	C₂×C₈	—	10	2	no	—
292	C₂×C₈	—	10	2	no	—
293	C₂×C₈	C₂²×D₅	1	1	yes	characteristic
294	C₂×C₈	C₂²×D₅	1	1	yes	characteristic
295	C₂×C₈	C₂²×D₅	1	1	yes	characteristic
296	C₂×C₈	C₂²×D₅	1	1	yes	characteristic
297	C₄⋊C₄	—	5	1	no	—
298	C₄⋊C₄	—	5	1	no	—
299	C₄⋊C₄	—	5	1	no	—
300	C₄⋊C₄	—	5	1	no	—
301	C₄⋊C₄	—	5	1	no	—
302	C₄⋊C₄	C₄×D₅	1	1	yes	characteristic
303	C₂²⋊C₄	—	5	1	no	—
304	C₂²⋊C₄	—	5	1	no	—
305	C₂²⋊C₄	—	5	1	no	—
306	C₂²⋊C₄	—	5	1	no	—
307	C₂²⋊C₄	—	5	1	no	—
308	C₂²⋊C₄	—	5	1	no	—
309	C₂²⋊C₄	—	5	1	no	—
310	C₂²⋊C₄	—	5	1	no	—
311	C₂²⋊C₄	C₄×D₅	1	1	yes	characteristic
312	C₂²⋊C₄	C₄×D₅	1	1	yes	characteristic
313	C₄²	—	5	1	no	—
314	C₄²	C₂²×D₅	1	1	yes	characteristic
315	C₂×C₅	—	4	1	no	—
316	C₂×C₅	—	4	1	no	—
317	C₂×C₅	C₂×C₄×D₄	1	1	yes	characteristic
318	C₂×C₅	C₂×#131	1	1	yes	characteristic
319	C₂×C₅	#568	1	1	yes	characteristic
320	D₅	—	2	2	no	—
321	D₅	—	2	2	no	—
322	D₅	—	4	1	no	—
323	C₂³	—	5	1	no	—
324	C₂³	—	5	1	no	—
325	C₂³	—	5	1	no	—
326	C₂³	—	10	2	no	—
327	C₂³	—	10	2	no	—
328	C₂³	—	20	1	no	—
329	C₂³	C₂×C₄×D₅	1	1	yes	characteristic
330	C₂³	C₂×C₄×D₅	1	1	yes	characteristic
331	Q₈	—	10	2	no	—
332	D₄	—	4	1	no	—
333	D₄	—	10	2	no	—
334	D₄	—	10	2	no	—
335	D₄	—	10	2	no	—
336	D₄	—	10	2	no	—
337	D₄	—	10	2	no	—
338	D₄	—	20	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	5	1	no	—
344	C₂×C₄	—	5	2	no	—
345	C₂×C₄	—	5	2	no	—
346	C₂×C₄	—	5	1	no	—
347	C₂×C₄	—	5	1	no	—
348	C₂×C₄	—	5	1	no	—
349	C₂×C₄	—	5	1	no	—
350	C₂×C₄	—	10	2	no	—
351	C₂×C₄	—	10	2	no	—
352	C₂×C₄	—	10	2	no	—
353	C₂×C₄	—	10	1	no	—
354	C₂×C₄	—	10	1	no	—
355	C₂×C₄	—	10	1	no	—
356	C₂×C₄	—	10	1	no	—
357	C₂×C₄	C₂×C₄×D₅	1	1	yes	characteristic
358	C₂×C₄	C₂×C₄×D₅	1	1	yes	characteristic
359	C₂×C₄	C₂×C₄×D₅	1	1	yes	characteristic
360	C₂×C₄	C₂×C₄×D₅	1	1	yes	characteristic
361	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
362	C₈	—	2	1	no	—
363	C₈	—	2	1	no	—
364	C₈	—	2	1	no	—
365	C₈	—	5	2	no	—
366	C₈	—	10	1	no	—
367	C₈	—	10	1	no	—
368	C₈	—	10	1	no	—
369	C₈	D₄×D₅	1	2	yes	—
370	C₅	#2933	1	1	yes	characteristic, complemented, Sylow
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	2	1	no	—
377	C₂²	—	5	2	no	—
378	C₂²	—	5	2	no	—
379	C₂²	—	10	1	no	—
380	C₂²	—	10	1	no	—
381	C₂²	—	10	1	no	—
382	C₂²	—	10	1	no	—
383	C₂²	—	10	1	no	—
384	C₂²	—	10	1	no	—
385	C₂²	—	10	1	no	—
386	C₂²	—	20	4	no	—
387	C₂²	C₂²×C₄×D₅	1	1	yes	characteristic
388	C₄	—	2	1	no	—
389	C₄	—	2	1	no	—
390	C₄	—	2	1	no	—
391	C₄	—	2	1	no	—
392	C₄	—	5	2	no	—
393	C₄	—	10	1	no	—
394	C₄	—	10	1	no	—
395	C₄	—	10	1	no	—
396	C₄	—	10	1	no	—
397	C₄	C₂×D₄×D₅	1	1	yes	characteristic
398	C₄	D₅×#41	1	1	yes	characteristic
399	C₂	—	4	1	no	—
400	C₂	—	4	1	no	—
401	C₂	—	10	2	no	—
402	C₂	—	10	2	no	—
403	C₂	—	20	1	no	—
404	C₂	C₄×D₄×D₅	1	1	yes	characteristic
405	C₂	#66079	1	1	yes	characteristic
406	C₂	D₅×#131	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₅
commutator, socle	C₂²×C₅	C₂³×C₄
Fitting	C₅×#435	C₂
prime radical	#65881	C₂
cosocle	C₂×C₄×C₅	C₂⁴
hypercenter	#435	D₅
hypocenter	C₅	#2933
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ #435

Complements

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

N	H ≅ G/N	type
1. C₂×D₅×M₁₆	C₂	semidirect
2. C₂×#4047	C₂	semidirect
4. C₅×#435	C₂	semidirect
5. #65417	C₂	semidirect
6. C₈×C₂²⋊D₅	C₂	semidirect
7. #65301	C₂	semidirect
8. #65128	C₂	semidirect
9. #65123	C₂	semidirect
10. #65017	C₂	semidirect
11. #65017	C₂	semidirect
12. #65016	C₂	semidirect
13. D₅×C₂²⋊C₈	C₂	semidirect
14. #64997	C₂	semidirect
15. #64995	C₂	semidirect
19. C₂²×C₅×C₈	C₂²	semidirect
26. C₂×#681	C₂²	semidirect
31. C₂×#676	C₂²	semidirect
36. C₂×C₈×D₅	C₂²	semidirect
45. C₅×C₄⋊C₈	C₂²	semidirect
47. C₅×C₂²⋊C₈	C₂²	semidirect
48. C₅×#97	C₂²	semidirect
50. C₂²⋊#168	C₂²	semidirect
53. #3952	C₂²	semidirect
54. #3952	C₂²	semidirect
55. #3947	C₂²	semidirect
56. #3946	C₂²	semidirect
57. #3946	C₂²	semidirect
58. C₈×Dic₅	C₂²	semidirect
59. C₄⋊#168	C₂²	semidirect
60. C₄×#168	C₂²	semidirect
115. #676	D₄	semidirect
129. #435	D₅	semidirect
198. C₂²×C₈	C₂×D₅	semidirect
215. C₄⋊C₈	C₂×D₅	semidirect
223. C₂²⋊C₈	C₂×D₅	semidirect
225. #97	C₂×D₅	semidirect
244. C₂×D₅	#131	semidirect
370. C₅	#2933	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₅×M₁₆	2
C₂×#4047	2
#65881	2
C₅×#435	2
#65417	2
C₈×C₂²⋊D₅	2
#65301	2
#65128	2
#65123	2
#65017	2
#65016	2
D₅×C₂²⋊C₈	2
#64997	2
#64995	2
#2933	5