Subgroups — D₅×#2170 #12252524

Order 1280.

662 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×#504	C₂	1	2	yes	maximal, complemented
2	D₅×#443	C₂	1	1	yes	maximal, characteristic
3	C₅×#2170	C₂	1	1	yes	maximal, characteristic, complemented
4	#10602245	C₂	1	2	yes	maximal, complemented
5	#10601716	C₂	1	1	yes	maximal, characteristic, complemented
6	D₅×#364	C₂	1	1	yes	maximal, characteristic, complemented
7	#10600093	C₂	1	1	yes	maximal, characteristic, complemented
8	D₅×#350	C₂	1	2	yes	maximal, complemented
9	#10599915	C₂	1	2	yes	maximal, complemented
10	#10599849	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×D₅×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	D₅×#135	C₄	1	1	yes	characteristic
13	D₅×#131	C₂²	1	2	yes	—
14	C₅×#504	C₂²	1	2	yes	complemented
15	C₅×#443	C₂²	1	1	yes	characteristic
16	#65485	C₄	1	1	yes	characteristic
17	#65433	C₂²	1	2	yes	—
18	#65429	C₂²	1	2	yes	complemented
19	#65196	—	2	2	no	—
20	#65196	C₂²	1	2	yes	complemented
21	D₅×M₃₂	—	2	2	no	—
22	D₅×M₃₂	C₂²	1	2	yes	—
23	#65190	—	2	2	no	—
24	#65190	C₂²	1	2	yes	complemented
25	C₂×D₅×C₁₆	—	2	2	no	—
26	C₂×D₅×C₁₆	C₂²	1	1	yes	characteristic
27	C₂×D₅×C₁₆	C₂²	1	1	yes	characteristic
28	#65184	C₄	1	1	yes	characteristic
29	D₅×#108	C₄	1	1	yes	characteristic
30	#65113	C₄	1	2	yes	—
31	D₅×#104	C₄	1	2	yes	—
32	#64989	C₂²	1	1	yes	characteristic
33	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
34	C₅×#364	C₂²	1	1	yes	characteristic, complemented
35	C₅×#350	C₂²	1	2	yes	complemented
36	C₄×C₅×C₁₆	C₂²	1	1	yes	characteristic, complemented
37	#64781	C₂²	1	2	yes	complemented
38	#64735	C₂²	1	2	yes	complemented
39	#64731	C₂²	1	2	yes	complemented
40	#64728	C₂²	1	2	yes	complemented
41	C₁₆×Dic₅	C₂²	1	1	yes	characteristic, complemented
42	C₁₆×Dic₅	C₂²	1	1	yes	characteristic, complemented
43	#64683	C₂²	1	1	yes	characteristic, complemented
44	C₄×#672	C₂²	1	1	yes	characteristic, complemented
45	C₂×#2170	—	5	1	no	maximal, Sylow
46	D₅×#41	C₂×C₄	1	2	yes	—
47	C₅×#135	C₂×C₄	1	1	yes	characteristic
48	C₅×#131	C₂³	1	2	yes	—
49	#4096	C₂×C₄	1	2	yes	—
50	#4094	C₂×C₄	1	2	yes	—
51	#4065	C₈	1	1	yes	characteristic
52	D₅×Q₁₆	C₈	1	1	yes	characteristic
53	#4062	C₈	1	2	yes	—
54	D₅×SD₁₆	C₈	1	2	yes	—
55	#4058	C₈	1	1	yes	characteristic
56	D₅×D₈	C₈	1	1	yes	characteristic
57	#4053	—	2	2	no	—
58	#4053	C₂×C₄	1	2	yes	—
59	D₅×M₁₆	—	2	2	no	—
60	D₅×M₁₆	C₂×C₄	1	2	yes	—
61	#4050	C₂×C₄	1	1	yes	characteristic
62	#4047	—	2	2	no	—
63	#4047	C₂³	1	2	yes	—
64	C₂×C₈×D₅	—	2	2	no	—
65	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
66	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
67	C₄²×D₅	C₂×C₄	1	1	yes	characteristic
68	C₅×M₃₂	—	2	2	no	—
69	C₅×M₃₂	C₂³	1	2	yes	—
70	C₂×C₅×C₁₆	—	2	2	no	—
71	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
72	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
73	C₅×#108	C₂×C₄	1	1	yes	characteristic
74	C₅×#104	C₂×C₄	1	2	yes	—
75	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
76	#3969	C₂×C₄	1	2	yes	—
77	#3957	C₂×C₄	1	2	yes	—
78	#3954	C₂×C₄	1	2	yes	—
79	#3951	C₂×C₄	1	1	yes	characteristic
80	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
81	C₈×Dic₅	C₂³	1	1	yes	characteristic
82	#3944	—	2	2	no	—
83	#3944	C₂³	1	2	yes	—
84	C₂×#672	—	2	2	no	—
85	C₂×#672	C₂³	1	1	yes	characteristic
86	C₂×#672	C₂³	1	1	yes	characteristic
87	#3937	C₂×C₄	1	2	yes	—
88	C₄×#168	C₂×C₄	1	1	yes	characteristic
89	#3930	—	2	2	no	—
90	#3930	—	2	2	no	—
91	#3930	—	2	2	no	—
92	D₅×C₁₆	—	2	2	no	—
93	D₅×C₁₆	—	2	1	no	—
94	D₅×C₁₆	—	2	1	no	—
95	D₅×C₁₆	—	2	2	no	—
96	D₅×C₁₆	—	2	2	no	—
97	D₅×C₁₆	D₄	1	1	yes	characteristic
98	D₅×C₁₆	D₄	1	1	yes	characteristic
99	D₅×C₁₆	D₄	1	1	yes	characteristic
100	D₅×C₁₆	D₄	1	1	yes	characteristic
101	C₂×#504	—	5	2	no	—
102	C₂×#443	—	5	1	no	—
103	#2170	—	5	2	no	—
104	#2170	—	5	1	no	—
105	#2170	—	5	1	no	—
106	#2170	—	5	2	no	—
107	#2170	—	5	1	no	—
108	#2170	D₅	1	1	yes	characteristic, direct product factor
109	C₂×#364	—	5	1	no	—
110	C₂×#350	—	5	2	no	—
111	C₂×C₄×C₁₆	—	5	1	no	—
112	C₅×#41	C₂²×C₄	1	2	yes	—
113	#713	C₂×C₈	1	2	yes	—
114	Q₈×D₅	C₂×C₈	1	2	yes	—
115	#711	—	2	2	no	—
116	#711	C₂×C₈	1	2	yes	—
117	D₄×D₅	—	2	2	no	—
118	D₄×D₅	C₂×C₈	1	2	yes	—
119	#709	—	2	2	no	—
120	#709	C₂²×C₄	1	2	yes	—
121	C₂×C₄×D₅	—	2	1	no	—
122	C₂×C₄×D₅	—	2	2	no	—
123	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
124	C₅×Q₁₆	C₂×C₈	1	1	yes	characteristic
125	C₅×SD₁₆	C₂×C₈	1	2	yes	—
126	C₅×D₈	C₂×C₈	1	1	yes	characteristic
127	C₅×M₁₆	—	2	2	no	—
128	C₅×M₁₆	C₂²×C₄	1	2	yes	—
129	C₂×C₅×C₈	—	2	2	no	—
130	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
132	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
133	#689	C₂×C₈	1	2	yes	—
134	#688	C₂×C₈	1	2	yes	—
135	#687	C₂×C₈	1	2	yes	—
136	#686	C₂×C₈	1	2	yes	—
137	C₄×Dic₅	—	2	1	no	—
138	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
139	#681	—	2	2	no	—
140	#681	C₂²×C₄	1	2	yes	—
141	C₂×#168	—	2	2	no	—
142	C₂×#168	C₂²×C₄	1	1	yes	characteristic
143	C₂×#168	C₂²×C₄	1	1	yes	characteristic
144	Dic₂₀	C₂×C₈	1	1	yes	characteristic
145	D₄₀	C₂×C₈	1	1	yes	characteristic
146	#677	C₂×C₈	1	2	yes	—
147	#676	—	2	2	no	—
148	#676	—	2	2	no	—
149	#676	—	2	2	no	—
150	C₈×D₅	—	2	2	no	—
151	C₈×D₅	—	2	2	no	—
152	C₈×D₅	—	2	2	no	—
153	C₈×D₅	C₂×C₈	1	1	yes	characteristic
154	C₈×D₅	C₂×C₈	1	1	yes	characteristic
155	C₈×D₅	C₂×C₈	1	1	yes	characteristic
156	C₈×D₅	C₂×C₈	1	1	yes	characteristic
157	C₈×D₅	C₂×D₄	1	1	yes	characteristic
158	C₈×D₅	C₂×D₄	1	1	yes	characteristic
159	C₈×D₅	#41	1	1	yes	characteristic
160	C₈×D₅	#41	1	1	yes	characteristic
161	C₅×C₁₆	—	2	2	no	—
162	C₅×C₁₆	—	2	1	no	—
163	C₅×C₁₆	C₂×D₄	1	1	yes	characteristic
164	C₅×C₁₆	C₂×D₄	1	1	yes	characteristic
165	#672	—	2	2	no	—
166	#672	—	2	1	no	—
167	#672	C₂×D₄	1	1	yes	characteristic
168	#672	C₂×D₄	1	1	yes	characteristic
169	C₂×#135	—	5	1	no	—
170	C₂×#131	—	5	2	no	—
171	#504	—	5	2	no	—
172	#504	—	5	2	no	—
173	#504	—	5	2	no	—
174	#504	—	10	2	no	—
175	#504	—	10	2	no	—
176	#504	C₂×D₅	1	2	yes	complemented
177	C₂×M₃₂	—	5	2	no	—
178	C₂×M₃₂	—	10	2	no	—
179	C₂²×C₁₆	—	5	1	no	—
180	C₂²×C₁₆	—	5	1	no	—
181	C₂²×C₁₆	—	10	2	no	—
182	#443	—	5	1	no	—
183	#443	—	5	2	no	—
184	#443	—	5	1	no	—
185	#443	—	5	2	no	—
186	#443	—	5	1	no	—
187	#443	C₂×D₅	1	1	yes	characteristic
188	C₂×#108	—	5	1	no	—
189	C₂×#104	—	5	2	no	—
190	C₂×C₄×C₈	—	5	1	no	—
191	#364	—	5	2	no	—
192	#364	—	5	1	no	—
193	#364	C₂×D₅	1	1	yes	characteristic, complemented
194	#350	—	5	2	no	—
195	#350	—	5	2	no	—
196	#350	—	5	2	no	—
197	#350	C₂×D₅	1	2	yes	complemented
198	C₄×C₁₆	—	5	1	no	—
199	C₄×C₁₆	—	5	1	no	—
200	C₄×C₁₆	—	5	1	no	—
201	C₄×C₁₆	C₂×D₅	1	1	yes	characteristic, complemented
202	C₂²×D₅	—	2	2	no	—
203	C₂²×D₅	#131	1	1	yes	characteristic
204	C₅×Q₈	C₂²×C₈	1	2	yes	—
205	C₅×D₄	—	2	2	no	—
206	C₅×D₄	C₂²×C₈	1	2	yes	—
207	C₂×C₄×C₅	—	2	1	no	—
208	C₂×C₄×C₅	—	2	2	no	—
209	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
210	C₂²⋊D₅	—	2	2	no	—
211	C₂²⋊D₅	—	2	2	no	—
212	C₂²⋊D₅	—	2	2	no	—
213	C₂×Dic₅	—	2	1	no	—
214	C₂×Dic₅	—	2	2	no	—
215	C₂×Dic₅	#131	1	1	yes	characteristic
216	D₂₀	—	2	2	no	—
217	D₂₀	C₂²×C₈	1	2	yes	—
218	C₄×D₅	—	2	4	no	—
219	C₄×D₅	—	2	2	no	—
220	C₄×D₅	—	2	2	no	—
221	C₄×D₅	—	2	2	no	—
222	C₄×D₅	C₄×D₄	1	1	yes	characteristic
223	C₄×D₅	C₄×D₄	1	1	yes	characteristic
224	C₄×D₅	C₂²×C₈	1	1	yes	characteristic
225	C₄×D₅	C₂²×C₈	1	1	yes	characteristic
226	Dic₁₀	—	2	2	no	—
227	Dic₁₀	C₂²×C₈	1	2	yes	—
228	C₅×C₈	—	2	2	no	—
229	C₅×C₈	C₂²×C₈	1	1	yes	characteristic
230	C₅×C₈	C₂²×C₈	1	1	yes	characteristic
231	C₅×C₈	C₂²×D₄	1	1	yes	characteristic
232	C₅×C₈	C₂×#41	1	1	yes	characteristic
233	#168	—	2	2	no	—
234	#168	C₄×D₄	1	1	yes	characteristic
235	#168	C₄×D₄	1	1	yes	characteristic
236	#168	C₂²×C₈	1	1	yes	characteristic
237	#168	C₂²×C₈	1	1	yes	characteristic
238	C₂×#41	—	5	2	no	—
239	#135	—	5	2	no	—
240	#135	—	5	1	no	—
241	#135	—	5	2	no	—
242	#135	—	5	1	no	—
243	#135	—	5	1	no	—
244	#135	C₄×D₅	1	1	yes	characteristic
245	C₂×Q₁₆	—	5	1	no	—
246	C₂×SD₁₆	—	5	2	no	—
247	C₂×D₈	—	5	1	no	—
248	#131	—	5	2	no	—
249	#131	—	5	2	no	—
250	#131	—	5	2	no	—
251	#131	—	10	2	no	—
252	#131	—	10	2	no	—
253	#131	C₂²×D₅	1	2	yes	—
254	C₂×M₁₆	—	5	2	no	—
255	C₂×M₁₆	—	10	2	no	—
256	C₂²×C₈	—	5	1	no	—
257	C₂²×C₈	—	5	1	no	—
258	C₂²×C₈	—	10	2	no	—
259	C₂×C₄²	—	5	1	no	—
260	M₃₂	—	2	2	no	—
261	M₃₂	—	5	2	no	—
262	M₃₂	—	10	2	no	—
263	M₃₂	—	10	2	no	—
264	M₃₂	—	10	2	no	—
265	M₃₂	—	10	2	no	—
266	M₃₂	C₂²×D₅	1	2	yes	—
267	C₂×C₁₆	—	2	2	no	—
268	C₂×C₁₆	—	5	1	no	—
269	C₂×C₁₆	—	5	1	no	—
270	C₂×C₁₆	—	5	1	no	—
271	C₂×C₁₆	—	5	1	no	—
272	C₂×C₁₆	—	5	1	no	—
273	C₂×C₁₆	—	5	1	no	—
274	C₂×C₁₆	—	10	2	no	—
275	C₂×C₁₆	—	10	1	no	—
276	C₂×C₁₆	—	10	1	no	—
277	C₂×C₁₆	—	10	2	no	—
278	C₂×C₁₆	—	10	2	no	—
279	C₂×C₁₆	—	10	2	no	—
280	C₂×C₁₆	C₂²×D₅	1	1	yes	characteristic
281	C₂×C₁₆	C₂²×D₅	1	1	yes	characteristic
282	#108	—	5	2	no	—
283	#108	—	5	1	no	—
284	#108	C₄×D₅	1	1	yes	characteristic
285	#104	—	5	2	no	—
286	#104	—	5	2	no	—
287	#104	—	5	2	no	—
288	#104	C₄×D₅	1	2	yes	—
289	C₄×C₈	—	5	1	no	—
290	C₄×C₈	—	5	1	no	—
291	C₄×C₈	—	5	1	no	—
292	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
293	C₂²×C₅	—	2	2	no	—
294	C₂²×C₅	C₂×#131	1	1	yes	characteristic
295	C₂×D₅	—	2	2	no	—
296	C₂×D₅	—	2	2	no	—
297	C₂×D₅	—	4	4	no	—
298	C₂×D₅	C₈×D₄	1	1	yes	characteristic
299	C₂×D₅	C₈×D₄	1	1	yes	characteristic
300	C₄×C₅	—	2	2	no	—
301	C₄×C₅	—	2	2	no	—
302	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
303	C₄×C₅	C₂³×C₈	1	1	yes	characteristic
304	Dic₅	—	2	2	no	—
305	Dic₅	—	2	2	no	—
306	Dic₅	C₈×D₄	1	1	yes	characteristic
307	Dic₅	C₈×D₄	1	1	yes	characteristic
308	#41	—	5	2	no	—
309	#41	—	5	2	no	—
310	#41	—	5	2	no	—
311	#41	—	10	2	no	—
312	#41	—	10	2	no	—
313	#41	C₂×C₄×D₅	1	2	yes	—
314	C₂×Q₈	—	5	2	no	—
315	C₂×D₄	—	5	2	no	—
316	C₂×D₄	—	10	2	no	—
317	C₂²×C₄	—	5	1	no	—
318	C₂²×C₄	—	10	2	no	—
319	C₂²×C₄	—	10	1	no	—
320	Q₁₆	—	5	2	no	—
321	Q₁₆	—	5	1	no	—
322	Q₁₆	C₈×D₅	1	1	yes	characteristic
323	SD₁₆	—	5	2	no	—
324	SD₁₆	—	5	2	no	—
325	SD₁₆	—	5	2	no	—
326	SD₁₆	C₈×D₅	1	2	yes	—
327	D₈	—	5	2	no	—
328	D₈	—	5	1	no	—
329	D₈	C₈×D₅	1	1	yes	characteristic
330	M₁₆	—	2	2	no	—
331	M₁₆	—	5	2	no	—
332	M₁₆	—	10	2	no	—
333	M₁₆	—	10	2	no	—
334	M₁₆	—	10	2	no	—
335	M₁₆	—	10	2	no	—
336	M₁₆	C₂×C₄×D₅	1	2	yes	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	5	1	no	—
339	C₂×C₈	—	5	1	no	—
340	C₂×C₈	—	5	1	no	—
341	C₂×C₈	—	5	1	no	—
342	C₂×C₈	—	5	1	no	—
343	C₂×C₈	—	5	1	no	—
344	C₂×C₈	—	5	1	no	—
345	C₂×C₈	—	5	1	no	—
346	C₂×C₈	—	5	1	no	—
347	C₂×C₈	—	5	1	no	—
348	C₂×C₈	—	10	2	no	—
349	C₂×C₈	—	10	2	no	—
350	C₂×C₈	—	10	2	no	—
351	C₂×C₈	—	10	2	no	—
352	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
353	C₂×C₈	C₂³×D₅	1	1	yes	characteristic
354	C₄²	—	5	1	no	—
355	C₄²	—	10	1	no	—
356	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
357	C₁₆	—	2	2	no	—
358	C₁₆	—	2	1	no	—
359	C₁₆	—	5	1	no	—
360	C₁₆	—	5	1	no	—
361	C₁₆	—	10	2	no	—
362	C₁₆	—	10	1	no	—
363	C₁₆	D₄×D₅	1	1	yes	characteristic
364	C₁₆	D₄×D₅	1	1	yes	characteristic
365	C₂×C₅	—	2	1	no	—
366	C₂×C₅	—	4	2	no	—
367	C₂×C₅	C₂×C₈×D₄	1	1	yes	characteristic
368	D₅	—	2	1	no	—
369	D₅	—	4	2	no	—
370	D₅	#2170	1	2	yes	direct product factor
371	C₂³	—	5	1	no	—
372	C₂³	—	10	2	no	—
373	Q₈	—	5	2	no	—
374	Q₈	—	10	2	no	—
375	Q₈	C₂×C₈×D₅	1	2	yes	—
376	D₄	—	2	2	no	—
377	D₄	—	5	2	no	—
378	D₄	—	10	2	no	—
379	D₄	—	10	2	no	—
380	D₄	—	10	2	no	—
381	D₄	—	10	2	no	—
382	D₄	C₂×C₈×D₅	1	2	yes	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	5	1	no	—
386	C₂×C₄	—	5	1	no	—
387	C₂×C₄	—	5	1	no	—
388	C₂×C₄	—	5	1	no	—
389	C₂×C₄	—	5	1	no	—
390	C₂×C₄	—	10	2	no	—
391	C₂×C₄	—	10	2	no	—
392	C₂×C₄	—	10	4	no	—
393	C₂×C₄	—	10	2	no	—
394	C₂×C₄	—	10	1	no	—
395	C₂×C₄	—	10	2	no	—
396	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
397	C₈	—	2	2	no	—
398	C₈	—	5	1	no	—
399	C₈	—	5	1	no	—
400	C₈	—	5	1	no	—
401	C₈	—	5	1	no	—
402	C₈	—	10	2	no	—
403	C₈	C₂×C₈×D₅	1	1	yes	characteristic
404	C₈	C₂×C₈×D₅	1	1	yes	characteristic
405	C₈	C₂×D₄×D₅	1	1	yes	characteristic
406	C₈	D₅×#41	1	1	yes	characteristic
407	C₅	C₂×#2170	1	1	yes	characteristic, complemented, Sylow
408	C₂²	—	2	2	no	—
409	C₂²	—	5	1	no	—
410	C₂²	—	5	1	no	—
411	C₂²	—	10	2	no	—
412	C₂²	—	10	2	no	—
413	C₂²	—	20	4	no	—
414	C₂²	D₅×#131	1	1	yes	characteristic
415	C₄	—	2	2	no	—
416	C₄	—	2	2	no	—
417	C₄	—	5	1	no	—
418	C₄	—	5	1	no	—
419	C₄	—	10	2	no	—
420	C₄	—	10	2	no	—
421	C₄	C₄×D₄×D₅	1	1	yes	characteristic
422	C₄	C₂²×C₈×D₅	1	1	yes	characteristic
423	C₂	—	2	1	no	—
424	C₂	—	4	2	no	—
425	C₂	—	5	2	no	—
426	C₂	—	10	1	no	—
427	C₂	—	20	2	no	—
428	C₂	C₈×D₄×D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	D₄×D₅
commutator	C₄×C₅	C₂³×C₈
Frattini	C₂×C₈	C₂³×D₅
Fitting	C₅×#2170	C₂
socle	C₂×C₅	C₂×C₈×D₄
prime radical	D₅×#135	C₄
cosocle	C₂×C₅×C₈	C₂⁴
hypercenter	#2170	D₅
hypocenter	C₅	C₂×#2170
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₁₆ ◁ C₂×C₁₆ ◁ #2170

Complements

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

N	H ≅ G/N	type
1. D₅×#504	C₂	semidirect
3. C₅×#2170	C₂	semidirect
4. #10602245	C₂	semidirect
5. #10601716	C₂	semidirect
6. D₅×#364	C₂	semidirect
7. #10600093	C₂	semidirect
8. D₅×#350	C₂	semidirect
9. #10599915	C₂	semidirect
10. #10599849	C₂	semidirect
11. C₄×D₅×C₁₆	C₂	semidirect
14. C₅×#504	C₂²	semidirect
18. #65429	C₂²	semidirect
20. #65196	C₂²	semidirect
24. #65190	C₂²	semidirect
34. C₅×#364	C₂²	semidirect
35. C₅×#350	C₂²	semidirect
36. C₄×C₅×C₁₆	C₂²	semidirect
37. #64781	C₂²	semidirect
38. #64735	C₂²	semidirect
39. #64731	C₂²	semidirect
40. #64728	C₂²	semidirect
41. C₁₆×Dic₅	C₂²	semidirect
42. C₁₆×Dic₅	C₂²	semidirect
43. #64683	C₂²	semidirect
44. C₄×#672	C₂²	semidirect
108. #2170	D₅	direct (N × H)
176. #504	C₂×D₅	semidirect
193. #364	C₂×D₅	semidirect
197. #350	C₂×D₅	semidirect
201. C₄×C₁₆	C₂×D₅	semidirect
370. D₅	#2170	direct (N × H)
407. C₅	C₂×#2170	semidirect

Maximal subgroups

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

subgroup	index
D₅×#504	2
D₅×#443	2
C₅×#2170	2
#10602245	2
#10601716	2
D₅×#364	2
#10600093	2
D₅×#350	2
#10599915	2
#10599849	2
C₄×D₅×C₁₆	2
C₂×#2170	5

Subgroups — D5×#2170 #12252524

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×#2170 #12252524