Subgroups — D₅×#2171 #12252530

Order 1280.

654 conjugacy classes of subgroups.

The subgroup lattice has 422 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×#2171	C₂	1	1	yes	maximal, characteristic, complemented
4	#10602246	C₂	1	2	yes	maximal, complemented
5	#10601717	C₂	1	1	yes	maximal, characteristic, complemented
6	D₅×#364	C₂	1	1	yes	maximal, characteristic, complemented
7	#10600094	C₂	1	1	yes	maximal, characteristic, complemented
8	D₅×#350	C₂	1	2	yes	maximal, complemented
9	#10599916	C₂	1	2	yes	maximal, complemented
10	#10599869	C₂	1	1	yes	maximal, characteristic, complemented
11	D₅×#346	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	C₅×#346	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	#64722	C₂²	1	1	yes	characteristic, complemented
42	#64722	C₂²	1	1	yes	characteristic, complemented
43	#64683	C₂²	1	1	yes	characteristic, complemented
44	#64681	C₂²	1	1	yes	characteristic, complemented
45	C₂×#2171	—	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	2	yes	—
98	D₅×C₁₆	D₄	1	2	yes	—
99	C₂×#504	—	5	2	no	—
100	C₂×#443	—	5	1	no	—
101	#2171	—	5	2	no	—
102	#2171	—	5	1	no	—
103	#2171	—	5	1	no	—
104	#2171	—	5	2	no	—
105	#2171	—	5	1	no	—
106	#2171	D₅	1	1	yes	characteristic, direct product factor
107	C₂×#364	—	5	1	no	—
108	C₂×#350	—	5	2	no	—
109	C₂×#346	—	5	1	no	—
110	C₅×#41	C₂²×C₄	1	2	yes	—
111	#713	C₂×C₈	1	2	yes	—
112	Q₈×D₅	C₂×C₈	1	2	yes	—
113	#711	—	2	2	no	—
114	#711	C₂×C₈	1	2	yes	—
115	D₄×D₅	—	2	2	no	—
116	D₄×D₅	C₂×C₈	1	2	yes	—
117	#709	—	2	2	no	—
118	#709	C₂²×C₄	1	2	yes	—
119	C₂×C₄×D₅	—	2	2	no	—
120	C₂×C₄×D₅	—	2	1	no	—
121	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
122	C₅×Q₁₆	C₂×C₈	1	1	yes	characteristic
123	C₅×SD₁₆	C₂×C₈	1	2	yes	—
124	C₅×D₈	C₂×C₈	1	1	yes	characteristic
125	C₅×M₁₆	—	2	2	no	—
126	C₅×M₁₆	C₂²×C₄	1	2	yes	—
127	C₂×C₅×C₈	—	2	2	no	—
128	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
130	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
131	#689	C₂×C₈	1	2	yes	—
132	#688	C₂×C₈	1	2	yes	—
133	#687	C₂×C₈	1	2	yes	—
134	#686	C₂×C₈	1	2	yes	—
135	C₄×Dic₅	—	2	1	no	—
136	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
137	#681	—	2	2	no	—
138	#681	C₂²×C₄	1	2	yes	—
139	C₂×#168	—	2	2	no	—
140	C₂×#168	C₂²×C₄	1	1	yes	characteristic
141	C₂×#168	C₂²×C₄	1	1	yes	characteristic
142	Dic₂₀	C₂×C₈	1	1	yes	characteristic
143	D₄₀	C₂×C₈	1	1	yes	characteristic
144	#677	C₂×C₈	1	2	yes	—
145	#676	—	2	2	no	—
146	#676	—	2	2	no	—
147	#676	—	2	2	no	—
148	C₈×D₅	—	2	2	no	—
149	C₈×D₅	—	2	2	no	—
150	C₈×D₅	—	2	2	no	—
151	C₈×D₅	C₂×C₈	1	1	yes	characteristic
152	C₈×D₅	C₂×C₈	1	1	yes	characteristic
153	C₈×D₅	C₂×C₈	1	1	yes	characteristic
154	C₈×D₅	C₂×C₈	1	1	yes	characteristic
155	C₈×D₅	C₂×D₄	1	1	yes	characteristic
156	C₈×D₅	C₂×D₄	1	1	yes	characteristic
157	C₈×D₅	#41	1	1	yes	characteristic
158	C₈×D₅	#41	1	1	yes	characteristic
159	C₅×C₁₆	—	2	2	no	—
160	C₅×C₁₆	—	2	1	no	—
161	C₅×C₁₆	C₂×D₄	1	2	yes	—
162	#672	—	2	2	no	—
163	#672	—	2	1	no	—
164	#672	C₂×D₄	1	2	yes	—
165	C₂×#135	—	5	1	no	—
166	C₂×#131	—	5	2	no	—
167	#504	—	5	2	no	—
168	#504	—	5	2	no	—
169	#504	—	5	2	no	—
170	#504	—	10	2	no	—
171	#504	—	10	2	no	—
172	#504	C₂×D₅	1	2	yes	complemented
173	C₂×M₃₂	—	5	2	no	—
174	C₂×M₃₂	—	10	2	no	—
175	C₂²×C₁₆	—	5	1	no	—
176	C₂²×C₁₆	—	5	1	no	—
177	C₂²×C₁₆	—	10	2	no	—
178	#443	—	5	1	no	—
179	#443	—	5	2	no	—
180	#443	—	5	1	no	—
181	#443	—	5	2	no	—
182	#443	—	5	1	no	—
183	#443	C₂×D₅	1	1	yes	characteristic
184	C₂×#108	—	5	1	no	—
185	C₂×#104	—	5	2	no	—
186	C₂×C₄×C₈	—	5	1	no	—
187	#364	—	5	2	no	—
188	#364	—	5	1	no	—
189	#364	C₂×D₅	1	1	yes	characteristic, complemented
190	#350	—	5	2	no	—
191	#350	—	5	2	no	—
192	#350	—	5	2	no	—
193	#350	C₂×D₅	1	2	yes	complemented
194	#346	—	5	1	no	—
195	#346	—	5	1	no	—
196	#346	—	5	1	no	—
197	#346	C₂×D₅	1	1	yes	characteristic, complemented
198	C₂²×D₅	—	2	2	no	—
199	C₂²×D₅	#131	1	1	yes	characteristic
200	C₅×Q₈	C₂²×C₈	1	2	yes	—
201	C₅×D₄	—	2	2	no	—
202	C₅×D₄	C₂²×C₈	1	2	yes	—
203	C₂×C₄×C₅	—	2	2	no	—
204	C₂×C₄×C₅	—	2	1	no	—
205	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
206	C₂²⋊D₅	—	2	2	no	—
207	C₂²⋊D₅	—	2	2	no	—
208	C₂²⋊D₅	—	2	2	no	—
209	C₂×Dic₅	—	2	2	no	—
210	C₂×Dic₅	—	2	1	no	—
211	C₂×Dic₅	#131	1	1	yes	characteristic
212	D₂₀	—	2	2	no	—
213	D₂₀	C₂²×C₈	1	2	yes	—
214	C₄×D₅	—	2	2	no	—
215	C₄×D₅	—	2	2	no	—
216	C₄×D₅	—	2	2	no	—
217	C₄×D₅	—	4	2	no	—
218	C₄×D₅	C₄×D₄	1	1	yes	characteristic
219	C₄×D₅	C₄×D₄	1	1	yes	characteristic
220	C₄×D₅	C₂²×C₈	1	1	yes	characteristic
221	C₄×D₅	C₂²×C₈	1	1	yes	characteristic
222	Dic₁₀	—	2	2	no	—
223	Dic₁₀	C₂²×C₈	1	2	yes	—
224	C₅×C₈	—	2	2	no	—
225	C₅×C₈	C₂²×C₈	1	1	yes	characteristic
226	C₅×C₈	C₂²×C₈	1	1	yes	characteristic
227	C₅×C₈	C₂²×D₄	1	1	yes	characteristic
228	C₅×C₈	C₂×#41	1	1	yes	characteristic
229	#168	—	2	2	no	—
230	#168	C₄×D₄	1	1	yes	characteristic
231	#168	C₄×D₄	1	1	yes	characteristic
232	#168	C₂²×C₈	1	1	yes	characteristic
233	#168	C₂²×C₈	1	1	yes	characteristic
234	C₂×#41	—	5	2	no	—
235	#135	—	5	2	no	—
236	#135	—	5	1	no	—
237	#135	—	5	2	no	—
238	#135	—	5	1	no	—
239	#135	—	5	1	no	—
240	#135	C₄×D₅	1	1	yes	characteristic
241	C₂×Q₁₆	—	5	1	no	—
242	C₂×SD₁₆	—	5	2	no	—
243	C₂×D₈	—	5	1	no	—
244	#131	—	5	2	no	—
245	#131	—	5	2	no	—
246	#131	—	5	2	no	—
247	#131	—	10	2	no	—
248	#131	—	10	2	no	—
249	#131	C₂²×D₅	1	2	yes	—
250	C₂×M₁₆	—	5	2	no	—
251	C₂×M₁₆	—	10	2	no	—
252	C₂²×C₈	—	5	1	no	—
253	C₂²×C₈	—	5	1	no	—
254	C₂²×C₈	—	10	2	no	—
255	C₂×C₄²	—	5	1	no	—
256	M₃₂	—	2	2	no	—
257	M₃₂	—	5	2	no	—
258	M₃₂	—	10	2	no	—
259	M₃₂	—	10	2	no	—
260	M₃₂	—	10	2	no	—
261	M₃₂	—	10	2	no	—
262	M₃₂	C₂²×D₅	1	2	yes	—
263	C₂×C₁₆	—	2	2	no	—
264	C₂×C₁₆	—	5	1	no	—
265	C₂×C₁₆	—	5	2	no	—
266	C₂×C₁₆	—	5	2	no	—
267	C₂×C₁₆	—	5	1	no	—
268	C₂×C₁₆	—	10	2	no	—
269	C₂×C₁₆	—	10	1	no	—
270	C₂×C₁₆	—	10	1	no	—
271	C₂×C₁₆	—	10	2	no	—
272	C₂×C₁₆	—	10	2	no	—
273	C₂×C₁₆	—	10	2	no	—
274	C₂×C₁₆	C₂²×D₅	1	1	yes	characteristic
275	C₂×C₁₆	C₂²×D₅	1	1	yes	characteristic
276	#108	—	5	2	no	—
277	#108	—	5	1	no	—
278	#108	C₄×D₅	1	1	yes	characteristic
279	#104	—	5	2	no	—
280	#104	—	5	2	no	—
281	#104	—	5	2	no	—
282	#104	C₄×D₅	1	2	yes	—
283	C₄×C₈	—	5	1	no	—
284	C₄×C₈	—	5	1	no	—
285	C₄×C₈	—	5	1	no	—
286	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
287	C₂²×C₅	—	2	2	no	—
288	C₂²×C₅	C₂×#131	1	1	yes	characteristic
289	C₂×D₅	—	2	2	no	—
290	C₂×D₅	—	2	2	no	—
291	C₂×D₅	—	4	4	no	—
292	C₂×D₅	C₈×D₄	1	1	yes	characteristic
293	C₂×D₅	C₈×D₄	1	1	yes	characteristic
294	C₄×C₅	—	2	2	no	—
295	C₄×C₅	—	4	1	no	—
296	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
297	C₄×C₅	C₂³×C₈	1	1	yes	characteristic
298	Dic₅	—	2	2	no	—
299	Dic₅	—	4	1	no	—
300	Dic₅	C₈×D₄	1	1	yes	characteristic
301	Dic₅	C₈×D₄	1	1	yes	characteristic
302	#41	—	5	2	no	—
303	#41	—	5	2	no	—
304	#41	—	5	2	no	—
305	#41	—	10	2	no	—
306	#41	—	10	2	no	—
307	#41	C₂×C₄×D₅	1	2	yes	—
308	C₂×Q₈	—	5	2	no	—
309	C₂×D₄	—	5	2	no	—
310	C₂×D₄	—	10	2	no	—
311	C₂²×C₄	—	5	1	no	—
312	C₂²×C₄	—	10	2	no	—
313	C₂²×C₄	—	10	1	no	—
314	Q₁₆	—	5	2	no	—
315	Q₁₆	—	5	1	no	—
316	Q₁₆	C₈×D₅	1	1	yes	characteristic
317	SD₁₆	—	5	2	no	—
318	SD₁₆	—	5	2	no	—
319	SD₁₆	—	5	2	no	—
320	SD₁₆	C₈×D₅	1	2	yes	—
321	D₈	—	5	2	no	—
322	D₈	—	5	1	no	—
323	D₈	C₈×D₅	1	1	yes	characteristic
324	M₁₆	—	2	2	no	—
325	M₁₆	—	5	2	no	—
326	M₁₆	—	10	2	no	—
327	M₁₆	—	10	2	no	—
328	M₁₆	—	10	2	no	—
329	M₁₆	—	10	2	no	—
330	M₁₆	C₂×C₄×D₅	1	2	yes	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	5	1	no	—
333	C₂×C₈	—	5	1	no	—
334	C₂×C₈	—	5	1	no	—
335	C₂×C₈	—	5	1	no	—
336	C₂×C₈	—	5	1	no	—
337	C₂×C₈	—	5	1	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	—	10	2	no	—
343	C₂×C₈	—	10	2	no	—
344	C₂×C₈	—	10	2	no	—
345	C₂×C₈	—	10	2	no	—
346	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
347	C₂×C₈	C₂³×D₅	1	1	yes	characteristic
348	C₄²	—	5	1	no	—
349	C₄²	—	10	1	no	—
350	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
351	C₁₆	—	2	2	no	—
352	C₁₆	—	2	1	no	—
353	C₁₆	—	5	2	no	—
354	C₁₆	—	10	2	no	—
355	C₁₆	—	10	1	no	—
356	C₁₆	D₄×D₅	1	2	yes	—
357	C₂×C₅	—	2	1	no	—
358	C₂×C₅	—	4	2	no	—
359	C₂×C₅	C₂×C₈×D₄	1	1	yes	characteristic
360	D₅	—	2	1	no	—
361	D₅	—	4	2	no	—
362	D₅	#2171	1	2	yes	direct product factor
363	C₂³	—	5	1	no	—
364	C₂³	—	10	2	no	—
365	Q₈	—	5	2	no	—
366	Q₈	—	10	2	no	—
367	Q₈	C₂×C₈×D₅	1	2	yes	—
368	D₄	—	2	2	no	—
369	D₄	—	5	2	no	—
370	D₄	—	10	2	no	—
371	D₄	—	10	2	no	—
372	D₄	—	10	2	no	—
373	D₄	—	10	2	no	—
374	D₄	C₂×C₈×D₅	1	2	yes	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	5	1	no	—
378	C₂×C₄	—	5	1	no	—
379	C₂×C₄	—	5	1	no	—
380	C₂×C₄	—	5	1	no	—
381	C₂×C₄	—	5	1	no	—
382	C₂×C₄	—	10	2	no	—
383	C₂×C₄	—	10	2	no	—
384	C₂×C₄	—	10	2	no	—
385	C₂×C₄	—	10	2	no	—
386	C₂×C₄	—	10	1	no	—
387	C₂×C₄	—	20	2	no	—
388	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
389	C₈	—	2	2	no	—
390	C₈	—	5	1	no	—
391	C₈	—	5	1	no	—
392	C₈	—	5	1	no	—
393	C₈	—	5	1	no	—
394	C₈	—	10	2	no	—
395	C₈	C₂×C₈×D₅	1	1	yes	characteristic
396	C₈	C₂×C₈×D₅	1	1	yes	characteristic
397	C₈	C₂×D₄×D₅	1	1	yes	characteristic
398	C₈	D₅×#41	1	1	yes	characteristic
399	C₅	C₂×#2171	1	1	yes	characteristic, complemented, Sylow
400	C₂²	—	2	2	no	—
401	C₂²	—	5	1	no	—
402	C₂²	—	5	1	no	—
403	C₂²	—	10	2	no	—
404	C₂²	—	10	2	no	—
405	C₂²	—	20	4	no	—
406	C₂²	D₅×#131	1	1	yes	characteristic
407	C₄	—	2	2	no	—
408	C₄	—	4	1	no	—
409	C₄	—	5	1	no	—
410	C₄	—	5	1	no	—
411	C₄	—	10	2	no	—
412	C₄	—	20	1	no	—
413	C₄	C₄×D₄×D₅	1	1	yes	characteristic
414	C₄	C₂²×C₈×D₅	1	1	yes	characteristic
415	C₂	—	2	1	no	—
416	C₂	—	4	2	no	—
417	C₂	—	5	2	no	—
418	C₂	—	10	1	no	—
419	C₂	—	20	2	no	—
420	C₂	C₈×D₄×D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂×D₄×D₅
commutator	C₄×C₅	C₂³×C₈
Frattini	C₂×C₈	C₂³×D₅
Fitting	C₅×#2171	C₂
socle	C₂×C₅	C₂×C₈×D₄
prime radical	D₅×#135	C₄
cosocle	C₂×C₅×C₈	C₂⁴
hypercenter	#2171	D₅
hypocenter	C₅	C₂×#2171
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₈ ◁ C₂×C₁₆ ◁ #2171

Complements

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

N	H ≅ G/N	type
1. D₅×#504	C₂	semidirect
3. C₅×#2171	C₂	semidirect
4. #10602246	C₂	semidirect
5. #10601717	C₂	semidirect
6. D₅×#364	C₂	semidirect
7. #10600094	C₂	semidirect
8. D₅×#350	C₂	semidirect
9. #10599916	C₂	semidirect
10. #10599869	C₂	semidirect
11. D₅×#346	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. C₅×#346	C₂²	semidirect
37. #64781	C₂²	semidirect
38. #64735	C₂²	semidirect
39. #64731	C₂²	semidirect
40. #64728	C₂²	semidirect
41. #64722	C₂²	semidirect
42. #64722	C₂²	semidirect
43. #64683	C₂²	semidirect
44. #64681	C₂²	semidirect
106. #2171	D₅	direct (N × H)
172. #504	C₂×D₅	semidirect
189. #364	C₂×D₅	semidirect
193. #350	C₂×D₅	semidirect
197. #346	C₂×D₅	semidirect
362. D₅	#2171	direct (N × H)
399. C₅	C₂×#2171	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×#2171	2
#10602246	2
#10601717	2
D₅×#364	2
#10600094	2
D₅×#350	2
#10599916	2
#10599869	2
D₅×#346	2
C₂×#2171	5

Subgroups — D5×#2171 #12252530

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×#2171 #12252530