Subgroups — C₂×C₅×#1717 #11942329

Order 1280.

966 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#493	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#492	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#487	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#486	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#486	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×#486	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1717	C₂	1	8	yes	maximal, direct product factor
8	C₂×C₅×#322	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₅×SD₁₆	—	2	2	no	—
10	C₂²×C₅×D₈	—	2	2	no	—
11	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
12	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₅×#127	C₂²	1	1	yes	characteristic
14	C₂×C₅×#127	C₂²	1	1	yes	characteristic
15	C₅×#493	—	2	2	no	—
16	C₅×#493	C₂²	1	4	yes	—
17	C₅×#492	—	2	2	no	—
18	C₅×#492	C₂²	1	4	yes	complemented
19	C₅×#487	—	2	2	no	—
20	C₅×#487	C₂²	1	4	yes	complemented
21	C₅×#486	—	2	2	no	—
22	C₅×#486	—	2	2	no	—
23	C₅×#486	—	2	2	no	—
24	C₅×#486	C₂²	1	4	yes	complemented
25	C₅×#486	C₂²	1	4	yes	complemented
26	C₅×#486	C₂²	1	4	yes	complemented
27	C₂×C₅×#103	—	2	2	no	—
28	C₂×C₅×#102	—	2	2	no	—
29	C₂×C₅×#102	—	2	2	no	—
30	C₂×C₅×#102	—	2	2	no	—
31	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
34	C₅×#322	C₂²	1	4	yes	complemented
35	C₂×#1717	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
36	C₂²×C₅×Q₈	—	2	1	no	—
37	C₂²×C₅×Q₈	—	2	1	no	—
38	C₂²×C₅×D₄	—	2	1	no	—
39	C₂²×C₅×D₄	—	2	1	no	—
40	C₂²×C₅×D₄	—	2	1	no	—
41	C₂²×C₅×D₄	—	2	1	no	—
42	C₂²×C₅×D₄	—	2	1	no	—
43	C₂²×C₅×D₄	—	2	1	no	—
44	C₂×C₅×SD₁₆	—	2	8	no	—
45	C₂×C₅×SD₁₆	—	4	8	no	—
46	C₂×C₅×D₈	—	2	8	no	—
47	C₂×C₅×D₈	—	4	8	no	—
48	C₂²×C₅×C₈	D₄	1	2	yes	—
49	C₂²×C₅×C₈	D₄	1	2	yes	—
50	C₂²×C₅×C₈	D₄	1	2	yes	—
51	C₅×C₄⋊Q₈	—	2	1	no	—
52	C₅×C₄⋊Q₈	—	2	1	no	—
53	C₅×C₄⋊Q₈	—	2	1	no	—
54	C₅×C₄⋊Q₈	—	2	1	no	—
55	C₅×C₄⋊Q₈	—	2	1	no	—
56	C₅×C₄⋊Q₈	—	2	1	no	—
57	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
58	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
59	C₅×#127	—	2	1	no	—
60	C₅×#127	—	2	1	no	—
61	C₅×#127	—	2	1	no	—
62	C₅×#127	—	2	1	no	—
63	C₅×#127	—	2	1	no	—
64	C₅×#127	—	2	1	no	—
65	C₅×#127	C₂³	1	2	yes	—
66	C₅×#127	C₂³	1	2	yes	—
67	C₂×C₅×C₄⋊C₄	—	2	1	no	—
68	C₂×C₅×C₄⋊C₄	—	2	1	no	—
69	C₂×C₅×C₄⋊C₄	—	2	1	no	—
70	C₂×C₅×C₄⋊C₄	—	2	1	no	—
71	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
72	C₅×#103	—	2	8	no	—
73	C₅×#102	—	2	8	no	—
74	C₅×#102	—	2	8	no	—
75	C₅×#102	—	2	8	no	—
76	C₄×C₅×C₈	D₄	1	2	yes	—
77	C₄×C₅×C₈	D₄	1	2	yes	—
78	C₄×C₅×C₈	D₄	1	2	yes	—
79	C₄×C₅×C₈	C₂³	1	2	yes	—
80	C₄×C₅×C₈	C₂³	1	2	yes	—
81	C₄×C₅×C₈	C₂³	1	2	yes	—
82	C₂×#493	C₂×C₅	1	1	yes	characteristic
83	C₂×#492	C₂×C₅	1	1	yes	characteristic, complemented
84	C₂×#487	C₂×C₅	1	1	yes	characteristic, complemented
85	C₂×#486	C₂×C₅	1	1	yes	characteristic, complemented
86	C₂×#486	C₂×C₅	1	1	yes	characteristic, complemented
87	C₂×#486	C₂×C₅	1	1	yes	characteristic, complemented
88	#1717	C₂×C₅	1	8	yes	direct product factor
89	C₂×#322	C₂×C₅	1	1	yes	characteristic, complemented
90	C₂⁴×C₅	—	4	1	no	—
91	C₂⁴×C₅	—	4	1	no	—
92	C₂×C₅×Q₈	—	2	2	no	—
93	C₂×C₅×Q₈	—	2	2	no	—
94	C₂×C₅×Q₈	—	4	1	no	—
95	C₂×C₅×Q₈	—	4	1	no	—
96	C₂×C₅×Q₈	—	4	4	no	—
97	C₂×C₅×Q₈	—	4	4	no	—
98	C₂×C₅×D₄	—	2	2	no	—
99	C₂×C₅×D₄	—	2	2	no	—
100	C₂×C₅×D₄	—	2	2	no	—
101	C₂×C₅×D₄	—	2	2	no	—
102	C₂×C₅×D₄	—	2	2	no	—
103	C₂×C₅×D₄	—	2	2	no	—
104	C₂×C₅×D₄	—	4	1	no	—
105	C₂×C₅×D₄	—	4	1	no	—
106	C₂×C₅×D₄	—	4	1	no	—
107	C₂×C₅×D₄	—	4	1	no	—
108	C₂×C₅×D₄	—	4	1	no	—
109	C₂×C₅×D₄	—	4	1	no	—
110	C₂×C₅×D₄	—	4	4	no	—
111	C₂×C₅×D₄	—	4	4	no	—
112	C₂×C₅×D₄	—	4	4	no	—
113	C₂×C₅×D₄	—	4	4	no	—
114	C₂×C₅×D₄	—	4	4	no	—
115	C₂×C₅×D₄	—	4	4	no	—
116	C₂²×C₄×C₅	—	4	1	no	—
117	C₂²×C₄×C₅	—	4	1	no	—
118	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
121	C₅×SD₁₆	—	4	16	no	—
122	C₅×D₈	—	4	16	no	—
123	C₂×C₅×C₈	—	2	4	no	—
124	C₂×C₅×C₈	—	2	4	no	—
125	C₂×C₅×C₈	—	2	4	no	—
126	C₂×C₅×C₈	C₂×D₄	1	4	yes	—
127	C₂×C₅×C₈	C₂×D₄	1	4	yes	—
128	C₂×C₅×C₈	C₂×D₄	1	4	yes	—
129	C₅×C₄⋊C₄	—	2	2	no	—
130	C₅×C₄⋊C₄	—	2	2	no	—
131	C₅×C₄⋊C₄	—	2	2	no	—
132	C₅×C₄⋊C₄	—	2	2	no	—
133	C₅×C₄⋊C₄	—	4	1	no	—
134	C₅×C₄⋊C₄	—	4	1	no	—
135	C₅×C₄⋊C₄	—	4	1	no	—
136	C₅×C₄⋊C₄	—	4	1	no	—
137	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
138	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
139	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
140	C₄²×C₅	C₂⁴	1	1	yes	characteristic
141	C₂²×SD₁₆	—	2	2	no	—
142	C₂²×D₈	—	2	2	no	—
143	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
144	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
145	C₂×#127	C₂²×C₅	1	1	yes	characteristic
146	C₂×#127	C₂²×C₅	1	1	yes	characteristic
147	#493	—	2	2	no	—
148	#493	C₂²×C₅	1	4	yes	—
149	#492	—	2	2	no	—
150	#492	C₂²×C₅	1	4	yes	complemented
151	#487	—	2	2	no	—
152	#487	C₂²×C₅	1	4	yes	complemented
153	#486	—	2	2	no	—
154	#486	—	2	2	no	—
155	#486	—	2	2	no	—
156	#486	C₂²×C₅	1	4	yes	complemented
157	#486	C₂²×C₅	1	4	yes	complemented
158	#486	C₂²×C₅	1	4	yes	complemented
159	C₂×#103	—	2	2	no	—
160	C₂×#102	—	2	2	no	—
161	C₂×#102	—	2	2	no	—
162	C₂×#102	—	2	2	no	—
163	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
164	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
165	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
166	#322	C₂²×C₅	1	4	yes	complemented
167	C₂³×C₅	—	4	2	no	—
168	C₂³×C₅	—	4	2	no	—
169	C₂³×C₅	—	8	2	no	—
170	C₂³×C₅	—	8	2	no	—
171	C₂³×C₅	—	8	2	no	—
172	C₂³×C₅	—	8	2	no	—
173	C₂³×C₅	—	8	2	no	—
174	C₂³×C₅	—	8	2	no	—
175	C₂³×C₅	#127	1	1	yes	characteristic
176	C₅×Q₈	—	4	4	no	—
177	C₅×Q₈	—	4	4	no	—
178	C₅×Q₈	—	8	2	no	—
179	C₅×Q₈	—	8	2	no	—
180	C₅×D₄	—	4	4	no	—
181	C₅×D₄	—	4	4	no	—
182	C₅×D₄	—	4	4	no	—
183	C₅×D₄	—	4	4	no	—
184	C₅×D₄	—	4	4	no	—
185	C₅×D₄	—	4	4	no	—
186	C₅×D₄	—	8	2	no	—
187	C₅×D₄	—	8	2	no	—
188	C₅×D₄	—	8	2	no	—
189	C₅×D₄	—	8	2	no	—
190	C₅×D₄	—	8	2	no	—
191	C₅×D₄	—	8	2	no	—
192	C₂×C₄×C₅	—	4	2	no	—
193	C₂×C₄×C₅	—	4	2	no	—
194	C₂×C₄×C₅	—	8	2	no	—
195	C₂×C₄×C₅	—	8	2	no	—
196	C₂×C₄×C₅	#127	1	1	yes	characteristic
197	C₂×C₄×C₅	#127	1	1	yes	characteristic
198	C₂×C₄×C₅	#127	1	1	yes	characteristic
199	C₂×C₄×C₅	#135	1	4	yes	—
200	C₂×C₄×C₅	AGL(1,ℤ/8)	1	4	yes	—
201	C₂×C₄×C₅	AGL(1,ℤ/8)	1	4	yes	—
202	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
203	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
204	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
205	C₅×C₈	—	2	4	no	—
206	C₅×C₈	—	2	4	no	—
207	C₅×C₈	—	2	4	no	—
208	C₂²×Q₈	—	2	1	no	—
209	C₂²×Q₈	—	2	1	no	—
210	C₂²×D₄	—	2	1	no	—
211	C₂²×D₄	—	2	1	no	—
212	C₂²×D₄	—	2	1	no	—
213	C₂²×D₄	—	2	1	no	—
214	C₂²×D₄	—	2	1	no	—
215	C₂²×D₄	—	2	1	no	—
216	C₂×SD₁₆	—	2	8	no	—
217	C₂×SD₁₆	—	4	8	no	—
218	C₂×D₈	—	2	8	no	—
219	C₂×D₈	—	4	8	no	—
220	C₂²×C₈	C₅×D₄	1	2	yes	—
221	C₂²×C₈	C₅×D₄	1	2	yes	—
222	C₂²×C₈	C₅×D₄	1	2	yes	—
223	C₄⋊Q₈	—	2	1	no	—
224	C₄⋊Q₈	—	2	1	no	—
225	C₄⋊Q₈	—	2	1	no	—
226	C₄⋊Q₈	—	2	1	no	—
227	C₄⋊Q₈	—	2	1	no	—
228	C₄⋊Q₈	—	2	1	no	—
229	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
230	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
231	#127	—	2	1	no	—
232	#127	—	2	1	no	—
233	#127	—	2	1	no	—
234	#127	—	2	1	no	—
235	#127	—	2	1	no	—
236	#127	—	2	1	no	—
237	#127	C₂³×C₅	1	2	yes	—
238	#127	C₂³×C₅	1	2	yes	—
239	C₂×C₄⋊C₄	—	2	1	no	—
240	C₂×C₄⋊C₄	—	2	1	no	—
241	C₂×C₄⋊C₄	—	2	1	no	—
242	C₂×C₄⋊C₄	—	2	1	no	—
243	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
244	#103	—	2	8	no	—
245	#102	—	2	8	no	—
246	#102	—	2	8	no	—
247	#102	—	2	8	no	—
248	C₄×C₈	C₅×D₄	1	2	yes	—
249	C₄×C₈	C₅×D₄	1	2	yes	—
250	C₄×C₈	C₅×D₄	1	2	yes	—
251	C₄×C₈	C₂³×C₅	1	2	yes	—
252	C₄×C₈	C₂³×C₅	1	2	yes	—
253	C₄×C₈	C₂³×C₅	1	2	yes	—
254	C₂²×C₅	—	8	2	no	—
255	C₂²×C₅	—	8	2	no	—
256	C₂²×C₅	—	8	2	no	—
257	C₂²×C₅	—	8	2	no	—
258	C₂²×C₅	—	8	2	no	—
259	C₂²×C₅	—	8	2	no	—
260	C₂²×C₅	—	16	4	no	—
261	C₂²×C₅	—	16	4	no	—
262	C₂²×C₅	#495	1	2	yes	—
263	C₂²×C₅	#496	1	2	yes	—
264	C₂²×C₅	#496	1	2	yes	—
265	C₂²×C₅	C₂×#127	1	1	yes	characteristic
266	C₄×C₅	—	8	2	no	—
267	C₄×C₅	—	8	2	no	—
268	C₄×C₅	#495	1	2	yes	—
269	C₄×C₅	#496	1	2	yes	—
270	C₄×C₅	#496	1	2	yes	—
271	C₄×C₅	C₂×#135	1	2	yes	—
272	C₄×C₅	C₂×AGL(1,ℤ/8)	1	2	yes	—
273	C₄×C₅	C₂×AGL(1,ℤ/8)	1	2	yes	—
274	C₂⁴	—	4	1	no	—
275	C₂⁴	—	4	1	no	—
276	C₂×Q₈	—	2	2	no	—
277	C₂×Q₈	—	2	2	no	—
278	C₂×Q₈	—	4	1	no	—
279	C₂×Q₈	—	4	1	no	—
280	C₂×Q₈	—	4	4	no	—
281	C₂×Q₈	—	4	4	no	—
282	C₂×D₄	—	2	2	no	—
283	C₂×D₄	—	2	2	no	—
284	C₂×D₄	—	2	2	no	—
285	C₂×D₄	—	2	2	no	—
286	C₂×D₄	—	2	2	no	—
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	—	4	1	no	—
289	C₂×D₄	—	4	1	no	—
290	C₂×D₄	—	4	1	no	—
291	C₂×D₄	—	4	1	no	—
292	C₂×D₄	—	4	1	no	—
293	C₂×D₄	—	4	1	no	—
294	C₂×D₄	—	4	4	no	—
295	C₂×D₄	—	4	4	no	—
296	C₂×D₄	—	4	4	no	—
297	C₂×D₄	—	4	4	no	—
298	C₂×D₄	—	4	4	no	—
299	C₂×D₄	—	4	4	no	—
300	C₂²×C₄	—	4	1	no	—
301	C₂²×C₄	—	4	1	no	—
302	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
303	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
304	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
305	SD₁₆	—	4	16	no	—
306	D₈	—	4	16	no	—
307	C₂×C₈	—	2	4	no	—
308	C₂×C₈	—	2	4	no	—
309	C₂×C₈	—	2	4	no	—
310	C₂×C₈	C₂×C₅×D₄	1	4	yes	—
311	C₂×C₈	C₂×C₅×D₄	1	4	yes	—
312	C₂×C₈	C₂×C₅×D₄	1	4	yes	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	4	1	no	—
318	C₄⋊C₄	—	4	1	no	—
319	C₄⋊C₄	—	4	1	no	—
320	C₄⋊C₄	—	4	1	no	—
321	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
322	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
323	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
324	C₄²	C₂⁴×C₅	1	1	yes	characteristic
325	C₂×C₅	—	16	2	no	—
326	C₂×C₅	—	16	2	no	—
327	C₂×C₅	#1717	1	4	yes	direct product factor
328	C₂×C₅	C₂×#495	1	1	yes	characteristic
329	C₂×C₅	C₂×#496	1	1	yes	characteristic
330	C₂×C₅	C₂×#496	1	1	yes	characteristic
331	C₂³	—	4	2	no	—
332	C₂³	—	4	2	no	—
333	C₂³	—	8	2	no	—
334	C₂³	—	8	2	no	—
335	C₂³	—	8	2	no	—
336	C₂³	—	8	2	no	—
337	C₂³	—	8	2	no	—
338	C₂³	—	8	2	no	—
339	C₂³	C₅×#127	1	1	yes	characteristic
340	Q₈	—	4	4	no	—
341	Q₈	—	4	4	no	—
342	Q₈	—	8	2	no	—
343	Q₈	—	8	2	no	—
344	D₄	—	4	4	no	—
345	D₄	—	4	4	no	—
346	D₄	—	4	4	no	—
347	D₄	—	4	4	no	—
348	D₄	—	4	4	no	—
349	D₄	—	4	4	no	—
350	D₄	—	8	2	no	—
351	D₄	—	8	2	no	—
352	D₄	—	8	2	no	—
353	D₄	—	8	2	no	—
354	D₄	—	8	2	no	—
355	D₄	—	8	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	8	2	no	—
359	C₂×C₄	—	8	2	no	—
360	C₂×C₄	C₅×#127	1	1	yes	characteristic
361	C₂×C₄	C₅×#127	1	1	yes	characteristic
362	C₂×C₄	C₅×#127	1	1	yes	characteristic
363	C₂×C₄	C₅×#135	1	4	yes	—
364	C₂×C₄	C₅×AGL(1,ℤ/8)	1	4	yes	—
365	C₂×C₄	C₅×AGL(1,ℤ/8)	1	4	yes	—
366	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
367	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
368	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
369	C₈	—	2	4	no	—
370	C₈	—	2	4	no	—
371	C₈	—	2	4	no	—
372	C₅	C₂×#1717	1	1	yes	characteristic, direct product factor, Sylow
373	C₂²	—	8	2	no	—
374	C₂²	—	8	2	no	—
375	C₂²	—	8	2	no	—
376	C₂²	—	8	2	no	—
377	C₂²	—	8	2	no	—
378	C₂²	—	8	2	no	—
379	C₂²	—	16	4	no	—
380	C₂²	—	16	4	no	—
381	C₂²	C₅×#495	1	2	yes	—
382	C₂²	C₅×#496	1	2	yes	—
383	C₂²	C₅×#496	1	2	yes	—
384	C₂²	C₂×C₅×#127	1	1	yes	characteristic
385	C₄	—	8	2	no	—
386	C₄	—	8	2	no	—
387	C₄	C₅×#495	1	2	yes	—
388	C₄	C₅×#496	1	2	yes	—
389	C₄	C₅×#496	1	2	yes	—
390	C₄	C₂×C₅×#135	1	2	yes	—
391	C₄	C₂×C₅×AGL(1,ℤ/8)	1	2	yes	—
392	C₄	C₂×C₅×AGL(1,ℤ/8)	1	2	yes	—
393	C₂	—	16	2	no	—
394	C₂	—	16	2	no	—
395	C₂	C₅×#1717	1	4	yes	direct product factor
396	C₂	C₂×C₅×#495	1	1	yes	characteristic
397	C₂	C₂×C₅×#496	1	1	yes	characteristic
398	C₂	C₂×C₅×#496	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	#127
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅
prime radical	C₂×C₅×#493	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#492	C₂	semidirect
3. C₂×C₅×#487	C₂	semidirect
4. C₂×C₅×#486	C₂	semidirect
5. C₂×C₅×#486	C₂	semidirect
6. C₂×C₅×#486	C₂	semidirect
7. C₅×#1717	C₂	direct (N × H)
8. C₂×C₅×#322	C₂	semidirect
18. C₅×#492	C₂²	semidirect
20. C₅×#487	C₂²	semidirect
24. C₅×#486	C₂²	semidirect
25. C₅×#486	C₂²	semidirect
26. C₅×#486	C₂²	semidirect
34. C₅×#322	C₂²	semidirect
35. C₂×#1717	C₅	direct (N × H)
83. C₂×#492	C₂×C₅	semidirect
84. C₂×#487	C₂×C₅	semidirect
85. C₂×#486	C₂×C₅	semidirect
86. C₂×#486	C₂×C₅	semidirect
87. C₂×#486	C₂×C₅	semidirect
88. #1717	C₂×C₅	direct (N × H)
89. C₂×#322	C₂×C₅	semidirect
150. #492	C₂²×C₅	semidirect
152. #487	C₂²×C₅	semidirect
156. #486	C₂²×C₅	semidirect
157. #486	C₂²×C₅	semidirect
158. #486	C₂²×C₅	semidirect
166. #322	C₂²×C₅	semidirect
327. C₂×C₅	#1717	direct (N × H)
372. C₅	C₂×#1717	direct (N × H)
395. C₂	C₅×#1717	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×#493	2
C₂×C₅×#492	2
C₂×C₅×#487	2
C₂×C₅×#486	2
C₅×#1717	2
C₂×C₅×#322	2
C₂×#1717	5

Subgroups — C2×C5×#1717 #11942329

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#1717 #11942329