Subgroups — C₂×C₅×#1702 #11941873

Order 1280.

734 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#486	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#462	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#460	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×#446	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1702	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₅×#334	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#332	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅×#331	C₂	1	1	yes	maximal, characteristic
9	C₂²×C₅×Q₁₆	—	2	1	no	—
10	C₂²×C₅×SD₁₆	—	2	1	no	—
11	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
12	C₂×C₅×#127	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
14	C₅×#486	—	2	2	no	—
15	C₅×#486	C₂²	1	4	yes	—
16	C₅×#462	—	2	2	no	—
17	C₅×#462	C₂²	1	4	yes	complemented
18	C₅×#460	—	2	2	no	—
19	C₅×#460	C₂²	1	4	yes	—
20	C₅×#446	—	2	2	no	—
21	C₅×#446	C₂²	1	4	yes	complemented
22	C₂×C₅×C₄⋊C₈	—	2	1	no	—
23	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₅×#103	—	2	1	no	—
27	C₂×C₅×#102	—	2	1	no	—
28	C₂×C₅×#102	—	2	1	no	—
29	C₂×C₅×#102	—	2	1	no	—
30	C₂×C₅×#97	—	2	1	no	—
31	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
32	C₅×#334	C₂²	1	4	yes	complemented
33	C₅×#332	C₂²	1	4	yes	complemented
34	C₅×#331	C₂²	1	4	yes	—
35	C₂×#1702	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
36	C₂²×C₅×Q₈	—	2	1	no	—
37	C₂²×C₅×Q₈	D₄	1	1	yes	characteristic
38	C₂²×C₅×D₄	—	2	1	no	—
39	C₂²×C₅×D₄	—	2	1	no	—
40	C₂²×C₅×D₄	—	2	1	no	—
41	C₂×C₅×Q₁₆	—	2	4	no	—
42	C₂×C₅×Q₁₆	—	4	4	no	—
43	C₂×C₅×SD₁₆	—	2	4	no	—
44	C₂×C₅×SD₁₆	—	4	4	no	—
45	C₂²×C₅×C₈	—	2	1	no	—
46	C₂²×C₅×C₈	—	2	1	no	—
47	C₂²×C₅×C₈	—	2	1	no	—
48	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
49	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
50	C₅×C₄⋊Q₈	—	2	1	no	—
51	C₅×C₄⋊Q₈	—	2	1	no	—
52	C₅×C₄⋊Q₈	—	2	1	no	—
53	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
54	C₅×#127	—	2	1	no	—
55	C₅×#127	—	2	1	no	—
56	C₅×#127	—	2	1	no	—
57	C₅×#127	C₂³	1	2	yes	—
58	C₄×C₅×Q₈	—	2	1	no	—
59	C₄×C₅×Q₈	—	2	1	no	—
60	C₄×C₅×Q₈	D₄	1	2	yes	—
61	C₄×C₅×Q₈	C₂³	1	2	yes	—
62	C₂×C₅×C₄⋊C₄	—	2	1	no	—
63	C₂×C₅×C₄⋊C₄	—	2	1	no	—
64	C₂×C₅×C₄⋊C₄	—	2	1	no	—
65	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
66	C₂×C₄²×C₅	—	2	1	no	—
67	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
68	C₅×C₄⋊C₈	—	2	4	no	—
69	C₅×C₄⋊C₈	—	2	1	no	—
70	C₅×C₄⋊C₈	—	2	1	no	—
71	C₅×C₄⋊C₈	—	2	1	no	—
72	C₅×C₄⋊C₈	C₂³	1	2	yes	—
73	C₅×C₄⋊C₈	C₂³	1	2	yes	—
74	C₅×C₄⋊C₈	C₂³	1	2	yes	—
75	C₅×#103	—	2	4	no	—
76	C₅×#102	—	2	4	no	—
77	C₅×#102	—	2	4	no	—
78	C₅×#102	—	2	4	no	—
79	C₅×#97	—	2	4	no	—
80	C₄×C₅×C₈	D₄	1	2	yes	—
81	C₄×C₅×C₈	C₂³	1	2	yes	—
82	C₂×#486	C₂×C₅	1	1	yes	characteristic
83	C₂×#462	C₂×C₅	1	1	yes	characteristic, complemented
84	C₂×#460	C₂×C₅	1	1	yes	characteristic
85	C₂×#446	C₂×C₅	1	1	yes	characteristic, complemented
86	#1702	C₂×C₅	1	8	yes	direct product factor
87	C₂×#334	C₂×C₅	1	1	yes	characteristic, complemented
88	C₂×#332	C₂×C₅	1	1	yes	characteristic, complemented
89	C₂×#331	C₂×C₅	1	1	yes	characteristic
90	C₂⁴×C₅	—	4	1	no	—
91	C₂×C₅×Q₈	—	2	1	no	—
92	C₂×C₅×Q₈	—	2	2	no	—
93	C₂×C₅×Q₈	—	2	2	no	—
94	C₂×C₅×Q₈	—	2	2	no	—
95	C₂×C₅×Q₈	—	4	1	no	—
96	C₂×C₅×Q₈	—	4	2	no	—
97	C₂×C₅×Q₈	—	4	2	no	—
98	C₂×C₅×Q₈	C₂×D₄	1	2	yes	—
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	—	4	1	no	—
103	C₂×C₅×D₄	—	4	1	no	—
104	C₂×C₅×D₄	—	4	1	no	—
105	C₂×C₅×D₄	—	4	2	no	—
106	C₂×C₅×D₄	—	4	2	no	—
107	C₂×C₅×D₄	—	4	2	no	—
108	C₂×C₅×D₄	—	4	2	no	—
109	C₂×C₅×D₄	—	8	2	no	—
110	C₂²×C₄×C₅	—	2	1	no	—
111	C₂²×C₄×C₅	—	2	1	no	—
112	C₂²×C₄×C₅	—	4	1	no	—
113	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₅	#41	1	1	yes	characteristic
116	C₅×Q₁₆	—	4	8	no	—
117	C₅×SD₁₆	—	4	8	no	—
118	C₂×C₅×C₈	—	2	2	no	—
119	C₂×C₅×C₈	—	2	2	no	—
120	C₂×C₅×C₈	—	2	2	no	—
121	C₂×C₅×C₈	—	2	2	no	—
122	C₂×C₅×C₈	—	2	2	no	—
123	C₂×C₅×C₈	—	4	2	no	—
124	C₂×C₅×C₈	—	4	2	no	—
125	C₂×C₅×C₈	—	4	2	no	—
126	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
127	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
128	C₅×C₄⋊C₄	—	2	2	no	—
129	C₅×C₄⋊C₄	—	2	1	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	C₂×D₄	1	2	yes	—
136	C₄²×C₅	—	2	2	no	—
137	C₄²×C₅	—	2	2	no	—
138	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
139	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
140	C₄²×C₅	#41	1	1	yes	characteristic
141	C₄²×C₅	C₂⁴	1	1	yes	characteristic
142	C₂²×Q₁₆	—	2	1	no	—
143	C₂²×SD₁₆	—	2	1	no	—
144	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
145	C₂×#127	C₂²×C₅	1	1	yes	characteristic
146	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
147	#486	—	2	2	no	—
148	#486	C₂²×C₅	1	4	yes	—
149	#462	—	2	2	no	—
150	#462	C₂²×C₅	1	4	yes	complemented
151	#460	—	2	2	no	—
152	#460	C₂²×C₅	1	4	yes	—
153	#446	—	2	2	no	—
154	#446	C₂²×C₅	1	4	yes	complemented
155	C₂×C₄⋊C₈	—	2	1	no	—
156	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
157	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
158	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
159	C₂×#103	—	2	1	no	—
160	C₂×#102	—	2	1	no	—
161	C₂×#102	—	2	1	no	—
162	C₂×#102	—	2	1	no	—
163	C₂×#97	—	2	1	no	—
164	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
165	#334	C₂²×C₅	1	4	yes	complemented
166	#332	C₂²×C₅	1	4	yes	complemented
167	#331	C₂²×C₅	1	4	yes	—
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	#121	1	1	yes	characteristic
173	C₅×Q₈	—	2	2	no	—
174	C₅×Q₈	—	2	2	no	—
175	C₅×Q₈	—	4	2	no	—
176	C₅×Q₈	—	4	2	no	—
177	C₅×Q₈	—	4	2	no	—
178	C₅×Q₈	—	8	2	no	—
179	C₅×D₄	—	4	2	no	—
180	C₅×D₄	—	4	2	no	—
181	C₅×D₄	—	4	2	no	—
182	C₅×D₄	—	4	2	no	—
183	C₅×D₄	—	8	2	no	—
184	C₅×D₄	—	8	2	no	—
185	C₅×D₄	—	8	2	no	—
186	C₅×D₄	—	8	2	no	—
187	C₂×C₄×C₅	—	2	2	no	—
188	C₂×C₄×C₅	—	2	2	no	—
189	C₂×C₄×C₅	—	2	2	no	—
190	C₂×C₄×C₅	—	4	2	no	—
191	C₂×C₄×C₅	—	4	2	no	—
192	C₂×C₄×C₅	—	4	2	no	—
193	C₂×C₄×C₅	—	8	2	no	—
194	C₂×C₄×C₅	#121	1	1	yes	characteristic
195	C₂×C₄×C₅	#121	1	1	yes	characteristic
196	C₂×C₄×C₅	#121	1	1	yes	characteristic
197	C₂×C₄×C₅	#135	1	2	yes	—
198	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
199	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
200	C₂×C₄×C₅	#137	1	2	yes	—
201	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
203	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
204	C₅×C₈	—	2	2	no	—
205	C₅×C₈	—	2	2	no	—
206	C₅×C₈	—	4	2	no	—
207	C₅×C₈	—	4	2	no	—
208	C₅×C₈	—	4	2	no	—
209	C₂²×Q₈	—	2	1	no	—
210	C₂²×Q₈	C₅×D₄	1	1	yes	characteristic
211	C₂²×D₄	—	2	1	no	—
212	C₂²×D₄	—	2	1	no	—
213	C₂²×D₄	—	2	1	no	—
214	C₂×Q₁₆	—	2	4	no	—
215	C₂×Q₁₆	—	4	4	no	—
216	C₂×SD₁₆	—	2	4	no	—
217	C₂×SD₁₆	—	4	4	no	—
218	C₂²×C₈	—	2	1	no	—
219	C₂²×C₈	—	2	1	no	—
220	C₂²×C₈	—	2	1	no	—
221	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
222	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
223	C₄⋊Q₈	—	2	1	no	—
224	C₄⋊Q₈	—	2	1	no	—
225	C₄⋊Q₈	—	2	1	no	—
226	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
227	#127	—	2	1	no	—
228	#127	—	2	1	no	—
229	#127	—	2	1	no	—
230	#127	C₂³×C₅	1	2	yes	—
231	C₄×Q₈	—	2	1	no	—
232	C₄×Q₈	—	2	1	no	—
233	C₄×Q₈	C₅×D₄	1	2	yes	—
234	C₄×Q₈	C₂³×C₅	1	2	yes	—
235	C₂×C₄⋊C₄	—	2	1	no	—
236	C₂×C₄⋊C₄	—	2	1	no	—
237	C₂×C₄⋊C₄	—	2	1	no	—
238	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
239	C₂×C₄²	—	2	1	no	—
240	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
241	C₄⋊C₈	—	2	4	no	—
242	C₄⋊C₈	—	2	1	no	—
243	C₄⋊C₈	—	2	1	no	—
244	C₄⋊C₈	—	2	1	no	—
245	C₄⋊C₈	C₂³×C₅	1	2	yes	—
246	C₄⋊C₈	C₂³×C₅	1	2	yes	—
247	C₄⋊C₈	C₂³×C₅	1	2	yes	—
248	#103	—	2	4	no	—
249	#102	—	2	4	no	—
250	#102	—	2	4	no	—
251	#102	—	2	4	no	—
252	#97	—	2	4	no	—
253	C₄×C₈	C₅×D₄	1	2	yes	—
254	C₄×C₈	C₂³×C₅	1	2	yes	—
255	C₂²×C₅	—	8	2	no	—
256	C₂²×C₅	—	8	2	no	—
257	C₂²×C₅	—	8	2	no	—
258	C₂²×C₅	—	16	4	no	—
259	C₂²×C₅	#464	1	2	yes	—
260	C₂²×C₅	#469	1	2	yes	—
261	C₂²×C₅	#471	1	2	yes	—
262	C₂²×C₅	C₂×#121	1	1	yes	characteristic
263	C₄×C₅	—	2	1	no	—
264	C₄×C₅	—	2	1	no	—
265	C₄×C₅	—	4	2	no	—
266	C₄×C₅	—	4	2	no	—
267	C₄×C₅	—	8	2	no	—
268	C₄×C₅	#464	1	2	yes	—
269	C₄×C₅	#469	1	2	yes	—
270	C₄×C₅	C₂×#135	1	1	yes	characteristic
271	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
272	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
273	C₄×C₅	C₂×#137	1	1	yes	characteristic
274	C₂⁴	—	4	1	no	—
275	C₂×Q₈	—	2	1	no	—
276	C₂×Q₈	—	2	2	no	—
277	C₂×Q₈	—	2	2	no	—
278	C₂×Q₈	—	2	2	no	—
279	C₂×Q₈	—	4	1	no	—
280	C₂×Q₈	—	4	2	no	—
281	C₂×Q₈	—	4	2	no	—
282	C₂×Q₈	C₂×C₅×D₄	1	2	yes	—
283	C₂×D₄	—	2	2	no	—
284	C₂×D₄	—	2	2	no	—
285	C₂×D₄	—	2	2	no	—
286	C₂×D₄	—	4	1	no	—
287	C₂×D₄	—	4	1	no	—
288	C₂×D₄	—	4	1	no	—
289	C₂×D₄	—	4	2	no	—
290	C₂×D₄	—	4	2	no	—
291	C₂×D₄	—	4	2	no	—
292	C₂×D₄	—	4	2	no	—
293	C₂×D₄	—	8	2	no	—
294	C₂²×C₄	—	2	1	no	—
295	C₂²×C₄	—	2	1	no	—
296	C₂²×C₄	—	4	1	no	—
297	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
298	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
299	C₂²×C₄	C₅×#41	1	1	yes	characteristic
300	Q₁₆	—	4	8	no	—
301	SD₁₆	—	4	8	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	4	2	no	—
308	C₂×C₈	—	4	2	no	—
309	C₂×C₈	—	4	2	no	—
310	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
311	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	2	1	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	C₂×C₅×D₄	1	2	yes	—
320	C₄²	—	2	2	no	—
321	C₄²	—	2	2	no	—
322	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
323	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
324	C₄²	C₅×#41	1	1	yes	characteristic
325	C₄²	C₂⁴×C₅	1	1	yes	characteristic
326	C₂×C₅	—	16	2	no	—
327	C₂×C₅	#1702	1	4	yes	direct product factor
328	C₂×C₅	C₂×#464	1	1	yes	characteristic
329	C₂×C₅	C₂×#469	1	1	yes	characteristic
330	C₂×C₅	C₂×#471	1	1	yes	characteristic
331	C₂³	—	4	2	no	—
332	C₂³	—	8	2	no	—
333	C₂³	—	8	2	no	—
334	C₂³	—	8	2	no	—
335	C₂³	C₅×#121	1	1	yes	characteristic
336	Q₈	—	2	2	no	—
337	Q₈	—	2	2	no	—
338	Q₈	—	4	2	no	—
339	Q₈	—	4	2	no	—
340	Q₈	—	4	2	no	—
341	Q₈	—	8	2	no	—
342	D₄	—	4	2	no	—
343	D₄	—	4	2	no	—
344	D₄	—	4	2	no	—
345	D₄	—	4	2	no	—
346	D₄	—	8	2	no	—
347	D₄	—	8	2	no	—
348	D₄	—	8	2	no	—
349	D₄	—	8	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	8	2	no	—
357	C₂×C₄	C₅×#121	1	1	yes	characteristic
358	C₂×C₄	C₅×#121	1	1	yes	characteristic
359	C₂×C₄	C₅×#121	1	1	yes	characteristic
360	C₂×C₄	C₅×#135	1	2	yes	—
361	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
362	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
363	C₂×C₄	C₅×#137	1	2	yes	—
364	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
365	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
366	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
367	C₈	—	2	2	no	—
368	C₈	—	2	2	no	—
369	C₈	—	4	2	no	—
370	C₈	—	4	2	no	—
371	C₈	—	4	2	no	—
372	C₅	C₂×#1702	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	—	16	4	no	—
377	C₂²	C₅×#464	1	2	yes	—
378	C₂²	C₅×#469	1	2	yes	—
379	C₂²	C₅×#471	1	2	yes	—
380	C₂²	C₂×C₅×#121	1	1	yes	characteristic
381	C₄	—	2	1	no	—
382	C₄	—	2	1	no	—
383	C₄	—	4	2	no	—
384	C₄	—	4	2	no	—
385	C₄	—	8	2	no	—
386	C₄	C₅×#464	1	2	yes	—
387	C₄	C₅×#469	1	2	yes	—
388	C₄	C₂×C₅×#135	1	1	yes	characteristic
389	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
390	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
391	C₄	C₂×C₅×#137	1	1	yes	characteristic
392	C₂	—	16	2	no	—
393	C₂	C₅×#1702	1	4	yes	direct product factor
394	C₂	C₂×C₅×#464	1	1	yes	characteristic
395	C₂	C₂×C₅×#469	1	1	yes	characteristic
396	C₂	C₂×C₅×#471	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅
prime radical	C₂×C₅×#127	C₂²
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×#462	C₂	semidirect
4. C₂×C₅×#446	C₂	semidirect
5. C₅×#1702	C₂	direct (N × H)
6. C₂×C₅×#334	C₂	semidirect
7. C₂×C₅×#332	C₂	semidirect
17. C₅×#462	C₂²	semidirect
21. C₅×#446	C₂²	semidirect
32. C₅×#334	C₂²	semidirect
33. C₅×#332	C₂²	semidirect
35. C₂×#1702	C₅	direct (N × H)
83. C₂×#462	C₂×C₅	semidirect
85. C₂×#446	C₂×C₅	semidirect
86. #1702	C₂×C₅	direct (N × H)
87. C₂×#334	C₂×C₅	semidirect
88. C₂×#332	C₂×C₅	semidirect
150. #462	C₂²×C₅	semidirect
154. #446	C₂²×C₅	semidirect
165. #334	C₂²×C₅	semidirect
166. #332	C₂²×C₅	semidirect
327. C₂×C₅	#1702	direct (N × H)
372. C₅	C₂×#1702	direct (N × H)
393. C₂	C₅×#1702	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×#486	2
C₂×C₅×#462	2
C₂×C₅×#460	2
C₂×C₅×#446	2
C₅×#1702	2
C₂×C₅×#334	2
C₂×C₅×#332	2
C₂×C₅×#331	2
C₂×#1702	5

Subgroups — C2×C5×#1702 #11941873

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#1702 #11941873