Subgroups — C₂×C₅×#1697 #11941858

Order 1280.

778 conjugacy classes of subgroups.

The subgroup lattice has 416 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, complemented
2	C₂×C₅×#476	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#459	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×#436	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1697	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₅×#335	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#333	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅×#331	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₅×D₈	—	2	1	no	—
10	C₂²×C₅×M₁₆	—	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×D₄	C₂²	1	1	yes	characteristic
14	C₅×#486	—	2	2	no	—
15	C₅×#486	C₂²	1	4	yes	complemented
16	C₅×#476	—	2	2	no	—
17	C₅×#476	C₂²	1	4	yes	complemented
18	C₅×#459	—	2	2	no	—
19	C₅×#459	C₂²	1	4	yes	—
20	C₅×#436	—	2	2	no	—
21	C₅×#436	C₂²	1	4	yes	complemented
22	C₂×C₅×#106	—	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×#102	—	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×C₂²⋊C₈	—	2	1	no	—
31	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
32	C₅×#335	C₂²	1	4	yes	complemented
33	C₅×#333	C₂²	1	4	yes	complemented
34	C₅×#331	C₂²	1	4	yes	complemented
35	C₂×#1697	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
36	C₂²×C₅×Q₈	—	2	1	no	—
37	C₂²×C₅×D₄	—	2	1	no	—
38	C₂²×C₅×D₄	—	2	1	no	—
39	C₂²×C₅×D₄	—	2	1	no	—
40	C₂²×C₅×D₄	D₄	1	1	yes	characteristic
41	C₂³×C₄×C₅	—	2	1	no	—
42	C₂×C₅×D₈	—	2	4	no	—
43	C₂×C₅×D₈	—	4	4	no	—
44	C₂×C₅×M₁₆	—	2	4	no	—
45	C₂×C₅×M₁₆	—	4	4	no	—
46	C₂²×C₅×C₈	—	2	1	no	—
47	C₂²×C₅×C₈	—	2	1	no	—
48	C₂²×C₅×C₈	—	2	1	no	—
49	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
50	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
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	C₂³	1	2	yes	—
55	C₅×#127	—	2	1	no	—
56	C₅×#127	—	2	1	no	—
57	C₅×#127	—	2	1	no	—
58	C₅×#127	C₂³	1	2	yes	—
59	C₄×C₅×D₄	—	2	1	no	—
60	C₄×C₅×D₄	—	2	1	no	—
61	C₄×C₅×D₄	D₄	1	2	yes	—
62	C₄×C₅×D₄	C₂³	1	2	yes	—
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×C₅×C₂²⋊C₄	—	2	1	no	—
67	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
68	C₅×#106	—	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×#102	—	2	4	no	—
76	C₅×#102	—	2	4	no	—
77	C₅×#102	—	2	4	no	—
78	C₅×#102	—	2	4	no	—
79	C₅×C₂²⋊C₈	—	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, complemented
83	C₂×#476	C₂×C₅	1	1	yes	characteristic, complemented
84	C₂×#459	C₂×C₅	1	1	yes	characteristic
85	C₂×#436	C₂×C₅	1	1	yes	characteristic, complemented
86	#1697	C₂×C₅	1	8	yes	direct product factor
87	C₂×#335	C₂×C₅	1	1	yes	characteristic, complemented
88	C₂×#333	C₂×C₅	1	1	yes	characteristic, complemented
89	C₂×#331	C₂×C₅	1	1	yes	characteristic, complemented
90	C₂⁴×C₅	—	2	1	no	—
91	C₂⁴×C₅	—	4	1	no	—
92	C₂×C₅×Q₈	—	2	2	no	—
93	C₂×C₅×Q₈	—	4	1	no	—
94	C₂×C₅×Q₈	—	8	2	no	—
95	C₂×C₅×D₄	—	2	1	no	—
96	C₂×C₅×D₄	—	2	2	no	—
97	C₂×C₅×D₄	—	2	2	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	—	4	1	no	—
102	C₂×C₅×D₄	—	4	1	no	—
103	C₂×C₅×D₄	—	4	1	no	—
104	C₂×C₅×D₄	—	4	2	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	—	8	2	no	—
109	C₂×C₅×D₄	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₅	—	2	1	no	—
111	C₂²×C₄×C₅	—	2	2	no	—
112	C₂²×C₄×C₅	—	2	2	no	—
113	C₂²×C₄×C₅	—	4	2	no	—
114	C₂²×C₄×C₅	—	4	2	no	—
115	C₂²×C₄×C₅	—	4	1	no	—
116	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₅	#41	1	1	yes	characteristic
119	C₅×D₈	—	4	8	no	—
120	C₅×M₁₆	—	4	8	no	—
121	C₂×C₅×C₈	—	2	2	no	—
122	C₂×C₅×C₈	—	2	2	no	—
123	C₂×C₅×C₈	—	2	2	no	—
124	C₂×C₅×C₈	—	2	2	no	—
125	C₂×C₅×C₈	—	2	2	no	—
126	C₂×C₅×C₈	—	4	2	no	—
127	C₂×C₅×C₈	—	4	2	no	—
128	C₂×C₅×C₈	—	4	2	no	—
129	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
130	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
131	C₅×C₄⋊C₄	—	2	1	no	—
132	C₅×C₄⋊C₄	—	2	2	no	—
133	C₅×C₄⋊C₄	—	2	2	no	—
134	C₅×C₄⋊C₄	—	4	1	no	—
135	C₅×C₄⋊C₄	—	4	1	no	—
136	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
137	C₅×C₂²⋊C₄	—	2	2	no	—
138	C₅×C₂²⋊C₄	—	2	2	no	—
139	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
140	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
141	C₄²×C₅	#41	1	1	yes	characteristic
142	C₄²×C₅	C₂⁴	1	1	yes	characteristic
143	C₂²×D₈	—	2	1	no	—
144	C₂²×M₁₆	—	2	1	no	—
145	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
146	C₂×#127	C₂²×C₅	1	1	yes	characteristic
147	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
148	#486	—	2	2	no	—
149	#486	C₂²×C₅	1	4	yes	complemented
150	#476	—	2	2	no	—
151	#476	C₂²×C₅	1	4	yes	complemented
152	#459	—	2	2	no	—
153	#459	C₂²×C₅	1	4	yes	—
154	#436	—	2	2	no	—
155	#436	C₂²×C₅	1	4	yes	complemented
156	C₂×#106	—	2	1	no	—
157	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
158	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
159	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
160	C₂×#102	—	2	1	no	—
161	C₂×#102	—	2	1	no	—
162	C₂×#102	—	2	1	no	—
163	C₂×#102	—	2	1	no	—
164	C₂×C₂²⋊C₈	—	2	1	no	—
165	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
166	#335	C₂²×C₅	1	4	yes	complemented
167	#333	C₂²×C₅	1	4	yes	complemented
168	#331	C₂²×C₅	1	4	yes	complemented
169	C₂³×C₅	—	2	2	no	—
170	C₂³×C₅	—	4	2	no	—
171	C₂³×C₅	—	4	2	no	—
172	C₂³×C₅	—	4	2	no	—
173	C₂³×C₅	—	4	2	no	—
174	C₂³×C₅	—	8	2	no	—
175	C₂³×C₅	—	8	2	no	—
176	C₂³×C₅	—	8	2	no	—
177	C₂³×C₅	#121	1	1	yes	characteristic
178	C₅×Q₈	—	8	2	no	—
179	C₅×Q₈	—	8	2	no	—
180	C₅×D₄	—	2	2	no	—
181	C₅×D₄	—	2	2	no	—
182	C₅×D₄	—	4	2	no	—
183	C₅×D₄	—	4	2	no	—
184	C₅×D₄	—	4	2	no	—
185	C₅×D₄	—	4	2	no	—
186	C₅×D₄	—	4	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	C₂×C₄×C₅	—	2	2	no	—
192	C₂×C₄×C₅	—	2	2	no	—
193	C₂×C₄×C₅	—	4	2	no	—
194	C₂×C₄×C₅	—	4	2	no	—
195	C₂×C₄×C₅	—	4	2	no	—
196	C₂×C₄×C₅	—	4	4	no	—
197	C₂×C₄×C₅	—	4	2	no	—
198	C₂×C₄×C₅	—	8	2	no	—
199	C₂×C₄×C₅	#121	1	1	yes	characteristic
200	C₂×C₄×C₅	#121	1	1	yes	characteristic
201	C₂×C₄×C₅	#121	1	1	yes	characteristic
202	C₂×C₄×C₅	#135	1	2	yes	—
203	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
204	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
205	C₂×C₄×C₅	#137	1	2	yes	—
206	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
207	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
208	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
209	C₅×C₈	—	2	2	no	—
210	C₅×C₈	—	2	2	no	—
211	C₅×C₈	—	4	2	no	—
212	C₅×C₈	—	4	2	no	—
213	C₅×C₈	—	4	2	no	—
214	C₂²×Q₈	—	2	1	no	—
215	C₂²×D₄	—	2	1	no	—
216	C₂²×D₄	—	2	1	no	—
217	C₂²×D₄	—	2	1	no	—
218	C₂²×D₄	C₅×D₄	1	1	yes	characteristic
219	C₂³×C₄	—	2	1	no	—
220	C₂×D₈	—	2	4	no	—
221	C₂×D₈	—	4	4	no	—
222	C₂×M₁₆	—	2	4	no	—
223	C₂×M₁₆	—	4	4	no	—
224	C₂²×C₈	—	2	1	no	—
225	C₂²×C₈	—	2	1	no	—
226	C₂²×C₈	—	2	1	no	—
227	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
228	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
229	C₄⋊Q₈	—	2	1	no	—
230	C₄⋊Q₈	—	2	1	no	—
231	C₄⋊Q₈	—	2	1	no	—
232	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
233	#127	—	2	1	no	—
234	#127	—	2	1	no	—
235	#127	—	2	1	no	—
236	#127	C₂³×C₅	1	2	yes	—
237	C₄×D₄	—	2	1	no	—
238	C₄×D₄	—	2	1	no	—
239	C₄×D₄	C₅×D₄	1	2	yes	—
240	C₄×D₄	C₂³×C₅	1	2	yes	—
241	C₂×C₄⋊C₄	—	2	1	no	—
242	C₂×C₄⋊C₄	—	2	1	no	—
243	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
244	C₂×C₂²⋊C₄	—	2	1	no	—
245	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
246	#106	—	2	4	no	—
247	C₄⋊C₈	—	2	1	no	—
248	C₄⋊C₈	—	2	1	no	—
249	C₄⋊C₈	—	2	1	no	—
250	C₄⋊C₈	C₂³×C₅	1	2	yes	—
251	C₄⋊C₈	C₂³×C₅	1	2	yes	—
252	C₄⋊C₈	C₂³×C₅	1	2	yes	—
253	#102	—	2	4	no	—
254	#102	—	2	4	no	—
255	#102	—	2	4	no	—
256	#102	—	2	4	no	—
257	C₂²⋊C₈	—	2	4	no	—
258	C₄×C₈	C₅×D₄	1	2	yes	—
259	C₄×C₈	C₂³×C₅	1	2	yes	—
260	C₂²×C₅	—	4	2	no	—
261	C₂²×C₅	—	4	2	no	—
262	C₂²×C₅	—	4	2	no	—
263	C₂²×C₅	—	8	4	no	—
264	C₂²×C₅	—	8	2	no	—
265	C₂²×C₅	—	8	2	no	—
266	C₂²×C₅	—	8	2	no	—
267	C₂²×C₅	—	16	4	no	—
268	C₂²×C₅	#463	1	2	yes	—
269	C₂²×C₅	#468	1	2	yes	—
270	C₂²×C₅	#472	1	2	yes	—
271	C₂²×C₅	C₂×#121	1	1	yes	characteristic
272	C₄×C₅	—	2	1	no	—
273	C₄×C₅	—	2	1	no	—
274	C₄×C₅	—	4	2	no	—
275	C₄×C₅	—	8	2	no	—
276	C₄×C₅	#463	1	2	yes	—
277	C₄×C₅	#468	1	2	yes	—
278	C₄×C₅	C₂×#135	1	1	yes	characteristic
279	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
280	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
281	C₄×C₅	C₂×#137	1	1	yes	characteristic
282	C₂⁴	—	2	1	no	—
283	C₂⁴	—	4	1	no	—
284	C₂×Q₈	—	2	2	no	—
285	C₂×Q₈	—	4	1	no	—
286	C₂×Q₈	—	8	2	no	—
287	C₂×D₄	—	2	1	no	—
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	4	1	no	—
294	C₂×D₄	—	4	1	no	—
295	C₂×D₄	—	4	1	no	—
296	C₂×D₄	—	4	2	no	—
297	C₂×D₄	—	4	2	no	—
298	C₂×D₄	—	4	2	no	—
299	C₂×D₄	—	4	2	no	—
300	C₂×D₄	—	8	2	no	—
301	C₂×D₄	C₂×C₅×D₄	1	2	yes	—
302	C₂²×C₄	—	2	1	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	4	2	no	—
306	C₂²×C₄	—	4	2	no	—
307	C₂²×C₄	—	4	1	no	—
308	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
309	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
310	C₂²×C₄	C₅×#41	1	1	yes	characteristic
311	D₈	—	4	8	no	—
312	M₁₆	—	4	8	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	4	2	no	—
319	C₂×C₈	—	4	2	no	—
320	C₂×C₈	—	4	2	no	—
321	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
322	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
323	C₄⋊C₄	—	2	1	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	4	1	no	—
327	C₄⋊C₄	—	4	1	no	—
328	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
329	C₂²⋊C₄	—	2	2	no	—
330	C₂²⋊C₄	—	2	2	no	—
331	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
332	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
333	C₄²	C₅×#41	1	1	yes	characteristic
334	C₄²	C₂⁴×C₅	1	1	yes	characteristic
335	C₂×C₅	—	8	2	no	—
336	C₂×C₅	—	16	2	no	—
337	C₂×C₅	#1697	1	4	yes	direct product factor
338	C₂×C₅	C₂×#463	1	1	yes	characteristic
339	C₂×C₅	C₂×#468	1	1	yes	characteristic
340	C₂×C₅	C₂×#472	1	1	yes	characteristic
341	C₂³	—	2	2	no	—
342	C₂³	—	4	2	no	—
343	C₂³	—	4	2	no	—
344	C₂³	—	4	2	no	—
345	C₂³	—	4	2	no	—
346	C₂³	—	8	2	no	—
347	C₂³	—	8	2	no	—
348	C₂³	—	8	2	no	—
349	C₂³	C₅×#121	1	1	yes	characteristic
350	Q₈	—	8	2	no	—
351	Q₈	—	8	2	no	—
352	D₄	—	2	2	no	—
353	D₄	—	2	2	no	—
354	D₄	—	4	2	no	—
355	D₄	—	4	2	no	—
356	D₄	—	4	2	no	—
357	D₄	—	4	2	no	—
358	D₄	—	4	2	no	—
359	D₄	—	8	2	no	—
360	D₄	—	8	2	no	—
361	D₄	—	8	2	no	—
362	D₄	—	8	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	4	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	8	2	no	—
371	C₂×C₄	C₅×#121	1	1	yes	characteristic
372	C₂×C₄	C₅×#121	1	1	yes	characteristic
373	C₂×C₄	C₅×#121	1	1	yes	characteristic
374	C₂×C₄	C₅×#135	1	2	yes	—
375	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
376	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
377	C₂×C₄	C₅×#137	1	2	yes	—
378	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
379	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
380	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
381	C₈	—	2	2	no	—
382	C₈	—	2	2	no	—
383	C₈	—	4	2	no	—
384	C₈	—	4	2	no	—
385	C₈	—	4	2	no	—
386	C₅	C₂×#1697	1	1	yes	characteristic, direct product factor, Sylow
387	C₂²	—	4	2	no	—
388	C₂²	—	4	2	no	—
389	C₂²	—	4	2	no	—
390	C₂²	—	8	4	no	—
391	C₂²	—	8	2	no	—
392	C₂²	—	8	2	no	—
393	C₂²	—	8	2	no	—
394	C₂²	—	16	4	no	—
395	C₂²	C₅×#463	1	2	yes	—
396	C₂²	C₅×#468	1	2	yes	—
397	C₂²	C₅×#472	1	2	yes	—
398	C₂²	C₂×C₅×#121	1	1	yes	characteristic
399	C₄	—	2	1	no	—
400	C₄	—	2	1	no	—
401	C₄	—	4	2	no	—
402	C₄	—	8	2	no	—
403	C₄	C₅×#463	1	2	yes	—
404	C₄	C₅×#468	1	2	yes	—
405	C₄	C₂×C₅×#135	1	1	yes	characteristic
406	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
407	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
408	C₄	C₂×C₅×#137	1	1	yes	characteristic
409	C₂	—	8	2	no	—
410	C₂	—	16	2	no	—
411	C₂	C₅×#1697	1	4	yes	direct product factor
412	C₂	C₂×C₅×#463	1	1	yes	characteristic
413	C₂	C₂×C₅×#468	1	1	yes	characteristic
414	C₂	C₂×C₅×#472	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅
prime radical	C₂×C₅×#459	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
1. C₂×C₅×#486	C₂	semidirect
2. C₂×C₅×#476	C₂	semidirect
4. C₂×C₅×#436	C₂	semidirect
5. C₅×#1697	C₂	direct (N × H)
6. C₂×C₅×#335	C₂	semidirect
7. C₂×C₅×#333	C₂	semidirect
8. C₂×C₅×#331	C₂	semidirect
15. C₅×#486	C₂²	semidirect
17. C₅×#476	C₂²	semidirect
21. C₅×#436	C₂²	semidirect
32. C₅×#335	C₂²	semidirect
33. C₅×#333	C₂²	semidirect
34. C₅×#331	C₂²	semidirect
35. C₂×#1697	C₅	direct (N × H)
82. C₂×#486	C₂×C₅	semidirect
83. C₂×#476	C₂×C₅	semidirect
85. C₂×#436	C₂×C₅	semidirect
86. #1697	C₂×C₅	direct (N × H)
87. C₂×#335	C₂×C₅	semidirect
88. C₂×#333	C₂×C₅	semidirect
89. C₂×#331	C₂×C₅	semidirect
149. #486	C₂²×C₅	semidirect
151. #476	C₂²×C₅	semidirect
155. #436	C₂²×C₅	semidirect
166. #335	C₂²×C₅	semidirect
167. #333	C₂²×C₅	semidirect
168. #331	C₂²×C₅	semidirect
337. C₂×C₅	#1697	direct (N × H)
386. C₅	C₂×#1697	direct (N × H)
411. C₂	C₅×#1697	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×#476	2
C₂×C₅×#459	2
C₂×C₅×#436	2
C₅×#1697	2
C₂×C₅×#335	2
C₂×C₅×#333	2
C₂×C₅×#331	2
C₂×#1697	5

Subgroups — C2×C5×#1697 #11941858

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#1697 #11941858