Subgroups — C₂×C₅×#2212 #11956311

Order 1280.

706 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#510	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#509	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#495	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#443	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2212	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₅×#364	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#362	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅×#361	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×#135	C₂²	1	1	yes	characteristic
10	C₂²×C₅×Q₁₆	C₂²	1	1	yes	characteristic
11	C₂²×C₅×SD₁₆	—	2	1	no	—
12	C₂²×C₅×D₈	C₂²	1	1	yes	characteristic
13	C₂×C₅×#131	—	2	1	no	—
14	C₂×C₅×#124	—	2	1	no	—
15	C₅×#510	—	2	2	no	—
16	C₅×#510	C₂²	1	4	yes	complemented
17	C₅×#509	—	2	2	no	—
18	C₅×#509	C₂²	1	4	yes	—
19	C₂×C₅×Q₃₂	—	2	1	no	—
20	C₂×C₅×SD₃₂	—	2	1	no	—
21	C₂×C₅×SD₃₂	—	2	1	no	—
22	C₂×C₅×D₁₆	—	2	1	no	—
23	C₂×C₅×M₃₂	C₂²	1	1	yes	characteristic
24	C₂×C₅×M₃₂	C₂²	1	1	yes	characteristic
25	C₅×#495	—	2	2	no	—
26	C₅×#495	C₂²	1	4	yes	complemented
27	C₅×#443	—	2	2	no	—
28	C₅×#443	C₂²	1	4	yes	complemented
29	C₂×C₅×#108	C₂²	1	1	yes	characteristic
30	C₂×C₅×#104	—	2	1	no	—
31	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
32	C₅×#364	C₂²	1	4	yes	complemented
33	C₅×#362	C₂²	1	4	yes	complemented
34	C₅×#361	C₂²	1	4	yes	complemented
35	C₂×#2212	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
36	C₂×C₅×#41	—	2	1	no	—
37	C₂²×C₅×Q₈	—	2	1	no	—
38	C₂²×C₅×D₄	—	2	1	no	—
39	C₅×#135	—	2	1	no	—
40	C₅×#135	—	2	1	no	—
41	C₅×#135	D₄	1	2	yes	—
42	C₅×#135	C₂³	1	2	yes	—
43	C₂×C₅×Q₁₆	—	2	1	no	—
44	C₂×C₅×Q₁₆	—	2	1	no	—
45	C₂×C₅×Q₁₆	—	2	1	no	—
46	C₂×C₅×Q₁₆	—	2	1	no	—
47	C₂×C₅×Q₁₆	—	2	1	no	—
48	C₂×C₅×Q₁₆	D₄	1	1	yes	characteristic
49	C₂×C₅×Q₁₆	C₂³	1	2	yes	—
50	C₂×C₅×SD₁₆	—	2	4	no	—
51	C₂×C₅×SD₁₆	—	2	1	no	—
52	C₂×C₅×SD₁₆	—	4	1	no	—
53	C₂×C₅×SD₁₆	—	4	1	no	—
54	C₂×C₅×SD₁₆	—	4	2	no	—
55	C₂×C₅×D₈	—	2	1	no	—
56	C₂×C₅×D₈	—	2	1	no	—
57	C₂×C₅×D₈	—	2	1	no	—
58	C₂×C₅×D₈	—	2	1	no	—
59	C₂×C₅×D₈	—	2	1	no	—
60	C₂×C₅×D₈	D₄	1	1	yes	characteristic
61	C₂×C₅×D₈	C₂³	1	2	yes	—
62	C₅×#131	—	2	4	no	—
63	C₅×#131	—	4	2	no	—
64	C₂×C₅×M₁₆	—	2	1	no	—
65	C₂×C₅×M₁₆	—	4	1	no	—
66	C₂²×C₅×C₈	—	4	1	no	—
67	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
68	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
69	C₅×#124	—	2	4	no	—
70	C₅×#124	—	4	2	no	—
71	C₂×C₅×C₂²⋊C₄	—	4	2	no	—
72	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
73	C₅×Q₃₂	—	2	4	no	—
74	C₅×SD₃₂	—	2	4	no	—
75	C₅×SD₃₂	—	2	4	no	—
76	C₅×D₁₆	—	2	4	no	—
77	C₅×M₃₂	—	2	1	no	—
78	C₅×M₃₂	—	2	1	no	—
79	C₅×M₃₂	C₂³	1	2	yes	—
80	C₅×M₃₂	C₂³	1	2	yes	—
81	C₂×C₅×C₁₆	—	2	1	no	—
82	C₂×C₅×C₁₆	—	2	1	no	—
83	C₅×#108	—	2	1	no	—
84	C₅×#108	C₂³	1	2	yes	—
85	C₅×#104	—	2	4	no	—
86	C₄×C₅×C₈	D₄	1	2	yes	—
87	C₄×C₅×C₈	C₂³	1	2	yes	—
88	C₂×#510	C₂×C₅	1	1	yes	characteristic, complemented
89	C₂×#509	C₂×C₅	1	1	yes	characteristic
90	C₂×#495	C₂×C₅	1	1	yes	characteristic, complemented
91	C₂×#443	C₂×C₅	1	1	yes	characteristic, complemented
92	#2212	C₂×C₅	1	8	yes	direct product factor
93	C₂×#364	C₂×C₅	1	1	yes	characteristic, complemented
94	C₂×#362	C₂×C₅	1	1	yes	characteristic, complemented
95	C₂×#361	C₂×C₅	1	1	yes	characteristic, complemented
96	C₂⁴×C₅	—	4	1	no	—
97	C₅×#41	—	2	2	no	—
98	C₅×#41	—	2	2	no	—
99	C₅×#41	—	4	1	no	—
100	C₅×#41	—	4	1	no	—
101	C₂×C₅×Q₈	—	2	1	no	—
102	C₂×C₅×Q₈	—	2	2	no	—
103	C₂×C₅×Q₈	—	4	1	no	—
104	C₂×C₅×Q₈	—	4	1	no	—
105	C₂×C₅×Q₈	—	4	1	no	—
106	C₂×C₅×Q₈	—	4	1	no	—
107	C₂×C₅×Q₈	—	4	1	no	—
108	C₂×C₅×D₄	—	2	1	no	—
109	C₂×C₅×D₄	—	2	2	no	—
110	C₂×C₅×D₄	—	4	1	no	—
111	C₂×C₅×D₄	—	4	1	no	—
112	C₂×C₅×D₄	—	4	1	no	—
113	C₂×C₅×D₄	—	4	1	no	—
114	C₂×C₅×D₄	—	4	1	no	—
115	C₂×C₅×D₄	—	4	1	no	—
116	C₂²×C₄×C₅	—	2	1	no	—
117	C₂²×C₄×C₅	—	4	1	no	—
118	C₂²×C₄×C₅	—	4	1	no	—
119	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
120	C₅×Q₁₆	—	2	1	no	—
121	C₅×Q₁₆	—	2	2	no	—
122	C₅×Q₁₆	—	2	2	no	—
123	C₅×Q₁₆	—	4	1	no	—
124	C₅×Q₁₆	—	4	1	no	—
125	C₅×Q₁₆	C₂×D₄	1	2	yes	—
126	C₅×SD₁₆	—	2	2	no	—
127	C₅×SD₁₆	—	2	2	no	—
128	C₅×SD₁₆	—	4	4	no	—
129	C₅×SD₁₆	—	4	4	no	—
130	C₅×D₈	—	2	1	no	—
131	C₅×D₈	—	2	2	no	—
132	C₅×D₈	—	2	2	no	—
133	C₅×D₈	—	4	1	no	—
134	C₅×D₈	—	4	1	no	—
135	C₅×D₈	C₂×D₄	1	2	yes	—
136	C₅×M₁₆	—	2	2	no	—
137	C₅×M₁₆	—	4	1	no	—
138	C₅×M₁₆	—	4	4	no	—
139	C₂×C₅×C₈	—	4	1	no	—
140	C₂×C₅×C₈	—	4	4	no	—
141	C₂×C₅×C₈	D₈	1	1	yes	characteristic
142	C₂×C₅×C₈	D₈	1	1	yes	characteristic
143	C₂×C₅×C₈	D₈	1	2	yes	—
144	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
145	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
146	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
147	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
148	C₂×C₅×C₈	#41	1	1	yes	characteristic
149	C₂×C₅×C₈	#41	1	1	yes	characteristic
150	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
151	C₅×C₂²⋊C₄	—	4	8	no	—
152	C₄²×C₅	—	2	1	no	—
153	C₄²×C₅	C₂×D₄	1	2	yes	—
154	C₅×C₁₆	—	2	2	no	—
155	C₅×C₁₆	—	2	2	no	—
156	C₂×#135	C₂²×C₅	1	1	yes	characteristic
157	C₂²×Q₁₆	C₂²×C₅	1	1	yes	characteristic
158	C₂²×SD₁₆	—	2	1	no	—
159	C₂²×D₈	C₂²×C₅	1	1	yes	characteristic
160	C₂×#131	—	2	1	no	—
161	C₂×#124	—	2	1	no	—
162	#510	—	2	2	no	—
163	#510	C₂²×C₅	1	4	yes	complemented
164	#509	—	2	2	no	—
165	#509	C₂²×C₅	1	4	yes	—
166	C₂×Q₃₂	—	2	1	no	—
167	C₂×SD₃₂	—	2	1	no	—
168	C₂×SD₃₂	—	2	1	no	—
169	C₂×D₁₆	—	2	1	no	—
170	C₂×M₃₂	C₂²×C₅	1	1	yes	characteristic
171	C₂×M₃₂	C₂²×C₅	1	1	yes	characteristic
172	#495	—	2	2	no	—
173	#495	C₂²×C₅	1	4	yes	complemented
174	#443	—	2	2	no	—
175	#443	C₂²×C₅	1	4	yes	complemented
176	C₂×#108	C₂²×C₅	1	1	yes	characteristic
177	C₂×#104	—	2	1	no	—
178	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
179	#364	C₂²×C₅	1	4	yes	complemented
180	#362	C₂²×C₅	1	4	yes	complemented
181	#361	C₂²×C₅	1	4	yes	complemented
182	C₂³×C₅	—	4	1	no	—
183	C₂³×C₅	—	4	2	no	—
184	C₂³×C₅	—	8	4	no	—
185	C₂³×C₅	—	8	1	no	—
186	C₂³×C₅	—	8	1	no	—
187	C₂³×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
188	C₅×Q₈	—	2	2	no	—
189	C₅×Q₈	—	4	1	no	—
190	C₅×Q₈	—	4	2	no	—
191	C₅×Q₈	—	4	2	no	—
192	C₅×Q₈	—	8	1	no	—
193	C₅×Q₈	—	8	1	no	—
194	C₅×D₄	—	2	2	no	—
195	C₅×D₄	—	4	2	no	—
196	C₅×D₄	—	4	2	no	—
197	C₅×D₄	—	4	2	no	—
198	C₅×D₄	—	4	2	no	—
199	C₅×D₄	—	4	1	no	—
200	C₅×D₄	—	8	1	no	—
201	C₅×D₄	—	8	1	no	—
202	C₂×C₄×C₅	—	2	2	no	—
203	C₂×C₄×C₅	—	4	2	no	—
204	C₂×C₄×C₅	—	4	1	no	—
205	C₂×C₄×C₅	—	4	2	no	—
206	C₂×C₄×C₅	—	4	2	no	—
207	C₂×C₄×C₅	—	4	2	no	—
208	C₂×C₄×C₅	—	8	1	no	—
209	C₂×C₄×C₅	—	8	1	no	—
210	C₂×C₄×C₅	#121	1	1	yes	characteristic
211	C₂×C₄×C₅	#121	1	1	yes	characteristic
212	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
213	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
214	C₂×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
215	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
216	C₅×C₈	—	4	2	no	—
217	C₅×C₈	#121	1	1	yes	characteristic
218	C₅×C₈	#121	1	1	yes	characteristic
219	C₅×C₈	C₂×D₈	1	2	yes	—
220	C₅×C₈	C₂×D₈	1	2	yes	—
221	C₅×C₈	C₂²×D₄	1	1	yes	characteristic
222	C₅×C₈	C₂×#41	1	1	yes	characteristic
223	C₂×#41	—	2	1	no	—
224	C₂²×Q₈	—	2	1	no	—
225	C₂²×D₄	—	2	1	no	—
226	#135	—	2	1	no	—
227	#135	—	2	1	no	—
228	#135	C₅×D₄	1	2	yes	—
229	#135	C₂³×C₅	1	2	yes	—
230	C₂×Q₁₆	—	2	1	no	—
231	C₂×Q₁₆	—	2	1	no	—
232	C₂×Q₁₆	—	2	1	no	—
233	C₂×Q₁₆	—	2	1	no	—
234	C₂×Q₁₆	—	2	1	no	—
235	C₂×Q₁₆	C₅×D₄	1	1	yes	characteristic
236	C₂×Q₁₆	C₂³×C₅	1	2	yes	—
237	C₂×SD₁₆	—	2	4	no	—
238	C₂×SD₁₆	—	2	1	no	—
239	C₂×SD₁₆	—	4	1	no	—
240	C₂×SD₁₆	—	4	1	no	—
241	C₂×SD₁₆	—	4	2	no	—
242	C₂×D₈	—	2	1	no	—
243	C₂×D₈	—	2	1	no	—
244	C₂×D₈	—	2	1	no	—
245	C₂×D₈	—	2	1	no	—
246	C₂×D₈	—	2	1	no	—
247	C₂×D₈	C₅×D₄	1	1	yes	characteristic
248	C₂×D₈	C₂³×C₅	1	2	yes	—
249	#131	—	2	4	no	—
250	#131	—	4	2	no	—
251	C₂×M₁₆	—	2	1	no	—
252	C₂×M₁₆	—	4	1	no	—
253	C₂²×C₈	—	4	1	no	—
254	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
255	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
256	#124	—	2	4	no	—
257	#124	—	4	2	no	—
258	C₂×C₂²⋊C₄	—	4	2	no	—
259	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
260	Q₃₂	—	2	4	no	—
261	SD₃₂	—	2	4	no	—
262	SD₃₂	—	2	4	no	—
263	D₁₆	—	2	4	no	—
264	M₃₂	—	2	1	no	—
265	M₃₂	—	2	1	no	—
266	M₃₂	C₂³×C₅	1	2	yes	—
267	M₃₂	C₂³×C₅	1	2	yes	—
268	C₂×C₁₆	—	2	1	no	—
269	C₂×C₁₆	—	2	1	no	—
270	#108	—	2	1	no	—
271	#108	C₂³×C₅	1	2	yes	—
272	#104	—	2	4	no	—
273	C₄×C₈	C₅×D₄	1	2	yes	—
274	C₄×C₈	C₂³×C₅	1	2	yes	—
275	C₂²×C₅	—	2	2	no	—
276	C₂²×C₅	—	4	2	no	—
277	C₂²×C₅	—	8	4	no	—
278	C₂²×C₅	—	8	2	no	—
279	C₂²×C₅	—	8	2	no	—
280	C₂²×C₅	—	16	2	no	—
281	C₂²×C₅	—	16	2	no	—
282	C₂²×C₅	#459	1	1	yes	characteristic
283	C₂²×C₅	#459	1	1	yes	characteristic
284	C₂²×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
285	C₄×C₅	—	4	2	no	—
286	C₄×C₅	—	4	2	no	—
287	C₄×C₅	—	8	2	no	—
288	C₄×C₅	#459	1	1	yes	characteristic
289	C₄×C₅	#459	1	1	yes	characteristic
290	C₄×C₅	C₂×#121	1	1	yes	characteristic
291	C₄×C₅	C₂²×D₈	1	1	yes	characteristic
292	C₂⁴	—	4	1	no	—
293	#41	—	2	2	no	—
294	#41	—	2	2	no	—
295	#41	—	4	1	no	—
296	#41	—	4	1	no	—
297	C₂×Q₈	—	2	1	no	—
298	C₂×Q₈	—	2	2	no	—
299	C₂×Q₈	—	4	1	no	—
300	C₂×Q₈	—	4	1	no	—
301	C₂×Q₈	—	4	1	no	—
302	C₂×Q₈	—	4	1	no	—
303	C₂×Q₈	—	4	1	no	—
304	C₂×D₄	—	2	1	no	—
305	C₂×D₄	—	2	2	no	—
306	C₂×D₄	—	4	1	no	—
307	C₂×D₄	—	4	1	no	—
308	C₂×D₄	—	4	1	no	—
309	C₂×D₄	—	4	1	no	—
310	C₂×D₄	—	4	1	no	—
311	C₂×D₄	—	4	1	no	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	4	1	no	—
314	C₂²×C₄	—	4	1	no	—
315	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
316	Q₁₆	—	2	1	no	—
317	Q₁₆	—	2	2	no	—
318	Q₁₆	—	2	2	no	—
319	Q₁₆	—	4	1	no	—
320	Q₁₆	—	4	1	no	—
321	Q₁₆	C₂×C₅×D₄	1	2	yes	—
322	SD₁₆	—	2	2	no	—
323	SD₁₆	—	2	2	no	—
324	SD₁₆	—	4	4	no	—
325	SD₁₆	—	4	4	no	—
326	D₈	—	2	1	no	—
327	D₈	—	2	2	no	—
328	D₈	—	2	2	no	—
329	D₈	—	4	1	no	—
330	D₈	—	4	1	no	—
331	D₈	C₂×C₅×D₄	1	2	yes	—
332	M₁₆	—	2	2	no	—
333	M₁₆	—	4	1	no	—
334	M₁₆	—	4	4	no	—
335	C₂×C₈	—	4	1	no	—
336	C₂×C₈	—	4	4	no	—
337	C₂×C₈	C₅×D₈	1	1	yes	characteristic
338	C₂×C₈	C₅×D₈	1	1	yes	characteristic
339	C₂×C₈	C₅×D₈	1	2	yes	—
340	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
341	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
342	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
343	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
344	C₂×C₈	C₅×#41	1	1	yes	characteristic
345	C₂×C₈	C₅×#41	1	1	yes	characteristic
346	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
347	C₂²⋊C₄	—	4	8	no	—
348	C₄²	—	2	1	no	—
349	C₄²	C₂×C₅×D₄	1	2	yes	—
350	C₁₆	—	2	2	no	—
351	C₁₆	—	2	2	no	—
352	C₂×C₅	—	2	1	no	—
353	C₂×C₅	—	2	1	no	—
354	C₂×C₅	—	8	2	no	—
355	C₂×C₅	—	16	2	no	—
356	C₂×C₅	#2212	1	2	yes	direct product factor
357	C₂×C₅	C₂×#459	1	1	yes	characteristic
358	C₂³	—	4	1	no	—
359	C₂³	—	4	2	no	—
360	C₂³	—	8	4	no	—
361	C₂³	—	8	1	no	—
362	C₂³	—	8	1	no	—
363	C₂³	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
364	Q₈	—	2	2	no	—
365	Q₈	—	4	1	no	—
366	Q₈	—	4	2	no	—
367	Q₈	—	4	2	no	—
368	Q₈	—	8	1	no	—
369	Q₈	—	8	1	no	—
370	D₄	—	2	2	no	—
371	D₄	—	4	2	no	—
372	D₄	—	4	2	no	—
373	D₄	—	4	1	no	—
374	D₄	—	4	2	no	—
375	D₄	—	4	2	no	—
376	D₄	—	8	1	no	—
377	D₄	—	8	1	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	8	1	no	—
385	C₂×C₄	—	8	1	no	—
386	C₂×C₄	C₅×#121	1	1	yes	characteristic
387	C₂×C₄	C₅×#121	1	1	yes	characteristic
388	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
389	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
390	C₂×C₄	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
391	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
392	C₈	—	4	2	no	—
393	C₈	C₅×#121	1	1	yes	characteristic
394	C₈	C₅×#121	1	1	yes	characteristic
395	C₈	C₂×C₅×D₈	1	2	yes	—
396	C₈	C₂×C₅×D₈	1	2	yes	—
397	C₈	C₂²×C₅×D₄	1	1	yes	characteristic
398	C₈	C₂×C₅×#41	1	1	yes	characteristic
399	C₅	C₂×#2212	1	1	yes	characteristic, direct product factor, Sylow
400	C₂²	—	2	2	no	—
401	C₂²	—	4	2	no	—
402	C₂²	—	8	4	no	—
403	C₂²	—	8	2	no	—
404	C₂²	—	8	2	no	—
405	C₂²	—	16	2	no	—
406	C₂²	—	16	2	no	—
407	C₂²	C₅×#459	1	1	yes	characteristic
408	C₂²	C₅×#459	1	1	yes	characteristic
409	C₂²	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
410	C₄	—	4	2	no	—
411	C₄	—	4	2	no	—
412	C₄	—	8	2	no	—
413	C₄	C₅×#459	1	1	yes	characteristic
414	C₄	C₅×#459	1	1	yes	characteristic
415	C₄	C₂×C₅×#121	1	1	yes	characteristic
416	C₄	C₂²×C₅×D₈	1	1	yes	characteristic
417	C₂	—	2	1	no	—
418	C₂	—	2	1	no	—
419	C₂	—	8	2	no	—
420	C₂	—	16	2	no	—
421	C₂	C₅×#2212	1	2	yes	direct product factor
422	C₂	C₂×C₅×#459	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	#459
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₅
prime radical	C₂×C₅×#509	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₂×C₄×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#510	C₂	semidirect
3. C₂×C₅×#495	C₂	semidirect
4. C₂×C₅×#443	C₂	semidirect
5. C₅×#2212	C₂	direct (N × H)
6. C₂×C₅×#364	C₂	semidirect
7. C₂×C₅×#362	C₂	semidirect
8. C₂×C₅×#361	C₂	semidirect
16. C₅×#510	C₂²	semidirect
26. C₅×#495	C₂²	semidirect
28. C₅×#443	C₂²	semidirect
32. C₅×#364	C₂²	semidirect
33. C₅×#362	C₂²	semidirect
34. C₅×#361	C₂²	semidirect
35. C₂×#2212	C₅	direct (N × H)
88. C₂×#510	C₂×C₅	semidirect
90. C₂×#495	C₂×C₅	semidirect
91. C₂×#443	C₂×C₅	semidirect
92. #2212	C₂×C₅	direct (N × H)
93. C₂×#364	C₂×C₅	semidirect
94. C₂×#362	C₂×C₅	semidirect
95. C₂×#361	C₂×C₅	semidirect
163. #510	C₂²×C₅	semidirect
173. #495	C₂²×C₅	semidirect
175. #443	C₂²×C₅	semidirect
179. #364	C₂²×C₅	semidirect
180. #362	C₂²×C₅	semidirect
181. #361	C₂²×C₅	semidirect
356. C₂×C₅	#2212	direct (N × H)
399. C₅	C₂×#2212	direct (N × H)
421. C₂	C₅×#2212	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×#510	2
C₂×C₅×#509	2
C₂×C₅×#495	2
C₂×C₅×#443	2
C₅×#2212	2
C₂×C₅×#364	2
C₂×C₅×#362	2
C₂×C₅×#361	2
C₂×#2212	5

Subgroups — C2×C5×#2212 #11956311

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#2212 #11956311