Subgroups — C₂×C₅×#2145 #11956107

Order 1280.

1170 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×#135	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₅×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#427	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2145	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₅×#360	C₂	1	4	yes	maximal, complemented
6	C₂²×C₅×#41	—	2	1	no	—
7	C₂×C₅×#135	—	2	1	no	—
8	C₂×C₅×#135	—	2	2	no	—
9	C₂×C₅×#135	—	2	1	no	—
10	C₂×C₅×#135	—	2	2	no	—
11	C₂×C₅×#135	C₄	1	2	yes	complemented
12	C₂×C₅×#135	C₄	1	4	yes	complemented
13	C₂×C₅×#135	C₂²	1	2	yes	—
14	C₂×C₅×#135	C₂²	1	4	yes	—
15	C₂²×C₅×Q₁₆	C₄	1	1	yes	characteristic, complemented
16	C₂²×C₅×SD₁₆	—	2	1	no	—
17	C₂²×C₅×D₈	C₄	1	1	yes	characteristic, complemented
18	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
19	C₂×C₅×#117	—	2	1	no	—
20	C₂×C₅×M₃₂	—	2	1	no	—
21	C₂×C₅×M₃₂	—	2	2	no	—
22	C₂×C₅×M₃₂	C₂²	1	2	yes	complemented
23	C₂×C₅×M₃₂	C₂²	1	4	yes	complemented
24	C₂²×C₅×C₁₆	—	2	1	no	—
25	C₅×#427	—	2	2	no	—
26	C₅×#427	C₂²	1	4	yes	complemented
27	C₂×C₅×#107	—	2	1	no	—
28	C₂×C₅×#106	C₂²	1	2	yes	complemented
29	C₅×#360	C₂²	1	16	yes	complemented
30	C₂×#2145	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
31	C₂×C₅×#41	—	2	4	no	—
32	C₂×C₅×#41	—	2	2	no	—
33	C₂×C₅×#41	—	2	2	no	—
34	C₂×C₅×#41	—	2	4	no	—
35	C₂×C₅×#41	—	4	2	no	—
36	C₂×C₅×#41	—	4	1	no	—
37	C₂×C₅×#41	—	4	1	no	—
38	C₂×C₅×#41	—	4	2	no	—
39	C₂²×C₅×Q₈	—	2	1	no	—
40	C₂²×C₅×D₄	—	2	1	no	—
41	C₂²×C₅×D₄	—	4	1	no	—
42	C₂³×C₄×C₅	—	4	1	no	—
43	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
44	C₅×#135	—	2	4	no	—
45	C₅×#135	—	2	4	no	—
46	C₅×#135	—	2	4	no	—
47	C₅×#135	—	2	2	no	—
48	C₅×#135	—	2	4	no	—
49	C₅×#135	—	2	4	no	—
50	C₅×#135	—	2	2	no	—
51	C₅×#135	C₂×C₄	1	4	yes	—
52	C₅×#135	C₂×C₄	1	8	yes	complemented
53	C₅×#135	C₂³	1	4	yes	—
54	C₂×C₅×Q₁₆	—	2	2	no	—
55	C₂×C₅×Q₁₆	—	2	1	no	—
56	C₂×C₅×Q₁₆	C₂×C₄	1	2	yes	—
57	C₂×C₅×Q₁₆	C₂×C₄	1	4	yes	complemented
58	C₂×C₅×SD₁₆	—	2	4	no	—
59	C₂×C₅×SD₁₆	—	2	2	no	—
60	C₂×C₅×SD₁₆	—	2	2	no	—
61	C₂×C₅×SD₁₆	—	2	4	no	—
62	C₂×C₅×D₈	—	2	2	no	—
63	C₂×C₅×D₈	—	2	1	no	—
64	C₂×C₅×D₈	C₂×C₄	1	2	yes	—
65	C₂×C₅×D₈	C₂×C₄	1	4	yes	complemented
66	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
67	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
68	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
69	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
70	C₂²×C₅×C₈	D₄	1	2	yes	—
71	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
72	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
73	C₂²×C₅×C₈	D₄	1	2	yes	—
74	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
75	C₂²×C₅×C₈	C₂³	1	2	yes	—
76	C₅×#117	—	2	4	no	—
77	C₅×#117	—	4	2	no	—
78	C₂×C₅×C₄⋊C₄	—	2	2	no	—
79	C₂×C₅×C₂²⋊C₄	—	4	1	no	—
80	C₂×C₄²×C₅	—	4	1	no	—
81	C₅×M₃₂	—	2	4	no	—
82	C₅×M₃₂	—	2	2	no	—
83	C₅×M₃₂	C₂³	1	4	yes	complemented
84	C₂×C₅×C₁₆	—	2	2	no	—
85	C₂×C₅×C₁₆	—	2	4	no	—
86	C₅×#107	—	2	4	no	—
87	C₅×#106	—	2	2	no	—
88	C₅×#106	C₂³	1	4	yes	complemented
89	C₂²×#135	C₂×C₅	1	1	yes	characteristic
90	C₂²×M₃₂	C₂×C₅	1	1	yes	characteristic, complemented
91	C₂×#427	C₂×C₅	1	1	yes	characteristic, complemented
92	#2145	C₂×C₅	1	8	yes	direct product factor
93	C₂×#360	C₂×C₅	1	4	yes	complemented
94	C₂⁴×C₅	—	4	1	no	—
95	C₂⁴×C₅	D₈	1	1	yes	characteristic
96	C₅×#41	—	2	4	no	—
97	C₅×#41	—	2	8	no	—
98	C₅×#41	—	2	4	no	—
99	C₅×#41	—	4	4	no	—
100	C₅×#41	—	4	4	no	—
101	C₅×#41	—	4	4	no	—
102	C₅×#41	—	4	4	no	—
103	C₅×#41	—	4	2	no	—
104	C₅×#41	—	4	2	no	—
105	C₅×#41	—	4	4	no	—
106	C₂×C₅×Q₈	—	2	2	no	—
107	C₂×C₅×Q₈	—	2	4	no	—
108	C₂×C₅×Q₈	—	4	2	no	—
109	C₂×C₅×Q₈	—	4	1	no	—
110	C₂×C₅×D₄	—	2	2	no	—
111	C₂×C₅×D₄	—	2	4	no	—
112	C₂×C₅×D₄	—	4	2	no	—
113	C₂×C₅×D₄	—	4	4	no	—
114	C₂×C₅×D₄	—	4	2	no	—
115	C₂×C₅×D₄	—	4	4	no	—
116	C₂×C₅×D₄	—	4	2	no	—
117	C₂×C₅×D₄	—	4	1	no	—
118	C₂²×C₄×C₅	—	4	1	no	—
119	C₂²×C₄×C₅	—	4	4	no	—
120	C₂²×C₄×C₅	—	4	2	no	—
121	C₂²×C₄×C₅	—	4	4	no	—
122	C₂²×C₄×C₅	—	4	2	no	—
123	C₂²×C₄×C₅	—	4	2	no	—
124	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
125	C₂²×C₄×C₅	C₂²⋊C₄	1	2	yes	—
126	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
127	C₂²×C₄×C₅	D₈	1	2	yes	—
128	C₂²×C₄×C₅	D₈	1	1	yes	characteristic
129	C₂²×C₄×C₅	SD₁₆	1	1	yes	characteristic
130	C₂²×C₄×C₅	SD₁₆	1	2	yes	—
131	C₂²×C₄×C₅	SD₁₆	1	1	yes	characteristic
132	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
134	C₅×Q₁₆	—	2	2	no	—
135	C₅×Q₁₆	—	2	4	no	—
136	C₅×Q₁₆	C₂²×C₄	1	4	yes	—
137	C₅×SD₁₆	—	2	4	no	—
138	C₅×SD₁₆	—	2	8	no	—
139	C₅×SD₁₆	—	2	4	no	—
140	C₅×D₈	—	2	2	no	—
141	C₅×D₈	—	2	4	no	—
142	C₅×D₈	C₂²×C₄	1	4	yes	—
143	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
144	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
145	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
146	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
147	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
148	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
149	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
150	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
152	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
153	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
154	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
155	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
156	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
157	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
158	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
159	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
160	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
161	C₅×C₄⋊C₄	—	2	4	no	—
162	C₅×C₄⋊C₄	—	4	2	no	—
163	C₅×C₂²⋊C₄	—	4	4	no	—
164	C₄²×C₅	—	4	4	no	—
165	C₅×C₁₆	—	2	4	no	—
166	C₂²×#41	—	2	1	no	—
167	C₂×#135	—	2	1	no	—
168	C₂×#135	—	2	2	no	—
169	C₂×#135	—	2	1	no	—
170	C₂×#135	—	2	2	no	—
171	C₂×#135	C₄×C₅	1	2	yes	complemented
172	C₂×#135	C₄×C₅	1	4	yes	complemented
173	C₂×#135	C₂²×C₅	1	2	yes	—
174	C₂×#135	C₂²×C₅	1	4	yes	—
175	C₂²×Q₁₆	C₄×C₅	1	1	yes	characteristic, complemented
176	C₂²×SD₁₆	—	2	1	no	—
177	C₂²×D₈	C₄×C₅	1	1	yes	characteristic, complemented
178	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
179	C₂×#117	—	2	1	no	—
180	C₂×M₃₂	—	2	1	no	—
181	C₂×M₃₂	—	2	2	no	—
182	C₂×M₃₂	C₂²×C₅	1	2	yes	complemented
183	C₂×M₃₂	C₂²×C₅	1	4	yes	complemented
184	C₂²×C₁₆	—	2	1	no	—
185	#427	—	2	2	no	—
186	#427	C₂²×C₅	1	4	yes	complemented
187	C₂×#107	—	2	1	no	—
188	C₂×#106	C₂²×C₅	1	2	yes	complemented
189	#360	C₂²×C₅	1	16	yes	complemented
190	C₂³×C₅	—	4	2	no	—
191	C₂³×C₅	—	4	4	no	—
192	C₂³×C₅	—	4	2	no	—
193	C₂³×C₅	—	8	4	no	—
194	C₂³×C₅	#102	1	1	yes	characteristic
195	C₂³×C₅	#102	1	1	yes	characteristic
196	C₂³×C₅	#102	1	2	yes	—
197	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
198	C₂³×C₅	C₂×D₈	1	2	yes	—
199	C₅×Q₈	—	2	4	no	—
200	C₅×Q₈	—	4	2	no	—
201	C₅×Q₈	—	4	4	no	—
202	C₅×D₄	—	2	4	no	—
203	C₅×D₄	—	4	4	no	—
204	C₅×D₄	—	4	4	no	—
205	C₅×D₄	—	4	8	no	—
206	C₅×D₄	—	4	2	no	—
207	C₅×D₄	—	4	4	no	—
208	C₂×C₄×C₅	—	4	4	no	—
209	C₂×C₄×C₅	—	4	2	no	—
210	C₂×C₄×C₅	—	4	4	no	—
211	C₂×C₄×C₅	—	4	4	no	—
212	C₂×C₄×C₅	—	4	8	no	—
213	C₂×C₄×C₅	—	4	4	no	—
214	C₂×C₄×C₅	—	8	4	no	—
215	C₂×C₄×C₅	#102	1	2	yes	—
216	C₂×C₄×C₅	#102	1	2	yes	—
217	C₂×C₄×C₅	#102	1	1	yes	characteristic
218	C₂×C₄×C₅	#102	1	2	yes	—
219	C₂×C₄×C₅	#102	1	2	yes	—
220	C₂×C₄×C₅	#102	1	2	yes	—
221	C₂×C₄×C₅	#102	1	1	yes	characteristic
222	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
223	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
224	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
225	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
226	C₂×C₄×C₅	C₂×D₈	1	2	yes	—
227	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
228	C₂×C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
229	C₂×C₄×C₅	C₂×SD₁₆	1	2	yes	—
230	C₂×C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
231	C₂×C₄×C₅	C₂×SD₁₆	1	2	yes	—
232	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
233	C₅×C₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
234	C₅×C₈	C₂×C₂²⋊C₄	1	2	yes	—
235	C₅×C₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
236	C₅×C₈	C₂×C₂²⋊C₄	1	2	yes	—
237	C₅×C₈	C₂³×C₄	1	1	yes	characteristic
238	C₅×C₈	C₂²×D₄	1	1	yes	characteristic
239	C₂×#41	—	2	2	no	—
240	C₂×#41	—	2	4	no	—
241	C₂×#41	—	2	2	no	—
242	C₂×#41	—	2	4	no	—
243	C₂×#41	—	4	1	no	—
244	C₂×#41	—	4	2	no	—
245	C₂×#41	—	4	1	no	—
246	C₂×#41	—	4	2	no	—
247	C₂²×Q₈	—	2	1	no	—
248	C₂²×D₄	—	2	1	no	—
249	C₂²×D₄	—	4	1	no	—
250	C₂³×C₄	—	4	1	no	—
251	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
252	#135	—	2	4	no	—
253	#135	—	2	4	no	—
254	#135	—	2	4	no	—
255	#135	—	2	2	no	—
256	#135	—	2	4	no	—
257	#135	—	2	4	no	—
258	#135	—	2	2	no	—
259	#135	C₂×C₄×C₅	1	4	yes	—
260	#135	C₂×C₄×C₅	1	8	yes	complemented
261	#135	C₂³×C₅	1	4	yes	—
262	C₂×Q₁₆	—	2	2	no	—
263	C₂×Q₁₆	—	2	1	no	—
264	C₂×Q₁₆	C₂×C₄×C₅	1	2	yes	—
265	C₂×Q₁₆	C₂×C₄×C₅	1	4	yes	complemented
266	C₂×SD₁₆	—	2	4	no	—
267	C₂×SD₁₆	—	2	2	no	—
268	C₂×SD₁₆	—	2	2	no	—
269	C₂×SD₁₆	—	2	4	no	—
270	C₂×D₈	—	2	2	no	—
271	C₂×D₈	—	2	1	no	—
272	C₂×D₈	C₂×C₄×C₅	1	2	yes	—
273	C₂×D₈	C₂×C₄×C₅	1	4	yes	complemented
274	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
275	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
276	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
277	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
278	C₂²×C₈	C₅×D₄	1	2	yes	—
279	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
280	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
281	C₂²×C₈	C₅×D₄	1	2	yes	—
282	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
283	C₂²×C₈	C₂³×C₅	1	2	yes	—
284	#117	—	2	4	no	—
285	#117	—	4	2	no	—
286	C₂×C₄⋊C₄	—	2	2	no	—
287	C₂×C₂²⋊C₄	—	4	1	no	—
288	C₂×C₄²	—	4	1	no	—
289	M₃₂	—	2	4	no	—
290	M₃₂	—	2	2	no	—
291	M₃₂	C₂³×C₅	1	4	yes	complemented
292	C₂×C₁₆	—	2	2	no	—
293	C₂×C₁₆	—	2	4	no	—
294	#107	—	2	4	no	—
295	#106	—	2	2	no	—
296	#106	C₂³×C₅	1	4	yes	complemented
297	C₂²×C₅	—	2	2	no	—
298	C₂²×C₅	—	2	2	no	—
299	C₂²×C₅	—	2	2	no	—
300	C₂²×C₅	—	4	2	no	—
301	C₂²×C₅	—	4	2	no	—
302	C₂²×C₅	—	4	4	no	—
303	C₂²×C₅	—	8	8	no	—
304	C₂²×C₅	—	8	4	no	—
305	C₂²×C₅	C₂×#102	1	2	yes	—
306	C₂²×C₅	C₂×#102	1	2	yes	—
307	C₂²×C₅	C₂×#102	1	1	yes	characteristic
308	C₂²×C₅	C₂×#102	1	1	yes	characteristic
309	C₂²×C₅	C₂²×D₈	1	1	yes	characteristic
310	C₄×C₅	—	4	4	no	—
311	C₄×C₅	—	8	4	no	—
312	C₄×C₅	C₂×#102	1	1	yes	characteristic
313	C₄×C₅	C₂×#102	1	2	yes	—
314	C₄×C₅	C₂×#102	1	2	yes	—
315	C₄×C₅	C₂×#102	1	1	yes	characteristic
316	C₄×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
317	C₄×C₅	C₂²×SD₁₆	1	1	yes	characteristic
318	C₂⁴	—	4	1	no	—
319	C₂⁴	C₅×D₈	1	1	yes	characteristic
320	#41	—	2	4	no	—
321	#41	—	2	8	no	—
322	#41	—	2	4	no	—
323	#41	—	4	4	no	—
324	#41	—	4	2	no	—
325	#41	—	4	2	no	—
326	#41	—	4	4	no	—
327	#41	—	4	4	no	—
328	#41	—	4	4	no	—
329	#41	—	4	4	no	—
330	C₂×Q₈	—	2	2	no	—
331	C₂×Q₈	—	2	4	no	—
332	C₂×Q₈	—	4	2	no	—
333	C₂×Q₈	—	4	1	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	4	no	—
336	C₂×D₄	—	4	2	no	—
337	C₂×D₄	—	4	4	no	—
338	C₂×D₄	—	4	2	no	—
339	C₂×D₄	—	4	4	no	—
340	C₂×D₄	—	4	2	no	—
341	C₂×D₄	—	4	1	no	—
342	C₂²×C₄	—	4	1	no	—
343	C₂²×C₄	—	4	4	no	—
344	C₂²×C₄	—	4	2	no	—
345	C₂²×C₄	—	4	4	no	—
346	C₂²×C₄	—	4	2	no	—
347	C₂²×C₄	—	4	2	no	—
348	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
349	C₂²×C₄	C₅×C₂²⋊C₄	1	2	yes	—
350	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
351	C₂²×C₄	C₅×D₈	1	1	yes	characteristic
352	C₂²×C₄	C₅×D₈	1	2	yes	—
353	C₂²×C₄	C₅×SD₁₆	1	1	yes	characteristic
354	C₂²×C₄	C₅×SD₁₆	1	1	yes	characteristic
355	C₂²×C₄	C₅×SD₁₆	1	2	yes	—
356	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
357	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
358	Q₁₆	—	2	2	no	—
359	Q₁₆	—	2	4	no	—
360	Q₁₆	C₂²×C₄×C₅	1	4	yes	—
361	SD₁₆	—	2	4	no	—
362	SD₁₆	—	2	8	no	—
363	SD₁₆	—	2	4	no	—
364	D₈	—	2	2	no	—
365	D₈	—	2	4	no	—
366	D₈	C₂²×C₄×C₅	1	4	yes	—
367	C₂×C₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
368	C₂×C₈	C₅×C₂²⋊C₄	1	2	yes	—
369	C₂×C₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
370	C₂×C₈	C₅×C₂²⋊C₄	1	2	yes	—
371	C₂×C₈	C₅×C₂²⋊C₄	1	2	yes	—
372	C₂×C₈	C₅×C₂²⋊C₄	1	2	yes	—
373	C₂×C₈	C₅×C₂²⋊C₄	1	2	yes	—
374	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
375	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
376	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
377	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
378	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
379	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
380	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
381	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
382	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
383	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
384	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
385	C₄⋊C₄	—	2	4	no	—
386	C₄⋊C₄	—	4	2	no	—
387	C₂²⋊C₄	—	4	4	no	—
388	C₄²	—	4	4	no	—
389	C₁₆	—	2	4	no	—
390	C₂×C₅	—	2	1	no	—
391	C₂×C₅	—	2	2	no	—
392	C₂×C₅	—	2	1	no	—
393	C₂×C₅	—	2	2	no	—
394	C₂×C₅	—	8	4	no	—
395	C₂×C₅	#2145	1	2	yes	direct product factor
396	C₂×C₅	C₂²×#102	1	1	yes	characteristic
397	C₂³	—	4	2	no	—
398	C₂³	—	4	4	no	—
399	C₂³	—	4	2	no	—
400	C₂³	—	8	4	no	—
401	C₂³	C₅×#102	1	1	yes	characteristic
402	C₂³	C₅×#102	1	1	yes	characteristic
403	C₂³	C₅×#102	1	2	yes	—
404	C₂³	C₂×C₅×D₈	1	1	yes	characteristic
405	C₂³	C₂×C₅×D₈	1	2	yes	—
406	Q₈	—	2	4	no	—
407	Q₈	—	4	2	no	—
408	Q₈	—	4	4	no	—
409	D₄	—	2	4	no	—
410	D₄	—	4	4	no	—
411	D₄	—	4	8	no	—
412	D₄	—	4	4	no	—
413	D₄	—	4	2	no	—
414	D₄	—	4	4	no	—
415	C₂×C₄	—	4	4	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	4	no	—
418	C₂×C₄	—	4	8	no	—
419	C₂×C₄	—	4	4	no	—
420	C₂×C₄	—	4	4	no	—
421	C₂×C₄	—	8	4	no	—
422	C₂×C₄	C₅×#102	1	2	yes	—
423	C₂×C₄	C₅×#102	1	1	yes	characteristic
424	C₂×C₄	C₅×#102	1	2	yes	—
425	C₂×C₄	C₅×#102	1	1	yes	characteristic
426	C₂×C₄	C₅×#102	1	2	yes	—
427	C₂×C₄	C₅×#102	1	2	yes	—
428	C₂×C₄	C₅×#102	1	2	yes	—
429	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
430	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
431	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
432	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
433	C₂×C₄	C₂×C₅×D₈	1	2	yes	—
434	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
435	C₂×C₄	C₂×C₅×SD₁₆	1	2	yes	—
436	C₂×C₄	C₂×C₅×SD₁₆	1	1	yes	characteristic
437	C₂×C₄	C₂×C₅×SD₁₆	1	1	yes	characteristic
438	C₂×C₄	C₂×C₅×SD₁₆	1	2	yes	—
439	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
440	C₈	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
441	C₈	C₂×C₅×C₂²⋊C₄	1	2	yes	—
442	C₈	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
443	C₈	C₂×C₅×C₂²⋊C₄	1	2	yes	—
444	C₈	C₂³×C₄×C₅	1	1	yes	characteristic
445	C₈	C₂²×C₅×D₄	1	1	yes	characteristic
446	C₅	C₂×#2145	1	1	yes	characteristic, direct product factor, Sylow
447	C₂²	—	2	2	no	—
448	C₂²	—	2	2	no	—
449	C₂²	—	2	2	no	—
450	C₂²	—	4	2	no	—
451	C₂²	—	4	2	no	—
452	C₂²	—	4	4	no	—
453	C₂²	—	8	8	no	—
454	C₂²	—	8	4	no	—
455	C₂²	C₂×C₅×#102	1	2	yes	—
456	C₂²	C₂×C₅×#102	1	1	yes	characteristic
457	C₂²	C₂×C₅×#102	1	2	yes	—
458	C₂²	C₂×C₅×#102	1	1	yes	characteristic
459	C₂²	C₂²×C₅×D₈	1	1	yes	characteristic
460	C₄	—	4	4	no	—
461	C₄	—	8	4	no	—
462	C₄	C₂×C₅×#102	1	2	yes	—
463	C₄	C₂×C₅×#102	1	1	yes	characteristic
464	C₄	C₂×C₅×#102	1	2	yes	—
465	C₄	C₂×C₅×#102	1	1	yes	characteristic
466	C₄	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
467	C₄	C₂²×C₅×SD₁₆	1	1	yes	characteristic
468	C₂	—	2	1	no	—
469	C₂	—	2	2	no	—
470	C₂	—	2	1	no	—
471	C₂	—	2	2	no	—
472	C₂	—	8	4	no	—
473	C₂	C₅×#2145	1	2	yes	direct product factor
474	C₂	C₂²×C₅×#102	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	#102
commutator	C₈	C₂³×C₄×C₅
Frattini, cosocle	C₂×C₈	C₂⁴×C₅
socle	C₂²×C₅	C₂×#102
prime radical	C₂²×C₅×#135	C₂
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂³×C₄×C₅ ◁ C₂³×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₅×M₃₂	C₂	semidirect
3. C₂×C₅×#427	C₂	semidirect
4. C₅×#2145	C₂	direct (N × H)
5. C₂×C₅×#360	C₂	semidirect
11. C₂×C₅×#135	C₄	semidirect
12. C₂×C₅×#135	C₄	semidirect
15. C₂²×C₅×Q₁₆	C₄	semidirect
17. C₂²×C₅×D₈	C₄	semidirect
22. C₂×C₅×M₃₂	C₂²	semidirect
23. C₂×C₅×M₃₂	C₂²	semidirect
26. C₅×#427	C₂²	semidirect
28. C₂×C₅×#106	C₂²	semidirect
29. C₅×#360	C₂²	semidirect
30. C₂×#2145	C₅	direct (N × H)
52. C₅×#135	C₂×C₄	semidirect
57. C₂×C₅×Q₁₆	C₂×C₄	semidirect
65. C₂×C₅×D₈	C₂×C₄	semidirect
83. C₅×M₃₂	C₂³	semidirect
88. C₅×#106	C₂³	semidirect
90. C₂²×M₃₂	C₂×C₅	semidirect
91. C₂×#427	C₂×C₅	semidirect
92. #2145	C₂×C₅	direct (N × H)
93. C₂×#360	C₂×C₅	semidirect
171. C₂×#135	C₄×C₅	semidirect
172. C₂×#135	C₄×C₅	semidirect
175. C₂²×Q₁₆	C₄×C₅	semidirect
177. C₂²×D₈	C₄×C₅	semidirect
182. C₂×M₃₂	C₂²×C₅	semidirect
183. C₂×M₃₂	C₂²×C₅	semidirect
186. #427	C₂²×C₅	semidirect
188. C₂×#106	C₂²×C₅	semidirect
189. #360	C₂²×C₅	semidirect
260. #135	C₂×C₄×C₅	semidirect
265. C₂×Q₁₆	C₂×C₄×C₅	semidirect
273. C₂×D₈	C₂×C₄×C₅	semidirect
291. M₃₂	C₂³×C₅	semidirect
296. #106	C₂³×C₅	semidirect
395. C₂×C₅	#2145	direct (N × H)
446. C₅	C₂×#2145	direct (N × H)
473. C₂	C₅×#2145	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₅×#135	2
C₂²×C₅×M₃₂	2
C₂×C₅×#427	2
C₅×#2145	2
C₂×C₅×#360	2
C₂×#2145	5

Subgroups — C2×C5×#2145 #11956107

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#2145 #11956107