Subgroups — C₂×C₅×#3123 #11983272

Order 1280.

2210 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#541	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#518	C₂	1	1	yes	maximal, characteristic
3	C₅×#3123	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₅×#485	C₂	1	2	yes	maximal, complemented
5	C₂×C₅×#478	C₂	1	2	yes	maximal, complemented
6	C₂×C₅×#461	C₂	1	2	yes	maximal, complemented
7	C₂×C₅×#450	C₂	1	2	yes	maximal
8	C₂×C₅×#440	C₂	1	2	yes	maximal, complemented
9	C₂×C₄×C₅×SD₁₆	C₂	1	2	yes	maximal, complemented
10	C₂×C₅×#433	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂³×C₅×D₄	C₂²	1	1	yes	characteristic
12	C₂²×C₅×SD₁₆	C₂²	1	2	yes	—
13	C₂²×C₅×SD₁₆	C₂²	1	2	yes	—
14	C₅×#541	—	2	4	no	—
15	C₅×#541	C₂²	1	8	yes	complemented
16	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
17	C₂×C₅×#126	—	2	2	no	—
18	C₂×C₅×#125	—	2	2	no	—
19	C₂×C₅×#125	C₂²	1	1	yes	characteristic, complemented
20	C₂×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
21	C₅×#518	—	2	4	no	—
22	C₅×#518	C₂²	1	8	yes	—
23	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	complemented
24	C₂×C₄×C₅×D₄	—	2	2	no	—
25	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
26	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
27	C₂×C₅×#117	C₂²	1	1	yes	characteristic
28	C₂×C₅×#117	C₂²	1	1	yes	characteristic
29	C₂²×C₅×C₂²⋊C₄	—	2	2	no	—
30	C₅×#485	C₂²	1	16	yes	complemented
31	C₅×#478	C₂²	1	16	yes	complemented
32	C₅×#461	C₂²	1	16	yes	complemented
33	C₅×#450	C₂²	1	16	yes	—
34	C₅×#440	C₂²	1	16	yes	complemented
35	C₄×C₅×SD₁₆	C₂²	1	16	yes	complemented
36	C₅×#433	C₂²	1	8	yes	complemented
37	C₂×C₅×#107	C₂²	1	2	yes	complemented
38	C₂×C₅×#106	C₂²	1	2	yes	complemented
39	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	complemented
40	C₂×C₅×#103	C₂²	1	2	yes	complemented
41	C₂×C₅×#103	C₂²	1	2	yes	complemented
42	C₂×C₅×#102	C₂²	1	2	yes	—
43	C₂×C₅×#102	C₂²	1	2	yes	—
44	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
45	C₂×C₅×#97	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
47	C₂×#3123	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
48	C₂⁵×C₅	—	2	1	no	—
49	C₂²×C₅×Q₈	C₂³	1	2	yes	—
50	C₂²×C₅×D₄	—	2	8	no	—
51	C₂²×C₅×D₄	—	2	1	no	—
52	C₂²×C₅×D₄	—	2	2	no	—
53	C₂²×C₅×D₄	C₂³	1	4	yes	—
54	C₂²×C₅×D₄	C₂³	1	2	yes	—
55	C₂³×C₄×C₅	—	2	2	no	—
56	C₂³×C₄×C₅	—	2	2	no	—
57	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
58	C₂×C₅×SD₁₆	—	2	8	no	—
59	C₂×C₅×SD₁₆	—	2	8	no	—
60	C₂×C₅×SD₁₆	C₂³	1	8	yes	—
61	C₂×C₅×SD₁₆	C₂³	1	8	yes	—
62	C₂²×C₅×C₈	C₂³	1	2	yes	—
63	C₂²×C₅×C₈	C₂³	1	2	yes	—
64	C₅×C₄⋊Q₈	—	2	2	no	—
65	C₅×C₄⋊Q₈	C₂³	1	4	yes	complemented
66	C₅×#126	—	2	16	no	—
67	C₅×#125	—	2	16	no	—
68	C₅×#125	—	2	2	no	—
69	C₅×#125	C₂³	1	4	yes	complemented
70	C₅×C₂²⋊Q₈	—	2	4	no	—
71	C₅×C₂²⋊Q₈	C₂³	1	8	yes	—
72	C₄×C₅×Q₈	—	2	4	no	—
73	C₄×C₅×Q₈	C₂³	1	8	yes	complemented
74	C₄×C₅×D₄	—	2	16	no	—
75	C₄×C₅×D₄	—	2	4	no	—
76	C₄×C₅×D₄	—	2	4	no	—
77	C₄×C₅×D₄	C₂³	1	8	yes	—
78	C₄×C₅×D₄	C₂³	1	8	yes	—
79	C₅×#117	—	2	2	no	—
80	C₅×#117	D₄	1	4	yes	—
81	C₅×#117	C₂³	1	4	yes	—
82	C₅×#117	C₂³	1	4	yes	—
83	C₂×C₅×C₄⋊C₄	—	2	2	no	—
84	C₂×C₅×C₄⋊C₄	—	2	2	no	—
85	C₂×C₅×C₄⋊C₄	—	2	2	no	—
86	C₂×C₅×C₄⋊C₄	—	2	2	no	—
87	C₂×C₅×C₄⋊C₄	D₄	1	2	yes	—
88	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
89	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
90	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
91	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
92	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
93	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
94	C₂×C₅×C₂²⋊C₄	—	2	16	no	—
95	C₂×C₅×C₂²⋊C₄	D₄	1	2	yes	—
96	C₂×C₄²×C₅	—	2	1	no	—
97	C₂×C₄²×C₅	—	2	2	no	—
98	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
100	C₅×#107	C₂³	1	8	yes	complemented
101	C₅×#106	C₂³	1	8	yes	complemented
102	C₅×C₄⋊C₈	C₂³	1	8	yes	complemented
103	C₅×#103	C₂³	1	8	yes	complemented
104	C₅×#103	C₂³	1	8	yes	complemented
105	C₅×#102	C₂³	1	8	yes	—
106	C₅×#102	C₂³	1	8	yes	—
107	C₅×C₂²⋊C₈	C₂³	1	8	yes	—
108	C₅×#97	C₂³	1	4	yes	complemented
109	C₄×C₅×C₈	C₂³	1	4	yes	complemented
110	C₂×#541	C₂×C₅	1	1	yes	characteristic, complemented
111	C₂×#518	C₂×C₅	1	1	yes	characteristic
112	#3123	C₂×C₅	1	16	yes	direct product factor
113	C₂×#485	C₂×C₅	1	2	yes	complemented
114	C₂×#478	C₂×C₅	1	2	yes	complemented
115	C₂×#461	C₂×C₅	1	2	yes	complemented
116	C₂×#450	C₂×C₅	1	2	yes	—
117	C₂×#440	C₂×C₅	1	2	yes	complemented
118	C₂×C₄×SD₁₆	C₂×C₅	1	2	yes	complemented
119	C₂×#433	C₂×C₅	1	1	yes	characteristic, complemented
120	C₂⁴×C₅	—	2	8	no	—
121	C₂⁴×C₅	—	2	2	no	—
122	C₂⁴×C₅	—	2	4	no	—
123	C₂⁴×C₅	—	8	4	no	—
124	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
125	C₂×C₅×Q₈	—	2	2	no	—
126	C₂×C₅×Q₈	—	2	4	no	—
127	C₂×C₅×Q₈	—	2	4	no	—
128	C₂×C₅×Q₈	C₂⁴	1	4	yes	—
129	C₂×C₅×D₄	—	2	8	no	—
130	C₂×C₅×D₄	—	2	16	no	—
131	C₂×C₅×D₄	—	2	16	no	—
132	C₂×C₅×D₄	—	2	4	no	—
133	C₂×C₅×D₄	—	2	2	no	—
134	C₂×C₅×D₄	—	2	4	no	—
135	C₂×C₅×D₄	#41	1	8	yes	—
136	C₂×C₅×D₄	C₂⁴	1	4	yes	—
137	C₂²×C₄×C₅	—	2	4	no	—
138	C₂²×C₄×C₅	—	2	2	no	—
139	C₂²×C₄×C₅	—	2	2	no	—
140	C₂²×C₄×C₅	—	2	2	no	—
141	C₂²×C₄×C₅	—	2	8	no	—
142	C₂²×C₄×C₅	—	2	8	no	—
143	C₂²×C₄×C₅	—	8	4	no	—
144	C₂²×C₄×C₅	—	8	4	no	—
145	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
146	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
147	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
149	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
150	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
151	C₅×SD₁₆	—	2	16	no	—
152	C₅×SD₁₆	—	2	16	no	—
153	C₂×C₅×C₈	—	2	4	no	—
154	C₂×C₅×C₈	—	2	4	no	—
155	C₂×C₅×C₈	C₂⁴	1	4	yes	—
156	C₂×C₅×C₈	C₂⁴	1	4	yes	—
157	C₅×C₄⋊C₄	—	2	8	no	—
158	C₅×C₄⋊C₄	—	2	8	no	—
159	C₅×C₄⋊C₄	—	2	8	no	—
160	C₅×C₄⋊C₄	—	2	8	no	—
161	C₅×C₄⋊C₄	—	2	2	no	—
162	C₅×C₄⋊C₄	—	2	2	no	—
163	C₅×C₄⋊C₄	C₂×D₄	1	8	yes	—
164	C₅×C₄⋊C₄	C₂⁴	1	4	yes	—
165	C₅×C₄⋊C₄	C₂⁴	1	4	yes	—
166	C₅×C₂²⋊C₄	—	2	4	no	—
167	C₅×C₂²⋊C₄	—	2	8	no	—
168	C₅×C₂²⋊C₄	—	2	8	no	—
169	C₅×C₂²⋊C₄	—	2	8	no	—
170	C₅×C₂²⋊C₄	C₂×D₄	1	8	yes	—
171	C₄²×C₅	—	2	4	no	—
172	C₄²×C₅	—	2	8	no	—
173	C₄²×C₅	C₂×D₄	1	2	yes	—
174	C₄²×C₅	C₂×D₄	1	2	yes	—
175	C₄²×C₅	C₂⁴	1	2	yes	—
176	C₄²×C₅	C₂⁴	1	2	yes	—
177	C₂³×D₄	C₂²×C₅	1	1	yes	characteristic
178	C₂²×SD₁₆	C₂²×C₅	1	2	yes	—
179	C₂²×SD₁₆	C₂²×C₅	1	2	yes	—
180	#541	—	2	4	no	—
181	#541	C₂²×C₅	1	8	yes	complemented
182	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
183	C₂×#126	—	2	2	no	—
184	C₂×#125	—	2	2	no	—
185	C₂×#125	C₂²×C₅	1	1	yes	characteristic, complemented
186	C₂×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
187	#518	—	2	4	no	—
188	#518	C₂²×C₅	1	8	yes	—
189	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	complemented
190	C₂×C₄×D₄	—	2	2	no	—
191	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
192	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
193	C₂×#117	C₂²×C₅	1	1	yes	characteristic
194	C₂×#117	C₂²×C₅	1	1	yes	characteristic
195	C₂²×C₂²⋊C₄	—	2	2	no	—
196	#485	C₂²×C₅	1	16	yes	complemented
197	#478	C₂²×C₅	1	16	yes	complemented
198	#461	C₂²×C₅	1	16	yes	complemented
199	#450	C₂²×C₅	1	16	yes	—
200	#440	C₂²×C₅	1	16	yes	complemented
201	C₄×SD₁₆	C₂²×C₅	1	16	yes	complemented
202	#433	C₂²×C₅	1	8	yes	complemented
203	C₂×#107	C₂²×C₅	1	2	yes	complemented
204	C₂×#106	C₂²×C₅	1	2	yes	complemented
205	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	complemented
206	C₂×#103	C₂²×C₅	1	2	yes	complemented
207	C₂×#103	C₂²×C₅	1	2	yes	complemented
208	C₂×#102	C₂²×C₅	1	2	yes	—
209	C₂×#102	C₂²×C₅	1	2	yes	—
210	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
211	C₂×#97	C₂²×C₅	1	1	yes	characteristic, complemented
212	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
213	C₂³×C₅	—	2	16	no	—
214	C₂³×C₅	—	2	2	no	—
215	C₂³×C₅	—	2	8	no	—
216	C₂³×C₅	—	2	4	no	—
217	C₂³×C₅	—	2	4	no	—
218	C₂³×C₅	—	4	4	no	—
219	C₂³×C₅	—	4	4	no	—
220	C₂³×C₅	—	8	8	no	—
221	C₂³×C₅	—	8	16	no	—
222	C₂³×C₅	C₂²×D₄	1	2	yes	—
223	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
224	C₅×Q₈	—	2	4	no	—
225	C₅×Q₈	—	2	4	no	—
226	C₅×Q₈	—	4	4	no	—
227	C₅×D₄	—	2	16	no	—
228	C₅×D₄	—	2	8	no	—
229	C₅×D₄	—	2	4	no	—
230	C₅×D₄	C₂×#41	1	8	yes	—
231	C₂×C₄×C₅	—	2	2	no	—
232	C₂×C₄×C₅	—	2	4	no	—
233	C₂×C₄×C₅	—	2	4	no	—
234	C₂×C₄×C₅	—	2	4	no	—
235	C₂×C₄×C₅	—	2	4	no	—
236	C₂×C₄×C₅	—	2	4	no	—
237	C₂×C₄×C₅	—	2	4	no	—
238	C₂×C₄×C₅	—	2	4	no	—
239	C₂×C₄×C₅	—	4	4	no	—
240	C₂×C₄×C₅	—	4	4	no	—
241	C₂×C₄×C₅	—	4	4	no	—
242	C₂×C₄×C₅	—	8	8	no	—
243	C₂×C₄×C₅	—	8	8	no	—
244	C₂×C₄×C₅	C₂²×D₄	1	4	yes	—
245	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
246	C₂×C₄×C₅	C₂²×D₄	1	4	yes	—
247	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
248	C₂×C₄×C₅	C₂×#41	1	4	yes	—
249	C₂×C₄×C₅	C₂⁵	1	1	yes	characteristic
250	C₅×C₈	—	2	4	no	—
251	C₅×C₈	—	2	4	no	—
252	C₂⁵	—	2	1	no	—
253	C₂²×Q₈	C₂³×C₅	1	2	yes	—
254	C₂²×D₄	—	2	8	no	—
255	C₂²×D₄	—	2	1	no	—
256	C₂²×D₄	—	2	2	no	—
257	C₂²×D₄	C₂³×C₅	1	4	yes	—
258	C₂²×D₄	C₂³×C₅	1	2	yes	—
259	C₂³×C₄	—	2	2	no	—
260	C₂³×C₄	—	2	2	no	—
261	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
262	C₂×SD₁₆	—	2	8	no	—
263	C₂×SD₁₆	—	2	8	no	—
264	C₂×SD₁₆	C₂³×C₅	1	8	yes	—
265	C₂×SD₁₆	C₂³×C₅	1	8	yes	—
266	C₂²×C₈	C₂³×C₅	1	2	yes	—
267	C₂²×C₈	C₂³×C₅	1	2	yes	—
268	C₄⋊Q₈	—	2	2	no	—
269	C₄⋊Q₈	C₂³×C₅	1	4	yes	complemented
270	#126	—	2	16	no	—
271	#125	—	2	16	no	—
272	#125	—	2	2	no	—
273	#125	C₂³×C₅	1	4	yes	complemented
274	C₂²⋊Q₈	—	2	4	no	—
275	C₂²⋊Q₈	C₂³×C₅	1	8	yes	—
276	C₄×Q₈	—	2	4	no	—
277	C₄×Q₈	C₂³×C₅	1	8	yes	complemented
278	C₄×D₄	—	2	16	no	—
279	C₄×D₄	—	2	4	no	—
280	C₄×D₄	—	2	4	no	—
281	C₄×D₄	C₂³×C₅	1	8	yes	—
282	C₄×D₄	C₂³×C₅	1	8	yes	—
283	#117	—	2	2	no	—
284	#117	C₅×D₄	1	4	yes	—
285	#117	C₂³×C₅	1	4	yes	—
286	#117	C₂³×C₅	1	4	yes	—
287	C₂×C₄⋊C₄	—	2	2	no	—
288	C₂×C₄⋊C₄	—	2	2	no	—
289	C₂×C₄⋊C₄	—	2	2	no	—
290	C₂×C₄⋊C₄	—	2	2	no	—
291	C₂×C₄⋊C₄	C₅×D₄	1	2	yes	—
292	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
293	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
294	C₂×C₂²⋊C₄	—	2	1	no	—
295	C₂×C₂²⋊C₄	—	2	2	no	—
296	C₂×C₂²⋊C₄	—	2	2	no	—
297	C₂×C₂²⋊C₄	—	2	2	no	—
298	C₂×C₂²⋊C₄	—	2	16	no	—
299	C₂×C₂²⋊C₄	C₅×D₄	1	2	yes	—
300	C₂×C₄²	—	2	1	no	—
301	C₂×C₄²	—	2	2	no	—
302	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
303	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
304	#107	C₂³×C₅	1	8	yes	complemented
305	#106	C₂³×C₅	1	8	yes	complemented
306	C₄⋊C₈	C₂³×C₅	1	8	yes	complemented
307	#103	C₂³×C₅	1	8	yes	complemented
308	#103	C₂³×C₅	1	8	yes	complemented
309	#102	C₂³×C₅	1	8	yes	—
310	#102	C₂³×C₅	1	8	yes	—
311	C₂²⋊C₈	C₂³×C₅	1	8	yes	—
312	#97	C₂³×C₅	1	4	yes	complemented
313	C₄×C₈	C₂³×C₅	1	4	yes	complemented
314	C₂²×C₅	—	2	2	no	—
315	C₂²×C₅	—	2	8	no	—
316	C₂²×C₅	—	2	4	no	—
317	C₂²×C₅	—	4	4	no	—
318	C₂²×C₅	—	4	16	no	—
319	C₂²×C₅	—	4	4	no	—
320	C₂²×C₅	—	4	4	no	—
321	C₂²×C₅	—	8	16	no	—
322	C₂²×C₅	#525	1	2	yes	—
323	C₂²×C₅	#577	1	4	yes	—
324	C₂²×C₅	C₂³×D₄	1	1	yes	characteristic
325	C₄×C₅	—	2	2	no	—
326	C₄×C₅	—	2	4	no	—
327	C₄×C₅	—	2	4	no	—
328	C₄×C₅	—	4	4	no	—
329	C₄×C₅	—	4	4	no	—
330	C₄×C₅	—	4	4	no	—
331	C₄×C₅	#525	1	2	yes	—
332	C₄×C₅	C₂²×#41	1	2	yes	—
333	C₂⁴	—	2	8	no	—
334	C₂⁴	—	2	2	no	—
335	C₂⁴	—	2	4	no	—
336	C₂⁴	—	8	4	no	—
337	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
338	C₂×Q₈	—	2	2	no	—
339	C₂×Q₈	—	2	4	no	—
340	C₂×Q₈	—	2	4	no	—
341	C₂×Q₈	C₂⁴×C₅	1	4	yes	—
342	C₂×D₄	—	2	8	no	—
343	C₂×D₄	—	2	16	no	—
344	C₂×D₄	—	2	16	no	—
345	C₂×D₄	—	2	4	no	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	—	2	4	no	—
348	C₂×D₄	C₅×#41	1	8	yes	—
349	C₂×D₄	C₂⁴×C₅	1	4	yes	—
350	C₂²×C₄	—	2	4	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	8	no	—
355	C₂²×C₄	—	2	8	no	—
356	C₂²×C₄	—	8	4	no	—
357	C₂²×C₄	—	8	4	no	—
358	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
359	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
360	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
361	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
362	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
363	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
364	SD₁₆	—	2	16	no	—
365	SD₁₆	—	2	16	no	—
366	C₂×C₈	—	2	4	no	—
367	C₂×C₈	—	2	4	no	—
368	C₂×C₈	C₂⁴×C₅	1	4	yes	—
369	C₂×C₈	C₂⁴×C₅	1	4	yes	—
370	C₄⋊C₄	—	2	8	no	—
371	C₄⋊C₄	—	2	8	no	—
372	C₄⋊C₄	—	2	8	no	—
373	C₄⋊C₄	—	2	8	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	C₂×C₅×D₄	1	8	yes	—
377	C₄⋊C₄	C₂⁴×C₅	1	4	yes	—
378	C₄⋊C₄	C₂⁴×C₅	1	4	yes	—
379	C₂²⋊C₄	—	2	4	no	—
380	C₂²⋊C₄	—	2	8	no	—
381	C₂²⋊C₄	—	2	8	no	—
382	C₂²⋊C₄	—	2	8	no	—
383	C₂²⋊C₄	C₂×C₅×D₄	1	8	yes	—
384	C₄²	—	2	4	no	—
385	C₄²	—	2	8	no	—
386	C₄²	C₂×C₅×D₄	1	2	yes	—
387	C₄²	C₂×C₅×D₄	1	2	yes	—
388	C₄²	C₂⁴×C₅	1	2	yes	—
389	C₄²	C₂⁴×C₅	1	2	yes	—
390	C₂×C₅	—	4	2	no	—
391	C₂×C₅	—	4	8	no	—
392	C₂×C₅	#3123	1	4	yes	direct product factor
393	C₂×C₅	C₂×#525	1	1	yes	characteristic
394	C₂×C₅	C₂×#577	1	2	yes	—
395	C₂³	—	2	16	no	—
396	C₂³	—	2	2	no	—
397	C₂³	—	2	8	no	—
398	C₂³	—	2	4	no	—
399	C₂³	—	2	4	no	—
400	C₂³	—	4	4	no	—
401	C₂³	—	4	4	no	—
402	C₂³	—	8	8	no	—
403	C₂³	—	8	16	no	—
404	C₂³	C₂²×C₅×D₄	1	2	yes	—
405	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
406	Q₈	—	2	4	no	—
407	Q₈	—	2	4	no	—
408	Q₈	—	4	4	no	—
409	D₄	—	2	16	no	—
410	D₄	—	2	8	no	—
411	D₄	—	2	4	no	—
412	D₄	C₂×C₅×#41	1	8	yes	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	2	4	no	—
421	C₂×C₄	—	4	4	no	—
422	C₂×C₄	—	4	4	no	—
423	C₂×C₄	—	4	4	no	—
424	C₂×C₄	—	8	8	no	—
425	C₂×C₄	—	8	8	no	—
426	C₂×C₄	C₂²×C₅×D₄	1	4	yes	—
427	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
428	C₂×C₄	C₂²×C₅×D₄	1	4	yes	—
429	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
430	C₂×C₄	C₂×C₅×#41	1	4	yes	—
431	C₂×C₄	C₂⁵×C₅	1	1	yes	characteristic
432	C₈	—	2	4	no	—
433	C₈	—	2	4	no	—
434	C₅	C₂×#3123	1	1	yes	characteristic, direct product factor, Sylow
435	C₂²	—	2	2	no	—
436	C₂²	—	2	8	no	—
437	C₂²	—	2	4	no	—
438	C₂²	—	4	4	no	—
439	C₂²	—	4	16	no	—
440	C₂²	—	4	4	no	—
441	C₂²	—	4	4	no	—
442	C₂²	—	8	16	no	—
443	C₂²	C₅×#525	1	2	yes	—
444	C₂²	C₅×#577	1	4	yes	—
445	C₂²	C₂³×C₅×D₄	1	1	yes	characteristic
446	C₄	—	2	2	no	—
447	C₄	—	2	4	no	—
448	C₄	—	2	4	no	—
449	C₄	—	4	4	no	—
450	C₄	—	4	4	no	—
451	C₄	—	4	4	no	—
452	C₄	C₅×#525	1	2	yes	—
453	C₄	C₂²×C₅×#41	1	2	yes	—
454	C₂	—	4	2	no	—
455	C₂	—	4	8	no	—
456	C₂	C₅×#3123	1	4	yes	direct product factor
457	C₂	C₂×C₅×#525	1	1	yes	characteristic
458	C₂	C₂×C₅×#577	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅
prime radical	C₂³×C₅×D₄	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₅×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#541	C₂	semidirect
3. C₅×#3123	C₂	direct (N × H)
4. C₂×C₅×#485	C₂	semidirect
5. C₂×C₅×#478	C₂	semidirect
6. C₂×C₅×#461	C₂	semidirect
8. C₂×C₅×#440	C₂	semidirect
9. C₂×C₄×C₅×SD₁₆	C₂	semidirect
10. C₂×C₅×#433	C₂	semidirect
15. C₅×#541	C₂²	semidirect
16. C₂×C₅×C₄⋊Q₈	C₂²	semidirect
19. C₂×C₅×#125	C₂²	semidirect
23. C₂×C₄×C₅×Q₈	C₂²	semidirect
30. C₅×#485	C₂²	semidirect
31. C₅×#478	C₂²	semidirect
32. C₅×#461	C₂²	semidirect
34. C₅×#440	C₂²	semidirect
35. C₄×C₅×SD₁₆	C₂²	semidirect
36. C₅×#433	C₂²	semidirect
37. C₂×C₅×#107	C₂²	semidirect
38. C₂×C₅×#106	C₂²	semidirect
39. C₂×C₅×C₄⋊C₈	C₂²	semidirect
40. C₂×C₅×#103	C₂²	semidirect
41. C₂×C₅×#103	C₂²	semidirect
45. C₂×C₅×#97	C₂²	semidirect
46. C₂×C₄×C₅×C₈	C₂²	semidirect
47. C₂×#3123	C₅	direct (N × H)
65. C₅×C₄⋊Q₈	C₂³	semidirect
69. C₅×#125	C₂³	semidirect
73. C₄×C₅×Q₈	C₂³	semidirect
100. C₅×#107	C₂³	semidirect
101. C₅×#106	C₂³	semidirect
102. C₅×C₄⋊C₈	C₂³	semidirect
103. C₅×#103	C₂³	semidirect
104. C₅×#103	C₂³	semidirect
108. C₅×#97	C₂³	semidirect
109. C₄×C₅×C₈	C₂³	semidirect
110. C₂×#541	C₂×C₅	semidirect
112. #3123	C₂×C₅	direct (N × H)
113. C₂×#485	C₂×C₅	semidirect
114. C₂×#478	C₂×C₅	semidirect
115. C₂×#461	C₂×C₅	semidirect
117. C₂×#440	C₂×C₅	semidirect
118. C₂×C₄×SD₁₆	C₂×C₅	semidirect
119. C₂×#433	C₂×C₅	semidirect
181. #541	C₂²×C₅	semidirect
182. C₂×C₄⋊Q₈	C₂²×C₅	semidirect
185. C₂×#125	C₂²×C₅	semidirect
189. C₂×C₄×Q₈	C₂²×C₅	semidirect
196. #485	C₂²×C₅	semidirect
197. #478	C₂²×C₅	semidirect
198. #461	C₂²×C₅	semidirect
200. #440	C₂²×C₅	semidirect
201. C₄×SD₁₆	C₂²×C₅	semidirect
202. #433	C₂²×C₅	semidirect
203. C₂×#107	C₂²×C₅	semidirect
204. C₂×#106	C₂²×C₅	semidirect
205. C₂×C₄⋊C₈	C₂²×C₅	semidirect
206. C₂×#103	C₂²×C₅	semidirect
207. C₂×#103	C₂²×C₅	semidirect
211. C₂×#97	C₂²×C₅	semidirect
212. C₂×C₄×C₈	C₂²×C₅	semidirect
269. C₄⋊Q₈	C₂³×C₅	semidirect
273. #125	C₂³×C₅	semidirect
277. C₄×Q₈	C₂³×C₅	semidirect
304. #107	C₂³×C₅	semidirect
305. #106	C₂³×C₅	semidirect
306. C₄⋊C₈	C₂³×C₅	semidirect
307. #103	C₂³×C₅	semidirect
308. #103	C₂³×C₅	semidirect
312. #97	C₂³×C₅	semidirect
313. C₄×C₈	C₂³×C₅	semidirect
392. C₂×C₅	#3123	direct (N × H)
434. C₅	C₂×#3123	direct (N × H)
456. C₂	C₅×#3123	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×#541	2
C₂×C₅×#518	2
C₅×#3123	2
C₂×C₅×#485	2
C₂×C₅×#478	2
C₂×C₅×#461	2
C₂×C₅×#450	2
C₂×C₅×#440	2
C₂×C₄×C₅×SD₁₆	2
C₂×C₅×#433	2
C₂×#3123	5

Subgroups — C2×C5×#3123 #11983272

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#3123 #11983272