Subgroups — C₂×C₅×#5166 #14426124

Order 1920.

1000 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×SD₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×Q₈×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₅×#216	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#936	C₂	1	1	yes	maximal, characteristic
5	C₂×C₅×#832	C₂	1	1	yes	maximal, characteristic
6	C₅×#5166	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₅×#816	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅×Dic₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×#464	—	3	1	no	maximal, Hall
10	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
12	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₅×SD₁₆	—	2	4	no	—
14	C₂×C₃×C₅×SD₁₆	C₂²	1	4	yes	—
15	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
16	C₂×C₅×#217	—	2	1	no	—
17	C₂×C₅×#217	—	2	1	no	—
18	C₅×Q₈×Dic₃	—	2	2	no	—
19	C₅×Q₈×Dic₃	C₂²	1	4	yes	complemented
20	C₂×C₅×#216	—	2	4	no	—
21	C₂×C₅×#216	C₂²	1	4	yes	complemented
22	C₅×#936	—	2	2	no	—
23	C₅×#936	C₂²	1	4	yes	—
24	C₂×C₅×C₄⋊Dic₃	—	2	1	no	—
25	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₅×Dic₃	—	2	1	no	—
27	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
28	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
29	C₅×#832	C₂²	1	4	yes	—
30	C₅×#816	C₂²	1	4	yes	complemented
31	C₅×Dic₃⋊C₈	C₂²	1	4	yes	complemented
32	C₂×#5166	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
33	C₂²×C₅×Q₁₆	—	3	1	no	—
34	C₂²×C₅×SD₁₆	D₃	1	1	yes	characteristic
35	C₂×C₅×#124	—	3	1	no	—
36	C₂×C₄×C₅×Q₈	—	3	1	no	—
37	C₅×#464	—	3	8	no	—
38	C₂×C₅×C₄⋊C₈	—	3	1	no	—
39	C₂×C₅×#103	—	3	1	no	—
40	C₂×C₅×#102	—	3	1	no	—
41	C₂⁴×C₃×C₅	—	2	1	no	—
42	C₂×C₃×C₅×Q₈	—	2	1	no	—
43	C₂×C₃×C₅×Q₈	—	2	2	no	—
44	C₂×C₃×C₅×Q₈	D₄	1	4	yes	—
45	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
46	C₂×C₃×C₅×D₄	—	2	2	no	—
47	C₂×C₃×C₅×D₄	—	2	1	no	—
48	C₂×C₃×C₅×D₄	—	2	2	no	—
49	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
50	C₂²×C₃×C₄×C₅	—	2	1	no	—
51	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
52	C₂²×C₅×Dic₃	—	2	1	no	—
53	C₂²×C₅×Dic₃	—	2	1	no	—
54	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
55	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
56	C₂×C₅×Dic₆	—	2	2	no	—
57	C₂×C₅×Dic₆	—	2	2	no	—
58	C₂×C₅×Dic₆	—	2	1	no	—
59	C₂×C₅×Dic₆	C₂³	1	2	yes	—
60	C₃×C₅×SD₁₆	—	2	8	no	—
61	C₂×C₃×C₅×C₈	—	2	2	no	—
62	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
63	C₅×#217	—	2	4	no	—
64	C₅×#217	—	2	4	no	—
65	C₅×#216	—	2	8	no	—
66	C₅×C₄⋊Dic₃	—	2	1	no	—
67	C₅×C₄⋊Dic₃	—	2	4	no	—
68	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
69	C₄×C₅×Dic₃	—	2	4	no	—
70	C₄×C₅×Dic₃	D₄	1	2	yes	—
71	C₄×C₅×Dic₃	C₂³	1	2	yes	—
72	C₂×C₅×C₃⋊C₈	—	2	2	no	—
73	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
74	C₂²×C₃×SD₁₆	C₂×C₅	1	1	yes	characteristic
75	C₂×Q₈×Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
76	C₂²×#216	C₂×C₅	1	1	yes	characteristic, complemented
77	C₂×#936	C₂×C₅	1	1	yes	characteristic
78	C₂×#832	C₂×C₅	1	1	yes	characteristic
79	#5166	C₂×C₅	1	8	yes	direct product factor
80	C₂×#816	C₂×C₅	1	1	yes	characteristic, complemented
81	C₂×Dic₃⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
82	C₂²×C₅×Q₈	—	3	1	no	—
83	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
84	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
85	C₂×C₅×Q₁₆	—	3	4	no	—
86	C₂×C₅×Q₁₆	—	6	4	no	—
87	C₂×C₅×SD₁₆	—	2	4	no	—
88	C₂×C₅×SD₁₆	C₂×D₃	1	4	yes	—
89	C₂²×C₅×C₈	—	3	1	no	—
90	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
91	C₅×#124	—	3	4	no	—
92	C₅×#124	—	6	2	no	—
93	C₄×C₅×Q₈	—	3	4	no	—
94	C₄×C₅×Q₈	—	6	2	no	—
95	C₂×C₅×C₄⋊C₄	—	3	1	no	—
96	C₂×C₅×C₄⋊C₄	—	6	1	no	—
97	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
98	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
99	C₂×C₄²×C₅	—	3	1	no	—
100	C₂×C₄²×C₅	—	6	1	no	—
101	C₅×C₄⋊C₈	—	3	4	no	—
102	C₅×#103	—	3	4	no	—
103	C₅×#102	—	3	4	no	—
104	C₂×#464	—	3	1	no	Sylow
105	C₂³×C₃×C₅	—	2	2	no	—
106	C₂³×C₃×C₅	—	4	2	no	—
107	C₂³×C₃×C₅	—	4	2	no	—
108	C₂³×C₃×C₅	—	4	2	no	—
109	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
110	C₃×C₅×Q₈	—	2	4	no	—
111	C₃×C₅×Q₈	—	2	2	no	—
112	C₃×C₅×Q₈	C₂×D₄	1	4	yes	—
113	C₃×C₅×D₄	—	2	2	no	—
114	C₃×C₅×D₄	—	2	2	no	—
115	C₃×C₅×D₄	—	4	2	no	—
116	C₂×C₃×C₄×C₅	—	2	4	no	—
117	C₂×C₃×C₄×C₅	—	2	2	no	—
118	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
119	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
120	C₂×C₃×C₄×C₅	#41	1	2	yes	—
121	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
122	C₂×C₅×Dic₃	—	2	2	no	—
123	C₂×C₅×Dic₃	—	2	2	no	—
124	C₂×C₅×Dic₃	—	2	2	no	—
125	C₂×C₅×Dic₃	—	2	2	no	—
126	C₂×C₅×Dic₃	—	4	2	no	—
127	C₂×C₅×Dic₃	—	4	2	no	—
128	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
129	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
130	C₅×Dic₆	—	2	2	no	—
131	C₅×Dic₆	—	2	2	no	—
132	C₅×Dic₆	—	4	2	no	—
133	C₃×C₅×C₈	—	2	2	no	—
134	C₅×C₃⋊C₈	—	2	2	no	—
135	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
136	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
137	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
138	C₂×C₃×SD₁₆	—	2	4	no	—
139	C₂×C₃×SD₁₆	C₂²×C₅	1	4	yes	—
140	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
141	C₂×#217	—	2	1	no	—
142	C₂×#217	—	2	1	no	—
143	Q₈×Dic₃	—	2	2	no	—
144	Q₈×Dic₃	C₂²×C₅	1	4	yes	complemented
145	C₂×#216	—	2	4	no	—
146	C₂×#216	C₂²×C₅	1	4	yes	complemented
147	#936	—	2	2	no	—
148	#936	C₂²×C₅	1	4	yes	—
149	C₂×C₄⋊Dic₃	—	2	1	no	—
150	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
151	C₂×C₄×Dic₃	—	2	1	no	—
152	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
153	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
154	#832	C₂²×C₅	1	4	yes	—
155	#816	C₂²×C₅	1	4	yes	complemented
156	Dic₃⋊C₈	C₂²×C₅	1	4	yes	complemented
157	C₂⁴×C₅	—	2	1	no	—
158	C₂×C₅×Q₈	—	2	1	no	—
159	C₂×C₅×Q₈	—	2	2	no	—
160	C₂×C₅×Q₈	—	3	2	no	—
161	C₂×C₅×Q₈	—	6	1	no	—
162	C₂×C₅×Q₈	—	6	2	no	—
163	C₂×C₅×Q₈	—	6	2	no	—
164	C₂×C₅×Q₈	#67	1	4	yes	—
165	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
166	C₂×C₅×D₄	—	2	1	no	—
167	C₂×C₅×D₄	—	2	2	no	—
168	C₂×C₅×D₄	—	2	2	no	—
169	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
170	C₂²×C₄×C₅	—	2	1	no	—
171	C₂²×C₄×C₅	—	3	1	no	—
172	C₂²×C₄×C₅	—	3	1	no	—
173	C₂²×C₄×C₅	—	6	1	no	—
174	C₂²×C₄×C₅	—	6	1	no	—
175	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
176	C₅×Q₁₆	—	6	8	no	—
177	C₅×SD₁₆	—	2	8	no	—
178	C₂×C₅×C₈	—	2	2	no	—
179	C₂×C₅×C₈	—	3	2	no	—
180	C₂×C₅×C₈	—	6	2	no	—
181	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
182	C₅×C₄⋊C₄	—	3	2	no	—
183	C₅×C₄⋊C₄	—	6	4	no	—
184	C₅×C₄⋊C₄	—	6	1	no	—
185	C₅×C₂²⋊C₄	—	6	4	no	—
186	C₅×C₂²⋊C₄	—	6	4	no	—
187	C₄²×C₅	—	3	2	no	—
188	C₄²×C₅	—	3	2	no	—
189	C₄²×C₅	—	6	4	no	—
190	C₂²×Q₁₆	—	3	1	no	—
191	C₂²×SD₁₆	C₅×D₃	1	1	yes	characteristic
192	C₂×#124	—	3	1	no	—
193	C₂×C₄×Q₈	—	3	1	no	—
194	#464	—	3	8	no	—
195	C₂×C₄⋊C₈	—	3	1	no	—
196	C₂×#103	—	3	1	no	—
197	C₂×#102	—	3	1	no	—
198	C₂²×C₃×C₅	—	4	2	no	—
199	C₂²×C₃×C₅	—	4	2	no	—
200	C₂²×C₃×C₅	—	4	2	no	—
201	C₂²×C₃×C₅	—	8	4	no	—
202	C₂²×C₃×C₅	#121	1	2	yes	—
203	C₂²×C₃×C₅	#135	1	2	yes	—
204	C₂²×C₃×C₅	#137	1	2	yes	—
205	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
206	C₃×C₄×C₅	—	2	4	no	—
207	C₃×C₄×C₅	#121	1	2	yes	—
208	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
209	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
210	C₅×Dic₃	—	2	2	no	—
211	C₅×Dic₃	—	2	2	no	—
212	C₅×Dic₃	—	4	2	no	—
213	C₅×Dic₃	—	4	2	no	—
214	C₂⁴×C₃	—	2	1	no	—
215	C₂×C₃×Q₈	—	2	1	no	—
216	C₂×C₃×Q₈	—	2	2	no	—
217	C₂×C₃×Q₈	C₅×D₄	1	4	yes	—
218	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
219	C₂×C₃×D₄	—	2	2	no	—
220	C₂×C₃×D₄	—	2	1	no	—
221	C₂×C₃×D₄	—	2	2	no	—
222	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
223	C₂²×C₃×C₄	—	2	1	no	—
224	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
225	C₂²×Dic₃	—	2	1	no	—
226	C₂²×Dic₃	—	2	1	no	—
227	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
228	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
229	C₂×Dic₆	—	2	2	no	—
230	C₂×Dic₆	—	2	2	no	—
231	C₂×Dic₆	—	2	1	no	—
232	C₂×Dic₆	C₂³×C₅	1	2	yes	—
233	C₃×SD₁₆	—	2	8	no	—
234	C₂×C₃×C₈	—	2	2	no	—
235	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
236	#217	—	2	4	no	—
237	#217	—	2	4	no	—
238	#216	—	2	8	no	—
239	C₄⋊Dic₃	—	2	1	no	—
240	C₄⋊Dic₃	—	2	4	no	—
241	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
242	C₄×Dic₃	—	2	4	no	—
243	C₄×Dic₃	C₅×D₄	1	2	yes	—
244	C₄×Dic₃	C₂³×C₅	1	2	yes	—
245	C₂×C₃⋊C₈	—	2	2	no	—
246	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
247	C₂³×C₅	—	2	2	no	—
248	C₂³×C₅	—	4	2	no	—
249	C₂³×C₅	—	4	2	no	—
250	C₂³×C₅	—	4	2	no	—
251	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
252	C₅×Q₈	—	2	4	no	—
253	C₅×Q₈	—	2	2	no	—
254	C₅×Q₈	—	6	2	no	—
255	C₅×Q₈	—	6	2	no	—
256	C₅×Q₈	—	12	2	no	—
257	C₅×Q₈	C₂×#67	1	4	yes	—
258	C₅×D₄	—	2	2	no	—
259	C₅×D₄	—	2	2	no	—
260	C₅×D₄	—	4	2	no	—
261	C₂×C₄×C₅	—	2	4	no	—
262	C₂×C₄×C₅	—	2	2	no	—
263	C₂×C₄×C₅	—	3	2	no	—
264	C₂×C₄×C₅	—	3	2	no	—
265	C₂×C₄×C₅	—	6	2	no	—
266	C₂×C₄×C₅	—	6	2	no	—
267	C₂×C₄×C₅	—	6	2	no	—
268	C₂×C₄×C₅	—	6	2	no	—
269	C₂×C₄×C₅	—	12	2	no	—
270	C₂×C₄×C₅	—	12	2	no	—
271	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
272	C₂×C₄×C₅	#237	1	2	yes	—
273	C₂×C₄×C₅	C₂×#67	1	2	yes	—
274	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
275	C₅×C₈	—	2	2	no	—
276	C₅×C₈	—	6	2	no	—
277	C₂²×Q₈	—	3	1	no	—
278	C₂²×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
279	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
280	C₂×Q₁₆	—	3	4	no	—
281	C₂×Q₁₆	—	6	4	no	—
282	C₂×SD₁₆	—	2	4	no	—
283	C₂×SD₁₆	C₂×C₅×D₃	1	4	yes	—
284	C₂²×C₈	—	3	1	no	—
285	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
286	#124	—	3	4	no	—
287	#124	—	6	2	no	—
288	C₄×Q₈	—	3	4	no	—
289	C₄×Q₈	—	6	2	no	—
290	C₂×C₄⋊C₄	—	3	1	no	—
291	C₂×C₄⋊C₄	—	6	1	no	—
292	C₂×C₂²⋊C₄	—	6	1	no	—
293	C₂×C₂²⋊C₄	—	6	1	no	—
294	C₂×C₄²	—	3	1	no	—
295	C₂×C₄²	—	6	1	no	—
296	C₄⋊C₈	—	3	4	no	—
297	#103	—	3	4	no	—
298	#102	—	3	4	no	—
299	C₂×C₃×C₅	—	8	2	no	—
300	C₂×C₃×C₅	#464	1	4	yes	complemented
301	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
302	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
303	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
304	C₂³×C₃	—	2	2	no	—
305	C₂³×C₃	—	4	2	no	—
306	C₂³×C₃	—	4	2	no	—
307	C₂³×C₃	—	4	2	no	—
308	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
309	C₃×Q₈	—	2	4	no	—
310	C₃×Q₈	—	2	2	no	—
311	C₃×Q₈	C₂×C₅×D₄	1	4	yes	—
312	C₃×D₄	—	2	2	no	—
313	C₃×D₄	—	2	2	no	—
314	C₃×D₄	—	4	2	no	—
315	C₂×C₃×C₄	—	2	4	no	—
316	C₂×C₃×C₄	—	2	2	no	—
317	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
318	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
319	C₂×C₃×C₄	C₅×#41	1	2	yes	—
320	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
321	C₂×Dic₃	—	2	2	no	—
322	C₂×Dic₃	—	2	2	no	—
323	C₂×Dic₃	—	2	2	no	—
324	C₂×Dic₃	—	2	2	no	—
325	C₂×Dic₃	—	4	2	no	—
326	C₂×Dic₃	—	4	2	no	—
327	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
328	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
329	Dic₆	—	2	2	no	—
330	Dic₆	—	2	2	no	—
331	Dic₆	—	4	2	no	—
332	C₃×C₈	—	2	2	no	—
333	C₃⋊C₈	—	2	2	no	—
334	C₂²×C₅	—	4	2	no	—
335	C₂²×C₅	—	4	2	no	—
336	C₂²×C₅	—	4	2	no	—
337	C₂²×C₅	—	8	4	no	—
338	C₂²×C₅	#915	1	2	yes	—
339	C₂²×C₅	#916	1	2	yes	—
340	C₂²×C₅	#939	1	2	yes	—
341	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
342	C₄×C₅	—	2	4	no	—
343	C₄×C₅	—	6	2	no	—
344	C₄×C₅	—	6	2	no	—
345	C₄×C₅	—	12	2	no	—
346	C₄×C₅	—	12	2	no	—
347	C₄×C₅	#939	1	2	yes	—
348	C₄×C₅	C₂×#237	1	1	yes	characteristic
349	C₄×C₅	C₂²×#67	1	1	yes	characteristic
350	C₂⁴	—	2	1	no	—
351	C₂×Q₈	—	2	1	no	—
352	C₂×Q₈	—	2	2	no	—
353	C₂×Q₈	—	3	2	no	—
354	C₂×Q₈	—	6	1	no	—
355	C₂×Q₈	—	6	2	no	—
356	C₂×Q₈	—	6	2	no	—
357	C₂×Q₈	C₅×#67	1	4	yes	—
358	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
359	C₂×D₄	—	2	1	no	—
360	C₂×D₄	—	2	2	no	—
361	C₂×D₄	—	2	2	no	—
362	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	3	1	no	—
365	C₂²×C₄	—	3	1	no	—
366	C₂²×C₄	—	6	1	no	—
367	C₂²×C₄	—	6	1	no	—
368	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
369	Q₁₆	—	6	8	no	—
370	SD₁₆	—	2	8	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	3	2	no	—
373	C₂×C₈	—	6	2	no	—
374	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
375	C₄⋊C₄	—	3	2	no	—
376	C₄⋊C₄	—	6	4	no	—
377	C₄⋊C₄	—	6	1	no	—
378	C₂²⋊C₄	—	6	4	no	—
379	C₂²⋊C₄	—	6	4	no	—
380	C₄²	—	3	2	no	—
381	C₄²	—	3	2	no	—
382	C₄²	—	6	4	no	—
383	C₃×C₅	C₂×#464	1	1	yes	characteristic, complemented, Hall
384	C₂²×C₃	—	4	2	no	—
385	C₂²×C₃	—	4	2	no	—
386	C₂²×C₃	—	4	2	no	—
387	C₂²×C₃	—	8	4	no	—
388	C₂²×C₃	C₅×#121	1	2	yes	—
389	C₂²×C₃	C₅×#135	1	2	yes	—
390	C₂²×C₃	C₅×#137	1	2	yes	—
391	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
392	C₃×C₄	—	2	4	no	—
393	C₃×C₄	C₅×#121	1	2	yes	—
394	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
395	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
396	Dic₃	—	2	2	no	—
397	Dic₃	—	2	2	no	—
398	Dic₃	—	4	2	no	—
399	Dic₃	—	4	2	no	—
400	C₂×C₅	—	8	2	no	—
401	C₂×C₅	#5166	1	4	yes	direct product factor
402	C₂×C₅	C₂×#915	1	1	yes	characteristic
403	C₂×C₅	C₂×#916	1	1	yes	characteristic
404	C₂×C₅	C₂×#939	1	1	yes	characteristic
405	C₂³	—	2	2	no	—
406	C₂³	—	4	2	no	—
407	C₂³	—	4	2	no	—
408	C₂³	—	4	2	no	—
409	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
410	Q₈	—	2	4	no	—
411	Q₈	—	2	2	no	—
412	Q₈	—	6	2	no	—
413	Q₈	—	6	2	no	—
414	Q₈	—	12	2	no	—
415	Q₈	C₂×C₅×#67	1	4	yes	—
416	D₄	—	2	2	no	—
417	D₄	—	2	2	no	—
418	D₄	—	4	2	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	3	2	no	—
422	C₂×C₄	—	3	2	no	—
423	C₂×C₄	—	6	2	no	—
424	C₂×C₄	—	6	2	no	—
425	C₂×C₄	—	6	2	no	—
426	C₂×C₄	—	6	2	no	—
427	C₂×C₄	—	12	2	no	—
428	C₂×C₄	—	12	2	no	—
429	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
430	C₂×C₄	C₅×#237	1	2	yes	—
431	C₂×C₄	C₂×C₅×#67	1	2	yes	—
432	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
433	C₈	—	2	2	no	—
434	C₈	—	6	2	no	—
435	C₂×C₃	—	8	2	no	—
436	C₂×C₃	C₅×#464	1	4	yes	complemented
437	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
438	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
439	C₂×C₃	C₂×C₅×#137	1	1	yes	characteristic
440	C₅	C₂×#5166	1	1	yes	characteristic, direct product factor, Sylow
441	C₂²	—	4	2	no	—
442	C₂²	—	4	2	no	—
443	C₂²	—	4	2	no	—
444	C₂²	—	8	4	no	—
445	C₂²	C₅×#915	1	2	yes	—
446	C₂²	C₅×#916	1	2	yes	—
447	C₂²	C₅×#939	1	2	yes	—
448	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
449	C₄	—	2	4	no	—
450	C₄	—	6	2	no	—
451	C₄	—	6	2	no	—
452	C₄	—	12	2	no	—
453	C₄	—	12	2	no	—
454	C₄	C₅×#939	1	2	yes	—
455	C₄	C₂×C₅×#237	1	1	yes	characteristic
456	C₄	C₂²×C₅×#67	1	1	yes	characteristic
457	C₃	C₂×C₅×#464	1	1	yes	characteristic, complemented, Sylow
458	C₂	—	8	2	no	—
459	C₂	C₅×#5166	1	4	yes	direct product factor
460	C₂	C₂×C₅×#915	1	1	yes	characteristic
461	C₂	C₂×C₅×#916	1	1	yes	characteristic
462	C₂	C₂×C₅×#939	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂²×C₃×C₅×SD₁₆	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂²×C₃×C₅×D₄	C₂²
hypercenter	C₂²×C₅×SD₁₆	D₃
hypocenter	C₃	C₂×C₅×#464
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂²×C₄×C₅ ◁ C₂²×C₅×SD₁₆

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×Q₈×Dic₃	C₂	semidirect
3. C₂²×C₅×#216	C₂	semidirect
6. C₅×#5166	C₂	direct (N × H)
7. C₂×C₅×#816	C₂	semidirect
8. C₂×C₅×Dic₃⋊C₈	C₂	semidirect
19. C₅×Q₈×Dic₃	C₂²	semidirect
21. C₂×C₅×#216	C₂²	semidirect
30. C₅×#816	C₂²	semidirect
31. C₅×Dic₃⋊C₈	C₂²	semidirect
32. C₂×#5166	C₅	direct (N × H)
75. C₂×Q₈×Dic₃	C₂×C₅	semidirect
76. C₂²×#216	C₂×C₅	semidirect
79. #5166	C₂×C₅	direct (N × H)
80. C₂×#816	C₂×C₅	semidirect
81. C₂×Dic₃⋊C₈	C₂×C₅	semidirect
144. Q₈×Dic₃	C₂²×C₅	semidirect
146. C₂×#216	C₂²×C₅	semidirect
155. #816	C₂²×C₅	semidirect
156. Dic₃⋊C₈	C₂²×C₅	semidirect
300. C₂×C₃×C₅	#464	semidirect
383. C₃×C₅	C₂×#464	semidirect
401. C₂×C₅	#5166	direct (N × H)
436. C₂×C₃	C₅×#464	semidirect
440. C₅	C₂×#5166	direct (N × H)
457. C₃	C₂×C₅×#464	semidirect
459. C₂	C₅×#5166	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×C₃×C₅×SD₁₆	2
C₂×C₅×Q₈×Dic₃	2
C₂²×C₅×#216	2
C₂×C₅×#936	2
C₂×C₅×#832	2
C₅×#5166	2
C₂×C₅×#816	2
C₂×C₅×Dic₃⋊C₈	2
C₂×C₅×#464	3
C₂×#5166	5

Subgroups — C2×C5×#5166 #14426124

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5166 #14426124