Subgroups — C₂×C₅×#5175 #14438724

Order 1920.

1312 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×C₃×C₅×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#944	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₅×#215	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#940	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₅×#214	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₅×#204	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5175	C₂	1	8	yes	maximal, direct product factor
8	C₂×C₅×C₈×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×#492	—	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×#67	—	2	2	no	—
13	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
14	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×SD₁₆	—	2	4	no	—
16	C₂×C₃×C₅×SD₁₆	C₂²	1	4	yes	complemented
17	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
18	C₅×#944	—	2	2	no	—
19	C₅×#944	C₂²	1	4	yes	complemented
20	C₂×C₅×#215	—	2	4	no	—
21	C₂×C₅×#215	C₂²	1	4	yes	complemented
22	C₅×#940	—	2	2	no	—
23	C₅×#940	C₂²	1	4	yes	—
24	C₂×C₅×#214	—	2	4	no	—
25	C₂×C₅×#214	C₂²	1	4	yes	complemented
26	C₂×C₅×Dic₃⋊C₄	—	2	2	no	—
27	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
28	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₅×#204	—	2	4	no	—
30	C₂×C₅×#204	C₂²	1	4	yes	complemented
31	C₅×C₈×Dic₃	C₂²	1	4	yes	complemented
32	C₂×#5175	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
33	C₂²×C₅×SD₁₆	—	3	1	no	—
34	C₂²×C₅×SD₁₆	—	3	1	no	—
35	C₂²×C₅×SD₁₆	—	3	1	no	—
36	C₂²×C₅×SD₁₆	D₃	1	1	yes	characteristic, complemented
37	C₂×C₅×C₄⋊Q₈	—	3	1	no	—
38	C₂×C₅×#127	—	3	1	no	—
39	C₅×#492	—	3	8	no	—
40	C₂×C₄×C₅×C₈	—	3	1	no	—
41	C₂⁴×C₃×C₅	—	2	1	no	—
42	C₂³×C₅×D₃	—	2	1	no	—
43	C₂×C₃×C₅×Q₈	—	2	1	no	—
44	C₂×C₃×C₅×Q₈	—	2	2	no	—
45	C₂×C₃×C₅×Q₈	—	2	2	no	—
46	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
47	C₂×C₃×C₅×D₄	—	2	2	no	—
48	C₂×C₃×C₅×D₄	—	2	2	no	—
49	C₂×C₃×C₅×D₄	—	2	1	no	—
50	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
51	C₂²×C₃×C₄×C₅	—	2	1	no	—
52	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
53	C₂×C₅×#67	—	2	8	no	—
54	C₂×C₅×#67	—	4	8	no	—
55	C₂²×C₅×Dic₃	—	2	1	no	—
56	C₂²×C₅×Dic₃	D₄	1	2	yes	—
57	C₂×C₅×D₁₂	—	2	2	no	—
58	C₂×C₅×D₁₂	—	2	2	no	—
59	C₂×C₅×D₁₂	—	2	1	no	—
60	C₂×C₅×D₁₂	C₂³	1	2	yes	—
61	C₂×C₅×Dic₆	—	2	2	no	—
62	C₂×C₅×Dic₆	—	2	2	no	—
63	C₂×C₅×Dic₆	—	2	1	no	—
64	C₂×C₅×Dic₆	C₂³	1	2	yes	—
65	C₃×C₅×SD₁₆	—	2	8	no	—
66	C₂×C₃×C₅×C₈	D₄	1	4	yes	complemented
67	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
68	C₅×#215	—	2	8	no	—
69	C₅×#214	—	2	8	no	—
70	C₅×Dic₃⋊C₄	—	2	8	no	—
71	C₄×C₅×Dic₃	D₄	1	2	yes	—
72	C₄×C₅×Dic₃	C₂³	1	2	yes	—
73	C₂×C₅×C₃⋊C₈	D₄	1	4	yes	complemented
74	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
75	C₅×#204	—	2	8	no	—
76	C₂²×C₃×SD₁₆	C₂×C₅	1	1	yes	characteristic, complemented
77	C₂×#944	C₂×C₅	1	1	yes	characteristic, complemented
78	C₂²×#215	C₂×C₅	1	1	yes	characteristic, complemented
79	C₂×#940	C₂×C₅	1	1	yes	characteristic
80	C₂²×#214	C₂×C₅	1	1	yes	characteristic, complemented
81	C₂²×#204	C₂×C₅	1	1	yes	characteristic, complemented
82	#5175	C₂×C₅	1	8	yes	direct product factor
83	C₂×C₈×Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
84	C₂²×C₅×Q₈	—	3	1	no	—
85	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
86	C₂²×C₅×D₄	—	3	1	no	—
87	C₂²×C₅×D₄	—	6	2	no	—
88	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
89	C₂×C₅×SD₁₆	—	2	4	no	—
90	C₂×C₅×SD₁₆	—	3	4	no	—
91	C₂×C₅×SD₁₆	—	3	4	no	—
92	C₂×C₅×SD₁₆	—	3	4	no	—
93	C₂×C₅×SD₁₆	—	6	4	no	—
94	C₂×C₅×SD₁₆	—	6	4	no	—
95	C₂×C₅×SD₁₆	—	6	4	no	—
96	C₂×C₅×SD₁₆	C₂×D₃	1	4	yes	complemented
97	C₂²×C₅×C₈	—	3	1	no	—
98	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
99	C₅×C₄⋊Q₈	—	3	4	no	—
100	C₅×C₄⋊Q₈	—	6	2	no	—
101	C₅×#127	—	3	4	no	—
102	C₅×#127	—	6	2	no	—
103	C₂×C₅×C₄⋊C₄	—	6	2	no	—
104	C₂×C₄²×C₅	—	3	1	no	—
105	C₄×C₅×C₈	—	3	4	no	—
106	C₂×#492	—	3	1	no	Sylow
107	C₂³×C₃×C₅	—	2	2	no	—
108	C₂³×C₃×C₅	—	4	2	no	—
109	C₂³×C₃×C₅	—	4	4	no	—
110	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₅×D₃	—	2	2	no	—
112	C₂²×C₅×D₃	—	4	2	no	—
113	C₂²×C₅×D₃	—	4	4	no	—
114	C₃×C₅×Q₈	—	2	2	no	—
115	C₃×C₅×Q₈	—	2	2	no	—
116	C₃×C₅×Q₈	—	4	2	no	—
117	C₃×C₅×D₄	—	2	2	no	—
118	C₃×C₅×D₄	—	2	2	no	—
119	C₃×C₅×D₄	—	4	2	no	—
120	C₂×C₃×C₄×C₅	—	2	2	no	—
121	C₂×C₃×C₄×C₅	—	4	2	no	—
122	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
123	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
124	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
125	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
126	C₅×#67	—	4	16	no	—
127	C₂×C₅×Dic₃	—	2	2	no	—
128	C₂×C₅×Dic₃	—	4	2	no	—
129	C₂×C₅×Dic₃	SD₁₆	1	8	yes	complemented
130	C₂×C₅×Dic₃	C₂×D₄	1	4	yes	—
131	C₅×D₁₂	—	2	2	no	—
132	C₅×D₁₂	—	2	2	no	—
133	C₅×D₁₂	—	4	2	no	—
134	C₅×Dic₆	—	2	2	no	—
135	C₅×Dic₆	—	2	2	no	—
136	C₅×Dic₆	—	4	2	no	—
137	C₃×C₅×C₈	C₂×D₄	1	4	yes	complemented
138	C₅×C₃⋊C₈	C₂×D₄	1	4	yes	complemented
139	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
140	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
141	C₂²×#67	—	2	2	no	—
142	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
143	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
144	C₂×C₃×SD₁₆	—	2	4	no	—
145	C₂×C₃×SD₁₆	C₂²×C₅	1	4	yes	complemented
146	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
147	#944	—	2	2	no	—
148	#944	C₂²×C₅	1	4	yes	complemented
149	C₂×#215	—	2	4	no	—
150	C₂×#215	C₂²×C₅	1	4	yes	complemented
151	#940	—	2	2	no	—
152	#940	C₂²×C₅	1	4	yes	—
153	C₂×#214	—	2	4	no	—
154	C₂×#214	C₂²×C₅	1	4	yes	complemented
155	C₂×Dic₃⋊C₄	—	2	2	no	—
156	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
157	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
158	C₂×#204	—	2	4	no	—
159	C₂×#204	C₂²×C₅	1	4	yes	complemented
160	C₈×Dic₃	C₂²×C₅	1	4	yes	complemented
161	C₂⁴×C₅	—	2	1	no	—
162	C₂⁴×C₅	—	6	1	no	—
163	C₂×C₅×Q₈	—	2	1	no	—
164	C₂×C₅×Q₈	—	2	2	no	—
165	C₂×C₅×Q₈	—	2	2	no	—
166	C₂×C₅×Q₈	—	3	2	no	—
167	C₂×C₅×Q₈	—	6	1	no	—
168	C₂×C₅×Q₈	—	6	2	no	—
169	C₂×C₅×Q₈	—	6	2	no	—
170	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
171	C₂×C₅×D₄	—	2	2	no	—
172	C₂×C₅×D₄	—	2	1	no	—
173	C₂×C₅×D₄	—	2	2	no	—
174	C₂×C₅×D₄	—	3	2	no	—
175	C₂×C₅×D₄	—	6	8	no	—
176	C₂×C₅×D₄	—	6	2	no	—
177	C₂×C₅×D₄	—	6	1	no	—
178	C₂×C₅×D₄	—	6	2	no	—
179	C₂×C₅×D₄	—	12	8	no	—
180	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
181	C₂²×C₄×C₅	—	2	1	no	—
182	C₂²×C₄×C₅	—	3	2	no	—
183	C₂²×C₄×C₅	—	6	1	no	—
184	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
185	C₅×SD₁₆	—	2	8	no	—
186	C₅×SD₁₆	—	6	8	no	—
187	C₅×SD₁₆	—	6	8	no	—
188	C₅×SD₁₆	—	6	8	no	—
189	C₂×C₅×C₈	—	3	4	no	—
190	C₂×C₅×C₈	—	3	2	no	—
191	C₂×C₅×C₈	#67	1	4	yes	complemented
192	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
193	C₅×C₄⋊C₄	—	6	8	no	—
194	C₄²×C₅	—	3	2	no	—
195	C₄²×C₅	—	3	2	no	—
196	C₂²×SD₁₆	—	3	1	no	—
197	C₂²×SD₁₆	—	3	1	no	—
198	C₂²×SD₁₆	—	3	1	no	—
199	C₂²×SD₁₆	C₅×D₃	1	1	yes	characteristic, complemented
200	C₂×C₄⋊Q₈	—	3	1	no	—
201	C₂×#127	—	3	1	no	—
202	#492	—	3	8	no	—
203	C₂×C₄×C₈	—	3	1	no	—
204	C₂²×C₃×C₅	—	4	2	no	—
205	C₂²×C₃×C₅	—	4	4	no	—
206	C₂²×C₃×C₅	—	8	4	no	—
207	C₂²×C₃×C₅	#127	1	2	yes	—
208	C₂²×C₃×C₅	C₂×SD₁₆	1	4	yes	—
209	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
210	C₂×C₅×D₃	—	4	2	no	—
211	C₂×C₅×D₃	—	4	4	no	—
212	C₂×C₅×D₃	—	8	4	no	—
213	C₃×C₄×C₅	—	4	2	no	—
214	C₃×C₄×C₅	#127	1	2	yes	—
215	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
216	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
217	C₅×Dic₃	—	4	2	no	—
218	C₅×Dic₃	C₂×SD₁₆	1	8	yes	complemented
219	C₂⁴×C₃	—	2	1	no	—
220	C₂³×D₃	—	2	1	no	—
221	C₂×C₃×Q₈	—	2	1	no	—
222	C₂×C₃×Q₈	—	2	2	no	—
223	C₂×C₃×Q₈	—	2	2	no	—
224	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
225	C₂×C₃×D₄	—	2	2	no	—
226	C₂×C₃×D₄	—	2	2	no	—
227	C₂×C₃×D₄	—	2	1	no	—
228	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
229	C₂²×C₃×C₄	—	2	1	no	—
230	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
231	C₂×#67	—	2	8	no	—
232	C₂×#67	—	4	8	no	—
233	C₂²×Dic₃	—	2	1	no	—
234	C₂²×Dic₃	C₅×D₄	1	2	yes	—
235	C₂×D₁₂	—	2	2	no	—
236	C₂×D₁₂	—	2	2	no	—
237	C₂×D₁₂	—	2	1	no	—
238	C₂×D₁₂	C₂³×C₅	1	2	yes	—
239	C₂×Dic₆	—	2	2	no	—
240	C₂×Dic₆	—	2	2	no	—
241	C₂×Dic₆	—	2	1	no	—
242	C₂×Dic₆	C₂³×C₅	1	2	yes	—
243	C₃×SD₁₆	—	2	8	no	—
244	C₂×C₃×C₈	C₅×D₄	1	4	yes	complemented
245	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
246	#215	—	2	8	no	—
247	#214	—	2	8	no	—
248	Dic₃⋊C₄	—	2	8	no	—
249	C₄×Dic₃	C₅×D₄	1	2	yes	—
250	C₄×Dic₃	C₂³×C₅	1	2	yes	—
251	C₂×C₃⋊C₈	C₅×D₄	1	4	yes	complemented
252	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
253	#204	—	2	8	no	—
254	C₂³×C₅	—	2	2	no	—
255	C₂³×C₅	—	4	4	no	—
256	C₂³×C₅	—	4	2	no	—
257	C₂³×C₅	—	6	2	no	—
258	C₂³×C₅	—	12	4	no	—
259	C₂³×C₅	—	12	2	no	—
260	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
261	C₅×Q₈	—	2	2	no	—
262	C₅×Q₈	—	2	2	no	—
263	C₅×Q₈	—	4	2	no	—
264	C₅×Q₈	—	6	2	no	—
265	C₅×Q₈	—	6	2	no	—
266	C₅×Q₈	—	12	2	no	—
267	C₅×D₄	—	2	2	no	—
268	C₅×D₄	—	2	2	no	—
269	C₅×D₄	—	4	2	no	—
270	C₅×D₄	—	6	2	no	—
271	C₅×D₄	—	6	2	no	—
272	C₅×D₄	—	12	16	no	—
273	C₅×D₄	—	12	2	no	—
274	C₂×C₄×C₅	—	2	2	no	—
275	C₂×C₄×C₅	—	3	8	no	—
276	C₂×C₄×C₅	—	3	4	no	—
277	C₂×C₄×C₅	—	4	2	no	—
278	C₂×C₄×C₅	—	6	2	no	—
279	C₂×C₄×C₅	—	12	2	no	—
280	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
281	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
282	C₂×C₄×C₅	C₂×#67	1	2	yes	—
283	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
284	C₅×C₈	—	3	4	no	—
285	C₅×C₈	C₂×#67	1	4	yes	complemented
286	C₂²×Q₈	—	3	1	no	—
287	C₂²×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
288	C₂²×D₄	—	3	1	no	—
289	C₂²×D₄	—	6	2	no	—
290	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
291	C₂×SD₁₆	—	2	4	no	—
292	C₂×SD₁₆	—	3	4	no	—
293	C₂×SD₁₆	—	3	4	no	—
294	C₂×SD₁₆	—	3	4	no	—
295	C₂×SD₁₆	—	6	4	no	—
296	C₂×SD₁₆	—	6	4	no	—
297	C₂×SD₁₆	—	6	4	no	—
298	C₂×SD₁₆	C₂×C₅×D₃	1	4	yes	complemented
299	C₂²×C₈	—	3	1	no	—
300	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
301	C₄⋊Q₈	—	3	4	no	—
302	C₄⋊Q₈	—	6	2	no	—
303	#127	—	3	4	no	—
304	#127	—	6	2	no	—
305	C₂×C₄⋊C₄	—	6	2	no	—
306	C₂×C₄²	—	3	1	no	—
307	C₄×C₈	—	3	4	no	—
308	C₂×C₃×C₅	—	8	2	no	—
309	C₂×C₃×C₅	#492	1	4	yes	complemented
310	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
311	C₂×C₃×C₅	C₂²×SD₁₆	1	2	yes	—
312	C₅×D₃	—	8	2	no	—
313	C₂³×C₃	—	2	2	no	—
314	C₂³×C₃	—	4	2	no	—
315	C₂³×C₃	—	4	4	no	—
316	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
317	C₂²×D₃	—	2	2	no	—
318	C₂²×D₃	—	4	2	no	—
319	C₂²×D₃	—	4	4	no	—
320	C₃×Q₈	—	2	2	no	—
321	C₃×Q₈	—	2	2	no	—
322	C₃×Q₈	—	4	2	no	—
323	C₃×D₄	—	2	2	no	—
324	C₃×D₄	—	2	2	no	—
325	C₃×D₄	—	4	2	no	—
326	C₂×C₃×C₄	—	2	2	no	—
327	C₂×C₃×C₄	—	4	2	no	—
328	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
329	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
330	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
331	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
332	#67	—	4	16	no	—
333	C₂×Dic₃	—	2	2	no	—
334	C₂×Dic₃	—	4	2	no	—
335	C₂×Dic₃	C₅×SD₁₆	1	8	yes	complemented
336	C₂×Dic₃	C₂×C₅×D₄	1	4	yes	—
337	D₁₂	—	2	2	no	—
338	D₁₂	—	2	2	no	—
339	D₁₂	—	4	2	no	—
340	Dic₆	—	2	2	no	—
341	Dic₆	—	2	2	no	—
342	Dic₆	—	4	2	no	—
343	C₃×C₈	C₂×C₅×D₄	1	4	yes	complemented
344	C₃⋊C₈	C₂×C₅×D₄	1	4	yes	complemented
345	C₂²×C₅	—	4	4	no	—
346	C₂²×C₅	—	4	2	no	—
347	C₂²×C₅	—	8	4	no	—
348	C₂²×C₅	—	12	4	no	—
349	C₂²×C₅	—	12	2	no	—
350	C₂²×C₅	—	24	4	no	—
351	C₂²×C₅	D₃×SD₁₆	1	4	yes	—
352	C₂²×C₅	#940	1	2	yes	—
353	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
354	C₄×C₅	—	3	8	no	—
355	C₄×C₅	—	4	2	no	—
356	C₄×C₅	—	12	2	no	—
357	C₄×C₅	#940	1	2	yes	—
358	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
359	C₄×C₅	C₂²×#67	1	1	yes	characteristic
360	C₂⁴	—	2	1	no	—
361	C₂⁴	—	6	1	no	—
362	C₂×Q₈	—	2	1	no	—
363	C₂×Q₈	—	2	2	no	—
364	C₂×Q₈	—	2	2	no	—
365	C₂×Q₈	—	3	2	no	—
366	C₂×Q₈	—	6	1	no	—
367	C₂×Q₈	—	6	2	no	—
368	C₂×Q₈	—	6	2	no	—
369	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
370	C₂×D₄	—	2	2	no	—
371	C₂×D₄	—	2	1	no	—
372	C₂×D₄	—	2	2	no	—
373	C₂×D₄	—	3	2	no	—
374	C₂×D₄	—	6	8	no	—
375	C₂×D₄	—	6	2	no	—
376	C₂×D₄	—	6	1	no	—
377	C₂×D₄	—	6	2	no	—
378	C₂×D₄	—	12	8	no	—
379	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	3	2	no	—
382	C₂²×C₄	—	6	1	no	—
383	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
384	SD₁₆	—	2	8	no	—
385	SD₁₆	—	6	8	no	—
386	SD₁₆	—	6	8	no	—
387	SD₁₆	—	6	8	no	—
388	C₂×C₈	—	3	4	no	—
389	C₂×C₈	—	3	2	no	—
390	C₂×C₈	C₅×#67	1	4	yes	complemented
391	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
392	C₄⋊C₄	—	6	8	no	—
393	C₄²	—	3	2	no	—
394	C₄²	—	3	2	no	—
395	C₃×C₅	C₂×#492	1	1	yes	characteristic, complemented, Hall
396	C₂²×C₃	—	4	2	no	—
397	C₂²×C₃	—	4	4	no	—
398	C₂²×C₃	—	8	4	no	—
399	C₂²×C₃	C₅×#127	1	2	yes	—
400	C₂²×C₃	C₂×C₅×SD₁₆	1	4	yes	—
401	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
402	C₂×D₃	—	4	2	no	—
403	C₂×D₃	—	4	4	no	—
404	C₂×D₃	—	8	4	no	—
405	C₃×C₄	—	4	2	no	—
406	C₃×C₄	C₅×#127	1	2	yes	—
407	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
408	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
409	Dic₃	—	4	2	no	—
410	Dic₃	C₂×C₅×SD₁₆	1	8	yes	complemented
411	C₂×C₅	—	8	2	no	—
412	C₂×C₅	—	24	2	no	—
413	C₂×C₅	#5175	1	4	yes	direct product factor
414	C₂×C₅	C₂×D₃×SD₁₆	1	2	yes	—
415	C₂×C₅	C₂×#940	1	1	yes	characteristic
416	C₂³	—	2	2	no	—
417	C₂³	—	4	4	no	—
418	C₂³	—	4	2	no	—
419	C₂³	—	6	2	no	—
420	C₂³	—	12	4	no	—
421	C₂³	—	12	2	no	—
422	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
423	Q₈	—	2	2	no	—
424	Q₈	—	2	2	no	—
425	Q₈	—	4	2	no	—
426	Q₈	—	6	2	no	—
427	Q₈	—	6	2	no	—
428	Q₈	—	12	2	no	—
429	D₄	—	2	2	no	—
430	D₄	—	2	2	no	—
431	D₄	—	4	2	no	—
432	D₄	—	6	2	no	—
433	D₄	—	6	2	no	—
434	D₄	—	12	16	no	—
435	D₄	—	12	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	3	8	no	—
438	C₂×C₄	—	3	4	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	6	2	no	—
441	C₂×C₄	—	12	2	no	—
442	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
443	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
444	C₂×C₄	C₂×C₅×#67	1	2	yes	—
445	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
446	C₈	—	3	4	no	—
447	C₈	C₂×C₅×#67	1	4	yes	complemented
448	C₂×C₃	—	8	2	no	—
449	C₂×C₃	C₅×#492	1	4	yes	complemented
450	C₂×C₃	C₂×C₅×#127	1	1	yes	characteristic
451	C₂×C₃	C₂²×C₅×SD₁₆	1	2	yes	—
452	D₃	—	8	2	no	—
453	C₅	C₂×#5175	1	1	yes	characteristic, direct product factor, Sylow
454	C₂²	—	4	4	no	—
455	C₂²	—	4	2	no	—
456	C₂²	—	8	4	no	—
457	C₂²	—	12	4	no	—
458	C₂²	—	12	2	no	—
459	C₂²	—	24	4	no	—
460	C₂²	C₅×D₃×SD₁₆	1	4	yes	—
461	C₂²	C₅×#940	1	2	yes	—
462	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
463	C₄	—	3	8	no	—
464	C₄	—	4	2	no	—
465	C₄	—	12	2	no	—
466	C₄	C₅×#940	1	2	yes	—
467	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
468	C₄	C₂²×C₅×#67	1	1	yes	characteristic
469	C₃	C₂×C₅×#492	1	1	yes	characteristic, complemented, Sylow
470	C₂	—	8	2	no	—
471	C₂	—	24	2	no	—
472	C₂	C₅×#5175	1	4	yes	direct product factor
473	C₂	C₂×C₅×D₃×SD₁₆	1	2	yes	—
474	C₂	C₂×C₅×#940	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	C₂×C₅×#940	C₂
hypercenter	C₂²×C₅×SD₁₆	D₃
hypocenter	C₃	C₂×C₅×#492
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
1. C₂²×C₃×C₅×SD₁₆	C₂	semidirect
2. C₂×C₅×#944	C₂	semidirect
3. C₂²×C₅×#215	C₂	semidirect
5. C₂²×C₅×#214	C₂	semidirect
6. C₂²×C₅×#204	C₂	semidirect
7. C₅×#5175	C₂	direct (N × H)
8. C₂×C₅×C₈×Dic₃	C₂	semidirect
16. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
19. C₅×#944	C₂²	semidirect
21. C₂×C₅×#215	C₂²	semidirect
25. C₂×C₅×#214	C₂²	semidirect
30. C₂×C₅×#204	C₂²	semidirect
31. C₅×C₈×Dic₃	C₂²	semidirect
32. C₂×#5175	C₅	direct (N × H)
36. C₂²×C₅×SD₁₆	D₃	semidirect
66. C₂×C₃×C₅×C₈	D₄	semidirect
73. C₂×C₅×C₃⋊C₈	D₄	semidirect
76. C₂²×C₃×SD₁₆	C₂×C₅	semidirect
77. C₂×#944	C₂×C₅	semidirect
78. C₂²×#215	C₂×C₅	semidirect
80. C₂²×#214	C₂×C₅	semidirect
81. C₂²×#204	C₂×C₅	semidirect
82. #5175	C₂×C₅	direct (N × H)
83. C₂×C₈×Dic₃	C₂×C₅	semidirect
96. C₂×C₅×SD₁₆	C₂×D₃	semidirect
129. C₂×C₅×Dic₃	SD₁₆	semidirect
137. C₃×C₅×C₈	C₂×D₄	semidirect
138. C₅×C₃⋊C₈	C₂×D₄	semidirect
145. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
148. #944	C₂²×C₅	semidirect
150. C₂×#215	C₂²×C₅	semidirect
154. C₂×#214	C₂²×C₅	semidirect
159. C₂×#204	C₂²×C₅	semidirect
160. C₈×Dic₃	C₂²×C₅	semidirect
191. C₂×C₅×C₈	#67	semidirect
199. C₂²×SD₁₆	C₅×D₃	semidirect
218. C₅×Dic₃	C₂×SD₁₆	semidirect
244. C₂×C₃×C₈	C₅×D₄	semidirect
251. C₂×C₃⋊C₈	C₅×D₄	semidirect
285. C₅×C₈	C₂×#67	semidirect
298. C₂×SD₁₆	C₂×C₅×D₃	semidirect
309. C₂×C₃×C₅	#492	semidirect
335. C₂×Dic₃	C₅×SD₁₆	semidirect
343. C₃×C₈	C₂×C₅×D₄	semidirect
344. C₃⋊C₈	C₂×C₅×D₄	semidirect
390. C₂×C₈	C₅×#67	semidirect
395. C₃×C₅	C₂×#492	semidirect
410. Dic₃	C₂×C₅×SD₁₆	semidirect
413. C₂×C₅	#5175	direct (N × H)
447. C₈	C₂×C₅×#67	semidirect
449. C₂×C₃	C₅×#492	semidirect
453. C₅	C₂×#5175	direct (N × H)
469. C₃	C₂×C₅×#492	semidirect
472. C₂	C₅×#5175	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×#944	2
C₂²×C₅×#215	2
C₂×C₅×#940	2
C₂²×C₅×#214	2
C₂²×C₅×#204	2
C₅×#5175	2
C₂×C₅×C₈×Dic₃	2
C₂×C₅×#492	3
C₂×#5175	5

Subgroups — C2×C5×#5175 #14438724

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5175 #14438724