Subgroups — C₂×C₅×#5727 #14482905

Order 1920.

3136 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×D₃×Q₈	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#946	C₂	1	2	yes	maximal, complemented
4	C₅×#5727	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₅×#896	C₂	1	4	yes	maximal, complemented
6	C₂×C₅×#893	C₂	1	2	yes	maximal
7	C₂×C₅×#888	C₂	1	2	yes	maximal, complemented
8	C₂×C₄×C₅×D₁₂	C₂	1	1	yes	maximal, characteristic
9	C₂×C₄×C₅×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅×D₄×Q₈	—	3	1	no	maximal, Hall
11	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	—
12	C₂×C₅×D₃×Q₈	—	2	16	no	—
13	C₂×C₅×D₃×Q₈	C₂²	1	16	yes	complemented
14	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
15	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
16	C₂²×C₄×C₅×D₃	C₂²	1	4	yes	—
17	C₂²×C₅×Dic₆	C₂²	1	4	yes	—
18	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
19	C₃×C₅×C₄⋊Q₈	C₂²	1	8	yes	complemented
20	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
21	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
22	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
23	C₅×#946	C₂²	1	16	yes	complemented
24	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
25	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
26	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
27	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
28	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
29	C₂×C₅×Dic₃⋊C₄	C₂²	1	4	yes	—
30	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
31	C₅×#896	C₂²	1	32	yes	complemented
32	C₅×#893	C₂²	1	16	yes	—
33	C₅×#888	C₂²	1	16	yes	complemented
34	C₄×C₅×D₁₂	C₂²	1	8	yes	—
35	C₄×C₅×Dic₆	C₂²	1	8	yes	complemented
36	C₂×#5727	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
37	C₂³×C₅×Q₈	—	3	2	no	—
38	C₅×D₄×Q₈	—	3	16	no	—
39	C₂×C₅×C₄⋊Q₈	—	3	2	no	—
40	C₂×C₅×C₄⋊Q₈	D₃	1	1	yes	characteristic, complemented
41	C₂×C₅×C₂²⋊Q₈	—	3	2	no	—
42	C₂×C₅×C₂²⋊Q₈	—	3	4	no	—
43	C₂×C₄×C₅×Q₈	—	3	1	no	—
44	C₂×C₄×C₅×D₄	—	3	2	no	—
45	C₂×C₄×C₅×D₄	—	3	1	no	—
46	C₂³×C₅×D₃	C₂³	1	2	yes	—
47	C₂×C₃×C₅×Q₈	—	2	8	no	—
48	C₂×C₃×C₅×Q₈	C₂³	1	8	yes	—
49	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
50	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
51	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
52	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
53	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
54	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
55	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
56	C₅×D₃×Q₈	—	2	64	no	—
57	C₂×C₅×D₁₂	Q₈	1	8	yes	complemented
58	C₂×C₅×D₁₂	C₂³	1	4	yes	—
59	C₂×C₄×C₅×D₃	—	2	8	no	—
60	C₂×C₄×C₅×D₃	—	2	16	no	—
61	C₂×C₄×C₅×D₃	C₂³	1	8	yes	—
62	C₂×C₄×C₅×D₃	C₂³	1	16	yes	—
63	C₂×C₅×Dic₆	—	2	16	no	—
64	C₂×C₅×Dic₆	D₄	1	8	yes	complemented
65	C₂×C₅×Dic₆	C₂³	1	16	yes	—
66	C₂×C₅×Dic₆	C₂³	1	4	yes	—
67	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	—
68	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	—
69	C₃×C₄²×C₅	C₂³	1	4	yes	—
70	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
71	C₅×(C₂×D₃)⋊C₄	C₂³	1	16	yes	—
72	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
73	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
74	C₅×Dic₃⋊C₄	C₂³	1	8	yes	—
75	C₅×Dic₃⋊C₄	C₂³	1	16	yes	—
76	C₄×C₅×Dic₃	C₂³	1	8	yes	—
77	C₂²×D₃×Q₈	C₂×C₅	1	2	yes	complemented
78	C₂×C₃×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
79	C₂×#946	C₂×C₅	1	2	yes	complemented
80	#5727	C₂×C₅	1	16	yes	direct product factor
81	C₂×#896	C₂×C₅	1	4	yes	complemented
82	C₂×#893	C₂×C₅	1	2	yes	—
83	C₂×#888	C₂×C₅	1	2	yes	complemented
84	C₂×C₄×D₁₂	C₂×C₅	1	1	yes	characteristic
85	C₂×C₄×Dic₆	C₂×C₅	1	1	yes	characteristic, complemented
86	C₂²×C₅×Q₈	—	3	16	no	—
87	C₂²×C₅×Q₈	—	3	1	no	—
88	C₂²×C₅×Q₈	—	3	4	no	—
89	C₂²×C₅×Q₈	—	6	16	no	—
90	C₂²×C₅×Q₈	C₂×D₃	1	2	yes	—
91	C₂²×C₅×D₄	—	3	1	no	—
92	C₂³×C₄×C₅	—	3	4	no	—
93	C₂³×C₄×C₅	—	3	2	no	—
94	C₅×C₄⋊Q₈	—	3	16	no	—
95	C₅×C₄⋊Q₈	C₂×D₃	1	8	yes	complemented
96	C₅×C₂²⋊Q₈	—	3	16	no	—
97	C₅×C₂²⋊Q₈	—	3	32	no	—
98	C₄×C₅×Q₈	—	3	8	no	—
99	C₄×C₅×D₄	—	3	16	no	—
100	C₄×C₅×D₄	—	3	8	no	—
101	C₂×C₅×C₄⋊C₄	—	3	2	no	—
102	C₂×C₅×C₄⋊C₄	—	3	4	no	—
103	C₂×C₅×C₄⋊C₄	—	3	1	no	—
104	C₂×C₅×C₄⋊C₄	—	3	1	no	—
105	C₂×C₅×C₄⋊C₄	C₂×D₃	1	2	yes	—
106	C₂×C₅×C₄⋊C₄	C₂×D₃	1	2	yes	—
107	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
108	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
109	C₂×C₄²×C₅	—	3	2	no	—
110	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
111	C₂×D₄×Q₈	—	3	1	no	Sylow
112	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
113	C₂²×C₅×D₃	—	2	4	no	—
114	C₂²×C₅×D₃	—	2	4	no	—
115	C₂²×C₅×D₃	C₂×Q₈	1	8	yes	complemented
116	C₂²×C₅×D₃	C₂⁴	1	4	yes	—
117	C₃×C₅×Q₈	—	2	16	no	—
118	C₂×C₃×C₄×C₅	—	2	8	no	—
119	C₂×C₃×C₄×C₅	—	2	2	no	—
120	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
121	C₂×C₃×C₄×C₅	C₂×Q₈	1	4	yes	complemented
122	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
123	C₂×C₃×C₄×C₅	C₂⁴	1	8	yes	—
124	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
125	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
126	C₂×C₅×Dic₃	—	2	4	no	—
127	C₂×C₅×Dic₃	—	2	4	no	—
128	C₂×C₅×Dic₃	C₂×D₄	1	8	yes	—
129	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
130	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
131	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
132	C₅×D₁₂	C₂×Q₈	1	16	yes	complemented
133	C₄×C₅×D₃	—	2	16	no	—
134	C₄×C₅×D₃	—	2	32	no	—
135	C₅×Dic₆	—	2	32	no	—
136	C₅×Dic₆	C₂×D₄	1	16	yes	complemented
137	C₂²×C₃×Q₈	C₂²×C₅	1	2	yes	—
138	C₂×D₃×Q₈	—	2	16	no	—
139	C₂×D₃×Q₈	C₂²×C₅	1	16	yes	complemented
140	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
141	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
142	C₂²×C₄×D₃	C₂²×C₅	1	4	yes	—
143	C₂²×Dic₆	C₂²×C₅	1	4	yes	—
144	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
145	C₃×C₄⋊Q₈	C₂²×C₅	1	8	yes	complemented
146	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
147	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
148	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
149	#946	C₂²×C₅	1	16	yes	complemented
150	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
151	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	4	yes	—
152	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
153	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
154	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
155	C₂×Dic₃⋊C₄	C₂²×C₅	1	4	yes	—
156	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
157	#896	C₂²×C₅	1	32	yes	complemented
158	#893	C₂²×C₅	1	16	yes	—
159	#888	C₂²×C₅	1	16	yes	complemented
160	C₄×D₁₂	C₂²×C₅	1	8	yes	—
161	C₄×Dic₆	C₂²×C₅	1	8	yes	complemented
162	C₂⁴×C₅	—	3	2	no	—
163	C₂×C₅×Q₈	—	2	8	no	—
164	C₂×C₅×Q₈	—	3	8	no	—
165	C₂×C₅×Q₈	—	3	4	no	—
166	C₂×C₅×Q₈	—	3	16	no	—
167	C₂×C₅×Q₈	—	6	16	no	—
168	C₂×C₅×Q₈	—	6	64	no	—
169	C₂×C₅×Q₈	C₂²×D₃	1	8	yes	—
170	C₂×C₅×D₄	—	3	8	no	—
171	C₂×C₅×D₄	—	3	4	no	—
172	C₂²×C₄×C₅	—	3	2	no	—
173	C₂²×C₄×C₅	—	3	2	no	—
174	C₂²×C₄×C₅	—	3	2	no	—
175	C₂²×C₄×C₅	—	3	16	no	—
176	C₂²×C₄×C₅	—	3	8	no	—
177	C₂²×C₄×C₅	—	6	16	no	—
178	C₂²×C₄×C₅	—	6	8	no	—
179	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
180	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
181	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
182	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
183	C₅×C₄⋊C₄	—	3	4	no	—
184	C₅×C₄⋊C₄	—	3	8	no	—
185	C₅×C₄⋊C₄	—	3	4	no	—
186	C₅×C₄⋊C₄	—	3	16	no	—
187	C₅×C₄⋊C₄	C₂²×D₃	1	8	yes	—
188	C₅×C₄⋊C₄	C₂²×D₃	1	8	yes	—
189	C₅×C₂²⋊C₄	—	3	16	no	—
190	C₅×C₂²⋊C₄	—	3	8	no	—
191	C₄²×C₅	—	3	8	no	—
192	C₄²×C₅	C₂²×D₃	1	4	yes	—
193	C₂³×Q₈	—	3	2	no	—
194	D₄×Q₈	—	3	16	no	—
195	C₂×C₄⋊Q₈	—	3	2	no	—
196	C₂×C₄⋊Q₈	C₅×D₃	1	1	yes	characteristic, complemented
197	C₂×C₂²⋊Q₈	—	3	2	no	—
198	C₂×C₂²⋊Q₈	—	3	4	no	—
199	C₂×C₄×Q₈	—	3	1	no	—
200	C₂×C₄×D₄	—	3	2	no	—
201	C₂×C₄×D₄	—	3	1	no	—
202	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
203	C₂²×C₃×C₅	C₂²×Q₈	1	2	yes	—
204	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
205	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
206	C₂×C₅×D₃	—	2	16	no	—
207	C₂×C₅×D₃	—	2	4	no	—
208	C₂×C₅×D₃	—	2	4	no	—
209	C₂×C₅×D₃	C₂²×Q₈	1	8	yes	complemented
210	C₃×C₄×C₅	—	2	8	no	—
211	C₃×C₄×C₅	—	2	2	no	—
212	C₃×C₄×C₅	C₂²×D₄	1	4	yes	—
213	C₃×C₄×C₅	C₂²×Q₈	1	4	yes	complemented
214	C₅×Dic₃	—	2	4	no	—
215	C₅×Dic₃	—	2	4	no	—
216	C₅×Dic₃	C₂²×D₄	1	8	yes	—
217	C₂³×D₃	C₂³×C₅	1	2	yes	—
218	C₂×C₃×Q₈	—	2	8	no	—
219	C₂×C₃×Q₈	C₂³×C₅	1	8	yes	—
220	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
221	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
222	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
223	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
224	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
225	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
226	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
227	D₃×Q₈	—	2	64	no	—
228	C₂×D₁₂	C₅×Q₈	1	8	yes	complemented
229	C₂×D₁₂	C₂³×C₅	1	4	yes	—
230	C₂×C₄×D₃	—	2	8	no	—
231	C₂×C₄×D₃	—	2	16	no	—
232	C₂×C₄×D₃	C₂³×C₅	1	8	yes	—
233	C₂×C₄×D₃	C₂³×C₅	1	16	yes	—
234	C₂×Dic₆	—	2	16	no	—
235	C₂×Dic₆	C₅×D₄	1	8	yes	complemented
236	C₂×Dic₆	C₂³×C₅	1	16	yes	—
237	C₂×Dic₆	C₂³×C₅	1	4	yes	—
238	C₃×C₄⋊C₄	C₂³×C₅	1	8	yes	—
239	C₃×C₄⋊C₄	C₂³×C₅	1	8	yes	—
240	C₃×C₄²	C₂³×C₅	1	4	yes	—
241	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
242	(C₂×D₃)⋊C₄	C₂³×C₅	1	16	yes	—
243	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
244	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
245	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
246	Dic₃⋊C₄	C₂³×C₅	1	16	yes	—
247	C₄×Dic₃	C₂³×C₅	1	8	yes	—
248	C₂³×C₅	—	3	8	no	—
249	C₂³×C₅	—	3	4	no	—
250	C₂³×C₅	—	6	4	no	—
251	C₂³×C₅	—	6	4	no	—
252	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
253	C₅×Q₈	—	2	16	no	—
254	C₅×Q₈	—	3	16	no	—
255	C₅×Q₈	—	6	32	no	—
256	C₅×D₄	—	3	16	no	—
257	C₂×C₄×C₅	—	2	8	no	—
258	C₂×C₄×C₅	—	2	2	no	—
259	C₂×C₄×C₅	—	3	8	no	—
260	C₂×C₄×C₅	—	3	4	no	—
261	C₂×C₄×C₅	—	3	4	no	—
262	C₂×C₄×C₅	—	3	4	no	—
263	C₂×C₄×C₅	—	6	32	no	—
264	C₂×C₄×C₅	—	6	4	no	—
265	C₂×C₄×C₅	—	6	4	no	—
266	C₂×C₄×C₅	—	6	16	no	—
267	C₂×C₄×C₅	D₃×D₄	1	4	yes	—
268	C₂×C₄×C₅	D₃×Q₈	1	4	yes	complemented
269	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
270	C₂×C₄×C₅	C₂³×D₃	1	8	yes	—
271	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
272	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
273	C₂²×Q₈	—	3	16	no	—
274	C₂²×Q₈	—	3	1	no	—
275	C₂²×Q₈	—	3	4	no	—
276	C₂²×Q₈	—	6	16	no	—
277	C₂²×Q₈	C₂×C₅×D₃	1	2	yes	—
278	C₂²×D₄	—	3	1	no	—
279	C₂³×C₄	—	3	4	no	—
280	C₂³×C₄	—	3	2	no	—
281	C₄⋊Q₈	—	3	16	no	—
282	C₄⋊Q₈	C₂×C₅×D₃	1	8	yes	complemented
283	C₂²⋊Q₈	—	3	16	no	—
284	C₂²⋊Q₈	—	3	32	no	—
285	C₄×Q₈	—	3	8	no	—
286	C₄×D₄	—	3	16	no	—
287	C₄×D₄	—	3	8	no	—
288	C₂×C₄⋊C₄	—	3	1	no	—
289	C₂×C₄⋊C₄	—	3	2	no	—
290	C₂×C₄⋊C₄	—	3	1	no	—
291	C₂×C₄⋊C₄	—	3	4	no	—
292	C₂×C₄⋊C₄	C₂×C₅×D₃	1	2	yes	—
293	C₂×C₄⋊C₄	C₂×C₅×D₃	1	2	yes	—
294	C₂×C₂²⋊C₄	—	3	4	no	—
295	C₂×C₂²⋊C₄	—	3	2	no	—
296	C₂×C₄²	—	3	2	no	—
297	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
298	C₂×C₃×C₅	D₄×Q₈	1	4	yes	complemented
299	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
300	C₂×C₃×C₅	C₂³×Q₈	1	1	yes	characteristic
301	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
302	C₅×D₃	—	2	8	no	—
303	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
304	C₂²×D₃	—	2	4	no	—
305	C₂²×D₃	—	2	4	no	—
306	C₂²×D₃	C₂×C₅×Q₈	1	8	yes	complemented
307	C₂²×D₃	C₂⁴×C₅	1	4	yes	—
308	C₃×Q₈	—	2	16	no	—
309	C₂×C₃×C₄	—	2	8	no	—
310	C₂×C₃×C₄	—	2	2	no	—
311	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
312	C₂×C₃×C₄	C₂×C₅×Q₈	1	4	yes	complemented
313	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
314	C₂×C₃×C₄	C₂⁴×C₅	1	8	yes	—
315	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
316	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
317	C₂×Dic₃	—	2	4	no	—
318	C₂×Dic₃	—	2	4	no	—
319	C₂×Dic₃	C₂×C₅×D₄	1	8	yes	—
320	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
321	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
322	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
323	D₁₂	C₂×C₅×Q₈	1	16	yes	complemented
324	C₄×D₃	—	2	16	no	—
325	C₄×D₃	—	2	32	no	—
326	Dic₆	—	2	32	no	—
327	Dic₆	C₂×C₅×D₄	1	16	yes	complemented
328	C₂²×C₅	—	3	8	no	—
329	C₂²×C₅	—	6	4	no	—
330	C₂²×C₅	—	6	4	no	—
331	C₂²×C₅	—	6	16	no	—
332	C₂²×C₅	C₂×D₃×D₄	1	2	yes	—
333	C₂²×C₅	C₂×D₃×Q₈	1	2	yes	—
334	C₂²×C₅	#1007	1	2	yes	—
335	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
336	C₄×C₅	—	2	8	no	—
337	C₄×C₅	—	2	2	no	—
338	C₄×C₅	—	3	8	no	—
339	C₄×C₅	—	6	4	no	—
340	C₄×C₅	—	6	4	no	—
341	C₄×C₅	C₂×D₃×D₄	1	4	yes	—
342	C₄×C₅	C₂×D₃×Q₈	1	4	yes	complemented
343	C₂⁴	—	3	2	no	—
344	C₂×Q₈	—	2	8	no	—
345	C₂×Q₈	—	3	8	no	—
346	C₂×Q₈	—	3	4	no	—
347	C₂×Q₈	—	3	16	no	—
348	C₂×Q₈	—	6	16	no	—
349	C₂×Q₈	—	6	64	no	—
350	C₂×Q₈	C₂²×C₅×D₃	1	8	yes	—
351	C₂×D₄	—	3	8	no	—
352	C₂×D₄	—	3	4	no	—
353	C₂²×C₄	—	3	2	no	—
354	C₂²×C₄	—	3	2	no	—
355	C₂²×C₄	—	3	2	no	—
356	C₂²×C₄	—	3	16	no	—
357	C₂²×C₄	—	3	8	no	—
358	C₂²×C₄	—	6	16	no	—
359	C₂²×C₄	—	6	8	no	—
360	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
361	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
362	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
363	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
364	C₄⋊C₄	—	3	4	no	—
365	C₄⋊C₄	—	3	8	no	—
366	C₄⋊C₄	—	3	4	no	—
367	C₄⋊C₄	—	3	16	no	—
368	C₄⋊C₄	C₂²×C₅×D₃	1	8	yes	—
369	C₄⋊C₄	C₂²×C₅×D₃	1	8	yes	—
370	C₂²⋊C₄	—	3	16	no	—
371	C₂²⋊C₄	—	3	8	no	—
372	C₄²	—	3	8	no	—
373	C₄²	C₂²×C₅×D₃	1	4	yes	—
374	C₃×C₅	C₂×D₄×Q₈	1	1	yes	characteristic, complemented, Hall
375	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
376	C₂²×C₃	C₂²×C₅×Q₈	1	2	yes	—
377	C₂²×C₃	C₅×2₋¹⁺⁴	1	2	yes	—
378	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
379	C₂×D₃	—	2	16	no	—
380	C₂×D₃	—	2	4	no	—
381	C₂×D₃	—	2	4	no	—
382	C₂×D₃	C₂²×C₅×Q₈	1	8	yes	complemented
383	C₃×C₄	—	2	8	no	—
384	C₃×C₄	—	2	2	no	—
385	C₃×C₄	C₂²×C₅×D₄	1	4	yes	—
386	C₃×C₄	C₂²×C₅×Q₈	1	4	yes	complemented
387	Dic₃	—	2	4	no	—
388	Dic₃	—	2	4	no	—
389	Dic₃	C₂²×C₅×D₄	1	8	yes	—
390	C₂×C₅	—	6	8	no	—
391	C₂×C₅	#5727	1	4	yes	direct product factor
392	C₂×C₅	C₂²×D₃×D₄	1	1	yes	characteristic
393	C₂×C₅	C₂²×D₃×Q₈	1	1	yes	characteristic
394	C₂×C₅	C₂×#1007	1	1	yes	characteristic
395	C₂³	—	3	8	no	—
396	C₂³	—	3	4	no	—
397	C₂³	—	6	4	no	—
398	C₂³	—	6	4	no	—
399	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
400	Q₈	—	2	16	no	—
401	Q₈	—	3	16	no	—
402	Q₈	—	6	32	no	—
403	D₄	—	3	16	no	—
404	C₂×C₄	—	2	8	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	3	8	no	—
407	C₂×C₄	—	3	4	no	—
408	C₂×C₄	—	3	4	no	—
409	C₂×C₄	—	3	4	no	—
410	C₂×C₄	—	6	32	no	—
411	C₂×C₄	—	6	4	no	—
412	C₂×C₄	—	6	4	no	—
413	C₂×C₄	—	6	16	no	—
414	C₂×C₄	C₅×D₃×D₄	1	4	yes	—
415	C₂×C₄	C₅×D₃×Q₈	1	4	yes	complemented
416	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
417	C₂×C₄	C₂³×C₅×D₃	1	8	yes	—
418	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
419	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
420	C₂×C₃	C₅×D₄×Q₈	1	4	yes	complemented
421	C₂×C₃	C₂³×C₅×D₄	1	1	yes	characteristic
422	C₂×C₃	C₂³×C₅×Q₈	1	1	yes	characteristic
423	C₂×C₃	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
424	D₃	—	2	8	no	—
425	C₅	C₂×#5727	1	1	yes	characteristic, direct product factor, Sylow
426	C₂²	—	3	8	no	—
427	C₂²	—	6	4	no	—
428	C₂²	—	6	4	no	—
429	C₂²	—	6	16	no	—
430	C₂²	C₂×C₅×D₃×D₄	1	2	yes	—
431	C₂²	C₂×C₅×D₃×Q₈	1	2	yes	—
432	C₂²	C₅×#1007	1	2	yes	—
433	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
434	C₄	—	2	8	no	—
435	C₄	—	2	2	no	—
436	C₄	—	3	8	no	—
437	C₄	—	6	4	no	—
438	C₄	—	6	4	no	—
439	C₄	C₂×C₅×D₃×D₄	1	4	yes	—
440	C₄	C₂×C₅×D₃×Q₈	1	4	yes	complemented
441	C₃	C₂×C₅×D₄×Q₈	1	1	yes	characteristic, complemented, Sylow
442	C₂	—	6	8	no	—
443	C₂	C₅×#5727	1	4	yes	direct product factor
444	C₂	C₂²×C₅×D₃×D₄	1	1	yes	characteristic
445	C₂	C₂²×C₅×D₃×Q₈	1	1	yes	characteristic
446	C₂	C₂×C₅×#1007	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₂×C₃×C₅×C₄⋊Q₈	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂²×C₅×D₁₂	C₂²
hypercenter	C₂×C₅×C₄⋊Q₈	D₃
hypocenter	C₃	C₂×C₅×D₄×Q₈
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₅×C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×D₃×Q₈	C₂	semidirect
2. C₂×C₃×C₅×C₄⋊Q₈	C₂	semidirect
3. C₂×C₅×#946	C₂	semidirect
4. C₅×#5727	C₂	direct (N × H)
5. C₂×C₅×#896	C₂	semidirect
7. C₂×C₅×#888	C₂	semidirect
9. C₂×C₄×C₅×Dic₆	C₂	semidirect
13. C₂×C₅×D₃×Q₈	C₂²	semidirect
19. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
23. C₅×#946	C₂²	semidirect
31. C₅×#896	C₂²	semidirect
33. C₅×#888	C₂²	semidirect
35. C₄×C₅×Dic₆	C₂²	semidirect
36. C₂×#5727	C₅	direct (N × H)
40. C₂×C₅×C₄⋊Q₈	D₃	semidirect
57. C₂×C₅×D₁₂	Q₈	semidirect
64. C₂×C₅×Dic₆	D₄	semidirect
77. C₂²×D₃×Q₈	C₂×C₅	semidirect
78. C₂×C₃×C₄⋊Q₈	C₂×C₅	semidirect
79. C₂×#946	C₂×C₅	semidirect
80. #5727	C₂×C₅	direct (N × H)
81. C₂×#896	C₂×C₅	semidirect
83. C₂×#888	C₂×C₅	semidirect
85. C₂×C₄×Dic₆	C₂×C₅	semidirect
95. C₅×C₄⋊Q₈	C₂×D₃	semidirect
115. C₂²×C₅×D₃	C₂×Q₈	semidirect
121. C₂×C₃×C₄×C₅	C₂×Q₈	semidirect
132. C₅×D₁₂	C₂×Q₈	semidirect
136. C₅×Dic₆	C₂×D₄	semidirect
139. C₂×D₃×Q₈	C₂²×C₅	semidirect
145. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
149. #946	C₂²×C₅	semidirect
157. #896	C₂²×C₅	semidirect
159. #888	C₂²×C₅	semidirect
161. C₄×Dic₆	C₂²×C₅	semidirect
196. C₂×C₄⋊Q₈	C₅×D₃	semidirect
209. C₂×C₅×D₃	C₂²×Q₈	semidirect
213. C₃×C₄×C₅	C₂²×Q₈	semidirect
228. C₂×D₁₂	C₅×Q₈	semidirect
235. C₂×Dic₆	C₅×D₄	semidirect
268. C₂×C₄×C₅	D₃×Q₈	semidirect
282. C₄⋊Q₈	C₂×C₅×D₃	semidirect
298. C₂×C₃×C₅	D₄×Q₈	semidirect
306. C₂²×D₃	C₂×C₅×Q₈	semidirect
312. C₂×C₃×C₄	C₂×C₅×Q₈	semidirect
323. D₁₂	C₂×C₅×Q₈	semidirect
327. Dic₆	C₂×C₅×D₄	semidirect
342. C₄×C₅	C₂×D₃×Q₈	semidirect
374. C₃×C₅	C₂×D₄×Q₈	semidirect
382. C₂×D₃	C₂²×C₅×Q₈	semidirect
386. C₃×C₄	C₂²×C₅×Q₈	semidirect
391. C₂×C₅	#5727	direct (N × H)
415. C₂×C₄	C₅×D₃×Q₈	semidirect
420. C₂×C₃	C₅×D₄×Q₈	semidirect
425. C₅	C₂×#5727	direct (N × H)
440. C₄	C₂×C₅×D₃×Q₈	semidirect
441. C₃	C₂×C₅×D₄×Q₈	semidirect
443. C₂	C₅×#5727	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×D₃×Q₈	2
C₂×C₃×C₅×C₄⋊Q₈	2
C₂×C₅×#946	2
C₅×#5727	2
C₂×C₅×#896	2
C₂×C₅×#893	2
C₂×C₅×#888	2
C₂×C₄×C₅×D₁₂	2
C₂×C₄×C₅×Dic₆	2
C₂×C₅×D₄×Q₈	3
C₂×#5727	5

Subgroups — C2×C5×#5727 #14482905

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5727 #14482905