Subgroups — C₅×D₃×D₄×Q₈ #14482896

Order 1920.

3136 conjugacy classes of subgroups.

The subgroup lattice has 580 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	C₃×C₅×D₄×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×Q₈×#67	C₂	1	2	yes	maximal, complemented
4	C₅×#5727	C₂	1	3	yes	maximal, complemented
5	C₅×D₃×C₄⋊Q₈	C₂	1	3	yes	maximal, complemented
6	C₅×#5632	C₂	1	6	yes	maximal, complemented
7	C₅×D₃×C₂²⋊Q₈	C₂	1	6	yes	maximal, complemented
8	C₅×Q₈×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×C₅×D₃×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₅×D₃×D₄	C₂	1	3	yes	maximal
11	C₅×D₄×Dic₆	C₂	1	3	yes	maximal, complemented
12	C₂×C₅×D₄×Q₈	—	3	1	no	maximal, Hall
13	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	complemented
14	C₂×C₅×D₃×Q₈	—	2	16	no	—
15	C₂×C₅×D₃×Q₈	C₂²	1	6	yes	—
16	C₂×C₅×D₃×Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₅×D₃×Q₈	C₂²	1	6	yes	complemented
18	C₂×C₅×D₃×Q₈	C₂²	1	2	yes	complemented
19	C₂×C₅×D₃×D₄	C₂²	1	1	yes	characteristic
20	C₂²×C₄×C₅×D₃	C₂²	1	6	yes	—
21	C₂²×C₅×Dic₆	C₂²	1	6	yes	complemented
22	C₃×C₅×C₄⋊Q₈	C₂²	1	3	yes	complemented
23	C₃×C₅×C₂²⋊Q₈	C₂²	1	6	yes	complemented
24	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
25	C₃×C₄×C₅×D₄	C₂²	1	3	yes	—
26	C₅×#946	C₂²	1	6	yes	complemented
27	C₅×Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
28	C₅×#944	C₂²	1	6	yes	complemented
29	C₅×D₄×Dic₃	C₂²	1	3	yes	—
30	C₄×C₅×#67	C₂²	1	6	yes	—
31	C₅×#924	C₂²	1	6	yes	complemented
32	C₅×#897	C₂²	1	6	yes	complemented
33	C₅×#896	C₂²	1	12	yes	complemented
34	C₅×#893	C₂²	1	3	yes	—
35	C₅×D₃×C₄⋊C₄	C₂²	1	3	yes	—
36	C₅×D₃×C₄⋊C₄	C₂²	1	6	yes	—
37	C₅×D₃×C₄⋊C₄	C₂²	1	3	yes	—
38	C₅×#888	C₂²	1	6	yes	complemented
39	C₅×#888	C₂²	1	6	yes	complemented
40	C₅×#887	C₂²	1	3	yes	complemented
41	C₅×#67⋊C₄	C₂²	1	6	yes	—
42	C₅×D₃×C₂²⋊C₄	C₂²	1	6	yes	—
43	C₅×#878	C₂²	1	12	yes	complemented
44	C₄×C₅×D₁₂	C₂²	1	3	yes	—
45	C₄²×C₅×D₃	C₂²	1	3	yes	—
46	C₅×#869	C₂²	1	3	yes	complemented
47	C₄×C₅×Dic₆	C₂²	1	3	yes	complemented
48	D₃×D₄×Q₈	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
49	C₂³×C₅×Q₈	—	3	2	no	—
50	C₅×D₄×Q₈	—	3	2	no	—
51	C₅×D₄×Q₈	—	3	3	no	—
52	C₅×D₄×Q₈	—	3	6	no	—
53	C₅×D₄×Q₈	—	3	1	no	—
54	C₅×D₄×Q₈	—	3	3	no	—
55	C₅×D₄×Q₈	D₃	1	1	yes	characteristic, direct product factor
56	C₂×C₅×C₄⋊Q₈	—	3	3	no	—
57	C₂×C₅×C₂²⋊Q₈	—	3	6	no	—
58	C₂×C₄×C₅×Q₈	—	3	1	no	—
59	C₂×C₄×C₅×D₄	—	3	3	no	—
60	C₂³×C₅×D₃	C₂³	1	2	yes	—
61	C₂×C₃×C₅×Q₈	—	2	8	no	—
62	C₂×C₃×C₅×Q₈	C₂³	1	6	yes	—
63	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
64	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
65	C₂²×C₃×C₄×C₅	C₂³	1	6	yes	—
66	C₂×C₅×#67	C₂³	1	2	yes	—
67	C₂²×C₅×Dic₃	C₂³	1	6	yes	—
68	C₅×D₃×Q₈	—	2	8	no	—
69	C₅×D₃×Q₈	—	2	24	no	—
70	C₅×D₃×Q₈	—	2	24	no	—
71	C₅×D₃×Q₈	D₄	1	8	yes	direct product factor
72	C₅×D₃×D₄	Q₈	1	8	yes	direct product factor
73	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
74	C₂×C₄×C₅×D₃	—	2	24	no	—
75	C₂×C₄×C₅×D₃	C₂³	1	3	yes	—
76	C₂×C₄×C₅×D₃	C₂³	1	6	yes	—
77	C₂×C₄×C₅×D₃	C₂³	1	6	yes	—
78	C₂×C₄×C₅×D₃	C₂³	1	6	yes	—
79	C₂×C₄×C₅×D₃	C₂³	1	3	yes	—
80	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
81	C₂×C₅×Dic₆	—	2	24	no	—
82	C₂×C₅×Dic₆	C₂³	1	6	yes	—
83	C₂×C₅×Dic₆	C₂³	1	12	yes	—
84	C₂×C₅×Dic₆	C₂³	1	3	yes	—
85	C₃×C₅×C₄⋊C₄	C₂³	1	3	yes	—
86	C₃×C₅×C₄⋊C₄	C₂³	1	3	yes	—
87	C₃×C₅×C₄⋊C₄	C₂³	1	6	yes	—
88	C₃×C₅×C₂²⋊C₄	C₂³	1	6	yes	—
89	C₃×C₄²×C₅	C₂³	1	3	yes	—
90	C₅×#217	C₂³	1	6	yes	—
91	C₅×(C₂×D₃)⋊C₄	C₂³	1	6	yes	—
92	C₅×(C₂×D₃)⋊C₄	C₂³	1	6	yes	—
93	C₅×C₄⋊Dic₃	C₂³	1	3	yes	—
94	C₅×C₄⋊Dic₃	C₂³	1	3	yes	—
95	C₅×C₄⋊Dic₃	C₂³	1	6	yes	—
96	C₅×Dic₃⋊C₄	C₂³	1	6	yes	—
97	C₅×Dic₃⋊C₄	C₂³	1	12	yes	—
98	C₅×Dic₃⋊C₄	C₂³	1	6	yes	—
99	C₄×C₅×Dic₃	C₂³	1	3	yes	—
100	C₄×C₅×Dic₃	C₂³	1	3	yes	—
101	C₄×C₅×Dic₃	C₂³	1	3	yes	—
102	C₂²×D₃×Q₈	C₂×C₅	1	2	yes	complemented
103	C₃×D₄×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
104	Q₈×#67	C₂×C₅	1	2	yes	complemented
105	#5727	C₂×C₅	1	3	yes	complemented
106	D₃×C₄⋊Q₈	C₂×C₅	1	3	yes	complemented
107	#5632	C₂×C₅	1	6	yes	complemented
108	D₃×C₂²⋊Q₈	C₂×C₅	1	6	yes	complemented
109	Q₈×D₁₂	C₂×C₅	1	1	yes	characteristic, complemented
110	C₄×D₃×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
111	C₄×D₃×D₄	C₂×C₅	1	3	yes	—
112	D₄×Dic₆	C₂×C₅	1	3	yes	complemented
113	C₂²×C₅×Q₈	—	3	1	no	—
114	C₂²×C₅×Q₈	—	3	6	no	—
115	C₂²×C₅×Q₈	—	3	6	no	—
116	C₂²×C₅×Q₈	—	3	2	no	—
117	C₂²×C₅×Q₈	—	3	6	no	—
118	C₂²×C₅×Q₈	—	6	16	no	—
119	C₂²×C₅×Q₈	C₂×D₃	1	2	yes	complemented
120	C₂²×C₅×D₄	—	3	1	no	—
121	C₂³×C₄×C₅	—	3	6	no	—
122	C₅×C₄⋊Q₈	—	3	6	no	—
123	C₅×C₄⋊Q₈	—	3	6	no	—
124	C₅×C₄⋊Q₈	—	3	6	no	—
125	C₅×C₄⋊Q₈	—	3	3	no	—
126	C₅×C₄⋊Q₈	C₂×D₃	1	3	yes	complemented
127	C₅×C₂²⋊Q₈	—	3	6	no	—
128	C₅×C₂²⋊Q₈	—	3	6	no	—
129	C₅×C₂²⋊Q₈	—	3	12	no	—
130	C₅×C₂²⋊Q₈	—	3	6	no	—
131	C₅×C₂²⋊Q₈	—	3	12	no	—
132	C₅×C₂²⋊Q₈	C₂×D₃	1	6	yes	complemented
133	C₄×C₅×Q₈	—	3	1	no	—
134	C₄×C₅×Q₈	—	3	3	no	—
135	C₄×C₅×Q₈	—	3	3	no	—
136	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
137	C₄×C₅×D₄	—	3	3	no	—
138	C₄×C₅×D₄	—	3	6	no	—
139	C₄×C₅×D₄	—	3	3	no	—
140	C₄×C₅×D₄	—	3	6	no	—
141	C₄×C₅×D₄	—	3	3	no	—
142	C₄×C₅×D₄	C₂×D₃	1	3	yes	—
143	C₂×C₅×C₄⋊C₄	—	3	3	no	—
144	C₂×C₅×C₄⋊C₄	—	3	3	no	—
145	C₂×C₅×C₄⋊C₄	—	3	6	no	—
146	C₂×C₅×C₂²⋊C₄	—	3	6	no	—
147	C₂×C₄²×C₅	—	3	3	no	—
148	C₂×D₄×Q₈	—	3	1	no	Sylow
149	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
150	C₂²×C₅×D₃	—	2	4	no	—
151	C₂²×C₅×D₃	—	2	4	no	—
152	C₂²×C₅×D₃	C₂×Q₈	1	8	yes	complemented
153	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
154	C₂²×C₅×D₃	C₂⁴	1	1	yes	characteristic
155	C₃×C₅×Q₈	—	2	12	no	—
156	C₃×C₅×Q₈	C₂×D₄	1	4	yes	complemented
157	C₃×C₅×D₄	C₂×Q₈	1	4	yes	complemented
158	C₂×C₃×C₄×C₅	—	2	12	no	—
159	C₂×C₃×C₄×C₅	C₂⁴	1	3	yes	—
160	C₂×C₃×C₄×C₅	C₂⁴	1	6	yes	—
161	C₂×C₃×C₄×C₅	C₂⁴	1	3	yes	—
162	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
163	C₅×#67	C₂×Q₈	1	8	yes	complemented
164	C₂×C₅×Dic₃	—	2	12	no	—
165	C₂×C₅×Dic₃	C₂⁴	1	3	yes	—
166	C₂×C₅×Dic₃	C₂⁴	1	6	yes	—
167	C₂×C₅×Dic₃	C₂⁴	1	3	yes	—
168	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
169	C₅×D₁₂	C₂×Q₈	1	4	yes	complemented
170	C₄×C₅×D₃	—	2	12	no	—
171	C₄×C₅×D₃	—	2	6	no	—
172	C₄×C₅×D₃	—	2	12	no	—
173	C₄×C₅×D₃	—	2	12	no	—
174	C₄×C₅×D₃	C₂×D₄	1	12	yes	—
175	C₄×C₅×D₃	C₂×Q₈	1	4	yes	complemented
176	C₅×Dic₆	—	2	12	no	—
177	C₅×Dic₆	—	2	24	no	—
178	C₅×Dic₆	C₂×D₄	1	12	yes	complemented
179	C₂²×C₃×Q₈	C₂²×C₅	1	2	yes	complemented
180	C₂×D₃×Q₈	—	2	16	no	—
181	C₂×D₃×Q₈	C₂²×C₅	1	6	yes	—
182	C₂×D₃×Q₈	C₂²×C₅	1	1	yes	characteristic
183	C₂×D₃×Q₈	C₂²×C₅	1	6	yes	complemented
184	C₂×D₃×Q₈	C₂²×C₅	1	2	yes	complemented
185	C₂×D₃×D₄	C₂²×C₅	1	1	yes	characteristic
186	C₂²×C₄×D₃	C₂²×C₅	1	6	yes	—
187	C₂²×Dic₆	C₂²×C₅	1	6	yes	complemented
188	C₃×C₄⋊Q₈	C₂²×C₅	1	3	yes	complemented
189	C₃×C₂²⋊Q₈	C₂²×C₅	1	6	yes	complemented
190	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
191	C₃×C₄×D₄	C₂²×C₅	1	3	yes	—
192	#946	C₂²×C₅	1	6	yes	complemented
193	Q₈×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
194	#944	C₂²×C₅	1	6	yes	complemented
195	D₄×Dic₃	C₂²×C₅	1	3	yes	—
196	C₄×#67	C₂²×C₅	1	6	yes	—
197	#924	C₂²×C₅	1	6	yes	complemented
198	#897	C₂²×C₅	1	6	yes	complemented
199	#896	C₂²×C₅	1	12	yes	complemented
200	#893	C₂²×C₅	1	3	yes	—
201	D₃×C₄⋊C₄	C₂²×C₅	1	3	yes	—
202	D₃×C₄⋊C₄	C₂²×C₅	1	6	yes	—
203	D₃×C₄⋊C₄	C₂²×C₅	1	3	yes	—
204	#888	C₂²×C₅	1	6	yes	complemented
205	#888	C₂²×C₅	1	6	yes	complemented
206	#887	C₂²×C₅	1	3	yes	complemented
207	#67⋊C₄	C₂²×C₅	1	6	yes	—
208	D₃×C₂²⋊C₄	C₂²×C₅	1	6	yes	—
209	#878	C₂²×C₅	1	12	yes	complemented
210	C₄×D₁₂	C₂²×C₅	1	3	yes	—
211	C₄²×D₃	C₂²×C₅	1	3	yes	—
212	#869	C₂²×C₅	1	3	yes	complemented
213	C₄×Dic₆	C₂²×C₅	1	3	yes	complemented
214	C₂⁴×C₅	—	3	2	no	—
215	C₂×C₅×Q₈	—	2	8	no	—
216	C₂×C₅×Q₈	—	3	8	no	—
217	C₂×C₅×Q₈	—	3	3	no	—
218	C₂×C₅×Q₈	—	3	12	no	—
219	C₂×C₅×Q₈	—	3	6	no	—
220	C₂×C₅×Q₈	—	6	24	no	—
221	C₂×C₅×Q₈	—	6	24	no	—
222	C₂×C₅×Q₈	—	6	24	no	—
223	C₂×C₅×Q₈	—	6	8	no	—
224	C₂×C₅×Q₈	C₂²×D₃	1	6	yes	—
225	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
226	C₂×C₅×D₄	—	3	2	no	—
227	C₂×C₅×D₄	—	3	8	no	—
228	C₂×C₅×D₄	—	3	1	no	—
229	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
230	C₂²×C₄×C₅	—	3	1	no	—
231	C₂²×C₄×C₅	—	3	3	no	—
232	C₂²×C₄×C₅	—	3	6	no	—
233	C₂²×C₄×C₅	—	3	3	no	—
234	C₂²×C₄×C₅	—	3	6	no	—
235	C₂²×C₄×C₅	—	3	6	no	—
236	C₂²×C₄×C₅	—	3	6	no	—
237	C₂²×C₄×C₅	—	6	24	no	—
238	C₂²×C₄×C₅	C₂²×D₃	1	6	yes	—
239	C₅×C₄⋊C₄	—	3	6	no	—
240	C₅×C₄⋊C₄	—	3	3	no	—
241	C₅×C₄⋊C₄	—	3	6	no	—
242	C₅×C₄⋊C₄	—	3	3	no	—
243	C₅×C₄⋊C₄	—	3	12	no	—
244	C₅×C₄⋊C₄	—	3	6	no	—
245	C₅×C₄⋊C₄	C₂²×D₃	1	3	yes	—
246	C₅×C₄⋊C₄	C₂²×D₃	1	3	yes	—
247	C₅×C₄⋊C₄	C₂²×D₃	1	6	yes	—
248	C₅×C₂²⋊C₄	—	3	6	no	—
249	C₅×C₂²⋊C₄	—	3	6	no	—
250	C₅×C₂²⋊C₄	—	3	6	no	—
251	C₅×C₂²⋊C₄	C₂²×D₃	1	6	yes	—
252	C₄²×C₅	—	3	3	no	—
253	C₄²×C₅	—	3	3	no	—
254	C₄²×C₅	—	3	3	no	—
255	C₄²×C₅	C₂²×D₃	1	3	yes	—
256	C₂³×Q₈	—	3	2	no	—
257	D₄×Q₈	—	3	2	no	—
258	D₄×Q₈	—	3	3	no	—
259	D₄×Q₈	—	3	6	no	—
260	D₄×Q₈	—	3	1	no	—
261	D₄×Q₈	—	3	3	no	—
262	D₄×Q₈	C₅×D₃	1	1	yes	characteristic, direct product factor
263	C₂×C₄⋊Q₈	—	3	3	no	—
264	C₂×C₂²⋊Q₈	—	3	6	no	—
265	C₂×C₄×Q₈	—	3	1	no	—
266	C₂×C₄×D₄	—	3	3	no	—
267	C₂²×C₃×C₅	—	2	2	no	—
268	C₂²×C₃×C₅	—	2	2	no	—
269	C₂²×C₃×C₅	C₂²×Q₈	1	4	yes	complemented
270	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
271	C₂×C₅×D₃	—	2	2	no	—
272	C₂×C₅×D₃	—	2	2	no	—
273	C₂×C₅×D₃	—	2	16	no	—
274	C₂×C₅×D₃	C₂²×D₄	1	2	yes	—
275	C₂×C₅×D₃	C₂²×Q₈	1	2	yes	—
276	C₂×C₅×D₃	C₂²×Q₈	1	4	yes	complemented
277	C₂×C₅×D₃	2₋¹⁺⁴	1	2	yes	—
278	C₃×C₄×C₅	—	2	6	no	—
279	C₃×C₄×C₅	—	2	3	no	—
280	C₃×C₄×C₅	C₂²×D₄	1	6	yes	—
281	C₃×C₄×C₅	C₂²×Q₈	1	2	yes	complemented
282	C₅×Dic₃	—	2	6	no	—
283	C₅×Dic₃	—	2	3	no	—
284	C₅×Dic₃	C₂²×D₄	1	6	yes	—
285	C₅×Dic₃	C₂²×Q₈	1	2	yes	complemented
286	C₂³×D₃	C₂³×C₅	1	2	yes	—
287	C₂×C₃×Q₈	—	2	8	no	—
288	C₂×C₃×Q₈	C₂³×C₅	1	6	yes	—
289	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
290	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
291	C₂²×C₃×C₄	C₂³×C₅	1	6	yes	—
292	C₂×#67	C₂³×C₅	1	2	yes	—
293	C₂²×Dic₃	C₂³×C₅	1	6	yes	—
294	D₃×Q₈	—	2	8	no	—
295	D₃×Q₈	—	2	24	no	—
296	D₃×Q₈	—	2	24	no	—
297	D₃×Q₈	C₅×D₄	1	8	yes	direct product factor
298	D₃×D₄	C₅×Q₈	1	8	yes	direct product factor
299	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
300	C₂×C₄×D₃	—	2	24	no	—
301	C₂×C₄×D₃	C₂³×C₅	1	3	yes	—
302	C₂×C₄×D₃	C₂³×C₅	1	6	yes	—
303	C₂×C₄×D₃	C₂³×C₅	1	6	yes	—
304	C₂×C₄×D₃	C₂³×C₅	1	6	yes	—
305	C₂×C₄×D₃	C₂³×C₅	1	3	yes	—
306	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
307	C₂×Dic₆	—	2	24	no	—
308	C₂×Dic₆	C₂³×C₅	1	6	yes	—
309	C₂×Dic₆	C₂³×C₅	1	12	yes	—
310	C₂×Dic₆	C₂³×C₅	1	3	yes	—
311	C₃×C₄⋊C₄	C₂³×C₅	1	3	yes	—
312	C₃×C₄⋊C₄	C₂³×C₅	1	3	yes	—
313	C₃×C₄⋊C₄	C₂³×C₅	1	6	yes	—
314	C₃×C₂²⋊C₄	C₂³×C₅	1	6	yes	—
315	C₃×C₄²	C₂³×C₅	1	3	yes	—
316	#217	C₂³×C₅	1	6	yes	—
317	(C₂×D₃)⋊C₄	C₂³×C₅	1	6	yes	—
318	(C₂×D₃)⋊C₄	C₂³×C₅	1	6	yes	—
319	C₄⋊Dic₃	C₂³×C₅	1	3	yes	—
320	C₄⋊Dic₃	C₂³×C₅	1	3	yes	—
321	C₄⋊Dic₃	C₂³×C₅	1	6	yes	—
322	Dic₃⋊C₄	C₂³×C₅	1	6	yes	—
323	Dic₃⋊C₄	C₂³×C₅	1	12	yes	—
324	Dic₃⋊C₄	C₂³×C₅	1	6	yes	—
325	C₄×Dic₃	C₂³×C₅	1	3	yes	—
326	C₄×Dic₃	C₂³×C₅	1	3	yes	—
327	C₄×Dic₃	C₂³×C₅	1	3	yes	—
328	C₂³×C₅	—	3	1	no	—
329	C₂³×C₅	—	3	8	no	—
330	C₂³×C₅	—	3	2	no	—
331	C₂³×C₅	—	6	4	no	—
332	C₂³×C₅	—	6	4	no	—
333	C₂³×C₅	C₂³×D₃	1	2	yes	—
334	C₅×Q₈	—	2	12	no	—
335	C₅×Q₈	—	3	12	no	—
336	C₅×Q₈	—	6	24	no	—
337	C₅×Q₈	—	6	12	no	—
338	C₅×Q₈	D₃×D₄	1	4	yes	direct product factor
339	C₅×D₄	—	3	8	no	—
340	C₅×D₄	—	3	4	no	—
341	C₅×D₄	D₃×Q₈	1	4	yes	direct product factor
342	C₂×C₄×C₅	—	2	12	no	—
343	C₂×C₄×C₅	—	3	1	no	—
344	C₂×C₄×C₅	—	3	3	no	—
345	C₂×C₄×C₅	—	3	12	no	—
346	C₂×C₄×C₅	—	3	4	no	—
347	C₂×C₄×C₅	—	3	3	no	—
348	C₂×C₄×C₅	—	3	6	no	—
349	C₂×C₄×C₅	—	6	12	no	—
350	C₂×C₄×C₅	—	6	6	no	—
351	C₂×C₄×C₅	—	6	12	no	—
352	C₂×C₄×C₅	—	6	12	no	—
353	C₂×C₄×C₅	—	6	12	no	—
354	C₂×C₄×C₅	C₂³×D₃	1	3	yes	—
355	C₂×C₄×C₅	C₂³×D₃	1	6	yes	—
356	C₂×C₄×C₅	C₂³×D₃	1	3	yes	—
357	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
358	C₂²×Q₈	—	3	1	no	—
359	C₂²×Q₈	—	3	6	no	—
360	C₂²×Q₈	—	3	6	no	—
361	C₂²×Q₈	—	3	2	no	—
362	C₂²×Q₈	—	3	6	no	—
363	C₂²×Q₈	—	6	16	no	—
364	C₂²×Q₈	C₂×C₅×D₃	1	2	yes	complemented
365	C₂²×D₄	—	3	1	no	—
366	C₂³×C₄	—	3	6	no	—
367	C₄⋊Q₈	—	3	6	no	—
368	C₄⋊Q₈	—	3	6	no	—
369	C₄⋊Q₈	—	3	6	no	—
370	C₄⋊Q₈	—	3	3	no	—
371	C₄⋊Q₈	C₂×C₅×D₃	1	3	yes	complemented
372	C₂²⋊Q₈	—	3	6	no	—
373	C₂²⋊Q₈	—	3	6	no	—
374	C₂²⋊Q₈	—	3	12	no	—
375	C₂²⋊Q₈	—	3	6	no	—
376	C₂²⋊Q₈	—	3	12	no	—
377	C₂²⋊Q₈	C₂×C₅×D₃	1	6	yes	complemented
378	C₄×Q₈	—	3	1	no	—
379	C₄×Q₈	—	3	3	no	—
380	C₄×Q₈	—	3	3	no	—
381	C₄×Q₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
382	C₄×D₄	—	3	3	no	—
383	C₄×D₄	—	3	6	no	—
384	C₄×D₄	—	3	3	no	—
385	C₄×D₄	—	3	6	no	—
386	C₄×D₄	—	3	3	no	—
387	C₄×D₄	C₂×C₅×D₃	1	3	yes	—
388	C₂×C₄⋊C₄	—	3	3	no	—
389	C₂×C₄⋊C₄	—	3	3	no	—
390	C₂×C₄⋊C₄	—	3	6	no	—
391	C₂×C₂²⋊C₄	—	3	6	no	—
392	C₂×C₄²	—	3	3	no	—
393	C₂×C₃×C₅	—	2	4	no	—
394	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
395	C₂×C₃×C₅	C₂³×Q₈	1	1	yes	characteristic
396	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
397	C₅×D₃	—	2	4	no	—
398	C₅×D₃	D₄×Q₈	1	4	yes	direct product factor
399	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
400	C₂²×D₃	—	2	4	no	—
401	C₂²×D₃	—	2	4	no	—
402	C₂²×D₃	C₂×C₅×Q₈	1	8	yes	complemented
403	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
404	C₂²×D₃	C₂⁴×C₅	1	1	yes	characteristic
405	C₃×Q₈	—	2	12	no	—
406	C₃×Q₈	C₂×C₅×D₄	1	4	yes	complemented
407	C₃×D₄	C₂×C₅×Q₈	1	4	yes	complemented
408	C₂×C₃×C₄	—	2	12	no	—
409	C₂×C₃×C₄	C₂⁴×C₅	1	3	yes	—
410	C₂×C₃×C₄	C₂⁴×C₅	1	6	yes	—
411	C₂×C₃×C₄	C₂⁴×C₅	1	3	yes	—
412	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
413	#67	C₂×C₅×Q₈	1	8	yes	complemented
414	C₂×Dic₃	—	2	12	no	—
415	C₂×Dic₃	C₂⁴×C₅	1	3	yes	—
416	C₂×Dic₃	C₂⁴×C₅	1	6	yes	—
417	C₂×Dic₃	C₂⁴×C₅	1	3	yes	—
418	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
419	D₁₂	C₂×C₅×Q₈	1	4	yes	complemented
420	C₄×D₃	—	2	12	no	—
421	C₄×D₃	—	2	6	no	—
422	C₄×D₃	—	2	12	no	—
423	C₄×D₃	—	2	12	no	—
424	C₄×D₃	C₂×C₅×D₄	1	12	yes	—
425	C₄×D₃	C₂×C₅×Q₈	1	4	yes	complemented
426	Dic₆	—	2	12	no	—
427	Dic₆	—	2	24	no	—
428	Dic₆	C₂×C₅×D₄	1	12	yes	complemented
429	C₂²×C₅	—	2	2	no	—
430	C₂²×C₅	—	2	2	no	—
431	C₂²×C₅	—	3	2	no	—
432	C₂²×C₅	—	3	2	no	—
433	C₂²×C₅	—	3	2	no	—
434	C₂²×C₅	—	3	4	no	—
435	C₂²×C₅	—	6	16	no	—
436	C₂²×C₅	—	6	2	no	—
437	C₂²×C₅	—	6	2	no	—
438	C₂²×C₅	C₂×D₃×Q₈	1	4	yes	complemented
439	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
440	C₄×C₅	—	2	6	no	—
441	C₄×C₅	—	2	3	no	—
442	C₄×C₅	—	3	6	no	—
443	C₄×C₅	—	3	2	no	—
444	C₄×C₅	—	6	6	no	—
445	C₄×C₅	—	6	3	no	—
446	C₄×C₅	C₂×D₃×D₄	1	6	yes	—
447	C₄×C₅	C₂×D₃×Q₈	1	2	yes	complemented
448	C₂⁴	—	3	2	no	—
449	C₂×Q₈	—	2	8	no	—
450	C₂×Q₈	—	3	8	no	—
451	C₂×Q₈	—	3	3	no	—
452	C₂×Q₈	—	3	12	no	—
453	C₂×Q₈	—	3	6	no	—
454	C₂×Q₈	—	6	24	no	—
455	C₂×Q₈	—	6	24	no	—
456	C₂×Q₈	—	6	24	no	—
457	C₂×Q₈	—	6	8	no	—
458	C₂×Q₈	C₂²×C₅×D₃	1	6	yes	—
459	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
460	C₂×D₄	—	3	2	no	—
461	C₂×D₄	—	3	8	no	—
462	C₂×D₄	—	3	1	no	—
463	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
464	C₂²×C₄	—	3	1	no	—
465	C₂²×C₄	—	3	3	no	—
466	C₂²×C₄	—	3	6	no	—
467	C₂²×C₄	—	3	3	no	—
468	C₂²×C₄	—	3	6	no	—
469	C₂²×C₄	—	3	6	no	—
470	C₂²×C₄	—	3	6	no	—
471	C₂²×C₄	—	6	24	no	—
472	C₂²×C₄	C₂²×C₅×D₃	1	6	yes	—
473	C₄⋊C₄	—	3	6	no	—
474	C₄⋊C₄	—	3	3	no	—
475	C₄⋊C₄	—	3	6	no	—
476	C₄⋊C₄	—	3	3	no	—
477	C₄⋊C₄	—	3	12	no	—
478	C₄⋊C₄	—	3	6	no	—
479	C₄⋊C₄	C₂²×C₅×D₃	1	3	yes	—
480	C₄⋊C₄	C₂²×C₅×D₃	1	3	yes	—
481	C₄⋊C₄	C₂²×C₅×D₃	1	6	yes	—
482	C₂²⋊C₄	—	3	6	no	—
483	C₂²⋊C₄	—	3	6	no	—
484	C₂²⋊C₄	—	3	6	no	—
485	C₂²⋊C₄	C₂²×C₅×D₃	1	6	yes	—
486	C₄²	—	3	3	no	—
487	C₄²	—	3	3	no	—
488	C₄²	—	3	3	no	—
489	C₄²	C₂²×C₅×D₃	1	3	yes	—
490	C₃×C₅	C₂×D₄×Q₈	1	1	yes	characteristic, complemented, Hall
491	C₂²×C₃	—	2	2	no	—
492	C₂²×C₃	—	2	2	no	—
493	C₂²×C₃	C₂²×C₅×Q₈	1	4	yes	complemented
494	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
495	C₂×D₃	—	2	2	no	—
496	C₂×D₃	—	2	2	no	—
497	C₂×D₃	—	2	16	no	—
498	C₂×D₃	C₂²×C₅×D₄	1	2	yes	—
499	C₂×D₃	C₂²×C₅×Q₈	1	2	yes	—
500	C₂×D₃	C₂²×C₅×Q₈	1	4	yes	complemented
501	C₂×D₃	C₅×2₋¹⁺⁴	1	2	yes	—
502	C₃×C₄	—	2	6	no	—
503	C₃×C₄	—	2	3	no	—
504	C₃×C₄	C₂²×C₅×D₄	1	6	yes	—
505	C₃×C₄	C₂²×C₅×Q₈	1	2	yes	complemented
506	Dic₃	—	2	6	no	—
507	Dic₃	—	2	3	no	—
508	Dic₃	C₂²×C₅×D₄	1	6	yes	—
509	Dic₃	C₂²×C₅×Q₈	1	2	yes	complemented
510	C₂×C₅	—	2	4	no	—
511	C₂×C₅	—	3	4	no	—
512	C₂×C₅	—	6	4	no	—
513	C₂×C₅	C₂²×D₃×D₄	1	1	yes	characteristic
514	C₂×C₅	C₂²×D₃×Q₈	1	1	yes	characteristic
515	C₂×C₅	D₃×2₋¹⁺⁴	1	1	yes	characteristic
516	C₂³	—	3	1	no	—
517	C₂³	—	3	8	no	—
518	C₂³	—	3	2	no	—
519	C₂³	—	6	4	no	—
520	C₂³	—	6	4	no	—
521	C₂³	C₂³×C₅×D₃	1	2	yes	—
522	Q₈	—	2	12	no	—
523	Q₈	—	3	12	no	—
524	Q₈	—	6	24	no	—
525	Q₈	—	6	12	no	—
526	Q₈	C₅×D₃×D₄	1	4	yes	direct product factor
527	D₄	—	3	8	no	—
528	D₄	—	3	4	no	—
529	D₄	C₅×D₃×Q₈	1	4	yes	direct product factor
530	C₂×C₄	—	2	12	no	—
531	C₂×C₄	—	3	1	no	—
532	C₂×C₄	—	3	3	no	—
533	C₂×C₄	—	3	12	no	—
534	C₂×C₄	—	3	4	no	—
535	C₂×C₄	—	3	3	no	—
536	C₂×C₄	—	3	6	no	—
537	C₂×C₄	—	6	12	no	—
538	C₂×C₄	—	6	12	no	—
539	C₂×C₄	—	6	6	no	—
540	C₂×C₄	—	6	12	no	—
541	C₂×C₄	—	6	12	no	—
542	C₂×C₄	C₂³×C₅×D₃	1	3	yes	—
543	C₂×C₄	C₂³×C₅×D₃	1	6	yes	—
544	C₂×C₄	C₂³×C₅×D₃	1	3	yes	—
545	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
546	C₂×C₃	—	2	4	no	—
547	C₂×C₃	C₂³×C₅×D₄	1	1	yes	characteristic
548	C₂×C₃	C₂³×C₅×Q₈	1	1	yes	characteristic
549	C₂×C₃	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
550	D₃	—	2	4	no	—
551	D₃	C₅×D₄×Q₈	1	4	yes	direct product factor
552	C₅	D₃×D₄×Q₈	1	1	yes	characteristic, direct product factor, Sylow
553	C₂²	—	2	2	no	—
554	C₂²	—	2	2	no	—
555	C₂²	—	3	2	no	—
556	C₂²	—	3	2	no	—
557	C₂²	—	3	2	no	—
558	C₂²	—	3	4	no	—
559	C₂²	—	6	16	no	—
560	C₂²	—	6	2	no	—
561	C₂²	—	6	2	no	—
562	C₂²	C₂×C₅×D₃×Q₈	1	4	yes	complemented
563	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
564	C₄	—	2	6	no	—
565	C₄	—	2	3	no	—
566	C₄	—	3	6	no	—
567	C₄	—	3	2	no	—
568	C₄	—	6	6	no	—
569	C₄	—	6	3	no	—
570	C₄	C₂×C₅×D₃×D₄	1	6	yes	—
571	C₄	C₂×C₅×D₃×Q₈	1	2	yes	complemented
572	C₃	C₂×C₅×D₄×Q₈	1	1	yes	characteristic, complemented, Sylow
573	C₂	—	2	4	no	—
574	C₂	—	3	4	no	—
575	C₂	—	6	4	no	—
576	C₂	C₂²×C₅×D₃×D₄	1	1	yes	characteristic
577	C₂	C₂²×C₅×D₃×Q₈	1	1	yes	characteristic
578	C₂	C₅×D₃×2₋¹⁺⁴	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂⁴×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₃×C₅×D₄×Q₈	C₂
socle	C₂²×C₃×C₅	C₂⁵
prime radical	C₂×C₅×D₃×D₄	C₂²
hypercenter	C₅×D₄×Q₈	D₃
hypocenter	C₃	C₂×C₅×D₄×Q₈
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₅×D₄×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. C₃×C₅×D₄×Q₈	C₂	semidirect
3. C₅×Q₈×#67	C₂	semidirect
4. C₅×#5727	C₂	semidirect
5. C₅×D₃×C₄⋊Q₈	C₂	semidirect
6. C₅×#5632	C₂	semidirect
7. C₅×D₃×C₂²⋊Q₈	C₂	semidirect
8. C₅×Q₈×D₁₂	C₂	semidirect
9. C₄×C₅×D₃×Q₈	C₂	semidirect
11. C₅×D₄×Dic₆	C₂	semidirect
13. C₂²×C₃×C₅×Q₈	C₂²	semidirect
17. C₂×C₅×D₃×Q₈	C₂²	semidirect
18. C₂×C₅×D₃×Q₈	C₂²	semidirect
21. C₂²×C₅×Dic₆	C₂²	semidirect
22. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
23. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
24. C₃×C₄×C₅×Q₈	C₂²	semidirect
26. C₅×#946	C₂²	semidirect
27. C₅×Q₈×Dic₃	C₂²	semidirect
28. C₅×#944	C₂²	semidirect
31. C₅×#924	C₂²	semidirect
32. C₅×#897	C₂²	semidirect
33. C₅×#896	C₂²	semidirect
38. C₅×#888	C₂²	semidirect
39. C₅×#888	C₂²	semidirect
40. C₅×#887	C₂²	semidirect
43. C₅×#878	C₂²	semidirect
46. C₅×#869	C₂²	semidirect
47. C₄×C₅×Dic₆	C₂²	semidirect
48. D₃×D₄×Q₈	C₅	direct (N × H)
55. C₅×D₄×Q₈	D₃	direct (N × H)
71. C₅×D₃×Q₈	D₄	direct (N × H)
72. C₅×D₃×D₄	Q₈	direct (N × H)
102. C₂²×D₃×Q₈	C₂×C₅	semidirect
103. C₃×D₄×Q₈	C₂×C₅	semidirect
104. Q₈×#67	C₂×C₅	semidirect
105. #5727	C₂×C₅	semidirect
106. D₃×C₄⋊Q₈	C₂×C₅	semidirect
107. #5632	C₂×C₅	semidirect
108. D₃×C₂²⋊Q₈	C₂×C₅	semidirect
109. Q₈×D₁₂	C₂×C₅	semidirect
110. C₄×D₃×Q₈	C₂×C₅	semidirect
112. D₄×Dic₆	C₂×C₅	semidirect
119. C₂²×C₅×Q₈	C₂×D₃	semidirect
126. C₅×C₄⋊Q₈	C₂×D₃	semidirect
132. C₅×C₂²⋊Q₈	C₂×D₃	semidirect
136. C₄×C₅×Q₈	C₂×D₃	semidirect
152. C₂²×C₅×D₃	C₂×Q₈	semidirect
156. C₃×C₅×Q₈	C₂×D₄	semidirect
157. C₃×C₅×D₄	C₂×Q₈	semidirect
163. C₅×#67	C₂×Q₈	semidirect
169. C₅×D₁₂	C₂×Q₈	semidirect
175. C₄×C₅×D₃	C₂×Q₈	semidirect
178. C₅×Dic₆	C₂×D₄	semidirect
179. C₂²×C₃×Q₈	C₂²×C₅	semidirect
183. C₂×D₃×Q₈	C₂²×C₅	semidirect
184. C₂×D₃×Q₈	C₂²×C₅	semidirect
187. C₂²×Dic₆	C₂²×C₅	semidirect
188. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
189. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
190. C₃×C₄×Q₈	C₂²×C₅	semidirect
192. #946	C₂²×C₅	semidirect
193. Q₈×Dic₃	C₂²×C₅	semidirect
194. #944	C₂²×C₅	semidirect
197. #924	C₂²×C₅	semidirect
198. #897	C₂²×C₅	semidirect
199. #896	C₂²×C₅	semidirect
204. #888	C₂²×C₅	semidirect
205. #888	C₂²×C₅	semidirect
206. #887	C₂²×C₅	semidirect
209. #878	C₂²×C₅	semidirect
212. #869	C₂²×C₅	semidirect
213. C₄×Dic₆	C₂²×C₅	semidirect
262. D₄×Q₈	C₅×D₃	direct (N × H)
269. C₂²×C₃×C₅	C₂²×Q₈	semidirect
276. C₂×C₅×D₃	C₂²×Q₈	semidirect
281. C₃×C₄×C₅	C₂²×Q₈	semidirect
285. C₅×Dic₃	C₂²×Q₈	semidirect
297. D₃×Q₈	C₅×D₄	direct (N × H)
298. D₃×D₄	C₅×Q₈	direct (N × H)
338. C₅×Q₈	D₃×D₄	direct (N × H)
341. C₅×D₄	D₃×Q₈	direct (N × H)
364. C₂²×Q₈	C₂×C₅×D₃	semidirect
371. C₄⋊Q₈	C₂×C₅×D₃	semidirect
377. C₂²⋊Q₈	C₂×C₅×D₃	semidirect
381. C₄×Q₈	C₂×C₅×D₃	semidirect
398. C₅×D₃	D₄×Q₈	direct (N × H)
402. C₂²×D₃	C₂×C₅×Q₈	semidirect
406. C₃×Q₈	C₂×C₅×D₄	semidirect
407. C₃×D₄	C₂×C₅×Q₈	semidirect
413. #67	C₂×C₅×Q₈	semidirect
419. D₁₂	C₂×C₅×Q₈	semidirect
425. C₄×D₃	C₂×C₅×Q₈	semidirect
428. Dic₆	C₂×C₅×D₄	semidirect
438. C₂²×C₅	C₂×D₃×Q₈	semidirect
447. C₄×C₅	C₂×D₃×Q₈	semidirect
490. C₃×C₅	C₂×D₄×Q₈	semidirect
493. C₂²×C₃	C₂²×C₅×Q₈	semidirect
500. C₂×D₃	C₂²×C₅×Q₈	semidirect
505. C₃×C₄	C₂²×C₅×Q₈	semidirect
509. Dic₃	C₂²×C₅×Q₈	semidirect
526. Q₈	C₅×D₃×D₄	direct (N × H)
529. D₄	C₅×D₃×Q₈	direct (N × H)
551. D₃	C₅×D₄×Q₈	direct (N × H)
552. C₅	D₃×D₄×Q₈	direct (N × H)
562. C₂²	C₂×C₅×D₃×Q₈	semidirect
571. C₄	C₂×C₅×D₃×Q₈	semidirect
572. C₃	C₂×C₅×D₄×Q₈	semidirect

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
C₃×C₅×D₄×Q₈	2
C₅×Q₈×#67	2
C₅×#5727	2
C₅×D₃×C₄⋊Q₈	2
C₅×#5632	2
C₅×D₃×C₂²⋊Q₈	2
C₅×Q₈×D₁₂	2
C₄×C₅×D₃×Q₈	2
C₄×C₅×D₃×D₄	2
C₅×D₄×Dic₆	2
C₂×C₅×D₄×Q₈	3
D₃×D₄×Q₈	5

Subgroups — C5×D3×D4×Q8 #14482896

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×D₄×Q₈ #14482896