Subgroups — C₂×C₅×Q₈×D₁₂ #14482911

Order 1920.

3136 conjugacy classes of subgroups.

The subgroup lattice has 304 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×C₄×C₅×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×Q₈×D₁₂	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₅×#897	C₂	1	6	yes	maximal, complemented
5	C₂×C₄×C₅×D₁₂	C₂	1	3	yes	maximal
6	C₂×C₅×#869	C₂	1	3	yes	maximal, complemented
7	C₂×C₅×D₄×Q₈	—	3	1	no	maximal, Hall
8	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
9	C₂×C₅×D₃×Q₈	—	2	16	no	—
10	C₂×C₅×D₃×Q₈	C₂²	1	16	yes	complemented
11	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
12	C₂²×C₄×C₅×D₃	C₂²	1	6	yes	—
13	C₂²×C₅×Dic₆	C₂²	1	6	yes	—
14	C₃×C₄×C₅×Q₈	C₂²	1	8	yes	complemented
15	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	3	yes	—
16	C₂×C₃×C₄²×C₅	C₂²	1	3	yes	—
17	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	6	yes	—
18	C₂×C₅×C₄⋊Dic₃	C₂²	1	3	yes	—
19	C₂×C₅×C₄⋊Dic₃	C₂²	1	6	yes	—
20	C₅×#897	C₂²	1	48	yes	complemented
21	C₄×C₅×D₁₂	C₂²	1	24	yes	—
22	C₅×#869	C₂²	1	24	yes	complemented
23	C₂×Q₈×D₁₂	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
24	C₂³×C₅×Q₈	—	3	2	no	—
25	C₅×D₄×Q₈	—	3	16	no	—
26	C₂×C₅×C₄⋊Q₈	—	3	3	no	—
27	C₂×C₅×C₂²⋊Q₈	—	3	6	no	—
28	C₂×C₄×C₅×Q₈	D₃	1	1	yes	characteristic, complemented
29	C₂×C₄×C₅×D₄	—	3	3	no	—
30	C₂³×C₅×D₃	C₂³	1	2	yes	—
31	C₂×C₃×C₅×Q₈	D₄	1	8	yes	complemented
32	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	—
33	C₂²×C₃×C₄×C₅	C₂³	1	3	yes	—
34	C₂²×C₃×C₄×C₅	C₂³	1	3	yes	—
35	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
36	C₂²×C₅×Dic₃	C₂³	1	6	yes	—
37	C₅×D₃×Q₈	—	2	64	no	—
38	C₂×C₅×D₁₂	Q₈	1	8	yes	direct product factor
39	C₂×C₅×D₁₂	C₂³	1	4	yes	—
40	C₂×C₄×C₅×D₃	—	2	24	no	—
41	C₂×C₄×C₅×D₃	C₂³	1	24	yes	—
42	C₂×C₅×Dic₆	—	2	24	no	—
43	C₂×C₅×Dic₆	C₂³	1	24	yes	—
44	C₃×C₅×C₄⋊C₄	C₂³	1	12	yes	—
45	C₃×C₄²×C₅	C₂³	1	12	yes	—
46	C₅×(C₂×D₃)⋊C₄	C₂³	1	24	yes	—
47	C₅×C₄⋊Dic₃	C₂³	1	12	yes	—
48	C₅×C₄⋊Dic₃	C₂³	1	24	yes	—
49	C₂²×D₃×Q₈	C₂×C₅	1	2	yes	complemented
50	C₂×C₃×C₄×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
51	Q₈×D₁₂	C₂×C₅	1	16	yes	direct product factor
52	C₂×#897	C₂×C₅	1	6	yes	complemented
53	C₂×C₄×D₁₂	C₂×C₅	1	3	yes	—
54	C₂×#869	C₂×C₅	1	3	yes	complemented
55	C₂²×C₅×Q₈	—	3	16	no	—
56	C₂²×C₅×Q₈	—	3	6	no	—
57	C₂²×C₅×Q₈	—	6	16	no	—
58	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
59	C₂²×C₅×D₄	—	3	1	no	—
60	C₂³×C₄×C₅	—	3	6	no	—
61	C₅×C₄⋊Q₈	—	3	24	no	—
62	C₅×C₂²⋊Q₈	—	3	48	no	—
63	C₄×C₅×Q₈	C₂×D₃	1	8	yes	complemented
64	C₄×C₅×D₄	—	3	24	no	—
65	C₂×C₅×C₄⋊C₄	—	3	3	no	—
66	C₂×C₅×C₄⋊C₄	—	3	6	no	—
67	C₂×C₅×C₄⋊C₄	C₂×D₃	1	3	yes	—
68	C₂×C₅×C₂²⋊C₄	—	3	6	no	—
69	C₂×C₄²×C₅	C₂×D₃	1	3	yes	—
70	C₂×D₄×Q₈	—	3	1	no	Sylow
71	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
72	C₂²×C₅×D₃	—	2	4	no	—
73	C₂²×C₅×D₃	—	2	4	no	—
74	C₂²×C₅×D₃	C₂×Q₈	1	8	yes	complemented
75	C₂²×C₅×D₃	C₂⁴	1	4	yes	—
76	C₃×C₅×Q₈	C₂×D₄	1	16	yes	complemented
77	C₂×C₃×C₄×C₅	—	2	6	no	—
78	C₂×C₃×C₄×C₅	C₂×D₄	1	12	yes	—
79	C₂×C₃×C₄×C₅	C₂×Q₈	1	4	yes	complemented
80	C₂×C₃×C₄×C₅	C₂⁴	1	6	yes	—
81	C₂×C₃×C₄×C₅	C₂⁴	1	6	yes	—
82	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
83	C₂×C₅×Dic₃	—	2	12	no	—
84	C₂×C₅×Dic₃	C₂⁴	1	12	yes	—
85	C₅×D₁₂	C₂×Q₈	1	16	yes	direct product factor
86	C₄×C₅×D₃	—	2	48	no	—
87	C₅×Dic₆	—	2	48	no	—
88	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
89	C₂×D₃×Q₈	—	2	16	no	—
90	C₂×D₃×Q₈	C₂²×C₅	1	16	yes	complemented
91	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
92	C₂²×C₄×D₃	C₂²×C₅	1	6	yes	—
93	C₂²×Dic₆	C₂²×C₅	1	6	yes	—
94	C₃×C₄×Q₈	C₂²×C₅	1	8	yes	complemented
95	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	3	yes	—
96	C₂×C₃×C₄²	C₂²×C₅	1	3	yes	—
97	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	6	yes	—
98	C₂×C₄⋊Dic₃	C₂²×C₅	1	3	yes	—
99	C₂×C₄⋊Dic₃	C₂²×C₅	1	6	yes	—
100	#897	C₂²×C₅	1	48	yes	complemented
101	C₄×D₁₂	C₂²×C₅	1	24	yes	—
102	#869	C₂²×C₅	1	24	yes	complemented
103	C₂⁴×C₅	—	3	2	no	—
104	C₂×C₅×Q₈	—	3	24	no	—
105	C₂×C₅×Q₈	—	6	64	no	—
106	C₂×C₅×Q₈	—	6	24	no	—
107	C₂×C₅×Q₈	D₁₂	1	8	yes	direct product factor
108	C₂×C₅×Q₈	C₂²×D₃	1	4	yes	—
109	C₂×C₅×D₄	—	3	8	no	—
110	C₂×C₅×D₄	—	3	4	no	—
111	C₂²×C₄×C₅	—	3	6	no	—
112	C₂²×C₄×C₅	—	3	24	no	—
113	C₂²×C₄×C₅	—	6	24	no	—
114	C₂²×C₄×C₅	C₂²×D₃	1	3	yes	—
115	C₂²×C₄×C₅	C₂²×D₃	1	3	yes	—
116	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
117	C₅×C₄⋊C₄	—	3	12	no	—
118	C₅×C₄⋊C₄	—	3	24	no	—
119	C₅×C₄⋊C₄	C₂²×D₃	1	12	yes	—
120	C₅×C₂²⋊C₄	—	3	24	no	—
121	C₄²×C₅	C₂²×D₃	1	12	yes	—
122	C₂³×Q₈	—	3	2	no	—
123	D₄×Q₈	—	3	16	no	—
124	C₂×C₄⋊Q₈	—	3	3	no	—
125	C₂×C₂²⋊Q₈	—	3	6	no	—
126	C₂×C₄×Q₈	C₅×D₃	1	1	yes	characteristic, complemented
127	C₂×C₄×D₄	—	3	3	no	—
128	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
129	C₂²×C₃×C₅	C₂²×Q₈	1	2	yes	—
130	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
131	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
132	C₂×C₅×D₃	—	2	16	no	—
133	C₂×C₅×D₃	—	2	4	no	—
134	C₂×C₅×D₃	—	2	4	no	—
135	C₂×C₅×D₃	C₂²×Q₈	1	8	yes	complemented
136	C₃×C₄×C₅	—	2	6	no	—
137	C₃×C₄×C₅	C₂²×D₄	1	12	yes	—
138	C₃×C₄×C₅	C₂²×Q₈	1	4	yes	complemented
139	C₅×Dic₃	—	2	12	no	—
140	C₂³×D₃	C₂³×C₅	1	2	yes	—
141	C₂×C₃×Q₈	C₅×D₄	1	8	yes	complemented
142	C₂×C₃×Q₈	C₂³×C₅	1	4	yes	—
143	C₂²×C₃×C₄	C₂³×C₅	1	3	yes	—
144	C₂²×C₃×C₄	C₂³×C₅	1	3	yes	—
145	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
146	C₂²×Dic₃	C₂³×C₅	1	6	yes	—
147	D₃×Q₈	—	2	64	no	—
148	C₂×D₁₂	C₅×Q₈	1	8	yes	direct product factor
149	C₂×D₁₂	C₂³×C₅	1	4	yes	—
150	C₂×C₄×D₃	—	2	24	no	—
151	C₂×C₄×D₃	C₂³×C₅	1	24	yes	—
152	C₂×Dic₆	—	2	24	no	—
153	C₂×Dic₆	C₂³×C₅	1	24	yes	—
154	C₃×C₄⋊C₄	C₂³×C₅	1	12	yes	—
155	C₃×C₄²	C₂³×C₅	1	12	yes	—
156	(C₂×D₃)⋊C₄	C₂³×C₅	1	24	yes	—
157	C₄⋊Dic₃	C₂³×C₅	1	12	yes	—
158	C₄⋊Dic₃	C₂³×C₅	1	24	yes	—
159	C₂³×C₅	—	3	8	no	—
160	C₂³×C₅	—	3	4	no	—
161	C₂³×C₅	—	6	4	no	—
162	C₂³×C₅	—	6	4	no	—
163	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
164	C₅×Q₈	—	6	48	no	—
165	C₅×Q₈	C₂×D₁₂	1	16	yes	direct product factor
166	C₅×D₄	—	3	16	no	—
167	C₂×C₄×C₅	—	2	6	no	—
168	C₂×C₄×C₅	—	3	12	no	—
169	C₂×C₄×C₅	—	6	12	no	—
170	C₂×C₄×C₅	—	6	48	no	—
171	C₂×C₄×C₅	C₂×D₁₂	1	12	yes	—
172	C₂×C₄×C₅	D₃×Q₈	1	4	yes	complemented
173	C₂×C₄×C₅	C₂³×D₃	1	6	yes	—
174	C₂×C₄×C₅	C₂³×D₃	1	6	yes	—
175	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
176	C₂²×Q₈	—	3	16	no	—
177	C₂²×Q₈	—	3	6	no	—
178	C₂²×Q₈	—	6	16	no	—
179	C₂²×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
180	C₂²×D₄	—	3	1	no	—
181	C₂³×C₄	—	3	6	no	—
182	C₄⋊Q₈	—	3	24	no	—
183	C₂²⋊Q₈	—	3	48	no	—
184	C₄×Q₈	C₂×C₅×D₃	1	8	yes	complemented
185	C₄×D₄	—	3	24	no	—
186	C₂×C₄⋊C₄	—	3	3	no	—
187	C₂×C₄⋊C₄	—	3	6	no	—
188	C₂×C₄⋊C₄	C₂×C₅×D₃	1	3	yes	—
189	C₂×C₂²⋊C₄	—	3	6	no	—
190	C₂×C₄²	C₂×C₅×D₃	1	3	yes	—
191	C₂×C₃×C₅	D₄×Q₈	1	4	yes	complemented
192	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
193	C₂×C₃×C₅	C₂³×Q₈	1	1	yes	characteristic
194	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
195	C₅×D₃	—	2	8	no	—
196	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
197	C₂²×D₃	—	2	4	no	—
198	C₂²×D₃	—	2	4	no	—
199	C₂²×D₃	C₂×C₅×Q₈	1	8	yes	complemented
200	C₂²×D₃	C₂⁴×C₅	1	4	yes	—
201	C₃×Q₈	C₂×C₅×D₄	1	16	yes	complemented
202	C₂×C₃×C₄	—	2	6	no	—
203	C₂×C₃×C₄	C₂×C₅×D₄	1	12	yes	—
204	C₂×C₃×C₄	C₂×C₅×Q₈	1	4	yes	complemented
205	C₂×C₃×C₄	C₂⁴×C₅	1	6	yes	—
206	C₂×C₃×C₄	C₂⁴×C₅	1	6	yes	—
207	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
208	C₂×Dic₃	—	2	12	no	—
209	C₂×Dic₃	C₂⁴×C₅	1	12	yes	—
210	D₁₂	C₂×C₅×Q₈	1	16	yes	direct product factor
211	C₄×D₃	—	2	48	no	—
212	Dic₆	—	2	48	no	—
213	C₂²×C₅	—	3	8	no	—
214	C₂²×C₅	—	6	4	no	—
215	C₂²×C₅	—	6	4	no	—
216	C₂²×C₅	—	6	16	no	—
217	C₂²×C₅	C₂²×D₁₂	1	2	yes	—
218	C₂²×C₅	C₂×D₃×Q₈	1	2	yes	—
219	C₂²×C₅	#1010	1	2	yes	—
220	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
221	C₄×C₅	—	2	6	no	—
222	C₄×C₅	—	6	12	no	—
223	C₄×C₅	C₂²×D₁₂	1	12	yes	—
224	C₄×C₅	C₂×D₃×Q₈	1	4	yes	complemented
225	C₂⁴	—	3	2	no	—
226	C₂×Q₈	—	3	24	no	—
227	C₂×Q₈	—	6	64	no	—
228	C₂×Q₈	—	6	24	no	—
229	C₂×Q₈	C₅×D₁₂	1	8	yes	direct product factor
230	C₂×Q₈	C₂²×C₅×D₃	1	4	yes	—
231	C₂×D₄	—	3	8	no	—
232	C₂×D₄	—	3	4	no	—
233	C₂²×C₄	—	3	6	no	—
234	C₂²×C₄	—	3	24	no	—
235	C₂²×C₄	—	6	24	no	—
236	C₂²×C₄	C₂²×C₅×D₃	1	3	yes	—
237	C₂²×C₄	C₂²×C₅×D₃	1	3	yes	—
238	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
239	C₄⋊C₄	—	3	12	no	—
240	C₄⋊C₄	—	3	24	no	—
241	C₄⋊C₄	C₂²×C₅×D₃	1	12	yes	—
242	C₂²⋊C₄	—	3	24	no	—
243	C₄²	C₂²×C₅×D₃	1	12	yes	—
244	C₃×C₅	C₂×D₄×Q₈	1	1	yes	characteristic, complemented, Hall
245	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
246	C₂²×C₃	C₂²×C₅×Q₈	1	2	yes	—
247	C₂²×C₃	C₅×2₋¹⁺⁴	1	2	yes	—
248	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
249	C₂×D₃	—	2	16	no	—
250	C₂×D₃	—	2	4	no	—
251	C₂×D₃	—	2	4	no	—
252	C₂×D₃	C₂²×C₅×Q₈	1	8	yes	complemented
253	C₃×C₄	—	2	6	no	—
254	C₃×C₄	C₂²×C₅×D₄	1	12	yes	—
255	C₃×C₄	C₂²×C₅×Q₈	1	4	yes	complemented
256	Dic₃	—	2	12	no	—
257	C₂×C₅	—	6	8	no	—
258	C₂×C₅	Q₈×D₁₂	1	4	yes	direct product factor
259	C₂×C₅	C₂³×D₁₂	1	1	yes	characteristic
260	C₂×C₅	C₂²×D₃×Q₈	1	1	yes	characteristic
261	C₂×C₅	C₂×#1010	1	1	yes	characteristic
262	C₂³	—	3	8	no	—
263	C₂³	—	3	4	no	—
264	C₂³	—	6	4	no	—
265	C₂³	—	6	4	no	—
266	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
267	Q₈	—	6	48	no	—
268	Q₈	C₂×C₅×D₁₂	1	16	yes	direct product factor
269	D₄	—	3	16	no	—
270	C₂×C₄	—	2	6	no	—
271	C₂×C₄	—	3	12	no	—
272	C₂×C₄	—	6	12	no	—
273	C₂×C₄	—	6	48	no	—
274	C₂×C₄	C₂×C₅×D₁₂	1	12	yes	—
275	C₂×C₄	C₅×D₃×Q₈	1	4	yes	complemented
276	C₂×C₄	C₂³×C₅×D₃	1	6	yes	—
277	C₂×C₄	C₂³×C₅×D₃	1	6	yes	—
278	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
279	C₂×C₃	C₅×D₄×Q₈	1	4	yes	complemented
280	C₂×C₃	C₂³×C₅×D₄	1	1	yes	characteristic
281	C₂×C₃	C₂³×C₅×Q₈	1	1	yes	characteristic
282	C₂×C₃	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
283	D₃	—	2	8	no	—
284	C₅	C₂×Q₈×D₁₂	1	1	yes	characteristic, direct product factor, Sylow
285	C₂²	—	3	8	no	—
286	C₂²	—	6	4	no	—
287	C₂²	—	6	4	no	—
288	C₂²	—	6	16	no	—
289	C₂²	C₂²×C₅×D₁₂	1	2	yes	—
290	C₂²	C₂×C₅×D₃×Q₈	1	2	yes	—
291	C₂²	C₅×#1010	1	2	yes	—
292	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
293	C₄	—	2	6	no	—
294	C₄	—	6	12	no	—
295	C₄	C₂²×C₅×D₁₂	1	12	yes	—
296	C₄	C₂×C₅×D₃×Q₈	1	4	yes	complemented
297	C₃	C₂×C₅×D₄×Q₈	1	1	yes	characteristic, complemented, Sylow
298	C₂	—	6	8	no	—
299	C₂	C₅×Q₈×D₁₂	1	4	yes	direct product factor
300	C₂	C₂³×C₅×D₁₂	1	1	yes	characteristic
301	C₂	C₂²×C₅×D₃×Q₈	1	1	yes	characteristic
302	C₂	C₂×C₅×#1010	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×C₄×C₅×Q₈	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂²×C₅×D₁₂	C₂²
hypercenter	C₂×C₄×C₅×Q₈	D₃
hypocenter	C₃	C₂×C₅×D₄×Q₈
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₄×C₅×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×C₄×C₅×Q₈	C₂	semidirect
3. C₅×Q₈×D₁₂	C₂	direct (N × H)
4. C₂×C₅×#897	C₂	semidirect
6. C₂×C₅×#869	C₂	semidirect
10. C₂×C₅×D₃×Q₈	C₂²	semidirect
14. C₃×C₄×C₅×Q₈	C₂²	semidirect
20. C₅×#897	C₂²	semidirect
22. C₅×#869	C₂²	semidirect
23. C₂×Q₈×D₁₂	C₅	direct (N × H)
28. C₂×C₄×C₅×Q₈	D₃	semidirect
31. C₂×C₃×C₅×Q₈	D₄	semidirect
38. C₂×C₅×D₁₂	Q₈	direct (N × H)
49. C₂²×D₃×Q₈	C₂×C₅	semidirect
50. C₂×C₃×C₄×Q₈	C₂×C₅	semidirect
51. Q₈×D₁₂	C₂×C₅	direct (N × H)
52. C₂×#897	C₂×C₅	semidirect
54. C₂×#869	C₂×C₅	semidirect
63. C₄×C₅×Q₈	C₂×D₃	semidirect
74. C₂²×C₅×D₃	C₂×Q₈	semidirect
76. C₃×C₅×Q₈	C₂×D₄	semidirect
79. C₂×C₃×C₄×C₅	C₂×Q₈	semidirect
85. C₅×D₁₂	C₂×Q₈	direct (N × H)
90. C₂×D₃×Q₈	C₂²×C₅	semidirect
94. C₃×C₄×Q₈	C₂²×C₅	semidirect
100. #897	C₂²×C₅	semidirect
102. #869	C₂²×C₅	semidirect
107. C₂×C₅×Q₈	D₁₂	direct (N × H)
126. C₂×C₄×Q₈	C₅×D₃	semidirect
135. C₂×C₅×D₃	C₂²×Q₈	semidirect
138. C₃×C₄×C₅	C₂²×Q₈	semidirect
141. C₂×C₃×Q₈	C₅×D₄	semidirect
148. C₂×D₁₂	C₅×Q₈	direct (N × H)
165. C₅×Q₈	C₂×D₁₂	direct (N × H)
172. C₂×C₄×C₅	D₃×Q₈	semidirect
184. C₄×Q₈	C₂×C₅×D₃	semidirect
191. C₂×C₃×C₅	D₄×Q₈	semidirect
199. C₂²×D₃	C₂×C₅×Q₈	semidirect
201. C₃×Q₈	C₂×C₅×D₄	semidirect
204. C₂×C₃×C₄	C₂×C₅×Q₈	semidirect
210. D₁₂	C₂×C₅×Q₈	direct (N × H)
224. C₄×C₅	C₂×D₃×Q₈	semidirect
229. C₂×Q₈	C₅×D₁₂	direct (N × H)
244. C₃×C₅	C₂×D₄×Q₈	semidirect
252. C₂×D₃	C₂²×C₅×Q₈	semidirect
255. C₃×C₄	C₂²×C₅×Q₈	semidirect
258. C₂×C₅	Q₈×D₁₂	direct (N × H)
268. Q₈	C₂×C₅×D₁₂	direct (N × H)
275. C₂×C₄	C₅×D₃×Q₈	semidirect
279. C₂×C₃	C₅×D₄×Q₈	semidirect
284. C₅	C₂×Q₈×D₁₂	direct (N × H)
296. C₄	C₂×C₅×D₃×Q₈	semidirect
297. C₃	C₂×C₅×D₄×Q₈	semidirect
299. C₂	C₅×Q₈×D₁₂	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×C₄×C₅×Q₈	2
C₅×Q₈×D₁₂	2
C₂×C₅×#897	2
C₂×C₄×C₅×D₁₂	2
C₂×C₅×#869	2
C₂×C₅×D₄×Q₈	3
C₂×Q₈×D₁₂	5

Subgroups — C2×C5×Q8×D12 #14482911

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×Q₈×D₁₂ #14482911