Subgroups — C₂²×D₈×D₁₅ #14509638

Order 1920.

3952 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₄×D₁₅	C₂	1	2	yes	maximal, complemented
2	C₂²×C₃×C₅×D₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#6715	C₂	1	2	yes	maximal, complemented
4	C₂×D₈×D₁₅	C₂	1	24	yes	maximal, direct product factor
5	C₂²×D₁₂₀	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₈×D₁₅	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×D₅×D₈	—	3	1	no	maximal, Hall
8	C₂⁴×D₁₅	—	2	2	no	—
9	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	complemented
10	C₂²×#1220	—	2	2	no	—
11	C₂×D₄×D₁₅	—	2	12	no	—
12	C₂×D₄×D₁₅	C₂²	1	24	yes	complemented
13	C₂²×D₆₀	C₂²	1	2	yes	complemented
14	C₂²×C₄×D₁₅	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×D₈	C₂²	1	12	yes	complemented
16	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
17	C₂×#6715	C₂²	1	24	yes	complemented
18	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic, complemented
19	D₈×D₁₅	C₂²	1	64	yes	direct product factor
20	C₂×D₁₂₀	C₂²	1	12	yes	complemented
21	C₂×C₈×D₁₅	C₂²	1	12	yes	complemented
22	C₂²×D₃×D₈	—	5	1	no	maximal, Hall
23	C₂²×D₄×D₅	—	3	2	no	—
24	C₂²×C₅×D₈	D₃	1	1	yes	characteristic, complemented
25	C₂²×#686	—	3	2	no	—
26	C₂×D₅×D₈	—	3	24	no	—
27	C₂²×D₄₀	—	3	1	no	—
28	C₂²×C₈×D₅	—	3	1	no	—
29	C₂⁴×C₃×C₅	—	2	2	no	—
30	C₂³×D₁₅	—	2	2	no	—
31	C₂³×D₁₅	—	2	24	no	—
32	C₂³×D₁₅	—	4	16	no	—
33	C₂³×D₁₅	D₄	1	1	yes	characteristic
34	C₂×C₃×C₅×D₄	—	2	6	no	—
35	C₂×C₃×C₅×D₄	C₂³	1	12	yes	complemented
36	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
37	C₂×#1220	—	2	24	no	—
38	C₂²×Dic₁₅	D₄	1	1	yes	characteristic
39	D₄×D₁₅	—	2	48	no	—
40	D₄×D₁₅	C₂³	1	32	yes	complemented
41	C₂×D₆₀	—	2	6	no	—
42	C₂×D₆₀	C₂³	1	12	yes	complemented
43	C₂×C₄×D₁₅	D₄	1	6	yes	—
44	C₂×C₄×D₁₅	C₂³	1	6	yes	—
45	C₃×C₅×D₈	C₂³	1	16	yes	complemented
46	C₂×C₃×C₅×C₈	C₂³	1	6	yes	complemented
47	#6715	C₂³	1	32	yes	complemented
48	C₂×C₃⋊#168	C₂³	1	6	yes	complemented
49	D₁₂₀	C₂³	1	16	yes	complemented
50	C₈×D₁₅	C₂³	1	16	yes	complemented
51	C₂²×D₃×D₄	—	5	2	no	—
52	C₂²×C₃×D₈	D₅	1	1	yes	characteristic, complemented
53	C₂²×#213	—	5	2	no	—
54	C₂×D₃×D₈	—	5	24	no	—
55	C₂²×D₂₄	—	5	1	no	—
56	C₂²×D₃×C₈	—	5	1	no	—
57	C₂⁴×D₅	—	6	2	no	—
58	C₂²×C₅×D₄	C₂×D₃	1	2	yes	complemented
59	C₂²×C₂²⋊D₅	—	6	2	no	—
60	C₂×D₄×D₅	—	3	24	no	—
61	C₂×D₄×D₅	—	6	12	no	—
62	C₂²×D₂₀	—	3	2	no	—
63	C₂²×C₄×D₅	—	3	1	no	—
64	C₂×C₅×D₈	C₂×D₃	1	12	yes	complemented
65	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic, complemented
66	C₂×#686	—	3	24	no	—
67	C₂²×#168	—	3	1	no	—
68	D₅×D₈	—	3	64	no	—
69	C₂×D₄₀	—	3	12	no	—
70	C₂×C₈×D₅	—	3	12	no	—
71	C₂³×D₈	—	15	1	no	Sylow
72	C₂³×C₃×C₅	—	2	12	no	—
73	C₂³×C₃×C₅	—	4	8	no	—
74	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
75	C₂²×D₁₅	—	2	12	no	—
76	C₂²×D₁₅	—	2	32	no	—
77	C₂²×D₁₅	—	4	8	no	—
78	C₂²×D₁₅	—	4	96	no	—
79	C₂²×D₁₅	D₈	1	8	yes	direct product factor
80	C₂²×D₁₅	C₂×D₄	1	6	yes	—
81	C₃×C₅×D₄	—	2	12	no	—
82	C₃×C₅×D₄	C₂⁴	1	8	yes	complemented
83	C₂×C₃×C₄×C₅	C₂×D₄	1	3	yes	—
84	C₂×C₃×C₄×C₅	C₂⁴	1	3	yes	—
85	#1220	—	2	32	no	—
86	C₂×Dic₁₅	C₂×D₄	1	6	yes	—
87	D₆₀	—	2	12	no	—
88	D₆₀	C₂⁴	1	8	yes	complemented
89	C₄×D₁₅	C₂×D₄	1	12	yes	—
90	C₄×D₁₅	C₂⁴	1	4	yes	—
91	C₃×C₅×C₈	C₂⁴	1	4	yes	complemented
92	C₃⋊#168	C₂⁴	1	4	yes	complemented
93	C₂⁴×D₃	—	10	2	no	—
94	C₂²×C₃×D₄	C₂×D₅	1	2	yes	complemented
95	C₂²×#67	—	10	2	no	—
96	C₂×D₃×D₄	—	5	24	no	—
97	C₂×D₃×D₄	—	10	12	no	—
98	C₂²×D₁₂	—	5	2	no	—
99	C₂²×C₄×D₃	—	5	1	no	—
100	C₂×C₃×D₈	C₂×D₅	1	12	yes	complemented
101	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic, complemented
102	C₂×#213	—	5	24	no	—
103	C₂²×C₃⋊C₈	—	5	1	no	—
104	D₃×D₈	—	5	64	no	—
105	C₂×D₂₄	—	5	12	no	—
106	C₂×D₃×C₈	—	5	12	no	—
107	C₂⁴×C₅	—	2	2	no	—
108	C₂³×D₅	—	3	1	no	—
109	C₂³×D₅	—	6	24	no	—
110	C₂³×D₅	—	6	2	no	—
111	C₂³×D₅	—	12	16	no	—
112	C₂×C₅×D₄	—	2	6	no	—
113	C₂×C₅×D₄	C₂²×D₃	1	12	yes	complemented
114	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
115	C₂×C₂²⋊D₅	—	6	24	no	—
116	C₂²×Dic₅	—	3	1	no	—
117	D₄×D₅	—	3	32	no	—
118	D₄×D₅	—	6	48	no	—
119	C₂×D₂₀	—	3	12	no	—
120	C₂×D₂₀	—	6	6	no	—
121	C₂×C₄×D₅	—	3	6	no	—
122	C₂×C₄×D₅	—	3	6	no	—
123	C₅×D₈	C₂²×D₃	1	16	yes	complemented
124	C₂×C₅×C₈	C₂²×D₃	1	6	yes	complemented
125	#686	—	3	32	no	—
126	C₂×#168	—	3	6	no	—
127	D₄₀	—	3	16	no	—
128	C₈×D₅	—	3	16	no	—
129	C₂³×D₄	—	15	2	no	—
130	C₂²×D₈	—	15	2	no	—
131	C₂²×D₈	—	15	24	no	—
132	C₂²×D₈	—	15	1	no	—
133	C₂²×D₈	D₁₅	1	1	yes	characteristic, direct product factor
134	C₂³×C₈	—	15	1	no	—
135	C₂²×C₃×C₅	—	2	8	no	—
136	C₂²×C₃×C₅	—	4	24	no	—
137	C₂²×C₃×C₅	C₂×D₈	1	4	yes	complemented
138	C₂²×C₃×C₅	C₂²×D₄	1	3	yes	—
139	C₂×D₁₅	—	2	8	no	—
140	C₂×D₁₅	—	4	24	no	—
141	C₂×D₁₅	—	4	64	no	—
142	C₂×D₁₅	C₂×D₈	1	24	yes	direct product factor
143	C₂×D₁₅	C₂²×D₄	1	4	yes	—
144	C₃×C₄×C₅	C₂²×D₄	1	3	yes	—
145	C₃×C₄×C₅	C₂⁵	1	1	yes	characteristic
146	Dic₁₅	C₂²×D₄	1	4	yes	—
147	C₂⁴×C₃	—	2	2	no	—
148	C₂³×D₃	—	5	1	no	—
149	C₂³×D₃	—	10	24	no	—
150	C₂³×D₃	—	10	2	no	—
151	C₂³×D₃	—	20	16	no	—
152	C₂×C₃×D₄	—	2	6	no	—
153	C₂×C₃×D₄	C₂²×D₅	1	12	yes	complemented
154	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
155	C₂×#67	—	10	24	no	—
156	C₂²×Dic₃	—	5	1	no	—
157	D₃×D₄	—	5	32	no	—
158	D₃×D₄	—	10	48	no	—
159	C₂×D₁₂	—	5	12	no	—
160	C₂×D₁₂	—	10	6	no	—
161	C₂×C₄×D₃	—	5	6	no	—
162	C₂×C₄×D₃	—	5	6	no	—
163	C₃×D₈	C₂²×D₅	1	16	yes	complemented
164	C₂×C₃×C₈	C₂²×D₅	1	6	yes	complemented
165	#213	—	5	32	no	—
166	C₂×C₃⋊C₈	—	5	6	no	—
167	D₂₄	—	5	16	no	—
168	D₃×C₈	—	5	16	no	—
169	C₂³×C₅	—	2	12	no	—
170	C₂³×C₅	—	4	8	no	—
171	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
172	C₂²×D₅	—	3	8	no	—
173	C₂²×D₅	—	3	6	no	—
174	C₂²×D₅	—	6	32	no	—
175	C₂²×D₅	—	6	12	no	—
176	C₂²×D₅	—	12	96	no	—
177	C₂²×D₅	—	12	8	no	—
178	C₅×D₄	—	2	12	no	—
179	C₅×D₄	C₂³×D₃	1	8	yes	complemented
180	C₂×C₄×C₅	D₃×D₄	1	3	yes	—
181	C₂×C₄×C₅	C₂³×D₃	1	3	yes	—
182	C₂²⋊D₅	—	6	32	no	—
183	C₂×Dic₅	—	3	6	no	—
184	D₂₀	—	3	8	no	—
185	D₂₀	—	6	12	no	—
186	C₄×D₅	—	3	12	no	—
187	C₄×D₅	—	3	4	no	—
188	C₅×C₈	C₂³×D₃	1	4	yes	complemented
189	#168	—	3	4	no	—
190	C₂⁵	—	30	2	no	—
191	C₂²×D₄	—	15	24	no	—
192	C₂²×D₄	—	15	2	no	—
193	C₂²×D₄	—	30	12	no	—
194	C₂²×D₄	—	30	2	no	—
195	C₂²×D₄	C₂×D₁₅	1	2	yes	complemented
196	C₂³×C₄	—	15	1	no	—
197	C₂×D₈	—	15	24	no	—
198	C₂×D₈	—	15	64	no	—
199	C₂×D₈	—	15	12	no	—
200	C₂×D₈	C₂×D₁₅	1	12	yes	direct product factor
201	C₂²×C₈	—	15	1	no	—
202	C₂²×C₈	—	15	12	no	—
203	C₂²×C₈	C₂×D₁₅	1	1	yes	characteristic, complemented
204	C₂×C₃×C₅	—	4	8	no	—
205	C₂×C₃×C₅	C₂²×D₈	1	6	yes	complemented
206	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
207	D₁₅	—	4	8	no	—
208	D₁₅	C₂²×D₈	1	8	yes	direct product factor
209	C₂³×C₃	—	2	12	no	—
210	C₂³×C₃	—	4	8	no	—
211	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
212	C₂²×D₃	—	5	6	no	—
213	C₂²×D₃	—	5	8	no	—
214	C₂²×D₃	—	10	32	no	—
215	C₂²×D₃	—	10	12	no	—
216	C₂²×D₃	—	20	96	no	—
217	C₂²×D₃	—	20	8	no	—
218	C₃×D₄	—	2	12	no	—
219	C₃×D₄	C₂³×D₅	1	8	yes	complemented
220	C₂×C₃×C₄	D₄×D₅	1	3	yes	—
221	C₂×C₃×C₄	C₂³×D₅	1	3	yes	—
222	#67	—	10	32	no	—
223	C₂×Dic₃	—	5	6	no	—
224	D₁₂	—	5	8	no	—
225	D₁₂	—	10	12	no	—
226	C₄×D₃	—	5	12	no	—
227	C₄×D₃	—	5	4	no	—
228	C₃×C₈	C₂³×D₅	1	4	yes	complemented
229	C₃⋊C₈	—	5	4	no	—
230	C₂²×C₅	—	2	8	no	—
231	C₂²×C₅	—	4	24	no	—
232	C₂²×C₅	D₃×D₈	1	4	yes	complemented
233	C₂²×C₅	C₂×D₃×D₄	1	3	yes	—
234	C₂×D₅	—	3	4	no	—
235	C₂×D₅	—	3	24	no	—
236	C₂×D₅	—	6	8	no	—
237	C₂×D₅	—	12	64	no	—
238	C₂×D₅	—	12	24	no	—
239	C₄×C₅	C₂×D₃×D₄	1	3	yes	—
240	C₄×C₅	C₂⁴×D₃	1	1	yes	characteristic
241	Dic₅	—	3	4	no	—
242	C₂⁴	—	2	2	no	—
243	C₂⁴	—	15	1	no	—
244	C₂⁴	—	30	24	no	—
245	C₂⁴	—	30	2	no	—
246	C₂⁴	—	60	16	no	—
247	C₂×D₄	—	2	6	no	—
248	C₂×D₄	—	15	32	no	—
249	C₂×D₄	—	15	12	no	—
250	C₂×D₄	—	30	48	no	—
251	C₂×D₄	—	30	24	no	—
252	C₂×D₄	—	30	6	no	—
253	C₂×D₄	C₂²×D₁₅	1	12	yes	complemented
254	C₂²×C₄	—	15	1	no	—
255	C₂²×C₄	—	15	6	no	—
256	C₂²×C₄	—	15	6	no	—
257	C₂²×C₄	C₂²×D₁₅	1	1	yes	characteristic
258	D₈	—	15	32	no	—
259	D₈	—	15	16	no	—
260	D₈	C₂²×D₁₅	1	16	yes	direct product factor
261	C₂×C₈	—	15	6	no	—
262	C₂×C₈	—	15	16	no	—
263	C₂×C₈	C₂²×D₁₅	1	6	yes	complemented
264	C₃×C₅	C₂³×D₈	1	1	yes	characteristic, complemented, Hall
265	C₂²×C₃	—	2	8	no	—
266	C₂²×C₃	—	4	24	no	—
267	C₂²×C₃	D₅×D₈	1	4	yes	complemented
268	C₂²×C₃	C₂×D₄×D₅	1	3	yes	—
269	C₂×D₃	—	5	24	no	—
270	C₂×D₃	—	5	4	no	—
271	C₂×D₃	—	10	8	no	—
272	C₂×D₃	—	20	64	no	—
273	C₂×D₃	—	20	24	no	—
274	C₃×C₄	C₂×D₄×D₅	1	3	yes	—
275	C₃×C₄	C₂⁴×D₅	1	1	yes	characteristic
276	Dic₃	—	5	4	no	—
277	C₂×C₅	—	4	8	no	—
278	C₂×C₅	C₂×D₃×D₈	1	6	yes	complemented
279	C₂×C₅	C₂²×D₃×D₄	1	1	yes	characteristic
280	D₅	—	3	8	no	—
281	D₅	—	12	8	no	—
282	C₂³	—	2	12	no	—
283	C₂³	—	4	8	no	—
284	C₂³	—	15	8	no	—
285	C₂³	—	15	6	no	—
286	C₂³	—	30	32	no	—
287	C₂³	—	30	12	no	—
288	C₂³	—	60	96	no	—
289	C₂³	—	60	8	no	—
290	C₂³	D₄×D₁₅	1	1	yes	characteristic
291	D₄	—	2	12	no	—
292	D₄	—	15	8	no	—
293	D₄	—	30	32	no	—
294	D₄	—	30	12	no	—
295	D₄	C₂³×D₁₅	1	8	yes	complemented
296	C₂×C₄	—	15	6	no	—
297	C₂×C₄	—	15	12	no	—
298	C₂×C₄	—	15	4	no	—
299	C₂×C₄	D₄×D₁₅	1	3	yes	—
300	C₂×C₄	C₂³×D₁₅	1	3	yes	—
301	C₈	—	15	4	no	—
302	C₈	C₂³×D₁₅	1	4	yes	complemented
303	C₂×C₃	—	4	8	no	—
304	C₂×C₃	C₂×D₅×D₈	1	6	yes	complemented
305	C₂×C₃	C₂²×D₄×D₅	1	1	yes	characteristic
306	D₃	—	5	8	no	—
307	D₃	—	20	8	no	—
308	C₅	C₂²×D₃×D₈	1	1	yes	characteristic, complemented, Sylow
309	C₂²	—	2	8	no	—
310	C₂²	—	4	24	no	—
311	C₂²	—	15	4	no	—
312	C₂²	—	15	24	no	—
313	C₂²	—	30	8	no	—
314	C₂²	—	60	64	no	—
315	C₂²	—	60	24	no	—
316	C₂²	D₈×D₁₅	1	4	yes	direct product factor
317	C₂²	C₂×D₄×D₁₅	1	3	yes	—
318	C₄	—	15	4	no	—
319	C₄	C₂×D₄×D₁₅	1	3	yes	—
320	C₄	C₂⁴×D₁₅	1	1	yes	characteristic
321	C₃	C₂²×D₅×D₈	1	1	yes	characteristic, complemented, Sylow
322	C₂	—	4	8	no	—
323	C₂	—	15	8	no	—
324	C₂	—	60	8	no	—
325	C₂	C₂×D₈×D₁₅	1	6	yes	direct product factor
326	C₂	C₂²×D₄×D₁₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₄×D₁₅
commutator, cosocle	C₃×C₄×C₅	C₂⁵
Frattini	C₄	C₂⁴×D₁₅
Fitting	C₂²×C₃×C₅×D₈	C₂
socle	C₂³×C₃×C₅	C₂×D₄
hypercenter	C₂²×D₈	D₁₅
hypocenter	C₃×C₅	C₂³×D₈
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×D₈

Complements

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

N	H ≅ G/N	type
1. C₂²×D₄×D₁₅	C₂	semidirect
2. C₂²×C₃×C₅×D₈	C₂	semidirect
3. C₂²×#6715	C₂	semidirect
4. C₂×D₈×D₁₅	C₂	direct (N × H)
5. C₂²×D₁₂₀	C₂	semidirect
6. C₂²×C₈×D₁₅	C₂	semidirect
9. C₂²×C₃×C₅×D₄	C₂²	semidirect
12. C₂×D₄×D₁₅	C₂²	semidirect
13. C₂²×D₆₀	C₂²	semidirect
15. C₂×C₃×C₅×D₈	C₂²	semidirect
16. C₂²×C₃×C₅×C₈	C₂²	semidirect
17. C₂×#6715	C₂²	semidirect
18. C₂²×C₃⋊#168	C₂²	semidirect
19. D₈×D₁₅	C₂²	direct (N × H)
20. C₂×D₁₂₀	C₂²	semidirect
21. C₂×C₈×D₁₅	C₂²	semidirect
24. C₂²×C₅×D₈	D₃	semidirect
35. C₂×C₃×C₅×D₄	C₂³	semidirect
40. D₄×D₁₅	C₂³	semidirect
42. C₂×D₆₀	C₂³	semidirect
45. C₃×C₅×D₈	C₂³	semidirect
46. C₂×C₃×C₅×C₈	C₂³	semidirect
47. #6715	C₂³	semidirect
48. C₂×C₃⋊#168	C₂³	semidirect
49. D₁₂₀	C₂³	semidirect
50. C₈×D₁₅	C₂³	semidirect
52. C₂²×C₃×D₈	D₅	semidirect
58. C₂²×C₅×D₄	C₂×D₃	semidirect
64. C₂×C₅×D₈	C₂×D₃	semidirect
65. C₂²×C₅×C₈	C₂×D₃	semidirect
79. C₂²×D₁₅	D₈	direct (N × H)
82. C₃×C₅×D₄	C₂⁴	semidirect
88. D₆₀	C₂⁴	semidirect
91. C₃×C₅×C₈	C₂⁴	semidirect
92. C₃⋊#168	C₂⁴	semidirect
94. C₂²×C₃×D₄	C₂×D₅	semidirect
100. C₂×C₃×D₈	C₂×D₅	semidirect
101. C₂²×C₃×C₈	C₂×D₅	semidirect
113. C₂×C₅×D₄	C₂²×D₃	semidirect
123. C₅×D₈	C₂²×D₃	semidirect
124. C₂×C₅×C₈	C₂²×D₃	semidirect
133. C₂²×D₈	D₁₅	direct (N × H)
137. C₂²×C₃×C₅	C₂×D₈	semidirect
142. C₂×D₁₅	C₂×D₈	direct (N × H)
153. C₂×C₃×D₄	C₂²×D₅	semidirect
163. C₃×D₈	C₂²×D₅	semidirect
164. C₂×C₃×C₈	C₂²×D₅	semidirect
179. C₅×D₄	C₂³×D₃	semidirect
188. C₅×C₈	C₂³×D₃	semidirect
195. C₂²×D₄	C₂×D₁₅	semidirect
200. C₂×D₈	C₂×D₁₅	direct (N × H)
203. C₂²×C₈	C₂×D₁₅	semidirect
205. C₂×C₃×C₅	C₂²×D₈	semidirect
208. D₁₅	C₂²×D₈	direct (N × H)
219. C₃×D₄	C₂³×D₅	semidirect
228. C₃×C₈	C₂³×D₅	semidirect
232. C₂²×C₅	D₃×D₈	semidirect
253. C₂×D₄	C₂²×D₁₅	semidirect
260. D₈	C₂²×D₁₅	direct (N × H)
263. C₂×C₈	C₂²×D₁₅	semidirect
264. C₃×C₅	C₂³×D₈	semidirect
267. C₂²×C₃	D₅×D₈	semidirect
278. C₂×C₅	C₂×D₃×D₈	semidirect
295. D₄	C₂³×D₁₅	semidirect
302. C₈	C₂³×D₁₅	semidirect
304. C₂×C₃	C₂×D₅×D₈	semidirect
308. C₅	C₂²×D₃×D₈	semidirect
316. C₂²	D₈×D₁₅	direct (N × H)
321. C₃	C₂²×D₅×D₈	semidirect
325. C₂	C₂×D₈×D₁₅	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×D₄×D₁₅	2
C₂²×C₃×C₅×D₈	2
C₂²×#6715	2
C₂×D₈×D₁₅	2
C₂²×D₁₂₀	2
C₂²×C₈×D₁₅	2
C₂²×D₅×D₈	3
C₂²×D₃×D₈	5

Subgroups — C22×D8×D15 #14509638

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×D₈×D₁₅ #14509638