Subgroups — C₂×#11756476 #14482414

Order 1920.

5072 conjugacy classes of subgroups.

The subgroup lattice has 352 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	4	yes	maximal, complemented
2	C₂×C₃×C₅×#127	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#91827	C₂	1	4	yes	maximal, complemented
4	C₂×#91826	C₂	1	4	yes	maximal, complemented
5	#11756476	C₂	1	16	yes	maximal, direct product factor
6	C₂×C₄×D₆₀	C₂	1	2	yes	maximal, complemented
7	C₂×#66051	—	3	1	no	maximal, Hall
8	C₂⁴×D₁₅	C₂²	1	4	yes	complemented
9	C₂²×C₃×C₅×D₄	C₂²	1	4	yes	complemented
10	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	complemented
11	C₂²×#1220	C₂²	1	8	yes	complemented
12	C₂×D₄×D₁₅	—	2	32	no	—
13	C₂×D₄×D₁₅	C₂²	1	32	yes	complemented
14	C₂²×D₆₀	C₂²	1	2	yes	—
15	C₂²×C₄×D₁₅	C₂²	1	4	yes	complemented
16	C₃×C₅×#127	C₂²	1	8	yes	complemented
17	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
18	C₂×#6719	C₂²	1	4	yes	complemented
19	#91827	C₂²	1	32	yes	complemented
20	#91826	C₂²	1	32	yes	complemented
21	C₂×#6714	C₂²	1	4	yes	complemented
22	C₂×C₄⋊Dic₁₅	C₂²	1	2	yes	complemented
23	C₄×D₆₀	C₂²	1	16	yes	complemented
24	C₂×#5717	—	5	1	no	maximal, Hall
25	C₂²×D₄×D₅	—	3	4	no	—
26	C₂×C₅×#127	D₃	1	1	yes	characteristic, complemented
27	C₂×#4084	—	3	4	no	—
28	C₂×#4083	—	3	4	no	—
29	#66051	—	3	16	no	—
30	C₂×C₄×D₂₀	—	3	2	no	—
31	C₂⁴×C₃×C₅	C₂³	1	4	yes	—
32	C₂³×D₁₅	—	2	32	no	—
33	C₂³×D₁₅	—	4	8	no	—
34	C₂³×D₁₅	C₂³	1	4	yes	—
35	C₂³×D₁₅	C₂³	1	16	yes	complemented
36	C₂×C₃×C₅×D₄	—	2	16	no	—
37	C₂×C₃×C₅×D₄	—	4	4	no	—
38	C₂×C₃×C₅×D₄	C₂³	1	16	yes	complemented
39	C₂×C₃×C₅×D₄	C₂³	1	8	yes	complemented
40	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
41	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
42	C₂×#1220	—	2	32	no	—
43	C₂×#1220	C₂³	1	32	yes	complemented
44	C₂²×Dic₁₅	C₂³	1	4	yes	—
45	D₄×D₁₅	—	2	128	no	—
46	C₂×D₆₀	D₄	1	16	yes	complemented
47	C₂×D₆₀	C₂³	1	8	yes	—
48	C₂×C₄×D₁₅	—	2	16	no	—
49	C₂×C₄×D₁₅	C₂³	1	16	yes	complemented
50	C₃×C₄²×C₅	C₂³	1	4	yes	complemented
51	#6719	C₂³	1	16	yes	complemented
52	#6714	C₂³	1	16	yes	complemented
53	C₄⋊Dic₁₅	C₂³	1	8	yes	complemented
54	C₂²×D₃×D₄	—	5	4	no	—
55	C₂×C₃×#127	D₅	1	1	yes	characteristic, complemented
56	C₂×#938	—	5	4	no	—
57	C₂×#937	—	5	4	no	—
58	#5717	—	5	16	no	—
59	C₂×C₄×D₁₂	—	5	2	no	—
60	C₂⁴×D₅	—	3	4	no	—
61	C₂²×C₅×D₄	C₂×D₃	1	4	yes	complemented
62	C₂²×C₅×D₄	C₂×D₃	1	2	yes	complemented
63	C₂²×C₂²⋊D₅	—	3	8	no	—
64	C₂×D₄×D₅	—	3	32	no	—
65	C₂×D₄×D₅	—	6	32	no	—
66	C₂²×D₂₀	—	3	2	no	—
67	C₂²×C₄×D₅	—	3	4	no	—
68	C₅×#127	C₂×D₃	1	8	yes	complemented
69	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic, complemented
70	C₂×C₂²⋊Dic₅	—	3	4	no	—
71	#4084	—	3	32	no	—
72	#4083	—	3	32	no	—
73	C₂×#685	—	3	4	no	—
74	C₂×C₄⋊Dic₅	—	3	2	no	—
75	C₄×D₂₀	—	3	16	no	—
76	C₂×D₄²	—	15	1	no	Sylow
77	C₂³×C₃×C₅	—	2	16	no	—
78	C₂³×C₃×C₅	—	2	8	no	—
79	C₂³×C₃×C₅	C₂⁴	1	8	yes	—
80	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
81	C₂²×D₁₅	—	2	8	no	—
82	C₂²×D₁₅	—	2	8	no	—
83	C₂²×D₁₅	—	2	64	no	—
84	C₂²×D₁₅	—	4	16	no	—
85	C₂²×D₁₅	—	4	64	no	—
86	C₂²×D₁₅	C₂×D₄	1	16	yes	complemented
87	C₂²×D₁₅	C₂⁴	1	8	yes	—
88	C₃×C₅×D₄	—	2	32	no	—
89	C₃×C₅×D₄	—	4	8	no	—
90	C₂×C₃×C₄×C₅	—	2	2	no	—
91	C₂×C₃×C₄×C₅	C₂×D₄	1	8	yes	complemented
92	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
93	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
94	#1220	—	2	64	no	—
95	C₂×Dic₁₅	—	2	8	no	—
96	C₂×Dic₁₅	C₂⁴	1	8	yes	—
97	D₆₀	C₂×D₄	1	32	yes	complemented
98	C₄×D₁₅	—	2	32	no	—
99	C₂⁴×D₃	—	5	4	no	—
100	C₂²×C₃×D₄	C₂×D₅	1	4	yes	complemented
101	C₂²×C₃×D₄	C₂×D₅	1	2	yes	complemented
102	C₂²×#67	—	5	8	no	—
103	C₂×D₃×D₄	—	5	32	no	—
104	C₂×D₃×D₄	—	10	32	no	—
105	C₂²×D₁₂	—	5	2	no	—
106	C₂²×C₄×D₃	—	5	4	no	—
107	C₃×#127	C₂×D₅	1	8	yes	complemented
108	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic, complemented
109	C₂×#217	—	5	4	no	—
110	#938	—	5	32	no	—
111	#937	—	5	32	no	—
112	C₂×(C₂×D₃)⋊C₄	—	5	4	no	—
113	C₂×C₄⋊Dic₃	—	5	2	no	—
114	C₄×D₁₂	—	5	16	no	—
115	C₂⁴×C₅	C₂²×D₃	1	4	yes	—
116	C₂³×D₅	—	3	4	no	—
117	C₂³×D₅	—	3	16	no	—
118	C₂³×D₅	—	6	32	no	—
119	C₂³×D₅	—	12	8	no	—
120	C₂×C₅×D₄	—	2	16	no	—
121	C₂×C₅×D₄	—	4	4	no	—
122	C₂×C₅×D₄	C₂²×D₃	1	16	yes	complemented
123	C₂×C₅×D₄	C₂²×D₃	1	8	yes	complemented
124	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
125	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
126	C₂×C₂²⋊D₅	—	3	32	no	—
127	C₂×C₂²⋊D₅	—	6	32	no	—
128	C₂²×Dic₅	—	3	4	no	—
129	D₄×D₅	—	6	128	no	—
130	C₂×D₂₀	—	3	16	no	—
131	C₂×D₂₀	—	3	8	no	—
132	C₂×C₄×D₅	—	3	16	no	—
133	C₂×C₄×D₅	—	6	16	no	—
134	C₄²×C₅	C₂²×D₃	1	4	yes	complemented
135	C₂²⋊Dic₅	—	3	16	no	—
136	#685	—	3	16	no	—
137	C₄⋊Dic₅	—	3	8	no	—
138	C₂³×D₄	—	15	4	no	—
139	D₄²	—	15	16	no	—
140	C₂×#127	D₁₅	1	1	yes	characteristic, complemented
141	C₂×#121	—	15	4	no	—
142	C₂×#120	—	15	4	no	—
143	C₂×C₄×D₄	—	15	2	no	—
144	C₂²×C₃×C₅	—	2	16	no	—
145	C₂²×C₃×C₅	—	2	8	no	—
146	C₂²×C₃×C₅	—	4	16	no	—
147	C₂²×C₃×C₅	C₂²×D₄	1	4	yes	—
148	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
149	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
150	C₂×D₁₅	—	2	32	no	—
151	C₂×D₁₅	—	2	8	no	—
152	C₂×D₁₅	—	2	8	no	—
153	C₂×D₁₅	—	4	64	no	—
154	C₂×D₁₅	C₂²×D₄	1	16	yes	complemented
155	C₃×C₄×C₅	—	2	2	no	—
156	C₃×C₄×C₅	C₂²×D₄	1	8	yes	complemented
157	Dic₁₅	—	2	8	no	—
158	C₂⁴×C₃	C₂²×D₅	1	4	yes	—
159	C₂³×D₃	—	5	4	no	—
160	C₂³×D₃	—	5	16	no	—
161	C₂³×D₃	—	10	32	no	—
162	C₂³×D₃	—	20	8	no	—
163	C₂×C₃×D₄	—	2	16	no	—
164	C₂×C₃×D₄	—	4	4	no	—
165	C₂×C₃×D₄	C₂²×D₅	1	16	yes	complemented
166	C₂×C₃×D₄	C₂²×D₅	1	8	yes	complemented
167	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
168	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
169	C₂×#67	—	5	32	no	—
170	C₂×#67	—	10	32	no	—
171	C₂²×Dic₃	—	5	4	no	—
172	D₃×D₄	—	10	128	no	—
173	C₂×D₁₂	—	5	16	no	—
174	C₂×D₁₂	—	5	8	no	—
175	C₂×C₄×D₃	—	5	16	no	—
176	C₂×C₄×D₃	—	10	16	no	—
177	C₃×C₄²	C₂²×D₅	1	4	yes	complemented
178	#217	—	5	16	no	—
179	(C₂×D₃)⋊C₄	—	5	16	no	—
180	C₄⋊Dic₃	—	5	8	no	—
181	C₂³×C₅	—	2	16	no	—
182	C₂³×C₅	—	2	8	no	—
183	C₂³×C₅	C₂³×D₃	1	8	yes	—
184	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
185	C₂²×D₅	—	3	16	no	—
186	C₂²×D₅	—	3	8	no	—
187	C₂²×D₅	—	6	64	no	—
188	C₂²×D₅	—	6	8	no	—
189	C₂²×D₅	—	6	8	no	—
190	C₂²×D₅	—	12	16	no	—
191	C₂²×D₅	—	12	64	no	—
192	C₅×D₄	—	2	32	no	—
193	C₅×D₄	—	4	8	no	—
194	C₂×C₄×C₅	—	2	2	no	—
195	C₂×C₄×C₅	D₃×D₄	1	8	yes	complemented
196	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
197	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
198	C₂²⋊D₅	—	6	64	no	—
199	C₂×Dic₅	—	3	8	no	—
200	C₂×Dic₅	—	6	8	no	—
201	D₂₀	—	3	32	no	—
202	C₄×D₅	—	6	32	no	—
203	C₂⁵	—	15	4	no	—
204	C₂²×D₄	—	15	8	no	—
205	C₂²×D₄	—	15	32	no	—
206	C₂²×D₄	—	15	2	no	—
207	C₂²×D₄	—	30	32	no	—
208	C₂²×D₄	C₂×D₁₅	1	4	yes	complemented
209	C₂²×D₄	C₂×D₁₅	1	2	yes	complemented
210	C₂³×C₄	—	15	4	no	—
211	#127	C₂×D₁₅	1	8	yes	complemented
212	#121	—	15	32	no	—
213	#120	—	15	32	no	—
214	C₄×D₄	—	15	16	no	—
215	C₂×C₄⋊C₄	—	15	2	no	—
216	C₂×C₂²⋊C₄	—	15	4	no	—
217	C₂×C₂²⋊C₄	—	15	4	no	—
218	C₂×C₄²	C₂×D₁₅	1	1	yes	characteristic, complemented
219	C₂×C₃×C₅	—	4	8	no	—
220	C₂×C₃×C₅	D₄²	1	4	yes	complemented
221	C₂×C₃×C₅	C₂³×D₄	1	2	yes	—
222	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
223	D₁₅	—	2	16	no	—
224	C₂³×C₃	—	2	16	no	—
225	C₂³×C₃	—	2	8	no	—
226	C₂³×C₃	C₂³×D₅	1	8	yes	—
227	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
228	C₂²×D₃	—	5	16	no	—
229	C₂²×D₃	—	5	8	no	—
230	C₂²×D₃	—	10	64	no	—
231	C₂²×D₃	—	10	8	no	—
232	C₂²×D₃	—	10	8	no	—
233	C₂²×D₃	—	20	16	no	—
234	C₂²×D₃	—	20	64	no	—
235	C₃×D₄	—	2	32	no	—
236	C₃×D₄	—	4	8	no	—
237	C₂×C₃×C₄	—	2	2	no	—
238	C₂×C₃×C₄	D₄×D₅	1	8	yes	complemented
239	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
240	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
241	#67	—	10	64	no	—
242	C₂×Dic₃	—	5	8	no	—
243	C₂×Dic₃	—	10	8	no	—
244	D₁₂	—	5	32	no	—
245	C₄×D₃	—	10	32	no	—
246	C₂²×C₅	—	2	16	no	—
247	C₂²×C₅	—	2	8	no	—
248	C₂²×C₅	—	4	16	no	—
249	C₂²×C₅	C₂×D₃×D₄	1	4	yes	—
250	C₂²×C₅	#1004	1	2	yes	—
251	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
252	C₂×D₅	—	3	16	no	—
253	C₂×D₅	—	6	8	no	—
254	C₂×D₅	—	6	8	no	—
255	C₂×D₅	—	6	32	no	—
256	C₂×D₅	—	12	64	no	—
257	C₄×C₅	—	2	2	no	—
258	C₄×C₅	C₂×D₃×D₄	1	8	yes	complemented
259	Dic₅	—	6	8	no	—
260	C₂⁴	—	15	4	no	—
261	C₂⁴	—	15	16	no	—
262	C₂⁴	—	30	32	no	—
263	C₂⁴	—	60	8	no	—
264	C₂⁴	C₂²×D₁₅	1	4	yes	—
265	C₂×D₄	—	2	16	no	—
266	C₂×D₄	—	4	4	no	—
267	C₂×D₄	—	15	32	no	—
268	C₂×D₄	—	15	16	no	—
269	C₂×D₄	—	15	8	no	—
270	C₂×D₄	—	30	128	no	—
271	C₂×D₄	—	30	32	no	—
272	C₂×D₄	C₂²×D₁₅	1	16	yes	complemented
273	C₂×D₄	C₂²×D₁₅	1	8	yes	complemented
274	C₂²×C₄	—	15	4	no	—
275	C₂²×C₄	—	15	16	no	—
276	C₂²×C₄	—	30	16	no	—
277	C₂²×C₄	C₂²×D₁₅	1	1	yes	characteristic
278	C₂²×C₄	C₂²×D₁₅	1	2	yes	—
279	C₄⋊C₄	—	15	8	no	—
280	C₂²⋊C₄	—	15	16	no	—
281	C₂²⋊C₄	—	15	16	no	—
282	C₄²	C₂²×D₁₅	1	4	yes	complemented
283	C₃×C₅	C₂×D₄²	1	1	yes	characteristic, complemented, Hall
284	C₂²×C₃	—	2	16	no	—
285	C₂²×C₃	—	2	8	no	—
286	C₂²×C₃	—	4	16	no	—
287	C₂²×C₃	C₂×D₄×D₅	1	4	yes	—
288	C₂²×C₃	#4144	1	2	yes	—
289	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
290	C₂×D₃	—	5	16	no	—
291	C₂×D₃	—	10	32	no	—
292	C₂×D₃	—	10	8	no	—
293	C₂×D₃	—	10	8	no	—
294	C₂×D₃	—	20	64	no	—
295	C₃×C₄	—	2	2	no	—
296	C₃×C₄	C₂×D₄×D₅	1	8	yes	complemented
297	Dic₃	—	10	8	no	—
298	C₂×C₅	—	4	8	no	—
299	C₂×C₅	#5717	1	4	yes	complemented
300	C₂×C₅	C₂²×D₃×D₄	1	2	yes	—
301	C₂×C₅	C₂×#1004	1	1	yes	characteristic
302	D₅	—	6	16	no	—
303	C₂³	—	2	16	no	—
304	C₂³	—	2	8	no	—
305	C₂³	—	15	16	no	—
306	C₂³	—	15	8	no	—
307	C₂³	—	30	64	no	—
308	C₂³	—	30	8	no	—
309	C₂³	—	30	8	no	—
310	C₂³	—	60	16	no	—
311	C₂³	—	60	64	no	—
312	C₂³	C₂³×D₁₅	1	8	yes	—
313	C₂³	C₂³×D₁₅	1	1	yes	characteristic
314	D₄	—	2	32	no	—
315	D₄	—	4	8	no	—
316	D₄	—	15	32	no	—
317	D₄	—	30	64	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	15	8	no	—
320	C₂×C₄	—	30	8	no	—
321	C₂×C₄	—	30	32	no	—
322	C₂×C₄	D₄×D₁₅	1	8	yes	complemented
323	C₂×C₄	C₂³×D₁₅	1	2	yes	—
324	C₂×C₄	C₂³×D₁₅	1	4	yes	—
325	C₂×C₃	—	4	8	no	—
326	C₂×C₃	#66051	1	4	yes	complemented
327	C₂×C₃	C₂²×D₄×D₅	1	2	yes	—
328	C₂×C₃	C₂×#4144	1	1	yes	characteristic
329	D₃	—	10	16	no	—
330	C₅	C₂×#5717	1	1	yes	characteristic, complemented, Sylow
331	C₂²	—	2	16	no	—
332	C₂²	—	2	8	no	—
333	C₂²	—	4	16	no	—
334	C₂²	—	15	16	no	—
335	C₂²	—	30	8	no	—
336	C₂²	—	30	8	no	—
337	C₂²	—	30	32	no	—
338	C₂²	—	60	64	no	—
339	C₂²	C₂×D₄×D₁₅	1	4	yes	—
340	C₂²	#92095	1	2	yes	—
341	C₂²	C₂⁴×D₁₅	1	1	yes	characteristic
342	C₄	—	2	2	no	—
343	C₄	—	30	8	no	—
344	C₄	C₂×D₄×D₁₅	1	8	yes	complemented
345	C₃	C₂×#66051	1	1	yes	characteristic, complemented, Sylow
346	C₂	—	4	8	no	—
347	C₂	—	30	16	no	—
348	C₂	#11756476	1	4	yes	direct product factor
349	C₂	C₂²×D₄×D₁₅	1	2	yes	—
350	C₂	C₂×#92095	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×D₁₅
commutator, cosocle	C₂²×C₃×C₅	C₂⁵
Frattini	C₂²	C₂⁴×D₁₅
Fitting	C₂×C₃×C₅×#127	C₂
socle	C₂³×C₃×C₅	C₂⁴
hypercenter	C₂×#127	D₁₅
hypocenter	C₃×C₅	C₂×D₄²
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂³ ◁ C₂×#127

Complements

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

N	H ≅ G/N	type
1. C₂²×D₄×D₁₅	C₂	semidirect
2. C₂×C₃×C₅×#127	C₂	semidirect
3. C₂×#91827	C₂	semidirect
4. C₂×#91826	C₂	semidirect
5. #11756476	C₂	direct (N × H)
6. C₂×C₄×D₆₀	C₂	semidirect
8. C₂⁴×D₁₅	C₂²	semidirect
9. C₂²×C₃×C₅×D₄	C₂²	semidirect
10. C₂²×C₃×C₅×D₄	C₂²	semidirect
11. C₂²×#1220	C₂²	semidirect
13. C₂×D₄×D₁₅	C₂²	semidirect
15. C₂²×C₄×D₁₅	C₂²	semidirect
16. C₃×C₅×#127	C₂²	semidirect
17. C₂×C₃×C₄²×C₅	C₂²	semidirect
18. C₂×#6719	C₂²	semidirect
19. #91827	C₂²	semidirect
20. #91826	C₂²	semidirect
21. C₂×#6714	C₂²	semidirect
22. C₂×C₄⋊Dic₁₅	C₂²	semidirect
23. C₄×D₆₀	C₂²	semidirect
26. C₂×C₅×#127	D₃	semidirect
35. C₂³×D₁₅	C₂³	semidirect
38. C₂×C₃×C₅×D₄	C₂³	semidirect
39. C₂×C₃×C₅×D₄	C₂³	semidirect
43. C₂×#1220	C₂³	semidirect
46. C₂×D₆₀	D₄	semidirect
49. C₂×C₄×D₁₅	C₂³	semidirect
50. C₃×C₄²×C₅	C₂³	semidirect
51. #6719	C₂³	semidirect
52. #6714	C₂³	semidirect
53. C₄⋊Dic₁₅	C₂³	semidirect
55. C₂×C₃×#127	D₅	semidirect
61. C₂²×C₅×D₄	C₂×D₃	semidirect
62. C₂²×C₅×D₄	C₂×D₃	semidirect
68. C₅×#127	C₂×D₃	semidirect
69. C₂×C₄²×C₅	C₂×D₃	semidirect
86. C₂²×D₁₅	C₂×D₄	semidirect
91. C₂×C₃×C₄×C₅	C₂×D₄	semidirect
97. D₆₀	C₂×D₄	semidirect
100. C₂²×C₃×D₄	C₂×D₅	semidirect
101. C₂²×C₃×D₄	C₂×D₅	semidirect
107. C₃×#127	C₂×D₅	semidirect
108. C₂×C₃×C₄²	C₂×D₅	semidirect
122. C₂×C₅×D₄	C₂²×D₃	semidirect
123. C₂×C₅×D₄	C₂²×D₃	semidirect
134. C₄²×C₅	C₂²×D₃	semidirect
140. C₂×#127	D₁₅	semidirect
154. C₂×D₁₅	C₂²×D₄	semidirect
156. C₃×C₄×C₅	C₂²×D₄	semidirect
165. C₂×C₃×D₄	C₂²×D₅	semidirect
166. C₂×C₃×D₄	C₂²×D₅	semidirect
177. C₃×C₄²	C₂²×D₅	semidirect
195. C₂×C₄×C₅	D₃×D₄	semidirect
208. C₂²×D₄	C₂×D₁₅	semidirect
209. C₂²×D₄	C₂×D₁₅	semidirect
211. #127	C₂×D₁₅	semidirect
218. C₂×C₄²	C₂×D₁₅	semidirect
220. C₂×C₃×C₅	D₄²	semidirect
238. C₂×C₃×C₄	D₄×D₅	semidirect
258. C₄×C₅	C₂×D₃×D₄	semidirect
272. C₂×D₄	C₂²×D₁₅	semidirect
273. C₂×D₄	C₂²×D₁₅	semidirect
282. C₄²	C₂²×D₁₅	semidirect
283. C₃×C₅	C₂×D₄²	semidirect
296. C₃×C₄	C₂×D₄×D₅	semidirect
299. C₂×C₅	#5717	semidirect
322. C₂×C₄	D₄×D₁₅	semidirect
326. C₂×C₃	#66051	semidirect
330. C₅	C₂×#5717	semidirect
344. C₄	C₂×D₄×D₁₅	semidirect
345. C₃	C₂×#66051	semidirect
348. C₂	#11756476	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
C₂×C₃×C₅×#127	2
C₂×#91827	2
C₂×#91826	2
#11756476	2
C₂×C₄×D₆₀	2
C₂×#66051	3
C₂×#5717	5

Subgroups — C2×#11756476 #14482414

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11756476 #14482414