Subgroups — C₂×#11748289 #14478371

Order 1920.

800 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4065	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₅×D₂₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#91112	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#828	C₂	1	1	yes	maximal, characteristic, complemented
5	#11748289	C₂	1	8	yes	maximal, direct product factor
6	C₂×#90938	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#90937	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#90934	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#65203	—	3	1	no	maximal, Hall
10	C₂×C₃×#713	—	2	1	no	—
11	C₂×D₅×D₁₂	—	2	1	no	—
12	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic, complemented
13	C₂×D₁₂₀	C₂²	1	1	yes	characteristic
14	C₂×C₅×D₂₄	C₂²	1	1	yes	characteristic
15	C₂×C₃×#688	—	2	1	no	—
16	C₃×#4065	—	2	2	no	—
17	C₃×#4065	C₂²	1	4	yes	complemented
18	C₂×C₃×D₄₀	C₂²	1	1	yes	characteristic, complemented
19	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
20	C₂×#6654	—	2	1	no	—
21	D₅×D₂₄	—	2	2	no	—
22	D₅×D₂₄	C₂²	1	4	yes	complemented
23	#91112	C₂²	1	4	yes	complemented
24	C₂×C₃⋊#672	C₂²	1	1	yes	characteristic, complemented
25	C₅×#828	C₂²	1	4	yes	complemented
26	C₂×C₅×C₃⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
27	#90938	C₂²	1	4	yes	complemented
28	#90937	C₂²	1	4	yes	complemented
29	#90934	C₂²	1	4	yes	complemented
30	C₂×#5193	—	5	1	no	maximal, Hall
31	C₂×#4065	D₃	1	1	yes	characteristic, complemented
32	C₂×D₅×D₈	—	3	1	no	—
33	C₂×C₅×SD₃₂	—	3	1	no	—
34	C₂×#3960	—	3	1	no	—
35	C₂×#3958	—	3	1	no	—
36	#65203	—	3	8	no	—
37	C₂×D₈₀	—	3	1	no	—
38	C₂×#3930	—	3	1	no	—
39	C₂²×D₃×D₅	—	4	1	no	—
40	C₂×C₃×C₅×Q₈	—	2	1	no	—
41	C₂×D₆₀	—	2	1	no	—
42	C₂×C₅×D₁₂	—	2	1	no	—
43	C₃×#713	—	2	4	no	—
44	C₃×#713	—	4	2	no	—
45	C₂×C₃×D₂₀	—	2	1	no	—
46	C₂×C₃×D₂₀	—	4	1	no	—
47	C₂×C₃×C₄×D₅	—	4	1	no	—
48	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
49	C₂×#1203	—	4	1	no	—
50	D₅×D₁₂	—	2	4	no	—
51	D₅×D₁₂	—	4	2	no	—
52	C₃×C₅×Q₁₆	—	2	1	no	—
53	C₃×C₅×Q₁₆	C₂³	1	2	yes	complemented
54	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
55	D₁₂₀	—	2	1	no	—
56	D₁₂₀	C₂³	1	2	yes	—
57	C₅×D₂₄	—	2	1	no	—
58	C₅×D₂₄	C₂³	1	2	yes	—
59	C₃×#688	—	2	4	no	—
60	C₂×C₃×#168	D₄	1	1	yes	characteristic
61	C₃×D₄₀	—	2	1	no	—
62	C₃×D₄₀	C₂³	1	2	yes	complemented
63	C₃×C₈×D₅	D₄	1	2	yes	—
64	C₃×C₈×D₅	C₂³	1	2	yes	—
65	#6654	—	2	4	no	—
66	C₃⋊#672	C₂³	1	2	yes	complemented
67	C₅×C₃⋊C₁₆	C₂³	1	2	yes	complemented
68	C₂×C₃×#135	—	5	1	no	—
69	C₂²×D₂₄	—	5	1	no	—
70	#5193	—	5	8	no	—
71	C₂×#828	—	5	1	no	—
72	C₂×#828	D₅	1	1	yes	characteristic, complemented
73	C₂×#826	—	5	1	no	—
74	C₂×#826	—	5	1	no	—
75	C₂×#812	—	5	1	no	—
76	C₂×#713	—	2	1	no	—
77	C₂×D₄×D₅	—	6	1	no	—
78	C₂×C₅×Q₁₆	C₂×D₃	1	1	yes	characteristic, complemented
79	C₂×C₅×D₈	—	3	1	no	—
80	C₂×#688	—	2	1	no	—
81	C₂×#686	—	6	1	no	—
82	#4065	—	2	2	no	—
83	#4065	C₂×D₃	1	4	yes	complemented
84	D₅×D₈	—	3	4	no	—
85	D₅×D₈	—	6	2	no	—
86	C₂×D₄₀	—	3	1	no	—
87	C₂×D₄₀	C₂×D₃	1	1	yes	characteristic, complemented
88	C₂×C₈×D₅	C₂×D₃	1	1	yes	characteristic
89	C₅×SD₃₂	—	3	4	no	—
90	C₂×C₅×C₁₆	—	3	1	no	—
91	#3960	—	3	4	no	—
92	#3958	—	3	4	no	—
93	C₂×#672	—	3	1	no	—
94	D₈₀	—	3	4	no	—
95	#3930	—	3	4	no	—
96	C₂×#509	—	15	1	no	Sylow
97	C₂²×D₁₅	—	4	1	no	—
98	C₂²×C₅×D₃	—	4	1	no	—
99	C₂²×C₃×D₅	—	4	1	no	—
100	C₂²×C₃×D₅	D₈	1	1	yes	characteristic
101	C₂×D₃×D₅	—	4	4	no	—
102	C₂×D₃×D₅	—	8	4	no	—
103	C₃×C₅×Q₈	—	2	2	no	—
104	C₃×C₅×Q₈	—	4	1	no	—
105	C₂×C₃×C₄×C₅	—	4	1	no	—
106	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
107	D₆₀	—	2	2	no	—
108	D₆₀	—	4	1	no	—
109	C₅×D₁₂	—	2	2	no	—
110	C₅×D₁₂	—	4	1	no	—
111	C₂×C₃×Dic₅	D₈	1	1	yes	characteristic
112	C₃×D₂₀	—	2	2	no	—
113	C₃×D₂₀	—	4	4	no	—
114	C₃×D₂₀	—	4	1	no	—
115	C₃×C₄×D₅	—	4	4	no	—
116	C₃×C₄×D₅	D₈	1	2	yes	—
117	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
118	#1203	—	4	4	no	—
119	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
120	C₃×C₅×C₈	C₂⁴	1	1	yes	characteristic
121	C₃×#168	C₂×D₄	1	2	yes	—
122	C₂×C₃×#41	—	10	1	no	—
123	C₂²×D₁₂	—	10	1	no	—
124	C₃×#135	—	5	4	no	—
125	C₃×#135	—	10	2	no	—
126	C₂×C₃×Q₁₆	C₂×D₅	1	1	yes	characteristic, complemented
127	C₂×C₃×SD₁₆	—	10	1	no	—
128	C₂×C₃×D₈	—	5	1	no	—
129	C₂²×C₃×C₈	—	5	1	no	—
130	C₂×D₂₄	—	5	1	no	—
131	C₂×D₂₄	—	5	4	no	—
132	C₂×D₂₄	—	10	2	no	—
133	C₂×D₂₄	—	10	1	no	—
134	C₂×D₂₄	C₂×D₅	1	1	yes	characteristic
135	#828	—	5	4	no	—
136	#828	C₂×D₅	1	4	yes	complemented
137	#826	—	5	4	no	—
138	#826	—	5	4	no	—
139	#812	—	5	4	no	—
140	C₂×C₃⋊C₁₆	—	5	1	no	—
141	C₂×C₃⋊C₁₆	C₂×D₅	1	1	yes	characteristic, complemented
142	C₂³×D₅	—	12	1	no	—
143	C₂×C₅×Q₈	—	2	1	no	—
144	C₂×C₅×D₄	—	6	1	no	—
145	C₂×C₂²⋊D₅	—	12	1	no	—
146	#713	—	2	4	no	—
147	#713	—	4	2	no	—
148	D₄×D₅	—	6	4	no	—
149	D₄×D₅	—	12	2	no	—
150	C₂×D₂₀	—	2	1	no	—
151	C₂×D₂₀	—	4	1	no	—
152	C₂×D₂₀	—	6	1	no	—
153	C₂×C₄×D₅	—	4	1	no	—
154	C₂×C₄×D₅	#67	1	1	yes	characteristic
155	C₅×Q₁₆	—	2	1	no	—
156	C₅×Q₁₆	C₂²×D₃	1	2	yes	complemented
157	C₅×D₈	—	3	2	no	—
158	C₅×D₈	—	6	1	no	—
159	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
160	#688	—	2	4	no	—
161	#686	—	6	4	no	—
162	C₂×#168	#67	1	1	yes	characteristic
163	D₄₀	—	2	1	no	—
164	D₄₀	—	3	2	no	—
165	D₄₀	—	6	1	no	—
166	D₄₀	C₂²×D₃	1	2	yes	complemented
167	C₈×D₅	#67	1	2	yes	—
168	C₈×D₅	C₂²×D₃	1	2	yes	—
169	C₅×C₁₆	—	3	2	no	—
170	#672	—	3	2	no	—
171	C₂×#135	—	5	1	no	—
172	C₂²×D₈	—	15	1	no	—
173	#509	—	15	8	no	—
174	C₂×SD₃₂	—	3	1	no	—
175	C₂×SD₃₂	—	15	1	no	—
176	C₂×D₁₆	—	15	1	no	—
177	C₂×D₁₆	—	15	1	no	—
178	C₂×M₃₂	—	15	1	no	—
179	C₂²×C₃×C₅	C₂×D₈	1	1	yes	characteristic
180	C₂×D₁₅	—	4	2	no	—
181	C₂×D₁₅	—	8	2	no	—
182	C₂×C₅×D₃	—	4	2	no	—
183	C₂×C₅×D₃	—	8	2	no	—
184	C₂×C₃×D₅	—	2	2	no	—
185	C₂×C₃×D₅	—	4	2	no	—
186	C₂×C₃×D₅	—	8	2	no	—
187	C₂×C₃×D₅	C₂×D₈	1	2	yes	—
188	D₃×D₅	—	8	8	no	—
189	C₃×C₄×C₅	—	4	2	no	—
190	C₃×C₄×C₅	C₂×D₈	1	1	yes	characteristic
191	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
192	C₃×Dic₅	C₂×D₈	1	2	yes	—
193	C₂³×D₃	—	20	1	no	—
194	C₃×#41	—	10	4	no	—
195	C₃×#41	—	20	2	no	—
196	C₂×C₃×Q₈	—	2	1	no	—
197	C₂×C₃×D₄	—	10	1	no	—
198	C₂×C₃×D₄	—	20	1	no	—
199	C₂²×C₃×C₄	—	5	1	no	—
200	C₂²×C₃×C₄	—	20	1	no	—
201	C₂×D₁₂	—	2	1	no	—
202	C₂×D₁₂	—	10	4	no	—
203	C₂×D₁₂	—	10	1	no	—
204	C₂×D₁₂	—	20	2	no	—
205	C₂×D₁₂	—	20	1	no	—
206	C₃×Q₁₆	—	2	1	no	—
207	C₃×Q₁₆	C₂²×D₅	1	2	yes	complemented
208	C₃×SD₁₆	—	10	4	no	—
209	C₃×D₈	—	5	2	no	—
210	C₃×D₈	—	10	1	no	—
211	C₂×C₃×C₈	—	5	1	no	—
212	C₂×C₃×C₈	—	5	2	no	—
213	C₂×C₃×C₈	—	5	2	no	—
214	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
215	D₂₄	—	2	1	no	—
216	D₂₄	—	5	2	no	—
217	D₂₄	—	10	4	no	—
218	D₂₄	—	10	1	no	—
219	D₂₄	C₂²×D₅	1	2	yes	—
220	C₃⋊C₁₆	—	5	2	no	—
221	C₃⋊C₁₆	C₂²×D₅	1	2	yes	complemented
222	C₂³×C₅	—	12	1	no	—
223	C₂²×D₅	—	4	1	no	—
224	C₂²×D₅	—	12	1	no	—
225	C₂²×D₅	—	12	4	no	—
226	C₂²×D₅	—	24	4	no	—
227	C₂²×D₅	#213	1	1	yes	characteristic
228	C₅×Q₈	—	2	2	no	—
229	C₅×Q₈	—	4	1	no	—
230	C₅×D₄	—	6	2	no	—
231	C₅×D₄	—	12	1	no	—
232	C₂×C₄×C₅	—	4	1	no	—
233	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
234	C₂²⋊D₅	—	12	4	no	—
235	C₂×Dic₅	#213	1	1	yes	characteristic
236	D₂₀	—	2	2	no	—
237	D₂₀	—	4	4	no	—
238	D₂₀	—	4	1	no	—
239	D₂₀	—	6	2	no	—
240	D₂₀	—	12	1	no	—
241	C₄×D₅	—	4	4	no	—
242	C₄×D₅	#213	1	2	yes	—
243	C₄×D₅	C₂×#67	1	2	yes	—
244	C₅×C₈	C₂×#67	1	1	yes	characteristic
245	C₅×C₈	C₂³×D₃	1	1	yes	characteristic
246	#168	C₂×#67	1	2	yes	—
247	C₂×#41	—	10	1	no	—
248	C₂²×D₄	—	30	1	no	—
249	#135	—	5	4	no	—
250	#135	—	10	2	no	—
251	C₂×Q₁₆	D₃×D₅	1	1	yes	characteristic, complemented
252	C₂×SD₁₆	—	10	1	no	—
253	C₂×D₈	—	3	1	no	—
254	C₂×D₈	—	5	1	no	—
255	C₂×D₈	—	15	4	no	—
256	C₂×D₈	—	15	1	no	—
257	C₂×D₈	—	30	2	no	—
258	C₂×D₈	—	30	1	no	—
259	C₂²×C₈	—	5	1	no	—
260	SD₃₂	—	3	4	no	—
261	SD₃₂	—	15	4	no	—
262	D₁₆	—	15	4	no	—
263	D₁₆	—	15	4	no	—
264	M₃₂	—	15	4	no	—
265	C₂×C₁₆	—	3	1	no	—
266	C₂×C₁₆	—	15	1	no	—
267	C₂×C₃×C₅	#509	1	2	yes	complemented
268	C₂×C₃×C₅	C₂²×D₈	1	1	yes	characteristic
269	D₁₅	—	8	2	no	—
270	C₃×D₅	—	2	2	no	—
271	C₃×D₅	—	8	2	no	—
272	C₅×D₃	—	8	2	no	—
273	C₂³×C₃	—	5	1	no	—
274	C₂³×C₃	—	20	1	no	—
275	C₂²×D₃	—	4	1	no	—
276	C₂²×D₃	—	20	4	no	—
277	C₂²×D₃	—	20	1	no	—
278	C₂²×D₃	—	40	4	no	—
279	C₃×Q₈	—	2	2	no	—
280	C₃×Q₈	—	4	1	no	—
281	C₃×D₄	—	10	2	no	—
282	C₃×D₄	—	20	4	no	—
283	C₃×D₄	—	20	1	no	—
284	C₂×C₃×C₄	—	4	1	no	—
285	C₂×C₃×C₄	—	5	1	no	—
286	C₂×C₃×C₄	—	5	2	no	—
287	C₂×C₃×C₄	—	5	2	no	—
288	C₂×C₃×C₄	—	20	4	no	—
289	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
290	D₁₂	—	2	2	no	—
291	D₁₂	—	4	1	no	—
292	D₁₂	—	10	2	no	—
293	D₁₂	—	20	4	no	—
294	D₁₂	—	20	1	no	—
295	C₃×C₈	—	5	2	no	—
296	C₃×C₈	D₄×D₅	1	1	yes	characteristic
297	C₃×C₈	C₂³×D₅	1	1	yes	characteristic
298	C₂²×C₅	—	12	2	no	—
299	C₂²×C₅	—	24	2	no	—
300	C₂²×C₅	C₂×#213	1	1	yes	characteristic
301	C₂×D₅	—	2	2	no	—
302	C₂×D₅	—	4	2	no	—
303	C₂×D₅	—	8	2	no	—
304	C₂×D₅	—	12	2	no	—
305	C₂×D₅	—	24	8	no	—
306	C₂×D₅	—	24	2	no	—
307	C₂×D₅	C₂×#213	1	2	yes	—
308	C₄×C₅	—	4	2	no	—
309	C₄×C₅	C₂×#213	1	1	yes	characteristic
310	C₄×C₅	C₂²×#67	1	1	yes	characteristic
311	Dic₅	C₂×#213	1	2	yes	—
312	C₂⁴	—	60	1	no	—
313	#41	—	10	4	no	—
314	#41	—	20	2	no	—
315	C₂×Q₈	—	2	1	no	—
316	C₂×D₄	—	6	1	no	—
317	C₂×D₄	—	10	1	no	—
318	C₂×D₄	—	20	1	no	—
319	C₂×D₄	—	30	4	no	—
320	C₂×D₄	—	30	1	no	—
321	C₂×D₄	—	60	2	no	—
322	C₂×D₄	—	60	1	no	—
323	C₂²×C₄	—	5	1	no	—
324	C₂²×C₄	—	20	1	no	—
325	Q₁₆	—	2	1	no	—
326	Q₁₆	C₂×D₃×D₅	1	2	yes	complemented
327	SD₁₆	—	10	4	no	—
328	D₈	—	3	2	no	—
329	D₈	—	5	2	no	—
330	D₈	—	6	1	no	—
331	D₈	—	10	1	no	—
332	D₈	—	15	2	no	—
333	D₈	—	30	4	no	—
334	D₈	—	30	1	no	—
335	C₂×C₈	—	5	1	no	—
336	C₂×C₈	—	5	2	no	—
337	C₂×C₈	—	5	2	no	—
338	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
339	C₁₆	—	3	2	no	—
340	C₁₆	—	15	2	no	—
341	C₃×C₅	C₂×#509	1	1	yes	characteristic, complemented, Hall
342	C₂²×C₃	—	5	2	no	—
343	C₂²×C₃	—	10	2	no	—
344	C₂²×C₃	—	20	2	no	—
345	C₂²×C₃	—	40	2	no	—
346	C₂²×C₃	D₅×D₈	1	1	yes	characteristic
347	C₂×D₃	—	4	2	no	—
348	C₂×D₃	—	8	2	no	—
349	C₂×D₃	—	20	2	no	—
350	C₂×D₃	—	40	8	no	—
351	C₂×D₃	—	40	2	no	—
352	C₃×C₄	—	4	2	no	—
353	C₃×C₄	—	5	2	no	—
354	C₃×C₄	D₅×D₈	1	1	yes	characteristic
355	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
356	C₂×C₅	—	24	2	no	—
357	C₂×C₅	#5193	1	2	yes	complemented
358	C₂×C₅	C₂²×#213	1	1	yes	characteristic
359	D₅	—	2	2	no	—
360	D₅	—	8	2	no	—
361	D₅	—	24	2	no	—
362	C₂³	—	5	1	no	—
363	C₂³	—	12	1	no	—
364	C₂³	—	20	1	no	—
365	C₂³	—	60	4	no	—
366	C₂³	—	60	1	no	—
367	C₂³	—	120	4	no	—
368	Q₈	—	2	2	no	—
369	Q₈	—	4	1	no	—
370	D₄	—	6	2	no	—
371	D₄	—	10	2	no	—
372	D₄	—	12	1	no	—
373	D₄	—	20	4	no	—
374	D₄	—	20	1	no	—
375	D₄	—	30	2	no	—
376	D₄	—	60	4	no	—
377	D₄	—	60	1	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	5	1	no	—
380	C₂×C₄	—	5	2	no	—
381	C₂×C₄	—	5	2	no	—
382	C₂×C₄	—	20	4	no	—
383	C₂×C₄	D₅×#67	1	1	yes	characteristic
384	C₈	—	5	2	no	—
385	C₈	D₅×#67	1	1	yes	characteristic
386	C₈	C₂²×D₃×D₅	1	1	yes	characteristic
387	C₂×C₃	—	10	2	no	—
388	C₂×C₃	—	40	2	no	—
389	C₂×C₃	#65203	1	2	yes	complemented
390	C₂×C₃	C₂×D₅×D₈	1	1	yes	characteristic
391	D₃	—	8	2	no	—
392	D₃	—	40	2	no	—
393	C₅	C₂×#5193	1	1	yes	characteristic, complemented, Sylow
394	C₂²	—	5	2	no	—
395	C₂²	—	10	2	no	—
396	C₂²	—	12	2	no	—
397	C₂²	—	20	2	no	—
398	C₂²	—	24	2	no	—
399	C₂²	—	40	2	no	—
400	C₂²	—	60	2	no	—
401	C₂²	—	120	8	no	—
402	C₂²	—	120	2	no	—
403	C₂²	D₅×#213	1	1	yes	characteristic
404	C₄	—	4	2	no	—
405	C₄	—	5	2	no	—
406	C₄	D₅×#213	1	1	yes	characteristic
407	C₄	C₂×D₅×#67	1	1	yes	characteristic
408	C₃	C₂×#65203	1	1	yes	characteristic, complemented, Sylow
409	C₂	—	10	2	no	—
410	C₂	—	24	2	no	—
411	C₂	—	40	2	no	—
412	C₂	—	120	2	no	—
413	C₂	#11748289	1	2	yes	direct product factor
414	C₂	C₂×D₅×#213	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₅×#213
commutator, cosocle	C₃×C₅×C₈	C₂⁴
Frattini	C₈	C₂²×D₃×D₅
Fitting	C₂×C₃×C₅×Q₁₆	C₂²
socle	C₂²×C₃×C₅	C₂×D₈
hypercenter	C₂×Q₁₆	D₃×D₅
hypocenter	C₃×C₅	C₂×#509
LCS	G ▷ C₃×C₅×C₈ ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#4065	C₂	semidirect
2. C₂×D₅×D₂₄	C₂	semidirect
3. C₂×#91112	C₂	semidirect
4. C₂×C₅×#828	C₂	semidirect
5. #11748289	C₂	direct (N × H)
6. C₂×#90938	C₂	semidirect
7. C₂×#90937	C₂	semidirect
8. C₂×#90934	C₂	semidirect
12. C₂×C₃×C₅×Q₁₆	C₂²	semidirect
17. C₃×#4065	C₂²	semidirect
18. C₂×C₃×D₄₀	C₂²	semidirect
22. D₅×D₂₄	C₂²	semidirect
23. #91112	C₂²	semidirect
24. C₂×C₃⋊#672	C₂²	semidirect
25. C₅×#828	C₂²	semidirect
26. C₂×C₅×C₃⋊C₁₆	C₂²	semidirect
27. #90938	C₂²	semidirect
28. #90937	C₂²	semidirect
29. #90934	C₂²	semidirect
31. C₂×#4065	D₃	semidirect
53. C₃×C₅×Q₁₆	C₂³	semidirect
62. C₃×D₄₀	C₂³	semidirect
66. C₃⋊#672	C₂³	semidirect
67. C₅×C₃⋊C₁₆	C₂³	semidirect
72. C₂×#828	D₅	semidirect
78. C₂×C₅×Q₁₆	C₂×D₃	semidirect
83. #4065	C₂×D₃	semidirect
87. C₂×D₄₀	C₂×D₃	semidirect
126. C₂×C₃×Q₁₆	C₂×D₅	semidirect
136. #828	C₂×D₅	semidirect
141. C₂×C₃⋊C₁₆	C₂×D₅	semidirect
156. C₅×Q₁₆	C₂²×D₃	semidirect
166. D₄₀	C₂²×D₃	semidirect
207. C₃×Q₁₆	C₂²×D₅	semidirect
221. C₃⋊C₁₆	C₂²×D₅	semidirect
251. C₂×Q₁₆	D₃×D₅	semidirect
267. C₂×C₃×C₅	#509	semidirect
326. Q₁₆	C₂×D₃×D₅	semidirect
341. C₃×C₅	C₂×#509	semidirect
357. C₂×C₅	#5193	semidirect
389. C₂×C₃	#65203	semidirect
393. C₅	C₂×#5193	semidirect
408. C₃	C₂×#65203	semidirect
413. C₂	#11748289	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃×#4065	2
C₂×D₅×D₂₄	2
C₂×#91112	2
C₂×C₅×#828	2
#11748289	2
C₂×#90938	2
C₂×#90937	2
C₂×#90934	2
C₂×#65203	3
C₂×#5193	5

Subgroups — C2×#11748289 #14478371

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11748289 #14478371