Subgroups — C₂×#11746821 #14478368

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×#91275	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₃×D₄₀	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₂₄₀	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#798	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#3932	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#90943	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#90938	C₂	1	1	yes	maximal, characteristic, complemented
8	#11746821	C₂	1	8	yes	maximal, direct product factor
9	C₂×#65197	—	3	1	no	maximal, Hall
10	C₂×D₃×D₂₀	—	2	1	no	—
11	C₂×#6769	—	2	1	no	—
12	C₂×D₁₂₀	C₂²	1	1	yes	characteristic
13	C₂×D₁₂₀	C₂²	1	1	yes	characteristic, complemented
14	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
15	C₂×C₃×Dic₂₀	C₂²	1	1	yes	characteristic, complemented
16	C₂×C₃×D₄₀	C₂²	1	1	yes	characteristic
17	C₂×#6658	—	2	1	no	—
18	C₂×#6653	—	2	1	no	—
19	#91275	—	2	2	no	—
20	#91275	C₂²	1	4	yes	complemented
21	D₃×D₄₀	—	2	2	no	—
22	D₃×D₄₀	C₂²	1	4	yes	complemented
23	C₂×C₃×C₅×C₁₆	C₂²	1	1	yes	characteristic, complemented
24	D₂₄₀	C₂²	1	4	yes	complemented
25	C₂×C₅×C₃⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
26	C₅×#798	C₂²	1	4	yes	complemented
27	C₃×#3932	C₂²	1	4	yes	complemented
28	#90943	C₂²	1	4	yes	complemented
29	#90938	C₂²	1	4	yes	complemented
30	C₂×#4914	—	5	1	no	maximal, Hall
31	C₂×#4050	—	3	1	no	—
32	C₂²×D₄₀	—	3	1	no	—
33	C₂×C₅×M₃₂	—	3	1	no	—
34	#65197	—	3	8	no	—
35	C₂×#3932	—	3	1	no	—
36	C₂×#3932	D₃	1	1	yes	characteristic, complemented
37	C₂×D₈₀	—	3	1	no	—
38	C₂×D₈₀	—	3	1	no	—
39	C₂²×D₃×D₅	—	4	1	no	—
40	C₂×D₆₀	—	2	1	no	—
41	C₂×D₆₀	—	2	1	no	—
42	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
43	C₂×C₃×D₂₀	—	2	1	no	—
44	C₂×C₃×Dic₁₀	—	2	1	no	—
45	C₂×#1203	—	4	1	no	—
46	C₂×#1202	—	4	1	no	—
47	C₂×#1200	—	4	1	no	—
48	D₃×D₂₀	—	2	4	no	—
49	D₃×D₂₀	—	4	2	no	—
50	#6769	—	2	4	no	—
51	#6769	—	4	2	no	—
52	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
53	D₁₂₀	—	2	1	no	—
54	D₁₂₀	—	2	1	no	—
55	D₁₂₀	C₂³	1	2	yes	—
56	D₁₂₀	C₂³	1	2	yes	complemented
57	C₂×C₅×C₃⋊C₈	D₄	1	1	yes	characteristic
58	C₅×D₃×C₈	D₄	1	2	yes	—
59	C₅×D₃×C₈	C₂³	1	2	yes	—
60	C₃×Dic₂₀	—	2	1	no	—
61	C₃×Dic₂₀	C₂³	1	2	yes	complemented
62	C₃×D₄₀	—	2	1	no	—
63	C₃×D₄₀	C₂³	1	2	yes	—
64	#6658	—	2	4	no	—
65	#6653	—	2	4	no	—
66	C₃×C₅×C₁₆	C₂³	1	2	yes	complemented
67	C₅×C₃⋊C₁₆	C₂³	1	2	yes	complemented
68	C₂×#919	—	5	1	no	—
69	C₂×D₃×D₈	—	5	1	no	—
70	C₂×C₃×SD₃₂	—	5	1	no	—
71	C₂×#828	—	5	1	no	—
72	C₂×#826	—	5	1	no	—
73	#4914	—	5	8	no	—
74	C₂×D₄₈	—	5	1	no	—
75	C₂×#798	D₅	1	1	yes	characteristic, complemented
76	C₂×#709	—	6	1	no	—
77	C₂²×D₂₀	—	6	1	no	—
78	C₂²×C₅×C₈	—	3	1	no	—
79	C₂×Dic₂₀	C₂×D₃	1	1	yes	characteristic, complemented
80	#4050	—	3	4	no	—
81	#4050	—	6	2	no	—
82	C₂×D₄₀	—	3	1	no	—
83	C₂×D₄₀	—	3	1	no	—
84	C₂×D₄₀	—	3	4	no	—
85	C₂×D₄₀	—	6	2	no	—
86	C₂×D₄₀	—	6	1	no	—
87	C₂×D₄₀	C₂×D₃	1	1	yes	characteristic
88	C₂×#677	—	6	1	no	—
89	C₅×M₃₂	—	3	4	no	—
90	C₂×C₅×C₁₆	—	3	1	no	—
91	C₂×C₅×C₁₆	C₂×D₃	1	1	yes	characteristic, complemented
92	#3932	—	3	4	no	—
93	#3932	C₂×D₃	1	4	yes	complemented
94	D₈₀	—	3	4	no	—
95	D₈₀	—	3	4	no	—
96	C₂×#509	—	15	1	no	Sylow
97	C₂²×D₁₅	—	4	1	no	—
98	C₂²×D₁₅	—	4	1	no	—
99	C₂²×C₅×D₃	D₈	1	1	yes	characteristic
100	C₂²×C₃×D₅	—	4	1	no	—
101	C₂×D₃×D₅	—	4	4	no	—
102	C₂×D₃×D₅	—	8	4	no	—
103	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
104	D₆₀	—	2	2	no	—
105	D₆₀	—	2	2	no	—
106	D₆₀	—	4	1	no	—
107	D₆₀	—	4	1	no	—
108	C₂×C₅×Dic₃	D₈	1	1	yes	characteristic
109	C₄×C₅×D₃	D₈	1	2	yes	—
110	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
111	C₂×C₃×Dic₅	—	4	1	no	—
112	C₃×D₂₀	—	2	2	no	—
113	C₃×D₂₀	—	4	1	no	—
114	C₃×Dic₁₀	—	2	2	no	—
115	C₃×Dic₁₀	—	4	1	no	—
116	#1203	—	4	4	no	—
117	#1202	—	4	4	no	—
118	#1200	—	4	4	no	—
119	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
120	C₃×C₅×C₈	C₂⁴	1	1	yes	characteristic
121	C₅×C₃⋊C₈	C₂×D₄	1	2	yes	—
122	C₂×#239	—	10	1	no	—
123	C₂×D₃×D₄	—	10	1	no	—
124	C₂×C₃×Q₁₆	—	5	1	no	—
125	C₂×C₃×D₈	—	5	1	no	—
126	C₂×#215	—	10	1	no	—
127	C₂×#213	—	10	1	no	—
128	#919	—	5	4	no	—
129	#919	—	10	2	no	—
130	D₃×D₈	—	5	4	no	—
131	D₃×D₈	—	10	2	no	—
132	C₂×D₂₄	—	5	1	no	—
133	C₂×D₂₄	—	5	1	no	—
134	C₂×D₃×C₈	C₂×D₅	1	1	yes	characteristic
135	C₃×SD₃₂	—	5	4	no	—
136	C₂×C₃×C₁₆	C₂×D₅	1	1	yes	characteristic, complemented
137	#828	—	5	4	no	—
138	#826	—	5	4	no	—
139	C₂×C₃⋊C₁₆	C₂×D₅	1	1	yes	characteristic, complemented
140	D₄₈	—	5	4	no	—
141	#798	C₂×D₅	1	4	yes	complemented
142	C₂³×D₅	—	12	1	no	—
143	C₂²×C₄×C₅	—	3	1	no	—
144	C₂×C₂²⋊D₅	—	12	1	no	—
145	#709	—	6	4	no	—
146	#709	—	12	2	no	—
147	C₂×D₂₀	—	2	1	no	—
148	C₂×D₂₀	—	6	4	no	—
149	C₂×D₂₀	—	6	1	no	—
150	C₂×D₂₀	—	6	1	no	—
151	C₂×D₂₀	—	12	2	no	—
152	C₂×D₂₀	—	12	1	no	—
153	C₂×C₄×D₅	—	12	1	no	—
154	C₂×Dic₁₀	—	2	1	no	—
155	C₂×C₅×C₈	—	3	1	no	—
156	C₂×C₅×C₈	—	3	2	no	—
157	C₂×C₅×C₈	—	3	2	no	—
158	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
159	Dic₂₀	—	2	1	no	—
160	Dic₂₀	C₂²×D₃	1	2	yes	complemented
161	D₄₀	—	2	1	no	—
162	D₄₀	—	3	2	no	—
163	D₄₀	—	3	2	no	—
164	D₄₀	—	6	4	no	—
165	D₄₀	—	6	1	no	—
166	D₄₀	—	6	1	no	—
167	D₄₀	C₂²×D₃	1	2	yes	—
168	#677	—	6	4	no	—
169	C₅×C₁₆	—	3	2	no	—
170	C₅×C₁₆	C₂²×D₃	1	2	yes	complemented
171	C₂×#135	—	15	1	no	—
172	C₂²×D₈	—	15	1	no	—
173	#509	—	15	8	no	—
174	C₂×SD₃₂	—	5	1	no	—
175	C₂×SD₃₂	—	15	1	no	—
176	C₂×D₁₆	—	15	1	no	—
177	C₂×D₁₆	—	15	1	no	—
178	C₂×M₃₂	—	3	1	no	—
179	C₂²×C₃×C₅	C₂×D₈	1	1	yes	characteristic
180	C₂×D₁₅	—	4	2	no	—
181	C₂×D₁₅	—	4	2	no	—
182	C₂×D₁₅	—	8	2	no	—
183	C₂×D₁₅	—	8	2	no	—
184	C₂×C₅×D₃	—	2	2	no	—
185	C₂×C₅×D₃	C₂×D₈	1	2	yes	—
186	C₂×C₃×D₅	—	4	2	no	—
187	C₂×C₃×D₅	—	8	2	no	—
188	D₃×D₅	—	8	8	no	—
189	C₃×C₄×C₅	C₂×D₈	1	1	yes	characteristic
190	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
191	C₃×Dic₅	—	4	2	no	—
192	C₅×Dic₃	C₂×D₈	1	2	yes	—
193	C₂³×D₃	—	20	1	no	—
194	C₂×C₃×Q₈	—	10	1	no	—
195	C₂×C₃×D₄	—	10	1	no	—
196	C₂×#67	—	20	1	no	—
197	#239	—	10	4	no	—
198	#239	—	20	2	no	—
199	D₃×D₄	—	10	4	no	—
200	D₃×D₄	—	20	2	no	—
201	C₂×D₁₂	—	10	1	no	—
202	C₂×D₁₂	—	10	1	no	—
203	C₂×D₁₂	—	20	1	no	—
204	C₂×C₄×D₃	—	20	1	no	—
205	C₂×C₄×D₃	D₂₀	1	1	yes	characteristic
206	C₃×Q₁₆	—	5	2	no	—
207	C₃×Q₁₆	—	10	1	no	—
208	C₃×D₈	—	5	2	no	—
209	C₃×D₈	—	10	1	no	—
210	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
211	#215	—	10	4	no	—
212	#213	—	10	4	no	—
213	C₂×C₃⋊C₈	D₂₀	1	1	yes	characteristic
214	D₂₄	—	5	2	no	—
215	D₂₄	—	5	2	no	—
216	D₂₄	—	10	1	no	—
217	D₂₄	—	10	1	no	—
218	D₃×C₈	D₂₀	1	2	yes	—
219	D₃×C₈	C₂²×D₅	1	2	yes	—
220	C₃×C₁₆	C₂²×D₅	1	2	yes	complemented
221	C₃⋊C₁₆	C₂²×D₅	1	2	yes	complemented
222	C₂³×C₅	—	3	1	no	—
223	C₂²×D₅	—	4	1	no	—
224	C₂²×D₅	—	12	4	no	—
225	C₂²×D₅	—	12	1	no	—
226	C₂²×D₅	—	12	1	no	—
227	C₂²×D₅	—	24	4	no	—
228	C₂×C₄×C₅	—	3	1	no	—
229	C₂×C₄×C₅	—	3	2	no	—
230	C₂×C₄×C₅	—	3	2	no	—
231	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
232	C₂²⋊D₅	—	12	4	no	—
233	C₂×Dic₅	—	4	1	no	—
234	D₂₀	—	2	2	no	—
235	D₂₀	—	4	1	no	—
236	D₂₀	—	6	2	no	—
237	D₂₀	—	6	2	no	—
238	D₂₀	—	12	4	no	—
239	D₂₀	—	12	1	no	—
240	D₂₀	—	12	1	no	—
241	C₄×D₅	—	12	4	no	—
242	Dic₁₀	—	2	2	no	—
243	Dic₁₀	—	4	1	no	—
244	C₅×C₈	—	3	2	no	—
245	C₅×C₈	D₃×D₄	1	1	yes	characteristic
246	C₅×C₈	C₂³×D₃	1	1	yes	characteristic
247	C₂×#41	—	30	1	no	—
248	C₂²×D₄	—	30	1	no	—
249	#135	—	15	4	no	—
250	#135	—	30	2	no	—
251	C₂×Q₁₆	—	5	1	no	—
252	C₂×SD₁₆	—	30	1	no	—
253	C₂×D₈	—	5	1	no	—
254	C₂×D₈	—	15	4	no	—
255	C₂×D₈	—	15	1	no	—
256	C₂×D₈	—	15	1	no	—
257	C₂×D₈	—	30	2	no	—
258	C₂×D₈	—	30	1	no	—
259	C₂²×C₈	—	3	1	no	—
260	SD₃₂	—	5	4	no	—
261	SD₃₂	—	15	4	no	—
262	D₁₆	—	15	4	no	—
263	D₁₆	—	15	4	no	—
264	M₃₂	—	3	4	no	—
265	C₂×C₁₆	—	3	1	no	—
266	C₂×C₁₆	D₃×D₅	1	1	yes	characteristic, complemented
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	D₁₅	—	8	2	no	—
271	C₃×D₅	—	8	2	no	—
272	C₅×D₃	—	2	2	no	—
273	C₂³×C₃	—	20	1	no	—
274	C₂²×D₃	—	20	1	no	—
275	C₂²×D₃	—	20	1	no	—
276	C₂²×D₃	—	20	4	no	—
277	C₂²×D₃	—	40	4	no	—
278	C₂²×D₃	D₄₀	1	1	yes	characteristic
279	C₃×Q₈	—	10	2	no	—
280	C₃×Q₈	—	20	1	no	—
281	C₃×D₄	—	10	2	no	—
282	C₃×D₄	—	20	1	no	—
283	C₂×C₃×C₄	—	20	1	no	—
284	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
285	#67	—	20	4	no	—
286	C₂×Dic₃	D₄₀	1	1	yes	characteristic
287	D₁₂	—	10	2	no	—
288	D₁₂	—	10	2	no	—
289	D₁₂	—	20	4	no	—
290	D₁₂	—	20	1	no	—
291	D₁₂	—	20	1	no	—
292	C₄×D₃	—	20	4	no	—
293	C₄×D₃	D₄₀	1	2	yes	—
294	C₄×D₃	C₂×D₂₀	1	2	yes	—
295	C₃×C₈	C₂×D₂₀	1	1	yes	characteristic
296	C₃×C₈	C₂³×D₅	1	1	yes	characteristic
297	C₃⋊C₈	C₂×D₂₀	1	2	yes	—
298	C₂²×C₅	—	3	2	no	—
299	C₂²×C₅	—	6	2	no	—
300	C₂²×C₅	D₃×D₈	1	1	yes	characteristic
301	C₂×D₅	—	4	2	no	—
302	C₂×D₅	—	8	2	no	—
303	C₂×D₅	—	12	2	no	—
304	C₂×D₅	—	12	2	no	—
305	C₂×D₅	—	24	8	no	—
306	C₂×D₅	—	24	2	no	—
307	C₂×D₅	—	24	2	no	—
308	C₄×C₅	—	3	2	no	—
309	C₄×C₅	D₃×D₈	1	1	yes	characteristic
310	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
311	Dic₅	—	4	2	no	—
312	C₂⁴	—	60	1	no	—
313	#41	—	30	4	no	—
314	#41	—	60	2	no	—
315	C₂×Q₈	—	10	1	no	—
316	C₂×D₄	—	10	1	no	—
317	C₂×D₄	—	30	4	no	—
318	C₂×D₄	—	30	1	no	—
319	C₂×D₄	—	30	1	no	—
320	C₂×D₄	—	60	2	no	—
321	C₂×D₄	—	60	1	no	—
322	C₂×D₄	—	60	1	no	—
323	C₂²×C₄	—	3	1	no	—
324	C₂²×C₄	—	60	1	no	—
325	Q₁₆	—	5	2	no	—
326	Q₁₆	—	10	1	no	—
327	SD₁₆	—	30	4	no	—
328	D₈	—	5	2	no	—
329	D₈	—	10	1	no	—
330	D₈	—	15	2	no	—
331	D₈	—	15	2	no	—
332	D₈	—	30	4	no	—
333	D₈	—	30	1	no	—
334	D₈	—	30	1	no	—
335	C₂×C₈	—	3	1	no	—
336	C₂×C₈	—	3	2	no	—
337	C₂×C₈	—	3	2	no	—
338	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
339	C₁₆	—	3	2	no	—
340	C₁₆	C₂×D₃×D₅	1	2	yes	complemented
341	C₃×C₅	C₂×#509	1	1	yes	characteristic, complemented, Hall
342	C₂²×C₃	—	20	2	no	—
343	C₂²×C₃	—	40	2	no	—
344	C₂²×C₃	C₂×D₄₀	1	1	yes	characteristic
345	C₂×D₃	—	2	2	no	—
346	C₂×D₃	—	20	2	no	—
347	C₂×D₃	—	20	2	no	—
348	C₂×D₃	—	40	8	no	—
349	C₂×D₃	—	40	2	no	—
350	C₂×D₃	—	40	2	no	—
351	C₂×D₃	C₂×D₄₀	1	2	yes	—
352	C₃×C₄	—	20	2	no	—
353	C₃×C₄	C₂×D₄₀	1	1	yes	characteristic
354	C₃×C₄	C₂²×D₂₀	1	1	yes	characteristic
355	Dic₃	C₂×D₄₀	1	2	yes	—
356	C₂×C₅	—	6	2	no	—
357	C₂×C₅	#4914	1	2	yes	complemented
358	C₂×C₅	C₂×D₃×D₈	1	1	yes	characteristic
359	D₅	—	8	2	no	—
360	D₅	—	24	2	no	—
361	D₅	—	24	2	no	—
362	C₂³	—	3	1	no	—
363	C₂³	—	20	1	no	—
364	C₂³	—	60	4	no	—
365	C₂³	—	60	1	no	—
366	C₂³	—	60	1	no	—
367	C₂³	—	120	4	no	—
368	Q₈	—	10	2	no	—
369	Q₈	—	20	1	no	—
370	D₄	—	10	2	no	—
371	D₄	—	20	1	no	—
372	D₄	—	30	2	no	—
373	D₄	—	30	2	no	—
374	D₄	—	60	4	no	—
375	D₄	—	60	4	no	—
376	D₄	—	60	1	no	—
377	D₄	—	60	1	no	—
378	C₂×C₄	—	3	1	no	—
379	C₂×C₄	—	3	2	no	—
380	C₂×C₄	—	3	2	no	—
381	C₂×C₄	—	20	1	no	—
382	C₂×C₄	—	60	4	no	—
383	C₂×C₄	D₃×D₂₀	1	1	yes	characteristic
384	C₈	—	3	2	no	—
385	C₈	D₃×D₂₀	1	1	yes	characteristic
386	C₈	C₂²×D₃×D₅	1	1	yes	characteristic
387	C₂×C₃	—	40	2	no	—
388	C₂×C₃	#65197	1	2	yes	complemented
389	C₂×C₃	C₂²×D₄₀	1	1	yes	characteristic
390	D₃	—	2	2	no	—
391	D₃	—	40	2	no	—
392	D₃	—	40	2	no	—
393	C₅	C₂×#4914	1	1	yes	characteristic, complemented, Sylow
394	C₂²	—	3	2	no	—
395	C₂²	—	6	2	no	—
396	C₂²	—	20	2	no	—
397	C₂²	—	40	2	no	—
398	C₂²	—	60	2	no	—
399	C₂²	—	60	2	no	—
400	C₂²	—	120	8	no	—
401	C₂²	—	120	2	no	—
402	C₂²	—	120	2	no	—
403	C₂²	D₃×D₄₀	1	1	yes	characteristic
404	C₄	—	3	2	no	—
405	C₄	—	20	2	no	—
406	C₄	D₃×D₄₀	1	1	yes	characteristic
407	C₄	C₂×D₃×D₂₀	1	1	yes	characteristic
408	C₃	C₂×#65197	1	1	yes	characteristic, complemented, Sylow
409	C₂	—	6	2	no	—
410	C₂	—	40	2	no	—
411	C₂	—	120	2	no	—
412	C₂	—	120	2	no	—
413	C₂	#11746821	1	2	yes	direct product factor
414	C₂	C₂×D₃×D₄₀	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₃×D₄₀
commutator, cosocle	C₃×C₅×C₈	C₂⁴
Frattini	C₈	C₂²×D₃×D₅
Fitting	C₂×C₃×C₅×C₁₆	C₂²
socle	C₂²×C₃×C₅	C₂×D₈
hypercenter	C₂×C₁₆	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×C₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×#91275	C₂	semidirect
2. C₂×D₃×D₄₀	C₂	semidirect
3. C₂×D₂₄₀	C₂	semidirect
4. C₂×C₅×#798	C₂	semidirect
5. C₂×C₃×#3932	C₂	semidirect
6. C₂×#90943	C₂	semidirect
7. C₂×#90938	C₂	semidirect
8. #11746821	C₂	direct (N × H)
13. C₂×D₁₂₀	C₂²	semidirect
15. C₂×C₃×Dic₂₀	C₂²	semidirect
20. #91275	C₂²	semidirect
22. D₃×D₄₀	C₂²	semidirect
23. C₂×C₃×C₅×C₁₆	C₂²	semidirect
24. D₂₄₀	C₂²	semidirect
25. C₂×C₅×C₃⋊C₁₆	C₂²	semidirect
26. C₅×#798	C₂²	semidirect
27. C₃×#3932	C₂²	semidirect
28. #90943	C₂²	semidirect
29. #90938	C₂²	semidirect
36. C₂×#3932	D₃	semidirect
56. D₁₂₀	C₂³	semidirect
61. C₃×Dic₂₀	C₂³	semidirect
66. C₃×C₅×C₁₆	C₂³	semidirect
67. C₅×C₃⋊C₁₆	C₂³	semidirect
75. C₂×#798	D₅	semidirect
79. C₂×Dic₂₀	C₂×D₃	semidirect
91. C₂×C₅×C₁₆	C₂×D₃	semidirect
93. #3932	C₂×D₃	semidirect
136. C₂×C₃×C₁₆	C₂×D₅	semidirect
139. C₂×C₃⋊C₁₆	C₂×D₅	semidirect
141. #798	C₂×D₅	semidirect
160. Dic₂₀	C₂²×D₃	semidirect
170. C₅×C₁₆	C₂²×D₃	semidirect
220. C₃×C₁₆	C₂²×D₅	semidirect
221. C₃⋊C₁₆	C₂²×D₅	semidirect
266. C₂×C₁₆	D₃×D₅	semidirect
267. C₂×C₃×C₅	#509	semidirect
340. C₁₆	C₂×D₃×D₅	semidirect
341. C₃×C₅	C₂×#509	semidirect
357. C₂×C₅	#4914	semidirect
388. C₂×C₃	#65197	semidirect
393. C₅	C₂×#4914	semidirect
408. C₃	C₂×#65197	semidirect
413. C₂	#11746821	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×#91275	2
C₂×D₃×D₄₀	2
C₂×D₂₄₀	2
C₂×C₅×#798	2
C₂×C₃×#3932	2
C₂×#90943	2
C₂×#90938	2
#11746821	2
C₂×#65197	3
C₂×#4914	5

Subgroups — C2×#11746821 #14478368

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11746821 #14478368