Subgroups — C₂×#11748291 #14478373

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×C₅×#919	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₃×D₄₀	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#91112	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#3960	C₂	1	1	yes	maximal, characteristic, complemented
5	#11748291	C₂	1	8	yes	maximal, direct product factor
6	C₂×#90939	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#90937	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#90935	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#65482	—	3	1	no	maximal, Hall
10	C₂×C₅×#239	—	2	1	no	—
11	C₂×D₃×D₂₀	—	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×#215	—	2	1	no	—
15	C₅×#919	—	2	2	no	—
16	C₅×#919	C₂²	1	4	yes	complemented
17	C₂×C₅×D₂₄	C₂²	1	1	yes	characteristic, complemented
18	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
19	C₂×C₃×D₄₀	C₂²	1	1	yes	characteristic
20	C₂×#6653	—	2	1	no	—
21	D₃×D₄₀	—	2	2	no	—
22	D₃×D₄₀	C₂²	1	4	yes	complemented
23	#91112	C₂²	1	4	yes	complemented
24	C₂×C₃⋊#672	C₂²	1	1	yes	characteristic, complemented
25	C₃×#3960	C₂²	1	4	yes	complemented
26	C₂×C₃×#672	C₂²	1	1	yes	characteristic, complemented
27	#90939	C₂²	1	4	yes	complemented
28	#90937	C₂²	1	4	yes	complemented
29	#90935	C₂²	1	4	yes	complemented
30	C₂×#4914	—	5	1	no	maximal, Hall
31	C₂×C₅×#135	—	3	1	no	—
32	C₂²×D₄₀	—	3	1	no	—
33	#65482	—	3	8	no	—
34	C₂×#3960	—	3	1	no	—
35	C₂×#3960	D₃	1	1	yes	characteristic, complemented
36	C₂×#3958	—	3	1	no	—
37	C₂×#3958	—	3	1	no	—
38	C₂×#3944	—	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	C₅×#239	—	2	4	no	—
43	C₅×#239	—	4	2	no	—
44	C₂×C₅×D₁₂	—	2	1	no	—
45	C₂×C₅×D₁₂	—	4	1	no	—
46	C₂×C₄×C₅×D₃	—	4	1	no	—
47	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
48	C₂×C₃×D₂₀	—	2	1	no	—
49	C₂×#1202	—	4	1	no	—
50	D₃×D₂₀	—	2	4	no	—
51	D₃×D₂₀	—	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×#215	—	2	4	no	—
58	C₂×C₅×C₃⋊C₈	D₄	1	1	yes	characteristic
59	C₅×D₂₄	—	2	1	no	—
60	C₅×D₂₄	C₂³	1	2	yes	complemented
61	C₅×D₃×C₈	D₄	1	2	yes	—
62	C₅×D₃×C₈	C₂³	1	2	yes	—
63	C₃×D₄₀	—	2	1	no	—
64	C₃×D₄₀	C₂³	1	2	yes	—
65	#6653	—	2	4	no	—
66	C₃⋊#672	C₂³	1	2	yes	complemented
67	C₃×#672	C₂³	1	2	yes	complemented
68	C₂×#919	D₅	1	1	yes	characteristic, complemented
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	—	5	1	no	—
76	C₂×C₅×#41	—	6	1	no	—
77	C₂²×D₂₀	—	6	1	no	—
78	C₅×#135	—	3	4	no	—
79	C₅×#135	—	6	2	no	—
80	C₂×C₅×Q₁₆	C₂×D₃	1	1	yes	characteristic, complemented
81	C₂×C₅×SD₁₆	—	6	1	no	—
82	C₂×C₅×D₈	—	3	1	no	—
83	C₂²×C₅×C₈	—	3	1	no	—
84	C₂×D₄₀	—	3	1	no	—
85	C₂×D₄₀	—	3	4	no	—
86	C₂×D₄₀	—	6	2	no	—
87	C₂×D₄₀	—	6	1	no	—
88	C₂×D₄₀	C₂×D₃	1	1	yes	characteristic
89	#3960	—	3	4	no	—
90	#3960	C₂×D₃	1	4	yes	complemented
91	#3958	—	3	4	no	—
92	#3958	—	3	4	no	—
93	#3944	—	3	4	no	—
94	C₂×#672	—	3	1	no	—
95	C₂×#672	C₂×D₃	1	1	yes	characteristic, complemented
96	C₂×#509	—	15	1	no	Sylow
97	C₂²×D₁₅	—	4	1	no	—
98	C₂²×C₅×D₃	—	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	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	C₂×C₅×Dic₃	D₈	1	1	yes	characteristic
110	C₅×D₁₂	—	2	2	no	—
111	C₅×D₁₂	—	4	4	no	—
112	C₅×D₁₂	—	4	1	no	—
113	C₄×C₅×D₃	—	4	4	no	—
114	C₄×C₅×D₃	D₈	1	2	yes	—
115	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
116	C₃×D₂₀	—	2	2	no	—
117	C₃×D₂₀	—	4	1	no	—
118	#1202	—	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	—	2	1	no	—
123	C₂×D₃×D₄	—	10	1	no	—
124	C₂×C₃×Q₁₆	C₂×D₅	1	1	yes	characteristic, complemented
125	C₂×C₃×D₈	—	5	1	no	—
126	C₂×#215	—	2	1	no	—
127	C₂×#213	—	10	1	no	—
128	#919	—	2	2	no	—
129	#919	C₂×D₅	1	4	yes	complemented
130	D₃×D₈	—	5	4	no	—
131	D₃×D₈	—	10	2	no	—
132	C₂×D₂₄	—	5	1	no	—
133	C₂×D₂₄	C₂×D₅	1	1	yes	characteristic, complemented
134	C₂×D₃×C₈	C₂×D₅	1	1	yes	characteristic
135	C₃×SD₃₂	—	5	4	no	—
136	C₂×C₃×C₁₆	—	5	1	no	—
137	#828	—	5	4	no	—
138	#826	—	5	4	no	—
139	C₂×C₃⋊C₁₆	—	5	1	no	—
140	D₄₈	—	5	4	no	—
141	#798	—	5	4	no	—
142	C₂³×D₅	—	12	1	no	—
143	C₅×#41	—	6	4	no	—
144	C₅×#41	—	12	2	no	—
145	C₂×C₅×Q₈	—	2	1	no	—
146	C₂×C₅×D₄	—	6	1	no	—
147	C₂×C₅×D₄	—	12	1	no	—
148	C₂²×C₄×C₅	—	3	1	no	—
149	C₂²×C₄×C₅	—	12	1	no	—
150	C₂×D₂₀	—	2	1	no	—
151	C₂×D₂₀	—	6	4	no	—
152	C₂×D₂₀	—	6	1	no	—
153	C₂×D₂₀	—	12	2	no	—
154	C₂×D₂₀	—	12	1	no	—
155	C₅×Q₁₆	—	2	1	no	—
156	C₅×Q₁₆	C₂²×D₃	1	2	yes	complemented
157	C₅×SD₁₆	—	6	4	no	—
158	C₅×D₈	—	3	2	no	—
159	C₅×D₈	—	6	1	no	—
160	C₂×C₅×C₈	—	3	1	no	—
161	C₂×C₅×C₈	—	3	2	no	—
162	C₂×C₅×C₈	—	3	2	no	—
163	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
164	D₄₀	—	2	1	no	—
165	D₄₀	—	3	2	no	—
166	D₄₀	—	6	4	no	—
167	D₄₀	—	6	1	no	—
168	D₄₀	C₂²×D₃	1	2	yes	—
169	#672	—	3	2	no	—
170	#672	C₂²×D₃	1	2	yes	complemented
171	C₂×#135	—	3	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	—	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	—	2	2	no	—
183	C₂×C₅×D₃	—	4	2	no	—
184	C₂×C₅×D₃	—	8	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	—	4	2	no	—
190	C₃×C₄×C₅	C₂×D₈	1	1	yes	characteristic
191	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
192	C₅×Dic₃	C₂×D₈	1	2	yes	—
193	C₂³×D₃	—	20	1	no	—
194	C₂×C₃×Q₈	—	2	1	no	—
195	C₂×C₃×D₄	—	10	1	no	—
196	C₂×#67	—	20	1	no	—
197	#239	—	2	4	no	—
198	#239	—	4	2	no	—
199	D₃×D₄	—	10	4	no	—
200	D₃×D₄	—	20	2	no	—
201	C₂×D₁₂	—	2	1	no	—
202	C₂×D₁₂	—	4	1	no	—
203	C₂×D₁₂	—	10	1	no	—
204	C₂×C₄×D₃	—	4	1	no	—
205	C₂×C₄×D₃	C₂²⋊D₅	1	1	yes	characteristic
206	C₃×Q₁₆	—	2	1	no	—
207	C₃×Q₁₆	C₂²×D₅	1	2	yes	complemented
208	C₃×D₈	—	5	2	no	—
209	C₃×D₈	—	10	1	no	—
210	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
211	#215	—	2	4	no	—
212	#213	—	10	4	no	—
213	C₂×C₃⋊C₈	C₂²⋊D₅	1	1	yes	characteristic
214	D₂₄	—	2	1	no	—
215	D₂₄	—	5	2	no	—
216	D₂₄	—	10	1	no	—
217	D₂₄	C₂²×D₅	1	2	yes	complemented
218	D₃×C₈	C₂²⋊D₅	1	2	yes	—
219	D₃×C₈	C₂²×D₅	1	2	yes	—
220	C₃×C₁₆	—	5	2	no	—
221	C₃⋊C₁₆	—	5	2	no	—
222	C₂³×C₅	—	3	1	no	—
223	C₂³×C₅	—	12	1	no	—
224	C₂²×D₅	—	4	1	no	—
225	C₂²×D₅	—	12	4	no	—
226	C₂²×D₅	—	12	1	no	—
227	C₂²×D₅	—	24	4	no	—
228	C₅×Q₈	—	2	2	no	—
229	C₅×Q₈	—	4	1	no	—
230	C₅×D₄	—	6	2	no	—
231	C₅×D₄	—	12	4	no	—
232	C₅×D₄	—	12	1	no	—
233	C₂×C₄×C₅	—	3	1	no	—
234	C₂×C₄×C₅	—	3	2	no	—
235	C₂×C₄×C₅	—	3	2	no	—
236	C₂×C₄×C₅	—	4	1	no	—
237	C₂×C₄×C₅	—	12	4	no	—
238	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
239	D₂₀	—	2	2	no	—
240	D₂₀	—	4	1	no	—
241	D₂₀	—	6	2	no	—
242	D₂₀	—	12	4	no	—
243	D₂₀	—	12	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	—	6	1	no	—
248	C₂²×D₄	—	30	1	no	—
249	#135	—	3	4	no	—
250	#135	—	6	2	no	—
251	C₂×Q₁₆	D₃×D₅	1	1	yes	characteristic, complemented
252	C₂×SD₁₆	—	6	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	—	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	—	15	4	no	—
265	C₂×C₁₆	—	5	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	—	8	2	no	—
271	C₅×D₃	—	2	2	no	—
272	C₅×D₃	—	8	2	no	—
273	C₂³×C₃	—	20	1	no	—
274	C₂²×D₃	—	4	1	no	—
275	C₂²×D₃	—	20	1	no	—
276	C₂²×D₃	—	20	4	no	—
277	C₂²×D₃	—	40	4	no	—
278	C₂²×D₃	#686	1	1	yes	characteristic
279	C₃×Q₈	—	2	2	no	—
280	C₃×Q₈	—	4	1	no	—
281	C₃×D₄	—	10	2	no	—
282	C₃×D₄	—	20	1	no	—
283	C₂×C₃×C₄	—	4	1	no	—
284	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
285	#67	—	20	4	no	—
286	C₂×Dic₃	#686	1	1	yes	characteristic
287	D₁₂	—	2	2	no	—
288	D₁₂	—	4	4	no	—
289	D₁₂	—	4	1	no	—
290	D₁₂	—	10	2	no	—
291	D₁₂	—	20	1	no	—
292	C₄×D₃	—	4	4	no	—
293	C₄×D₃	#686	1	2	yes	—
294	C₄×D₃	C₂×C₂²⋊D₅	1	2	yes	—
295	C₃×C₈	C₂×C₂²⋊D₅	1	1	yes	characteristic
296	C₃×C₈	C₂³×D₅	1	1	yes	characteristic
297	C₃⋊C₈	C₂×C₂²⋊D₅	1	2	yes	—
298	C₂²×C₅	—	3	2	no	—
299	C₂²×C₅	—	6	2	no	—
300	C₂²×C₅	—	12	2	no	—
301	C₂²×C₅	—	24	2	no	—
302	C₂²×C₅	D₃×D₈	1	1	yes	characteristic
303	C₂×D₅	—	4	2	no	—
304	C₂×D₅	—	8	2	no	—
305	C₂×D₅	—	12	2	no	—
306	C₂×D₅	—	24	8	no	—
307	C₂×D₅	—	24	2	no	—
308	C₄×C₅	—	3	2	no	—
309	C₄×C₅	—	4	2	no	—
310	C₄×C₅	D₃×D₈	1	1	yes	characteristic
311	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
312	C₂⁴	—	60	1	no	—
313	#41	—	6	4	no	—
314	#41	—	12	2	no	—
315	C₂×Q₈	—	2	1	no	—
316	C₂×D₄	—	6	1	no	—
317	C₂×D₄	—	10	1	no	—
318	C₂×D₄	—	12	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	—	3	1	no	—
324	C₂²×C₄	—	12	1	no	—
325	Q₁₆	—	2	1	no	—
326	Q₁₆	C₂×D₃×D₅	1	2	yes	complemented
327	SD₁₆	—	6	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	—	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	—	5	2	no	—
340	C₁₆	—	15	2	no	—
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×#686	1	1	yes	characteristic
345	C₂×D₃	—	2	2	no	—
346	C₂×D₃	—	4	2	no	—
347	C₂×D₃	—	8	2	no	—
348	C₂×D₃	—	20	2	no	—
349	C₂×D₃	—	40	8	no	—
350	C₂×D₃	—	40	2	no	—
351	C₂×D₃	C₂×#686	1	2	yes	—
352	C₃×C₄	—	4	2	no	—
353	C₃×C₄	C₂×#686	1	1	yes	characteristic
354	C₃×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
355	Dic₃	C₂×#686	1	2	yes	—
356	C₂×C₅	—	6	2	no	—
357	C₂×C₅	—	24	2	no	—
358	C₂×C₅	#4914	1	2	yes	complemented
359	C₂×C₅	C₂×D₃×D₈	1	1	yes	characteristic
360	D₅	—	8	2	no	—
361	D₅	—	24	2	no	—
362	C₂³	—	3	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	4	no	—
373	D₄	—	12	1	no	—
374	D₄	—	20	1	no	—
375	D₄	—	30	2	no	—
376	D₄	—	60	4	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	—	4	1	no	—
382	C₂×C₄	—	12	4	no	—
383	C₂×C₄	D₃×C₂²⋊D₅	1	1	yes	characteristic
384	C₈	—	3	2	no	—
385	C₈	D₃×C₂²⋊D₅	1	1	yes	characteristic
386	C₈	C₂²×D₃×D₅	1	1	yes	characteristic
387	C₂×C₃	—	40	2	no	—
388	C₂×C₃	#65482	1	2	yes	complemented
389	C₂×C₃	C₂²×#686	1	1	yes	characteristic
390	D₃	—	2	2	no	—
391	D₃	—	8	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	—	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	D₃×#686	1	1	yes	characteristic
404	C₄	—	3	2	no	—
405	C₄	—	4	2	no	—
406	C₄	D₃×#686	1	1	yes	characteristic
407	C₄	C₂×D₃×C₂²⋊D₅	1	1	yes	characteristic
408	C₃	C₂×#65482	1	1	yes	characteristic, complemented, Sylow
409	C₂	—	6	2	no	—
410	C₂	—	24	2	no	—
411	C₂	—	40	2	no	—
412	C₂	—	120	2	no	—
413	C₂	#11748291	1	2	yes	direct product factor
414	C₂	C₂×D₃×#686	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₃×#686
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×C₅×#919	C₂	semidirect
2. C₂×D₃×D₄₀	C₂	semidirect
3. C₂×#91112	C₂	semidirect
4. C₂×C₃×#3960	C₂	semidirect
5. #11748291	C₂	direct (N × H)
6. C₂×#90939	C₂	semidirect
7. C₂×#90937	C₂	semidirect
8. C₂×#90935	C₂	semidirect
12. C₂×C₃×C₅×Q₁₆	C₂²	semidirect
16. C₅×#919	C₂²	semidirect
17. C₂×C₅×D₂₄	C₂²	semidirect
22. D₃×D₄₀	C₂²	semidirect
23. #91112	C₂²	semidirect
24. C₂×C₃⋊#672	C₂²	semidirect
25. C₃×#3960	C₂²	semidirect
26. C₂×C₃×#672	C₂²	semidirect
27. #90939	C₂²	semidirect
28. #90937	C₂²	semidirect
29. #90935	C₂²	semidirect
35. C₂×#3960	D₃	semidirect
53. C₃×C₅×Q₁₆	C₂³	semidirect
60. C₅×D₂₄	C₂³	semidirect
66. C₃⋊#672	C₂³	semidirect
67. C₃×#672	C₂³	semidirect
68. C₂×#919	D₅	semidirect
80. C₂×C₅×Q₁₆	C₂×D₃	semidirect
90. #3960	C₂×D₃	semidirect
95. C₂×#672	C₂×D₃	semidirect
124. C₂×C₃×Q₁₆	C₂×D₅	semidirect
129. #919	C₂×D₅	semidirect
133. C₂×D₂₄	C₂×D₅	semidirect
156. C₅×Q₁₆	C₂²×D₃	semidirect
170. #672	C₂²×D₃	semidirect
207. C₃×Q₁₆	C₂²×D₅	semidirect
217. D₂₄	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
358. C₂×C₅	#4914	semidirect
388. C₂×C₃	#65482	semidirect
393. C₅	C₂×#4914	semidirect
408. C₃	C₂×#65482	semidirect
413. C₂	#11748291	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×C₅×#919	2
C₂×D₃×D₄₀	2
C₂×#91112	2
C₂×C₃×#3960	2
#11748291	2
C₂×#90939	2
C₂×#90937	2
C₂×#90935	2
C₂×#65482	3
C₂×#4914	5

Subgroups — C2×#11748291 #14478373

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11748291 #14478373