Subgroups — C₂×#11751293 #14429429

Order 1920.

896 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	C₂²×C₃×C₅×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#91831	C₂	1	2	yes	maximal
3	C₂×#91790	C₂	1	1	yes	maximal, characteristic
4	C₂×#91120	C₂	1	2	yes	maximal, complemented
5	#11751293	C₂	1	8	yes	maximal, direct product factor
6	C₂×#91103	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#65481	—	3	1	no	maximal, Hall
8	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	—
9	C₂×#6817	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₅×Q₁₆	—	2	1	no	—
11	C₂×C₃×C₅×Q₁₆	—	2	1	no	—
12	C₂×C₃×C₅×Q₁₆	—	2	2	no	—
13	C₂×C₃×C₅×Q₁₆	C₂²	1	4	yes	complemented
14	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
15	C₂×#6718	—	2	2	no	—
16	#91831	—	2	4	no	—
17	#91831	C₂²	1	8	yes	—
18	C₂×#6717	—	2	2	no	—
19	C₂×#6710	C₂²	1	2	yes	—
20	C₂×#6710	C₂²	1	1	yes	characteristic
21	#91790	—	2	2	no	—
22	#91790	C₂²	1	4	yes	—
23	C₂×#6705	—	2	1	no	—
24	C₂×C₈×D₁₅	—	2	1	no	—
25	#91120	C₂²	1	8	yes	complemented
26	#91103	C₂²	1	4	yes	complemented
27	C₂×#5192	—	5	1	no	maximal, Hall
28	C₂²×C₅×Q₁₆	D₃	1	1	yes	characteristic, complemented
29	C₂×#4088	—	3	2	no	—
30	C₂×#4047	—	3	1	no	—
31	C₂×#3968	—	3	2	no	—
32	#65481	—	3	8	no	—
33	C₂×#3951	—	3	1	no	—
34	C₂×C₃×C₅×Q₈	—	2	2	no	—
35	C₂×C₃×C₅×Q₈	—	2	2	no	—
36	C₂×C₃×C₅×Q₈	—	2	2	no	—
37	C₂×C₃×C₅×Q₈	—	2	2	no	—
38	C₂×C₃×C₅×Q₈	—	2	2	no	—
39	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	—
40	C₂²×C₃×C₄×C₅	—	2	2	no	—
41	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
42	C₂×#1220	—	2	1	no	—
43	#6817	—	2	1	no	—
44	#6817	—	2	1	no	—
45	#6817	D₄	1	2	yes	—
46	#6817	C₂³	1	2	yes	—
47	C₂×D₆₀	D₄	1	1	yes	characteristic
48	C₂×C₄×D₁₅	—	2	1	no	—
49	C₂×Dic₃₀	D₄	1	1	yes	characteristic
50	C₃×C₅×Q₁₆	—	2	4	no	—
51	C₃×C₅×Q₁₆	—	2	4	no	—
52	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
53	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
54	C₂×C₃×C₅×C₈	D₄	1	2	yes	—
55	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
56	#6718	—	2	8	no	—
57	#6717	—	2	8	no	—
58	#6710	—	2	1	no	—
59	#6710	—	2	2	no	—
60	#6710	C₂³	1	2	yes	—
61	#6710	C₂³	1	4	yes	—
62	C₂×C₃⋊#168	—	2	1	no	—
63	C₂×C₃⋊#168	—	2	2	no	—
64	#6705	—	2	4	no	—
65	C₈×D₁₅	—	2	4	no	—
66	C₂²×C₃×Q₁₆	D₅	1	1	yes	characteristic, complemented
67	C₂×#942	—	5	2	no	—
68	C₂×#901	—	5	1	no	—
69	C₂×#836	—	5	2	no	—
70	#5192	—	5	8	no	—
71	C₂×#819	—	5	1	no	—
72	C₂²×C₅×Q₈	C₂×D₃	1	2	yes	—
73	C₂×#709	—	3	1	no	—
74	C₂×C₅×Q₁₆	—	2	1	no	—
75	C₂×C₅×Q₁₆	—	2	1	no	—
76	C₂×C₅×Q₁₆	—	2	2	no	—
77	C₂×C₅×Q₁₆	C₂×D₃	1	4	yes	complemented
78	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
79	C₂×#689	—	6	2	no	—
80	#4088	—	3	8	no	—
81	#4088	—	6	4	no	—
82	C₂×#688	—	6	2	no	—
83	C₂×#681	—	3	1	no	—
84	C₂×#681	—	3	2	no	—
85	#4047	—	3	4	no	—
86	#4047	—	6	2	no	—
87	C₂×#676	—	6	1	no	—
88	C₂×C₈×D₅	—	6	1	no	—
89	#3968	—	3	8	no	—
90	#3951	—	3	4	no	—
91	C₂×#473	—	15	1	no	Sylow
92	C₂³×C₃×C₅	#41	1	1	yes	characteristic
93	C₂²×D₁₅	—	2	1	no	—
94	C₃×C₅×Q₈	—	2	4	no	—
95	C₃×C₅×Q₈	—	2	4	no	—
96	C₃×C₅×Q₈	—	4	2	no	—
97	C₃×C₅×Q₈	—	4	2	no	—
98	C₂×C₃×C₄×C₅	—	2	4	no	—
99	C₂×C₃×C₄×C₅	—	4	2	no	—
100	C₂×C₃×C₄×C₅	—	4	2	no	—
101	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
102	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
103	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
104	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
105	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
106	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
107	#1220	—	2	2	no	—
108	#1220	—	2	2	no	—
109	C₂×Dic₁₅	—	2	1	no	—
110	D₆₀	—	2	1	no	—
111	D₆₀	C₂×D₄	1	2	yes	—
112	C₄×D₁₅	—	2	2	no	—
113	C₄×D₁₅	—	2	2	no	—
114	Dic₃₀	—	2	1	no	—
115	Dic₃₀	C₂×D₄	1	2	yes	—
116	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
117	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
118	C₃⋊#168	—	2	2	no	—
119	C₃⋊#168	—	2	4	no	—
120	C₂²×C₃×Q₈	C₂×D₅	1	2	yes	—
121	C₂×#235	—	5	1	no	—
122	C₂×C₃×Q₁₆	—	2	1	no	—
123	C₂×C₃×Q₁₆	—	2	1	no	—
124	C₂×C₃×Q₁₆	—	2	2	no	—
125	C₂×C₃×Q₁₆	C₂×D₅	1	4	yes	complemented
126	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
127	C₂×#216	—	10	2	no	—
128	#942	—	5	8	no	—
129	#942	—	10	4	no	—
130	C₂×#215	—	10	2	no	—
131	C₂×#208	—	5	1	no	—
132	C₂×#208	—	5	2	no	—
133	#901	—	5	4	no	—
134	#901	—	10	2	no	—
135	C₂×ΓL(1,𝔽₂₅)	—	10	1	no	—
136	C₂×D₃×C₈	—	10	1	no	—
137	#836	—	5	8	no	—
138	#819	—	5	4	no	—
139	C₂×C₅×Q₈	—	2	2	no	—
140	C₂×C₅×Q₈	—	2	2	no	—
141	C₂×C₅×Q₈	—	2	2	no	—
142	C₂×C₅×Q₈	—	2	2	no	—
143	C₂×C₅×Q₈	—	2	2	no	—
144	C₂×C₅×Q₈	C₂²×D₃	1	4	yes	—
145	C₂²×C₄×C₅	—	2	2	no	—
146	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
147	C₂×C₂²⋊D₅	—	6	1	no	—
148	#709	—	3	2	no	—
149	#709	—	3	2	no	—
150	#709	—	6	1	no	—
151	#709	—	6	1	no	—
152	C₂×D₂₀	—	3	1	no	—
153	C₂×C₄×D₅	—	6	1	no	—
154	C₂×Dic₁₀	—	3	1	no	—
155	C₅×Q₁₆	—	2	4	no	—
156	C₅×Q₁₆	—	2	4	no	—
157	C₂×C₅×C₈	#67	1	1	yes	characteristic
158	C₂×C₅×C₈	#67	1	1	yes	characteristic
159	C₂×C₅×C₈	#67	1	2	yes	—
160	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
161	#689	—	6	8	no	—
162	#688	—	6	8	no	—
163	#681	—	3	4	no	—
164	#681	—	3	2	no	—
165	#681	—	6	2	no	—
166	#681	—	6	1	no	—
167	C₂×#168	—	6	2	no	—
168	C₂×#168	—	6	1	no	—
169	#676	—	6	4	no	—
170	C₈×D₅	—	6	4	no	—
171	C₂×#137	—	15	2	no	—
172	C₂²×Q₁₆	D₁₅	1	1	yes	characteristic, complemented
173	C₂×#131	—	15	1	no	—
174	#473	—	15	8	no	—
175	C₂×#108	—	15	1	no	—
176	C₂×#101	—	15	2	no	—
177	C₂²×C₃×C₅	—	2	2	no	—
178	C₂²×C₃×C₅	#121	1	1	yes	characteristic
179	C₂²×C₃×C₅	#121	1	1	yes	characteristic
180	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
181	C₂×D₁₅	—	2	2	no	—
182	C₂×D₁₅	—	4	2	no	—
183	C₃×C₄×C₅	—	4	4	no	—
184	C₃×C₄×C₅	#121	1	1	yes	characteristic
185	C₃×C₄×C₅	#121	1	1	yes	characteristic
186	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
187	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
188	Dic₁₅	—	2	2	no	—
189	C₂×C₃×Q₈	—	2	2	no	—
190	C₂×C₃×Q₈	—	2	2	no	—
191	C₂×C₃×Q₈	—	2	2	no	—
192	C₂×C₃×Q₈	—	2	2	no	—
193	C₂×C₃×Q₈	—	2	2	no	—
194	C₂×C₃×Q₈	C₂²×D₅	1	4	yes	—
195	C₂²×C₃×C₄	—	2	2	no	—
196	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
197	C₂×#67	—	10	1	no	—
198	#235	—	5	2	no	—
199	#235	—	5	2	no	—
200	#235	—	10	1	no	—
201	#235	—	10	1	no	—
202	C₂×D₁₂	—	5	1	no	—
203	C₂×C₄×D₃	—	10	1	no	—
204	C₂×Dic₆	—	5	1	no	—
205	C₃×Q₁₆	—	2	4	no	—
206	C₃×Q₁₆	—	2	4	no	—
207	C₂×C₃×C₈	C₂²⋊D₅	1	1	yes	characteristic
208	C₂×C₃×C₈	C₂²⋊D₅	1	1	yes	characteristic
209	C₂×C₃×C₈	C₂²⋊D₅	1	2	yes	—
210	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
211	#216	—	10	8	no	—
212	#215	—	10	8	no	—
213	#208	—	5	4	no	—
214	#208	—	5	2	no	—
215	#208	—	10	2	no	—
216	#208	—	10	1	no	—
217	C₂×C₃⋊C₈	—	10	2	no	—
218	C₂×C₃⋊C₈	—	10	1	no	—
219	ΓL(1,𝔽₂₅)	—	10	4	no	—
220	D₃×C₈	—	10	4	no	—
221	C₂³×C₅	#237	1	1	yes	characteristic
222	C₂²×D₅	—	6	1	no	—
223	C₅×Q₈	—	2	4	no	—
224	C₅×Q₈	—	2	4	no	—
225	C₅×Q₈	—	4	2	no	—
226	C₅×Q₈	—	4	2	no	—
227	C₂×C₄×C₅	—	2	4	no	—
228	C₂×C₄×C₅	—	4	2	no	—
229	C₂×C₄×C₅	—	4	2	no	—
230	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
231	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
232	C₂×C₄×C₅	#237	1	1	yes	characteristic
233	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
234	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
235	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
236	C₂²⋊D₅	—	6	2	no	—
237	C₂²⋊D₅	—	6	2	no	—
238	C₂×Dic₅	—	6	1	no	—
239	D₂₀	—	3	2	no	—
240	D₂₀	—	6	1	no	—
241	C₄×D₅	—	6	2	no	—
242	C₄×D₅	—	6	2	no	—
243	Dic₁₀	—	3	2	no	—
244	Dic₁₀	—	6	1	no	—
245	C₅×C₈	C₂×#67	1	2	yes	—
246	C₅×C₈	C₂×#67	1	2	yes	—
247	#168	—	6	4	no	—
248	#168	—	6	2	no	—
249	C₂×#41	—	15	1	no	—
250	C₂²×Q₈	C₂×D₁₅	1	2	yes	—
251	#137	—	15	8	no	—
252	#137	—	30	4	no	—
253	C₂×Q₁₆	—	2	1	no	—
254	C₂×Q₁₆	—	2	1	no	—
255	C₂×Q₁₆	—	2	2	no	—
256	C₂×Q₁₆	—	30	2	no	—
257	C₂×Q₁₆	C₂×D₁₅	1	4	yes	complemented
258	C₂×SD₁₆	—	30	2	no	—
259	#131	—	15	4	no	—
260	#131	—	30	2	no	—
261	C₂×M₁₆	—	15	1	no	—
262	C₂×M₁₆	—	15	2	no	—
263	C₂×M₁₆	—	30	1	no	—
264	C₂²×C₈	—	30	1	no	—
265	C₂²×C₈	C₂×D₁₅	1	1	yes	characteristic
266	#108	—	15	4	no	—
267	#101	—	15	8	no	—
268	C₂×C₃×C₅	—	2	1	no	—
269	C₂×C₃×C₅	—	2	1	no	—
270	C₂×C₃×C₅	#473	1	2	yes	complemented
271	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
272	D₁₅	—	4	2	no	—
273	C₂³×C₃	#711	1	1	yes	characteristic
274	C₂²×D₃	—	10	1	no	—
275	C₃×Q₈	—	2	4	no	—
276	C₃×Q₈	—	2	4	no	—
277	C₃×Q₈	—	4	2	no	—
278	C₃×Q₈	—	4	2	no	—
279	C₂×C₃×C₄	—	2	4	no	—
280	C₂×C₃×C₄	—	4	2	no	—
281	C₂×C₃×C₄	—	4	2	no	—
282	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
283	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
284	C₂×C₃×C₄	#711	1	1	yes	characteristic
285	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
286	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
287	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
288	#67	—	10	2	no	—
289	#67	—	10	2	no	—
290	C₂×Dic₃	—	10	1	no	—
291	D₁₂	—	5	2	no	—
292	D₁₂	—	10	1	no	—
293	C₄×D₃	—	10	2	no	—
294	C₄×D₃	—	10	2	no	—
295	Dic₆	—	5	2	no	—
296	Dic₆	—	10	1	no	—
297	C₃×C₈	C₂×C₂²⋊D₅	1	2	yes	—
298	C₃×C₈	C₂×C₂²⋊D₅	1	2	yes	—
299	C₃⋊C₈	—	10	4	no	—
300	C₃⋊C₈	—	10	2	no	—
301	C₂²×C₅	—	2	2	no	—
302	C₂²×C₅	#938	1	1	yes	characteristic
303	C₂²×C₅	#938	1	1	yes	characteristic
304	C₂²×C₅	C₂×#237	1	1	yes	characteristic
305	C₂×D₅	—	6	2	no	—
306	C₂×D₅	—	12	2	no	—
307	C₄×C₅	—	4	4	no	—
308	C₄×C₅	#938	1	1	yes	characteristic
309	C₄×C₅	#938	1	1	yes	characteristic
310	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
311	C₄×C₅	C₂²×#67	1	1	yes	characteristic
312	Dic₅	—	6	2	no	—
313	#41	—	15	2	no	—
314	#41	—	15	2	no	—
315	#41	—	30	1	no	—
316	#41	—	30	1	no	—
317	C₂×Q₈	—	2	2	no	—
318	C₂×Q₈	—	2	2	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	15	1	no	—
323	C₂×Q₈	C₂²×D₁₅	1	4	yes	—
324	C₂×D₄	—	15	1	no	—
325	C₂×D₄	—	30	1	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	30	1	no	—
328	C₂²×C₄	C₂²×D₁₅	1	1	yes	characteristic
329	Q₁₆	—	2	4	no	—
330	Q₁₆	—	2	4	no	—
331	Q₁₆	—	30	8	no	—
332	SD₁₆	—	30	8	no	—
333	M₁₆	—	15	2	no	—
334	M₁₆	—	15	4	no	—
335	M₁₆	—	30	2	no	—
336	M₁₆	—	30	1	no	—
337	M₁₆	—	30	4	no	—
338	C₂×C₈	—	30	2	no	—
339	C₂×C₈	—	30	1	no	—
340	C₂×C₈	—	30	4	no	—
341	C₂×C₈	#1220	1	1	yes	characteristic
342	C₂×C₈	#1220	1	1	yes	characteristic
343	C₂×C₈	#1220	1	2	yes	—
344	C₂×C₈	C₂²×D₁₅	1	2	yes	—
345	C₃×C₅	C₂×#473	1	1	yes	characteristic, complemented, Hall
346	C₂²×C₃	—	2	2	no	—
347	C₂²×C₃	#4084	1	1	yes	characteristic
348	C₂²×C₃	#4084	1	1	yes	characteristic
349	C₂²×C₃	C₂×#711	1	1	yes	characteristic
350	C₂×D₃	—	10	2	no	—
351	C₂×D₃	—	20	2	no	—
352	C₃×C₄	—	4	4	no	—
353	C₃×C₄	#4084	1	1	yes	characteristic
354	C₃×C₄	#4084	1	1	yes	characteristic
355	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
356	C₃×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
357	Dic₃	—	10	2	no	—
358	C₂×C₅	—	2	1	no	—
359	C₂×C₅	—	2	1	no	—
360	C₂×C₅	#5192	1	2	yes	complemented
361	C₂×C₅	C₂×#938	1	1	yes	characteristic
362	D₅	—	12	2	no	—
363	C₂³	—	30	1	no	—
364	C₂³	#6819	1	1	yes	characteristic
365	Q₈	—	2	4	no	—
366	Q₈	—	2	4	no	—
367	Q₈	—	4	2	no	—
368	Q₈	—	4	2	no	—
369	Q₈	—	15	2	no	—
370	Q₈	—	30	1	no	—
371	D₄	—	15	2	no	—
372	D₄	—	30	2	no	—
373	D₄	—	30	2	no	—
374	D₄	—	30	1	no	—
375	C₂×C₄	—	2	4	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	30	1	no	—
379	C₂×C₄	—	30	2	no	—
380	C₂×C₄	—	30	2	no	—
381	C₂×C₄	D₄×D₁₅	1	1	yes	characteristic
382	C₂×C₄	D₄×D₁₅	1	1	yes	characteristic
383	C₂×C₄	#6819	1	1	yes	characteristic
384	C₂×C₄	C₂×#1220	1	1	yes	characteristic
385	C₂×C₄	C₂×#1220	1	1	yes	characteristic
386	C₂×C₄	C₂³×D₁₅	1	1	yes	characteristic
387	C₈	—	30	4	no	—
388	C₈	—	30	2	no	—
389	C₈	C₂×#1220	1	2	yes	—
390	C₈	C₂×#1220	1	2	yes	—
391	C₂×C₃	—	2	1	no	—
392	C₂×C₃	—	2	1	no	—
393	C₂×C₃	#65481	1	2	yes	complemented
394	C₂×C₃	C₂×#4084	1	1	yes	characteristic
395	D₃	—	20	2	no	—
396	C₅	C₂×#5192	1	1	yes	characteristic, complemented, Sylow
397	C₂²	—	2	2	no	—
398	C₂²	—	30	2	no	—
399	C₂²	—	60	2	no	—
400	C₂²	#91827	1	1	yes	characteristic
401	C₂²	#91827	1	1	yes	characteristic
402	C₂²	C₂×#6819	1	1	yes	characteristic
403	C₄	—	4	4	no	—
404	C₄	—	30	2	no	—
405	C₄	#91827	1	1	yes	characteristic
406	C₄	#91827	1	1	yes	characteristic
407	C₄	C₂×D₄×D₁₅	1	1	yes	characteristic
408	C₄	C₂²×#1220	1	1	yes	characteristic
409	C₃	C₂×#65481	1	1	yes	characteristic, complemented, Sylow
410	C₂	—	2	1	no	—
411	C₂	—	2	1	no	—
412	C₂	—	60	2	no	—
413	C₂	#11751293	1	2	yes	direct product factor
414	C₂	C₂×#91827	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#91827
commutator, cosocle	C₂×C₃×C₄×C₅	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₅
Fitting	C₂²×C₃×C₅×Q₁₆	C₂
socle	C₂²×C₃×C₅	#121
prime radical	C₂×#6817	C₂²
hypercenter	C₂²×Q₁₆	D₁₅
hypocenter	C₃×C₅	C₂×#473
LCS	G ▷ C₂×C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×Q₁₆

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₅×Q₁₆	C₂	semidirect
4. C₂×#91120	C₂	semidirect
5. #11751293	C₂	direct (N × H)
6. C₂×#91103	C₂	semidirect
13. C₂×C₃×C₅×Q₁₆	C₂²	semidirect
25. #91120	C₂²	semidirect
26. #91103	C₂²	semidirect
28. C₂²×C₅×Q₁₆	D₃	semidirect
66. C₂²×C₃×Q₁₆	D₅	semidirect
77. C₂×C₅×Q₁₆	C₂×D₃	semidirect
125. C₂×C₃×Q₁₆	C₂×D₅	semidirect
172. C₂²×Q₁₆	D₁₅	semidirect
257. C₂×Q₁₆	C₂×D₁₅	semidirect
270. C₂×C₃×C₅	#473	semidirect
345. C₃×C₅	C₂×#473	semidirect
360. C₂×C₅	#5192	semidirect
393. C₂×C₃	#65481	semidirect
396. C₅	C₂×#5192	semidirect
409. C₃	C₂×#65481	semidirect
413. C₂	#11751293	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×C₃×C₅×Q₁₆	2
C₂×#91831	2
C₂×#91790	2
C₂×#91120	2
#11751293	2
C₂×#91103	2
C₂×#65481	3
C₂×#5192	5

Subgroups — C2×#11751293 #14429429

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11751293 #14429429