Subgroups — C₂×C₄×#6738 #14411186

Order 1920.

1520 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#6738	C₂	1	2	yes	maximal
2	C₂×C₄×#1200	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₃⋊#170	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×C₄×#170	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×Dic₃×#170	C₂	1	2	yes	maximal, complemented
6	C₄×#6738	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₄×D₅⋊C₈	—	3	1	no	maximal, Hall
8	C₂²×C₄×D₁₅	C₄	1	1	yes	characteristic
9	C₂²×#1200	C₄	1	1	yes	characteristic
10	C₂²×#1200	C₂²	1	1	yes	characteristic
11	C₂²×C₃⋊#170	C₂²	1	2	yes	—
12	C₂²×C₃×#170	C₂²	1	2	yes	—
13	C₂×#6738	C₄	1	16	yes	direct product factor
14	C₂×#6738	C₂²	1	8	yes	—
15	C₂×C₄×C₅×Dic₃	C₄	1	1	yes	characteristic
16	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
17	C₂×Dic₃×Dic₅	C₄	1	1	yes	characteristic
18	C₂×Dic₃×Dic₅	C₂²	1	1	yes	characteristic
19	C₄×#1200	C₄	1	4	yes	—
20	C₄×#1200	C₂²	1	4	yes	—
21	C₄×C₃⋊#170	C₂²	1	4	yes	complemented
22	C₃×C₄×#170	C₂²	1	4	yes	complemented
23	Dic₃×#170	C₂²	1	8	yes	complemented
24	C₂×C₄×D₃×C₈	—	5	1	no	maximal, Hall
25	C₂²×D₅⋊C₈	—	3	2	no	—
26	C₂×C₄²×D₅	—	3	1	no	—
27	C₂×C₄×#170	—	3	1	no	—
28	C₂×C₄×#170	—	3	2	no	—
29	C₂×C₄×#170	D₃	1	1	yes	characteristic, complemented
30	C₄×D₅⋊C₈	—	3	8	no	—
31	C₂³×D₁₅	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
33	C₂²×Dic₁₅	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄×D₁₅	C₈	1	8	yes	complemented
35	C₂×C₄×D₁₅	C₂×C₄	1	4	yes	—
36	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
37	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
38	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
40	C₂×#1200	C₈	1	8	yes	complemented
41	C₂×#1200	C₂×C₄	1	2	yes	—
42	C₂×#1200	C₂×C₄	1	8	yes	—
43	C₂×#1200	C₂×C₄	1	4	yes	—
44	C₂×#1200	C₂³	1	2	yes	—
45	C₂×C₃⋊#170	C₂×C₄	1	8	yes	complemented
46	C₂×C₃⋊#170	C₂³	1	4	yes	—
47	C₂×C₃×#170	C₂×C₄	1	8	yes	complemented
48	C₂×C₃×#170	C₂³	1	4	yes	—
49	#6738	C₂×C₄	1	32	yes	direct product factor
50	C₄×C₅×Dic₃	C₂×C₄	1	4	yes	—
51	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
52	C₃×C₄×Dic₅	C₂³	1	2	yes	—
53	Dic₃×Dic₅	C₂×C₄	1	2	yes	—
54	Dic₃×Dic₅	C₂×C₄	1	4	yes	—
55	Dic₃×Dic₅	C₂³	1	2	yes	—
56	C₂²×D₃×C₈	—	5	2	no	—
57	C₂×C₄²×D₃	—	5	1	no	—
58	C₂×C₃×C₄×C₈	—	5	1	no	—
59	C₂×C₈×Dic₃	—	5	2	no	—
60	C₂×C₄×C₃⋊C₈	—	5	1	no	—
61	C₄×D₃×C₈	—	5	8	no	—
62	C₂²×C₄×D₅	—	3	1	no	—
63	C₂²×C₄×D₅	—	3	1	no	—
64	C₂²×C₄×D₅	—	3	1	no	—
65	C₂²×#170	—	3	2	no	—
66	C₂²×#170	C₂×D₃	1	2	yes	—
67	C₂×D₅⋊C₈	—	3	16	no	—
68	C₂×D₅⋊C₈	—	3	8	no	—
69	C₂×C₄²×C₅	—	3	1	no	—
70	C₂×C₄×Dic₅	—	3	1	no	—
71	C₂×C₄×Dic₅	—	3	1	no	—
72	C₂×C₄×Dic₅	C₂×D₃	1	1	yes	characteristic
73	C₄²×D₅	—	3	4	no	—
74	C₄²×D₅	—	3	4	no	—
75	C₄×#170	—	3	8	no	—
76	C₄×#170	—	3	4	no	—
77	C₄×#170	C₂×D₃	1	4	yes	complemented
78	C₂²×C₄×C₈	—	15	1	no	Sylow
79	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
80	C₂²×D₁₅	C₄²	1	4	yes	—
81	C₂²×D₁₅	C₂×C₈	1	4	yes	—
82	C₂²×D₁₅	C₂×C₈	1	4	yes	—
83	C₂²×D₁₅	C₂²×C₄	1	2	yes	—
84	C₂×C₃×C₄×C₅	C₂×C₈	1	4	yes	complemented
85	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
86	C₂×Dic₁₅	C₂×C₈	1	4	yes	complemented
87	C₂×Dic₁₅	C₂²×C₄	1	2	yes	—
88	C₄×D₁₅	C₂×C₈	1	16	yes	complemented
89	C₂×C₅×Dic₃	C₄²	1	4	yes	—
90	C₂×C₅×Dic₃	C₂×C₈	1	4	yes	complemented
91	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
92	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
93	C₂×C₃×Dic₅	C₂×C₈	1	4	yes	complemented
94	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
95	C₂×C₃×Dic₅	C₂²×C₄	1	4	yes	—
96	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
97	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
98	#1200	C₄²	1	8	yes	—
99	#1200	C₂×C₈	1	16	yes	complemented
100	#1200	C₂²×C₄	1	8	yes	—
101	C₃⋊#170	C₂²×C₄	1	8	yes	complemented
102	C₃×#170	C₂²×C₄	1	8	yes	complemented
103	C₂²×C₄×D₃	—	5	1	no	—
104	C₂²×C₄×D₃	—	5	1	no	—
105	C₂²×C₄×D₃	—	5	1	no	—
106	C₂²×C₃×C₈	—	5	2	no	—
107	C₂×C₃×C₄²	—	5	1	no	—
108	C₂×C₄×Dic₃	—	5	1	no	—
109	C₂×C₄×Dic₃	—	5	1	no	—
110	C₂×C₄×Dic₃	AGL(1,𝔽₅)	1	1	yes	characteristic
111	C₂²×C₃⋊C₈	—	5	2	no	—
112	C₂×D₃×C₈	—	5	16	no	—
113	C₂×D₃×C₈	—	5	8	no	—
114	C₄²×D₃	—	5	4	no	—
115	C₄²×D₃	—	5	4	no	—
116	C₃×C₄×C₈	—	5	4	no	—
117	C₈×Dic₃	—	5	8	no	—
118	C₄×C₃⋊C₈	—	5	4	no	—
119	C₂³×D₅	—	3	1	no	—
120	C₂²×C₄×C₅	—	3	1	no	—
121	C₂²×C₄×C₅	—	3	1	no	—
122	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
123	C₂²×Dic₅	—	3	1	no	—
124	C₂²×Dic₅	C₄×D₃	1	1	yes	characteristic
125	C₂²×Dic₅	C₂²×D₃	1	1	yes	characteristic
126	C₂×C₄×D₅	—	3	8	no	—
127	C₂×C₄×D₅	—	3	4	no	—
128	C₂×C₄×D₅	—	3	8	no	—
129	C₂×C₄×D₅	—	3	8	no	—
130	C₂×C₄×D₅	—	3	2	no	—
131	C₂×C₄×D₅	—	3	4	no	—
132	C₂×C₄×D₅	—	3	2	no	—
133	C₂×#170	—	3	8	no	—
134	C₂×#170	—	3	4	no	—
135	C₂×#170	C₄×D₃	1	8	yes	complemented
136	C₂×#170	C₂²×D₃	1	4	yes	—
137	D₅⋊C₈	—	3	32	no	—
138	C₄²×C₅	—	3	4	no	—
139	C₄×Dic₅	—	3	2	no	—
140	C₄×Dic₅	—	3	4	no	—
141	C₄×Dic₅	—	3	2	no	—
142	C₄×Dic₅	C₄×D₃	1	2	yes	—
143	C₄×Dic₅	C₂²×D₃	1	2	yes	—
144	C₂³×C₈	—	15	2	no	—
145	C₂²×C₄²	—	15	1	no	—
146	C₂×C₄×C₈	—	5	1	no	—
147	C₂×C₄×C₈	—	15	8	no	—
148	C₂×C₄×C₈	—	15	1	no	—
149	C₂×C₄×C₈	—	15	2	no	—
150	C₂²×C₃×C₅	C₂×C₄²	1	2	yes	—
151	C₂²×C₃×C₅	C₂²×C₈	1	2	yes	—
152	C₂²×C₃×C₅	C₂²×C₈	1	2	yes	—
153	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
154	C₂×D₁₅	C₄×C₈	1	16	yes	complemented
155	C₂×D₁₅	C₂×C₄²	1	4	yes	—
156	C₂×D₁₅	C₂²×C₈	1	4	yes	—
157	C₂×D₁₅	C₂²×C₈	1	4	yes	—
158	C₃×C₄×C₅	C₂²×C₈	1	4	yes	complemented
159	Dic₁₅	C₂²×C₈	1	4	yes	complemented
160	C₃×Dic₅	C₂×C₄²	1	2	yes	—
161	C₃×Dic₅	C₂²×C₈	1	4	yes	complemented
162	C₃×Dic₅	C₂³×C₄	1	2	yes	—
163	C₅×Dic₃	C₂×C₄²	1	4	yes	—
164	C₅×Dic₃	C₂²×C₈	1	4	yes	complemented
165	C₂³×D₃	—	5	1	no	—
166	C₂²×C₃×C₄	—	5	1	no	—
167	C₂²×C₃×C₄	—	5	1	no	—
168	C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
169	C₂²×Dic₃	—	5	1	no	—
170	C₂²×Dic₃	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
171	C₂²×Dic₃	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
172	C₂×C₄×D₃	—	5	8	no	—
173	C₂×C₄×D₃	—	5	4	no	—
174	C₂×C₄×D₃	—	5	8	no	—
175	C₂×C₄×D₃	—	5	8	no	—
176	C₂×C₄×D₃	—	5	4	no	—
177	C₂×C₄×D₃	—	5	2	no	—
178	C₂×C₄×D₃	—	5	2	no	—
179	C₂×C₃×C₈	—	5	4	no	—
180	C₂×C₃×C₈	—	5	8	no	—
181	C₃×C₄²	—	5	2	no	—
182	C₃×C₄²	—	5	2	no	—
183	C₄×Dic₃	—	5	2	no	—
184	C₄×Dic₃	—	5	4	no	—
185	C₄×Dic₃	—	5	2	no	—
186	C₄×Dic₃	C₂×AGL(1,𝔽₅)	1	4	yes	—
187	C₂×C₃⋊C₈	—	5	4	no	—
188	C₂×C₃⋊C₈	—	5	8	no	—
189	D₃×C₈	—	5	32	no	—
190	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
191	C₂²×D₅	—	3	4	no	—
192	C₂²×D₅	—	3	4	no	—
193	C₂²×D₅	—	3	4	no	—
194	C₂²×D₅	—	3	2	no	—
195	C₂×C₄×C₅	—	3	4	no	—
196	C₂×C₄×C₅	—	3	4	no	—
197	C₂×C₄×C₅	—	3	2	no	—
198	C₂×C₄×C₅	—	3	2	no	—
199	C₂×C₄×C₅	D₃×C₈	1	4	yes	complemented
200	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
201	C₂×Dic₅	—	3	4	no	—
202	C₂×Dic₅	—	3	2	no	—
203	C₂×Dic₅	D₃×C₈	1	4	yes	complemented
204	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
205	C₂×Dic₅	C₂×C₄×D₃	1	4	yes	—
206	C₂×Dic₅	C₂×C₄×D₃	1	2	yes	—
207	C₂×Dic₅	C₂³×D₃	1	1	yes	characteristic
208	C₄×D₅	—	3	16	no	—
209	C₄×D₅	—	3	8	no	—
210	C₄×D₅	—	3	16	no	—
211	C₄×D₅	—	3	8	no	—
212	#170	—	3	8	no	—
213	#170	C₂×C₄×D₃	1	8	yes	complemented
214	C₂³×C₄	—	15	1	no	—
215	C₂³×C₄	—	15	1	no	—
216	C₂³×C₄	—	15	1	no	—
217	C₂²×C₈	—	5	2	no	—
218	C₂²×C₈	—	15	16	no	—
219	C₂²×C₈	—	15	8	no	—
220	C₂²×C₈	—	15	2	no	—
221	C₂×C₄²	—	3	1	no	—
222	C₂×C₄²	—	5	1	no	—
223	C₂×C₄²	—	15	4	no	—
224	C₂×C₄²	—	15	4	no	—
225	C₂×C₄²	—	15	1	no	—
226	C₂×C₄²	—	15	1	no	—
227	C₄×C₈	—	5	4	no	—
228	C₄×C₈	—	15	4	no	—
229	C₄×C₈	—	15	8	no	—
230	C₂×C₃×C₅	C₂×C₄×C₈	1	4	yes	complemented
231	C₂×C₃×C₅	C₂²×C₄²	1	1	yes	characteristic
232	C₂×C₃×C₅	C₂³×C₈	1	1	yes	characteristic
233	C₂×C₃×C₅	C₂³×C₈	1	1	yes	characteristic
234	D₁₅	C₂×C₄×C₈	1	8	yes	complemented
235	C₂³×C₃	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
236	C₂²×D₃	—	5	4	no	—
237	C₂²×D₃	—	5	4	no	—
238	C₂²×D₃	—	5	4	no	—
239	C₂²×D₃	—	5	2	no	—
240	C₂×C₃×C₄	—	5	4	no	—
241	C₂×C₃×C₄	—	5	4	no	—
242	C₂×C₃×C₄	—	5	2	no	—
243	C₂×C₃×C₄	—	5	1	no	—
244	C₂×C₃×C₄	—	5	1	no	—
245	C₂×C₃×C₄	D₅⋊C₈	1	4	yes	complemented
246	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	2	yes	—
247	C₂×Dic₃	—	5	4	no	—
248	C₂×Dic₃	—	5	2	no	—
249	C₂×Dic₃	D₅⋊C₈	1	4	yes	complemented
250	C₂×Dic₃	C₄×AGL(1,𝔽₅)	1	4	yes	—
251	C₂×Dic₃	C₂²×AGL(1,𝔽₅)	1	2	yes	—
252	C₂×Dic₃	C₂²×AGL(1,𝔽₅)	1	2	yes	—
253	C₄×D₃	—	5	16	no	—
254	C₄×D₃	—	5	16	no	—
255	C₄×D₃	—	5	8	no	—
256	C₄×D₃	—	5	8	no	—
257	C₃×C₈	—	5	8	no	—
258	C₃⋊C₈	—	5	8	no	—
259	C₂²×C₅	C₄²×D₃	1	2	yes	—
260	C₂²×C₅	C₂×D₃×C₈	1	2	yes	—
261	C₂²×C₅	C₂×D₃×C₈	1	2	yes	—
262	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
263	C₂×D₅	—	3	16	no	—
264	C₂×D₅	—	3	4	no	—
265	C₂×D₅	—	3	4	no	—
266	C₂×D₅	—	3	4	no	—
267	C₄×C₅	—	3	4	no	—
268	C₄×C₅	—	3	4	no	—
269	C₄×C₅	C₂×D₃×C₈	1	4	yes	complemented
270	Dic₅	—	3	4	no	—
271	Dic₅	C₄²×D₃	1	2	yes	—
272	Dic₅	C₂×D₃×C₈	1	4	yes	complemented
273	Dic₅	C₂²×C₄×D₃	1	2	yes	—
274	C₂⁴	—	15	1	no	—
275	C₂²×C₄	—	3	1	no	—
276	C₂²×C₄	—	3	1	no	—
277	C₂²×C₄	—	5	1	no	—
278	C₂²×C₄	—	5	1	no	—
279	C₂²×C₄	—	15	2	no	—
280	C₂²×C₄	—	15	4	no	—
281	C₂²×C₄	—	15	2	no	—
282	C₂²×C₄	—	15	8	no	—
283	C₂²×C₄	—	15	8	no	—
284	C₂²×C₄	—	15	1	no	—
285	C₂²×C₄	—	15	8	no	—
286	C₂²×C₄	—	15	4	no	—
287	C₂²×C₄	D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
288	C₂×C₈	—	5	4	no	—
289	C₂×C₈	—	5	8	no	—
290	C₂×C₈	—	15	32	no	—
291	C₂×C₈	—	15	4	no	—
292	C₂×C₈	—	15	8	no	—
293	C₄²	—	3	4	no	—
294	C₄²	—	5	2	no	—
295	C₄²	—	5	2	no	—
296	C₄²	—	15	2	no	—
297	C₄²	—	15	4	no	—
298	C₄²	—	15	2	no	—
299	C₃×C₅	C₂²×C₄×C₈	1	1	yes	characteristic, complemented, Hall
300	C₂²×C₃	C₂×D₅⋊C₈	1	2	yes	—
301	C₂²×C₃	C₂×D₅⋊C₈	1	2	yes	—
302	C₂²×C₃	C₂×C₄×AGL(1,𝔽₅)	1	2	yes	—
303	C₂²×C₃	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
304	C₂×D₃	—	5	16	no	—
305	C₂×D₃	—	5	4	no	—
306	C₂×D₃	—	5	4	no	—
307	C₂×D₃	—	5	4	no	—
308	C₃×C₄	—	5	4	no	—
309	C₃×C₄	—	5	2	no	—
310	C₃×C₄	—	5	2	no	—
311	C₃×C₄	C₂×D₅⋊C₈	1	4	yes	complemented
312	Dic₃	—	5	4	no	—
313	Dic₃	C₂×D₅⋊C₈	1	4	yes	complemented
314	Dic₃	C₂×C₄×AGL(1,𝔽₅)	1	4	yes	—
315	C₂×C₅	C₄×D₃×C₈	1	4	yes	complemented
316	C₂×C₅	C₂×C₄²×D₃	1	1	yes	characteristic
317	C₂×C₅	C₂²×D₃×C₈	1	1	yes	characteristic
318	C₂×C₅	C₂²×D₃×C₈	1	1	yes	characteristic
319	D₅	—	3	8	no	—
320	C₂³	—	15	4	no	—
321	C₂³	—	15	4	no	—
322	C₂³	—	15	4	no	—
323	C₂³	—	15	2	no	—
324	C₂³	C₂×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
325	C₂×C₄	—	3	4	no	—
326	C₂×C₄	—	3	4	no	—
327	C₂×C₄	—	3	2	no	—
328	C₂×C₄	—	3	2	no	—
329	C₂×C₄	—	5	4	no	—
330	C₂×C₄	—	5	4	no	—
331	C₂×C₄	—	5	1	no	—
332	C₂×C₄	—	5	2	no	—
333	C₂×C₄	—	5	1	no	—
334	C₂×C₄	—	15	8	no	—
335	C₂×C₄	—	15	16	no	—
336	C₂×C₄	—	15	8	no	—
337	C₂×C₄	—	15	4	no	—
338	C₂×C₄	—	15	2	no	—
339	C₂×C₄	—	15	16	no	—
340	C₂×C₄	#6738	1	4	yes	direct product factor
341	C₂×C₄	C₂×D₃×AGL(1,𝔽₅)	1	2	yes	—
342	C₈	—	5	8	no	—
343	C₈	—	15	8	no	—
344	C₂×C₃	C₄×D₅⋊C₈	1	4	yes	complemented
345	C₂×C₃	C₂²×D₅⋊C₈	1	1	yes	characteristic
346	C₂×C₃	C₂²×D₅⋊C₈	1	1	yes	characteristic
347	C₂×C₃	C₂²×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
348	D₃	—	5	8	no	—
349	C₅	C₂×C₄×D₃×C₈	1	1	yes	characteristic, complemented, Sylow
350	C₂²	—	15	4	no	—
351	C₂²	—	15	4	no	—
352	C₂²	—	15	4	no	—
353	C₂²	—	15	16	no	—
354	C₂²	D₃×D₅⋊C₈	1	2	yes	—
355	C₂²	C₄×D₃×AGL(1,𝔽₅)	1	2	yes	—
356	C₂²	C₂×#6738	1	2	yes	—
357	C₂²	C₂²×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
358	C₄	—	3	4	no	—
359	C₄	—	3	4	no	—
360	C₄	—	5	4	no	—
361	C₄	—	5	2	no	—
362	C₄	—	5	2	no	—
363	C₄	—	15	4	no	—
364	C₄	C₂×#6738	1	4	yes	direct product factor
365	C₃	C₂×C₄×D₅⋊C₈	1	1	yes	characteristic, complemented, Sylow
366	C₂	—	15	8	no	—
367	C₂	C₄×#6738	1	4	yes	direct product factor
368	C₂	C₂×D₃×D₅⋊C₈	1	1	yes	characteristic
369	C₂	C₂×C₄×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
370	C₂	C₂²×#6738	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²×C₄	D₃×AGL(1,𝔽₅)
commutator, hypocenter	C₃×C₅	C₂²×C₄×C₈
Frattini	C₂²	C₂²×D₃×AGL(1,𝔽₅)
Fitting	C₂²×C₃×C₄×C₅	C₂×C₄
socle	C₂³×C₃×C₅	C₂²×C₄
prime radical	C₂³×D₁₅	C₂×C₄
cosocle	C₂×C₃×Dic₅	C₂⁴
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
3. C₂×C₄×C₃⋊#170	C₂	semidirect
4. C₂×C₃×C₄×#170	C₂	semidirect
5. C₂×Dic₃×#170	C₂	semidirect
6. C₄×#6738	C₂	direct (N × H)
13. C₂×#6738	C₄	direct (N × H)
21. C₄×C₃⋊#170	C₂²	semidirect
22. C₃×C₄×#170	C₂²	semidirect
23. Dic₃×#170	C₂²	semidirect
29. C₂×C₄×#170	D₃	semidirect
34. C₂×C₄×D₁₅	C₈	semidirect
40. C₂×#1200	C₈	semidirect
45. C₂×C₃⋊#170	C₂×C₄	semidirect
47. C₂×C₃×#170	C₂×C₄	semidirect
49. #6738	C₂×C₄	direct (N × H)
77. C₄×#170	C₂×D₃	semidirect
84. C₂×C₃×C₄×C₅	C₂×C₈	semidirect
86. C₂×Dic₁₅	C₂×C₈	semidirect
88. C₄×D₁₅	C₂×C₈	semidirect
90. C₂×C₅×Dic₃	C₂×C₈	semidirect
93. C₂×C₃×Dic₅	C₂×C₈	semidirect
99. #1200	C₂×C₈	semidirect
101. C₃⋊#170	C₂²×C₄	semidirect
102. C₃×#170	C₂²×C₄	semidirect
135. C₂×#170	C₄×D₃	semidirect
154. C₂×D₁₅	C₄×C₈	semidirect
158. C₃×C₄×C₅	C₂²×C₈	semidirect
159. Dic₁₅	C₂²×C₈	semidirect
161. C₃×Dic₅	C₂²×C₈	semidirect
164. C₅×Dic₃	C₂²×C₈	semidirect
199. C₂×C₄×C₅	D₃×C₈	semidirect
203. C₂×Dic₅	D₃×C₈	semidirect
213. #170	C₂×C₄×D₃	semidirect
230. C₂×C₃×C₅	C₂×C₄×C₈	semidirect
234. D₁₅	C₂×C₄×C₈	semidirect
245. C₂×C₃×C₄	D₅⋊C₈	semidirect
249. C₂×Dic₃	D₅⋊C₈	semidirect
269. C₄×C₅	C₂×D₃×C₈	semidirect
272. Dic₅	C₂×D₃×C₈	semidirect
299. C₃×C₅	C₂²×C₄×C₈	semidirect
311. C₃×C₄	C₂×D₅⋊C₈	semidirect
313. Dic₃	C₂×D₅⋊C₈	semidirect
315. C₂×C₅	C₄×D₃×C₈	semidirect
340. C₂×C₄	#6738	direct (N × H)
344. C₂×C₃	C₄×D₅⋊C₈	semidirect
349. C₅	C₂×C₄×D₃×C₈	semidirect
364. C₄	C₂×#6738	direct (N × H)
365. C₃	C₂×C₄×D₅⋊C₈	semidirect
367. C₂	C₄×#6738	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×#6738	2
C₂×C₄×#1200	2
C₂×C₄×C₃⋊#170	2
C₂×C₃×C₄×#170	2
C₂×Dic₃×#170	2
C₄×#6738	2
C₂×C₄×D₅⋊C₈	3
C₂×C₄×D₃×C₈	5

Subgroups — C2×C4×#6738 #14411186

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×#6738 #14411186