Subgroups — C₂×#11746489 #14281505

Order 1920.

688 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₅×D₁₂	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊(C₃⋊#170)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₄×#170	C₂	1	1	yes	maximal, characteristic, complemented
4	#11746489	C₂	1	4	yes	maximal, direct product factor
5	C₂×D₄⋊#170	—	3	1	no	maximal, Hall
6	C₂²×C₅×D₁₂	C₄	1	1	yes	characteristic
7	C₂²×D₃×Dic₅	—	2	1	no	—
8	C₂²×C₃⋊#170	—	2	1	no	—
9	C₂²×C₃×#170	—	2	1	no	—
10	C₂×C₄⋊Dic₁₅	C₄	1	1	yes	characteristic
11	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
12	C₂×(C₂×D₃)⋊Dic₅	—	2	1	no	—
13	Dic₅×D₁₂	—	2	1	no	—
14	Dic₅×D₁₂	—	2	1	no	—
15	Dic₅×D₁₂	C₄	1	2	yes	—
16	Dic₅×D₁₂	C₂²	1	2	yes	—
17	C₄⋊(C₃⋊#170)	—	2	1	no	—
18	C₄⋊(C₃⋊#170)	C₂²	1	2	yes	complemented
19	C₃×C₄×#170	—	2	1	no	—
20	C₃×C₄×#170	C₂²	1	2	yes	complemented
21	C₂×#4459	—	5	1	no	maximal, Hall
22	C₂×D₄×Dic₅	—	3	1	no	—
23	C₂×C₄⋊#170	—	3	1	no	—
24	C₂×C₄×#170	D₃	1	1	yes	characteristic, complemented
25	D₄⋊#170	—	3	4	no	—
26	C₂³×C₅×D₃	—	2	1	no	—
27	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
28	C₂²×Dic₁₅	—	2	1	no	—
29	C₂×C₅×D₁₂	—	2	1	no	—
30	C₂×C₅×D₁₂	—	2	2	no	—
31	C₂×C₅×D₁₂	C₈	1	4	yes	complemented
32	C₂×C₅×D₁₂	C₂×C₄	1	2	yes	—
33	C₂²×C₃×Dic₅	D₄	1	1	yes	characteristic
34	C₂²×C₃×Dic₅	D₄	1	1	yes	characteristic
35	C₂×D₃×Dic₅	—	2	2	no	—
36	C₂×D₃×Dic₅	—	2	2	no	—
37	C₂×D₃×Dic₅	—	4	2	no	—
38	C₂×D₃×Dic₅	—	4	2	no	—
39	C₂×C₃⋊#170	—	2	2	no	—
40	C₂×C₃⋊#170	—	4	2	no	—
41	C₂×C₃×#170	—	2	4	no	—
42	C₂×C₃×#170	—	2	2	no	—
43	C₄⋊Dic₁₅	—	2	1	no	—
44	C₄⋊Dic₁₅	C₂×C₄	1	2	yes	—
45	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
46	C₃×C₄×Dic₅	D₄	1	1	yes	characteristic
47	C₃×C₄×Dic₅	D₄	1	1	yes	characteristic
48	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
49	(C₂×D₃)⋊Dic₅	—	2	2	no	—
50	(C₂×D₃)⋊Dic₅	—	2	2	no	—
51	C₂×C₄×D₁₂	—	5	1	no	—
52	C₂×C₃×C₄×C₈	—	5	1	no	—
53	C₂×C₄⋊(C₃⋊C₈)	—	5	1	no	—
54	#4459	—	5	4	no	—
55	C₂²×C₅×D₄	—	3	1	no	—
56	C₂³×Dic₅	—	6	1	no	—
57	C₂²×#170	—	2	1	no	—
58	C₂²×#170	—	6	1	no	—
59	C₂×C₂²⋊Dic₅	—	6	1	no	—
60	D₄×Dic₅	—	3	2	no	—
61	D₄×Dic₅	—	3	2	no	—
62	D₄×Dic₅	—	6	1	no	—
63	D₄×Dic₅	—	6	1	no	—
64	C₂×C₄⋊Dic₅	—	3	1	no	—
65	C₂×C₄×Dic₅	C₂×D₃	1	1	yes	characteristic
66	C₄⋊#170	—	3	2	no	—
67	C₄⋊#170	—	6	1	no	—
68	C₄×#170	—	2	1	no	—
69	C₄×#170	C₂×D₃	1	2	yes	complemented
70	C₂×D₄⋊C₈	—	15	1	no	Sylow
71	C₂³×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
72	C₂²×C₅×D₃	—	2	4	no	—
73	C₂²×C₅×D₃	—	2	2	no	—
74	C₂²×C₅×D₃	—	4	2	no	—
75	C₂²×C₅×D₃	—	4	2	no	—
76	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
77	C₂×C₃×C₄×C₅	C₂×C₈	1	2	yes	—
78	C₂×C₃×C₄×C₅	M₁₆	1	2	yes	—
79	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
80	C₂×Dic₁₅	—	2	2	no	—
81	C₂×Dic₁₅	—	4	2	no	—
82	C₅×D₁₂	—	2	4	no	—
83	C₅×D₁₂	—	2	2	no	—
84	C₅×D₁₂	C₂×C₈	1	4	yes	complemented
85	C₂×C₃×Dic₅	—	2	2	no	—
86	C₂×C₃×Dic₅	C₂²⋊C₄	1	1	yes	characteristic
87	C₂×C₃×Dic₅	C₂²⋊C₄	1	1	yes	characteristic
88	C₂×C₃×Dic₅	D₈	1	2	yes	—
89	C₂×C₃×Dic₅	SD₁₆	1	2	yes	—
90	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
91	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
92	D₃×Dic₅	—	4	4	no	—
93	D₃×Dic₅	—	4	2	no	—
94	D₃×Dic₅	—	4	2	no	—
95	C₃⋊#170	—	4	2	no	—
96	C₃×#170	—	2	4	no	—
97	C₂²×D₁₂	AGL(1,𝔽₅)	1	1	yes	characteristic
98	C₂²×C₄×D₃	—	10	1	no	—
99	C₂²×C₃×C₈	—	10	1	no	—
100	C₂×C₃×C₄²	—	5	1	no	—
101	C₂×(C₂×D₃)⋊C₄	—	10	1	no	—
102	C₂×C₄⋊Dic₃	—	5	1	no	—
103	C₂²×C₃⋊C₈	—	10	1	no	—
104	C₄×D₁₂	—	5	2	no	—
105	C₄×D₁₂	—	5	2	no	—
106	C₄×D₁₂	—	10	1	no	—
107	C₄×D₁₂	—	10	1	no	—
108	C₃×C₄×C₈	—	5	2	no	—
109	C₃×C₄×C₈	—	10	1	no	—
110	C₄⋊(C₃⋊C₈)	—	5	2	no	—
111	C₄⋊(C₃⋊C₈)	—	10	1	no	—
112	C₂⁴×C₅	—	6	1	no	—
113	C₂×C₅×D₄	—	3	4	no	—
114	C₂×C₅×D₄	—	3	2	no	—
115	C₂×C₅×D₄	—	6	2	no	—
116	C₂×C₅×D₄	—	6	1	no	—
117	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
118	C₂²×Dic₅	—	6	1	no	—
119	C₂²×Dic₅	—	6	2	no	—
120	C₂²×Dic₅	—	6	2	no	—
121	C₂²×Dic₅	—	12	2	no	—
122	C₂²×Dic₅	—	12	2	no	—
123	C₂²×Dic₅	D₁₂	1	1	yes	characteristic
124	C₂²×Dic₅	#67	1	1	yes	characteristic
125	C₂×#170	—	2	4	no	—
126	C₂×#170	—	2	2	no	—
127	C₂×#170	—	6	2	no	—
128	C₂×#170	—	12	2	no	—
129	C₂²⋊Dic₅	—	6	2	no	—
130	C₂²⋊Dic₅	—	6	2	no	—
131	C₄⋊Dic₅	—	3	2	no	—
132	C₄⋊Dic₅	—	6	1	no	—
133	C₄×Dic₅	C₄×D₃	1	1	yes	characteristic
134	C₄×Dic₅	D₁₂	1	1	yes	characteristic
135	C₄×Dic₅	#67	1	1	yes	characteristic
136	C₄×Dic₅	C₂²×D₃	1	1	yes	characteristic
137	C₂×C₄×D₄	—	15	1	no	—
138	C₂×C₄⋊C₈	—	15	1	no	—
139	C₂×C₄×C₈	—	5	1	no	—
140	D₄⋊C₈	—	15	4	no	—
141	C₂²×C₃×C₅	C₂²⋊C₈	1	2	yes	—
142	C₂²×C₃×C₅	#102	1	2	yes	—
143	C₂²×C₃×C₅	#104	1	2	yes	—
144	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
145	C₂×C₅×D₃	—	2	4	no	—
146	C₂×C₅×D₃	—	4	8	no	—
147	C₂×C₅×D₃	—	4	2	no	—
148	C₂×C₅×D₃	—	4	2	no	—
149	C₃×C₄×C₅	C₂²⋊C₈	1	2	yes	—
150	C₃×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
151	C₃×C₄×C₅	C₂×M₁₆	1	1	yes	characteristic
152	Dic₁₅	—	4	2	no	—
153	C₃×Dic₅	—	2	1	no	—
154	C₃×Dic₅	—	2	1	no	—
155	C₃×Dic₅	#102	1	2	yes	—
156	C₃×Dic₅	C₂×D₈	1	1	yes	characteristic
157	C₃×Dic₅	C₂×SD₁₆	1	1	yes	characteristic
158	C₂³×D₃	—	2	1	no	—
159	C₂²×C₃×C₄	—	5	1	no	—
160	C₂²×C₃×C₄	—	5	1	no	—
161	C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
162	C₂²×Dic₃	—	10	1	no	—
163	C₂×D₁₂	—	2	2	no	—
164	C₂×D₁₂	—	2	1	no	—
165	C₂×D₁₂	#170	1	4	yes	complemented
166	C₂×D₁₂	C₂×AGL(1,𝔽₅)	1	2	yes	—
167	C₂×C₄×D₃	—	10	2	no	—
168	C₂×C₄×D₃	—	10	2	no	—
169	C₂×C₄×D₃	—	20	2	no	—
170	C₂×C₄×D₃	—	20	2	no	—
171	C₂×C₃×C₈	—	10	2	no	—
172	C₂×C₃×C₈	—	10	4	no	—
173	C₃×C₄²	—	5	1	no	—
174	C₃×C₄²	—	5	1	no	—
175	C₃×C₄²	—	5	1	no	—
176	C₃×C₄²	—	5	1	no	—
177	(C₂×D₃)⋊C₄	—	10	2	no	—
178	(C₂×D₃)⋊C₄	—	10	2	no	—
179	C₄⋊Dic₃	—	5	2	no	—
180	C₄⋊Dic₃	—	10	1	no	—
181	C₂×C₃⋊C₈	—	10	2	no	—
182	C₂×C₃⋊C₈	—	20	2	no	—
183	C₂³×C₅	—	6	4	no	—
184	C₂³×C₅	—	6	2	no	—
185	C₂³×C₅	—	12	2	no	—
186	C₂³×C₅	—	12	2	no	—
187	C₂³×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
188	C₅×D₄	—	3	4	no	—
189	C₅×D₄	—	6	4	no	—
190	C₅×D₄	—	6	2	no	—
191	C₂×C₄×C₅	D₃×C₈	1	2	yes	—
192	C₂×C₄×C₅	ΓL(1,𝔽₂₅)	1	2	yes	—
193	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
194	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
195	C₂×Dic₅	—	2	2	no	—
196	C₂×Dic₅	—	6	2	no	—
197	C₂×Dic₅	—	12	2	no	—
198	C₂×Dic₅	—	12	4	no	—
199	C₂×Dic₅	—	12	2	no	—
200	C₂×Dic₅	—	12	2	no	—
201	C₂×Dic₅	#204	1	2	yes	—
202	C₂×Dic₅	D₂₄	1	2	yes	—
203	C₂×Dic₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
204	C₂×Dic₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
205	C₂×Dic₅	C₂×D₁₂	1	1	yes	characteristic
206	C₂×Dic₅	C₂×#67	1	1	yes	characteristic
207	#170	—	2	4	no	—
208	#170	—	12	2	no	—
209	C₂²×D₄	—	3	1	no	—
210	C₂³×C₄	—	30	1	no	—
211	C₂²×C₈	—	10	1	no	—
212	C₂²×C₈	—	30	1	no	—
213	C₄×D₄	—	15	2	no	—
214	C₄×D₄	—	15	2	no	—
215	C₄×D₄	—	30	1	no	—
216	C₄×D₄	—	30	1	no	—
217	C₂×C₄⋊C₄	—	15	1	no	—
218	C₂×C₂²⋊C₄	—	30	1	no	—
219	C₂×C₄²	—	5	1	no	—
220	C₄⋊C₈	—	15	2	no	—
221	C₄⋊C₈	—	30	1	no	—
222	C₄×C₈	—	5	2	no	—
223	C₄×C₈	—	10	1	no	—
224	C₂×C₃×C₅	D₄⋊C₈	1	4	yes	complemented
225	C₂×C₃×C₅	C₂×C₂²⋊C₈	1	1	yes	characteristic
226	C₂×C₃×C₅	C₂×#102	1	1	yes	characteristic
227	C₂×C₃×C₅	C₂×#104	1	1	yes	characteristic
228	C₅×D₃	—	4	4	no	—
229	C₂³×C₃	C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
230	C₂²×D₃	—	2	2	no	—
231	C₂²×D₃	—	2	4	no	—
232	C₂²×D₃	—	4	2	no	—
233	C₂²×D₃	—	4	2	no	—
234	C₂×C₃×C₄	—	5	1	no	—
235	C₂×C₃×C₄	—	5	1	no	—
236	C₂×C₃×C₄	—	5	2	no	—
237	C₂×C₃×C₄	—	5	2	no	—
238	C₂×C₃×C₄	—	5	1	no	—
239	C₂×C₃×C₄	—	5	1	no	—
240	C₂×C₃×C₄	—	10	2	no	—
241	C₂×C₃×C₄	C₂×#170	1	2	yes	—
242	C₂×C₃×C₄	#704	1	2	yes	—
243	C₂×C₃×C₄	C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
244	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
245	C₂×Dic₃	—	10	2	no	—
246	C₂×Dic₃	—	20	2	no	—
247	D₁₂	—	2	2	no	—
248	D₁₂	—	2	4	no	—
249	D₁₂	C₂×#170	1	4	yes	complemented
250	C₄×D₃	—	20	4	no	—
251	C₄×D₃	—	20	2	no	—
252	C₄×D₃	—	20	2	no	—
253	C₃×C₈	—	10	4	no	—
254	C₃⋊C₈	—	20	2	no	—
255	C₂²×C₅	—	6	4	no	—
256	C₂²×C₅	—	12	2	no	—
257	C₂²×C₅	—	12	8	no	—
258	C₂²×C₅	—	12	2	no	—
259	C₂²×C₅	#805	1	2	yes	—
260	C₂²×C₅	(C₂×D₃)⋊C₈	1	2	yes	—
261	C₂²×C₅	#821	1	2	yes	—
262	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
263	C₄×C₅	(C₂×D₃)⋊C₈	1	2	yes	—
264	C₄×C₅	C₂×D₃×C₈	1	1	yes	characteristic
265	C₄×C₅	C₂×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
266	Dic₅	—	2	1	no	—
267	Dic₅	—	2	1	no	—
268	Dic₅	—	12	2	no	—
269	Dic₅	#821	1	2	yes	—
270	Dic₅	C₂×#204	1	1	yes	characteristic
271	Dic₅	C₂×D₂₄	1	1	yes	characteristic
272	C₂⁴	—	6	1	no	—
273	C₂×D₄	—	3	4	no	—
274	C₂×D₄	—	3	2	no	—
275	C₂×D₄	—	6	1	no	—
276	C₂×D₄	—	6	2	no	—
277	C₂²×C₄	—	5	1	no	—
278	C₂²×C₄	—	5	1	no	—
279	C₂²×C₄	—	30	2	no	—
280	C₂²×C₄	—	30	2	no	—
281	C₂²×C₄	—	30	1	no	—
282	C₂²×C₄	—	60	2	no	—
283	C₂²×C₄	—	60	2	no	—
284	C₂²×C₄	D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
285	C₂×C₈	—	10	2	no	—
286	C₂×C₈	—	10	4	no	—
287	C₂×C₈	—	30	2	no	—
288	C₂×C₈	—	60	2	no	—
289	C₄⋊C₄	—	15	2	no	—
290	C₄⋊C₄	—	30	1	no	—
291	C₂²⋊C₄	—	30	2	no	—
292	C₂²⋊C₄	—	30	2	no	—
293	C₄²	—	5	1	no	—
294	C₄²	—	5	1	no	—
295	C₄²	—	5	1	no	—
296	C₄²	—	5	1	no	—
297	C₃×C₅	C₂×D₄⋊C₈	1	1	yes	characteristic, complemented, Hall
298	C₂²×C₃	#4007	1	2	yes	—
299	C₂²×C₃	#4008	1	2	yes	—
300	C₂²×C₃	C₂²⋊#170	1	2	yes	—
301	C₂²×C₃	C₂×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
302	C₂×D₃	—	2	4	no	—
303	C₂×D₃	—	4	8	no	—
304	C₂×D₃	—	4	2	no	—
305	C₂×D₃	—	4	2	no	—
306	C₃×C₄	—	5	2	no	—
307	C₃×C₄	—	5	1	no	—
308	C₃×C₄	—	5	1	no	—
309	C₃×C₄	—	10	1	no	—
310	C₃×C₄	—	10	1	no	—
311	C₃×C₄	C₂²⋊#170	1	2	yes	—
312	C₃×C₄	C₂²×#170	1	1	yes	characteristic
313	C₃×C₄	C₂×#704	1	1	yes	characteristic
314	Dic₃	—	20	2	no	—
315	C₂×C₅	—	12	4	no	—
316	C₂×C₅	#4459	1	4	yes	complemented
317	C₂×C₅	C₂×#805	1	1	yes	characteristic
318	C₂×C₅	C₂×(C₂×D₃)⋊C₈	1	1	yes	characteristic
319	C₂×C₅	C₂×#821	1	1	yes	characteristic
320	C₂³	—	6	2	no	—
321	C₂³	—	6	4	no	—
322	C₂³	—	12	2	no	—
323	C₂³	—	12	2	no	—
324	C₂³	(C₂×D₃)⋊AGL(1,𝔽₅)	1	1	yes	characteristic
325	D₄	—	3	4	no	—
326	D₄	—	6	2	no	—
327	D₄	—	6	4	no	—
328	C₂×C₄	—	5	2	no	—
329	C₂×C₄	—	5	2	no	—
330	C₂×C₄	—	5	1	no	—
331	C₂×C₄	—	5	1	no	—
332	C₂×C₄	—	5	1	no	—
333	C₂×C₄	—	5	1	no	—
334	C₂×C₄	—	10	2	no	—
335	C₂×C₄	—	30	2	no	—
336	C₂×C₄	—	60	2	no	—
337	C₂×C₄	—	60	4	no	—
338	C₂×C₄	—	60	2	no	—
339	C₂×C₄	—	60	2	no	—
340	C₂×C₄	(C₂×D₃)⋊AGL(1,𝔽₅)	1	1	yes	characteristic
341	C₂×C₄	D₃×#170	1	2	yes	—
342	C₂×C₄	#6739	1	2	yes	—
343	C₂×C₄	C₂×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
344	C₈	—	10	4	no	—
345	C₈	—	60	2	no	—
346	C₂×C₃	D₄⋊#170	1	4	yes	complemented
347	C₂×C₃	C₂×#4007	1	1	yes	characteristic
348	C₂×C₃	C₂×#4008	1	1	yes	characteristic
349	C₂×C₃	C₂×C₂²⋊#170	1	1	yes	characteristic
350	D₃	—	4	4	no	—
351	C₅	C₂×#4459	1	1	yes	characteristic, complemented, Sylow
352	C₂²	—	6	4	no	—
353	C₂²	—	12	2	no	—
354	C₂²	—	12	2	no	—
355	C₂²	—	12	8	no	—
356	C₂²	#91152	1	2	yes	—
357	C₂²	#91156	1	2	yes	—
358	C₂²	(C₂×D₃)⋊#170	1	2	yes	—
359	C₂²	C₂×(C₂×D₃)⋊AGL(1,𝔽₅)	1	1	yes	characteristic
360	C₄	—	5	1	no	—
361	C₄	—	5	2	no	—
362	C₄	—	5	1	no	—
363	C₄	—	10	1	no	—
364	C₄	—	10	1	no	—
365	C₄	—	60	2	no	—
366	C₄	(C₂×D₃)⋊#170	1	2	yes	—
367	C₄	C₂×D₃×#170	1	1	yes	characteristic
368	C₄	C₂×#6739	1	1	yes	characteristic
369	C₃	C₂×D₄⋊#170	1	1	yes	characteristic, complemented, Sylow
370	C₂	—	12	4	no	—
371	C₂	#11746489	1	4	yes	direct product factor
372	C₂	C₂×#91152	1	1	yes	characteristic
373	C₂	C₂×#91156	1	1	yes	characteristic
374	C₂	C₂×(C₂×D₃)⋊#170	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	(C₂×D₃)⋊AGL(1,𝔽₅)
commutator	C₃×C₄×C₅	C₂²×C₈
Frattini	C₂×C₄	C₂×D₃×AGL(1,𝔽₅)
Fitting	C₂²×C₃×C₄×C₅	C₂×C₄
socle	C₂³×C₃×C₅	C₂²⋊C₄
prime radical	C₂²×C₅×D₁₂	C₄
cosocle	C₃×C₄×Dic₅	C₂³
hypercenter	C₂²×C₄	D₃×AGL(1,𝔽₅)
hypocenter	C₃×C₅	C₂×D₄⋊C₈
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
2. C₂×C₄⋊(C₃⋊#170)	C₂	semidirect
3. C₂×C₃×C₄×#170	C₂	semidirect
4. #11746489	C₂	direct (N × H)
18. C₄⋊(C₃⋊#170)	C₂²	semidirect
20. C₃×C₄×#170	C₂²	semidirect
24. C₂×C₄×#170	D₃	semidirect
31. C₂×C₅×D₁₂	C₈	semidirect
69. C₄×#170	C₂×D₃	semidirect
84. C₅×D₁₂	C₂×C₈	semidirect
165. C₂×D₁₂	#170	semidirect
224. C₂×C₃×C₅	D₄⋊C₈	semidirect
249. D₁₂	C₂×#170	semidirect
297. C₃×C₅	C₂×D₄⋊C₈	semidirect
316. C₂×C₅	#4459	semidirect
346. C₂×C₃	D₄⋊#170	semidirect
351. C₅	C₂×#4459	semidirect
369. C₃	C₂×D₄⋊#170	semidirect
371. C₂	#11746489	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×Dic₅×D₁₂	2
C₂×C₄⋊(C₃⋊#170)	2
C₂×C₃×C₄×#170	2
#11746489	2
C₂×D₄⋊#170	3
C₂×#4459	5

Subgroups — C2×#11746489 #14281505

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11746489 #14281505