Subgroups — C₃×#66108 #11755785

Order 960.

536 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	C₃×#4149	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#4144	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#4096	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#686	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#4062	C₂	1	2	yes	maximal, complemented
7	C₃×#4060	C₂	1	2	yes	maximal, complemented
8	C₃×#4057	C₂	1	2	yes	maximal, complemented
9	C₃×D₅×D₈	C₂	1	2	yes	maximal, complemented
10	C₃×#4054	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#4053	C₂	1	1	yes	maximal, characteristic, complemented
12	#66108	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃×C₅×#41	C₂²	1	1	yes	characteristic, complemented
14	C₂×C₃×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
15	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
16	C₃×#713	C₂²	1	2	yes	complemented
17	C₃×#711	—	2	1	no	—
18	C₃×#711	C₂²	1	2	yes	complemented
19	C₃×D₄×D₅	—	2	2	no	—
20	C₃×D₄×D₅	—	2	1	no	—
21	C₃×D₄×D₅	C₂²	1	2	yes	complemented
22	C₃×D₄×D₅	C₂²	1	2	yes	complemented
23	C₃×#709	—	2	1	no	—
24	C₃×#709	C₂²	1	1	yes	characteristic
25	C₃×#709	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₃×D₂₀	—	2	1	no	—
27	C₂×C₃×D₂₀	C₂²	1	1	yes	characteristic, complemented
28	C₃×C₅×SD₁₆	C₂²	1	2	yes	complemented
29	C₃×C₅×D₈	C₂²	1	2	yes	complemented
30	C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic, complemented
31	C₃×#689	C₂²	1	1	yes	characteristic, complemented
32	C₃×#688	C₂²	1	1	yes	characteristic, complemented
33	C₃×#687	C₂²	1	1	yes	characteristic, complemented
34	C₃×#686	C₂²	1	2	yes	complemented
35	C₃×#686	C₂²	1	2	yes	complemented
36	C₃×#686	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₃×#168	C₂²	1	1	yes	characteristic, complemented
38	C₃×D₄₀	C₂²	1	2	yes	complemented
39	C₃×#677	C₂²	1	2	yes	complemented
40	C₃×#676	C₂²	1	2	yes	complemented
41	C₃×C₈×D₅	C₂²	1	2	yes	complemented
42	C₃×#576	—	5	1	no	maximal, Hall
43	#4149	C₂×C₃	1	1	yes	characteristic, complemented
44	#4144	C₂×C₃	1	1	yes	characteristic, complemented
45	C₅×AGL(1,ℤ/8)	C₂×C₃	1	1	yes	characteristic, complemented
46	#4096	C₂×C₃	1	1	yes	characteristic, complemented
47	C₂×#686	C₂×C₃	1	1	yes	characteristic, complemented
48	#4062	C₂×C₃	1	2	yes	complemented
49	#4060	C₂×C₃	1	2	yes	complemented
50	#4057	C₂×C₃	1	2	yes	complemented
51	D₅×D₈	C₂×C₃	1	2	yes	complemented
52	#4054	C₂×C₃	1	1	yes	characteristic, complemented
53	#4053	C₂×C₃	1	1	yes	characteristic, complemented
54	C₂³×C₃×C₅	—	2	1	no	—
55	C₂²×C₃×D₅	—	2	1	no	—
56	C₂²×C₃×D₅	—	2	2	no	—
57	C₂²×C₃×D₅	—	2	2	no	—
58	C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
59	C₃×C₅×D₄	—	2	1	no	—
60	C₃×C₅×D₄	—	2	1	no	—
61	C₃×C₅×D₄	C₂³	1	2	yes	—
62	C₃×C₅×D₄	C₂³	1	1	yes	characteristic
63	C₂×C₃×C₄×C₅	—	2	1	no	—
64	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
65	C₃×C₂²⋊D₅	—	2	1	no	—
66	C₃×C₂²⋊D₅	—	2	2	no	—
67	C₃×C₂²⋊D₅	—	2	2	no	—
68	C₃×C₂²⋊D₅	—	2	2	no	—
69	C₃×C₂²⋊D₅	D₄	1	2	yes	—
70	C₂×C₃×Dic₅	—	2	2	no	—
71	C₃×D₂₀	—	2	2	no	—
72	C₃×D₂₀	—	2	1	no	—
73	C₃×D₂₀	D₄	1	1	yes	characteristic
74	C₃×D₂₀	C₂³	1	2	yes	—
75	C₃×D₂₀	C₂³	1	1	yes	characteristic
76	C₃×C₄×D₅	—	2	1	no	—
77	C₃×C₄×D₅	—	2	2	no	—
78	C₃×C₄×D₅	C₂³	1	2	yes	—
79	C₃×Dic₁₀	D₄	1	1	yes	characteristic
80	C₃×Dic₁₀	C₂³	1	1	yes	characteristic
81	C₃×C₅×C₈	C₂³	1	2	yes	—
82	C₃×#168	C₂³	1	1	yes	characteristic
83	C₃×#168	C₂³	1	1	yes	characteristic
84	C₃×H(5,𝔽₂)	—	5	1	no	—
85	C₃×H(5,𝔽₂)	—	5	1	no	—
86	C₃×AGL(1,ℤ/8)	—	5	2	no	—
87	C₃×AGL(1,ℤ/8)	—	5	2	no	—
88	C₃×AGL(1,ℤ/8)	—	5	1	no	—
89	C₃×AGL(1,ℤ/8)	D₅	1	1	yes	characteristic, complemented
90	C₃×#135	—	5	1	no	—
91	C₃×#135	—	5	2	no	—
92	C₂×C₃×D₈	—	5	1	no	—
93	C₂×C₃×D₈	—	5	2	no	—
94	C₃×#131	—	5	1	no	—
95	C₅×#41	C₂²×C₃	1	1	yes	characteristic, complemented
96	C₂×C₅×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
97	C₂×C₂²⋊D₅	—	2	2	no	—
98	#713	C₂²×C₃	1	2	yes	complemented
99	#711	—	2	1	no	—
100	#711	C₂²×C₃	1	2	yes	complemented
101	D₄×D₅	—	2	2	no	—
102	D₄×D₅	—	2	1	no	—
103	D₄×D₅	C₂²×C₃	1	2	yes	complemented
104	D₄×D₅	C₂²×C₃	1	2	yes	complemented
105	#709	—	2	1	no	—
106	#709	C₂²×C₃	1	1	yes	characteristic
107	#709	C₂²×C₃	1	1	yes	characteristic, complemented
108	C₂×D₂₀	—	2	1	no	—
109	C₂×D₂₀	C₂²×C₃	1	1	yes	characteristic, complemented
110	C₅×SD₁₆	C₂²×C₃	1	2	yes	complemented
111	C₅×D₈	C₂²×C₃	1	2	yes	complemented
112	C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
113	#689	C₂²×C₃	1	1	yes	characteristic, complemented
114	#688	C₂²×C₃	1	1	yes	characteristic, complemented
115	#687	C₂²×C₃	1	1	yes	characteristic, complemented
116	#686	C₂²×C₃	1	1	yes	characteristic, complemented
117	#686	C₂²×C₃	1	2	yes	complemented
118	#686	C₂²×C₃	1	2	yes	complemented
119	C₂×#168	C₂²×C₃	1	1	yes	characteristic, complemented
120	D₄₀	C₂²×C₃	1	2	yes	complemented
121	#677	C₂²×C₃	1	2	yes	complemented
122	#676	C₂²×C₃	1	2	yes	complemented
123	C₈×D₅	C₂²×C₃	1	2	yes	complemented
124	#576	—	5	1	no	Sylow
125	C₂²×C₃×C₅	—	2	2	no	—
126	C₂²×C₃×C₅	—	2	1	no	—
127	C₂²×C₃×C₅	—	8	1	no	—
128	C₂²×C₃×C₅	C₂×D₄	1	1	yes	characteristic
129	C₂×C₃×D₅	—	2	2	no	—
130	C₂×C₃×D₅	—	2	1	no	—
131	C₂×C₃×D₅	—	8	2	no	—
132	C₂×C₃×D₅	—	8	2	no	—
133	C₂×C₃×D₅	—	8	1	no	—
134	C₂×C₃×D₅	C₂×D₄	1	2	yes	—
135	C₃×C₄×C₅	—	2	1	no	—
136	C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
137	C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
138	C₃×Dic₅	—	2	1	no	—
139	C₃×Dic₅	C₂×D₄	1	2	yes	—
140	C₃×#41	—	5	1	no	—
141	C₃×#41	—	5	2	no	—
142	C₃×#41	—	5	2	no	—
143	C₃×#41	—	5	1	no	—
144	C₃×#41	—	10	1	no	—
145	C₃×#41	—	10	1	no	—
146	C₃×#41	C₂×D₅	1	1	yes	characteristic, complemented
147	C₂×C₃×D₄	—	5	2	no	—
148	C₂×C₃×D₄	—	5	2	no	—
149	C₂×C₃×D₄	—	5	1	no	—
150	C₂×C₃×D₄	—	10	1	no	—
151	C₂×C₃×D₄	—	10	2	no	—
152	C₂×C₃×D₄	—	10	1	no	—
153	C₂×C₃×D₄	—	10	2	no	—
154	C₂×C₃×D₄	C₂×D₅	1	1	yes	characteristic, complemented
155	C₃×Q₁₆	—	5	1	no	—
156	C₃×SD₁₆	—	5	1	no	—
157	C₃×SD₁₆	—	5	1	no	—
158	C₃×SD₁₆	—	5	2	no	—
159	C₃×SD₁₆	C₂×D₅	1	2	yes	complemented
160	C₃×D₈	—	5	2	no	—
161	C₃×D₈	—	5	1	no	—
162	C₃×D₈	—	5	2	no	—
163	C₃×D₈	—	5	2	no	—
164	C₃×D₈	C₂×D₅	1	2	yes	complemented
165	C₃×M₁₆	—	5	2	no	—
166	C₃×M₁₆	C₂×D₅	1	1	yes	characteristic, complemented
167	C₂×C₃×C₈	—	5	1	no	—
168	C₂×C₃×C₈	—	5	2	no	—
169	C₂³×C₅	—	2	1	no	—
170	C₂²×D₅	—	2	1	no	—
171	C₂²×D₅	—	2	2	no	—
172	C₂²×D₅	—	2	2	no	—
173	C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
174	C₅×D₄	—	2	1	no	—
175	C₅×D₄	—	2	1	no	—
176	C₅×D₄	C₂³×C₃	1	2	yes	—
177	C₅×D₄	C₂³×C₃	1	1	yes	characteristic
178	C₂×C₄×C₅	—	2	1	no	—
179	C₂×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
180	C₂²⋊D₅	—	2	1	no	—
181	C₂²⋊D₅	—	2	2	no	—
182	C₂²⋊D₅	—	2	2	no	—
183	C₂²⋊D₅	—	2	2	no	—
184	C₂²⋊D₅	C₃×D₄	1	2	yes	—
185	C₂×Dic₅	—	2	2	no	—
186	D₂₀	—	2	2	no	—
187	D₂₀	—	2	1	no	—
188	D₂₀	C₃×D₄	1	1	yes	characteristic
189	D₂₀	C₂³×C₃	1	2	yes	—
190	D₂₀	C₂³×C₃	1	1	yes	characteristic
191	C₄×D₅	—	2	1	no	—
192	C₄×D₅	—	2	2	no	—
193	C₄×D₅	C₂³×C₃	1	2	yes	—
194	Dic₁₀	C₃×D₄	1	1	yes	characteristic
195	Dic₁₀	C₂³×C₃	1	1	yes	characteristic
196	C₅×C₈	C₂³×C₃	1	2	yes	—
197	#168	C₂³×C₃	1	1	yes	characteristic
198	#168	C₂³×C₃	1	1	yes	characteristic
199	H(5,𝔽₂)	—	5	1	no	—
200	H(5,𝔽₂)	—	5	1	no	—
201	AGL(1,ℤ/8)	—	5	2	no	—
202	AGL(1,ℤ/8)	—	5	2	no	—
203	AGL(1,ℤ/8)	—	5	1	no	—
204	AGL(1,ℤ/8)	C₃×D₅	1	1	yes	characteristic, complemented
205	#135	—	5	1	no	—
206	#135	—	5	2	no	—
207	C₂×D₈	—	5	1	no	—
208	C₂×D₈	—	5	2	no	—
209	#131	—	5	1	no	—
210	C₂×C₃×C₅	—	2	1	no	—
211	C₂×C₃×C₅	—	4	1	no	—
212	C₂×C₃×C₅	—	4	2	no	—
213	C₂×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
214	C₃×D₅	—	2	2	no	—
215	C₃×D₅	—	4	2	no	—
216	C₃×D₅	—	4	1	no	—
217	C₂³×C₃	—	2	1	no	—
218	C₂³×C₃	—	10	2	no	—
219	C₂³×C₃	—	10	2	no	—
220	C₂³×C₃	—	10	1	no	—
221	C₃×Q₈	—	5	1	no	—
222	C₃×Q₈	—	5	1	no	—
223	C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
224	C₃×D₄	—	2	1	no	—
225	C₃×D₄	—	2	1	no	—
226	C₃×D₄	—	5	2	no	—
227	C₃×D₄	—	5	1	no	—
228	C₃×D₄	—	5	2	no	—
229	C₃×D₄	—	5	1	no	—
230	C₃×D₄	—	10	2	no	—
231	C₃×D₄	—	10	2	no	—
232	C₃×D₄	—	10	2	no	—
233	C₃×D₄	—	10	2	no	—
234	C₃×D₄	—	10	1	no	—
235	C₃×D₄	—	10	1	no	—
236	C₃×D₄	C₂²×D₅	1	2	yes	—
237	C₃×D₄	C₂²×D₅	1	1	yes	characteristic
238	C₂×C₃×C₄	—	2	1	no	—
239	C₂×C₃×C₄	—	5	2	no	—
240	C₂×C₃×C₄	—	10	2	no	—
241	C₂×C₃×C₄	—	10	2	no	—
242	C₂×C₃×C₄	—	10	1	no	—
243	C₂×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
244	C₃×C₈	—	5	1	no	—
245	C₃×C₈	—	5	1	no	—
246	C₃×C₈	C₂²×D₅	1	2	yes	—
247	C₂²×C₅	—	2	2	no	—
248	C₂²×C₅	—	2	1	no	—
249	C₂²×C₅	—	8	1	no	—
250	C₂²×C₅	C₂×C₃×D₄	1	1	yes	characteristic
251	C₂×D₅	—	2	2	no	—
252	C₂×D₅	—	2	1	no	—
253	C₂×D₅	—	8	2	no	—
254	C₂×D₅	—	8	2	no	—
255	C₂×D₅	—	8	1	no	—
256	C₂×D₅	C₂×C₃×D₄	1	2	yes	—
257	C₄×C₅	—	2	1	no	—
258	C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
259	C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
260	Dic₅	—	2	1	no	—
261	Dic₅	C₂×C₃×D₄	1	2	yes	—
262	#41	—	5	1	no	—
263	#41	—	5	2	no	—
264	#41	—	5	2	no	—
265	#41	—	5	1	no	—
266	#41	—	10	1	no	—
267	#41	—	10	1	no	—
268	#41	C₂×C₃×D₅	1	1	yes	characteristic, complemented
269	C₂×D₄	—	5	2	no	—
270	C₂×D₄	—	5	2	no	—
271	C₂×D₄	—	5	1	no	—
272	C₂×D₄	—	10	1	no	—
273	C₂×D₄	—	10	2	no	—
274	C₂×D₄	—	10	1	no	—
275	C₂×D₄	—	10	2	no	—
276	C₂×D₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
277	Q₁₆	—	5	1	no	—
278	SD₁₆	—	5	1	no	—
279	SD₁₆	—	5	1	no	—
280	SD₁₆	—	5	2	no	—
281	SD₁₆	C₂×C₃×D₅	1	2	yes	complemented
282	D₈	—	5	2	no	—
283	D₈	—	5	1	no	—
284	D₈	—	5	2	no	—
285	D₈	—	5	2	no	—
286	D₈	C₂×C₃×D₅	1	2	yes	complemented
287	M₁₆	—	5	2	no	—
288	M₁₆	C₂×C₃×D₅	1	1	yes	characteristic, complemented
289	C₂×C₈	—	5	1	no	—
290	C₂×C₈	—	5	2	no	—
291	C₃×C₅	#576	1	1	yes	characteristic, complemented, Hall
292	C₂²×C₃	—	2	1	no	—
293	C₂²×C₃	—	2	2	no	—
294	C₂²×C₃	—	5	2	no	—
295	C₂²×C₃	—	8	1	no	—
296	C₂²×C₃	—	10	2	no	—
297	C₂²×C₃	—	10	1	no	—
298	C₂²×C₃	—	40	1	no	—
299	C₂²×C₃	—	40	2	no	—
300	C₂²×C₃	—	40	2	no	—
301	C₂²×C₃	D₄×D₅	1	1	yes	characteristic
302	C₃×C₄	—	2	1	no	—
303	C₃×C₄	—	5	2	no	—
304	C₃×C₄	—	10	1	no	—
305	C₃×C₄	D₄×D₅	1	1	yes	characteristic
306	C₃×C₄	C₂³×D₅	1	1	yes	characteristic
307	C₂×C₅	—	2	1	no	—
308	C₂×C₅	—	4	1	no	—
309	C₂×C₅	—	4	2	no	—
310	C₂×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
311	D₅	—	2	2	no	—
312	D₅	—	4	2	no	—
313	D₅	—	4	1	no	—
314	C₂³	—	2	1	no	—
315	C₂³	—	10	2	no	—
316	C₂³	—	10	2	no	—
317	C₂³	—	10	1	no	—
318	Q₈	—	5	1	no	—
319	Q₈	—	5	1	no	—
320	Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
321	D₄	—	2	1	no	—
322	D₄	—	2	1	no	—
323	D₄	—	5	2	no	—
324	D₄	—	5	1	no	—
325	D₄	—	5	2	no	—
326	D₄	—	5	1	no	—
327	D₄	—	10	2	no	—
328	D₄	—	10	2	no	—
329	D₄	—	10	2	no	—
330	D₄	—	10	2	no	—
331	D₄	—	10	1	no	—
332	D₄	—	10	1	no	—
333	D₄	C₂²×C₃×D₅	1	2	yes	—
334	D₄	C₂²×C₃×D₅	1	1	yes	characteristic
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	5	2	no	—
337	C₂×C₄	—	10	2	no	—
338	C₂×C₄	—	10	2	no	—
339	C₂×C₄	—	10	1	no	—
340	C₂×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
341	C₈	—	5	1	no	—
342	C₈	—	5	1	no	—
343	C₈	C₂²×C₃×D₅	1	2	yes	—
344	C₂×C₃	—	2	1	no	—
345	C₂×C₃	—	4	2	no	—
346	C₂×C₃	—	4	1	no	—
347	C₂×C₃	—	10	2	no	—
348	C₂×C₃	—	20	2	no	—
349	C₂×C₃	—	20	1	no	—
350	C₂×C₃	C₂×D₄×D₅	1	1	yes	characteristic
351	C₅	C₃×#576	1	1	yes	characteristic, complemented, Sylow
352	C₂²	—	2	1	no	—
353	C₂²	—	2	2	no	—
354	C₂²	—	5	2	no	—
355	C₂²	—	8	1	no	—
356	C₂²	—	10	2	no	—
357	C₂²	—	10	1	no	—
358	C₂²	—	40	1	no	—
359	C₂²	—	40	2	no	—
360	C₂²	—	40	2	no	—
361	C₂²	C₃×D₄×D₅	1	1	yes	characteristic
362	C₄	—	2	1	no	—
363	C₄	—	5	2	no	—
364	C₄	—	10	1	no	—
365	C₄	C₃×D₄×D₅	1	1	yes	characteristic
366	C₄	C₂³×C₃×D₅	1	1	yes	characteristic
367	C₃	#66108	1	1	yes	characteristic, direct product factor, Sylow
368	C₂	—	2	1	no	—
369	C₂	—	4	2	no	—
370	C₂	—	4	1	no	—
371	C₂	—	10	2	no	—
372	C₂	—	20	2	no	—
373	C₂	—	20	1	no	—
374	C₂	C₂×C₃×D₄×D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	C₂×D₄×D₅
commutator, cosocle	C₄×C₅	C₂⁴×C₃
Frattini	C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×AGL(1,ℤ/8)	C₂
socle	C₂×C₃×C₅	C₂²×D₄
hypercenter	C₃×AGL(1,ℤ/8)	D₅
hypocenter	C₅	C₃×#576
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃×C₄ ◁ C₃×AGL(1,ℤ/8)

Complements

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

N	H ≅ G/N	type
1. C₃×#4149	C₂	semidirect
2. C₃×#4144	C₂	semidirect
3. C₃×C₅×AGL(1,ℤ/8)	C₂	semidirect
4. C₃×#4096	C₂	semidirect
5. C₂×C₃×#686	C₂	semidirect
6. C₃×#4062	C₂	semidirect
7. C₃×#4060	C₂	semidirect
8. C₃×#4057	C₂	semidirect
9. C₃×D₅×D₈	C₂	semidirect
10. C₃×#4054	C₂	semidirect
11. C₃×#4053	C₂	semidirect
12. #66108	C₃	direct (N × H)
13. C₃×C₅×#41	C₂²	semidirect
14. C₂×C₃×C₅×D₄	C₂²	semidirect
16. C₃×#713	C₂²	semidirect
18. C₃×#711	C₂²	semidirect
21. C₃×D₄×D₅	C₂²	semidirect
22. C₃×D₄×D₅	C₂²	semidirect
25. C₃×#709	C₂²	semidirect
27. C₂×C₃×D₂₀	C₂²	semidirect
28. C₃×C₅×SD₁₆	C₂²	semidirect
29. C₃×C₅×D₈	C₂²	semidirect
30. C₃×C₅×M₁₆	C₂²	semidirect
31. C₃×#689	C₂²	semidirect
32. C₃×#688	C₂²	semidirect
33. C₃×#687	C₂²	semidirect
34. C₃×#686	C₂²	semidirect
35. C₃×#686	C₂²	semidirect
36. C₃×#686	C₂²	semidirect
37. C₂×C₃×#168	C₂²	semidirect
38. C₃×D₄₀	C₂²	semidirect
39. C₃×#677	C₂²	semidirect
40. C₃×#676	C₂²	semidirect
41. C₃×C₈×D₅	C₂²	semidirect
43. #4149	C₂×C₃	semidirect
44. #4144	C₂×C₃	semidirect
45. C₅×AGL(1,ℤ/8)	C₂×C₃	semidirect
46. #4096	C₂×C₃	semidirect
47. C₂×#686	C₂×C₃	semidirect
48. #4062	C₂×C₃	semidirect
49. #4060	C₂×C₃	semidirect
50. #4057	C₂×C₃	semidirect
51. D₅×D₈	C₂×C₃	semidirect
52. #4054	C₂×C₃	semidirect
53. #4053	C₂×C₃	semidirect
89. C₃×AGL(1,ℤ/8)	D₅	semidirect
95. C₅×#41	C₂²×C₃	semidirect
96. C₂×C₅×D₄	C₂²×C₃	semidirect
98. #713	C₂²×C₃	semidirect
100. #711	C₂²×C₃	semidirect
103. D₄×D₅	C₂²×C₃	semidirect
104. D₄×D₅	C₂²×C₃	semidirect
107. #709	C₂²×C₃	semidirect
109. C₂×D₂₀	C₂²×C₃	semidirect
110. C₅×SD₁₆	C₂²×C₃	semidirect
111. C₅×D₈	C₂²×C₃	semidirect
112. C₅×M₁₆	C₂²×C₃	semidirect
113. #689	C₂²×C₃	semidirect
114. #688	C₂²×C₃	semidirect
115. #687	C₂²×C₃	semidirect
116. #686	C₂²×C₃	semidirect
117. #686	C₂²×C₃	semidirect
118. #686	C₂²×C₃	semidirect
119. C₂×#168	C₂²×C₃	semidirect
120. D₄₀	C₂²×C₃	semidirect
121. #677	C₂²×C₃	semidirect
122. #676	C₂²×C₃	semidirect
123. C₈×D₅	C₂²×C₃	semidirect
146. C₃×#41	C₂×D₅	semidirect
154. C₂×C₃×D₄	C₂×D₅	semidirect
159. C₃×SD₁₆	C₂×D₅	semidirect
164. C₃×D₈	C₂×D₅	semidirect
166. C₃×M₁₆	C₂×D₅	semidirect
204. AGL(1,ℤ/8)	C₃×D₅	semidirect
268. #41	C₂×C₃×D₅	semidirect
276. C₂×D₄	C₂×C₃×D₅	semidirect
281. SD₁₆	C₂×C₃×D₅	semidirect
286. D₈	C₂×C₃×D₅	semidirect
288. M₁₆	C₂×C₃×D₅	semidirect
291. C₃×C₅	#576	semidirect
351. C₅	C₃×#576	semidirect
367. C₃	#66108	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×#4149	2
C₃×#4144	2
C₃×C₅×AGL(1,ℤ/8)	2
C₃×#4096	2
C₂×C₃×#686	2
C₃×#4062	2
C₃×#4060	2
C₃×#4057	2
C₃×D₅×D₈	2
C₃×#4054	2
C₃×#4053	2
#66108	3
C₃×#576	5

Subgroups — C3×#66108 #11755785

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#66108 #11755785