Subgroups — C₃×#10611626 #14458231

Order 1920.

888 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#66105	C₂	1	2	yes	maximal, complemented
2	C₃×#66087	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#443	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65432	C₂	1	2	yes	maximal, complemented
5	C₃×#65185	C₂	1	2	yes	maximal, complemented
6	C₃×#65115	C₂	1	4	yes	maximal, complemented
7	C₃×#64989	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#64988	C₂	1	1	yes	maximal, characteristic, complemented
9	#10611626	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃×#4150	C₂²	1	4	yes	—
11	C₃×C₅×#135	C₂²	1	1	yes	characteristic
12	C₃×C₅×#131	C₂²	1	2	yes	—
13	C₃×#4097	C₂²	1	4	yes	—
14	C₃×D₅×Q₁₆	—	2	2	no	—
15	C₃×#4061	—	2	4	no	—
16	C₃×#4058	—	2	2	no	—
17	C₃×#4055	—	2	4	no	—
18	C₃×#4055	C₂²	1	4	yes	—
19	C₂×C₃×Dic₂₀	—	2	2	no	—
20	C₂×C₃×Dic₂₀	C₂²	1	2	yes	—
21	C₂×C₃×Dic₂₀	C₂²	1	2	yes	—
22	C₃×#4050	—	2	2	no	—
23	C₃×#4050	C₂²	1	1	yes	characteristic
24	C₃×#4047	C₂²	1	2	yes	—
25	C₃×#4015	C₂²	1	2	yes	—
26	C₃×C₅×#108	C₂²	1	1	yes	characteristic
27	C₃×C₅×#104	C₂²	1	2	yes	—
28	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
29	C₃×#3956	C₂²	1	4	yes	—
30	C₃×#3951	C₂²	1	1	yes	characteristic
31	C₃×#3937	C₂²	1	2	yes	—
32	C₃×#3293	—	5	1	no	maximal, Hall
33	#66105	C₂×C₃	1	2	yes	complemented
34	#66087	C₂×C₃	1	2	yes	complemented
35	C₅×#443	C₂×C₃	1	1	yes	characteristic, complemented
36	#65432	C₂×C₃	1	2	yes	complemented
37	#65185	C₂×C₃	1	2	yes	complemented
38	#65115	C₂×C₃	1	4	yes	complemented
39	#64989	C₂×C₃	1	1	yes	characteristic, complemented
40	#64988	C₂×C₃	1	1	yes	characteristic, complemented
41	C₃×C₅×#41	C₂³	1	2	yes	—
42	C₃×Q₈×D₅	—	2	4	no	—
43	C₃×#711	—	2	4	no	—
44	C₃×#711	—	4	4	no	—
45	C₃×#709	—	2	4	no	—
46	C₃×#709	C₂³	1	2	yes	—
47	C₂×C₃×Dic₁₀	—	2	4	no	—
48	C₂×C₃×Dic₁₀	C₂³	1	4	yes	—
49	C₃×C₅×Q₁₆	D₄	1	1	yes	characteristic
50	C₃×C₅×SD₁₆	D₄	1	2	yes	—
51	C₃×C₅×D₈	D₄	1	1	yes	characteristic
52	C₃×C₅×M₁₆	—	2	2	no	—
53	C₃×C₅×M₁₆	C₂³	1	2	yes	—
54	C₂×C₃×C₅×C₈	—	2	2	no	—
55	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
56	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
57	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
58	C₃×#689	—	2	4	no	—
59	C₃×#687	—	2	4	no	—
60	C₃×C₄⋊Dic₅	—	4	2	no	—
61	C₃×#681	C₂³	1	2	yes	—
62	C₃×Dic₂₀	—	2	4	no	—
63	C₃×Dic₂₀	—	2	2	no	—
64	C₃×Dic₂₀	—	2	2	no	—
65	C₃×Dic₂₀	—	2	2	no	—
66	C₃×Dic₂₀	—	2	2	no	—
67	C₃×Dic₂₀	D₄	1	1	yes	characteristic
68	C₃×D₄₀	D₄	1	1	yes	characteristic
69	C₃×#677	—	2	4	no	—
70	C₃×#677	D₄	1	2	yes	—
71	C₃×#676	—	2	2	no	—
72	C₃×C₈×D₅	—	2	2	no	—
73	C₃×#578	—	5	2	no	—
74	C₃×#578	—	5	2	no	—
75	C₃×#494	—	5	1	no	—
76	C₃×#473	—	5	2	no	—
77	C₃×#473	—	5	2	no	—
78	C₃×#456	—	5	4	no	—
79	C₃×#443	—	5	1	no	—
80	C₃×#443	D₅	1	1	yes	characteristic, complemented
81	#4150	C₂²×C₃	1	4	yes	—
82	C₅×#135	C₂²×C₃	1	1	yes	characteristic
83	C₅×#131	C₂²×C₃	1	2	yes	—
84	#4097	C₂²×C₃	1	4	yes	—
85	D₅×Q₁₆	—	2	2	no	—
86	#4061	—	2	4	no	—
87	#4058	—	2	2	no	—
88	#4055	—	2	4	no	—
89	#4055	C₂²×C₃	1	4	yes	—
90	C₂×Dic₂₀	—	2	2	no	—
91	C₂×Dic₂₀	C₂²×C₃	1	2	yes	—
92	C₂×Dic₂₀	C₂²×C₃	1	2	yes	—
93	#4050	—	2	2	no	—
94	#4050	C₂²×C₃	1	1	yes	characteristic
95	#4047	C₂²×C₃	1	2	yes	—
96	#4015	C₂²×C₃	1	2	yes	—
97	C₅×#108	C₂²×C₃	1	1	yes	characteristic
98	C₅×#104	C₂²×C₃	1	2	yes	—
99	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
100	#3956	C₂²×C₃	1	4	yes	—
101	#3951	C₂²×C₃	1	1	yes	characteristic
102	#3937	C₂²×C₃	1	2	yes	—
103	#3293	—	5	1	no	Sylow
104	C₃×C₅×Q₈	C₂×D₄	1	2	yes	—
105	C₃×C₅×D₄	—	2	2	no	—
106	C₃×C₅×D₄	C₂×D₄	1	2	yes	—
107	C₂×C₃×C₄×C₅	—	2	1	no	—
108	C₂×C₃×C₄×C₅	—	2	2	no	—
109	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
110	C₃×C₂²⋊D₅	—	2	2	no	—
111	C₃×C₂²⋊D₅	—	4	4	no	—
112	C₂×C₃×Dic₅	—	2	4	no	—
113	C₂×C₃×Dic₅	—	4	4	no	—
114	C₃×D₂₀	C₂×D₄	1	2	yes	—
115	C₃×C₄×D₅	—	2	2	no	—
116	C₃×C₄×D₅	—	4	4	no	—
117	C₃×Dic₁₀	—	2	4	no	—
118	C₃×Dic₁₀	—	2	4	no	—
119	C₃×Dic₁₀	—	4	4	no	—
120	C₃×Dic₁₀	C₂×D₄	1	2	yes	—
121	C₃×C₅×C₈	—	2	2	no	—
122	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
123	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
124	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
125	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
126	C₃×#168	—	2	2	no	—
127	C₃×2₋¹⁺⁴	—	5	4	no	—
128	C₃×#137	—	5	4	no	—
129	C₃×#137	—	5	4	no	—
130	C₃×#137	—	10	4	no	—
131	C₃×#137	—	10	4	no	—
132	C₃×#135	—	5	1	no	—
133	C₃×#135	—	10	2	no	—
134	C₃×#135	—	10	2	no	—
135	C₃×#135	C₂×D₅	1	1	yes	characteristic
136	C₂×C₃×Q₁₆	—	5	2	no	—
137	C₂×C₃×Q₁₆	—	5	2	no	—
138	C₂×C₃×Q₁₆	—	10	2	no	—
139	C₂×C₃×Q₁₆	—	10	2	no	—
140	C₃×#131	—	5	2	no	—
141	C₃×#131	C₂×D₅	1	2	yes	—
142	C₃×C₄⋊Q₈	—	5	2	no	—
143	C₃×#108	—	5	1	no	—
144	C₃×#108	C₂×D₅	1	1	yes	characteristic
145	C₃×#104	—	5	2	no	—
146	C₃×#104	C₂×D₅	1	2	yes	—
147	C₃×#101	—	5	4	no	—
148	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic
149	C₅×#41	C₂³×C₃	1	2	yes	—
150	Q₈×D₅	—	2	4	no	—
151	#711	—	2	4	no	—
152	#711	—	4	4	no	—
153	#709	—	2	4	no	—
154	#709	C₂³×C₃	1	2	yes	—
155	C₂×Dic₁₀	—	2	4	no	—
156	C₂×Dic₁₀	C₂³×C₃	1	4	yes	—
157	C₅×Q₁₆	C₃×D₄	1	1	yes	characteristic
158	C₅×SD₁₆	C₃×D₄	1	2	yes	—
159	C₅×D₈	C₃×D₄	1	1	yes	characteristic
160	C₅×M₁₆	—	2	2	no	—
161	C₅×M₁₆	C₂³×C₃	1	2	yes	—
162	C₂×C₅×C₈	—	2	2	no	—
163	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
164	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
165	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
166	#689	—	2	4	no	—
167	#687	—	2	4	no	—
168	C₄⋊Dic₅	—	4	2	no	—
169	#681	C₂³×C₃	1	2	yes	—
170	Dic₂₀	—	2	4	no	—
171	Dic₂₀	—	2	2	no	—
172	Dic₂₀	—	2	2	no	—
173	Dic₂₀	—	2	2	no	—
174	Dic₂₀	—	2	2	no	—
175	Dic₂₀	C₃×D₄	1	1	yes	characteristic
176	D₄₀	C₃×D₄	1	1	yes	characteristic
177	#677	—	2	4	no	—
178	#677	C₃×D₄	1	2	yes	—
179	#676	—	2	2	no	—
180	C₈×D₅	—	2	2	no	—
181	#578	—	5	2	no	—
182	#578	—	5	2	no	—
183	#494	—	5	1	no	—
184	#473	—	5	2	no	—
185	#473	—	5	2	no	—
186	#456	—	5	4	no	—
187	#443	—	5	1	no	—
188	#443	C₃×D₅	1	1	yes	characteristic, complemented
189	C₂²×C₃×C₅	—	2	2	no	—
190	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
191	C₂×C₃×D₅	—	2	2	no	—
192	C₃×C₄×C₅	—	2	2	no	—
193	C₃×C₄×C₅	—	2	2	no	—
194	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
195	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
196	C₃×Dic₅	—	2	2	no	—
197	C₃×Dic₅	—	4	4	no	—
198	C₃×#41	—	5	2	no	—
199	C₃×#41	—	10	4	no	—
200	C₃×#41	—	10	4	no	—
201	C₃×#41	—	20	4	no	—
202	C₃×#41	C₂²×D₅	1	2	yes	—
203	C₂×C₃×Q₈	—	5	4	no	—
204	C₂×C₃×Q₈	—	10	4	no	—
205	C₂×C₃×Q₈	—	10	4	no	—
206	C₃×Q₁₆	—	5	1	no	—
207	C₃×Q₁₆	—	10	4	no	—
208	C₃×Q₁₆	—	10	4	no	—
209	C₃×Q₁₆	—	10	2	no	—
210	C₃×Q₁₆	—	10	2	no	—
211	C₃×Q₁₆	—	10	2	no	—
212	C₃×Q₁₆	—	10	2	no	—
213	C₃×Q₁₆	D₂₀	1	1	yes	characteristic
214	C₃×SD₁₆	—	5	2	no	—
215	C₃×SD₁₆	—	10	4	no	—
216	C₃×SD₁₆	—	10	4	no	—
217	C₃×SD₁₆	D₂₀	1	2	yes	—
218	C₃×D₈	—	5	1	no	—
219	C₃×D₈	D₂₀	1	1	yes	characteristic
220	C₃×M₁₆	—	2	2	no	—
221	C₃×M₁₆	—	5	2	no	—
222	C₃×M₁₆	—	10	2	no	—
223	C₃×M₁₆	C₂²×D₅	1	2	yes	—
224	C₂×C₃×C₈	—	2	2	no	—
225	C₂×C₃×C₈	—	10	2	no	—
226	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
227	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
228	C₃×C₄⋊C₄	—	20	2	no	—
229	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
230	C₅×Q₈	C₂×C₃×D₄	1	2	yes	—
231	C₅×D₄	—	2	2	no	—
232	C₅×D₄	C₂×C₃×D₄	1	2	yes	—
233	C₂×C₄×C₅	—	2	1	no	—
234	C₂×C₄×C₅	—	2	2	no	—
235	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
236	C₂²⋊D₅	—	2	2	no	—
237	C₂²⋊D₅	—	4	4	no	—
238	C₂×Dic₅	—	2	4	no	—
239	C₂×Dic₅	—	4	4	no	—
240	D₂₀	C₂×C₃×D₄	1	2	yes	—
241	C₄×D₅	—	2	2	no	—
242	C₄×D₅	—	4	4	no	—
243	Dic₁₀	—	2	4	no	—
244	Dic₁₀	—	2	4	no	—
245	Dic₁₀	—	4	4	no	—
246	Dic₁₀	C₂×C₃×D₄	1	2	yes	—
247	C₅×C₈	—	2	2	no	—
248	C₅×C₈	C₂×C₃×D₄	1	1	yes	characteristic
249	C₅×C₈	C₂×C₃×D₄	1	1	yes	characteristic
250	C₅×C₈	C₂×C₃×D₄	1	1	yes	characteristic
251	C₅×C₈	C₂×C₃×D₄	1	1	yes	characteristic
252	#168	—	2	2	no	—
253	2₋¹⁺⁴	—	5	4	no	—
254	#137	—	5	4	no	—
255	#137	—	5	4	no	—
256	#137	—	10	4	no	—
257	#137	—	10	4	no	—
258	#135	—	5	1	no	—
259	#135	—	10	2	no	—
260	#135	—	10	2	no	—
261	#135	C₂×C₃×D₅	1	1	yes	characteristic
262	C₂×Q₁₆	—	5	2	no	—
263	C₂×Q₁₆	—	5	2	no	—
264	C₂×Q₁₆	—	10	2	no	—
265	C₂×Q₁₆	—	10	2	no	—
266	#131	—	5	2	no	—
267	#131	C₂×C₃×D₅	1	2	yes	—
268	C₄⋊Q₈	—	5	2	no	—
269	#108	—	5	1	no	—
270	#108	C₂×C₃×D₅	1	1	yes	characteristic
271	#104	—	5	2	no	—
272	#104	C₂×C₃×D₅	1	2	yes	—
273	#101	—	5	4	no	—
274	C₄×C₈	C₂×C₃×D₅	1	1	yes	characteristic
275	C₂×C₃×C₅	—	2	1	no	—
276	C₂×C₃×C₅	—	4	2	no	—
277	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
278	C₃×D₅	—	4	2	no	—
279	C₃×Q₈	—	5	2	no	—
280	C₃×Q₈	—	10	4	no	—
281	C₃×Q₈	—	10	4	no	—
282	C₃×Q₈	—	20	4	no	—
283	C₃×Q₈	C₂×D₂₀	1	2	yes	—
284	C₃×D₄	—	2	2	no	—
285	C₃×D₄	—	5	2	no	—
286	C₃×D₄	—	10	2	no	—
287	C₃×D₄	—	20	4	no	—
288	C₃×D₄	C₂×D₂₀	1	2	yes	—
289	C₂×C₃×C₄	—	2	1	no	—
290	C₂×C₃×C₄	—	2	2	no	—
291	C₂×C₃×C₄	—	10	2	no	—
292	C₂×C₃×C₄	—	10	4	no	—
293	C₂×C₃×C₄	—	20	4	no	—
294	C₂×C₃×C₄	—	20	4	no	—
295	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
296	C₃×C₈	—	2	2	no	—
297	C₃×C₈	—	10	2	no	—
298	C₃×C₈	C₂×D₂₀	1	1	yes	characteristic
299	C₃×C₈	C₂×D₂₀	1	1	yes	characteristic
300	C₃×C₈	D₄×D₅	1	1	yes	characteristic
301	C₃×C₈	D₄×D₅	1	1	yes	characteristic
302	C₂²×C₅	—	2	2	no	—
303	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
304	C₂×D₅	—	2	2	no	—
305	C₄×C₅	—	2	2	no	—
306	C₄×C₅	—	2	2	no	—
307	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
308	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
309	Dic₅	—	2	2	no	—
310	Dic₅	—	4	4	no	—
311	#41	—	5	2	no	—
312	#41	—	10	4	no	—
313	#41	—	10	4	no	—
314	#41	—	20	4	no	—
315	#41	C₂²×C₃×D₅	1	2	yes	—
316	C₂×Q₈	—	5	4	no	—
317	C₂×Q₈	—	10	4	no	—
318	C₂×Q₈	—	10	4	no	—
319	Q₁₆	—	5	1	no	—
320	Q₁₆	—	10	4	no	—
321	Q₁₆	—	10	4	no	—
322	Q₁₆	—	10	2	no	—
323	Q₁₆	—	10	2	no	—
324	Q₁₆	—	10	2	no	—
325	Q₁₆	—	10	2	no	—
326	Q₁₆	C₃×D₂₀	1	1	yes	characteristic
327	SD₁₆	—	5	2	no	—
328	SD₁₆	—	10	4	no	—
329	SD₁₆	—	10	4	no	—
330	SD₁₆	C₃×D₂₀	1	2	yes	—
331	D₈	—	5	1	no	—
332	D₈	C₃×D₂₀	1	1	yes	characteristic
333	M₁₆	—	2	2	no	—
334	M₁₆	—	5	2	no	—
335	M₁₆	—	10	2	no	—
336	M₁₆	C₂²×C₃×D₅	1	2	yes	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	10	2	no	—
339	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
340	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
341	C₄⋊C₄	—	20	2	no	—
342	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
343	C₃×C₅	#3293	1	1	yes	characteristic, complemented, Hall
344	C₂²×C₃	—	2	2	no	—
345	C₂²×C₃	—	10	2	no	—
346	C₂²×C₃	#4149	1	1	yes	characteristic
347	C₃×C₄	—	2	2	no	—
348	C₃×C₄	—	2	2	no	—
349	C₃×C₄	—	10	2	no	—
350	C₃×C₄	—	20	4	no	—
351	C₃×C₄	C₂²×D₂₀	1	1	yes	characteristic
352	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
353	C₂×C₅	—	2	1	no	—
354	C₂×C₅	—	4	2	no	—
355	C₂×C₅	C₃×D₄²	1	1	yes	characteristic
356	D₅	—	4	2	no	—
357	Q₈	—	5	2	no	—
358	Q₈	—	10	4	no	—
359	Q₈	—	10	4	no	—
360	Q₈	—	20	4	no	—
361	Q₈	C₂×C₃×D₂₀	1	2	yes	—
362	D₄	—	2	2	no	—
363	D₄	—	5	2	no	—
364	D₄	—	10	2	no	—
365	D₄	—	20	4	no	—
366	D₄	C₂×C₃×D₂₀	1	2	yes	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	10	2	no	—
370	C₂×C₄	—	10	4	no	—
371	C₂×C₄	—	20	4	no	—
372	C₂×C₄	—	20	4	no	—
373	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
374	C₈	—	2	2	no	—
375	C₈	—	10	2	no	—
376	C₈	C₂×C₃×D₂₀	1	1	yes	characteristic
377	C₈	C₂×C₃×D₂₀	1	1	yes	characteristic
378	C₈	C₃×D₄×D₅	1	1	yes	characteristic
379	C₈	C₃×D₄×D₅	1	1	yes	characteristic
380	C₂×C₃	—	2	1	no	—
381	C₂×C₃	—	4	2	no	—
382	C₂×C₃	—	20	2	no	—
383	C₂×C₃	D₄×D₂₀	1	1	yes	characteristic
384	C₅	C₃×#3293	1	1	yes	characteristic, complemented, Sylow
385	C₂²	—	2	2	no	—
386	C₂²	—	10	2	no	—
387	C₂²	C₃×#4149	1	1	yes	characteristic
388	C₄	—	2	2	no	—
389	C₄	—	2	2	no	—
390	C₄	—	10	2	no	—
391	C₄	—	20	4	no	—
392	C₄	C₂²×C₃×D₂₀	1	1	yes	characteristic
393	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
394	C₃	#10611626	1	1	yes	characteristic, direct product factor, Sylow
395	C₂	—	2	1	no	—
396	C₂	—	4	2	no	—
397	C₂	—	20	2	no	—
398	C₂	C₃×D₄×D₂₀	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	D₄×D₂₀
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#443	C₂
socle	C₂×C₃×C₅	D₄²
hypercenter	C₃×#443	D₅
hypocenter	C₅	C₃×#3293
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃×C₄ ◁ C₃×#443

Complements

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

N	H ≅ G/N	type
1. C₃×#66105	C₂	semidirect
2. C₃×#66087	C₂	semidirect
3. C₃×C₅×#443	C₂	semidirect
4. C₃×#65432	C₂	semidirect
5. C₃×#65185	C₂	semidirect
6. C₃×#65115	C₂	semidirect
7. C₃×#64989	C₂	semidirect
8. C₃×#64988	C₂	semidirect
9. #10611626	C₃	direct (N × H)
33. #66105	C₂×C₃	semidirect
34. #66087	C₂×C₃	semidirect
35. C₅×#443	C₂×C₃	semidirect
36. #65432	C₂×C₃	semidirect
37. #65185	C₂×C₃	semidirect
38. #65115	C₂×C₃	semidirect
39. #64989	C₂×C₃	semidirect
40. #64988	C₂×C₃	semidirect
80. C₃×#443	D₅	semidirect
188. #443	C₃×D₅	semidirect
343. C₃×C₅	#3293	semidirect
384. C₅	C₃×#3293	semidirect
394. C₃	#10611626	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×#66105	2
C₃×#66087	2
C₃×C₅×#443	2
C₃×#65432	2
C₃×#65185	2
C₃×#65115	2
C₃×#64989	2
C₃×#64988	2
#10611626	3
C₃×#3293	5

Subgroups — C3×#10611626 #14458231

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10611626 #14458231