Subgroups — C₃×#10611625 #14458177

Order 1920.

952 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	C₃×#66103	C₂	1	2	yes	maximal, complemented
2	C₃×#66086	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#443	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65431	C₂	1	2	yes	maximal, complemented
5	C₃×#65186	C₂	1	2	yes	maximal, complemented
6	C₃×#65111	C₂	1	4	yes	maximal, complemented
7	C₃×#64989	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#64984	C₂	1	1	yes	maximal, characteristic, complemented
9	#10611625	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃×#4149	C₂²	1	4	yes	complemented
11	C₃×C₅×#135	C₂²	1	1	yes	characteristic
12	C₃×C₅×#131	C₂²	1	2	yes	complemented
13	C₃×#4095	C₂²	1	4	yes	complemented
14	C₃×#4065	—	2	2	no	—
15	C₃×#4060	—	2	4	no	—
16	C₃×D₅×D₈	—	2	2	no	—
17	C₃×#4054	—	2	4	no	—
18	C₃×#4054	C₂²	1	4	yes	complemented
19	C₃×#4050	—	2	2	no	—
20	C₃×#4050	C₂²	1	1	yes	characteristic
21	C₂×C₃×D₄₀	—	2	2	no	—
22	C₂×C₃×D₄₀	C₂²	1	2	yes	complemented
23	C₂×C₃×D₄₀	C₂²	1	2	yes	complemented
24	C₃×#4047	C₂²	1	2	yes	complemented
25	C₃×#4020	C₂²	1	2	yes	complemented
26	C₃×C₅×#108	C₂²	1	1	yes	characteristic, complemented
27	C₃×C₅×#104	C₂²	1	2	yes	complemented
28	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
29	C₃×#3955	C₂²	1	4	yes	complemented
30	C₃×#3951	C₂²	1	1	yes	characteristic, complemented
31	C₃×#3937	C₂²	1	2	yes	complemented
32	C₃×#3292	—	5	1	no	maximal, Hall
33	#66103	C₂×C₃	1	2	yes	complemented
34	#66086	C₂×C₃	1	2	yes	complemented
35	C₅×#443	C₂×C₃	1	1	yes	characteristic, complemented
36	#65431	C₂×C₃	1	2	yes	complemented
37	#65186	C₂×C₃	1	2	yes	complemented
38	#65111	C₂×C₃	1	4	yes	complemented
39	#64989	C₂×C₃	1	1	yes	characteristic, complemented
40	#64984	C₂×C₃	1	1	yes	characteristic, complemented
41	C₃×C₅×#41	C₂³	1	2	yes	—
42	C₃×#713	—	2	4	no	—
43	C₃×D₄×D₅	—	2	4	no	—
44	C₃×D₄×D₅	—	4	4	no	—
45	C₃×#709	—	2	4	no	—
46	C₃×#709	C₂³	1	2	yes	—
47	C₂×C₃×D₂₀	—	2	4	no	—
48	C₂×C₃×D₂₀	—	4	2	no	—
49	C₂×C₃×D₂₀	C₂³	1	4	yes	—
50	C₃×C₅×Q₁₆	D₄	1	1	yes	characteristic, complemented
51	C₃×C₅×SD₁₆	D₄	1	2	yes	complemented
52	C₃×C₅×D₈	D₄	1	1	yes	characteristic, complemented
53	C₃×C₅×M₁₆	—	2	2	no	—
54	C₃×C₅×M₁₆	C₂³	1	2	yes	—
55	C₂×C₃×C₅×C₈	—	2	2	no	—
56	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
57	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
58	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
59	C₃×#688	—	2	4	no	—
60	C₃×#686	—	2	4	no	—
61	C₃×#681	C₂³	1	2	yes	—
62	C₃×Dic₂₀	D₄	1	1	yes	characteristic, complemented
63	C₃×D₄₀	—	2	4	no	—
64	C₃×D₄₀	—	2	2	no	—
65	C₃×D₄₀	—	2	2	no	—
66	C₃×D₄₀	—	2	2	no	—
67	C₃×D₄₀	—	2	2	no	—
68	C₃×D₄₀	D₄	1	1	yes	characteristic, complemented
69	C₃×#677	—	2	4	no	—
70	C₃×#677	D₄	1	2	yes	complemented
71	C₃×#676	—	2	2	no	—
72	C₃×C₈×D₅	—	2	2	no	—
73	C₃×#576	—	5	2	no	—
74	C₃×#576	—	5	2	no	—
75	C₃×#493	—	5	1	no	—
76	C₃×#472	—	5	2	no	—
77	C₃×#472	—	5	2	no	—
78	C₃×#453	—	5	4	no	—
79	C₃×#443	—	5	1	no	—
80	C₃×#443	D₅	1	1	yes	characteristic, complemented
81	#4149	C₂²×C₃	1	4	yes	complemented
82	C₅×#135	C₂²×C₃	1	1	yes	characteristic
83	C₅×#131	C₂²×C₃	1	2	yes	complemented
84	#4095	C₂²×C₃	1	4	yes	complemented
85	#4065	—	2	2	no	—
86	#4060	—	2	4	no	—
87	D₅×D₈	—	2	2	no	—
88	#4054	—	2	4	no	—
89	#4054	C₂²×C₃	1	4	yes	complemented
90	#4050	—	2	2	no	—
91	#4050	C₂²×C₃	1	1	yes	characteristic
92	C₂×D₄₀	—	2	2	no	—
93	C₂×D₄₀	C₂²×C₃	1	2	yes	complemented
94	C₂×D₄₀	C₂²×C₃	1	2	yes	complemented
95	#4047	C₂²×C₃	1	2	yes	complemented
96	#4020	C₂²×C₃	1	2	yes	complemented
97	C₅×#108	C₂²×C₃	1	1	yes	characteristic, complemented
98	C₅×#104	C₂²×C₃	1	2	yes	complemented
99	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
100	#3955	C₂²×C₃	1	4	yes	complemented
101	#3951	C₂²×C₃	1	1	yes	characteristic, complemented
102	#3937	C₂²×C₃	1	2	yes	complemented
103	#3292	—	5	1	no	Sylow
104	C₂²×C₃×D₅	—	2	4	no	—
105	C₂²×C₃×D₅	—	4	4	no	—
106	C₃×C₅×Q₈	C₂×D₄	1	2	yes	—
107	C₃×C₅×D₄	—	2	2	no	—
108	C₃×C₅×D₄	C₂×D₄	1	2	yes	—
109	C₂×C₃×C₄×C₅	—	2	1	no	—
110	C₂×C₃×C₄×C₅	—	2	2	no	—
111	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
112	C₃×C₂²⋊D₅	—	2	2	no	—
113	C₃×C₂²⋊D₅	—	4	4	no	—
114	C₃×D₂₀	—	2	4	no	—
115	C₃×D₂₀	—	2	4	no	—
116	C₃×D₂₀	—	4	4	no	—
117	C₃×D₂₀	—	8	4	no	—
118	C₃×D₂₀	C₂×D₄	1	2	yes	—
119	C₃×C₄×D₅	—	2	2	no	—
120	C₃×C₄×D₅	—	4	4	no	—
121	C₃×Dic₁₀	C₂×D₄	1	2	yes	—
122	C₃×C₅×C₈	—	2	2	no	—
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×C₅×C₈	C₂×D₄	1	1	yes	characteristic
127	C₃×#168	—	2	2	no	—
128	C₃×H(5,𝔽₂)	—	5	4	no	—
129	C₃×AGL(1,ℤ/8)	—	5	4	no	—
130	C₃×AGL(1,ℤ/8)	—	5	4	no	—
131	C₃×AGL(1,ℤ/8)	—	10	4	no	—
132	C₃×AGL(1,ℤ/8)	—	10	4	no	—
133	C₃×#135	—	5	1	no	—
134	C₃×#135	—	10	2	no	—
135	C₃×#135	—	10	2	no	—
136	C₃×#135	C₂×D₅	1	1	yes	characteristic
137	C₂×C₃×D₈	—	5	2	no	—
138	C₂×C₃×D₈	—	5	2	no	—
139	C₂×C₃×D₈	—	10	2	no	—
140	C₂×C₃×D₈	—	10	2	no	—
141	C₃×#131	—	5	2	no	—
142	C₃×#131	C₂×D₅	1	2	yes	complemented
143	C₃×#127	—	5	2	no	—
144	C₃×#108	—	5	1	no	—
145	C₃×#108	C₂×D₅	1	1	yes	characteristic, complemented
146	C₃×#104	—	5	2	no	—
147	C₃×#104	C₂×D₅	1	2	yes	complemented
148	C₃×#100	—	5	4	no	—
149	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic, complemented
150	C₅×#41	C₂³×C₃	1	2	yes	—
151	#713	—	2	4	no	—
152	D₄×D₅	—	2	4	no	—
153	D₄×D₅	—	4	4	no	—
154	#709	—	2	4	no	—
155	#709	C₂³×C₃	1	2	yes	—
156	C₂×D₂₀	—	2	4	no	—
157	C₂×D₂₀	—	4	2	no	—
158	C₂×D₂₀	C₂³×C₃	1	4	yes	—
159	C₅×Q₁₆	C₃×D₄	1	1	yes	characteristic, complemented
160	C₅×SD₁₆	C₃×D₄	1	2	yes	complemented
161	C₅×D₈	C₃×D₄	1	1	yes	characteristic, complemented
162	C₅×M₁₆	—	2	2	no	—
163	C₅×M₁₆	C₂³×C₃	1	2	yes	—
164	C₂×C₅×C₈	—	2	2	no	—
165	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
166	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
167	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
168	#688	—	2	4	no	—
169	#686	—	2	4	no	—
170	#681	C₂³×C₃	1	2	yes	—
171	Dic₂₀	C₃×D₄	1	1	yes	characteristic, complemented
172	D₄₀	—	2	4	no	—
173	D₄₀	—	2	2	no	—
174	D₄₀	—	2	2	no	—
175	D₄₀	—	2	2	no	—
176	D₄₀	—	2	2	no	—
177	D₄₀	C₃×D₄	1	1	yes	characteristic, complemented
178	#677	—	2	4	no	—
179	#677	C₃×D₄	1	2	yes	complemented
180	#676	—	2	2	no	—
181	C₈×D₅	—	2	2	no	—
182	#576	—	5	2	no	—
183	#576	—	5	2	no	—
184	#493	—	5	1	no	—
185	#472	—	5	2	no	—
186	#472	—	5	2	no	—
187	#453	—	5	4	no	—
188	#443	—	5	1	no	—
189	#443	C₃×D₅	1	1	yes	characteristic, complemented
190	C₂²×C₃×C₅	—	2	2	no	—
191	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
192	C₂×C₃×D₅	—	2	2	no	—
193	C₂×C₃×D₅	—	4	4	no	—
194	C₂×C₃×D₅	—	8	4	no	—
195	C₂×C₃×D₅	—	16	4	no	—
196	C₃×C₄×C₅	—	2	2	no	—
197	C₃×C₄×C₅	—	2	2	no	—
198	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
199	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
200	C₃×Dic₅	—	2	2	no	—
201	C₃×#41	—	5	2	no	—
202	C₃×#41	—	10	4	no	—
203	C₃×#41	—	10	4	no	—
204	C₃×#41	C₂²×D₅	1	2	yes	—
205	C₂×C₃×D₄	—	5	4	no	—
206	C₂×C₃×D₄	—	10	4	no	—
207	C₂×C₃×D₄	—	10	4	no	—
208	C₂×C₃×D₄	—	20	2	no	—
209	C₂×C₃×D₄	—	20	4	no	—
210	C₃×Q₁₆	—	5	1	no	—
211	C₃×Q₁₆	D₂₀	1	1	yes	characteristic, complemented
212	C₃×SD₁₆	—	5	2	no	—
213	C₃×SD₁₆	—	10	4	no	—
214	C₃×SD₁₆	—	10	4	no	—
215	C₃×SD₁₆	D₂₀	1	2	yes	complemented
216	C₃×D₈	—	5	1	no	—
217	C₃×D₈	—	10	4	no	—
218	C₃×D₈	—	10	4	no	—
219	C₃×D₈	—	10	2	no	—
220	C₃×D₈	—	10	2	no	—
221	C₃×D₈	—	10	2	no	—
222	C₃×D₈	—	10	2	no	—
223	C₃×D₈	D₂₀	1	1	yes	characteristic, complemented
224	C₃×M₁₆	—	2	2	no	—
225	C₃×M₁₆	—	5	2	no	—
226	C₃×M₁₆	—	10	2	no	—
227	C₃×M₁₆	C₂²×D₅	1	2	yes	—
228	C₂×C₃×C₈	—	2	2	no	—
229	C₂×C₃×C₈	—	10	2	no	—
230	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
231	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
232	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
233	C₂²×D₅	—	2	4	no	—
234	C₂²×D₅	—	4	4	no	—
235	C₅×Q₈	C₂×C₃×D₄	1	2	yes	—
236	C₅×D₄	—	2	2	no	—
237	C₅×D₄	C₂×C₃×D₄	1	2	yes	—
238	C₂×C₄×C₅	—	2	1	no	—
239	C₂×C₄×C₅	—	2	2	no	—
240	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
241	C₂²⋊D₅	—	2	2	no	—
242	C₂²⋊D₅	—	4	4	no	—
243	D₂₀	—	2	4	no	—
244	D₂₀	—	2	4	no	—
245	D₂₀	—	4	4	no	—
246	D₂₀	—	8	4	no	—
247	D₂₀	C₂×C₃×D₄	1	2	yes	—
248	C₄×D₅	—	2	2	no	—
249	C₄×D₅	—	4	4	no	—
250	Dic₁₀	C₂×C₃×D₄	1	2	yes	—
251	C₅×C₈	—	2	2	no	—
252	C₅×C₈	C₂×C₃×D₄	1	1	yes	characteristic
253	C₅×C₈	C₂×C₃×D₄	1	1	yes	characteristic
254	C₅×C₈	C₂×C₃×D₄	1	1	yes	characteristic
255	C₅×C₈	C₂×C₃×D₄	1	1	yes	characteristic
256	#168	—	2	2	no	—
257	H(5,𝔽₂)	—	5	4	no	—
258	AGL(1,ℤ/8)	—	5	4	no	—
259	AGL(1,ℤ/8)	—	5	4	no	—
260	AGL(1,ℤ/8)	—	10	4	no	—
261	AGL(1,ℤ/8)	—	10	4	no	—
262	#135	—	5	1	no	—
263	#135	—	10	2	no	—
264	#135	—	10	2	no	—
265	#135	C₂×C₃×D₅	1	1	yes	characteristic
266	C₂×D₈	—	5	2	no	—
267	C₂×D₈	—	5	2	no	—
268	C₂×D₈	—	10	2	no	—
269	C₂×D₈	—	10	2	no	—
270	#131	—	5	2	no	—
271	#131	C₂×C₃×D₅	1	2	yes	complemented
272	#127	—	5	2	no	—
273	#108	—	5	1	no	—
274	#108	C₂×C₃×D₅	1	1	yes	characteristic, complemented
275	#104	—	5	2	no	—
276	#104	C₂×C₃×D₅	1	2	yes	complemented
277	#100	—	5	4	no	—
278	C₄×C₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
279	C₂×C₃×C₅	—	2	1	no	—
280	C₂×C₃×C₅	—	4	2	no	—
281	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
282	C₃×D₅	—	4	2	no	—
283	C₃×D₅	—	8	4	no	—
284	C₂³×C₃	—	10	4	no	—
285	C₂³×C₃	—	20	4	no	—
286	C₃×Q₈	—	5	2	no	—
287	C₃×Q₈	C₂×D₂₀	1	2	yes	—
288	C₃×D₄	—	2	2	no	—
289	C₃×D₄	—	5	2	no	—
290	C₃×D₄	—	10	2	no	—
291	C₃×D₄	—	10	4	no	—
292	C₃×D₄	—	10	4	no	—
293	C₃×D₄	—	20	4	no	—
294	C₃×D₄	—	20	4	no	—
295	C₃×D₄	—	40	4	no	—
296	C₃×D₄	C₂×D₂₀	1	2	yes	—
297	C₂×C₃×C₄	—	2	1	no	—
298	C₂×C₃×C₄	—	2	2	no	—
299	C₂×C₃×C₄	—	10	2	no	—
300	C₂×C₃×C₄	—	20	4	no	—
301	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
302	C₃×C₈	—	2	2	no	—
303	C₃×C₈	—	10	2	no	—
304	C₃×C₈	C₂×D₂₀	1	1	yes	characteristic
305	C₃×C₈	C₂×D₂₀	1	1	yes	characteristic
306	C₃×C₈	D₄×D₅	1	1	yes	characteristic
307	C₃×C₈	D₄×D₅	1	1	yes	characteristic
308	C₂²×C₅	—	2	2	no	—
309	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
310	C₂×D₅	—	2	2	no	—
311	C₂×D₅	—	4	4	no	—
312	C₂×D₅	—	8	4	no	—
313	C₂×D₅	—	16	4	no	—
314	C₄×C₅	—	2	2	no	—
315	C₄×C₅	—	2	2	no	—
316	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
317	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
318	Dic₅	—	2	2	no	—
319	#41	—	5	2	no	—
320	#41	—	10	4	no	—
321	#41	—	10	4	no	—
322	#41	C₂²×C₃×D₅	1	2	yes	—
323	C₂×D₄	—	5	4	no	—
324	C₂×D₄	—	10	4	no	—
325	C₂×D₄	—	10	4	no	—
326	C₂×D₄	—	20	2	no	—
327	C₂×D₄	—	20	4	no	—
328	Q₁₆	—	5	1	no	—
329	Q₁₆	C₃×D₂₀	1	1	yes	characteristic, complemented
330	SD₁₆	—	5	2	no	—
331	SD₁₆	—	10	4	no	—
332	SD₁₆	—	10	4	no	—
333	SD₁₆	C₃×D₂₀	1	2	yes	complemented
334	D₈	—	5	1	no	—
335	D₈	—	10	4	no	—
336	D₈	—	10	4	no	—
337	D₈	—	10	2	no	—
338	D₈	—	10	2	no	—
339	D₈	—	10	2	no	—
340	D₈	—	10	2	no	—
341	D₈	C₃×D₂₀	1	1	yes	characteristic, complemented
342	M₁₆	—	2	2	no	—
343	M₁₆	—	5	2	no	—
344	M₁₆	—	10	2	no	—
345	M₁₆	C₂²×C₃×D₅	1	2	yes	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	10	2	no	—
348	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
349	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
350	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
351	C₃×C₅	#3292	1	1	yes	characteristic, complemented, Hall
352	C₂²×C₃	—	2	2	no	—
353	C₂²×C₃	—	10	2	no	—
354	C₂²×C₃	—	20	4	no	—
355	C₂²×C₃	—	40	4	no	—
356	C₂²×C₃	—	80	4	no	—
357	C₂²×C₃	#4149	1	1	yes	characteristic
358	C₃×C₄	—	2	2	no	—
359	C₃×C₄	—	2	2	no	—
360	C₃×C₄	—	10	2	no	—
361	C₃×C₄	C₂²×D₂₀	1	1	yes	characteristic
362	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
363	C₂×C₅	—	2	1	no	—
364	C₂×C₅	—	4	2	no	—
365	C₂×C₅	C₃×D₄²	1	1	yes	characteristic
366	D₅	—	4	2	no	—
367	D₅	—	8	4	no	—
368	C₂³	—	10	4	no	—
369	C₂³	—	20	4	no	—
370	Q₈	—	5	2	no	—
371	Q₈	C₂×C₃×D₂₀	1	2	yes	—
372	D₄	—	2	2	no	—
373	D₄	—	5	2	no	—
374	D₄	—	10	2	no	—
375	D₄	—	10	4	no	—
376	D₄	—	10	4	no	—
377	D₄	—	20	4	no	—
378	D₄	—	20	4	no	—
379	D₄	—	40	4	no	—
380	D₄	C₂×C₃×D₂₀	1	2	yes	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	10	2	no	—
384	C₂×C₄	—	20	4	no	—
385	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
386	C₈	—	2	2	no	—
387	C₈	—	10	2	no	—
388	C₈	C₂×C₃×D₂₀	1	1	yes	characteristic
389	C₈	C₂×C₃×D₂₀	1	1	yes	characteristic
390	C₈	C₃×D₄×D₅	1	1	yes	characteristic
391	C₈	C₃×D₄×D₅	1	1	yes	characteristic
392	C₂×C₃	—	2	1	no	—
393	C₂×C₃	—	4	2	no	—
394	C₂×C₃	—	20	2	no	—
395	C₂×C₃	—	40	4	no	—
396	C₂×C₃	D₄×D₂₀	1	1	yes	characteristic
397	C₅	C₃×#3292	1	1	yes	characteristic, complemented, Sylow
398	C₂²	—	2	2	no	—
399	C₂²	—	10	2	no	—
400	C₂²	—	20	4	no	—
401	C₂²	—	40	4	no	—
402	C₂²	—	80	4	no	—
403	C₂²	C₃×#4149	1	1	yes	characteristic
404	C₄	—	2	2	no	—
405	C₄	—	2	2	no	—
406	C₄	—	10	2	no	—
407	C₄	C₂²×C₃×D₂₀	1	1	yes	characteristic
408	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
409	C₃	#10611625	1	1	yes	characteristic, direct product factor, Sylow
410	C₂	—	2	1	no	—
411	C₂	—	4	2	no	—
412	C₂	—	20	2	no	—
413	C₂	—	40	4	no	—
414	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×#3292
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×#66103	C₂	semidirect
2. C₃×#66086	C₂	semidirect
3. C₃×C₅×#443	C₂	semidirect
4. C₃×#65431	C₂	semidirect
5. C₃×#65186	C₂	semidirect
6. C₃×#65111	C₂	semidirect
7. C₃×#64989	C₂	semidirect
8. C₃×#64984	C₂	semidirect
9. #10611625	C₃	direct (N × H)
10. C₃×#4149	C₂²	semidirect
12. C₃×C₅×#131	C₂²	semidirect
13. C₃×#4095	C₂²	semidirect
18. C₃×#4054	C₂²	semidirect
22. C₂×C₃×D₄₀	C₂²	semidirect
23. C₂×C₃×D₄₀	C₂²	semidirect
24. C₃×#4047	C₂²	semidirect
25. C₃×#4020	C₂²	semidirect
26. C₃×C₅×#108	C₂²	semidirect
27. C₃×C₅×#104	C₂²	semidirect
28. C₃×C₄×C₅×C₈	C₂²	semidirect
29. C₃×#3955	C₂²	semidirect
30. C₃×#3951	C₂²	semidirect
31. C₃×#3937	C₂²	semidirect
33. #66103	C₂×C₃	semidirect
34. #66086	C₂×C₃	semidirect
35. C₅×#443	C₂×C₃	semidirect
36. #65431	C₂×C₃	semidirect
37. #65186	C₂×C₃	semidirect
38. #65111	C₂×C₃	semidirect
39. #64989	C₂×C₃	semidirect
40. #64984	C₂×C₃	semidirect
50. C₃×C₅×Q₁₆	D₄	semidirect
51. C₃×C₅×SD₁₆	D₄	semidirect
52. C₃×C₅×D₈	D₄	semidirect
62. C₃×Dic₂₀	D₄	semidirect
68. C₃×D₄₀	D₄	semidirect
70. C₃×#677	D₄	semidirect
80. C₃×#443	D₅	semidirect
81. #4149	C₂²×C₃	semidirect
83. C₅×#131	C₂²×C₃	semidirect
84. #4095	C₂²×C₃	semidirect
89. #4054	C₂²×C₃	semidirect
93. C₂×D₄₀	C₂²×C₃	semidirect
94. C₂×D₄₀	C₂²×C₃	semidirect
95. #4047	C₂²×C₃	semidirect
96. #4020	C₂²×C₃	semidirect
97. C₅×#108	C₂²×C₃	semidirect
98. C₅×#104	C₂²×C₃	semidirect
99. C₄×C₅×C₈	C₂²×C₃	semidirect
100. #3955	C₂²×C₃	semidirect
101. #3951	C₂²×C₃	semidirect
102. #3937	C₂²×C₃	semidirect
142. C₃×#131	C₂×D₅	semidirect
145. C₃×#108	C₂×D₅	semidirect
147. C₃×#104	C₂×D₅	semidirect
149. C₃×C₄×C₈	C₂×D₅	semidirect
159. C₅×Q₁₆	C₃×D₄	semidirect
160. C₅×SD₁₆	C₃×D₄	semidirect
161. C₅×D₈	C₃×D₄	semidirect
171. Dic₂₀	C₃×D₄	semidirect
177. D₄₀	C₃×D₄	semidirect
179. #677	C₃×D₄	semidirect
189. #443	C₃×D₅	semidirect
211. C₃×Q₁₆	D₂₀	semidirect
215. C₃×SD₁₆	D₂₀	semidirect
223. C₃×D₈	D₂₀	semidirect
271. #131	C₂×C₃×D₅	semidirect
274. #108	C₂×C₃×D₅	semidirect
276. #104	C₂×C₃×D₅	semidirect
278. C₄×C₈	C₂×C₃×D₅	semidirect
329. Q₁₆	C₃×D₂₀	semidirect
333. SD₁₆	C₃×D₂₀	semidirect
341. D₈	C₃×D₂₀	semidirect
351. C₃×C₅	#3292	semidirect
397. C₅	C₃×#3292	semidirect
409. C₃	#10611625	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×#66103	2
C₃×#66086	2
C₃×C₅×#443	2
C₃×#65431	2
C₃×#65186	2
C₃×#65111	2
C₃×#64989	2
C₃×#64984	2
#10611625	3
C₃×#3292	5

Subgroups — C3×#10611625 #14458177

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10611625 #14458177