Subgroups — C₃×#10599176 #14284766

Order 1920.

688 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₅×#127	C₂	1	1	yes	maximal, characteristic
2	C₃×#65126	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#65122	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#331	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#64764	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#64705	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#64705	C₂	1	1	yes	maximal, characteristic, complemented
8	#10599176	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×D₄×D₅	—	2	1	no	—
10	C₂×C₃×D₄×D₅	—	2	1	no	—
11	C₂×C₃×D₄×D₅	C₄	1	2	yes	—
12	C₃×C₅×#127	C₂²	1	1	yes	characteristic
13	C₃×#4086	—	2	1	no	—
14	C₃×#4086	—	2	1	no	—
15	C₃×#4086	C₄	1	2	yes	—
16	C₂×C₃×#676	—	2	1	no	—
17	C₃×#4020	C₂²	1	1	yes	characteristic
18	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
19	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
20	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
21	C₃×#3952	—	2	1	no	—
22	C₃×#3946	—	2	1	no	—
23	C₃×C₈×Dic₅	—	2	1	no	—
24	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic, complemented
25	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic, complemented
26	C₃×#1545	—	5	1	no	maximal, Hall
27	D₅×#127	C₂×C₃	1	1	yes	characteristic
28	#65126	C₂×C₃	1	1	yes	characteristic, complemented
29	#65122	C₂×C₃	1	1	yes	characteristic, complemented
30	C₅×#331	C₂×C₃	1	1	yes	characteristic, complemented
31	#64764	C₂×C₃	1	1	yes	characteristic, complemented
32	#64705	C₂×C₃	1	1	yes	characteristic, complemented
33	#64705	C₂×C₃	1	1	yes	characteristic, complemented
34	C₂³×C₃×D₅	—	2	2	no	—
35	C₂×C₃×C₅×D₄	—	2	1	no	—
36	C₂×C₃×C₅×D₄	—	2	1	no	—
37	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	—
38	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
39	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
40	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
41	C₃×D₄×D₅	—	4	2	no	—
42	C₃×D₄×D₅	—	4	2	no	—
43	C₃×D₄×D₅	—	4	4	no	—
44	C₃×D₄×D₅	—	4	2	no	—
45	C₃×D₄×D₅	—	4	2	no	—
46	C₂×C₃×D₂₀	—	2	1	no	—
47	C₂×C₃×D₂₀	—	2	1	no	—
48	C₂×C₃×D₂₀	C₂×C₄	1	2	yes	—
49	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
50	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
51	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
52	C₂×C₃×C₅×C₈	—	2	1	no	—
53	C₂×C₃×C₅×C₈	—	2	1	no	—
54	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
55	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
56	C₃×C₄×Dic₅	D₄	1	1	yes	characteristic
57	C₃×C₄×Dic₅	D₄	1	1	yes	characteristic
58	C₂×C₃×#168	—	2	1	no	—
59	C₂×C₃×#168	—	2	1	no	—
60	C₃×#676	—	4	2	no	—
61	C₂×C₃×#127	—	5	1	no	—
62	C₃×#431	—	5	1	no	—
63	C₃×#423	—	5	1	no	—
64	C₃×#331	—	5	1	no	—
65	C₃×#331	—	5	1	no	—
66	C₃×#331	—	5	1	no	—
67	C₃×#331	D₅	1	1	yes	characteristic, complemented
68	C₂×D₄×D₅	—	2	1	no	—
69	C₂×D₄×D₅	—	2	1	no	—
70	C₂×D₄×D₅	C₃×C₄	1	2	yes	—
71	C₅×#127	C₂²×C₃	1	1	yes	characteristic
72	#4086	—	2	1	no	—
73	#4086	—	2	1	no	—
74	#4086	C₃×C₄	1	2	yes	—
75	C₂×#676	—	2	1	no	—
76	#4020	C₂²×C₃	1	1	yes	characteristic
77	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
78	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
79	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
80	#3952	—	2	1	no	—
81	#3946	—	2	1	no	—
82	C₈×Dic₅	—	2	1	no	—
83	C₄⋊#168	C₂²×C₃	1	1	yes	characteristic, complemented
84	C₄⋊#168	C₂²×C₃	1	1	yes	characteristic, complemented
85	#1545	—	5	1	no	Sylow
86	C₂³×C₃×C₅	—	2	2	no	—
87	C₂²×C₃×D₅	—	2	2	no	—
88	C₂²×C₃×D₅	—	4	4	no	—
89	C₂²×C₃×D₅	—	4	4	no	—
90	C₂²×C₃×D₅	—	4	4	no	—
91	C₂²×C₃×D₅	C₂²⋊C₄	1	1	yes	characteristic
92	C₃×C₅×D₄	—	4	2	no	—
93	C₃×C₅×D₄	—	4	1	no	—
94	C₃×C₅×D₄	—	4	1	no	—
95	C₃×C₅×D₄	—	4	1	no	—
96	C₃×C₅×D₄	—	4	1	no	—
97	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
99	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
100	C₃×C₂²⋊D₅	—	4	4	no	—
101	C₃×C₂²⋊D₅	—	4	4	no	—
102	C₃×C₂²⋊D₅	—	4	4	no	—
103	C₂×C₃×Dic₅	C₂²⋊C₄	1	1	yes	characteristic
104	C₂×C₃×Dic₅	C₂²⋊C₄	1	1	yes	characteristic
105	C₂×C₃×Dic₅	C₂²⋊C₄	1	1	yes	characteristic
106	C₃×D₂₀	—	4	2	no	—
107	C₃×D₂₀	—	4	1	no	—
108	C₃×D₂₀	—	4	1	no	—
109	C₃×D₂₀	—	4	1	no	—
110	C₃×D₂₀	—	4	1	no	—
111	C₃×C₄×D₅	—	2	1	no	—
112	C₃×C₄×D₅	—	2	1	no	—
113	C₃×C₄×D₅	—	2	2	no	—
114	C₃×C₄×D₅	D₈	1	2	yes	—
115	C₃×C₄×D₅	SD₁₆	1	2	yes	—
116	C₃×C₅×C₈	—	4	1	no	—
117	C₃×C₅×C₈	—	4	1	no	—
118	C₃×#168	—	4	1	no	—
119	C₃×#168	—	4	1	no	—
120	C₂²×C₃×D₄	—	5	2	no	—
121	C₂²×C₃×D₄	—	10	1	no	—
122	C₂²×C₃×D₄	—	10	1	no	—
123	C₂×C₃×M₁₆	—	10	1	no	—
124	C₃×#127	—	5	2	no	—
125	C₃×#127	—	5	1	no	—
126	C₃×#127	—	10	1	no	—
127	C₃×#127	—	10	1	no	—
128	C₃×#127	C₂×D₅	1	1	yes	characteristic
129	C₂×C₃×C₄²	—	5	1	no	—
130	C₃×C₄⋊C₈	—	5	1	no	—
131	C₃×C₄⋊C₈	—	5	1	no	—
132	C₃×C₄⋊C₈	—	10	1	no	—
133	C₃×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic, complemented
134	C₃×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic, complemented
135	C₃×C₂²⋊C₈	—	10	1	no	—
136	C₃×C₄×C₈	—	10	1	no	—
137	C₂³×D₅	—	2	2	no	—
138	C₂×C₅×D₄	—	2	1	no	—
139	C₂×C₅×D₄	—	2	1	no	—
140	C₂×C₅×D₄	C₂×C₃×C₄	1	2	yes	—
141	C₂×C₂²⋊D₅	—	2	2	no	—
142	C₂×C₂²⋊D₅	—	2	2	no	—
143	C₂×C₂²⋊D₅	—	2	2	no	—
144	D₄×D₅	—	4	2	no	—
145	D₄×D₅	—	4	2	no	—
146	D₄×D₅	—	4	4	no	—
147	D₄×D₅	—	4	2	no	—
148	D₄×D₅	—	4	2	no	—
149	C₂×D₂₀	—	2	1	no	—
150	C₂×D₂₀	—	2	1	no	—
151	C₂×D₂₀	C₂×C₃×C₄	1	2	yes	—
152	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
153	C₂×C₄×D₅	C₃×D₄	1	1	yes	characteristic
154	C₂×C₄×D₅	C₃×D₄	1	1	yes	characteristic
155	C₂×C₅×C₈	—	2	1	no	—
156	C₂×C₅×C₈	—	2	1	no	—
157	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
158	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
159	C₄×Dic₅	C₃×D₄	1	1	yes	characteristic
160	C₄×Dic₅	C₃×D₄	1	1	yes	characteristic
161	C₂×#168	—	2	1	no	—
162	C₂×#168	—	2	1	no	—
163	#676	—	4	2	no	—
164	C₂×#127	—	5	1	no	—
165	#431	—	5	1	no	—
166	#423	—	5	1	no	—
167	#331	—	5	1	no	—
168	#331	—	5	1	no	—
169	#331	—	5	1	no	—
170	#331	C₃×D₅	1	1	yes	characteristic, complemented
171	C₂²×C₃×C₅	—	4	2	no	—
172	C₂²×C₃×C₅	—	4	2	no	—
173	C₂²×C₃×C₅	—	4	2	no	—
174	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
175	C₂×C₃×D₅	—	2	1	no	—
176	C₂×C₃×D₅	—	2	1	no	—
177	C₂×C₃×D₅	—	4	2	no	—
178	C₂×C₃×D₅	—	4	2	no	—
179	C₂×C₃×D₅	—	4	2	no	—
180	C₂×C₃×D₅	—	8	8	no	—
181	C₂×C₃×D₅	#102	1	2	yes	—
182	C₃×C₄×C₅	—	2	1	no	—
183	C₃×C₄×C₅	C₂×D₈	1	1	yes	characteristic
184	C₃×C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
185	C₃×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
186	C₃×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
187	C₃×Dic₅	—	2	1	no	—
188	C₃×Dic₅	#100	1	2	yes	—
189	C₃×Dic₅	#102	1	2	yes	—
190	C₂⁴×C₃	—	10	2	no	—
191	C₂×C₃×D₄	—	2	1	no	—
192	C₂×C₃×D₄	—	2	1	no	—
193	C₂×C₃×D₄	—	5	2	no	—
194	C₂×C₃×D₄	—	10	2	no	—
195	C₂×C₃×D₄	—	10	2	no	—
196	C₂×C₃×D₄	—	10	2	no	—
197	C₂×C₃×D₄	—	10	1	no	—
198	C₂×C₃×D₄	—	10	1	no	—
199	C₂×C₃×D₄	—	20	2	no	—
200	C₂×C₃×D₄	—	20	2	no	—
201	C₂×C₃×D₄	—	20	2	no	—
202	C₂×C₃×D₄	—	20	2	no	—
203	C₂×C₃×D₄	—	20	4	no	—
204	C₂×C₃×D₄	C₄×D₅	1	2	yes	—
205	C₂²×C₃×C₄	—	5	1	no	—
206	C₂²×C₃×C₄	—	5	1	no	—
207	C₂²×C₃×C₄	—	5	1	no	—
208	C₃×M₁₆	—	20	2	no	—
209	C₂×C₃×C₈	—	2	1	no	—
210	C₂×C₃×C₈	—	2	1	no	—
211	C₂×C₃×C₈	—	10	1	no	—
212	C₂×C₃×C₈	—	10	1	no	—
213	C₃×C₄²	—	5	1	no	—
214	C₃×C₄²	—	5	1	no	—
215	C₃×C₄²	—	5	1	no	—
216	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
217	C₂³×C₅	—	2	2	no	—
218	C₂²×D₅	—	2	2	no	—
219	C₂²×D₅	—	4	4	no	—
220	C₂²×D₅	—	4	4	no	—
221	C₂²×D₅	—	4	4	no	—
222	C₂²×D₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
223	C₅×D₄	—	4	2	no	—
224	C₅×D₄	—	4	1	no	—
225	C₅×D₄	—	4	1	no	—
226	C₅×D₄	—	4	1	no	—
227	C₅×D₄	—	4	1	no	—
228	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
229	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
230	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
231	C₂²⋊D₅	—	4	4	no	—
232	C₂²⋊D₅	—	4	4	no	—
233	C₂²⋊D₅	—	4	4	no	—
234	C₂×Dic₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
235	C₂×Dic₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
236	C₂×Dic₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
237	D₂₀	—	4	2	no	—
238	D₂₀	—	4	1	no	—
239	D₂₀	—	4	1	no	—
240	D₂₀	—	4	1	no	—
241	D₂₀	—	4	1	no	—
242	C₄×D₅	—	2	1	no	—
243	C₄×D₅	—	2	1	no	—
244	C₄×D₅	—	2	2	no	—
245	C₄×D₅	C₃×D₈	1	2	yes	—
246	C₄×D₅	C₃×SD₁₆	1	2	yes	—
247	C₅×C₈	—	4	1	no	—
248	C₅×C₈	—	4	1	no	—
249	#168	—	4	1	no	—
250	#168	—	4	1	no	—
251	C₂²×D₄	—	5	2	no	—
252	C₂²×D₄	—	10	1	no	—
253	C₂²×D₄	—	10	1	no	—
254	C₂×M₁₆	—	10	1	no	—
255	#127	—	5	2	no	—
256	#127	—	5	1	no	—
257	#127	—	10	1	no	—
258	#127	—	10	1	no	—
259	#127	C₂×C₃×D₅	1	1	yes	characteristic
260	C₂×C₄²	—	5	1	no	—
261	C₄⋊C₈	—	5	1	no	—
262	C₄⋊C₈	—	5	1	no	—
263	C₄⋊C₈	—	10	1	no	—
264	C₄⋊C₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
265	C₄⋊C₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
266	C₂²⋊C₈	—	10	1	no	—
267	C₄×C₈	—	10	1	no	—
268	C₂×C₃×C₅	—	8	2	no	—
269	C₂×C₃×C₅	C₂×#100	1	1	yes	characteristic
270	C₂×C₃×C₅	C₂×#102	1	1	yes	characteristic
271	C₂×C₃×C₅	#418	1	1	yes	characteristic
272	C₃×D₅	—	2	2	no	—
273	C₃×D₅	—	8	2	no	—
274	C₂³×C₃	—	2	2	no	—
275	C₂³×C₃	—	5	1	no	—
276	C₂³×C₃	—	10	2	no	—
277	C₂³×C₃	—	20	4	no	—
278	C₂³×C₃	—	20	4	no	—
279	C₂³×C₃	—	20	4	no	—
280	C₃×D₄	—	4	2	no	—
281	C₃×D₄	—	4	1	no	—
282	C₃×D₄	—	4	1	no	—
283	C₃×D₄	—	4	1	no	—
284	C₃×D₄	—	4	1	no	—
285	C₃×D₄	—	20	2	no	—
286	C₃×D₄	—	20	4	no	—
287	C₃×D₄	—	20	4	no	—
288	C₃×D₄	—	20	4	no	—
289	C₃×D₄	—	20	1	no	—
290	C₃×D₄	—	20	1	no	—
291	C₃×D₄	—	20	1	no	—
292	C₃×D₄	—	20	1	no	—
293	C₂×C₃×C₄	—	5	1	no	—
294	C₂×C₃×C₄	—	5	1	no	—
295	C₂×C₃×C₄	—	5	2	no	—
296	C₂×C₃×C₄	—	5	2	no	—
297	C₂×C₃×C₄	—	5	1	no	—
298	C₂×C₃×C₄	—	10	2	no	—
299	C₂×C₃×C₄	—	10	1	no	—
300	C₂×C₃×C₄	—	10	1	no	—
301	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
302	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
303	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
304	C₃×C₈	—	4	1	no	—
305	C₃×C₈	—	4	1	no	—
306	C₃×C₈	—	20	1	no	—
307	C₃×C₈	—	20	1	no	—
308	C₂²×C₅	—	4	2	no	—
309	C₂²×C₅	—	4	2	no	—
310	C₂²×C₅	—	4	2	no	—
311	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
312	C₂×D₅	—	2	1	no	—
313	C₂×D₅	—	2	1	no	—
314	C₂×D₅	—	4	2	no	—
315	C₂×D₅	—	4	2	no	—
316	C₂×D₅	—	4	2	no	—
317	C₂×D₅	—	8	8	no	—
318	C₂×D₅	C₃×#102	1	2	yes	—
319	C₄×C₅	—	2	1	no	—
320	C₄×C₅	C₂×C₃×D₈	1	1	yes	characteristic
321	C₄×C₅	C₂×C₃×SD₁₆	1	1	yes	characteristic
322	C₄×C₅	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
323	C₄×C₅	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
324	Dic₅	—	2	1	no	—
325	Dic₅	C₃×#100	1	2	yes	—
326	Dic₅	C₃×#102	1	2	yes	—
327	C₂⁴	—	10	2	no	—
328	C₂×D₄	—	2	1	no	—
329	C₂×D₄	—	2	1	no	—
330	C₂×D₄	—	5	2	no	—
331	C₂×D₄	—	10	2	no	—
332	C₂×D₄	—	10	2	no	—
333	C₂×D₄	—	10	2	no	—
334	C₂×D₄	—	10	1	no	—
335	C₂×D₄	—	10	1	no	—
336	C₂×D₄	—	20	2	no	—
337	C₂×D₄	—	20	2	no	—
338	C₂×D₄	—	20	2	no	—
339	C₂×D₄	—	20	2	no	—
340	C₂×D₄	—	20	4	no	—
341	C₂×D₄	C₃×C₄×D₅	1	2	yes	—
342	C₂²×C₄	—	5	1	no	—
343	C₂²×C₄	—	5	1	no	—
344	C₂²×C₄	—	5	1	no	—
345	M₁₆	—	20	2	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	10	1	no	—
349	C₂×C₈	—	10	1	no	—
350	C₄²	—	5	1	no	—
351	C₄²	—	5	1	no	—
352	C₄²	—	5	1	no	—
353	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
354	C₃×C₅	#1545	1	1	yes	characteristic, complemented, Hall
355	C₂²×C₃	—	4	2	no	—
356	C₂²×C₃	—	4	2	no	—
357	C₂²×C₃	—	4	2	no	—
358	C₂²×C₃	—	5	2	no	—
359	C₂²×C₃	—	10	1	no	—
360	C₂²×C₃	—	10	1	no	—
361	C₂²×C₃	—	20	2	no	—
362	C₂²×C₃	—	20	2	no	—
363	C₂²×C₃	—	20	2	no	—
364	C₂²×C₃	—	40	8	no	—
365	C₂²×C₃	D₅×C₂²⋊C₄	1	1	yes	characteristic
366	C₃×C₄	—	2	1	no	—
367	C₃×C₄	—	5	2	no	—
368	C₃×C₄	—	5	2	no	—
369	C₃×C₄	—	10	1	no	—
370	C₃×C₄	D₅×D₈	1	1	yes	characteristic
371	C₃×C₄	#4057	1	1	yes	characteristic
372	C₃×C₄	D₅×SD₁₆	1	1	yes	characteristic
373	C₃×C₄	#4060	1	1	yes	characteristic
374	C₂×C₅	—	8	2	no	—
375	C₂×C₅	C₂×C₃×#100	1	1	yes	characteristic
376	C₂×C₅	C₂×C₃×#102	1	1	yes	characteristic
377	C₂×C₅	C₃×#418	1	1	yes	characteristic
378	D₅	—	2	2	no	—
379	D₅	—	8	2	no	—
380	C₂³	—	2	2	no	—
381	C₂³	—	5	1	no	—
382	C₂³	—	10	2	no	—
383	C₂³	—	20	4	no	—
384	C₂³	—	20	4	no	—
385	C₂³	—	20	4	no	—
386	D₄	—	4	2	no	—
387	D₄	—	4	1	no	—
388	D₄	—	4	1	no	—
389	D₄	—	4	1	no	—
390	D₄	—	4	1	no	—
391	D₄	—	20	2	no	—
392	D₄	—	20	4	no	—
393	D₄	—	20	4	no	—
394	D₄	—	20	4	no	—
395	D₄	—	20	1	no	—
396	D₄	—	20	1	no	—
397	D₄	—	20	1	no	—
398	D₄	—	20	1	no	—
399	C₂×C₄	—	5	1	no	—
400	C₂×C₄	—	5	1	no	—
401	C₂×C₄	—	5	2	no	—
402	C₂×C₄	—	5	2	no	—
403	C₂×C₄	—	5	1	no	—
404	C₂×C₄	—	10	2	no	—
405	C₂×C₄	—	10	1	no	—
406	C₂×C₄	—	10	1	no	—
407	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
408	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
409	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
410	C₈	—	4	1	no	—
411	C₈	—	4	1	no	—
412	C₈	—	20	1	no	—
413	C₈	—	20	1	no	—
414	C₂×C₃	—	8	2	no	—
415	C₂×C₃	—	10	2	no	—
416	C₂×C₃	—	40	2	no	—
417	C₂×C₃	D₅×#100	1	1	yes	characteristic
418	C₂×C₃	D₅×#102	1	1	yes	characteristic
419	C₂×C₃	#65059	1	1	yes	characteristic
420	C₅	C₃×#1545	1	1	yes	characteristic, complemented, Sylow
421	C₂²	—	4	2	no	—
422	C₂²	—	4	2	no	—
423	C₂²	—	4	2	no	—
424	C₂²	—	5	2	no	—
425	C₂²	—	10	1	no	—
426	C₂²	—	10	1	no	—
427	C₂²	—	20	2	no	—
428	C₂²	—	20	2	no	—
429	C₂²	—	20	2	no	—
430	C₂²	—	40	8	no	—
431	C₂²	C₃×D₅×C₂²⋊C₄	1	1	yes	characteristic
432	C₄	—	2	1	no	—
433	C₄	—	5	2	no	—
434	C₄	—	5	2	no	—
435	C₄	—	10	1	no	—
436	C₄	C₃×D₅×D₈	1	1	yes	characteristic
437	C₄	C₃×#4057	1	1	yes	characteristic
438	C₄	C₃×D₅×SD₁₆	1	1	yes	characteristic
439	C₄	C₃×#4060	1	1	yes	characteristic
440	C₃	#10599176	1	1	yes	characteristic, direct product factor, Sylow
441	C₂	—	8	2	no	—
442	C₂	—	10	2	no	—
443	C₂	—	40	2	no	—
444	C₂	C₃×D₅×#100	1	1	yes	characteristic
445	C₂	C₃×D₅×#102	1	1	yes	characteristic
446	C₂	C₃×#65059	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	D₅×C₂²⋊C₄
commutator	C₂×C₄×C₅	C₂²×C₃×C₄
Frattini	C₄²	C₂²×C₃×D₅
Fitting	C₃×C₅×#331	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₃×D₅×#127	C₂
cosocle	C₄²×C₅	C₂³×C₃
hypercenter	C₃×#331	D₅
hypocenter	C₅	C₃×#1545
LCS	G ▷ C₂×C₄×C₅ ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×#331

Complements

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

N	H ≅ G/N	type
2. C₃×#65126	C₂	semidirect
3. C₃×#65122	C₂	semidirect
4. C₃×C₅×#331	C₂	semidirect
5. C₃×#64764	C₂	semidirect
6. C₃×#64705	C₂	semidirect
7. C₃×#64705	C₂	semidirect
8. #10599176	C₃	direct (N × H)
19. C₃×C₅×C₄⋊C₈	C₂²	semidirect
20. C₃×C₅×C₄⋊C₈	C₂²	semidirect
24. C₃×C₄⋊#168	C₂²	semidirect
25. C₃×C₄⋊#168	C₂²	semidirect
28. #65126	C₂×C₃	semidirect
29. #65122	C₂×C₃	semidirect
30. C₅×#331	C₂×C₃	semidirect
31. #64764	C₂×C₃	semidirect
32. #64705	C₂×C₃	semidirect
33. #64705	C₂×C₃	semidirect
67. C₃×#331	D₅	semidirect
78. C₅×C₄⋊C₈	C₂²×C₃	semidirect
79. C₅×C₄⋊C₈	C₂²×C₃	semidirect
83. C₄⋊#168	C₂²×C₃	semidirect
84. C₄⋊#168	C₂²×C₃	semidirect
133. C₃×C₄⋊C₈	C₂×D₅	semidirect
134. C₃×C₄⋊C₈	C₂×D₅	semidirect
170. #331	C₃×D₅	semidirect
264. C₄⋊C₈	C₂×C₃×D₅	semidirect
265. C₄⋊C₈	C₂×C₃×D₅	semidirect
354. C₃×C₅	#1545	semidirect
420. C₅	C₃×#1545	semidirect
440. C₃	#10599176	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×D₅×#127	2
C₃×#65126	2
C₃×#65122	2
C₃×C₅×#331	2
C₃×#64764	2
C₃×#64705	2
#10599176	3
C₃×#1545	5

Subgroups — C3×#10599176 #14284766

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10599176 #14284766