Subgroups — C₃×#10613492 #14439124

Order 1920.

1312 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4060	C₂	1	4	yes	maximal, complemented
2	C₃×#66059	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₅×#127	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#492	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65465	C₂	1	4	yes	maximal, complemented
6	C₃×#65374	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65362	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#64984	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₄×#676	C₂	1	1	yes	maximal, characteristic, complemented
10	#10613492	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₃×#713	C₂²	1	2	yes	—
12	C₂×C₃×D₄×D₅	—	2	2	no	—
13	C₂×C₃×D₄×D₅	C₂²	1	2	yes	—
14	C₂×C₃×C₅×SD₁₆	C₂²	1	4	yes	complemented
15	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
16	C₃×C₅×#127	C₂²	1	1	yes	characteristic
17	C₃×#4093	C₂²	1	2	yes	complemented
18	C₂×C₃×#688	C₂²	1	4	yes	complemented
19	C₃×#4086	—	2	2	no	—
20	C₃×#4086	C₂²	1	2	yes	—
21	C₂×C₃×#686	C₂²	1	4	yes	complemented
22	C₃×#4060	—	2	16	no	—
23	C₂×C₃×D₄₀	C₂²	1	4	yes	complemented
24	C₂×C₃×#676	C₂²	1	2	yes	—
25	C₃×#4041	—	2	2	no	—
26	C₃×#4039	—	2	2	no	—
27	C₃×#4020	C₂²	1	1	yes	characteristic
28	C₃×#4020	C₂²	1	1	yes	characteristic, complemented
29	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
30	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
31	C₃×#3947	C₂²	1	2	yes	complemented
32	C₃×C₄×#168	C₂²	1	1	yes	characteristic, complemented
33	C₃×#3151	—	5	1	no	maximal, Hall
34	C₂×#4060	C₂×C₃	1	4	yes	complemented
35	#66059	C₂×C₃	1	1	yes	characteristic, complemented
36	D₅×#127	C₂×C₃	1	1	yes	characteristic, complemented
37	C₅×#492	C₂×C₃	1	1	yes	characteristic, complemented
38	#65465	C₂×C₃	1	4	yes	complemented
39	#65374	C₂×C₃	1	1	yes	characteristic, complemented
40	#65362	C₂×C₃	1	1	yes	characteristic, complemented
41	#64984	C₂×C₃	1	1	yes	characteristic, complemented
42	C₄×#676	C₂×C₃	1	1	yes	characteristic, complemented
43	C₂³×C₃×D₅	—	2	2	no	—
44	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
45	C₂×C₃×C₅×D₄	—	2	2	no	—
46	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
47	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
48	C₂×C₃×C₂²⋊D₅	—	2	4	no	—
49	C₃×#713	—	2	8	no	—
50	C₃×D₄×D₅	—	2	8	no	—
51	C₃×D₄×D₅	—	4	8	no	—
52	C₂×C₃×D₂₀	—	2	2	no	—
53	C₂×C₃×D₂₀	—	2	2	no	—
54	C₂×C₃×D₂₀	—	2	2	no	—
55	C₂×C₃×D₂₀	C₂³	1	2	yes	—
56	C₂×C₃×D₂₀	C₂³	1	2	yes	—
57	C₂×C₃×C₄×D₅	—	2	2	no	—
58	C₂×C₃×C₄×D₅	D₄	1	2	yes	—
59	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
60	C₃×C₅×SD₁₆	—	2	8	no	—
61	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
62	C₃×C₅×C₄⋊C₄	—	2	2	no	—
63	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
64	C₃×#688	—	2	8	no	—
65	C₃×#686	—	2	8	no	—
66	C₃×#685	—	2	4	no	—
67	C₃×C₄×Dic₅	D₄	1	2	yes	—
68	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
69	C₂×C₃×#168	C₂³	1	2	yes	—
70	C₃×D₄₀	—	2	8	no	—
71	C₃×#676	D₄	1	8	yes	complemented
72	C₂×C₃×AGL(1,ℤ/8)	—	5	4	no	—
73	C₃×#532	—	5	1	no	—
74	C₂×C₃×#127	—	5	1	no	—
75	C₃×#496	—	5	4	no	—
76	C₃×#493	—	5	1	no	—
77	C₃×#493	—	5	1	no	—
78	C₃×#492	—	5	1	no	—
79	C₃×#492	D₅	1	1	yes	characteristic, complemented
80	C₃×C₄×M₁₆	—	5	1	no	—
81	C₂×#713	C₂²×C₃	1	2	yes	—
82	C₂×D₄×D₅	—	2	2	no	—
83	C₂×D₄×D₅	C₂²×C₃	1	2	yes	—
84	C₂×C₅×SD₁₆	C₂²×C₃	1	4	yes	complemented
85	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
86	C₅×#127	C₂²×C₃	1	1	yes	characteristic
87	#4093	C₂²×C₃	1	2	yes	complemented
88	C₂×#688	C₂²×C₃	1	4	yes	complemented
89	#4086	—	2	2	no	—
90	#4086	C₂²×C₃	1	2	yes	—
91	C₂×#686	C₂²×C₃	1	4	yes	complemented
92	#4060	—	2	16	no	—
93	C₂×D₄₀	C₂²×C₃	1	4	yes	complemented
94	C₂×#676	C₂²×C₃	1	2	yes	—
95	#4041	—	2	2	no	—
96	#4039	—	2	2	no	—
97	#4020	C₂²×C₃	1	1	yes	characteristic
98	#4020	C₂²×C₃	1	1	yes	characteristic, complemented
99	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
100	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
101	#3947	C₂²×C₃	1	2	yes	complemented
102	C₄×#168	C₂²×C₃	1	1	yes	characteristic, complemented
103	#3151	—	5	1	no	Sylow
104	C₂³×C₃×C₅	—	2	2	no	—
105	C₂²×C₃×D₅	—	2	2	no	—
106	C₂²×C₃×D₅	—	2	2	no	—
107	C₂²×C₃×D₅	—	4	8	no	—
108	C₂²×C₃×D₅	—	4	4	no	—
109	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
110	C₃×C₅×Q₈	—	2	4	no	—
111	C₃×C₅×D₄	—	2	4	no	—
112	C₃×C₅×D₄	—	4	4	no	—
113	C₂×C₃×C₄×C₅	—	2	2	no	—
114	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
115	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
116	C₃×C₂²⋊D₅	—	4	8	no	—
117	C₃×C₂²⋊D₅	—	4	4	no	—
118	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
119	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
120	C₃×D₂₀	—	2	4	no	—
121	C₃×D₂₀	—	2	4	no	—
122	C₃×D₂₀	—	4	4	no	—
123	C₃×D₂₀	—	4	4	no	—
124	C₃×D₂₀	—	4	4	no	—
125	C₃×C₄×D₅	—	2	4	no	—
126	C₃×C₄×D₅	—	4	4	no	—
127	C₃×C₄×D₅	C₂×D₄	1	4	yes	—
128	C₃×C₅×C₈	C₂×D₄	1	4	yes	complemented
129	C₃×#168	C₂×D₄	1	4	yes	complemented
130	C₂×C₃×#41	—	5	2	no	—
131	C₂²×C₃×D₄	—	5	2	no	—
132	C₂²×C₃×D₄	—	10	2	no	—
133	C₃×AGL(1,ℤ/8)	—	10	16	no	—
134	C₂×C₃×SD₁₆	—	5	4	no	—
135	C₂×C₃×SD₁₆	C₂×D₅	1	4	yes	complemented
136	C₂×C₃×D₈	—	5	4	no	—
137	C₂×C₃×D₈	—	5	4	no	—
138	C₂×C₃×M₁₆	—	5	2	no	—
139	C₃×C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
140	C₃×#127	—	5	2	no	—
141	C₃×#127	—	5	1	no	—
142	C₃×#127	—	5	1	no	—
143	C₃×#127	—	10	2	no	—
144	C₃×#127	C₂×D₅	1	1	yes	characteristic
145	C₃×#124	—	5	2	no	—
146	C₃×#121	—	10	2	no	—
147	C₃×C₄×D₄	—	10	2	no	—
148	C₂×C₃×C₄²	—	5	1	no	—
149	C₃×#97	—	5	2	no	—
150	C₃×C₄×C₈	—	5	1	no	—
151	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic, complemented
152	C₂³×D₅	—	2	2	no	—
153	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
154	C₂×C₅×D₄	—	2	2	no	—
155	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
156	C₂×C₂²⋊D₅	—	2	4	no	—
157	C₂×C₂²⋊D₅	—	2	2	no	—
158	#713	—	2	8	no	—
159	D₄×D₅	—	2	8	no	—
160	D₄×D₅	—	4	8	no	—
161	C₂×D₂₀	—	2	2	no	—
162	C₂×D₂₀	—	2	2	no	—
163	C₂×D₂₀	—	2	2	no	—
164	C₂×D₂₀	C₂³×C₃	1	2	yes	—
165	C₂×D₂₀	C₂³×C₃	1	2	yes	—
166	C₂×C₄×D₅	—	2	2	no	—
167	C₂×C₄×D₅	C₃×D₄	1	2	yes	—
168	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
169	C₅×SD₁₆	—	2	8	no	—
170	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
171	C₅×C₄⋊C₄	—	2	2	no	—
172	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
173	#688	—	2	8	no	—
174	#686	—	2	8	no	—
175	#685	—	2	4	no	—
176	C₄×Dic₅	C₃×D₄	1	2	yes	—
177	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
178	C₂×#168	C₂³×C₃	1	2	yes	—
179	D₄₀	—	2	8	no	—
180	#676	C₃×D₄	1	8	yes	complemented
181	C₂×AGL(1,ℤ/8)	—	5	4	no	—
182	#532	—	5	1	no	—
183	C₂×#127	—	5	1	no	—
184	#496	—	5	4	no	—
185	#493	—	5	1	no	—
186	#493	—	5	1	no	—
187	#492	—	5	1	no	—
188	#492	C₃×D₅	1	1	yes	characteristic, complemented
189	C₄×M₁₆	—	5	1	no	—
190	C₂²×C₃×C₅	—	4	2	no	—
191	C₂²×C₃×C₅	—	4	4	no	—
192	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₃×D₅	—	2	2	no	—
194	C₂×C₃×D₅	—	4	2	no	—
195	C₂×C₃×D₅	—	4	2	no	—
196	C₂×C₃×D₅	—	4	4	no	—
197	C₂×C₃×D₅	—	4	4	no	—
198	C₂×C₃×D₅	—	8	8	no	—
199	C₂×C₃×D₅	#127	1	2	yes	—
200	C₃×C₄×C₅	—	4	2	no	—
201	C₃×C₄×C₅	AGL(1,ℤ/8)	1	4	yes	complemented
202	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
203	C₃×Dic₅	—	2	2	no	—
204	C₃×Dic₅	#127	1	2	yes	—
205	C₂⁴×C₃	—	10	2	no	—
206	C₃×#41	—	10	8	no	—
207	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
208	C₂×C₃×D₄	—	2	2	no	—
209	C₂×C₃×D₄	—	5	2	no	—
210	C₂×C₃×D₄	—	5	2	no	—
211	C₂×C₃×D₄	—	10	2	no	—
212	C₂×C₃×D₄	—	10	8	no	—
213	C₂×C₃×D₄	—	10	4	no	—
214	C₂×C₃×D₄	—	10	2	no	—
215	C₂×C₃×D₄	—	10	2	no	—
216	C₂×C₃×D₄	—	10	2	no	—
217	C₂×C₃×D₄	—	20	8	no	—
218	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
219	C₂²×C₃×C₄	—	5	1	no	—
220	C₂²×C₃×C₄	—	5	2	no	—
221	C₂²×C₃×C₄	—	10	2	no	—
222	C₃×SD₁₆	—	2	8	no	—
223	C₃×SD₁₆	—	10	8	no	—
224	C₃×D₈	—	10	8	no	—
225	C₃×D₈	—	10	8	no	—
226	C₃×M₁₆	—	5	8	no	—
227	C₂×C₃×C₈	—	5	2	no	—
228	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
229	C₃×C₄⋊C₄	—	2	2	no	—
230	C₃×C₂²⋊C₄	—	10	4	no	—
231	C₃×C₄²	—	5	2	no	—
232	C₃×C₄²	—	5	1	no	—
233	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
234	C₂³×C₅	—	2	2	no	—
235	C₂²×D₅	—	2	2	no	—
236	C₂²×D₅	—	2	2	no	—
237	C₂²×D₅	—	4	8	no	—
238	C₂²×D₅	—	4	4	no	—
239	C₂²×D₅	C₂×C₃×D₄	1	1	yes	characteristic
240	C₅×Q₈	—	2	4	no	—
241	C₅×D₄	—	2	4	no	—
242	C₅×D₄	—	4	4	no	—
243	C₂×C₄×C₅	—	2	2	no	—
244	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
245	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
246	C₂²⋊D₅	—	4	8	no	—
247	C₂²⋊D₅	—	4	4	no	—
248	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
249	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
250	D₂₀	—	2	4	no	—
251	D₂₀	—	2	4	no	—
252	D₂₀	—	4	4	no	—
253	D₂₀	—	4	4	no	—
254	D₂₀	—	4	4	no	—
255	C₄×D₅	—	2	4	no	—
256	C₄×D₅	—	4	4	no	—
257	C₄×D₅	C₂×C₃×D₄	1	4	yes	—
258	C₅×C₈	C₂×C₃×D₄	1	4	yes	complemented
259	#168	C₂×C₃×D₄	1	4	yes	complemented
260	C₂×#41	—	5	2	no	—
261	C₂²×D₄	—	5	2	no	—
262	C₂²×D₄	—	10	2	no	—
263	AGL(1,ℤ/8)	—	10	16	no	—
264	C₂×SD₁₆	—	5	4	no	—
265	C₂×SD₁₆	C₂×C₃×D₅	1	4	yes	complemented
266	C₂×D₈	—	5	4	no	—
267	C₂×D₈	—	5	4	no	—
268	C₂×M₁₆	—	5	2	no	—
269	C₄⋊Q₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
270	#127	—	5	2	no	—
271	#127	—	5	1	no	—
272	#127	—	5	1	no	—
273	#127	—	10	2	no	—
274	#127	C₂×C₃×D₅	1	1	yes	characteristic
275	#124	—	5	2	no	—
276	#121	—	10	2	no	—
277	C₄×D₄	—	10	2	no	—
278	C₂×C₄²	—	5	1	no	—
279	#97	—	5	2	no	—
280	C₄×C₈	—	5	1	no	—
281	C₄×C₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
282	C₂×C₃×C₅	—	8	2	no	—
283	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
284	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	2	yes	—
285	C₃×D₅	—	2	2	no	—
286	C₃×D₅	—	8	2	no	—
287	C₃×D₅	—	8	2	no	—
288	C₂³×C₃	—	2	2	no	—
289	C₂³×C₃	—	5	1	no	—
290	C₂³×C₃	—	10	2	no	—
291	C₂³×C₃	—	10	2	no	—
292	C₂³×C₃	—	20	4	no	—
293	C₂³×C₃	—	20	8	no	—
294	C₃×Q₈	—	2	4	no	—
295	C₃×D₄	—	2	4	no	—
296	C₃×D₄	—	4	4	no	—
297	C₃×D₄	—	10	4	no	—
298	C₃×D₄	—	10	4	no	—
299	C₃×D₄	—	20	4	no	—
300	C₃×D₄	—	20	4	no	—
301	C₃×D₄	—	20	8	no	—
302	C₃×D₄	—	20	4	no	—
303	C₃×D₄	—	20	4	no	—
304	C₂×C₃×C₄	—	2	2	no	—
305	C₂×C₃×C₄	—	5	1	no	—
306	C₂×C₃×C₄	—	5	4	no	—
307	C₂×C₃×C₄	—	5	2	no	—
308	C₂×C₃×C₄	—	10	4	no	—
309	C₂×C₃×C₄	—	20	4	no	—
310	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
311	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
312	C₃×C₈	—	5	4	no	—
313	C₃×C₈	D₄×D₅	1	4	yes	complemented
314	C₂²×C₅	—	4	4	no	—
315	C₂²×C₅	—	4	2	no	—
316	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
317	C₂×D₅	—	2	2	no	—
318	C₂×D₅	—	4	4	no	—
319	C₂×D₅	—	4	4	no	—
320	C₂×D₅	—	4	2	no	—
321	C₂×D₅	—	4	2	no	—
322	C₂×D₅	—	8	8	no	—
323	C₂×D₅	C₃×#127	1	2	yes	—
324	C₄×C₅	—	4	2	no	—
325	C₄×C₅	C₃×AGL(1,ℤ/8)	1	4	yes	complemented
326	C₄×C₅	C₂²×C₃×D₄	1	2	yes	—
327	Dic₅	—	2	2	no	—
328	Dic₅	C₃×#127	1	2	yes	—
329	C₂⁴	—	10	2	no	—
330	#41	—	10	8	no	—
331	C₂×Q₈	C₂²×C₃×D₅	1	2	yes	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	5	2	no	—
334	C₂×D₄	—	5	2	no	—
335	C₂×D₄	—	10	2	no	—
336	C₂×D₄	—	10	8	no	—
337	C₂×D₄	—	10	4	no	—
338	C₂×D₄	—	10	2	no	—
339	C₂×D₄	—	10	2	no	—
340	C₂×D₄	—	10	2	no	—
341	C₂×D₄	—	20	8	no	—
342	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
343	C₂²×C₄	—	5	1	no	—
344	C₂²×C₄	—	5	2	no	—
345	C₂²×C₄	—	10	2	no	—
346	SD₁₆	—	2	8	no	—
347	SD₁₆	—	10	8	no	—
348	D₈	—	10	8	no	—
349	D₈	—	10	8	no	—
350	M₁₆	—	5	8	no	—
351	C₂×C₈	—	5	2	no	—
352	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
353	C₄⋊C₄	—	2	2	no	—
354	C₂²⋊C₄	—	10	4	no	—
355	C₄²	—	5	2	no	—
356	C₄²	—	5	1	no	—
357	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
358	C₃×C₅	#3151	1	1	yes	characteristic, complemented, Hall
359	C₂²×C₃	—	4	2	no	—
360	C₂²×C₃	—	4	4	no	—
361	C₂²×C₃	—	5	2	no	—
362	C₂²×C₃	—	10	2	no	—
363	C₂²×C₃	—	20	2	no	—
364	C₂²×C₃	—	20	2	no	—
365	C₂²×C₃	—	20	4	no	—
366	C₂²×C₃	—	20	4	no	—
367	C₂²×C₃	—	40	8	no	—
368	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
369	C₃×C₄	—	4	2	no	—
370	C₃×C₄	—	5	2	no	—
371	C₃×C₄	—	10	2	no	—
372	C₃×C₄	#4060	1	4	yes	complemented
373	C₃×C₄	C₂×D₄×D₅	1	2	yes	—
374	C₂×C₅	—	8	2	no	—
375	C₂×C₅	C₂×C₃×#127	1	1	yes	characteristic
376	C₂×C₅	C₂×C₃×AGL(1,ℤ/8)	1	2	yes	—
377	D₅	—	2	2	no	—
378	D₅	—	8	2	no	—
379	D₅	—	8	2	no	—
380	C₂³	—	2	2	no	—
381	C₂³	—	5	1	no	—
382	C₂³	—	10	2	no	—
383	C₂³	—	10	2	no	—
384	C₂³	—	20	4	no	—
385	C₂³	—	20	8	no	—
386	Q₈	—	2	4	no	—
387	D₄	—	2	4	no	—
388	D₄	—	4	4	no	—
389	D₄	—	10	4	no	—
390	D₄	—	10	4	no	—
391	D₄	—	20	4	no	—
392	D₄	—	20	4	no	—
393	D₄	—	20	8	no	—
394	D₄	—	20	4	no	—
395	D₄	—	20	4	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	5	1	no	—
398	C₂×C₄	—	5	4	no	—
399	C₂×C₄	—	5	2	no	—
400	C₂×C₄	—	10	4	no	—
401	C₂×C₄	—	20	4	no	—
402	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
403	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
404	C₈	—	5	4	no	—
405	C₈	C₃×D₄×D₅	1	4	yes	complemented
406	C₂×C₃	—	8	2	no	—
407	C₂×C₃	—	10	2	no	—
408	C₂×C₃	—	40	2	no	—
409	C₂×C₃	—	40	2	no	—
410	C₂×C₃	D₅×#127	1	1	yes	characteristic
411	C₂×C₃	C₂×#4060	1	2	yes	—
412	C₅	C₃×#3151	1	1	yes	characteristic, complemented, Sylow
413	C₂²	—	4	2	no	—
414	C₂²	—	4	4	no	—
415	C₂²	—	5	2	no	—
416	C₂²	—	10	2	no	—
417	C₂²	—	20	2	no	—
418	C₂²	—	20	2	no	—
419	C₂²	—	20	4	no	—
420	C₂²	—	20	4	no	—
421	C₂²	—	40	8	no	—
422	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
423	C₄	—	4	2	no	—
424	C₄	—	5	2	no	—
425	C₄	—	10	2	no	—
426	C₄	C₃×#4060	1	4	yes	complemented
427	C₄	C₂×C₃×D₄×D₅	1	2	yes	—
428	C₃	#10613492	1	1	yes	characteristic, direct product factor, Sylow
429	C₂	—	8	2	no	—
430	C₂	—	10	2	no	—
431	C₂	—	40	2	no	—
432	C₂	—	40	2	no	—
433	C₂	C₃×D₅×#127	1	1	yes	characteristic
434	C₂	C₂×C₃×#4060	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂×D₄×D₅
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#492	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₃×#492	D₅
hypocenter	C₅	C₃×#3151
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×#492

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#4060	C₂	semidirect
2. C₃×#66059	C₂	semidirect
3. C₃×D₅×#127	C₂	semidirect
4. C₃×C₅×#492	C₂	semidirect
5. C₃×#65465	C₂	semidirect
6. C₃×#65374	C₂	semidirect
7. C₃×#65362	C₂	semidirect
8. C₃×#64984	C₂	semidirect
9. C₃×C₄×#676	C₂	semidirect
10. #10613492	C₃	direct (N × H)
14. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
15. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
17. C₃×#4093	C₂²	semidirect
18. C₂×C₃×#688	C₂²	semidirect
21. C₂×C₃×#686	C₂²	semidirect
23. C₂×C₃×D₄₀	C₂²	semidirect
28. C₃×#4020	C₂²	semidirect
30. C₃×C₄×C₅×C₈	C₂²	semidirect
31. C₃×#3947	C₂²	semidirect
32. C₃×C₄×#168	C₂²	semidirect
34. C₂×#4060	C₂×C₃	semidirect
35. #66059	C₂×C₃	semidirect
36. D₅×#127	C₂×C₃	semidirect
37. C₅×#492	C₂×C₃	semidirect
38. #65465	C₂×C₃	semidirect
39. #65374	C₂×C₃	semidirect
40. #65362	C₂×C₃	semidirect
41. #64984	C₂×C₃	semidirect
42. C₄×#676	C₂×C₃	semidirect
71. C₃×#676	D₄	semidirect
79. C₃×#492	D₅	semidirect
84. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
85. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
87. #4093	C₂²×C₃	semidirect
88. C₂×#688	C₂²×C₃	semidirect
91. C₂×#686	C₂²×C₃	semidirect
93. C₂×D₄₀	C₂²×C₃	semidirect
98. #4020	C₂²×C₃	semidirect
100. C₄×C₅×C₈	C₂²×C₃	semidirect
101. #3947	C₂²×C₃	semidirect
102. C₄×#168	C₂²×C₃	semidirect
128. C₃×C₅×C₈	C₂×D₄	semidirect
129. C₃×#168	C₂×D₄	semidirect
135. C₂×C₃×SD₁₆	C₂×D₅	semidirect
139. C₃×C₄⋊Q₈	C₂×D₅	semidirect
151. C₃×C₄×C₈	C₂×D₅	semidirect
180. #676	C₃×D₄	semidirect
188. #492	C₃×D₅	semidirect
201. C₃×C₄×C₅	AGL(1,ℤ/8)	semidirect
258. C₅×C₈	C₂×C₃×D₄	semidirect
259. #168	C₂×C₃×D₄	semidirect
265. C₂×SD₁₆	C₂×C₃×D₅	semidirect
269. C₄⋊Q₈	C₂×C₃×D₅	semidirect
281. C₄×C₈	C₂×C₃×D₅	semidirect
313. C₃×C₈	D₄×D₅	semidirect
325. C₄×C₅	C₃×AGL(1,ℤ/8)	semidirect
358. C₃×C₅	#3151	semidirect
372. C₃×C₄	#4060	semidirect
405. C₈	C₃×D₄×D₅	semidirect
412. C₅	C₃×#3151	semidirect
426. C₄	C₃×#4060	semidirect
428. C₃	#10613492	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×C₃×#4060	2
C₃×#66059	2
C₃×D₅×#127	2
C₃×C₅×#492	2
C₃×#65465	2
C₃×#65374	2
C₃×#65362	2
C₃×#64984	2
C₃×C₄×#676	2
#10613492	3
C₃×#3151	5

Subgroups — C3×#10613492 #14439124

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10613492 #14439124