Subgroups — C₃×#10611299 #14471592

Order 1920.

700 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#65877	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#65876	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₄×C₅×D₈	C₂	1	1	yes	maximal, characteristic
4	C₃×#65442	C₂	1	2	yes	maximal
5	C₃×#65308	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65297	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65166	C₂	1	2	yes	maximal, complemented
8	C₃×#65057	C₂	1	2	yes	maximal, complemented
9	C₃×#65047	C₂	1	2	yes	maximal, complemented
10	C₃×#64970	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₈×Dic₁₀	C₂	1	1	yes	maximal, characteristic, complemented
12	#10611299	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
14	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
15	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
16	C₃×#4082	C₂²	1	2	yes	—
17	C₃×D₄×Dic₅	C₂²	1	2	yes	—
18	C₂×C₃×#687	C₂²	1	2	yes	—
19	C₃×#4072	—	2	1	no	—
20	C₂×C₃×C₄⋊Dic₅	—	2	1	no	—
21	C₃×#4070	—	2	1	no	—
22	C₃×#4070	—	2	1	no	—
23	C₃×#4036	C₂²	1	2	yes	—
24	C₃×#4033	C₂²	1	2	yes	—
25	C₃×#4025	—	2	2	no	—
26	C₃×#4024	—	2	2	no	—
27	C₃×#4015	C₂²	1	1	yes	characteristic
28	C₃×#4015	C₂²	1	1	yes	characteristic
29	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic
30	C₃×C₅×#107	C₂²	1	1	yes	characteristic
31	C₃×C₅×#102	C₂²	1	1	yes	characteristic
32	C₃×C₅×#102	C₂²	1	1	yes	characteristic
33	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
34	C₃×#3964	C₂²	1	2	yes	—
35	C₃×#3948	C₂²	1	2	yes	—
36	C₃×#3948	C₂²	1	2	yes	—
37	C₃×#3946	C₂²	1	2	yes	—
38	C₃×C₈×Dic₅	C₂²	1	2	yes	—
39	C₃×#3942	C₂²	1	2	yes	—
40	C₃×#3940	C₂²	1	2	yes	—
41	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic
42	C₃×#3360	—	5	1	no	maximal, Hall
43	#65877	C₂×C₃	1	1	yes	characteristic, complemented
44	#65876	C₂×C₃	1	1	yes	characteristic, complemented
45	C₄×C₅×D₈	C₂×C₃	1	1	yes	characteristic
46	#65442	C₂×C₃	1	2	yes	—
47	#65308	C₂×C₃	1	1	yes	characteristic, complemented
48	#65297	C₂×C₃	1	1	yes	characteristic, complemented
49	#65166	C₂×C₃	1	2	yes	complemented
50	#65057	C₂×C₃	1	2	yes	complemented
51	#65047	C₂×C₃	1	2	yes	complemented
52	#64970	C₂×C₃	1	1	yes	characteristic, complemented
53	C₈×Dic₁₀	C₂×C₃	1	1	yes	characteristic, complemented
54	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
55	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
56	C₂²×C₃×C₄×C₅	—	2	1	no	—
57	C₂²×C₃×C₄×C₅	—	2	1	no	—
58	C₂²×C₃×Dic₅	—	2	2	no	—
59	C₂×C₃×Dic₁₀	—	2	1	no	—
60	C₂×C₃×Dic₁₀	D₄	1	1	yes	characteristic
61	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
62	C₃×C₅×D₈	—	2	2	no	—
63	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
64	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
65	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
66	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
67	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
68	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
69	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
70	C₃×C₂²⋊Dic₅	—	2	2	no	—
71	C₃×C₂²⋊Dic₅	—	2	2	no	—
72	C₃×C₂²⋊Dic₅	—	2	2	no	—
73	C₃×#687	—	2	4	no	—
74	C₃×C₄⋊Dic₅	—	2	1	no	—
75	C₃×C₄⋊Dic₅	—	2	1	no	—
76	C₃×C₄⋊Dic₅	—	2	1	no	—
77	C₃×C₄⋊Dic₅	—	2	2	no	—
78	C₃×C₄⋊Dic₅	D₄	1	1	yes	characteristic
79	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
80	C₃×#683	—	2	2	no	—
81	C₃×#683	—	2	2	no	—
82	C₃×#683	D₄	1	2	yes	—
83	C₃×C₄×Dic₅	—	2	2	no	—
84	C₃×C₄×Dic₅	C₂³	1	2	yes	—
85	C₂×C₃×#168	C₂³	1	2	yes	—
86	C₃×#556	—	5	1	no	—
87	C₃×#554	—	5	1	no	—
88	C₃×#488	—	5	2	no	—
89	C₃×#487	—	5	1	no	—
90	C₃×#479	—	5	2	no	—
91	C₃×#476	—	5	1	no	—
92	C₃×#463	—	5	2	no	—
93	C₃×#461	—	5	1	no	—
94	C₃×C₈×Q₈	—	5	1	no	—
95	C₃×C₄×SD₁₆	—	5	2	no	—
96	C₃×C₄×D₈	D₅	1	1	yes	characteristic
97	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic
98	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
99	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
100	#4082	C₂²×C₃	1	2	yes	—
101	D₄×Dic₅	C₂²×C₃	1	2	yes	—
102	C₂×#687	C₂²×C₃	1	2	yes	—
103	#4072	—	2	1	no	—
104	C₂×C₄⋊Dic₅	—	2	1	no	—
105	#4070	—	2	1	no	—
106	#4070	—	2	1	no	—
107	#4036	C₂²×C₃	1	2	yes	—
108	#4033	C₂²×C₃	1	2	yes	—
109	#4025	—	2	2	no	—
110	#4024	—	2	2	no	—
111	#4015	C₂²×C₃	1	1	yes	characteristic
112	#4015	C₂²×C₃	1	1	yes	characteristic
113	C₄×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
114	C₅×#107	C₂²×C₃	1	1	yes	characteristic
115	C₅×#102	C₂²×C₃	1	1	yes	characteristic
116	C₅×#102	C₂²×C₃	1	1	yes	characteristic
117	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
118	#3964	C₂²×C₃	1	2	yes	—
119	#3948	C₂²×C₃	1	2	yes	—
120	#3948	C₂²×C₃	1	2	yes	—
121	#3946	C₂²×C₃	1	2	yes	—
122	C₈×Dic₅	C₂²×C₃	1	2	yes	—
123	#3942	C₂²×C₃	1	2	yes	—
124	#3940	C₂²×C₃	1	2	yes	—
125	C₄⋊#168	C₂²×C₃	1	1	yes	characteristic
126	#3360	—	5	1	no	Sylow
127	C₂³×C₃×C₅	—	2	1	no	—
128	C₂³×C₃×C₅	—	2	1	no	—
129	C₃×C₅×D₄	—	2	1	no	—
130	C₃×C₅×D₄	—	2	1	no	—
131	C₃×C₅×D₄	—	2	1	no	—
132	C₃×C₅×D₄	#41	1	2	yes	—
133	C₂×C₃×C₄×C₅	—	2	1	no	—
134	C₂×C₃×C₄×C₅	—	2	1	no	—
135	C₂×C₃×C₄×C₅	—	4	2	no	—
136	C₂×C₃×C₄×C₅	—	4	2	no	—
137	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
138	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
139	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
140	C₂×C₃×Dic₅	—	2	2	no	—
141	C₂×C₃×Dic₅	—	2	2	no	—
142	C₂×C₃×Dic₅	—	8	2	no	—
143	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
144	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
145	C₃×Dic₁₀	—	2	2	no	—
146	C₃×Dic₁₀	—	2	2	no	—
147	C₃×Dic₁₀	—	2	2	no	—
148	C₃×Dic₁₀	—	8	1	no	—
149	C₃×C₅×C₈	—	2	1	no	—
150	C₃×C₅×C₈	—	2	1	no	—
151	C₃×#168	—	2	2	no	—
152	C₂×C₃×SD₁₆	—	5	2	no	—
153	C₂×C₃×D₈	C₂×D₅	1	1	yes	characteristic
154	C₃×C₄⋊Q₈	—	5	1	no	—
155	C₃×C₄⋊Q₈	—	5	1	no	—
156	C₃×#126	—	10	2	no	—
157	C₃×#125	—	5	2	no	—
158	C₃×#124	—	5	2	no	—
159	C₃×C₂²⋊Q₈	—	10	2	no	—
160	C₃×C₂²⋊Q₈	—	10	1	no	—
161	C₃×C₂²⋊Q₈	—	10	1	no	—
162	C₃×C₄×Q₈	—	5	1	no	—
163	C₃×C₄×Q₈	—	5	2	no	—
164	C₃×C₄×D₄	—	5	2	no	—
165	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic
166	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic
167	C₃×#117	—	10	1	no	—
168	C₂×C₃×C₄⋊C₄	—	10	1	no	—
169	C₃×#107	C₂×D₅	1	1	yes	characteristic
170	C₃×#106	—	5	2	no	—
171	C₃×C₄⋊C₈	—	5	2	no	—
172	C₃×C₄⋊C₈	—	5	1	no	—
173	C₃×#103	—	5	2	no	—
174	C₃×#103	—	5	2	no	—
175	C₃×#103	—	5	2	no	—
176	C₃×#102	—	5	2	no	—
177	C₃×#102	C₂×D₅	1	1	yes	characteristic
178	C₃×#102	C₂×D₅	1	1	yes	characteristic
179	C₃×C₄×C₈	—	5	2	no	—
180	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic
181	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
182	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
183	C₂²×C₄×C₅	—	2	1	no	—
184	C₂²×C₄×C₅	—	2	1	no	—
185	C₂²×Dic₅	—	2	2	no	—
186	C₂×Dic₁₀	—	2	1	no	—
187	C₂×Dic₁₀	C₃×D₄	1	1	yes	characteristic
188	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
189	C₅×D₈	—	2	2	no	—
190	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
191	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
192	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
193	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
194	C₅×C₂²⋊C₄	—	2	1	no	—
195	C₅×C₂²⋊C₄	—	2	1	no	—
196	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
197	C₂²⋊Dic₅	—	2	2	no	—
198	C₂²⋊Dic₅	—	2	2	no	—
199	C₂²⋊Dic₅	—	2	2	no	—
200	#687	—	2	4	no	—
201	C₄⋊Dic₅	—	2	1	no	—
202	C₄⋊Dic₅	—	2	1	no	—
203	C₄⋊Dic₅	—	2	1	no	—
204	C₄⋊Dic₅	—	2	2	no	—
205	C₄⋊Dic₅	C₃×D₄	1	1	yes	characteristic
206	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
207	#683	—	2	2	no	—
208	#683	—	2	2	no	—
209	#683	C₃×D₄	1	2	yes	—
210	C₄×Dic₅	—	2	2	no	—
211	C₄×Dic₅	C₂³×C₃	1	2	yes	—
212	C₂×#168	C₂³×C₃	1	2	yes	—
213	#556	—	5	1	no	—
214	#554	—	5	1	no	—
215	#488	—	5	2	no	—
216	#487	—	5	1	no	—
217	#479	—	5	2	no	—
218	#476	—	5	1	no	—
219	#463	—	5	2	no	—
220	#461	—	5	1	no	—
221	C₈×Q₈	—	5	1	no	—
222	C₄×SD₁₆	—	5	2	no	—
223	C₄×D₈	C₃×D₅	1	1	yes	characteristic
224	C₂²×C₃×C₅	—	2	2	no	—
225	C₂²×C₃×C₅	—	4	1	no	—
226	C₂²×C₃×C₅	—	4	1	no	—
227	C₂²×C₃×C₅	—	4	1	no	—
228	C₂²×C₃×C₅	—	4	1	no	—
229	C₂²×C₃×C₅	—	4	1	no	—
230	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
231	C₃×C₄×C₅	—	2	1	no	—
232	C₃×C₄×C₅	—	4	1	no	—
233	C₃×C₄×C₅	—	4	1	no	—
234	C₃×C₄×C₅	#135	1	2	yes	—
235	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
236	C₃×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
237	C₃×Dic₅	—	2	2	no	—
238	C₃×Dic₅	—	2	2	no	—
239	C₃×Dic₅	—	4	2	no	—
240	C₃×Dic₅	—	4	2	no	—
241	C₂×C₃×Q₈	—	5	1	no	—
242	C₂×C₃×Q₈	—	5	2	no	—
243	C₂×C₃×Q₈	—	10	1	no	—
244	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
245	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
246	C₂²×C₃×C₄	—	2	1	no	—
247	C₂²×C₃×C₄	—	2	1	no	—
248	C₂²×C₃×C₄	—	10	2	no	—
249	C₃×SD₁₆	—	10	4	no	—
250	C₃×D₈	—	2	2	no	—
251	C₂×C₃×C₈	—	5	2	no	—
252	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
253	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
254	C₃×C₄⋊C₄	—	5	2	no	—
255	C₃×C₄⋊C₄	—	5	1	no	—
256	C₃×C₄⋊C₄	—	5	2	no	—
257	C₃×C₄⋊C₄	—	10	2	no	—
258	C₃×C₄⋊C₄	—	10	2	no	—
259	C₃×C₄⋊C₄	—	10	2	no	—
260	C₃×C₄⋊C₄	—	10	1	no	—
261	C₃×C₄⋊C₄	—	10	1	no	—
262	C₃×C₄⋊C₄	—	10	1	no	—
263	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
264	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
265	C₃×C₂²⋊C₄	—	2	1	no	—
266	C₃×C₂²⋊C₄	—	2	1	no	—
267	C₃×C₂²⋊C₄	—	10	2	no	—
268	C₃×C₂²⋊C₄	—	10	2	no	—
269	C₃×C₂²⋊C₄	—	10	2	no	—
270	C₃×C₄²	—	5	2	no	—
271	C₃×C₄²	—	10	2	no	—
272	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
273	C₂³×C₅	—	2	1	no	—
274	C₂³×C₅	—	2	1	no	—
275	C₅×D₄	—	2	1	no	—
276	C₅×D₄	—	2	1	no	—
277	C₅×D₄	—	2	1	no	—
278	C₅×D₄	C₃×#41	1	2	yes	—
279	C₂×C₄×C₅	—	2	1	no	—
280	C₂×C₄×C₅	—	2	1	no	—
281	C₂×C₄×C₅	—	4	2	no	—
282	C₂×C₄×C₅	—	4	2	no	—
283	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
284	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
285	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
286	C₂×Dic₅	—	2	2	no	—
287	C₂×Dic₅	—	2	2	no	—
288	C₂×Dic₅	—	8	2	no	—
289	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
290	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
291	Dic₁₀	—	2	2	no	—
292	Dic₁₀	—	2	2	no	—
293	Dic₁₀	—	2	2	no	—
294	Dic₁₀	—	8	1	no	—
295	C₅×C₈	—	2	1	no	—
296	C₅×C₈	—	2	1	no	—
297	#168	—	2	2	no	—
298	C₂×SD₁₆	—	5	2	no	—
299	C₂×D₈	C₂×C₃×D₅	1	1	yes	characteristic
300	C₄⋊Q₈	—	5	1	no	—
301	C₄⋊Q₈	—	5	1	no	—
302	#126	—	10	2	no	—
303	#125	—	5	2	no	—
304	#124	—	5	2	no	—
305	C₂²⋊Q₈	—	10	2	no	—
306	C₂²⋊Q₈	—	10	1	no	—
307	C₂²⋊Q₈	—	10	1	no	—
308	C₄×Q₈	—	5	1	no	—
309	C₄×Q₈	—	5	2	no	—
310	C₄×D₄	—	5	2	no	—
311	C₄×D₄	C₂×C₃×D₅	1	1	yes	characteristic
312	C₄×D₄	C₂×C₃×D₅	1	1	yes	characteristic
313	#117	—	10	1	no	—
314	C₂×C₄⋊C₄	—	10	1	no	—
315	#107	C₂×C₃×D₅	1	1	yes	characteristic
316	#106	—	5	2	no	—
317	C₄⋊C₈	—	5	2	no	—
318	C₄⋊C₈	—	5	1	no	—
319	#103	—	5	2	no	—
320	#103	—	5	2	no	—
321	#103	—	5	2	no	—
322	#102	—	5	2	no	—
323	#102	C₂×C₃×D₅	1	1	yes	characteristic
324	#102	C₂×C₃×D₅	1	1	yes	characteristic
325	C₄×C₈	—	5	2	no	—
326	C₄×C₈	C₂×C₃×D₅	1	1	yes	characteristic
327	C₂×C₃×C₅	—	4	2	no	—
328	C₂×C₃×C₅	—	8	1	no	—
329	C₂×C₃×C₅	#548	1	1	yes	characteristic
330	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
331	C₂×C₃×C₅	#577	1	1	yes	characteristic
332	C₂³×C₃	—	2	1	no	—
333	C₂³×C₃	—	2	1	no	—
334	C₃×Q₈	—	10	2	no	—
335	C₃×Q₈	—	10	2	no	—
336	C₃×Q₈	—	10	2	no	—
337	C₃×Q₈	—	40	1	no	—
338	C₃×D₄	—	2	1	no	—
339	C₃×D₄	—	2	1	no	—
340	C₃×D₄	—	2	1	no	—
341	C₃×D₄	#709	1	2	yes	—
342	C₂×C₃×C₄	—	2	1	no	—
343	C₂×C₃×C₄	—	2	1	no	—
344	C₂×C₃×C₄	—	4	2	no	—
345	C₂×C₃×C₄	—	4	2	no	—
346	C₂×C₃×C₄	—	5	2	no	—
347	C₂×C₃×C₄	—	5	2	no	—
348	C₂×C₃×C₄	—	10	2	no	—
349	C₂×C₃×C₄	—	10	2	no	—
350	C₂×C₃×C₄	—	40	2	no	—
351	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
352	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
353	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
354	C₃×C₈	—	2	1	no	—
355	C₃×C₈	—	2	1	no	—
356	C₃×C₈	—	10	2	no	—
357	C₂²×C₅	—	2	2	no	—
358	C₂²×C₅	—	4	1	no	—
359	C₂²×C₅	—	4	1	no	—
360	C₂²×C₅	—	4	1	no	—
361	C₂²×C₅	—	4	1	no	—
362	C₂²×C₅	—	4	1	no	—
363	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
364	C₄×C₅	—	2	1	no	—
365	C₄×C₅	—	4	1	no	—
366	C₄×C₅	—	4	1	no	—
367	C₄×C₅	C₃×#135	1	2	yes	—
368	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
369	C₄×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
370	Dic₅	—	2	2	no	—
371	Dic₅	—	2	2	no	—
372	Dic₅	—	4	2	no	—
373	Dic₅	—	4	2	no	—
374	C₂×Q₈	—	5	1	no	—
375	C₂×Q₈	—	5	2	no	—
376	C₂×Q₈	—	10	1	no	—
377	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
378	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	10	2	no	—
382	SD₁₆	—	10	4	no	—
383	D₈	—	2	2	no	—
384	C₂×C₈	—	5	2	no	—
385	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
386	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
387	C₄⋊C₄	—	5	1	no	—
388	C₄⋊C₄	—	5	2	no	—
389	C₄⋊C₄	—	5	2	no	—
390	C₄⋊C₄	—	10	2	no	—
391	C₄⋊C₄	—	10	2	no	—
392	C₄⋊C₄	—	10	2	no	—
393	C₄⋊C₄	—	10	1	no	—
394	C₄⋊C₄	—	10	1	no	—
395	C₄⋊C₄	—	10	1	no	—
396	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
397	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
398	C₂²⋊C₄	—	2	1	no	—
399	C₂²⋊C₄	—	2	1	no	—
400	C₂²⋊C₄	—	10	2	no	—
401	C₂²⋊C₄	—	10	2	no	—
402	C₂²⋊C₄	—	10	2	no	—
403	C₄²	—	5	2	no	—
404	C₄²	—	10	2	no	—
405	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
406	C₃×C₅	#3360	1	1	yes	characteristic, complemented, Hall
407	C₂²×C₃	—	2	2	no	—
408	C₂²×C₃	—	4	1	no	—
409	C₂²×C₃	—	4	1	no	—
410	C₂²×C₃	—	4	1	no	—
411	C₂²×C₃	—	4	1	no	—
412	C₂²×C₃	—	4	1	no	—
413	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
414	C₃×C₄	—	2	1	no	—
415	C₃×C₄	—	4	1	no	—
416	C₃×C₄	—	4	1	no	—
417	C₃×C₄	—	10	2	no	—
418	C₃×C₄	—	10	2	no	—
419	C₃×C₄	—	20	2	no	—
420	C₃×C₄	—	20	2	no	—
421	C₃×C₄	#4058	1	2	yes	—
422	C₃×C₄	C₂×#709	1	1	yes	characteristic
423	C₃×C₄	#4150	1	1	yes	characteristic
424	C₂×C₅	—	4	2	no	—
425	C₂×C₅	—	8	1	no	—
426	C₂×C₅	C₃×#548	1	1	yes	characteristic
427	C₂×C₅	C₂×C₃×#135	1	1	yes	characteristic
428	C₂×C₅	C₃×#577	1	1	yes	characteristic
429	C₂³	—	2	1	no	—
430	C₂³	—	2	1	no	—
431	Q₈	—	10	2	no	—
432	Q₈	—	10	2	no	—
433	Q₈	—	10	2	no	—
434	Q₈	—	40	1	no	—
435	D₄	—	2	1	no	—
436	D₄	—	2	1	no	—
437	D₄	—	2	1	no	—
438	D₄	C₃×#709	1	2	yes	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	5	2	no	—
444	C₂×C₄	—	5	2	no	—
445	C₂×C₄	—	10	2	no	—
446	C₂×C₄	—	10	2	no	—
447	C₂×C₄	—	40	2	no	—
448	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
449	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
450	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
451	C₈	—	2	1	no	—
452	C₈	—	2	1	no	—
453	C₈	—	10	2	no	—
454	C₂×C₃	—	4	2	no	—
455	C₂×C₃	—	8	1	no	—
456	C₂×C₃	#65886	1	1	yes	characteristic
457	C₂×C₃	C₂×#4058	1	1	yes	characteristic
458	C₂×C₃	#66104	1	1	yes	characteristic
459	C₅	C₃×#3360	1	1	yes	characteristic, complemented, Sylow
460	C₂²	—	2	2	no	—
461	C₂²	—	4	1	no	—
462	C₂²	—	4	1	no	—
463	C₂²	—	4	1	no	—
464	C₂²	—	4	1	no	—
465	C₂²	—	4	1	no	—
466	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
467	C₄	—	2	1	no	—
468	C₄	—	4	1	no	—
469	C₄	—	4	1	no	—
470	C₄	—	10	2	no	—
471	C₄	—	10	2	no	—
472	C₄	—	20	2	no	—
473	C₄	—	20	2	no	—
474	C₄	C₃×#4058	1	2	yes	—
475	C₄	C₂×C₃×#709	1	1	yes	characteristic
476	C₄	C₃×#4150	1	1	yes	characteristic
477	C₃	#10611299	1	1	yes	characteristic, direct product factor, Sylow
478	C₂	—	4	2	no	—
479	C₂	—	8	1	no	—
480	C₂	C₃×#65886	1	1	yes	characteristic
481	C₂	C₂×C₃×#4058	1	1	yes	characteristic
482	C₂	C₃×#66104	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×D₄×D₅
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₄×C₅×D₈	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₃×C₅×D₈	C₂²
hypercenter	C₃×C₄×D₈	D₅
hypocenter	C₅	C₃×#3360
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×C₄×D₈

Complements

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

N	H ≅ G/N	type
1. C₃×#65877	C₂	semidirect
2. C₃×#65876	C₂	semidirect
5. C₃×#65308	C₂	semidirect
6. C₃×#65297	C₂	semidirect
7. C₃×#65166	C₂	semidirect
8. C₃×#65057	C₂	semidirect
9. C₃×#65047	C₂	semidirect
10. C₃×#64970	C₂	semidirect
11. C₃×C₈×Dic₁₀	C₂	semidirect
12. #10611299	C₃	direct (N × H)
43. #65877	C₂×C₃	semidirect
44. #65876	C₂×C₃	semidirect
47. #65308	C₂×C₃	semidirect
48. #65297	C₂×C₃	semidirect
49. #65166	C₂×C₃	semidirect
50. #65057	C₂×C₃	semidirect
51. #65047	C₂×C₃	semidirect
52. #64970	C₂×C₃	semidirect
53. C₈×Dic₁₀	C₂×C₃	semidirect
406. C₃×C₅	#3360	semidirect
459. C₅	C₃×#3360	semidirect
477. C₃	#10611299	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×#65877	2
C₃×#65876	2
C₃×C₄×C₅×D₈	2
C₃×#65442	2
C₃×#65308	2
C₃×#65297	2
C₃×#65166	2
C₃×#65057	2
C₃×#65047	2
C₃×#64970	2
C₃×C₈×Dic₁₀	2
#10611299	3
C₃×#3360	5

Subgroups — C3×#10611299 #14471592

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10611299 #14471592