Subgroups — C₃²×#5691 #13179069

Order 1728.

1628 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×#125	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃²×#898	C₂	1	2	yes	maximal, complemented
3	C₃²×#897	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃²×#895	C₂	1	1	yes	maximal, characteristic
5	C₃²×#894	C₂	1	2	yes	maximal, complemented
6	C₃²×#893	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃²×#893	C₂	1	2	yes	maximal, complemented
8	C₃²×#892	C₂	1	2	yes	maximal, complemented
9	C₃²×#887	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃²×#875	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃²×C₄²×D₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃²×#529	—	3	1	no	maximal
13	C₃×#5691	C₃	1	4	yes	maximal, direct product factor
14	C₂×C₃²×D₁₂	C₂²	1	1	yes	characteristic
15	C₂×C₃²×D₁₂	C₂²	1	2	yes	—
16	C₂×C₃²×C₄×D₃	C₂²	1	1	yes	characteristic
17	C₂×C₃²×C₄×D₃	C₂²	1	1	yes	characteristic
18	C₂×C₃²×C₄×D₃	C₂²	1	1	yes	characteristic
19	C₂×C₃²×C₄×D₃	C₂²	1	2	yes	—
20	C₂×C₃²×Dic₆	C₂²	1	1	yes	characteristic
21	C₃³×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₃³×C₄⋊C₄	C₂²	1	2	yes	—
23	C₃³×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₃³×C₄⋊C₄	C₂²	1	2	yes	—
25	C₃³×C₄²	C₂²	1	1	yes	characteristic
26	C₃²×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
27	C₃²×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
28	C₃²×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
29	C₃²×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
30	C₃²×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
31	C₃²×C₄⋊Dic₃	C₂²	1	2	yes	—
32	C₃²×Dic₃⋊C₄	C₂²	1	2	yes	—
33	C₃²×C₄×Dic₃	C₂²	1	1	yes	characteristic
34	C₃²×C₄×Dic₃	C₂²	1	1	yes	characteristic
35	C₃²×C₄×Dic₃	C₂²	1	1	yes	characteristic
36	C₃²×C₄×Dic₃	C₂²	1	2	yes	—
37	C₃²×#126	—	3	2	no	—
38	C₃²×#125	—	2	4	no	—
39	C₃²×#125	D₃	1	1	yes	characteristic, complemented
40	C₃²×#125	C₂×C₃	1	4	yes	complemented
41	C₃²×#124	—	3	1	no	—
42	C₃²×#123	—	3	2	no	—
43	C₃²×C₂²⋊Q₈	—	3	1	no	—
44	C₃²×#121	—	3	1	no	—
45	C₃²×C₄×Q₈	—	3	1	no	—
46	C₃²×C₄×D₄	—	3	1	no	—
47	C₃²×C₄×D₄	—	3	2	no	—
48	C₃²×#117	—	3	2	no	—
49	C₂×C₃²×C₄²	—	3	1	no	—
50	C₃×#898	C₂×C₃	1	8	yes	complemented
51	C₃×#897	C₂×C₃	1	4	yes	complemented
52	C₃×#895	C₂×C₃	1	4	yes	—
53	C₃×#894	C₂×C₃	1	8	yes	complemented
54	C₃×#893	C₂×C₃	1	8	yes	complemented
55	C₃×#893	C₂×C₃	1	4	yes	complemented
56	C₃×#892	C₂×C₃	1	8	yes	complemented
57	C₃×#887	C₂×C₃	1	4	yes	complemented
58	C₃×#875	C₂×C₃	1	4	yes	complemented
59	C₃×C₄²×D₃	C₂×C₃	1	4	yes	complemented
60	C₂²×C₃²×D₃	C₂³	1	2	yes	—
61	C₂²×C₃²×D₃	C₂³	1	1	yes	characteristic
62	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
63	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
64	C₂×C₃³×C₄	C₂³	1	2	yes	—
65	C₂×C₃³×C₄	C₂³	1	2	yes	—
66	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
67	C₂×C₃²×Dic₃	C₂³	1	2	yes	—
68	C₂×C₃²×Dic₃	C₂³	1	1	yes	characteristic
69	C₂×C₃²×Dic₃	C₂³	1	1	yes	characteristic
70	C₂×C₃²×Dic₃	C₂³	1	1	yes	characteristic
71	C₃²×D₁₂	—	2	4	no	—
72	C₃²×D₁₂	—	2	2	no	—
73	C₃²×C₄×D₃	—	2	2	no	—
74	C₃²×C₄×D₃	—	2	2	no	—
75	C₃²×C₄×D₃	—	2	2	no	—
76	C₃²×C₄×D₃	—	2	4	no	—
77	C₃²×Dic₆	—	2	2	no	—
78	C₃×#529	—	3	4	no	—
79	#5691	C₃²	1	1	yes	characteristic, direct product factor
80	C₂×C₃²×Q₈	—	3	1	no	—
81	C₂×C₃²×D₄	—	3	2	no	—
82	C₂×C₃²×D₄	—	3	1	no	—
83	C₂²×C₃²×C₄	—	3	1	no	—
84	C₂²×C₃²×C₄	—	3	1	no	—
85	C₂²×C₃²×C₄	—	3	1	no	—
86	C₂²×C₃²×C₄	—	3	2	no	—
87	C₂×C₃×D₁₂	C₂²×C₃	1	8	yes	—
88	C₂×C₃×D₁₂	C₂²×C₃	1	4	yes	—
89	C₂×C₃×C₄×D₃	C₂²×C₃	1	8	yes	—
90	C₂×C₃×C₄×D₃	C₂²×C₃	1	4	yes	—
91	C₂×C₃×C₄×D₃	C₂²×C₃	1	4	yes	—
92	C₂×C₃×C₄×D₃	C₂²×C₃	1	4	yes	—
93	C₂×C₃×Dic₆	C₂²×C₃	1	4	yes	—
94	C₃²×C₄⋊C₄	—	2	4	no	—
95	C₃²×C₄⋊C₄	—	2	4	no	—
96	C₃²×C₄⋊C₄	—	2	8	no	—
97	C₃²×C₄⋊C₄	—	2	8	no	—
98	C₃²×C₄⋊C₄	—	3	2	no	—
99	C₃²×C₄⋊C₄	—	3	2	no	—
100	C₃²×C₄⋊C₄	C₂×D₃	1	2	yes	—
101	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
102	C₃²×C₄⋊C₄	C₂×D₃	1	2	yes	—
103	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
104	C₃²×C₄⋊C₄	C₂²×C₃	1	4	yes	—
105	C₃²×C₄⋊C₄	C₂²×C₃	1	8	yes	—
106	C₃²×C₄⋊C₄	C₂²×C₃	1	4	yes	—
107	C₃²×C₄⋊C₄	C₂²×C₃	1	8	yes	—
108	C₃²×C₂²⋊C₄	—	3	2	no	—
109	C₃²×C₂²⋊C₄	—	3	2	no	—
110	C₃²×C₂²⋊C₄	—	3	2	no	—
111	C₃²×C₂²⋊C₄	—	3	2	no	—
112	C₃²×C₂²⋊C₄	—	3	2	no	—
113	C₃²×C₄²	—	2	4	no	—
114	C₃²×C₄²	—	3	1	no	—
115	C₃²×C₄²	—	3	1	no	—
116	C₃²×C₄²	—	3	1	no	—
117	C₃²×C₄²	—	3	2	no	—
118	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic
119	C₃²×C₄²	C₂²×C₃	1	4	yes	—
120	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	8	yes	—
121	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	8	yes	—
122	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	8	yes	—
123	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	8	yes	—
124	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	8	yes	—
125	C₃×C₄⋊Dic₃	C₂²×C₃	1	8	yes	—
126	C₃×Dic₃⋊C₄	C₂²×C₃	1	8	yes	—
127	C₃×C₄×Dic₃	C₂²×C₃	1	8	yes	—
128	C₃×C₄×Dic₃	C₂²×C₃	1	4	yes	—
129	C₃×C₄×Dic₃	C₂²×C₃	1	4	yes	—
130	C₃×C₄×Dic₃	C₂²×C₃	1	4	yes	—
131	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
132	C₂×C₃²×D₃	—	2	1	no	—
133	C₂×C₃²×D₃	—	2	1	no	—
134	C₂×C₃²×D₃	—	2	2	no	—
135	C₂×C₃²×D₃	—	2	2	no	—
136	C₂×C₃²×D₃	—	2	2	no	—
137	C₂×C₃²×D₃	#41	1	2	yes	—
138	C₃³×C₄	—	2	1	no	—
139	C₃³×C₄	—	2	1	no	—
140	C₃³×C₄	—	2	2	no	—
141	C₃³×C₄	—	2	2	no	—
142	C₃³×C₄	#41	1	2	yes	—
143	C₃²×Dic₃	—	2	2	no	—
144	C₃²×Dic₃	—	2	1	no	—
145	C₃²×Dic₃	—	2	1	no	—
146	C₃²×Dic₃	#41	1	2	yes	—
147	C₃×#126	—	3	8	no	—
148	C₃×#125	—	2	4	no	—
149	C₃×#125	C₃×D₃	1	4	yes	complemented
150	C₃×#125	C₂×C₃²	1	1	yes	characteristic, complemented
151	C₃×#124	—	3	4	no	—
152	C₃×#123	—	3	8	no	—
153	C₃×C₂²⋊Q₈	—	3	4	no	—
154	C₃×#121	—	3	4	no	—
155	C₃×C₄×Q₈	—	3	4	no	—
156	C₃×C₄×D₄	—	3	4	no	—
157	C₃×C₄×D₄	—	3	8	no	—
158	C₃×#117	—	3	8	no	—
159	C₂×C₃×C₄²	—	3	4	no	—
160	#898	C₂×C₃²	1	2	yes	complemented
161	#897	C₂×C₃²	1	1	yes	characteristic, complemented
162	#895	C₂×C₃²	1	1	yes	characteristic
163	#894	C₂×C₃²	1	2	yes	complemented
164	#893	C₂×C₃²	1	1	yes	characteristic, complemented
165	#893	C₂×C₃²	1	2	yes	complemented
166	#892	C₂×C₃²	1	2	yes	complemented
167	#887	C₂×C₃²	1	1	yes	characteristic, complemented
168	#875	C₂×C₃²	1	1	yes	characteristic, complemented
169	C₄²×D₃	C₂×C₃²	1	1	yes	characteristic, complemented
170	C₂³×C₃²	—	3	1	no	—
171	C₂³×C₃²	—	3	2	no	—
172	C₂²×C₃×D₃	C₂³×C₃	1	8	yes	—
173	C₂²×C₃×D₃	C₂³×C₃	1	4	yes	—
174	C₃²×Q₈	—	6	2	no	—
175	C₃²×D₄	—	6	4	no	—
176	C₃²×D₄	—	6	2	no	—
177	C₂×C₃²×C₄	—	2	4	no	—
178	C₂×C₃²×C₄	—	2	4	no	—
179	C₂×C₃²×C₄	—	2	4	no	—
180	C₂×C₃²×C₄	—	2	8	no	—
181	C₂×C₃²×C₄	—	2	8	no	—
182	C₂×C₃²×C₄	—	3	1	no	—
183	C₂×C₃²×C₄	—	3	1	no	—
184	C₂×C₃²×C₄	—	3	1	no	—
185	C₂×C₃²×C₄	—	3	2	no	—
186	C₂×C₃²×C₄	—	6	2	no	—
187	C₂×C₃²×C₄	—	6	4	no	—
188	C₂×C₃²×C₄	—	6	2	no	—
189	C₂×C₃²×C₄	—	6	2	no	—
190	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
191	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
192	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
193	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
194	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
195	C₂×C₃²×C₄	C₂³×C₃	1	8	yes	—
196	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
197	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
198	C₂×C₃²×C₄	C₂³×C₃	1	8	yes	—
199	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
200	C₂×C₃×Dic₃	C₂³×C₃	1	4	yes	—
201	C₂×C₃×Dic₃	C₂³×C₃	1	4	yes	—
202	C₂×C₃×Dic₃	C₂³×C₃	1	8	yes	—
203	C₂×C₃×Dic₃	C₂³×C₃	1	4	yes	—
204	C₃×D₁₂	—	2	16	no	—
205	C₃×D₁₂	—	2	8	no	—
206	C₃×C₄×D₃	—	2	8	no	—
207	C₃×C₄×D₃	—	2	8	no	—
208	C₃×C₄×D₃	—	2	8	no	—
209	C₃×C₄×D₃	—	2	16	no	—
210	C₃×Dic₆	—	2	8	no	—
211	#529	—	3	1	no	Sylow
212	C₂×C₃³	C₂×#41	1	1	yes	characteristic
213	C₂×C₃³	C₂×#41	1	1	yes	characteristic
214	C₂×C₃³	C₂×#41	1	1	yes	characteristic
215	C₃²×D₃	—	2	2	no	—
216	C₃²×D₃	—	4	2	no	—
217	C₂×C₃×Q₈	—	3	4	no	—
218	C₂×C₃×D₄	—	3	8	no	—
219	C₂×C₃×D₄	—	3	4	no	—
220	C₂²×C₃×C₄	—	3	4	no	—
221	C₂²×C₃×C₄	—	3	4	no	—
222	C₂²×C₃×C₄	—	3	4	no	—
223	C₂²×C₃×C₄	—	3	8	no	—
224	C₂×D₁₂	C₂²×C₃²	1	1	yes	characteristic
225	C₂×D₁₂	C₂²×C₃²	1	2	yes	—
226	C₂×C₄×D₃	C₂²×C₃²	1	1	yes	characteristic
227	C₂×C₄×D₃	C₂²×C₃²	1	1	yes	characteristic
228	C₂×C₄×D₃	C₂²×C₃²	1	1	yes	characteristic
229	C₂×C₄×D₃	C₂²×C₃²	1	2	yes	—
230	C₂×Dic₆	C₂²×C₃²	1	1	yes	characteristic
231	C₃×C₄⋊C₄	—	2	8	no	—
232	C₃×C₄⋊C₄	—	2	4	no	—
233	C₃×C₄⋊C₄	—	2	8	no	—
234	C₃×C₄⋊C₄	—	2	4	no	—
235	C₃×C₄⋊C₄	—	3	8	no	—
236	C₃×C₄⋊C₄	—	3	8	no	—
237	C₃×C₄⋊C₄	C₂×C₃×D₃	1	8	yes	—
238	C₃×C₄⋊C₄	C₂×C₃×D₃	1	4	yes	—
239	C₃×C₄⋊C₄	C₂×C₃×D₃	1	8	yes	—
240	C₃×C₄⋊C₄	C₂×C₃×D₃	1	4	yes	—
241	C₃×C₄⋊C₄	C₂²×C₃²	1	1	yes	characteristic
242	C₃×C₄⋊C₄	C₂²×C₃²	1	2	yes	—
243	C₃×C₄⋊C₄	C₂²×C₃²	1	1	yes	characteristic
244	C₃×C₄⋊C₄	C₂²×C₃²	1	2	yes	—
245	C₃×C₂²⋊C₄	—	3	8	no	—
246	C₃×C₂²⋊C₄	—	3	8	no	—
247	C₃×C₂²⋊C₄	—	3	8	no	—
248	C₃×C₂²⋊C₄	—	3	8	no	—
249	C₃×C₂²⋊C₄	—	3	8	no	—
250	C₃×C₄²	—	2	4	no	—
251	C₃×C₄²	—	3	4	no	—
252	C₃×C₄²	—	3	4	no	—
253	C₃×C₄²	—	3	4	no	—
254	C₃×C₄²	—	3	8	no	—
255	C₃×C₄²	C₂×C₃×D₃	1	4	yes	—
256	C₃×C₄²	C₂²×C₃²	1	1	yes	characteristic
257	(C₂×D₃)⋊C₄	C₂²×C₃²	1	2	yes	—
258	(C₂×D₃)⋊C₄	C₂²×C₃²	1	2	yes	—
259	(C₂×D₃)⋊C₄	C₂²×C₃²	1	2	yes	—
260	(C₂×D₃)⋊C₄	C₂²×C₃²	1	2	yes	—
261	(C₂×D₃)⋊C₄	C₂²×C₃²	1	2	yes	—
262	C₄⋊Dic₃	C₂²×C₃²	1	2	yes	—
263	Dic₃⋊C₄	C₂²×C₃²	1	2	yes	—
264	C₄×Dic₃	C₂²×C₃²	1	1	yes	characteristic
265	C₄×Dic₃	C₂²×C₃²	1	1	yes	characteristic
266	C₄×Dic₃	C₂²×C₃²	1	1	yes	characteristic
267	C₄×Dic₃	C₂²×C₃²	1	2	yes	—
268	C₂²×C₃²	—	2	4	no	—
269	C₂²×C₃²	—	3	2	no	—
270	C₂²×C₃²	—	6	1	no	—
271	C₂²×C₃²	—	6	1	no	—
272	C₂²×C₃²	—	6	2	no	—
273	C₂²×C₃²	—	6	2	no	—
274	C₂²×C₃²	—	6	2	no	—
275	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
276	C₂²×C₃²	C₂⁴×C₃	1	4	yes	—
277	C₂×C₃×D₃	—	2	4	no	—
278	C₂×C₃×D₃	—	2	4	no	—
279	C₂×C₃×D₃	—	2	8	no	—
280	C₂×C₃×D₃	—	2	8	no	—
281	C₂×C₃×D₃	—	2	8	no	—
282	C₂×C₃×D₃	C₃×#41	1	8	yes	—
283	C₃²×C₄	—	2	1	no	—
284	C₃²×C₄	—	2	2	no	—
285	C₃²×C₄	—	2	1	no	—
286	C₃²×C₄	—	2	2	no	—
287	C₃²×C₄	—	2	8	no	—
288	C₃²×C₄	—	2	4	no	—
289	C₃²×C₄	—	2	4	no	—
290	C₃²×C₄	—	2	8	no	—
291	C₃²×C₄	—	2	8	no	—
292	C₃²×C₄	—	3	2	no	—
293	C₃²×C₄	—	4	4	no	—
294	C₃²×C₄	—	4	4	no	—
295	C₃²×C₄	—	4	8	no	—
296	C₃²×C₄	—	4	8	no	—
297	C₃²×C₄	—	6	1	no	—
298	C₃²×C₄	—	6	2	no	—
299	C₃²×C₄	—	6	1	no	—
300	C₃²×C₄	#239	1	2	yes	—
301	C₃²×C₄	C₃×#41	1	8	yes	—
302	C₃×Dic₃	—	2	8	no	—
303	C₃×Dic₃	—	2	4	no	—
304	C₃×Dic₃	—	2	4	no	—
305	C₃×Dic₃	C₃×#41	1	8	yes	—
306	#126	—	3	2	no	—
307	#125	C₃²×D₃	1	1	yes	characteristic, complemented
308	#124	—	3	1	no	—
309	#123	—	3	2	no	—
310	C₂²⋊Q₈	—	3	1	no	—
311	#121	—	3	1	no	—
312	C₄×Q₈	—	3	1	no	—
313	C₄×D₄	—	3	1	no	—
314	C₄×D₄	—	3	2	no	—
315	#117	—	3	2	no	—
316	C₂×C₄²	—	3	1	no	—
317	C₃³	#529	1	1	yes	characteristic, complemented, Sylow
318	C₂³×C₃	—	3	4	no	—
319	C₂³×C₃	—	3	8	no	—
320	C₂²×D₃	C₂³×C₃²	1	2	yes	—
321	C₂²×D₃	C₂³×C₃²	1	1	yes	characteristic
322	C₃×Q₈	—	6	8	no	—
323	C₃×D₄	—	6	16	no	—
324	C₃×D₄	—	6	8	no	—
325	C₂×C₃×C₄	—	2	4	no	—
326	C₂×C₃×C₄	—	2	4	no	—
327	C₂×C₃×C₄	—	2	4	no	—
328	C₂×C₃×C₄	—	2	8	no	—
329	C₂×C₃×C₄	—	2	8	no	—
330	C₂×C₃×C₄	—	3	4	no	—
331	C₂×C₃×C₄	—	3	4	no	—
332	C₂×C₃×C₄	—	3	4	no	—
333	C₂×C₃×C₄	—	3	8	no	—
334	C₂×C₃×C₄	—	6	8	no	—
335	C₂×C₃×C₄	—	6	16	no	—
336	C₂×C₃×C₄	—	6	8	no	—
337	C₂×C₃×C₄	—	6	8	no	—
338	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
339	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
340	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
341	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
342	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
343	C₂×C₃×C₄	C₂³×C₃²	1	2	yes	—
344	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
345	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
346	C₂×C₃×C₄	C₂³×C₃²	1	2	yes	—
347	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
348	C₂×Dic₃	C₂³×C₃²	1	1	yes	characteristic
349	C₂×Dic₃	C₂³×C₃²	1	1	yes	characteristic
350	C₂×Dic₃	C₂³×C₃²	1	2	yes	—
351	C₂×Dic₃	C₂³×C₃²	1	1	yes	characteristic
352	D₁₂	—	2	4	no	—
353	D₁₂	—	2	2	no	—
354	C₄×D₃	—	2	2	no	—
355	C₄×D₃	—	2	2	no	—
356	C₄×D₃	—	2	2	no	—
357	C₄×D₃	—	2	4	no	—
358	Dic₆	—	2	2	no	—
359	C₂×C₃²	—	2	4	no	—
360	C₂×C₃²	—	2	4	no	—
361	C₂×C₃²	—	2	4	no	—
362	C₂×C₃²	—	6	2	no	—
363	C₂×C₃²	—	12	2	no	—
364	C₂×C₃²	C₂×#239	1	1	yes	characteristic
365	C₂×C₃²	D₃×#41	1	1	yes	characteristic
366	C₂×C₃²	D₃×#41	1	1	yes	characteristic
367	C₂×C₃²	C₂×C₃×#41	1	4	yes	—
368	C₂×C₃²	C₂×C₃×#41	1	4	yes	—
369	C₂×C₃²	C₂×C₃×#41	1	4	yes	—
370	C₃×D₃	—	2	8	no	—
371	C₃×D₃	—	4	8	no	—
372	C₂×Q₈	—	3	1	no	—
373	C₂×D₄	—	3	2	no	—
374	C₂×D₄	—	3	1	no	—
375	C₂²×C₄	—	3	1	no	—
376	C₂²×C₄	—	3	1	no	—
377	C₂²×C₄	—	3	1	no	—
378	C₂²×C₄	—	3	2	no	—
379	C₄⋊C₄	—	3	2	no	—
380	C₄⋊C₄	—	3	2	no	—
381	C₄⋊C₄	C₂×C₃²×D₃	1	2	yes	—
382	C₄⋊C₄	C₂×C₃²×D₃	1	1	yes	characteristic
383	C₄⋊C₄	C₂×C₃²×D₃	1	2	yes	—
384	C₄⋊C₄	C₂×C₃²×D₃	1	1	yes	characteristic
385	C₂²⋊C₄	—	3	2	no	—
386	C₂²⋊C₄	—	3	2	no	—
387	C₂²⋊C₄	—	3	2	no	—
388	C₂²⋊C₄	—	3	2	no	—
389	C₂²⋊C₄	—	3	2	no	—
390	C₄²	—	3	1	no	—
391	C₄²	—	3	1	no	—
392	C₄²	—	3	1	no	—
393	C₄²	—	3	2	no	—
394	C₄²	C₂×C₃²×D₃	1	1	yes	characteristic
395	C₂²×C₃	—	2	4	no	—
396	C₂²×C₃	—	3	8	no	—
397	C₂²×C₃	—	6	4	no	—
398	C₂²×C₃	—	6	4	no	—
399	C₂²×C₃	—	6	8	no	—
400	C₂²×C₃	—	6	8	no	—
401	C₂²×C₃	—	6	8	no	—
402	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
403	C₂²×C₃	C₂⁴×C₃²	1	1	yes	characteristic
404	C₂×D₃	—	2	1	no	—
405	C₂×D₃	—	2	1	no	—
406	C₂×D₃	—	2	2	no	—
407	C₂×D₃	—	2	2	no	—
408	C₂×D₃	—	2	2	no	—
409	C₂×D₃	C₃²×#41	1	2	yes	—
410	C₃×C₄	—	2	4	no	—
411	C₃×C₄	—	2	8	no	—
412	C₃×C₄	—	2	4	no	—
413	C₃×C₄	—	2	8	no	—
414	C₃×C₄	—	2	1	no	—
415	C₃×C₄	—	2	1	no	—
416	C₃×C₄	—	2	2	no	—
417	C₃×C₄	—	2	2	no	—
418	C₃×C₄	—	2	8	no	—
419	C₃×C₄	—	3	8	no	—
420	C₃×C₄	—	4	4	no	—
421	C₃×C₄	—	4	4	no	—
422	C₃×C₄	—	4	8	no	—
423	C₃×C₄	—	4	8	no	—
424	C₃×C₄	—	6	4	no	—
425	C₃×C₄	—	6	8	no	—
426	C₃×C₄	—	6	4	no	—
427	C₃×C₄	C₃×#239	1	8	yes	—
428	C₃×C₄	C₃²×#41	1	2	yes	—
429	Dic₃	—	2	2	no	—
430	Dic₃	—	2	1	no	—
431	Dic₃	—	2	1	no	—
432	Dic₃	C₃²×#41	1	2	yes	—
433	C₃²	—	2	4	no	—
434	C₃²	#5691	1	1	yes	characteristic, direct product factor
435	C₃²	C₃×#529	1	4	yes	complemented
436	C₂³	—	3	1	no	—
437	C₂³	—	3	2	no	—
438	Q₈	—	6	2	no	—
439	D₄	—	6	4	no	—
440	D₄	—	6	2	no	—
441	C₂×C₄	—	3	1	no	—
442	C₂×C₄	—	3	1	no	—
443	C₂×C₄	—	3	1	no	—
444	C₂×C₄	—	3	2	no	—
445	C₂×C₄	—	6	2	no	—
446	C₂×C₄	—	6	4	no	—
447	C₂×C₄	—	6	2	no	—
448	C₂×C₄	—	6	2	no	—
449	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
450	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
451	C₂×C₄	C₂²×C₃²×D₃	1	2	yes	—
452	C₂×C₄	C₂²×C₃²×D₃	1	2	yes	—
453	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
454	C₂×C₃	—	2	4	no	—
455	C₂×C₃	—	2	4	no	—
456	C₂×C₃	—	2	4	no	—
457	C₂×C₃	—	6	8	no	—
458	C₂×C₃	—	12	8	no	—
459	C₂×C₃	C₂×C₃×#239	1	4	yes	—
460	C₂×C₃	C₃×D₃×#41	1	4	yes	—
461	C₂×C₃	C₃×D₃×#41	1	4	yes	—
462	C₂×C₃	C₂×C₃²×#41	1	1	yes	characteristic
463	C₂×C₃	C₂×C₃²×#41	1	1	yes	characteristic
464	C₂×C₃	C₂×C₃²×#41	1	1	yes	characteristic
465	D₃	—	2	2	no	—
466	D₃	—	4	2	no	—
467	C₂²	—	3	2	no	—
468	C₂²	—	6	1	no	—
469	C₂²	—	6	1	no	—
470	C₂²	—	6	2	no	—
471	C₂²	—	6	2	no	—
472	C₂²	—	6	2	no	—
473	C₂²	C₂³×C₃²×D₃	1	1	yes	characteristic
474	C₄	—	2	1	no	—
475	C₄	—	2	2	no	—
476	C₄	—	2	1	no	—
477	C₄	—	2	2	no	—
478	C₄	—	3	2	no	—
479	C₄	—	6	1	no	—
480	C₄	—	6	2	no	—
481	C₄	—	6	1	no	—
482	C₄	C₃²×#239	1	2	yes	—
483	C₃	—	2	4	no	—
484	C₃	C₃×#5691	1	4	yes	direct product factor
485	C₃	C₃²×#529	1	1	yes	characteristic, complemented
486	C₂	—	6	2	no	—
487	C₂	—	12	2	no	—
488	C₂	C₂×C₃²×#239	1	1	yes	characteristic
489	C₂	C₃²×D₃×#41	1	1	yes	characteristic
490	C₂	C₃²×D₃×#41	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃²	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁴×C₃²
Frattini	C₂²	C₂³×C₃²×D₃
Fitting	C₃³×#125	C₂
socle	C₂²×C₃³	C₂⁴
prime radical	C₃²×#895	C₂
hypercenter	C₃²×#125	D₃
hypocenter	C₃	C₃²×#529
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃² ◁ C₃²×#125

Complements

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

N	H ≅ G/N	type
1. C₃³×#125	C₂	semidirect
2. C₃²×#898	C₂	semidirect
3. C₃²×#897	C₂	semidirect
5. C₃²×#894	C₂	semidirect
6. C₃²×#893	C₂	semidirect
7. C₃²×#893	C₂	semidirect
8. C₃²×#892	C₂	semidirect
9. C₃²×#887	C₂	semidirect
10. C₃²×#875	C₂	semidirect
11. C₃²×C₄²×D₃	C₂	semidirect
13. C₃×#5691	C₃	direct (N × H)
39. C₃²×#125	D₃	semidirect
40. C₃²×#125	C₂×C₃	semidirect
50. C₃×#898	C₂×C₃	semidirect
51. C₃×#897	C₂×C₃	semidirect
53. C₃×#894	C₂×C₃	semidirect
54. C₃×#893	C₂×C₃	semidirect
55. C₃×#893	C₂×C₃	semidirect
56. C₃×#892	C₂×C₃	semidirect
57. C₃×#887	C₂×C₃	semidirect
58. C₃×#875	C₂×C₃	semidirect
59. C₃×C₄²×D₃	C₂×C₃	semidirect
79. #5691	C₃²	direct (N × H)
149. C₃×#125	C₃×D₃	semidirect
150. C₃×#125	C₂×C₃²	semidirect
160. #898	C₂×C₃²	semidirect
161. #897	C₂×C₃²	semidirect
163. #894	C₂×C₃²	semidirect
164. #893	C₂×C₃²	semidirect
165. #893	C₂×C₃²	semidirect
166. #892	C₂×C₃²	semidirect
167. #887	C₂×C₃²	semidirect
168. #875	C₂×C₃²	semidirect
169. C₄²×D₃	C₂×C₃²	semidirect
307. #125	C₃²×D₃	semidirect
317. C₃³	#529	semidirect
434. C₃²	#5691	direct (N × H)
435. C₃²	C₃×#529	semidirect
484. C₃	C₃×#5691	direct (N × H)
485. C₃	C₃²×#529	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃³×#125	2
C₃²×#898	2
C₃²×#897	2
C₃²×#895	2
C₃²×#894	2
C₃²×#893	2
C₃²×#892	2
C₃²×#887	2
C₃²×#875	2
C₃²×C₄²×D₃	2
C₃²×#529	3
C₃×#5691	3

Subgroups — C32×#5691 #13179069

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#5691 #13179069