Subgroups — C₃×#10589801 #13153160

Order 1728.

644 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×#125	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#63460	C₂	1	2	yes	maximal, complemented
3	C₃×#63460	C₂	1	2	yes	maximal, complemented
4	C₃×#63459	C₂	1	2	yes	maximal, complemented
5	C₃×#63458	C₂	1	2	yes	maximal, complemented
6	C₃×#63456	C₂	1	2	yes	maximal
7	C₃×#63450	C₂	1	2	yes	maximal, complemented
8	C₃×#63437	C₂	1	1	yes	maximal, characteristic
9	C₃×#63432	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#5699	—	3	1	no	maximal
11	#10589801	C₃	1	1	yes	maximal, characteristic, direct product factor
12	C₂×C₃×D₃₆	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₄×D₉	C₂²	1	2	yes	—
14	C₂×C₃×Dic₁₈	C₂²	1	1	yes	characteristic
15	C₂×C₃×Dic₁₈	C₂²	1	2	yes	—
16	C₃×C₉×C₄⋊C₄	C₂²	1	2	yes	—
17	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₃×C₉×C₄⋊C₄	C₂²	1	2	yes	—
19	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₃×C₄²×C₉	C₂²	1	1	yes	characteristic
21	C₃×(C₂×D₉)⋊C₄	C₂²	1	2	yes	—
22	C₃×(C₂×D₉)⋊C₄	C₂²	1	2	yes	—
23	C₃×(C₂×D₉)⋊C₄	C₂²	1	2	yes	—
24	C₃×(C₂×D₉)⋊C₄	C₂²	1	2	yes	—
25	C₃×(C₂×D₉)⋊C₄	C₂²	1	2	yes	—
26	C₃×C₄⋊Dic₉	C₂²	1	1	yes	characteristic
27	C₃×C₄⋊Dic₉	C₂²	1	1	yes	characteristic
28	C₃×C₄⋊Dic₉	C₂²	1	2	yes	—
29	C₃×Dic₉⋊C₄	C₂²	1	2	yes	—
30	C₃×Dic₉⋊C₄	C₂²	1	2	yes	—
31	C₃×Dic₉⋊C₄	C₂²	1	2	yes	—
32	C₃×C₄×Dic₉	C₂²	1	2	yes	—
33	C₃²×#125	D₃	1	1	yes	characteristic
34	C₃×#898	—	3	2	no	—
35	C₃×#898	—	3	2	no	—
36	C₃×#897	—	3	2	no	—
37	C₃×#896	—	3	2	no	—
38	C₃×#894	—	3	2	no	—
39	C₃×#888	—	3	2	no	—
40	C₃×#875	—	3	1	no	—
41	C₃×#870	—	3	1	no	—
42	C₉×#125	—	2	1	no	—
43	C₉×#125	C₂×C₃	1	1	yes	characteristic, complemented
44	#63460	C₂×C₃	1	2	yes	complemented
45	#63460	C₂×C₃	1	2	yes	complemented
46	#63459	C₂×C₃	1	2	yes	complemented
47	#63458	C₂×C₃	1	2	yes	complemented
48	#63456	C₂×C₃	1	2	yes	—
49	#63450	C₂×C₃	1	2	yes	complemented
50	#63437	C₂×C₃	1	1	yes	characteristic
51	#63432	C₂×C₃	1	1	yes	characteristic, complemented
52	C₂²×C₃×D₉	C₂³	1	2	yes	—
53	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
54	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
55	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
56	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
57	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
58	C₂×C₃×Dic₉	C₂³	1	2	yes	—
59	C₂×C₃×Dic₉	C₂³	1	2	yes	—
60	C₂×C₃×Dic₉	C₂³	1	2	yes	—
61	C₃×D₃₆	—	4	1	no	—
62	C₃×C₄×D₉	—	4	2	no	—
63	C₃×Dic₁₈	—	4	1	no	—
64	C₃×Dic₁₈	—	4	2	no	—
65	C₃×#563	—	9	1	no	—
66	#5699	—	3	1	no	—
67	C₂×C₃×D₁₂	—	3	1	no	—
68	C₂×C₃×C₄×D₃	—	3	2	no	—
69	C₂×C₃×Dic₆	—	3	1	no	—
70	C₂×C₃×Dic₆	—	3	2	no	—
71	C₃²×C₄⋊C₄	C₂×D₃	1	2	yes	—
72	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
73	C₃²×C₄⋊C₄	C₂×D₃	1	2	yes	—
74	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
75	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic
76	C₃×(C₂×D₃)⋊C₄	—	3	2	no	—
77	C₃×(C₂×D₃)⋊C₄	—	3	2	no	—
78	C₃×(C₂×D₃)⋊C₄	—	3	2	no	—
79	C₃×(C₂×D₃)⋊C₄	—	3	2	no	—
80	C₃×(C₂×D₃)⋊C₄	—	3	2	no	—
81	C₃×C₄⋊Dic₃	—	3	2	no	—
82	C₃×C₄⋊Dic₃	—	3	1	no	—
83	C₃×C₄⋊Dic₃	—	3	1	no	—
84	C₃×Dic₃⋊C₄	—	3	2	no	—
85	C₃×Dic₃⋊C₄	—	3	2	no	—
86	C₃×Dic₃⋊C₄	—	3	2	no	—
87	C₃×C₄×Dic₃	—	3	2	no	—
88	C₂×D₃₆	C₂²×C₃	1	1	yes	characteristic
89	C₂×C₄×D₉	C₂²×C₃	1	2	yes	—
90	C₂×Dic₁₈	C₂²×C₃	1	1	yes	characteristic
91	C₂×Dic₁₈	C₂²×C₃	1	2	yes	—
92	C₉×C₄⋊C₄	—	2	1	no	—
93	C₉×C₄⋊C₄	—	2	1	no	—
94	C₉×C₄⋊C₄	—	2	2	no	—
95	C₉×C₄⋊C₄	—	2	2	no	—
96	C₉×C₄⋊C₄	C₂²×C₃	1	2	yes	—
97	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
98	C₉×C₄⋊C₄	C₂²×C₃	1	2	yes	—
99	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
100	C₄²×C₉	—	2	1	no	—
101	C₄²×C₉	C₂²×C₃	1	1	yes	characteristic
102	(C₂×D₉)⋊C₄	C₂²×C₃	1	2	yes	—
103	(C₂×D₉)⋊C₄	C₂²×C₃	1	2	yes	—
104	(C₂×D₉)⋊C₄	C₂²×C₃	1	2	yes	—
105	(C₂×D₉)⋊C₄	C₂²×C₃	1	2	yes	—
106	(C₂×D₉)⋊C₄	C₂²×C₃	1	2	yes	—
107	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
108	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
109	C₄⋊Dic₉	C₂²×C₃	1	2	yes	—
110	Dic₉⋊C₄	C₂²×C₃	1	2	yes	—
111	Dic₉⋊C₄	C₂²×C₃	1	2	yes	—
112	Dic₉⋊C₄	C₂²×C₃	1	2	yes	—
113	C₄×Dic₉	C₂²×C₃	1	2	yes	—
114	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
115	C₂×C₃×D₉	—	2	2	no	—
116	C₂×C₃×D₉	—	2	2	no	—
117	C₂×C₃×D₉	—	2	2	no	—
118	C₃×C₄×C₉	—	2	2	no	—
119	C₃×C₄×C₉	—	2	1	no	—
120	C₃×C₄×C₉	—	2	1	no	—
121	C₃×C₄×C₉	—	2	2	no	—
122	C₃×C₄×C₉	—	2	1	no	—
123	C₃×Dic₉	—	2	2	no	—
124	C₃×Dic₉	—	2	2	no	—
125	C₃×Dic₉	—	2	2	no	—
126	C₃×C₄⋊Q₈	—	9	2	no	—
127	C₃×#126	—	9	2	no	—
128	C₃×#126	—	9	2	no	—
129	C₃×#125	—	2	1	no	—
130	C₃×#125	—	9	1	no	—
131	C₃×#125	D₉	1	1	yes	characteristic, complemented
132	C₃×#125	C₃×D₃	1	1	yes	characteristic
133	C₃×#124	—	9	1	no	—
134	C₃×#123	—	9	2	no	—
135	C₃×C₂²⋊Q₈	—	9	2	no	—
136	C₃×C₂²⋊Q₈	—	9	2	no	—
137	#898	—	3	2	no	—
138	#898	—	3	2	no	—
139	#897	—	3	2	no	—
140	#896	—	3	2	no	—
141	#894	—	3	2	no	—
142	#888	—	3	2	no	—
143	#875	—	3	1	no	—
144	#870	—	3	1	no	—
145	C₂²×C₃×D₃	—	3	2	no	—
146	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
147	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
148	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
149	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
150	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
151	C₂×C₃×Dic₃	—	3	2	no	—
152	C₂×C₃×Dic₃	—	3	2	no	—
153	C₂×C₃×Dic₃	—	3	2	no	—
154	C₃×D₁₂	—	12	1	no	—
155	C₃×C₄×D₃	—	12	2	no	—
156	C₃×Dic₆	—	12	1	no	—
157	C₃×Dic₆	—	12	2	no	—
158	C₂²×D₉	C₂³×C₃	1	2	yes	—
159	C₂×C₄×C₉	—	2	1	no	—
160	C₂×C₄×C₉	—	2	1	no	—
161	C₂×C₄×C₉	—	2	1	no	—
162	C₂×C₄×C₉	—	2	2	no	—
163	C₂×C₄×C₉	—	2	2	no	—
164	C₂×C₄×C₉	C₂³×C₃	1	2	yes	—
165	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
166	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
167	C₂×C₄×C₉	C₂³×C₃	1	2	yes	—
168	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
169	C₂×Dic₉	C₂³×C₃	1	2	yes	—
170	C₂×Dic₉	C₂³×C₃	1	2	yes	—
171	C₂×Dic₉	C₂³×C₃	1	2	yes	—
172	D₃₆	—	4	1	no	—
173	C₄×D₉	—	4	2	no	—
174	Dic₁₈	—	4	1	no	—
175	Dic₁₈	—	4	2	no	—
176	#563	—	9	1	no	Sylow
177	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
178	C₂×C₃×C₉	2₋¹⁺⁴	1	1	yes	characteristic
179	C₂×C₃×C₉	2₋¹⁺⁴	1	1	yes	characteristic
180	C₃×D₉	—	4	2	no	—
181	C₂×C₃×Q₈	—	9	2	no	—
182	C₂×C₃×Q₈	—	9	1	no	—
183	C₂×C₃×D₄	—	9	1	no	—
184	C₂²×C₃×C₄	—	9	2	no	—
185	C₂×D₁₂	—	3	1	no	—
186	C₂×C₄×D₃	—	3	2	no	—
187	C₂×Dic₆	—	3	1	no	—
188	C₂×Dic₆	—	3	2	no	—
189	C₃×C₄⋊C₄	—	2	1	no	—
190	C₃×C₄⋊C₄	—	2	2	no	—
191	C₃×C₄⋊C₄	—	2	2	no	—
192	C₃×C₄⋊C₄	—	2	1	no	—
193	C₃×C₄⋊C₄	—	9	2	no	—
194	C₃×C₄⋊C₄	—	9	2	no	—
195	C₃×C₄⋊C₄	—	9	2	no	—
196	C₃×C₄⋊C₄	—	9	1	no	—
197	C₃×C₄⋊C₄	—	9	2	no	—
198	C₃×C₄⋊C₄	—	9	1	no	—
199	C₃×C₄⋊C₄	C₂×D₉	1	1	yes	characteristic
200	C₃×C₄⋊C₄	C₂×D₉	1	2	yes	—
201	C₃×C₄⋊C₄	C₂×D₉	1	2	yes	—
202	C₃×C₄⋊C₄	C₂×D₉	1	1	yes	characteristic
203	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
204	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
205	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
206	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
207	C₃×C₂²⋊C₄	—	9	2	no	—
208	C₃×C₂²⋊C₄	—	9	2	no	—
209	C₃×C₂²⋊C₄	—	9	2	no	—
210	C₃×C₂²⋊C₄	—	9	2	no	—
211	C₃×C₂²⋊C₄	—	9	2	no	—
212	C₃×C₄²	—	2	1	no	—
213	C₃×C₄²	—	9	2	no	—
214	C₃×C₄²	C₂×D₉	1	1	yes	characteristic
215	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
216	(C₂×D₃)⋊C₄	—	3	2	no	—
217	(C₂×D₃)⋊C₄	—	3	2	no	—
218	(C₂×D₃)⋊C₄	—	3	2	no	—
219	(C₂×D₃)⋊C₄	—	3	2	no	—
220	(C₂×D₃)⋊C₄	—	3	2	no	—
221	C₄⋊Dic₃	—	3	1	no	—
222	C₄⋊Dic₃	—	3	1	no	—
223	C₄⋊Dic₃	—	3	2	no	—
224	Dic₃⋊C₄	—	3	2	no	—
225	Dic₃⋊C₄	—	3	2	no	—
226	Dic₃⋊C₄	—	3	2	no	—
227	C₄×Dic₃	—	3	2	no	—
228	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
229	C₂×C₃×D₃	—	6	2	no	—
230	C₂×C₃×D₃	—	6	2	no	—
231	C₂×C₃×D₃	—	6	2	no	—
232	C₃²×C₄	—	2	1	no	—
233	C₃²×C₄	—	2	2	no	—
234	C₃²×C₄	—	2	1	no	—
235	C₃²×C₄	—	2	2	no	—
236	C₃²×C₄	—	2	1	no	—
237	C₃×Dic₃	—	6	2	no	—
238	C₃×Dic₃	—	6	2	no	—
239	C₃×Dic₃	—	6	2	no	—
240	C₂²×C₉	—	2	1	no	—
241	C₂²×C₉	C₂⁴×C₃	1	1	yes	characteristic
242	C₂×D₉	—	2	2	no	—
243	C₂×D₉	—	2	2	no	—
244	C₂×D₉	—	2	2	no	—
245	C₄×C₉	—	2	2	no	—
246	C₄×C₉	—	2	2	no	—
247	C₄×C₉	—	2	1	no	—
248	C₄×C₉	—	2	1	no	—
249	C₄×C₉	—	2	2	no	—
250	C₄×C₉	—	2	1	no	—
251	C₄×C₉	—	4	2	no	—
252	C₄×C₉	—	4	1	no	—
253	C₄×C₉	—	4	1	no	—
254	C₄×C₉	—	4	2	no	—
255	Dic₉	—	2	2	no	—
256	Dic₉	—	2	2	no	—
257	Dic₉	—	2	2	no	—
258	C₄⋊Q₈	—	9	2	no	—
259	#126	—	9	2	no	—
260	#126	—	9	2	no	—
261	#125	—	9	1	no	—
262	#125	C₃×D₉	1	1	yes	characteristic, complemented
263	#124	—	9	1	no	—
264	#123	—	9	2	no	—
265	C₂²⋊Q₈	—	9	2	no	—
266	C₂²⋊Q₈	—	9	2	no	—
267	C₃×C₉	#563	1	1	yes	characteristic, complemented, Sylow
268	C₂³×C₃	—	9	2	no	—
269	C₂²×D₃	—	3	2	no	—
270	C₃×Q₈	—	36	2	no	—
271	C₃×Q₈	—	36	1	no	—
272	C₃×D₄	—	36	1	no	—
273	C₂×C₃×C₄	—	2	1	no	—
274	C₂×C₃×C₄	—	2	1	no	—
275	C₂×C₃×C₄	—	2	1	no	—
276	C₂×C₃×C₄	—	2	2	no	—
277	C₂×C₃×C₄	—	2	2	no	—
278	C₂×C₃×C₄	—	9	2	no	—
279	C₂×C₃×C₄	—	9	2	no	—
280	C₂×C₃×C₄	—	9	2	no	—
281	C₂×C₃×C₄	—	36	2	no	—
282	C₂×C₃×C₄	C₂²×D₉	1	2	yes	—
283	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
284	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
285	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
286	C₂×C₃×C₄	C₂²×D₉	1	2	yes	—
287	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
288	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
289	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
290	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
291	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
292	C₂×Dic₃	—	3	2	no	—
293	C₂×Dic₃	—	3	2	no	—
294	C₂×Dic₃	—	3	2	no	—
295	D₁₂	—	12	1	no	—
296	C₄×D₃	—	12	2	no	—
297	Dic₆	—	12	1	no	—
298	Dic₆	—	12	2	no	—
299	C₂×C₃²	#1007	1	1	yes	characteristic
300	C₂×C₃²	#1009	1	1	yes	characteristic
301	C₂×C₃²	#1010	1	1	yes	characteristic
302	C₃×D₃	—	12	2	no	—
303	C₂×C₉	—	2	1	no	—
304	C₂×C₉	—	2	1	no	—
305	C₂×C₉	—	2	1	no	—
306	C₂×C₉	C₃×H(5,𝔽₂)	1	1	yes	characteristic
307	C₂×C₉	C₃×2₋¹⁺⁴	1	1	yes	characteristic
308	C₂×C₉	C₃×2₋¹⁺⁴	1	1	yes	characteristic
309	D₉	—	4	2	no	—
310	C₂×Q₈	—	9	2	no	—
311	C₂×Q₈	—	9	1	no	—
312	C₂×D₄	—	9	1	no	—
313	C₂²×C₄	—	9	2	no	—
314	C₄⋊C₄	—	9	1	no	—
315	C₄⋊C₄	—	9	2	no	—
316	C₄⋊C₄	—	9	2	no	—
317	C₄⋊C₄	—	9	2	no	—
318	C₄⋊C₄	—	9	2	no	—
319	C₄⋊C₄	—	9	1	no	—
320	C₄⋊C₄	C₂×C₃×D₉	1	1	yes	characteristic
321	C₄⋊C₄	C₂×C₃×D₉	1	2	yes	—
322	C₄⋊C₄	C₂×C₃×D₉	1	2	yes	—
323	C₄⋊C₄	C₂×C₃×D₉	1	1	yes	characteristic
324	C₂²⋊C₄	—	9	2	no	—
325	C₂²⋊C₄	—	9	2	no	—
326	C₂²⋊C₄	—	9	2	no	—
327	C₂²⋊C₄	—	9	2	no	—
328	C₂²⋊C₄	—	9	2	no	—
329	C₄²	—	9	2	no	—
330	C₄²	C₂×C₃×D₉	1	1	yes	characteristic
331	C₂²×C₃	—	2	1	no	—
332	C₂²×C₃	—	18	2	no	—
333	C₂²×C₃	—	18	2	no	—
334	C₂²×C₃	—	18	2	no	—
335	C₂²×C₃	C₂³×D₉	1	1	yes	characteristic
336	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
337	C₂×D₃	—	6	2	no	—
338	C₂×D₃	—	6	2	no	—
339	C₂×D₃	—	6	2	no	—
340	C₃×C₄	—	2	2	no	—
341	C₃×C₄	—	2	1	no	—
342	C₃×C₄	—	2	2	no	—
343	C₃×C₄	—	2	1	no	—
344	C₃×C₄	—	2	2	no	—
345	C₃×C₄	—	2	1	no	—
346	C₃×C₄	—	2	1	no	—
347	C₃×C₄	—	2	2	no	—
348	C₃×C₄	—	2	1	no	—
349	C₃×C₄	—	2	2	no	—
350	C₃×C₄	—	2	1	no	—
351	C₃×C₄	—	4	2	no	—
352	C₃×C₄	—	4	1	no	—
353	C₃×C₄	—	4	1	no	—
354	C₃×C₄	—	4	2	no	—
355	C₃×C₄	—	18	2	no	—
356	C₃×C₄	—	18	2	no	—
357	C₃×C₄	—	18	2	no	—
358	Dic₃	—	6	2	no	—
359	Dic₃	—	6	2	no	—
360	Dic₃	—	6	2	no	—
361	C₃²	#5699	1	1	yes	characteristic
362	C₉	—	2	1	no	—
363	C₉	C₃×#563	1	1	yes	characteristic, complemented
364	C₂³	—	9	2	no	—
365	Q₈	—	36	2	no	—
366	Q₈	—	36	1	no	—
367	D₄	—	36	1	no	—
368	C₂×C₄	—	9	2	no	—
369	C₂×C₄	—	9	2	no	—
370	C₂×C₄	—	9	2	no	—
371	C₂×C₄	—	36	2	no	—
372	C₂×C₄	C₂²×C₃×D₉	1	2	yes	—
373	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
374	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
375	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
376	C₂×C₄	C₂²×C₃×D₉	1	2	yes	—
377	C₂×C₃	—	2	1	no	—
378	C₂×C₃	—	2	1	no	—
379	C₂×C₃	—	2	1	no	—
380	C₂×C₃	—	36	2	no	—
381	C₂×C₃	#63713	1	1	yes	characteristic
382	C₂×C₃	#63715	1	1	yes	characteristic
383	C₂×C₃	#63716	1	1	yes	characteristic
384	C₂×C₃	C₃×#1007	1	1	yes	characteristic
385	C₂×C₃	C₃×#1009	1	1	yes	characteristic
386	C₂×C₃	C₃×#1010	1	1	yes	characteristic
387	D₃	—	12	2	no	—
388	C₂²	—	18	2	no	—
389	C₂²	—	18	2	no	—
390	C₂²	—	18	2	no	—
391	C₂²	C₂³×C₃×D₉	1	1	yes	characteristic
392	C₄	—	2	1	no	—
393	C₄	—	2	2	no	—
394	C₄	—	2	1	no	—
395	C₄	—	2	2	no	—
396	C₄	—	2	1	no	—
397	C₄	—	18	2	no	—
398	C₄	—	18	2	no	—
399	C₄	—	18	2	no	—
400	C₃	—	2	1	no	—
401	C₃	#10589801	1	1	yes	characteristic, direct product factor
402	C₃	C₃×#5699	1	1	yes	characteristic
403	C₂	—	36	2	no	—
404	C₂	C₃×#63713	1	1	yes	characteristic
405	C₂	C₃×#63715	1	1	yes	characteristic
406	C₂	C₃×#63716	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂³×D₉
commutator, cosocle	C₂²×C₉	C₂⁴×C₃
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₃×C₉×#125	C₂
socle	C₂²×C₃²	C₂³×D₃
prime radical	C₂×C₃×D₃₆	C₂²
hypercenter	C₃×#125	D₉
hypocenter	C₉	C₃×#563
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#125

Complements

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

N	H ≅ G/N	type
1. C₃×C₉×#125	C₂	semidirect
2. C₃×#63460	C₂	semidirect
3. C₃×#63460	C₂	semidirect
4. C₃×#63459	C₂	semidirect
5. C₃×#63458	C₂	semidirect
7. C₃×#63450	C₂	semidirect
9. C₃×#63432	C₂	semidirect
11. #10589801	C₃	direct (N × H)
43. C₉×#125	C₂×C₃	semidirect
44. #63460	C₂×C₃	semidirect
45. #63460	C₂×C₃	semidirect
46. #63459	C₂×C₃	semidirect
47. #63458	C₂×C₃	semidirect
49. #63450	C₂×C₃	semidirect
51. #63432	C₂×C₃	semidirect
131. C₃×#125	D₉	semidirect
262. #125	C₃×D₉	semidirect
267. C₃×C₉	#563	semidirect
363. C₉	C₃×#563	semidirect
401. C₃	#10589801	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×C₉×#125	2
C₃×#63460	2
C₃×#63459	2
C₃×#63458	2
C₃×#63456	2
C₃×#63450	2
C₃×#63437	2
C₃×#63432	2
C₃×#5699	3
#10589801	3

Subgroups — C3×#10589801 #13153160

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10589801 #13153160