Subgroups — #28356053

Order 13851.

1058 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#13095333	C₃	1	2	yes	maximal, complemented
2	C₃×#13095332	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃×3₋¹⁺²×C₁₉⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
4	#17987430	C₃	1	2	yes	maximal, complemented
5	#17987430	C₃	1	2	yes	maximal, complemented
6	#17987430	C₃	1	2	yes	maximal, complemented
7	#17987428	C₃	1	2	yes	maximal, complemented
8	#17987427	C₃	1	2	yes	maximal, complemented
9	#17987426	C₃	1	1	yes	maximal, characteristic, complemented
10	#17987425	C₃	1	1	yes	maximal, characteristic, complemented
11	#17987424	C₃	1	2	yes	maximal, complemented
12	#17987424	C₃	1	2	yes	maximal, complemented
13	#17987424	C₃	1	2	yes	maximal, complemented
14	#17987424	C₃	1	2	yes	maximal, complemented
15	#17987424	C₃	1	2	yes	maximal, complemented
16	#17987424	C₃	1	2	yes	maximal, complemented
17	#17987423	C₃	1	2	yes	maximal, complemented
18	#17987422	C₃	1	2	yes	maximal, complemented
19	#17987422	C₃	1	2	yes	maximal, complemented
20	#17987422	C₃	1	2	yes	maximal, complemented
21	#17987420	C₃	1	1	yes	maximal, characteristic, complemented
22	#17987419	C₃	1	1	yes	maximal, characteristic, complemented
23	(C₃×C₁₉⋊C₃)⋊H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
24	C₁₉×C₉⋊H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic, complemented
25	C₃³×C₁₉⋊C₃	C₃²	1	1	yes	characteristic
26	#13095333	—	3	18	no	—
27	#13095332	—	3	9	no	—
28	C₃×#10587025	C₃²	1	2	yes	—
29	C₃×#10587025	C₃²	1	2	yes	complemented
30	C₃×#10587025	C₃²	1	2	yes	complemented
31	C₃×#10587022	C₃²	1	1	yes	characteristic
32	C₃×#10587022	C₃²	1	2	yes	—
33	C₃×#10587022	C₃²	1	1	yes	characteristic
34	C₃×#10587022	C₃²	1	2	yes	—
35	C₃×#10587022	C₃²	1	2	yes	complemented
36	C₃×#10587022	C₃²	1	2	yes	complemented
37	C₃×#10587022	C₃²	1	2	yes	complemented
38	C₃×#10587023	C₃²	1	1	yes	characteristic
39	C₃×#10587023	C₃²	1	2	yes	—
40	C₃×#10587023	C₃²	1	1	yes	characteristic
41	C₃×#10587023	C₃²	1	2	yes	—
42	C₃×#10587023	C₃²	1	2	yes	complemented
43	C₃×#10587023	C₃²	1	2	yes	complemented
44	C₃×#10587023	C₃²	1	2	yes	complemented
45	3₋¹⁺²×C₁₉⋊C₃	—	3	9	no	—
46	C₃×C₃²⋊(C₁₉⋊C₃)	C₃²	1	1	yes	characteristic
47	C₃×C₃²⋊(C₁₉⋊C₃)	C₃²	1	2	yes	—
48	C₃×C₃²⋊(C₁₉⋊C₃)	C₃²	1	2	yes	—
49	C₃×C₃²⋊(C₁₉⋊C₃)	C₃²	1	2	yes	—
50	C₃×C₃²⋊(C₁₉⋊C₃)	C₃²	1	2	yes	—
51	C₃×C₃²⋊(C₁₉⋊C₃)	C₃²	1	1	yes	characteristic
52	C₃×C₃²⋊(C₁₉⋊C₃)	C₃²	1	1	yes	characteristic
53	C₃²×#4294	C₃²	1	2	yes	complemented
54	C₃×C₉×C₁₉⋊C₃	C₃²	1	2	yes	—
55	C₃×C₉×C₁₉⋊C₃	C₃²	1	1	yes	characteristic
56	C₃×C₉×C₁₉⋊C₃	C₃²	1	2	yes	complemented
57	C₃×C₉×C₁₉⋊C₃	C₃²	1	2	yes	complemented
58	C₃×C₉×C₁₉⋊C₃	C₃²	1	2	yes	complemented
59	C₃²⋊#4294	C₃²	1	2	yes	—
60	C₃²⋊#4294	C₃²	1	2	yes	—
61	C₃²⋊#4294	C₃²	1	2	yes	complemented
62	C₃²⋊#4294	C₃²	1	2	yes	complemented
63	C₃²⋊#4294	C₃²	1	2	yes	complemented
64	C₃²⋊#4294	C₃²	1	2	yes	complemented
65	C₃²⋊#4294	C₃²	1	2	yes	complemented
66	C₃²⋊#4294	C₃²	1	2	yes	complemented
67	#13095303	C₃²	1	2	yes	—
68	#13095303	C₃²	1	2	yes	—
69	#13095303	C₃²	1	1	yes	characteristic
70	#13095303	C₃²	1	1	yes	characteristic
71	#13095303	C₃²	1	2	yes	—
72	#13095303	C₃²	1	2	yes	—
73	#13095303	C₃²	1	1	yes	characteristic
74	#13095303	C₃²	1	1	yes	characteristic
75	#13095303	C₃²	1	2	yes	complemented
76	#13095303	C₃²	1	2	yes	complemented
77	#13095303	C₃²	1	2	yes	complemented
78	#13095303	C₃²	1	2	yes	complemented
79	#13095303	C₃²	1	2	yes	complemented
80	#13095303	C₃²	1	2	yes	complemented
81	#13095303	C₃²	1	2	yes	complemented
82	#13095303	C₃²	1	2	yes	complemented
83	#13095303	C₃²	1	2	yes	complemented
84	#13095303	C₃²	1	2	yes	complemented
85	#13095303	C₃²	1	2	yes	complemented
86	#13095303	C₃²	1	2	yes	complemented
87	#13095303	C₃²	1	2	yes	complemented
88	#13095303	C₃²	1	2	yes	complemented
89	#13095303	C₃²	1	2	yes	complemented
90	#13095303	C₃²	1	2	yes	complemented
91	#13095303	C₃²	1	2	yes	complemented
92	#13095303	C₃²	1	2	yes	complemented
93	C₃×C₁₉×3₋¹⁺²	C₃²	1	1	yes	characteristic
94	C₃×C₁₉×3₋¹⁺²	C₃²	1	2	yes	complemented
95	C₃×C₁₉×H(3,𝔽₃)	C₃²	1	1	yes	characteristic
96	C₃²×C₉×C₁₉	C₃²	1	1	yes	characteristic, complemented
97	C₁₉×C₃²⋊C₉	C₃²	1	1	yes	characteristic
98	C₁₉×C₃²⋊C₉	C₃²	1	1	yes	characteristic
99	C₁₉×C₃²⋊C₉	C₃²	1	2	yes	complemented
100	C₁₉×C₃²⋊C₉	C₃²	1	2	yes	complemented
101	C₁₉×C₃²⋊C₉	C₃²	1	2	yes	complemented
102	#10624882	—	19	1	no	maximal, Sylow
103	C₃³×C₁₉	C₃³	1	1	yes	characteristic
104	C₃³×C₁₉	C₃³	1	1	yes	characteristic
105	C₃³×C₁₉	C₃³	1	2	yes	—
106	C₃²×C₁₉⋊C₃	—	3	3	no	—
107	C₃²×C₁₉⋊C₃	—	9	1	no	—
108	C₃²×C₁₉⋊C₃	—	9	1	no	—
109	C₃²×C₁₉⋊C₃	—	9	1	no	—
110	C₃²×C₁₉⋊C₃	C₃³	1	1	yes	characteristic
111	C₃²×C₁₉⋊C₃	C₃³	1	1	yes	characteristic
112	C₃²×C₁₉⋊C₃	C₃³	1	2	yes	—
113	C₃²×C₁₉⋊C₃	C₃³	1	2	yes	—
114	C₃²×C₁₉⋊C₃	C₃³	1	2	yes	—
115	C₃²×C₁₉⋊C₃	C₃³	1	1	yes	characteristic
116	C₁₉×3₋¹⁺²	—	3	3	no	—
117	C₁₉×3₋¹⁺²	—	3	6	no	—
118	C₁₉×H(3,𝔽₃)	—	9	1	no	—
119	C₃×C₉×C₁₉	—	3	3	no	—
120	C₃×C₉×C₁₉	C₃³	1	1	yes	characteristic
121	C₃×C₉×C₁₉	C₃³	1	1	yes	characteristic
122	C₃×C₉×C₁₉	C₃³	1	2	yes	—
123	C₃×C₉×C₁₉	C₃³	1	2	yes	—
124	C₃×C₉×C₁₉	C₃³	1	2	yes	—
125	C₃×C₉×C₁₉	C₃³	1	1	yes	characteristic
126	C₃²⋊(C₁₉⋊C₃)	—	3	3	no	—
127	C₃²⋊(C₁₉⋊C₃)	—	3	6	no	—
128	C₃²⋊(C₁₉⋊C₃)	—	9	2	no	—
129	C₃²⋊(C₁₉⋊C₃)	—	9	2	no	—
130	C₃²⋊(C₁₉⋊C₃)	—	9	1	no	—
131	C₃²⋊(C₁₉⋊C₃)	—	9	1	no	—
132	C₃²⋊(C₁₉⋊C₃)	—	9	2	no	—
133	#10587025	—	3	6	no	—
134	#10587025	—	3	6	no	—
135	#10587025	—	3	6	no	—
136	C₃×#4294	—	3	6	no	—
137	C₃×#4294	C₃³	1	2	yes	—
138	C₃×#4294	C₃³	1	2	yes	—
139	C₃×#4294	C₃³	1	2	yes	—
140	C₃×#4294	C₃³	1	2	yes	—
141	C₃×#4294	C₃³	1	2	yes	—
142	C₃×#4294	C₃³	1	2	yes	—
143	C₃×#4294	C₃³	1	2	yes	—
144	C₃×#4294	C₃³	1	2	yes	—
145	C₃×#4294	C₃³	1	2	yes	—
146	#10587023	—	3	3	no	—
147	#10587023	—	3	6	no	—
148	#10587023	—	3	3	no	—
149	#10587023	—	3	6	no	—
150	#10587023	—	3	6	no	—
151	#10587023	—	3	6	no	—
152	#10587023	—	3	6	no	—
153	#10587022	—	3	3	no	—
154	#10587022	—	3	6	no	—
155	#10587022	—	3	3	no	—
156	#10587022	—	3	6	no	—
157	#10587022	—	3	6	no	—
158	#10587022	—	3	6	no	—
159	#10587022	—	3	6	no	—
160	C₉×C₁₉⋊C₃	—	3	6	no	—
161	C₉×C₁₉⋊C₃	—	3	6	no	—
162	C₉×C₁₉⋊C₃	—	3	6	no	—
163	C₉×C₁₉⋊C₃	—	3	6	no	—
164	C₉×C₁₉⋊C₃	H(3,𝔽₃)	1	9	yes	complemented
165	C₃×#737	—	19	2	no	—
166	C₃×#737	—	19	1	no	—
167	C₃²×3₋¹⁺²	—	19	1	no	—
168	#6893	—	19	2	no	—
169	#6893	—	19	2	no	—
170	#6893	—	19	2	no	—
171	C₉⋊H(3,𝔽₃)	—	19	2	no	—
172	C₉⋊H(3,𝔽₃)	—	19	2	no	—
173	C₉⋊H(3,𝔽₃)	—	19	2	no	—
174	C₉⋊H(3,𝔽₃)	—	19	2	no	—
175	C₉⋊H(3,𝔽₃)	—	19	1	no	—
176	C₉⋊H(3,𝔽₃)	—	19	1	no	—
177	C₉⋊H(3,𝔽₃)	—	19	2	no	—
178	C₉⋊H(3,𝔽₃)	—	19	2	no	—
179	C₉⋊H(3,𝔽₃)	—	19	2	no	—
180	C₉⋊H(3,𝔽₃)	—	19	2	no	—
181	C₉⋊H(3,𝔽₃)	—	19	2	no	—
182	C₉⋊H(3,𝔽₃)	—	19	2	no	—
183	C₉⋊H(3,𝔽₃)	—	19	2	no	—
184	C₉⋊H(3,𝔽₃)	—	19	2	no	—
185	C₉⋊H(3,𝔽₃)	C₁₉⋊C₃	1	1	yes	characteristic, complemented
186	#6891	—	19	1	no	—
187	#6891	—	19	1	no	—
188	C₃²⋊H(3,𝔽₃)	—	19	1	no	—
189	C₃²×C₁₉	—	3	2	no	—
190	C₃²×C₁₉	—	3	1	no	—
191	C₃²×C₁₉	—	3	1	no	—
192	C₃²×C₁₉	—	3	1	no	—
193	C₃²×C₁₉	—	3	1	no	—
194	C₃²×C₁₉	—	3	2	no	—
195	C₃²×C₁₉	—	3	1	no	—
196	C₃²×C₁₉	—	3	2	no	—
197	C₃²×C₁₉	—	3	1	no	—
198	C₃²×C₁₉	—	3	2	no	—
199	C₃²×C₁₉	—	3	1	no	—
200	C₃²×C₁₉	—	3	1	no	—
201	C₃²×C₁₉	C₃⁴	1	1	yes	characteristic
202	C₃×C₁₉⋊C₃	—	3	1	no	—
203	C₃×C₁₉⋊C₃	—	3	1	no	—
204	C₃×C₁₉⋊C₃	—	3	1	no	—
205	C₃×C₁₉⋊C₃	—	3	2	no	—
206	C₃×C₁₉⋊C₃	—	3	2	no	—
207	C₃×C₁₉⋊C₃	—	3	2	no	—
208	C₃×C₁₉⋊C₃	—	3	1	no	—
209	C₃×C₁₉⋊C₃	—	3	1	no	—
210	C₃×C₁₉⋊C₃	—	3	1	no	—
211	C₃×C₁₉⋊C₃	—	3	1	no	—
212	C₃×C₁₉⋊C₃	—	3	2	no	—
213	C₃×C₁₉⋊C₃	—	3	2	no	—
214	C₃×C₁₉⋊C₃	—	3	2	no	—
215	C₃×C₁₉⋊C₃	—	3	2	no	—
216	C₃×C₁₉⋊C₃	—	3	2	no	—
217	C₃×C₁₉⋊C₃	—	3	2	no	—
218	C₃×C₁₉⋊C₃	—	3	2	no	—
219	C₃×C₁₉⋊C₃	—	3	2	no	—
220	C₃×C₁₉⋊C₃	—	3	2	no	—
221	C₃×C₁₉⋊C₃	—	3	1	no	—
222	C₃×C₁₉⋊C₃	—	3	1	no	—
223	C₃×C₁₉⋊C₃	—	3	1	no	—
224	C₃×C₁₉⋊C₃	—	3	1	no	—
225	C₃×C₁₉⋊C₃	—	9	9	no	—
226	C₃×C₁₉⋊C₃	C₃×H(3,𝔽₃)	1	3	yes	—
227	C₉×C₁₉	—	3	2	no	—
228	C₉×C₁₉	—	3	2	no	—
229	C₉×C₁₉	—	3	2	no	—
230	C₉×C₁₉	—	3	1	no	—
231	C₉×C₁₉	—	3	1	no	—
232	C₉×C₁₉	C₃×H(3,𝔽₃)	1	3	yes	—
233	#4294	—	3	2	no	—
234	#4294	—	3	2	no	—
235	#4294	—	3	2	no	—
236	#4294	—	3	2	no	—
237	#4294	—	3	2	no	—
238	#4294	—	3	2	no	—
239	#4294	—	3	2	no	—
240	#4294	—	3	2	no	—
241	#4294	C₃×H(3,𝔽₃)	1	6	yes	—
242	C₃⁴	—	19	1	no	—
243	#737	—	57	9	no	—
244	#737	—	57	18	no	—
245	C₃×3₋¹⁺²	—	19	2	no	—
246	C₃×3₋¹⁺²	—	19	2	no	—
247	C₃×3₋¹⁺²	—	19	2	no	—
248	C₃×3₋¹⁺²	—	19	2	no	—
249	C₃×3₋¹⁺²	—	19	1	no	—
250	C₃×3₋¹⁺²	—	19	2	no	—
251	C₃×3₋¹⁺²	—	19	1	no	—
252	C₃×3₋¹⁺²	—	19	2	no	—
253	C₃×3₋¹⁺²	—	19	1	no	—
254	C₃×3₋¹⁺²	—	19	2	no	—
255	C₃×3₋¹⁺²	—	19	2	no	—
256	C₃×3₋¹⁺²	—	19	2	no	—
257	C₃×3₋¹⁺²	—	19	2	no	—
258	C₃×3₋¹⁺²	—	19	1	no	—
259	C₃×3₋¹⁺²	—	19	2	no	—
260	C₃×3₋¹⁺²	—	19	2	no	—
261	C₃×3₋¹⁺²	—	19	2	no	—
262	C₃×3₋¹⁺²	—	57	9	no	—
263	C₃×3₋¹⁺²	C₃×C₁₉⋊C₃	1	1	yes	characteristic
264	C₃×3₋¹⁺²	C₃×C₁₉⋊C₃	1	2	yes	complemented
265	C₃×H(3,𝔽₃)	—	19	2	no	—
266	C₃×H(3,𝔽₃)	—	19	1	no	—
267	C₃×H(3,𝔽₃)	—	19	2	no	—
268	C₃×H(3,𝔽₃)	—	19	2	no	—
269	C₃×H(3,𝔽₃)	—	19	2	no	—
270	C₃×H(3,𝔽₃)	—	19	1	no	—
271	C₃×H(3,𝔽₃)	—	19	1	no	—
272	C₃×H(3,𝔽₃)	C₃×C₁₉⋊C₃	1	1	yes	characteristic
273	C₃²×C₉	—	19	1	no	—
274	C₃²×C₉	—	19	2	no	—
275	C₃²×C₉	—	19	2	no	—
276	C₃²×C₉	—	19	2	no	—
277	C₃²×C₉	—	19	2	no	—
278	C₃²×C₉	—	19	2	no	—
279	C₃²×C₉	C₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented
280	C₃²⋊C₉	—	19	2	no	—
281	C₃²⋊C₉	—	19	2	no	—
282	C₃²⋊C₉	—	19	2	no	—
283	C₃²⋊C₉	—	19	2	no	—
284	C₃²⋊C₉	—	19	2	no	—
285	C₃²⋊C₉	—	19	2	no	—
286	C₃²⋊C₉	—	19	2	no	—
287	C₃²⋊C₉	—	19	2	no	—
288	C₃²⋊C₉	—	19	2	no	—
289	C₃²⋊C₉	—	19	2	no	—
290	C₃²⋊C₉	—	19	2	no	—
291	C₃²⋊C₉	—	19	2	no	—
292	C₃²⋊C₉	—	19	1	no	—
293	C₃²⋊C₉	—	19	1	no	—
294	C₃²⋊C₉	—	19	1	no	—
295	C₃²⋊C₉	—	19	1	no	—
296	C₃²⋊C₉	—	19	2	no	—
297	C₃²⋊C₉	—	19	2	no	—
298	C₃²⋊C₉	—	19	2	no	—
299	C₃²⋊C₉	—	19	2	no	—
300	C₃²⋊C₉	—	19	2	no	—
301	C₃²⋊C₉	—	19	2	no	—
302	C₃²⋊C₉	—	19	2	no	—
303	C₃²⋊C₉	—	19	2	no	—
304	C₃²⋊C₉	—	19	2	no	—
305	C₃²⋊C₉	—	19	2	no	—
306	C₃²⋊C₉	—	19	2	no	—
307	C₃²⋊C₉	—	19	2	no	—
308	C₃²⋊C₉	—	19	2	no	—
309	C₃²⋊C₉	—	19	2	no	—
310	C₃²⋊C₉	—	19	2	no	—
311	C₃²⋊C₉	—	19	2	no	—
312	C₃²⋊C₉	—	19	2	no	—
313	C₃²⋊C₉	—	19	2	no	—
314	C₃²⋊C₉	C₃×C₁₉⋊C₃	1	1	yes	characteristic
315	C₃²⋊C₉	C₃×C₁₉⋊C₃	1	1	yes	characteristic
316	C₃²⋊C₉	C₃×C₁₉⋊C₃	1	2	yes	complemented
317	C₃²⋊C₉	C₃×C₁₉⋊C₃	1	2	yes	complemented
318	C₃²⋊C₉	C₃×C₁₉⋊C₃	1	2	yes	complemented
319	C₃×C₁₉	—	9	1	no	—
320	C₃×C₁₉	—	9	2	no	—
321	C₃×C₁₉	—	9	1	no	—
322	C₃×C₁₉	C₃²×H(3,𝔽₃)	1	1	yes	characteristic
323	C₃×C₁₉	3₋¹⁺⁴	1	1	yes	characteristic
324	C₃×C₁₉	3₋¹⁺⁴	1	1	yes	characteristic
325	C₃×C₁₉	3₋¹⁺⁴	1	1	yes	characteristic
326	C₁₉⋊C₃	—	3	3	no	—
327	C₁₉⋊C₃	—	9	2	no	—
328	C₁₉⋊C₃	—	9	2	no	—
329	C₁₉⋊C₃	—	9	2	no	—
330	C₁₉⋊C₃	—	9	1	no	—
331	C₁₉⋊C₃	—	9	1	no	—
332	C₃³	—	19	1	no	—
333	C₃³	—	19	2	no	—
334	C₃³	—	19	2	no	—
335	C₃³	—	19	2	no	—
336	C₃³	—	19	1	no	—
337	C₃³	—	19	1	no	—
338	C₃³	—	57	3	no	—
339	C₃³	—	171	1	no	—
340	C₃³	—	171	1	no	—
341	C₃³	—	171	1	no	—
342	C₃³	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
343	C₃³	C₃²×C₁₉⋊C₃	1	2	yes	—
344	C₃³	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
345	3₋¹⁺²	—	3	3	no	—
346	3₋¹⁺²	—	3	6	no	—
347	3₋¹⁺²	—	57	6	no	—
348	3₋¹⁺²	—	57	6	no	—
349	3₋¹⁺²	—	57	6	no	—
350	3₋¹⁺²	—	57	6	no	—
351	3₋¹⁺²	—	57	6	no	—
352	3₋¹⁺²	—	57	6	no	—
353	3₋¹⁺²	—	57	3	no	—
354	3₋¹⁺²	—	57	6	no	—
355	3₋¹⁺²	—	57	3	no	—
356	3₋¹⁺²	—	57	6	no	—
357	3₋¹⁺²	—	57	6	no	—
358	3₋¹⁺²	—	57	6	no	—
359	3₋¹⁺²	—	57	6	no	—
360	3₋¹⁺²	—	57	3	no	—
361	3₋¹⁺²	—	57	6	no	—
362	3₋¹⁺²	—	57	3	no	—
363	3₋¹⁺²	—	57	6	no	—
364	H(3,𝔽₃)	—	9	1	no	—
365	H(3,𝔽₃)	—	57	3	no	—
366	H(3,𝔽₃)	—	57	6	no	—
367	H(3,𝔽₃)	—	171	2	no	—
368	H(3,𝔽₃)	—	171	1	no	—
369	H(3,𝔽₃)	—	171	2	no	—
370	H(3,𝔽₃)	—	171	1	no	—
371	H(3,𝔽₃)	—	171	2	no	—
372	C₃×C₉	—	3	3	no	—
373	C₃×C₉	—	19	2	no	—
374	C₃×C₉	—	19	9	no	—
375	C₃×C₉	—	19	2	no	—
376	C₃×C₉	—	19	2	no	—
377	C₃×C₉	—	19	2	no	—
378	C₃×C₉	—	19	2	no	—
379	C₃×C₉	—	19	2	no	—
380	C₃×C₉	—	19	2	no	—
381	C₃×C₉	—	19	2	no	—
382	C₃×C₉	—	19	2	no	—
383	C₃×C₉	—	57	6	no	—
384	C₃×C₉	—	57	6	no	—
385	C₃×C₉	—	57	6	no	—
386	C₃×C₉	—	57	6	no	—
387	C₃×C₉	—	57	6	no	—
388	C₃×C₉	C₃²×C₁₉⋊C₃	1	2	yes	—
389	C₃×C₉	C₃²×C₁₉⋊C₃	1	2	yes	—
390	C₃×C₉	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
391	C₃×C₉	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
392	C₃×C₉	C₃²×C₁₉⋊C₃	1	2	yes	—
393	C₃×C₉	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
394	C₁₉	#10624882	1	1	yes	characteristic, complemented, Sylow
395	C₃²	—	3	1	no	—
396	C₃²	—	3	2	no	—
397	C₃²	—	3	1	no	—
398	C₃²	—	3	2	no	—
399	C₃²	—	3	1	no	—
400	C₃²	—	3	1	no	—
401	C₃²	—	3	2	no	—
402	C₃²	—	3	1	no	—
403	C₃²	—	3	1	no	—
404	C₃²	—	3	1	no	—
405	C₃²	—	3	2	no	—
406	C₃²	—	3	1	no	—
407	C₃²	—	19	3	no	—
408	C₃²	—	57	1	no	—
409	C₃²	—	57	1	no	—
410	C₃²	—	57	1	no	—
411	C₃²	—	57	2	no	—
412	C₃²	—	57	2	no	—
413	C₃²	—	57	2	no	—
414	C₃²	—	57	1	no	—
415	C₃²	—	57	1	no	—
416	C₃²	—	57	1	no	—
417	C₃²	—	57	2	no	—
418	C₃²	—	57	2	no	—
419	C₃²	—	57	2	no	—
420	C₃²	—	57	1	no	—
421	C₃²	—	57	1	no	—
422	C₃²	—	57	2	no	—
423	C₃²	—	57	2	no	—
424	C₃²	—	57	2	no	—
425	C₃²	—	57	1	no	—
426	C₃²	—	57	2	no	—
427	C₃²	—	57	2	no	—
428	C₃²	—	57	2	no	—
429	C₃²	—	57	1	no	—
430	C₃²	—	57	1	no	—
431	C₃²	—	171	9	no	—
432	C₃²	C₃³×C₁₉⋊C₃	1	1	yes	characteristic
433	C₉	—	3	1	no	—
434	C₉	—	3	1	no	—
435	C₉	—	3	2	no	—
436	C₉	—	3	2	no	—
437	C₉	—	3	2	no	—
438	C₉	—	19	6	no	—
439	C₉	—	57	2	no	—
440	C₉	—	57	2	no	—
441	C₉	—	57	2	no	—
442	C₉	—	57	2	no	—
443	C₉	—	57	2	no	—
444	C₉	—	57	2	no	—
445	C₉	—	57	2	no	—
446	C₉	—	57	2	no	—
447	C₉	H(3,𝔽₃)×C₁₉⋊C₃	1	3	yes	—
448	C₃	—	9	1	no	—
449	C₃	—	9	1	no	—
450	C₃	—	9	2	no	—
451	C₃	—	57	3	no	—
452	C₃	—	171	1	no	—
453	C₃	—	171	1	no	—
454	C₃	—	171	2	no	—
455	C₃	—	171	2	no	—
456	C₃	—	171	2	no	—
457	C₃	C₃×H(3,𝔽₃)×C₁₉⋊C₃	1	1	yes	characteristic
458	C₃	#17987544	1	1	yes	characteristic
459	C₃	#17987545	1	1	yes	characteristic
460	C₃	#17987546	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₃²	C₃³×C₁₉⋊C₃
commutator, socle, cosocle	C₃²×C₁₉	C₃⁴
Fitting	C₁₉×C₉⋊H(3,𝔽₃)	C₃
prime radical	(C₃×C₁₉⋊C₃)⋊H(3,𝔽₃)	C₃
hypercenter	C₉⋊H(3,𝔽₃)	C₁₉⋊C₃
hypocenter	C₁₉	#10624882
LCS	G ▷ C₃²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃² ◁ C₉⋊H(3,𝔽₃)

Complements

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

N	H ≅ G/N	type
1. C₃×#13095333	C₃	semidirect
2. C₃×#13095332	C₃	semidirect
3. C₃×3₋¹⁺²×C₁₉⋊C₃	C₃	semidirect
4. #17987430	C₃	semidirect
5. #17987430	C₃	semidirect
6. #17987430	C₃	semidirect
7. #17987428	C₃	semidirect
8. #17987427	C₃	semidirect
9. #17987426	C₃	semidirect
10. #17987425	C₃	semidirect
11. #17987424	C₃	semidirect
12. #17987424	C₃	semidirect
13. #17987424	C₃	semidirect
14. #17987424	C₃	semidirect
15. #17987424	C₃	semidirect
16. #17987424	C₃	semidirect
17. #17987423	C₃	semidirect
18. #17987422	C₃	semidirect
19. #17987422	C₃	semidirect
20. #17987422	C₃	semidirect
21. #17987420	C₃	semidirect
22. #17987419	C₃	semidirect
24. C₁₉×C₉⋊H(3,𝔽₃)	C₃	semidirect
29. C₃×#10587025	C₃²	semidirect
30. C₃×#10587025	C₃²	semidirect
35. C₃×#10587022	C₃²	semidirect
36. C₃×#10587022	C₃²	semidirect
37. C₃×#10587022	C₃²	semidirect
42. C₃×#10587023	C₃²	semidirect
43. C₃×#10587023	C₃²	semidirect
44. C₃×#10587023	C₃²	semidirect
53. C₃²×#4294	C₃²	semidirect
56. C₃×C₉×C₁₉⋊C₃	C₃²	semidirect
57. C₃×C₉×C₁₉⋊C₃	C₃²	semidirect
58. C₃×C₉×C₁₉⋊C₃	C₃²	semidirect
61. C₃²⋊#4294	C₃²	semidirect
62. C₃²⋊#4294	C₃²	semidirect
63. C₃²⋊#4294	C₃²	semidirect
64. C₃²⋊#4294	C₃²	semidirect
65. C₃²⋊#4294	C₃²	semidirect
66. C₃²⋊#4294	C₃²	semidirect
75. #13095303	C₃²	semidirect
76. #13095303	C₃²	semidirect
77. #13095303	C₃²	semidirect
78. #13095303	C₃²	semidirect
79. #13095303	C₃²	semidirect
80. #13095303	C₃²	semidirect
81. #13095303	C₃²	semidirect
82. #13095303	C₃²	semidirect
83. #13095303	C₃²	semidirect
84. #13095303	C₃²	semidirect
85. #13095303	C₃²	semidirect
86. #13095303	C₃²	semidirect
87. #13095303	C₃²	semidirect
88. #13095303	C₃²	semidirect
89. #13095303	C₃²	semidirect
90. #13095303	C₃²	semidirect
91. #13095303	C₃²	semidirect
92. #13095303	C₃²	semidirect
94. C₃×C₁₉×3₋¹⁺²	C₃²	semidirect
96. C₃²×C₉×C₁₉	C₃²	semidirect
99. C₁₉×C₃²⋊C₉	C₃²	semidirect
100. C₁₉×C₃²⋊C₉	C₃²	semidirect
101. C₁₉×C₃²⋊C₉	C₃²	semidirect
164. C₉×C₁₉⋊C₃	H(3,𝔽₃)	semidirect
185. C₉⋊H(3,𝔽₃)	C₁₉⋊C₃	semidirect
264. C₃×3₋¹⁺²	C₃×C₁₉⋊C₃	semidirect
279. C₃²×C₉	C₃×C₁₉⋊C₃	semidirect
316. C₃²⋊C₉	C₃×C₁₉⋊C₃	semidirect
317. C₃²⋊C₉	C₃×C₁₉⋊C₃	semidirect
318. C₃²⋊C₉	C₃×C₁₉⋊C₃	semidirect
394. C₁₉	#10624882	semidirect

Maximal subgroups

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

subgroup	index
C₃×#13095333	3
C₃×#13095332	3
C₃×3₋¹⁺²×C₁₉⋊C₃	3
#17987430	3
#17987428	3
#17987427	3
#17987426	3
#17987425	3
#17987424	3
#17987423	3
#17987422	3
#17987420	3
#17987419	3
(C₃×C₁₉⋊C₃)⋊H(3,𝔽₃)	3
C₁₉×C₉⋊H(3,𝔽₃)	3
#10624882	19