Subgroups — #28356107

Order 13851.

764 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17987432	C₃	1	2	yes	maximal, complemented
2	#17987431	C₃	1	1	yes	maximal, characteristic, complemented
3	#17987430	C₃	1	2	yes	maximal, complemented
4	#17987430	C₃	1	2	yes	maximal, complemented
5	#17987430	C₃	1	2	yes	maximal, complemented
6	#17987427	C₃	1	2	yes	maximal, complemented
7	#17987426	C₃	1	1	yes	maximal, characteristic, complemented
8	#17987424	C₃	1	2	yes	maximal, complemented
9	#17987424	C₃	1	2	yes	maximal, complemented
10	#17987424	C₃	1	2	yes	maximal, 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	#17987423	C₃	1	2	yes	maximal, complemented
15	#17987422	C₃	1	2	yes	maximal, complemented
16	#17987422	C₃	1	2	yes	maximal, complemented
17	#17987422	C₃	1	2	yes	maximal, complemented
18	#17987419	C₃	1	1	yes	maximal, characteristic, complemented
19	#17987418	C₃	1	1	yes	maximal, characteristic, complemented
20	(C₃×C₁₉⋊C₃)⋊H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
21	C₉×C₃²⋊(C₁₉⋊C₃)	C₃	1	1	yes	maximal, characteristic, complemented
22	#17987406	C₃	1	2	yes	maximal, complemented
23	C₁₉⋊C₃×C₃²⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
24	C₁₉×C₉⋊H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic, complemented
25	C₃³×C₁₉⋊C₃	C₃²	1	1	yes	characteristic
26	C₃×#10587025	C₃²	1	2	yes	—
27	C₃×#10587025	C₃²	1	2	yes	complemented
28	C₃×#10587025	C₃²	1	2	yes	complemented
29	C₃×#10587022	C₃²	1	2	yes	complemented
30	C₃×#10587022	C₃²	1	2	yes	complemented
31	C₃×#10587022	C₃²	1	2	yes	complemented
32	C₃×#10587023	C₃²	1	2	yes	—
33	C₃×#10587023	C₃²	1	1	yes	characteristic
34	C₃×#10587023	C₃²	1	2	yes	complemented
35	C₃×#10587023	C₃²	1	2	yes	complemented
36	C₃×#10587023	C₃²	1	2	yes	complemented
37	C₃×C₃²⋊(C₁₉⋊C₃)	C₃²	1	2	yes	—
38	C₃×C₃²⋊(C₁₉⋊C₃)	C₃²	1	1	yes	characteristic
39	C₃×C₃²⋊(C₁₉⋊C₃)	C₃²	1	2	yes	—
40	C₃×C₃²⋊(C₁₉⋊C₃)	C₃²	1	2	yes	—
41	C₃×C₃²⋊(C₁₉⋊C₃)	C₃²	1	1	yes	characteristic
42	C₃×C₃²⋊(C₁₉⋊C₃)	C₃²	1	1	yes	characteristic
43	C₃×C₃²⋊(C₁₉⋊C₃)	C₃²	1	2	yes	—
44	C₃²×#4294	C₃²	1	2	yes	complemented
45	C₃×C₉×C₁₉⋊C₃	C₃²	1	1	yes	characteristic
46	C₃×C₉×C₁₉⋊C₃	C₃²	1	2	yes	—
47	C₃×C₉×C₁₉⋊C₃	C₃²	1	2	yes	complemented
48	C₃×C₉×C₁₉⋊C₃	C₃²	1	2	yes	complemented
49	C₃×C₉×C₁₉⋊C₃	C₃²	1	2	yes	complemented
50	C₃²⋊#4294	C₃²	1	2	yes	—
51	C₃²⋊#4294	C₃²	1	2	yes	—
52	C₃²⋊#4294	C₃²	1	2	yes	complemented
53	C₃²⋊#4294	C₃²	1	2	yes	complemented
54	C₃²⋊#4294	C₃²	1	2	yes	complemented
55	C₃²⋊#4294	C₃²	1	2	yes	complemented
56	C₃²⋊#4294	C₃²	1	2	yes	complemented
57	C₃²⋊#4294	C₃²	1	2	yes	complemented
58	#13095303	C₃²	1	2	yes	—
59	#13095303	C₃²	1	1	yes	characteristic
60	#13095303	C₃²	1	1	yes	characteristic
61	#13095303	C₃²	1	2	yes	—
62	#13095303	C₃²	1	2	yes	—
63	#13095303	C₃²	1	2	yes	—
64	#13095303	C₃²	1	1	yes	characteristic
65	#13095303	C₃²	1	1	yes	characteristic
66	#13095303	C₃²	1	1	yes	characteristic
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	complemented
73	#13095303	C₃²	1	2	yes	complemented
74	#13095303	C₃²	1	2	yes	complemented
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	C₃×C₁₉×3₋¹⁺²	C₃²	1	1	yes	characteristic
91	C₃×C₁₉×3₋¹⁺²	C₃²	1	2	yes	complemented
92	C₃×C₁₉×H(3,𝔽₃)	C₃²	1	1	yes	characteristic
93	C₃²×C₉×C₁₉	C₃²	1	1	yes	characteristic, complemented
94	C₁₉×C₃²⋊C₉	C₃²	1	1	yes	characteristic
95	C₁₉×C₃²⋊C₉	C₃²	1	1	yes	characteristic
96	C₁₉×C₃²⋊C₉	C₃²	1	2	yes	complemented
97	C₁₉×C₃²⋊C₉	C₃²	1	2	yes	complemented
98	C₁₉×C₃²⋊C₉	C₃²	1	2	yes	complemented
99	#10624888	—	19	1	no	maximal, Sylow
100	C₃³×C₁₉	C₃³	1	1	yes	characteristic
101	C₃³×C₁₉	C₃³	1	1	yes	characteristic
102	C₃³×C₁₉	C₃³	1	2	yes	—
103	C₃²×C₁₉⋊C₃	—	3	3	no	—
104	C₃²×C₁₉⋊C₃	—	9	1	no	—
105	C₃²×C₁₉⋊C₃	—	9	1	no	—
106	C₃²×C₁₉⋊C₃	—	9	1	no	—
107	C₃²×C₁₉⋊C₃	C₃³	1	1	yes	characteristic
108	C₃²×C₁₉⋊C₃	C₃³	1	1	yes	characteristic
109	C₃²×C₁₉⋊C₃	C₃³	1	2	yes	—
110	C₃²×C₁₉⋊C₃	C₃³	1	2	yes	—
111	C₃²×C₁₉⋊C₃	C₃³	1	2	yes	—
112	C₃²×C₁₉⋊C₃	C₃³	1	1	yes	characteristic
113	C₁₉×3₋¹⁺²	—	9	1	no	—
114	C₁₉×3₋¹⁺²	—	9	2	no	—
115	C₁₉×H(3,𝔽₃)	—	9	1	no	—
116	C₃×C₉×C₁₉	—	9	1	no	—
117	C₃×C₉×C₁₉	C₃³	1	1	yes	characteristic
118	C₃×C₉×C₁₉	C₃³	1	1	yes	characteristic
119	C₃×C₉×C₁₉	C₃³	1	2	yes	—
120	C₃×C₉×C₁₉	C₃³	1	2	yes	—
121	C₃×C₉×C₁₉	C₃³	1	2	yes	—
122	C₃×C₉×C₁₉	C₃³	1	1	yes	characteristic
123	C₃²⋊(C₁₉⋊C₃)	—	3	6	no	—
124	C₃²⋊(C₁₉⋊C₃)	—	3	3	no	—
125	C₃²⋊(C₁₉⋊C₃)	—	9	2	no	—
126	C₃²⋊(C₁₉⋊C₃)	—	9	1	no	—
127	C₃²⋊(C₁₉⋊C₃)	—	9	2	no	—
128	C₃²⋊(C₁₉⋊C₃)	—	9	1	no	—
129	C₃²⋊(C₁₉⋊C₃)	—	9	2	no	—
130	#10587025	—	9	2	no	—
131	#10587025	—	9	2	no	—
132	#10587025	—	9	2	no	—
133	C₃×#4294	—	9	2	no	—
134	C₃×#4294	C₃³	1	2	yes	—
135	C₃×#4294	C₃³	1	2	yes	—
136	C₃×#4294	C₃³	1	2	yes	—
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	#10587023	—	9	2	no	—
144	#10587023	—	9	1	no	—
145	#10587023	—	9	2	no	—
146	#10587023	—	9	2	no	—
147	#10587023	—	9	2	no	—
148	#10587022	—	9	2	no	—
149	#10587022	—	9	2	no	—
150	#10587022	—	9	2	no	—
151	C₉×C₁₉⋊C₃	—	9	1	no	—
152	C₉×C₁₉⋊C₃	—	9	2	no	—
153	C₉×C₁₉⋊C₃	—	9	2	no	—
154	C₉×C₁₉⋊C₃	—	9	2	no	—
155	C₉×C₁₉⋊C₃	—	9	2	no	—
156	#6893	—	19	2	no	—
157	#6893	—	19	1	no	—
158	#6893	—	19	2	no	—
159	#6893	—	19	2	no	—
160	#6893	—	19	2	no	—
161	C₉⋊H(3,𝔽₃)	—	19	2	no	—
162	C₉⋊H(3,𝔽₃)	—	19	2	no	—
163	C₉⋊H(3,𝔽₃)	—	19	2	no	—
164	C₉⋊H(3,𝔽₃)	—	19	2	no	—
165	C₉⋊H(3,𝔽₃)	—	19	1	no	—
166	C₉⋊H(3,𝔽₃)	—	19	2	no	—
167	C₉⋊H(3,𝔽₃)	—	19	2	no	—
168	C₉⋊H(3,𝔽₃)	—	19	2	no	—
169	C₉⋊H(3,𝔽₃)	—	19	2	no	—
170	C₉⋊H(3,𝔽₃)	—	19	2	no	—
171	C₉⋊H(3,𝔽₃)	—	19	2	no	—
172	C₉⋊H(3,𝔽₃)	—	19	2	no	—
173	C₉⋊H(3,𝔽₃)	C₁₉⋊C₃	1	1	yes	characteristic, complemented
174	#6891	—	19	1	no	—
175	#6891	—	19	1	no	—
176	C₃²⋊H(3,𝔽₃)	—	19	1	no	—
177	C₉×H(3,𝔽₃)	—	19	1	no	—
178	C₉×H(3,𝔽₃)	—	19	2	no	—
179	C₃×C₃²⋊C₉	—	19	1	no	—
180	C₃²×C₁₉	—	3	1	no	—
181	C₃²×C₁₉	—	3	2	no	—
182	C₃²×C₁₉	—	3	1	no	—
183	C₃²×C₁₉	—	3	2	no	—
184	C₃²×C₁₉	—	3	1	no	—
185	C₃²×C₁₉	—	3	1	no	—
186	C₃²×C₁₉	—	3	1	no	—
187	C₃²×C₁₉	—	3	1	no	—
188	C₃²×C₁₉	—	3	2	no	—
189	C₃²×C₁₉	—	3	1	no	—
190	C₃²×C₁₉	—	3	2	no	—
191	C₃²×C₁₉	—	3	1	no	—
192	C₃²×C₁₉	C₃⁴	1	1	yes	characteristic
193	C₃×C₁₉⋊C₃	—	3	1	no	—
194	C₃×C₁₉⋊C₃	—	3	1	no	—
195	C₃×C₁₉⋊C₃	—	3	1	no	—
196	C₃×C₁₉⋊C₃	—	3	2	no	—
197	C₃×C₁₉⋊C₃	—	3	2	no	—
198	C₃×C₁₉⋊C₃	—	3	2	no	—
199	C₃×C₁₉⋊C₃	—	3	1	no	—
200	C₃×C₁₉⋊C₃	—	3	1	no	—
201	C₃×C₁₉⋊C₃	—	3	2	no	—
202	C₃×C₁₉⋊C₃	—	3	2	no	—
203	C₃×C₁₉⋊C₃	—	3	2	no	—
204	C₃×C₁₉⋊C₃	—	3	1	no	—
205	C₃×C₁₉⋊C₃	—	3	1	no	—
206	C₃×C₁₉⋊C₃	—	3	1	no	—
207	C₃×C₁₉⋊C₃	—	3	2	no	—
208	C₃×C₁₉⋊C₃	—	3	2	no	—
209	C₃×C₁₉⋊C₃	—	3	2	no	—
210	C₃×C₁₉⋊C₃	—	3	2	no	—
211	C₃×C₁₉⋊C₃	—	3	2	no	—
212	C₃×C₁₉⋊C₃	—	3	2	no	—
213	C₃×C₁₉⋊C₃	—	3	1	no	—
214	C₃×C₁₉⋊C₃	—	3	1	no	—
215	C₃×C₁₉⋊C₃	—	3	1	no	—
216	C₃×C₁₉⋊C₃	—	9	9	no	—
217	C₃×C₁₉⋊C₃	#737	1	3	yes	—
218	C₉×C₁₉	—	3	1	no	—
219	C₉×C₁₉	—	3	2	no	—
220	C₉×C₁₉	—	3	2	no	—
221	C₉×C₁₉	—	3	2	no	—
222	C₉×C₁₉	—	3	1	no	—
223	C₉×C₁₉	—	3	1	no	—
224	#4294	—	3	2	no	—
225	#4294	—	3	2	no	—
226	#4294	—	3	2	no	—
227	#4294	—	3	2	no	—
228	#4294	—	3	2	no	—
229	#4294	—	3	2	no	—
230	#4294	—	3	2	no	—
231	#4294	—	3	2	no	—
232	#4294	—	3	2	no	—
233	C₃⁴	—	19	1	no	—
234	C₃×3₋¹⁺²	—	19	2	no	—
235	C₃×3₋¹⁺²	—	19	2	no	—
236	C₃×3₋¹⁺²	—	19	2	no	—
237	C₃×3₋¹⁺²	—	19	2	no	—
238	C₃×3₋¹⁺²	—	19	1	no	—
239	C₃×3₋¹⁺²	—	19	2	no	—
240	C₃×3₋¹⁺²	—	19	2	no	—
241	C₃×3₋¹⁺²	—	19	2	no	—
242	C₃×3₋¹⁺²	—	19	2	no	—
243	C₃×3₋¹⁺²	—	19	2	no	—
244	C₃×3₋¹⁺²	—	19	2	no	—
245	C₃×3₋¹⁺²	C₃×C₁₉⋊C₃	1	1	yes	characteristic
246	C₃×3₋¹⁺²	C₃×C₁₉⋊C₃	1	2	yes	complemented
247	C₃×H(3,𝔽₃)	—	19	2	no	—
248	C₃×H(3,𝔽₃)	—	19	1	no	—
249	C₃×H(3,𝔽₃)	—	19	2	no	—
250	C₃×H(3,𝔽₃)	—	19	2	no	—
251	C₃×H(3,𝔽₃)	—	19	1	no	—
252	C₃×H(3,𝔽₃)	—	19	2	no	—
253	C₃×H(3,𝔽₃)	—	19	1	no	—
254	C₃×H(3,𝔽₃)	C₃×C₁₉⋊C₃	1	1	yes	characteristic
255	C₃²×C₉	—	19	2	no	—
256	C₃²×C₉	—	19	1	no	—
257	C₃²×C₉	—	19	2	no	—
258	C₃²×C₉	—	19	2	no	—
259	C₃²×C₉	—	19	2	no	—
260	C₃²×C₉	—	19	2	no	—
261	C₃²×C₉	C₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented
262	C₃²⋊C₉	—	19	2	no	—
263	C₃²⋊C₉	—	19	2	no	—
264	C₃²⋊C₉	—	19	2	no	—
265	C₃²⋊C₉	—	19	2	no	—
266	C₃²⋊C₉	—	19	2	no	—
267	C₃²⋊C₉	—	19	2	no	—
268	C₃²⋊C₉	—	19	2	no	—
269	C₃²⋊C₉	—	19	2	no	—
270	C₃²⋊C₉	—	19	2	no	—
271	C₃²⋊C₉	—	19	1	no	—
272	C₃²⋊C₉	—	19	2	no	—
273	C₃²⋊C₉	—	19	1	no	—
274	C₃²⋊C₉	—	19	1	no	—
275	C₃²⋊C₉	—	19	2	no	—
276	C₃²⋊C₉	—	19	1	no	—
277	C₃²⋊C₉	—	19	2	no	—
278	C₃²⋊C₉	—	19	1	no	—
279	C₃²⋊C₉	—	19	2	no	—
280	C₃²⋊C₉	—	19	1	no	—
281	C₃²⋊C₉	—	19	2	no	—
282	C₃²⋊C₉	—	19	1	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	2	no	—
293	C₃²⋊C₉	—	19	2	no	—
294	C₃²⋊C₉	—	19	2	no	—
295	C₃²⋊C₉	—	19	2	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	C₃×C₁₉⋊C₃	1	1	yes	characteristic
303	C₃²⋊C₉	C₃×C₁₉⋊C₃	1	1	yes	characteristic
304	C₃²⋊C₉	C₃×C₁₉⋊C₃	1	2	yes	complemented
305	C₃²⋊C₉	C₃×C₁₉⋊C₃	1	2	yes	complemented
306	C₃²⋊C₉	C₃×C₁₉⋊C₃	1	2	yes	complemented
307	C₃×C₁₉	—	9	1	no	—
308	C₃×C₁₉	—	9	2	no	—
309	C₃×C₁₉	—	9	1	no	—
310	C₃×C₁₉	C₃×#737	1	1	yes	characteristic
311	C₃×C₁₉	H(5,𝔽₃)	1	1	yes	characteristic
312	C₃×C₁₉	3₋¹⁺⁴	1	1	yes	characteristic
313	C₃×C₁₉	3₋¹⁺⁴	1	1	yes	characteristic
314	C₁₉⋊C₃	—	3	3	no	—
315	C₁₉⋊C₃	—	9	2	no	—
316	C₁₉⋊C₃	—	9	2	no	—
317	C₁₉⋊C₃	—	9	2	no	—
318	C₁₉⋊C₃	—	9	1	no	—
319	C₁₉⋊C₃	—	9	1	no	—
320	C₃³	—	19	1	no	—
321	C₃³	—	19	1	no	—
322	C₃³	—	19	2	no	—
323	C₃³	—	19	2	no	—
324	C₃³	—	19	2	no	—
325	C₃³	—	19	1	no	—
326	C₃³	—	57	3	no	—
327	C₃³	—	171	1	no	—
328	C₃³	—	171	1	no	—
329	C₃³	—	171	1	no	—
330	C₃³	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
331	C₃³	C₃²×C₁₉⋊C₃	1	2	yes	—
332	C₃³	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
333	3₋¹⁺²	—	9	1	no	—
334	3₋¹⁺²	—	9	2	no	—
335	3₋¹⁺²	—	171	2	no	—
336	3₋¹⁺²	—	171	2	no	—
337	3₋¹⁺²	—	171	2	no	—
338	3₋¹⁺²	—	171	2	no	—
339	3₋¹⁺²	—	171	1	no	—
340	3₋¹⁺²	—	171	2	no	—
341	3₋¹⁺²	—	171	2	no	—
342	3₋¹⁺²	—	171	2	no	—
343	3₋¹⁺²	—	171	2	no	—
344	3₋¹⁺²	—	171	2	no	—
345	3₋¹⁺²	—	171	2	no	—
346	H(3,𝔽₃)	—	9	1	no	—
347	H(3,𝔽₃)	—	57	6	no	—
348	H(3,𝔽₃)	—	57	3	no	—
349	H(3,𝔽₃)	—	171	1	no	—
350	H(3,𝔽₃)	—	171	2	no	—
351	H(3,𝔽₃)	—	171	2	no	—
352	H(3,𝔽₃)	—	171	1	no	—
353	H(3,𝔽₃)	—	171	2	no	—
354	C₃×C₉	—	9	1	no	—
355	C₃×C₉	—	19	2	no	—
356	C₃×C₉	—	19	2	no	—
357	C₃×C₉	—	19	2	no	—
358	C₃×C₉	—	19	2	no	—
359	C₃×C₉	—	19	2	no	—
360	C₃×C₉	—	19	2	no	—
361	C₃×C₉	—	19	2	no	—
362	C₃×C₉	—	19	2	no	—
363	C₃×C₉	—	19	2	no	—
364	C₃×C₉	—	171	1	no	—
365	C₃×C₉	—	171	2	no	—
366	C₃×C₉	—	171	2	no	—
367	C₃×C₉	—	171	2	no	—
368	C₃×C₉	—	171	2	no	—
369	C₃×C₉	—	171	2	no	—
370	C₃×C₉	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
371	C₃×C₉	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
372	C₃×C₉	C₃²×C₁₉⋊C₃	1	2	yes	—
373	C₃×C₉	C₃²×C₁₉⋊C₃	1	2	yes	—
374	C₃×C₉	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
375	C₃×C₉	C₃²×C₁₉⋊C₃	1	2	yes	—
376	C₁₉	#10624888	1	1	yes	characteristic, complemented, Sylow
377	C₃²	—	3	2	no	—
378	C₃²	—	3	1	no	—
379	C₃²	—	3	1	no	—
380	C₃²	—	3	1	no	—
381	C₃²	—	3	2	no	—
382	C₃²	—	3	1	no	—
383	C₃²	—	3	2	no	—
384	C₃²	—	3	1	no	—
385	C₃²	—	3	1	no	—
386	C₃²	—	3	1	no	—
387	C₃²	—	3	2	no	—
388	C₃²	—	3	1	no	—
389	C₃²	—	19	3	no	—
390	C₃²	—	57	1	no	—
391	C₃²	—	57	1	no	—
392	C₃²	—	57	1	no	—
393	C₃²	—	57	2	no	—
394	C₃²	—	57	2	no	—
395	C₃²	—	57	2	no	—
396	C₃²	—	57	1	no	—
397	C₃²	—	57	1	no	—
398	C₃²	—	57	2	no	—
399	C₃²	—	57	2	no	—
400	C₃²	—	57	2	no	—
401	C₃²	—	57	1	no	—
402	C₃²	—	57	1	no	—
403	C₃²	—	57	1	no	—
404	C₃²	—	57	2	no	—
405	C₃²	—	57	2	no	—
406	C₃²	—	57	2	no	—
407	C₃²	—	57	1	no	—
408	C₃²	—	57	2	no	—
409	C₃²	—	57	2	no	—
410	C₃²	—	57	2	no	—
411	C₃²	—	57	1	no	—
412	C₃²	—	57	1	no	—
413	C₃²	—	171	9	no	—
414	C₃²	C₃³×C₁₉⋊C₃	1	1	yes	characteristic
415	C₉	—	3	1	no	—
416	C₉	—	3	1	no	—
417	C₉	—	3	1	no	—
418	C₉	—	3	2	no	—
419	C₉	—	3	2	no	—
420	C₉	—	3	2	no	—
421	C₉	—	57	2	no	—
422	C₉	—	57	2	no	—
423	C₉	—	57	2	no	—
424	C₉	—	57	2	no	—
425	C₉	—	57	2	no	—
426	C₉	—	57	2	no	—
427	C₉	—	57	2	no	—
428	C₉	—	57	2	no	—
429	C₉	—	57	2	no	—
430	C₃	—	9	1	no	—
431	C₃	—	9	1	no	—
432	C₃	—	9	2	no	—
433	C₃	—	57	3	no	—
434	C₃	—	171	1	no	—
435	C₃	—	171	1	no	—
436	C₃	—	171	2	no	—
437	C₃	—	171	2	no	—
438	C₃	—	171	2	no	—
439	C₃	C₁₉⋊C₃×#737	1	1	yes	characteristic
440	C₃	C₁₉⋊H(5,𝔽₃)	1	1	yes	characteristic
441	C₃	#17987544	1	1	yes	characteristic
442	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	#10624888
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. #17987432	C₃	semidirect
2. #17987431	C₃	semidirect
3. #17987430	C₃	semidirect
4. #17987430	C₃	semidirect
5. #17987430	C₃	semidirect
6. #17987427	C₃	semidirect
7. #17987426	C₃	semidirect
8. #17987424	C₃	semidirect
9. #17987424	C₃	semidirect
10. #17987424	C₃	semidirect
11. #17987424	C₃	semidirect
12. #17987424	C₃	semidirect
13. #17987424	C₃	semidirect
14. #17987423	C₃	semidirect
15. #17987422	C₃	semidirect
16. #17987422	C₃	semidirect
17. #17987422	C₃	semidirect
18. #17987419	C₃	semidirect
19. #17987418	C₃	semidirect
21. C₉×C₃²⋊(C₁₉⋊C₃)	C₃	semidirect
22. #17987406	C₃	semidirect
23. C₁₉⋊C₃×C₃²⋊C₉	C₃	semidirect
24. C₁₉×C₉⋊H(3,𝔽₃)	C₃	semidirect
27. C₃×#10587025	C₃²	semidirect
28. C₃×#10587025	C₃²	semidirect
29. C₃×#10587022	C₃²	semidirect
30. C₃×#10587022	C₃²	semidirect
31. C₃×#10587022	C₃²	semidirect
34. C₃×#10587023	C₃²	semidirect
35. C₃×#10587023	C₃²	semidirect
36. C₃×#10587023	C₃²	semidirect
44. C₃²×#4294	C₃²	semidirect
47. C₃×C₉×C₁₉⋊C₃	C₃²	semidirect
48. C₃×C₉×C₁₉⋊C₃	C₃²	semidirect
49. C₃×C₉×C₁₉⋊C₃	C₃²	semidirect
52. C₃²⋊#4294	C₃²	semidirect
53. C₃²⋊#4294	C₃²	semidirect
54. C₃²⋊#4294	C₃²	semidirect
55. C₃²⋊#4294	C₃²	semidirect
56. C₃²⋊#4294	C₃²	semidirect
57. C₃²⋊#4294	C₃²	semidirect
72. #13095303	C₃²	semidirect
73. #13095303	C₃²	semidirect
74. #13095303	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
91. C₃×C₁₉×3₋¹⁺²	C₃²	semidirect
93. C₃²×C₉×C₁₉	C₃²	semidirect
96. C₁₉×C₃²⋊C₉	C₃²	semidirect
97. C₁₉×C₃²⋊C₉	C₃²	semidirect
98. C₁₉×C₃²⋊C₉	C₃²	semidirect
173. C₉⋊H(3,𝔽₃)	C₁₉⋊C₃	semidirect
246. C₃×3₋¹⁺²	C₃×C₁₉⋊C₃	semidirect
261. C₃²×C₉	C₃×C₁₉⋊C₃	semidirect
304. C₃²⋊C₉	C₃×C₁₉⋊C₃	semidirect
305. C₃²⋊C₉	C₃×C₁₉⋊C₃	semidirect
306. C₃²⋊C₉	C₃×C₁₉⋊C₃	semidirect
376. C₁₉	#10624888	semidirect

Maximal subgroups

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

subgroup	index
#17987432	3
#17987431	3
#17987430	3
#17987427	3
#17987426	3
#17987424	3
#17987423	3
#17987422	3
#17987419	3
#17987418	3
(C₃×C₁₉⋊C₃)⋊H(3,𝔽₃)	3
C₉×C₃²⋊(C₁₉⋊C₃)	3
#17987406	3
C₁₉⋊C₃×C₃²⋊C₉	3
C₁₉×C₉⋊H(3,𝔽₃)	3
#10624888	19