Subgroups — #28356110

Order 13851.

764 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17987432	C₃	1	3	yes	maximal, complemented
2	#17987430	C₃	1	3	yes	maximal, complemented
3	#17987430	C₃	1	3	yes	maximal, complemented
4	#17987428	C₃	1	1	yes	maximal, characteristic, complemented
5	#17987428	C₃	1	3	yes	maximal, complemented
6	#17987427	C₃	1	1	yes	maximal, characteristic, complemented
7	#17987427	C₃	1	3	yes	maximal, complemented
8	#17987426	C₃	1	1	yes	maximal, characteristic, complemented
9	#17987425	C₃	1	1	yes	maximal, characteristic, complemented
10	#17987424	C₃	1	3	yes	maximal, complemented
11	#17987424	C₃	1	3	yes	maximal, complemented
12	#17987423	C₃	1	1	yes	maximal, characteristic, complemented
13	#17987422	C₃	1	3	yes	maximal, complemented
14	#17987422	C₃	1	3	yes	maximal, complemented
15	#17987420	C₃	1	1	yes	maximal, characteristic, complemented
16	#17987419	C₃	1	1	yes	maximal, characteristic, complemented
17	(C₃×C₁₉⋊C₃)⋊H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
18	H(3,𝔽₃)×#4294	C₃	1	1	yes	maximal, characteristic, complemented
19	#17987406	C₃	1	1	yes	maximal, characteristic, complemented
20	#17987406	C₃	1	1	yes	maximal, characteristic, complemented
21	C₃×#13095303	C₃	1	1	yes	maximal, characteristic, complemented
22	C₁₉×C₉⋊H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic, complemented
23	C₃³×C₁₉⋊C₃	C₃²	1	1	yes	characteristic
24	C₃×#10587025	C₃²	1	3	yes	complemented
25	C₃×#10587022	C₃²	1	3	yes	—
26	C₃×#10587022	C₃²	1	3	yes	complemented
27	C₃×#10587022	C₃²	1	3	yes	complemented
28	C₃×#10587023	C₃²	1	3	yes	—
29	C₃×#10587023	C₃²	1	3	yes	complemented
30	C₃×#10587023	C₃²	1	3	yes	complemented
31	C₃×C₃²⋊(C₁₉⋊C₃)	C₃²	1	1	yes	characteristic
32	C₃×C₃²⋊(C₁₉⋊C₃)	C₃²	1	1	yes	characteristic
33	C₃×C₃²⋊(C₁₉⋊C₃)	C₃²	1	3	yes	—
34	C₃×C₃²⋊(C₁₉⋊C₃)	C₃²	1	3	yes	—
35	C₃×C₃²⋊(C₁₉⋊C₃)	C₃²	1	3	yes	—
36	C₃²×#4294	C₃²	1	1	yes	characteristic
37	C₃²×#4294	C₃²	1	1	yes	characteristic
38	C₃²×#4294	C₃²	1	3	yes	complemented
39	C₃×C₉×C₁₉⋊C₃	C₃²	1	3	yes	complemented
40	C₃×C₉×C₁₉⋊C₃	C₃²	1	3	yes	complemented
41	C₃²⋊#4294	C₃²	1	1	yes	characteristic
42	C₃²⋊#4294	C₃²	1	1	yes	characteristic
43	C₃²⋊#4294	C₃²	1	1	yes	characteristic
44	C₃²⋊#4294	C₃²	1	1	yes	characteristic
45	C₃²⋊#4294	C₃²	1	3	yes	complemented
46	C₃²⋊#4294	C₃²	1	3	yes	complemented
47	C₃²⋊#4294	C₃²	1	3	yes	complemented
48	C₃²⋊#4294	C₃²	1	3	yes	complemented
49	#13095303	C₃²	1	1	yes	characteristic
50	#13095303	C₃²	1	1	yes	characteristic
51	#13095303	C₃²	1	1	yes	characteristic
52	#13095303	C₃²	1	1	yes	characteristic
53	#13095303	C₃²	1	1	yes	characteristic
54	#13095303	C₃²	1	1	yes	characteristic
55	#13095303	C₃²	1	1	yes	characteristic
56	#13095303	C₃²	1	1	yes	characteristic
57	#13095303	C₃²	1	1	yes	characteristic
58	#13095303	C₃²	1	3	yes	—
59	#13095303	C₃²	1	3	yes	—
60	#13095303	C₃²	1	3	yes	—
61	#13095303	C₃²	1	3	yes	—
62	#13095303	C₃²	1	3	yes	complemented
63	#13095303	C₃²	1	3	yes	complemented
64	#13095303	C₃²	1	3	yes	complemented
65	#13095303	C₃²	1	3	yes	complemented
66	#13095303	C₃²	1	3	yes	complemented
67	#13095303	C₃²	1	3	yes	complemented
68	#13095303	C₃²	1	3	yes	complemented
69	#13095303	C₃²	1	3	yes	complemented
70	#13095303	C₃²	1	3	yes	complemented
71	#13095303	C₃²	1	3	yes	complemented
72	#13095303	C₃²	1	3	yes	complemented
73	#13095303	C₃²	1	3	yes	complemented
74	C₃×C₁₉×3₋¹⁺²	C₃²	1	3	yes	complemented
75	C₃×C₁₉×H(3,𝔽₃)	C₃²	1	1	yes	characteristic
76	C₃²×C₉×C₁₉	C₃²	1	1	yes	characteristic
77	C₁₉×C₃²⋊C₉	C₃²	1	1	yes	characteristic
78	C₁₉×C₃²⋊C₉	C₃²	1	1	yes	characteristic
79	C₁₉×C₃²⋊C₉	C₃²	1	3	yes	complemented
80	C₁₉×C₃²⋊C₉	C₃²	1	3	yes	complemented
81	#10624888	—	19	1	no	maximal, Sylow
82	C₃³×C₁₉	C₃³	1	3	yes	—
83	C₃³×C₁₉	C₃³	1	1	yes	characteristic
84	C₃²×C₁₉⋊C₃	—	3	3	no	—
85	C₃²×C₁₉⋊C₃	—	9	1	no	—
86	C₃²×C₁₉⋊C₃	—	9	1	no	—
87	C₃²×C₁₉⋊C₃	—	9	1	no	—
88	C₃²×C₁₉⋊C₃	C₃³	1	1	yes	characteristic
89	C₃²×C₁₉⋊C₃	C₃³	1	1	yes	characteristic
90	C₃²×C₁₉⋊C₃	C₃³	1	1	yes	characteristic
91	C₃²×C₁₉⋊C₃	C₃³	1	3	yes	—
92	C₃²×C₁₉⋊C₃	C₃³	1	3	yes	—
93	C₁₉×3₋¹⁺²	—	9	3	no	—
94	C₁₉×H(3,𝔽₃)	—	3	3	no	—
95	C₃×C₉×C₁₉	—	9	1	no	—
96	C₃×C₉×C₁₉	C₃³	1	3	yes	—
97	C₃×C₉×C₁₉	C₃³	1	3	yes	—
98	C₃×C₉×C₁₉	C₃³	1	1	yes	characteristic
99	C₃×C₉×C₁₉	C₃³	1	1	yes	characteristic
100	C₃×C₉×C₁₉	C₃³	1	1	yes	characteristic
101	C₃²⋊(C₁₉⋊C₃)	—	3	3	no	—
102	C₃²⋊(C₁₉⋊C₃)	—	3	3	no	—
103	C₃²⋊(C₁₉⋊C₃)	—	9	3	no	—
104	C₃²⋊(C₁₉⋊C₃)	—	9	3	no	—
105	C₃²⋊(C₁₉⋊C₃)	—	9	3	no	—
106	#10587025	—	9	3	no	—
107	C₃×#4294	—	9	1	no	—
108	C₃×#4294	—	9	1	no	—
109	C₃×#4294	—	9	3	no	—
110	C₃×#4294	C₃³	1	1	yes	characteristic
111	C₃×#4294	C₃³	1	1	yes	characteristic
112	C₃×#4294	C₃³	1	1	yes	characteristic
113	C₃×#4294	C₃³	1	1	yes	characteristic
114	C₃×#4294	C₃³	1	1	yes	characteristic
115	C₃×#4294	C₃³	1	1	yes	characteristic
116	C₃×#4294	C₃³	1	3	yes	—
117	C₃×#4294	C₃³	1	3	yes	—
118	C₃×#4294	C₃³	1	3	yes	—
119	C₃×#4294	C₃³	1	3	yes	—
120	#10587023	—	9	3	no	—
121	#10587023	—	9	3	no	—
122	#10587023	—	9	3	no	—
123	#10587022	—	9	3	no	—
124	#10587022	—	9	3	no	—
125	#10587022	—	9	3	no	—
126	C₉×C₁₉⋊C₃	—	9	3	no	—
127	C₉×C₁₉⋊C₃	—	9	3	no	—
128	#6893	—	19	3	no	—
129	#6893	—	19	3	no	—
130	#6893	—	19	3	no	—
131	C₉⋊H(3,𝔽₃)	—	19	3	no	—
132	C₉⋊H(3,𝔽₃)	—	19	3	no	—
133	C₉⋊H(3,𝔽₃)	—	19	1	no	—
134	C₉⋊H(3,𝔽₃)	—	19	1	no	—
135	C₉⋊H(3,𝔽₃)	—	19	1	no	—
136	C₉⋊H(3,𝔽₃)	—	19	1	no	—
137	C₉⋊H(3,𝔽₃)	—	19	1	no	—
138	C₉⋊H(3,𝔽₃)	—	19	3	no	—
139	C₉⋊H(3,𝔽₃)	—	19	3	no	—
140	C₉⋊H(3,𝔽₃)	—	19	3	no	—
141	C₉⋊H(3,𝔽₃)	—	19	3	no	—
142	C₉⋊H(3,𝔽₃)	C₁₉⋊C₃	1	1	yes	characteristic, complemented
143	#6891	—	19	1	no	—
144	#6891	—	19	1	no	—
145	C₃²⋊H(3,𝔽₃)	—	19	1	no	—
146	C₉×H(3,𝔽₃)	—	19	1	no	—
147	C₉×H(3,𝔽₃)	—	19	1	no	—
148	C₉×H(3,𝔽₃)	—	19	1	no	—
149	C₃×C₃²⋊C₉	—	19	1	no	—
150	C₃²×C₁₉	—	3	1	no	—
151	C₃²×C₁₉	—	3	1	no	—
152	C₃²×C₁₉	—	3	1	no	—
153	C₃²×C₁₉	—	3	3	no	—
154	C₃²×C₁₉	—	3	3	no	—
155	C₃²×C₁₉	—	3	3	no	—
156	C₃²×C₁₉	—	3	3	no	—
157	C₃²×C₁₉	#737	1	3	yes	—
158	C₃²×C₁₉	C₃⁴	1	1	yes	characteristic
159	C₃×C₁₉⋊C₃	—	3	3	no	—
160	C₃×C₁₉⋊C₃	—	3	3	no	—
161	C₃×C₁₉⋊C₃	—	3	1	no	—
162	C₃×C₁₉⋊C₃	—	3	1	no	—
163	C₃×C₁₉⋊C₃	—	3	1	no	—
164	C₃×C₁₉⋊C₃	—	3	3	no	—
165	C₃×C₁₉⋊C₃	—	3	3	no	—
166	C₃×C₁₉⋊C₃	—	3	1	no	—
167	C₃×C₁₉⋊C₃	—	3	1	no	—
168	C₃×C₁₉⋊C₃	—	3	1	no	—
169	C₃×C₁₉⋊C₃	—	3	1	no	—
170	C₃×C₁₉⋊C₃	—	3	1	no	—
171	C₃×C₁₉⋊C₃	—	3	3	no	—
172	C₃×C₁₉⋊C₃	—	3	3	no	—
173	C₃×C₁₉⋊C₃	—	3	3	no	—
174	C₃×C₁₉⋊C₃	—	3	3	no	—
175	C₃×C₁₉⋊C₃	—	3	1	no	—
176	C₃×C₁₉⋊C₃	—	3	1	no	—
177	C₃×C₁₉⋊C₃	—	3	1	no	—
178	C₃×C₁₉⋊C₃	—	3	1	no	—
179	C₃×C₁₉⋊C₃	—	9	9	no	—
180	C₉×C₁₉	—	3	3	no	—
181	C₉×C₁₉	—	3	3	no	—
182	C₉×C₁₉	—	3	1	no	—
183	C₉×C₁₉	—	3	1	no	—
184	C₉×C₁₉	—	3	1	no	—
185	#4294	—	3	1	no	—
186	#4294	—	3	1	no	—
187	#4294	—	3	3	no	—
188	#4294	—	3	3	no	—
189	#4294	—	3	3	no	—
190	#4294	—	3	1	no	—
191	#4294	—	3	3	no	—
192	#4294	—	3	1	no	—
193	#4294	—	3	1	no	—
194	#4294	—	3	1	no	—
195	C₃⁴	—	19	1	no	—
196	C₃×3₋¹⁺²	—	19	3	no	—
197	C₃×3₋¹⁺²	—	19	3	no	—
198	C₃×3₋¹⁺²	—	19	3	no	—
199	C₃×3₋¹⁺²	—	19	3	no	—
200	C₃×3₋¹⁺²	—	19	3	no	—
201	C₃×3₋¹⁺²	—	19	3	no	—
202	C₃×3₋¹⁺²	—	19	3	no	—
203	C₃×3₋¹⁺²	C₃×C₁₉⋊C₃	1	3	yes	complemented
204	C₃×H(3,𝔽₃)	—	19	1	no	—
205	C₃×H(3,𝔽₃)	—	19	1	no	—
206	C₃×H(3,𝔽₃)	—	19	3	no	—
207	C₃×H(3,𝔽₃)	—	19	3	no	—
208	C₃×H(3,𝔽₃)	—	19	3	no	—
209	C₃×H(3,𝔽₃)	C₃×C₁₉⋊C₃	1	1	yes	characteristic
210	C₃²×C₉	—	19	1	no	—
211	C₃²×C₉	—	19	1	no	—
212	C₃²×C₉	—	19	3	no	—
213	C₃²×C₉	—	19	3	no	—
214	C₃²×C₉	—	19	3	no	—
215	C₃²×C₉	C₃×C₁₉⋊C₃	1	1	yes	characteristic
216	C₃²⋊C₉	—	19	1	no	—
217	C₃²⋊C₉	—	19	1	no	—
218	C₃²⋊C₉	—	19	1	no	—
219	C₃²⋊C₉	—	19	1	no	—
220	C₃²⋊C₉	—	19	3	no	—
221	C₃²⋊C₉	—	19	3	no	—
222	C₃²⋊C₉	—	19	3	no	—
223	C₃²⋊C₉	—	19	3	no	—
224	C₃²⋊C₉	—	19	1	no	—
225	C₃²⋊C₉	—	19	1	no	—
226	C₃²⋊C₉	—	19	1	no	—
227	C₃²⋊C₉	—	19	1	no	—
228	C₃²⋊C₉	—	19	1	no	—
229	C₃²⋊C₉	—	19	1	no	—
230	C₃²⋊C₉	—	19	1	no	—
231	C₃²⋊C₉	—	19	1	no	—
232	C₃²⋊C₉	—	19	1	no	—
233	C₃²⋊C₉	—	19	3	no	—
234	C₃²⋊C₉	—	19	3	no	—
235	C₃²⋊C₉	—	19	3	no	—
236	C₃²⋊C₉	—	19	3	no	—
237	C₃²⋊C₉	—	19	3	no	—
238	C₃²⋊C₉	—	19	3	no	—
239	C₃²⋊C₉	—	19	3	no	—
240	C₃²⋊C₉	—	19	3	no	—
241	C₃²⋊C₉	—	19	3	no	—
242	C₃²⋊C₉	—	19	3	no	—
243	C₃²⋊C₉	—	19	3	no	—
244	C₃²⋊C₉	—	19	3	no	—
245	C₃²⋊C₉	—	19	3	no	—
246	C₃²⋊C₉	—	19	3	no	—
247	C₃²⋊C₉	—	19	3	no	—
248	C₃²⋊C₉	—	19	3	no	—
249	C₃²⋊C₉	C₃×C₁₉⋊C₃	1	1	yes	characteristic
250	C₃²⋊C₉	C₃×C₁₉⋊C₃	1	1	yes	characteristic
251	C₃²⋊C₉	C₃×C₁₉⋊C₃	1	3	yes	complemented
252	C₃²⋊C₉	C₃×C₁₉⋊C₃	1	3	yes	complemented
253	C₃×C₁₉	—	3	3	no	—
254	C₃×C₁₉	—	9	3	no	—
255	C₃×C₁₉	C₃×#737	1	1	yes	characteristic
256	C₃×C₁₉	H(5,𝔽₃)	1	1	yes	characteristic
257	C₃×C₁₉	3₋¹⁺⁴	1	1	yes	characteristic
258	C₃×C₁₉	3₋¹⁺⁴	1	1	yes	characteristic
259	C₁₉⋊C₃	—	9	3	no	—
260	C₁₉⋊C₃	—	9	3	no	—
261	C₁₉⋊C₃	—	9	1	no	—
262	C₁₉⋊C₃	—	9	1	no	—
263	C₁₉⋊C₃	—	9	1	no	—
264	C₃³	—	19	1	no	—
265	C₃³	—	19	3	no	—
266	C₃³	—	19	3	no	—
267	C₃³	—	19	1	no	—
268	C₃³	—	19	1	no	—
269	C₃³	—	57	3	no	—
270	C₃³	—	171	1	no	—
271	C₃³	—	171	1	no	—
272	C₃³	—	171	1	no	—
273	C₃³	C₃²×C₁₉⋊C₃	1	3	yes	—
274	C₃³	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
275	3₋¹⁺²	—	9	3	no	—
276	3₋¹⁺²	—	171	3	no	—
277	3₋¹⁺²	—	171	3	no	—
278	3₋¹⁺²	—	171	3	no	—
279	3₋¹⁺²	—	171	3	no	—
280	3₋¹⁺²	—	171	3	no	—
281	3₋¹⁺²	—	171	3	no	—
282	3₋¹⁺²	—	171	3	no	—
283	H(3,𝔽₃)	—	3	3	no	—
284	H(3,𝔽₃)	—	57	3	no	—
285	H(3,𝔽₃)	—	57	3	no	—
286	H(3,𝔽₃)	—	171	3	no	—
287	H(3,𝔽₃)	—	171	3	no	—
288	H(3,𝔽₃)	—	171	3	no	—
289	C₃×C₉	—	9	1	no	—
290	C₃×C₉	—	19	1	no	—
291	C₃×C₉	—	19	1	no	—
292	C₃×C₉	—	19	1	no	—
293	C₃×C₉	—	19	1	no	—
294	C₃×C₉	—	19	1	no	—
295	C₃×C₉	—	19	1	no	—
296	C₃×C₉	—	19	3	no	—
297	C₃×C₉	—	19	3	no	—
298	C₃×C₉	—	19	3	no	—
299	C₃×C₉	—	19	3	no	—
300	C₃×C₉	—	171	3	no	—
301	C₃×C₉	—	171	3	no	—
302	C₃×C₉	—	171	1	no	—
303	C₃×C₉	—	171	3	no	—
304	C₃×C₉	—	171	1	no	—
305	C₃×C₉	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
306	C₃×C₉	C₃²×C₁₉⋊C₃	1	3	yes	—
307	C₃×C₉	C₃²×C₁₉⋊C₃	1	3	yes	—
308	C₃×C₉	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
309	C₃×C₉	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
310	C₁₉	#10624888	1	1	yes	characteristic, complemented, Sylow
311	C₃²	—	3	1	no	—
312	C₃²	—	3	1	no	—
313	C₃²	—	3	1	no	—
314	C₃²	—	3	3	no	—
315	C₃²	—	3	3	no	—
316	C₃²	—	3	3	no	—
317	C₃²	—	3	3	no	—
318	C₃²	—	57	3	no	—
319	C₃²	—	57	3	no	—
320	C₃²	—	57	1	no	—
321	C₃²	—	57	1	no	—
322	C₃²	—	57	1	no	—
323	C₃²	—	57	3	no	—
324	C₃²	—	57	3	no	—
325	C₃²	—	57	1	no	—
326	C₃²	—	57	1	no	—
327	C₃²	—	57	1	no	—
328	C₃²	—	57	1	no	—
329	C₃²	—	57	3	no	—
330	C₃²	—	57	3	no	—
331	C₃²	—	57	1	no	—
332	C₃²	—	57	1	no	—
333	C₃²	—	57	1	no	—
334	C₃²	—	57	3	no	—
335	C₃²	—	57	3	no	—
336	C₃²	—	57	1	no	—
337	C₃²	—	57	1	no	—
338	C₃²	—	171	9	no	—
339	C₃²	#13095333	1	3	yes	—
340	C₃²	C₃³×C₁₉⋊C₃	1	1	yes	characteristic
341	C₉	—	3	1	no	—
342	C₉	—	3	1	no	—
343	C₉	—	3	1	no	—
344	C₉	—	3	3	no	—
345	C₉	—	3	3	no	—
346	C₉	—	57	1	no	—
347	C₉	—	57	1	no	—
348	C₉	—	57	1	no	—
349	C₉	—	57	3	no	—
350	C₉	—	57	3	no	—
351	C₉	—	57	1	no	—
352	C₉	—	57	3	no	—
353	C₉	—	57	1	no	—
354	C₉	—	57	3	no	—
355	C₉	—	57	1	no	—
356	C₃	—	3	3	no	—
357	C₃	—	9	3	no	—
358	C₃	—	171	1	no	—
359	C₃	—	171	1	no	—
360	C₃	—	171	1	no	—
361	C₃	—	171	3	no	—
362	C₃	—	171	3	no	—
363	C₃	C₃×#13095333	1	1	yes	characteristic
364	C₃	C₁₉⋊H(5,𝔽₃)	1	1	yes	characteristic
365	C₃	#17987544	1	1	yes	characteristic
366	C₃	#17987545	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. #17987430	C₃	semidirect
3. #17987430	C₃	semidirect
4. #17987428	C₃	semidirect
5. #17987428	C₃	semidirect
6. #17987427	C₃	semidirect
7. #17987427	C₃	semidirect
8. #17987426	C₃	semidirect
9. #17987425	C₃	semidirect
10. #17987424	C₃	semidirect
11. #17987424	C₃	semidirect
12. #17987423	C₃	semidirect
13. #17987422	C₃	semidirect
14. #17987422	C₃	semidirect
15. #17987420	C₃	semidirect
16. #17987419	C₃	semidirect
18. H(3,𝔽₃)×#4294	C₃	semidirect
19. #17987406	C₃	semidirect
20. #17987406	C₃	semidirect
21. C₃×#13095303	C₃	semidirect
22. C₁₉×C₉⋊H(3,𝔽₃)	C₃	semidirect
24. C₃×#10587025	C₃²	semidirect
26. C₃×#10587022	C₃²	semidirect
27. C₃×#10587022	C₃²	semidirect
29. C₃×#10587023	C₃²	semidirect
30. C₃×#10587023	C₃²	semidirect
38. C₃²×#4294	C₃²	semidirect
39. C₃×C₉×C₁₉⋊C₃	C₃²	semidirect
40. C₃×C₉×C₁₉⋊C₃	C₃²	semidirect
45. C₃²⋊#4294	C₃²	semidirect
46. C₃²⋊#4294	C₃²	semidirect
47. C₃²⋊#4294	C₃²	semidirect
48. C₃²⋊#4294	C₃²	semidirect
62. #13095303	C₃²	semidirect
63. #13095303	C₃²	semidirect
64. #13095303	C₃²	semidirect
65. #13095303	C₃²	semidirect
66. #13095303	C₃²	semidirect
67. #13095303	C₃²	semidirect
68. #13095303	C₃²	semidirect
69. #13095303	C₃²	semidirect
70. #13095303	C₃²	semidirect
71. #13095303	C₃²	semidirect
72. #13095303	C₃²	semidirect
73. #13095303	C₃²	semidirect
74. C₃×C₁₉×3₋¹⁺²	C₃²	semidirect
79. C₁₉×C₃²⋊C₉	C₃²	semidirect
80. C₁₉×C₃²⋊C₉	C₃²	semidirect
142. C₉⋊H(3,𝔽₃)	C₁₉⋊C₃	semidirect
203. C₃×3₋¹⁺²	C₃×C₁₉⋊C₃	semidirect
251. C₃²⋊C₉	C₃×C₁₉⋊C₃	semidirect
252. C₃²⋊C₉	C₃×C₁₉⋊C₃	semidirect
310. 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
#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
H(3,𝔽₃)×#4294	3
#17987406	3
C₃×#13095303	3
C₁₉×C₉⋊H(3,𝔽₃)	3
#10624888	19