Subgroups — #28356093

Order 13851.

698 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#13095332	C₃	1	1	yes	maximal, characteristic
2	#17987472	C₃	1	1	yes	maximal, characteristic, complemented
3	#17987471	C₃	1	1	yes	maximal, characteristic, complemented
4	#17987468	C₃	1	1	yes	maximal, characteristic, complemented
5	#17987465	C₃	1	1	yes	maximal, characteristic, complemented
6	#17987465	C₃	1	1	yes	maximal, characteristic, complemented
7	#17987464	C₃	1	1	yes	maximal, characteristic, complemented
8	#17987464	C₃	1	1	yes	maximal, characteristic, complemented
9	#17987460	C₃	1	1	yes	maximal, characteristic, complemented
10	#17987460	C₃	1	1	yes	maximal, characteristic, complemented
11	#17987451	C₃	1	1	yes	maximal, characteristic, complemented
12	#17987450	C₃	1	1	yes	maximal, characteristic, complemented
13	#17987449	C₃	1	1	yes	maximal, characteristic, complemented
14	#17987449	C₃	1	1	yes	maximal, characteristic, complemented
15	#17987449	C₃	1	1	yes	maximal, characteristic, complemented
16	#17987449	C₃	1	1	yes	maximal, characteristic, complemented
17	#17987447	C₃	1	1	yes	maximal, characteristic, complemented
18	#17987446	C₃	1	1	yes	maximal, characteristic, complemented
19	#17987446	C₃	1	1	yes	maximal, characteristic, complemented
20	#17987439	C₃	1	1	yes	maximal, characteristic, complemented
21	#17987438	C₃	1	1	yes	maximal, characteristic, complemented
22	#17987437	C₃	1	1	yes	maximal, characteristic, complemented
23	#17987437	C₃	1	1	yes	maximal, characteristic, complemented
24	#17987436	C₃	1	1	yes	maximal, characteristic, complemented
25	#17987436	C₃	1	1	yes	maximal, characteristic, complemented
26	#17987434	C₃	1	1	yes	maximal, characteristic, complemented
27	#17987434	C₃	1	1	yes	maximal, characteristic, complemented
28	#17987434	C₃	1	1	yes	maximal, characteristic, complemented
29	#17987434	C₃	1	1	yes	maximal, characteristic, complemented
30	#17987433	C₃	1	1	yes	maximal, characteristic, complemented
31	#17987433	C₃	1	1	yes	maximal, characteristic, complemented
32	#17987433	C₃	1	1	yes	maximal, characteristic, complemented
33	#17987433	C₃	1	1	yes	maximal, characteristic, complemented
34	#17987424	C₃	1	1	yes	maximal, characteristic
35	#17987424	C₃	1	1	yes	maximal, characteristic
36	#17987422	C₃	1	1	yes	maximal, characteristic
37	#17987404	C₃	1	1	yes	maximal, characteristic, complemented
38	#17987404	C₃	1	1	yes	maximal, characteristic, complemented
39	C₁₉⋊C₃×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
40	C₁₉×#6894	C₃	1	1	yes	maximal, characteristic, complemented
41	#13095332	—	3	9	no	—
42	C₃×#10587025	C₃²	1	1	yes	characteristic
43	C₃×#10587025	C₃²	1	1	yes	characteristic
44	C₃×#10587025	C₃²	1	1	yes	characteristic
45	C₃×#10587025	C₃²	1	1	yes	characteristic
46	C₃×#10587022	C₃²	1	1	yes	characteristic
47	C₃×#10587022	C₃²	1	1	yes	characteristic
48	C₃×#10587022	C₃²	1	1	yes	characteristic
49	C₃×#10587022	C₃²	1	1	yes	characteristic
50	C₃×#10587022	C₃²	1	1	yes	characteristic
51	C₃×#10587022	C₃²	1	1	yes	characteristic
52	C₃×#10587023	C₃²	1	1	yes	characteristic
53	C₃×#10587023	C₃²	1	1	yes	characteristic
54	C₃×#10587023	C₃²	1	1	yes	characteristic
55	C₃×#10587023	C₃²	1	1	yes	characteristic
56	C₃×#10587023	C₃²	1	1	yes	characteristic
57	C₃×#10587023	C₃²	1	1	yes	characteristic
58	C₃×C₃²⋊(C₁₉⋊C₃)	C₃²	1	1	yes	characteristic
59	C₃×C₉×C₁₉⋊C₃	C₃²	1	1	yes	characteristic
60	C₃×C₉×C₁₉⋊C₃	C₃²	1	1	yes	characteristic
61	C₃×C₉×C₁₉⋊C₃	C₃²	1	1	yes	characteristic
62	C₃×C₉×C₁₉⋊C₃	C₃²	1	1	yes	characteristic
63	C₃×C₉×C₁₉⋊C₃	C₃²	1	1	yes	characteristic
64	C₃×C₉×C₁₉⋊C₃	C₃²	1	1	yes	characteristic
65	#13095307	C₃²	1	1	yes	characteristic
66	#13095307	C₃²	1	1	yes	characteristic
67	#13095307	C₃²	1	1	yes	characteristic
68	#13095307	C₃²	1	1	yes	characteristic
69	#13095307	C₃²	1	1	yes	characteristic
70	#13095307	C₃²	1	1	yes	characteristic
71	#13095307	C₃²	1	1	yes	characteristic
72	#13095307	C₃²	1	1	yes	characteristic
73	#13095307	C₃²	1	1	yes	characteristic
74	#13095306	C₃²	1	1	yes	characteristic
75	#13095306	C₃²	1	1	yes	characteristic
76	#13095306	C₃²	1	1	yes	characteristic
77	#13095306	C₃²	1	1	yes	characteristic
78	#13095306	C₃²	1	1	yes	characteristic
79	#13095306	C₃²	1	1	yes	characteristic
80	#13095306	C₃²	1	1	yes	characteristic
81	#13095306	C₃²	1	1	yes	characteristic
82	#13095306	C₃²	1	1	yes	characteristic
83	#13095305	C₃²	1	1	yes	characteristic
84	#13095305	C₃²	1	1	yes	characteristic
85	#13095305	C₃²	1	1	yes	characteristic
86	#13095305	C₃²	1	1	yes	characteristic
87	#13095305	C₃²	1	1	yes	characteristic
88	#13095305	C₃²	1	1	yes	characteristic
89	#13095305	C₃²	1	1	yes	characteristic
90	#13095305	C₃²	1	1	yes	characteristic
91	#13095305	C₃²	1	1	yes	characteristic
92	#13095305	C₃²	1	1	yes	characteristic
93	#13095305	C₃²	1	1	yes	characteristic
94	#13095305	C₃²	1	1	yes	characteristic
95	#13095305	C₃²	1	1	yes	characteristic
96	#13095305	C₃²	1	1	yes	characteristic
97	#13095305	C₃²	1	1	yes	characteristic
98	#13095305	C₃²	1	1	yes	characteristic
99	#13095305	C₃²	1	1	yes	characteristic
100	#13095305	C₃²	1	1	yes	characteristic
101	#13095305	C₃²	1	1	yes	characteristic
102	#13095305	C₃²	1	1	yes	characteristic
103	#13095305	C₃²	1	1	yes	characteristic
104	#13095305	C₃²	1	1	yes	characteristic
105	#13095305	C₃²	1	1	yes	characteristic
106	#13095305	C₃²	1	1	yes	characteristic
107	#13095305	C₃²	1	1	yes	characteristic
108	#13095305	C₃²	1	1	yes	characteristic
109	#13095305	C₃²	1	1	yes	characteristic
110	#13095305	C₃²	1	1	yes	characteristic
111	#13095305	C₃²	1	1	yes	characteristic
112	#13095305	C₃²	1	1	yes	characteristic
113	#13095305	C₃²	1	1	yes	characteristic
114	#13095305	C₃²	1	1	yes	characteristic
115	#13095305	C₃²	1	1	yes	characteristic
116	#13095305	C₃²	1	1	yes	characteristic
117	#13095305	C₃²	1	1	yes	characteristic
118	#13095305	C₃²	1	1	yes	characteristic
119	#13095305	C₃²	1	1	yes	characteristic
120	#13095305	C₃²	1	1	yes	characteristic
121	#13095305	C₃²	1	1	yes	characteristic
122	#13095305	C₃²	1	1	yes	characteristic
123	#13095305	C₃²	1	1	yes	characteristic
124	#13095305	C₃²	1	1	yes	characteristic
125	#13095305	C₃²	1	1	yes	characteristic
126	#13095305	C₃²	1	1	yes	characteristic
127	#13095305	C₃²	1	1	yes	characteristic
128	#13095305	C₃²	1	1	yes	characteristic
129	#13095305	C₃²	1	1	yes	characteristic
130	#13095305	C₃²	1	1	yes	characteristic
131	C₃²⋊#4294	C₃²	1	1	yes	characteristic
132	C₃²⋊#4294	C₃²	1	1	yes	characteristic
133	C₃²⋊#4294	C₃²	1	1	yes	characteristic
134	C₃²⋊#4294	C₃²	1	1	yes	characteristic
135	#13095303	C₃²	1	1	yes	characteristic
136	#13095303	C₃²	1	1	yes	characteristic
137	#13095303	C₃²	1	1	yes	characteristic
138	#13095303	C₃²	1	1	yes	characteristic
139	#13095303	C₃²	1	1	yes	characteristic
140	#13095303	C₃²	1	1	yes	characteristic
141	#13095303	C₃²	1	1	yes	characteristic
142	#13095303	C₃²	1	1	yes	characteristic
143	#13095303	C₃²	1	1	yes	characteristic
144	#13095303	C₃²	1	1	yes	characteristic
145	#13095303	C₃²	1	1	yes	characteristic
146	#13095303	C₃²	1	1	yes	characteristic
147	#13095303	C₃²	1	1	yes	characteristic
148	#13095303	C₃²	1	1	yes	characteristic
149	#13095303	C₃²	1	1	yes	characteristic
150	#13095303	C₃²	1	1	yes	characteristic
151	#13095303	C₃²	1	1	yes	characteristic
152	#13095303	C₃²	1	1	yes	characteristic
153	C₉×#4294	C₃²	1	1	yes	characteristic
154	C₉×#4294	C₃²	1	1	yes	characteristic
155	C₉×#4294	C₃²	1	1	yes	characteristic
156	C₉×#4294	C₃²	1	1	yes	characteristic
157	C₉×#4294	C₃²	1	1	yes	characteristic
158	C₉×#4294	C₃²	1	1	yes	characteristic
159	C₃×C₁₉×3₋¹⁺²	C₃²	1	1	yes	characteristic
160	C₃²×C₉×C₁₉	C₃²	1	1	yes	characteristic
161	C₁₉×C₉⋊C₉	C₃²	1	1	yes	characteristic
162	C₁₉×C₉⋊C₉	C₃²	1	1	yes	characteristic
163	C₁₉×C₉⋊C₉	C₃²	1	1	yes	characteristic
164	C₁₉×C₉⋊C₉	C₃²	1	1	yes	characteristic
165	C₁₉×C₉⋊C₉	C₃²	1	1	yes	characteristic
166	C₁₉×C₉⋊C₉	C₃²	1	1	yes	characteristic
167	C₁₉×C₉⋊C₉	C₃²	1	1	yes	characteristic
168	C₁₉×C₉⋊C₉	C₃²	1	1	yes	characteristic
169	C₁₉×C₉⋊C₉	C₃²	1	1	yes	characteristic
170	C₁₉×C₃²⋊C₉	C₃²	1	1	yes	characteristic
171	C₁₉×C₃²⋊C₉	C₃²	1	1	yes	characteristic
172	#10624887	—	19	1	no	maximal, Sylow
173	C₃³×C₁₉	C₃³	1	1	yes	characteristic
174	C₃²×C₁₉⋊C₃	C₃³	1	1	yes	characteristic
175	C₃²×C₁₉⋊C₃	C₃³	1	1	yes	characteristic
176	C₃²×C₁₉⋊C₃	C₃³	1	1	yes	characteristic
177	C₁₉×3₋¹⁺²	—	9	1	no	—
178	C₃×C₉×C₁₉	—	3	3	no	—
179	C₃×C₉×C₁₉	C₃³	1	1	yes	characteristic
180	C₃×C₉×C₁₉	C₃³	1	1	yes	characteristic
181	C₃×C₉×C₁₉	C₃³	1	1	yes	characteristic
182	C₃×C₉×C₁₉	C₃³	1	1	yes	characteristic
183	C₃×C₉×C₁₉	C₃³	1	1	yes	characteristic
184	C₃×C₉×C₁₉	C₃³	1	1	yes	characteristic
185	C₃×C₉×C₁₉	C₃³	1	1	yes	characteristic
186	C₃×C₉×C₁₉	C₃³	1	1	yes	characteristic
187	C₃×C₉×C₁₉	C₃³	1	1	yes	characteristic
188	C₃×C₉×C₁₉	C₃³	1	1	yes	characteristic
189	C₃×C₉×C₁₉	C₃³	1	1	yes	characteristic
190	C₃×C₉×C₁₉	C₃³	1	1	yes	characteristic
191	C₃²⋊(C₁₉⋊C₃)	—	3	3	no	—
192	#10587025	—	3	3	no	—
193	#10587025	—	3	3	no	—
194	#10587025	—	9	1	no	—
195	#10587025	—	9	1	no	—
196	C₃×#4294	C₃³	1	1	yes	characteristic
197	C₃×#4294	C₃³	1	1	yes	characteristic
198	C₃×#4294	C₃³	1	1	yes	characteristic
199	C₃×#4294	C₃³	1	1	yes	characteristic
200	C₃×#4294	C₃³	1	1	yes	characteristic
201	C₃×#4294	C₃³	1	1	yes	characteristic
202	C₃×#4294	C₃³	1	1	yes	characteristic
203	C₃×#4294	C₃³	1	1	yes	characteristic
204	C₃×#4294	C₃³	1	1	yes	characteristic
205	C₃×#4294	C₃³	1	1	yes	characteristic
206	C₃×#4294	C₃³	1	1	yes	characteristic
207	C₃×#4294	C₃³	1	1	yes	characteristic
208	C₃×#4294	C₃³	1	1	yes	characteristic
209	C₃×#4294	C₃³	1	1	yes	characteristic
210	C₃×#4294	C₃³	1	1	yes	characteristic
211	C₃×#4294	C₃³	1	1	yes	characteristic
212	C₃×#4294	C₃³	1	1	yes	characteristic
213	C₃×#4294	C₃³	1	1	yes	characteristic
214	C₃×#4294	C₃³	1	1	yes	characteristic
215	C₃×#4294	C₃³	1	1	yes	characteristic
216	C₃×#4294	C₃³	1	1	yes	characteristic
217	C₃×#4294	C₃³	1	1	yes	characteristic
218	C₃×#4294	C₃³	1	1	yes	characteristic
219	C₃×#4294	C₃³	1	1	yes	characteristic
220	#10587023	—	3	3	no	—
221	#10587023	—	3	3	no	—
222	#10587023	—	3	3	no	—
223	#10587023	—	9	1	no	—
224	#10587023	—	9	1	no	—
225	#10587023	—	9	1	no	—
226	#10587022	—	3	3	no	—
227	#10587022	—	3	3	no	—
228	#10587022	—	3	3	no	—
229	#10587022	—	9	1	no	—
230	#10587022	—	9	1	no	—
231	#10587022	—	9	1	no	—
232	C₉×C₁₉⋊C₃	—	3	3	no	—
233	C₉×C₁₉⋊C₃	—	3	3	no	—
234	C₉×C₁₉⋊C₃	—	9	1	no	—
235	C₉×C₁₉⋊C₃	—	9	1	no	—
236	C₉×C₁₉⋊C₃	—	9	1	no	—
237	C₉×C₁₉⋊C₃	3₋¹⁺²	1	9	yes	complemented
238	C₃×#737	—	19	1	no	—
239	#6900	—	19	1	no	—
240	#6900	—	19	1	no	—
241	#6900	—	19	1	no	—
242	#6899	—	19	1	no	—
243	#6899	—	19	1	no	—
244	#6899	—	19	1	no	—
245	#6899	—	19	1	no	—
246	#6899	—	19	1	no	—
247	#6899	—	19	1	no	—
248	#6896	—	19	1	no	—
249	#6896	—	19	1	no	—
250	#6896	—	19	1	no	—
251	#6896	—	19	1	no	—
252	#6896	—	19	1	no	—
253	#6896	—	19	1	no	—
254	#6896	—	19	1	no	—
255	#6896	—	19	1	no	—
256	#6896	—	19	1	no	—
257	#6894	—	19	1	no	—
258	#6894	—	19	1	no	—
259	#6894	—	19	1	no	—
260	#6894	—	19	1	no	—
261	#6894	—	19	1	no	—
262	#6894	—	19	1	no	—
263	#6894	—	19	1	no	—
264	#6894	—	19	1	no	—
265	#6894	—	19	1	no	—
266	#6894	—	19	1	no	—
267	#6894	—	19	1	no	—
268	#6894	—	19	1	no	—
269	#6894	—	19	1	no	—
270	#6894	—	19	1	no	—
271	#6894	C₁₉⋊C₃	1	1	yes	characteristic, complemented
272	C₉⋊H(3,𝔽₃)	—	19	1	no	—
273	C₉⋊H(3,𝔽₃)	—	19	1	no	—
274	C₉⋊H(3,𝔽₃)	—	19	1	no	—
275	#6887	—	19	1	no	—
276	#6887	—	19	1	no	—
277	C₃×C₉⋊C₉	—	19	1	no	—
278	C₃²×C₁₉	—	3	1	no	—
279	C₃²×C₁₉	—	3	1	no	—
280	C₃²×C₁₉	—	3	1	no	—
281	C₃²×C₁₉	—	3	1	no	—
282	C₃²×C₁₉	C₃⁴	1	1	yes	characteristic
283	C₃×C₁₉⋊C₃	—	3	1	no	—
284	C₃×C₁₉⋊C₃	—	3	1	no	—
285	C₃×C₁₉⋊C₃	—	3	1	no	—
286	C₃×C₁₉⋊C₃	—	3	1	no	—
287	C₃×C₁₉⋊C₃	—	3	1	no	—
288	C₃×C₁₉⋊C₃	—	3	1	no	—
289	C₃×C₁₉⋊C₃	—	3	1	no	—
290	C₃×C₁₉⋊C₃	—	3	1	no	—
291	C₃×C₁₉⋊C₃	—	3	1	no	—
292	C₃×C₁₉⋊C₃	—	3	1	no	—
293	C₃×C₁₉⋊C₃	—	3	1	no	—
294	C₃×C₁₉⋊C₃	C₃×3₋¹⁺²	1	3	yes	—
295	C₉×C₁₉	—	3	1	no	—
296	C₉×C₁₉	—	3	1	no	—
297	C₉×C₁₉	—	3	1	no	—
298	C₉×C₁₉	—	3	1	no	—
299	C₉×C₁₉	—	3	1	no	—
300	C₉×C₁₉	—	3	1	no	—
301	C₉×C₁₉	—	3	1	no	—
302	C₉×C₁₉	—	3	1	no	—
303	C₉×C₁₉	—	3	1	no	—
304	C₉×C₁₉	—	3	1	no	—
305	C₉×C₁₉	—	3	1	no	—
306	C₉×C₁₉	C₃×3₋¹⁺²	1	3	yes	—
307	#4294	—	3	1	no	—
308	#4294	—	3	1	no	—
309	#4294	—	3	1	no	—
310	#4294	—	3	1	no	—
311	#4294	—	3	1	no	—
312	#4294	—	3	1	no	—
313	#4294	—	3	1	no	—
314	#4294	—	3	1	no	—
315	#4294	—	3	1	no	—
316	#4294	—	3	1	no	—
317	#4294	—	3	1	no	—
318	#4294	—	3	1	no	—
319	#4294	—	3	1	no	—
320	#4294	—	3	1	no	—
321	#4294	—	3	1	no	—
322	#4294	—	3	1	no	—
323	#4294	—	3	1	no	—
324	#4294	—	3	1	no	—
325	#4294	—	3	1	no	—
326	#4294	—	3	1	no	—
327	#4294	—	3	1	no	—
328	#4294	—	3	1	no	—
329	#4294	C₃×3₋¹⁺²	1	3	yes	—
330	#4294	C₃×3₋¹⁺²	1	3	yes	—
331	#737	—	57	9	no	—
332	C₃×3₋¹⁺²	—	19	1	no	—
333	C₃×3₋¹⁺²	—	19	1	no	—
334	C₃×3₋¹⁺²	—	19	1	no	—
335	C₃×3₋¹⁺²	—	19	1	no	—
336	C₃×3₋¹⁺²	—	19	1	no	—
337	C₃×3₋¹⁺²	—	19	1	no	—
338	C₃×3₋¹⁺²	—	19	1	no	—
339	C₃×3₋¹⁺²	—	19	1	no	—
340	C₃×3₋¹⁺²	—	19	1	no	—
341	C₃×3₋¹⁺²	—	19	1	no	—
342	C₃×3₋¹⁺²	—	19	1	no	—
343	C₃×3₋¹⁺²	—	19	1	no	—
344	C₃×3₋¹⁺²	—	19	1	no	—
345	C₃×3₋¹⁺²	—	19	1	no	—
346	C₃×3₋¹⁺²	—	19	1	no	—
347	C₃×3₋¹⁺²	—	19	1	no	—
348	C₃×3₋¹⁺²	C₃×C₁₉⋊C₃	1	1	yes	characteristic
349	C₃×H(3,𝔽₃)	—	19	1	no	—
350	C₃²×C₉	—	19	1	no	—
351	C₃²×C₉	—	19	1	no	—
352	C₃²×C₉	—	19	1	no	—
353	C₃²×C₉	—	19	1	no	—
354	C₃²×C₉	—	19	1	no	—
355	C₃²×C₉	—	19	1	no	—
356	C₃²×C₉	C₃×C₁₉⋊C₃	1	1	yes	characteristic
357	C₉⋊C₉	—	19	1	no	—
358	C₉⋊C₉	—	19	1	no	—
359	C₉⋊C₉	—	19	1	no	—
360	C₉⋊C₉	—	19	1	no	—
361	C₉⋊C₉	—	19	1	no	—
362	C₉⋊C₉	—	19	1	no	—
363	C₉⋊C₉	—	19	1	no	—
364	C₉⋊C₉	—	19	1	no	—
365	C₉⋊C₉	—	19	1	no	—
366	C₉⋊C₉	—	19	1	no	—
367	C₉⋊C₉	—	19	1	no	—
368	C₉⋊C₉	—	19	1	no	—
369	C₉⋊C₉	—	19	1	no	—
370	C₉⋊C₉	—	19	1	no	—
371	C₉⋊C₉	—	19	1	no	—
372	C₉⋊C₉	—	19	1	no	—
373	C₉⋊C₉	—	19	1	no	—
374	C₉⋊C₉	—	19	1	no	—
375	C₉⋊C₉	—	19	1	no	—
376	C₉⋊C₉	—	19	1	no	—
377	C₉⋊C₉	—	19	1	no	—
378	C₉⋊C₉	—	19	1	no	—
379	C₉⋊C₉	—	19	1	no	—
380	C₉⋊C₉	—	19	1	no	—
381	C₉⋊C₉	—	19	1	no	—
382	C₉⋊C₉	—	19	1	no	—
383	C₉⋊C₉	—	19	1	no	—
384	C₉⋊C₉	—	19	1	no	—
385	C₉⋊C₉	—	19	1	no	—
386	C₉⋊C₉	—	19	1	no	—
387	C₉⋊C₉	—	19	1	no	—
388	C₉⋊C₉	—	19	1	no	—
389	C₉⋊C₉	—	19	1	no	—
390	C₉⋊C₉	—	19	1	no	—
391	C₉⋊C₉	—	19	1	no	—
392	C₉⋊C₉	—	19	1	no	—
393	C₉⋊C₉	—	19	1	no	—
394	C₉⋊C₉	—	19	1	no	—
395	C₉⋊C₉	—	19	1	no	—
396	C₉⋊C₉	—	19	1	no	—
397	C₉⋊C₉	—	19	1	no	—
398	C₉⋊C₉	—	19	1	no	—
399	C₉⋊C₉	—	19	1	no	—
400	C₉⋊C₉	—	19	1	no	—
401	C₉⋊C₉	—	19	1	no	—
402	C₉⋊C₉	—	19	1	no	—
403	C₉⋊C₉	—	19	1	no	—
404	C₉⋊C₉	—	19	1	no	—
405	C₉⋊C₉	—	19	1	no	—
406	C₉⋊C₉	—	19	1	no	—
407	C₉⋊C₉	—	19	1	no	—
408	C₉⋊C₉	—	19	1	no	—
409	C₉⋊C₉	—	19	1	no	—
410	C₉⋊C₉	—	19	1	no	—
411	C₉⋊C₉	—	19	1	no	—
412	C₉⋊C₉	—	19	1	no	—
413	C₉⋊C₉	—	19	1	no	—
414	C₉⋊C₉	—	19	1	no	—
415	C₉⋊C₉	—	19	1	no	—
416	C₉⋊C₉	—	19	1	no	—
417	C₉⋊C₉	—	19	1	no	—
418	C₉⋊C₉	—	19	1	no	—
419	C₉⋊C₉	—	19	1	no	—
420	C₉⋊C₉	—	19	1	no	—
421	C₉⋊C₉	—	19	1	no	—
422	C₉⋊C₉	—	19	1	no	—
423	C₉⋊C₉	C₃×C₁₉⋊C₃	1	1	yes	characteristic
424	C₉⋊C₉	C₃×C₁₉⋊C₃	1	1	yes	characteristic
425	C₉⋊C₉	C₃×C₁₉⋊C₃	1	1	yes	characteristic
426	C₉⋊C₉	C₃×C₁₉⋊C₃	1	1	yes	characteristic
427	C₉⋊C₉	C₃×C₁₉⋊C₃	1	1	yes	characteristic
428	C₉⋊C₉	C₃×C₁₉⋊C₃	1	1	yes	characteristic
429	C₉⋊C₉	C₃×C₁₉⋊C₃	1	1	yes	characteristic
430	C₉⋊C₉	C₃×C₁₉⋊C₃	1	1	yes	characteristic
431	C₉⋊C₉	C₃×C₁₉⋊C₃	1	1	yes	characteristic
432	C₃²⋊C₉	—	19	1	no	—
433	C₃²⋊C₉	—	19	1	no	—
434	C₃²⋊C₉	—	19	1	no	—
435	C₃²⋊C₉	—	19	1	no	—
436	C₃²⋊C₉	—	19	1	no	—
437	C₃²⋊C₉	—	19	1	no	—
438	C₃²⋊C₉	—	19	1	no	—
439	C₃²⋊C₉	—	19	1	no	—
440	C₃²⋊C₉	—	19	1	no	—
441	C₃²⋊C₉	—	19	1	no	—
442	C₃²⋊C₉	—	19	1	no	—
443	C₃²⋊C₉	—	19	1	no	—
444	C₃²⋊C₉	—	19	1	no	—
445	C₃²⋊C₉	—	19	1	no	—
446	C₃²⋊C₉	—	19	1	no	—
447	C₃²⋊C₉	—	19	1	no	—
448	C₃²⋊C₉	—	19	1	no	—
449	C₃²⋊C₉	—	19	1	no	—
450	C₃²⋊C₉	—	19	1	no	—
451	C₃²⋊C₉	—	19	1	no	—
452	C₃²⋊C₉	—	19	1	no	—
453	C₃²⋊C₉	—	19	1	no	—
454	C₃²⋊C₉	C₃×C₁₉⋊C₃	1	1	yes	characteristic
455	C₃²⋊C₉	C₃×C₁₉⋊C₃	1	1	yes	characteristic
456	C₉²	—	19	1	no	—
457	C₉²	—	19	1	no	—
458	C₉²	—	19	1	no	—
459	C₉²	—	19	1	no	—
460	C₉²	—	19	1	no	—
461	C₉²	—	19	1	no	—
462	C₃×C₁₉	—	9	1	no	—
463	C₃×C₁₉	C₃²×3₋¹⁺²	1	1	yes	characteristic
464	C₃×C₁₉	3₋¹⁺⁴	1	1	yes	characteristic
465	C₃×C₁₉	3₋¹⁺⁴	1	1	yes	characteristic
466	C₃×C₁₉	3₋¹⁺⁴	1	1	yes	characteristic
467	C₁₉⋊C₃	—	3	3	no	—
468	C₁₉⋊C₃	—	9	1	no	—
469	C₁₉⋊C₃	—	9	1	no	—
470	C₃³	—	19	1	no	—
471	C₃³	—	19	1	no	—
472	C₃³	—	19	1	no	—
473	C₃³	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
474	3₋¹⁺²	—	9	1	no	—
475	3₋¹⁺²	—	57	3	no	—
476	3₋¹⁺²	—	57	3	no	—
477	3₋¹⁺²	—	57	3	no	—
478	3₋¹⁺²	—	57	3	no	—
479	3₋¹⁺²	—	57	3	no	—
480	3₋¹⁺²	—	57	3	no	—
481	3₋¹⁺²	—	57	3	no	—
482	3₋¹⁺²	—	57	3	no	—
483	3₋¹⁺²	—	171	1	no	—
484	3₋¹⁺²	—	171	1	no	—
485	3₋¹⁺²	—	171	1	no	—
486	3₋¹⁺²	—	171	1	no	—
487	3₋¹⁺²	—	171	1	no	—
488	3₋¹⁺²	—	171	1	no	—
489	3₋¹⁺²	—	171	1	no	—
490	3₋¹⁺²	—	171	1	no	—
491	H(3,𝔽₃)	—	57	3	no	—
492	C₃×C₉	—	3	3	no	—
493	C₃×C₉	—	19	1	no	—
494	C₃×C₉	—	19	1	no	—
495	C₃×C₉	—	19	9	no	—
496	C₃×C₉	—	19	1	no	—
497	C₃×C₉	—	19	1	no	—
498	C₃×C₉	—	19	1	no	—
499	C₃×C₉	—	19	1	no	—
500	C₃×C₉	—	19	1	no	—
501	C₃×C₉	—	19	1	no	—
502	C₃×C₉	—	19	1	no	—
503	C₃×C₉	—	19	1	no	—
504	C₃×C₉	—	19	1	no	—
505	C₃×C₉	—	19	1	no	—
506	C₃×C₉	—	19	1	no	—
507	C₃×C₉	—	19	1	no	—
508	C₃×C₉	—	19	1	no	—
509	C₃×C₉	—	19	1	no	—
510	C₃×C₉	—	19	1	no	—
511	C₃×C₉	—	19	1	no	—
512	C₃×C₉	—	19	1	no	—
513	C₃×C₉	—	19	1	no	—
514	C₃×C₉	—	19	1	no	—
515	C₃×C₉	—	19	1	no	—
516	C₃×C₉	—	19	1	no	—
517	C₃×C₉	—	19	1	no	—
518	C₃×C₉	—	57	3	no	—
519	C₃×C₉	—	57	3	no	—
520	C₃×C₉	—	171	1	no	—
521	C₃×C₉	—	171	1	no	—
522	C₃×C₉	—	171	1	no	—
523	C₃×C₉	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
524	C₃×C₉	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
525	C₃×C₉	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
526	C₃×C₉	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
527	C₃×C₉	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
528	C₃×C₉	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
529	C₃×C₉	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
530	C₃×C₉	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
531	C₃×C₉	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
532	C₃×C₉	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
533	C₃×C₉	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
534	C₃×C₉	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
535	C₁₉	#10624887	1	1	yes	characteristic, complemented, Sylow
536	C₃²	—	3	1	no	—
537	C₃²	—	3	1	no	—
538	C₃²	—	3	1	no	—
539	C₃²	—	3	1	no	—
540	C₃²	—	19	3	no	—
541	C₃²	—	57	1	no	—
542	C₃²	—	57	1	no	—
543	C₃²	—	57	1	no	—
544	C₃²	—	57	1	no	—
545	C₃²	—	57	1	no	—
546	C₃²	—	57	1	no	—
547	C₃²	—	57	1	no	—
548	C₃²	—	57	1	no	—
549	C₃²	—	57	1	no	—
550	C₃²	—	57	1	no	—
551	C₃²	—	57	1	no	—
552	C₃²	C₃³×C₁₉⋊C₃	1	1	yes	characteristic
553	C₉	—	3	1	no	—
554	C₉	—	3	1	no	—
555	C₉	—	3	1	no	—
556	C₉	—	3	1	no	—
557	C₉	—	3	1	no	—
558	C₉	—	3	1	no	—
559	C₉	—	3	1	no	—
560	C₉	—	3	1	no	—
561	C₉	—	3	1	no	—
562	C₉	—	3	1	no	—
563	C₉	—	3	1	no	—
564	C₉	—	19	3	no	—
565	C₉	—	19	3	no	—
566	C₉	—	57	1	no	—
567	C₉	—	57	1	no	—
568	C₉	—	57	1	no	—
569	C₉	—	57	1	no	—
570	C₉	—	57	1	no	—
571	C₉	—	57	1	no	—
572	C₉	—	57	1	no	—
573	C₉	—	57	1	no	—
574	C₉	—	57	1	no	—
575	C₉	—	57	1	no	—
576	C₉	—	57	1	no	—
577	C₉	—	57	1	no	—
578	C₉	—	57	1	no	—
579	C₉	—	57	1	no	—
580	C₉	—	57	1	no	—
581	C₉	—	57	1	no	—
582	C₉	—	57	1	no	—
583	C₉	—	57	1	no	—
584	C₉	—	57	1	no	—
585	C₉	—	57	1	no	—
586	C₉	—	57	1	no	—
587	C₉	—	57	1	no	—
588	C₉	3₋¹⁺²×C₁₉⋊C₃	1	3	yes	—
589	C₃	—	9	1	no	—
590	C₃	—	57	3	no	—
591	C₃	—	171	1	no	—
592	C₃	—	171	1	no	—
593	C₃	C₃×3₋¹⁺²×C₁₉⋊C₃	1	1	yes	characteristic
594	C₃	#17987544	1	1	yes	characteristic
595	C₃	#17987545	1	1	yes	characteristic
596	C₃	#17987546	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₃²	C₃³×C₁₉⋊C₃
commutator, socle, cosocle	C₃²×C₁₉	C₃⁴
Fitting	C₁₉×#6894	C₃
prime radical	C₃×C₃²⋊(C₁₉⋊C₃)	C₃²
hypercenter	#6894	C₁₉⋊C₃
hypocenter	C₁₉	#10624887
LCS	G ▷ C₃²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃² ◁ #6894

Complements

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

N	H ≅ G/N	type
2. #17987472	C₃	semidirect
3. #17987471	C₃	semidirect
4. #17987468	C₃	semidirect
5. #17987465	C₃	semidirect
6. #17987465	C₃	semidirect
7. #17987464	C₃	semidirect
8. #17987464	C₃	semidirect
9. #17987460	C₃	semidirect
10. #17987460	C₃	semidirect
11. #17987451	C₃	semidirect
12. #17987450	C₃	semidirect
13. #17987449	C₃	semidirect
14. #17987449	C₃	semidirect
15. #17987449	C₃	semidirect
16. #17987449	C₃	semidirect
17. #17987447	C₃	semidirect
18. #17987446	C₃	semidirect
19. #17987446	C₃	semidirect
20. #17987439	C₃	semidirect
21. #17987438	C₃	semidirect
22. #17987437	C₃	semidirect
23. #17987437	C₃	semidirect
24. #17987436	C₃	semidirect
25. #17987436	C₃	semidirect
26. #17987434	C₃	semidirect
27. #17987434	C₃	semidirect
28. #17987434	C₃	semidirect
29. #17987434	C₃	semidirect
30. #17987433	C₃	semidirect
31. #17987433	C₃	semidirect
32. #17987433	C₃	semidirect
33. #17987433	C₃	semidirect
37. #17987404	C₃	semidirect
38. #17987404	C₃	semidirect
39. C₁₉⋊C₃×C₉⋊C₉	C₃	semidirect
40. C₁₉×#6894	C₃	semidirect
237. C₉×C₁₉⋊C₃	3₋¹⁺²	semidirect
271. #6894	C₁₉⋊C₃	semidirect
535. C₁₉	#10624887	semidirect

Maximal subgroups

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

subgroup	index
C₃×#13095332	3
#17987472	3
#17987471	3
#17987468	3
#17987465	3
#17987464	3
#17987460	3
#17987451	3
#17987450	3
#17987449	3
#17987447	3
#17987446	3
#17987439	3
#17987438	3
#17987437	3
#17987436	3
#17987434	3
#17987433	3
#17987424	3
#17987422	3
#17987404	3
C₁₉⋊C₃×C₉⋊C₉	3
C₁₉×#6894	3
#10624887	19