Subgroups — #18082619

Order 4864.

598 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14563397	C₂	1	1	yes	maximal, characteristic
2	#14561865	C₂	1	1	yes	maximal, characteristic
3	#14561513	C₂	1	2	yes	maximal
4	#14561513	C₂	1	2	yes	maximal
5	C₁₉×#2851	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄⋊Dic₁₉	—	2	1	no	—
7	C₂×C₂²⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
8	C₂×#10597260	—	2	1	no	—
9	C₂×C₁₉⋊#95	—	2	1	no	—
10	C₂×C₁₉⋊#95	C₂²	1	2	yes	—
11	#11926299	—	2	1	no	—
12	C₂×C₁₉×#125	C₄	1	1	yes	characteristic, complemented
13	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
14	C₁₉×#389	C₄	1	1	yes	characteristic, complemented
15	C₁₉×#389	C₄	1	1	yes	characteristic, complemented
16	C₁₉×#387	—	2	1	no	—
17	C₁₉×#387	—	2	1	no	—
18	C₁₉×#385	—	2	1	no	—
19	C₁₉×#385	—	2	1	no	—
20	C₁₉×#382	C₄	1	1	yes	characteristic, complemented
21	C₁₉×#380	C₂²	1	1	yes	characteristic
22	C₁₉×#380	C₂²	1	1	yes	characteristic
23	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
24	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
25	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
26	C₂³×Dic₁₉	—	2	2	no	—
27	C₁₉×#125	—	4	2	no	—
28	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
29	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
30	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
31	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
32	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
33	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
36	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
37	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
38	C₂×C₄²×C₁₉	—	4	2	no	—
39	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
42	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
43	C₂×C₄⋊Dic₁₉	—	2	4	no	—
44	C₂×C₄⋊Dic₁₉	—	4	2	no	—
45	C₂×C₄⋊Dic₁₉	—	4	2	no	—
46	C₂²×C₁₉⋊C₈	—	2	2	no	—
47	C₁₉×#95	—	2	1	no	—
48	C₁₉×#95	—	2	1	no	—
49	C₁₉×#95	—	2	1	no	—
50	C₁₉×#95	—	2	1	no	—
51	C₁₉×#95	—	2	1	no	—
52	C₁₉×#95	—	2	1	no	—
53	C₁₉⋊#95	—	2	4	no	—
54	C₁₉⋊#95	—	4	2	no	—
55	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
56	C₂²⋊(C₁₉⋊C₈)	Q₈	1	4	yes	—
57	#10597260	—	4	2	no	—
58	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
59	C₂²×C₄×C₁₉	—	2	1	no	—
60	C₂²×C₄×C₁₉	—	2	1	no	—
61	C₂²×C₄×C₁₉	—	2	2	no	—
62	C₂²×C₄×C₁₉	—	2	2	no	—
63	C₂²×C₄×C₁₉	—	2	1	no	—
64	C₂²×C₄×C₁₉	—	2	1	no	—
65	C₂²×C₄×C₁₉	—	2	1	no	—
66	C₂²×C₄×C₁₉	—	2	1	no	—
67	C₂²×C₄×C₁₉	—	2	1	no	—
68	C₂²×C₄×C₁₉	—	2	1	no	—
69	C₂²×C₄×C₁₉	—	4	1	no	—
70	C₂²×C₄×C₁₉	—	4	1	no	—
71	C₂²×C₄×C₁₉	—	4	1	no	—
72	C₂²×C₄×C₁₉	—	4	1	no	—
73	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
80	C₂²×C₄×C₁₉	#41	1	2	yes	—
81	C₂²×Dic₁₉	—	2	4	no	—
82	C₂²×Dic₁₉	—	4	2	no	—
83	C₂²×Dic₁₉	—	4	2	no	—
84	C₂²×Dic₁₉	—	4	2	no	—
85	C₂²×Dic₁₉	—	4	2	no	—
86	C₂²×Dic₁₉	—	4	2	no	—
87	C₂²×Dic₁₉	—	4	2	no	—
88	C₄⋊C₄×C₁₉	—	4	1	no	—
89	C₄⋊C₄×C₁₉	—	4	1	no	—
90	C₄⋊C₄×C₁₉	—	4	1	no	—
91	C₄⋊C₄×C₁₉	—	4	1	no	—
92	C₄⋊C₄×C₁₉	—	4	2	no	—
93	C₄⋊C₄×C₁₉	—	4	2	no	—
94	C₄⋊C₄×C₁₉	—	4	2	no	—
95	C₄⋊C₄×C₁₉	—	4	2	no	—
96	C₂²⋊C₄×C₁₉	—	4	1	no	—
97	C₂²⋊C₄×C₁₉	—	4	1	no	—
98	C₂²⋊C₄×C₁₉	—	4	1	no	—
99	C₂²⋊C₄×C₁₉	—	4	1	no	—
100	C₄²×C₁₉	—	2	2	no	—
101	C₄²×C₁₉	—	2	2	no	—
102	C₄²×C₁₉	—	4	1	no	—
103	C₄²×C₁₉	—	4	1	no	—
104	C₄⋊Dic₁₉	—	4	8	no	—
105	C₂×C₁₉⋊C₈	—	2	4	no	—
106	C₂×C₁₉⋊C₈	—	4	2	no	—
107	C₂×C₁₉⋊C₈	—	4	2	no	—
108	#9887	—	19	1	no	maximal, Sylow
109	C₂³×C₁₉	—	2	1	no	—
110	C₂³×C₁₉	—	2	1	no	—
111	C₂³×C₁₉	—	2	1	no	—
112	C₂³×C₁₉	—	2	1	no	—
113	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
114	C₂³×C₁₉	#124	1	1	yes	characteristic
115	C₂³×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
116	C₂³×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
117	C₂³×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
118	C₂³×C₁₉	#137	1	1	yes	characteristic
119	C₂³×C₁₉	#137	1	1	yes	characteristic
120	C₂×C₄×C₁₉	—	2	4	no	—
121	C₂×C₄×C₁₉	—	2	4	no	—
122	C₂×C₄×C₁₉	—	2	1	no	—
123	C₂×C₄×C₁₉	—	2	1	no	—
124	C₂×C₄×C₁₉	—	2	1	no	—
125	C₂×C₄×C₁₉	—	2	1	no	—
126	C₂×C₄×C₁₉	—	2	1	no	—
127	C₂×C₄×C₁₉	—	2	1	no	—
128	C₂×C₄×C₁₉	—	2	1	no	—
129	C₂×C₄×C₁₉	—	2	1	no	—
130	C₂×C₄×C₁₉	—	2	1	no	—
131	C₂×C₄×C₁₉	—	2	1	no	—
132	C₂×C₄×C₁₉	—	2	1	no	—
133	C₂×C₄×C₁₉	—	2	1	no	—
134	C₂×C₄×C₁₉	—	2	1	no	—
135	C₂×C₄×C₁₉	—	2	1	no	—
136	C₂×C₄×C₁₉	—	4	2	no	—
137	C₂×C₄×C₁₉	—	4	2	no	—
138	C₂×C₄×C₁₉	—	4	2	no	—
139	C₂×C₄×C₁₉	—	4	2	no	—
140	C₂×C₄×C₁₉	—	4	1	no	—
141	C₂×C₄×C₁₉	—	4	1	no	—
142	C₂×C₄×C₁₉	—	4	1	no	—
143	C₂×C₄×C₁₉	—	4	1	no	—
144	C₂×C₄×C₁₉	—	4	1	no	—
145	C₂×C₄×C₁₉	—	4	1	no	—
146	C₂×C₄×C₁₉	—	4	1	no	—
147	C₂×C₄×C₁₉	—	4	1	no	—
148	C₂×C₄×C₁₉	—	4	1	no	—
149	C₂×C₄×C₁₉	—	4	1	no	—
150	C₂×C₄×C₁₉	—	4	1	no	—
151	C₂×C₄×C₁₉	—	4	1	no	—
152	C₂×C₄×C₁₉	#99	1	2	yes	—
153	C₂×C₄×C₁₉	#104	1	2	yes	—
154	C₂×C₄×C₁₉	C₄×Q₈	1	2	yes	—
155	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
156	C₂×Dic₁₉	—	4	4	no	—
157	C₂×Dic₁₉	—	4	4	no	—
158	C₂×Dic₁₉	—	4	4	no	—
159	C₂×Dic₁₉	—	8	2	no	—
160	C₂×Dic₁₉	—	8	2	no	—
161	C₂×Dic₁₉	—	8	2	no	—
162	C₂×Dic₁₉	—	8	2	no	—
163	C₁₉⋊C₈	—	4	4	no	—
164	#2851	D₁₉	1	1	yes	characteristic
165	#1749	—	19	1	no	—
166	C₄⋊#95	—	19	1	no	—
167	#1294	—	19	2	no	—
168	#1294	—	19	2	no	—
169	C₂²×C₁₉	—	2	1	no	—
170	C₂²×C₁₉	—	2	1	no	—
171	C₂²×C₁₉	—	2	1	no	—
172	C₂²×C₁₉	—	2	1	no	—
173	C₂²×C₁₉	—	2	1	no	—
174	C₂²×C₁₉	—	2	1	no	—
175	C₂²×C₁₉	—	2	1	no	—
176	C₂²×C₁₉	—	2	1	no	—
177	C₂²×C₁₉	—	2	1	no	—
178	C₂²×C₁₉	—	2	1	no	—
179	C₂²×C₁₉	—	2	1	no	—
180	C₂²×C₁₉	—	2	1	no	—
181	C₂²×C₁₉	#391	1	1	yes	characteristic
182	C₂²×C₁₉	C₂×#99	1	1	yes	characteristic
183	C₂²×C₁₉	#410	1	1	yes	characteristic
184	C₂²×C₁₉	#417	1	1	yes	characteristic
185	C₂²×C₁₉	#417	1	1	yes	characteristic
186	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
187	C₂²×C₁₉	#421	1	1	yes	characteristic
188	C₂²×C₁₉	#490	1	1	yes	characteristic
189	C₂²×C₁₉	#491	1	1	yes	characteristic
190	C₂²×C₁₉	#501	1	1	yes	characteristic
191	C₂²×C₁₉	#501	1	1	yes	characteristic
192	C₄×C₁₉	—	2	2	no	—
193	C₄×C₁₉	—	2	2	no	—
194	C₄×C₁₉	—	2	2	no	—
195	C₄×C₁₉	—	2	2	no	—
196	C₄×C₁₉	—	4	1	no	—
197	C₄×C₁₉	—	4	1	no	—
198	C₄×C₁₉	—	8	1	no	—
199	C₄×C₁₉	—	8	1	no	—
200	C₄×C₁₉	—	8	1	no	—
201	C₄×C₁₉	—	8	1	no	—
202	Dic₁₉	—	8	4	no	—
203	C₂×#125	Dic₁₉	1	1	yes	characteristic, complemented
204	C₂²×C₄⋊C₄	—	38	1	no	—
205	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
206	C₂×C₂²⋊C₈	—	19	2	no	—
207	C₂×#97	—	38	1	no	—
208	#389	Dic₁₉	1	1	yes	characteristic, complemented
209	#389	Dic₁₉	1	1	yes	characteristic, complemented
210	#387	—	2	1	no	—
211	#387	—	2	1	no	—
212	#385	—	2	1	no	—
213	#385	—	2	1	no	—
214	#382	Dic₁₉	1	1	yes	characteristic, complemented
215	#380	C₂×D₁₉	1	1	yes	characteristic
216	#380	C₂×D₁₉	1	1	yes	characteristic
217	C₂×#95	—	19	2	no	—
218	C₂×#95	—	38	1	no	—
219	#336	—	38	1	no	—
220	C₂×C₁₉	—	2	1	no	—
221	C₂×C₁₉	—	2	1	no	—
222	C₂×C₁₉	—	2	1	no	—
223	C₂×C₁₉	—	2	1	no	—
224	C₂×C₁₉	#1504	1	1	yes	characteristic
225	C₂×C₁₉	#1509	1	1	yes	characteristic
226	C₂×C₁₉	#1512	1	1	yes	characteristic
227	C₂×C₁₉	#1513	1	1	yes	characteristic
228	C₂×C₁₉	#1986	1	1	yes	characteristic
229	C₂×C₁₉	#1992	1	1	yes	characteristic
230	C₂×C₁₉	#1996	1	1	yes	characteristic
231	C₂³×C₄	—	38	2	no	—
232	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
233	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
234	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
235	C₂²×C₈	—	38	2	no	—
236	#125	—	4	2	no	—
237	C₂×C₄⋊C₄	—	2	1	no	—
238	C₂×C₄⋊C₄	—	2	1	no	—
239	C₂×C₄⋊C₄	—	2	1	no	—
240	C₂×C₄⋊C₄	—	2	1	no	—
241	C₂×C₄⋊C₄	—	38	4	no	—
242	C₂×C₄⋊C₄	—	76	2	no	—
243	C₂×C₄⋊C₄	—	76	2	no	—
244	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
245	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
246	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
247	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
248	C₂×C₂²⋊C₄	—	2	1	no	—
249	C₂×C₂²⋊C₄	—	2	1	no	—
250	C₂×C₄²	—	4	2	no	—
251	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
252	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
253	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
254	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
255	C₂²⋊C₈	—	19	4	no	—
256	C₂²⋊C₈	—	38	2	no	—
257	#97	—	76	2	no	—
258	#95	—	2	1	no	—
259	#95	—	2	1	no	—
260	#95	—	2	1	no	—
261	#95	—	2	1	no	—
262	#95	—	2	1	no	—
263	#95	—	2	1	no	—
264	#95	—	38	4	no	—
265	#95	—	76	2	no	—
266	C₁₉	#9887	1	1	yes	characteristic, complemented, Sylow
267	C₂⁴	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
268	C₂²×C₄	—	2	1	no	—
269	C₂²×C₄	—	2	1	no	—
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	2	1	no	—
273	C₂²×C₄	—	2	1	no	—
274	C₂²×C₄	—	2	1	no	—
275	C₂²×C₄	—	2	1	no	—
276	C₂²×C₄	—	2	1	no	—
277	C₂²×C₄	—	2	1	no	—
278	C₂²×C₄	—	4	1	no	—
279	C₂²×C₄	—	4	1	no	—
280	C₂²×C₄	—	4	1	no	—
281	C₂²×C₄	—	4	1	no	—
282	C₂²×C₄	—	38	4	no	—
283	C₂²×C₄	—	76	2	no	—
284	C₂²×C₄	—	76	2	no	—
285	C₂²×C₄	—	76	2	no	—
286	C₂²×C₄	—	76	2	no	—
287	C₂²×C₄	—	76	2	no	—
288	C₂²×C₄	—	76	2	no	—
289	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
290	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
291	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
292	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
293	C₂²×C₄	Q₈×D₁₉	1	2	yes	—
294	C₂²×C₄	#64545	1	2	yes	—
295	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
296	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
297	C₂×C₈	—	38	4	no	—
298	C₂×C₈	—	76	2	no	—
299	C₂×C₈	—	76	2	no	—
300	C₄⋊C₄	—	4	1	no	—
301	C₄⋊C₄	—	4	1	no	—
302	C₄⋊C₄	—	4	1	no	—
303	C₄⋊C₄	—	4	1	no	—
304	C₄⋊C₄	—	4	2	no	—
305	C₄⋊C₄	—	4	2	no	—
306	C₄⋊C₄	—	4	2	no	—
307	C₄⋊C₄	—	4	2	no	—
308	C₄⋊C₄	—	76	8	no	—
309	C₂²⋊C₄	—	4	1	no	—
310	C₂²⋊C₄	—	4	1	no	—
311	C₂²⋊C₄	—	4	1	no	—
312	C₂²⋊C₄	—	4	1	no	—
313	C₄²	—	2	2	no	—
314	C₄²	—	2	2	no	—
315	C₄²	—	4	1	no	—
316	C₄²	—	4	1	no	—
317	C₂³	—	2	1	no	—
318	C₂³	—	2	1	no	—
319	C₂³	—	2	1	no	—
320	C₂³	—	2	1	no	—
321	C₂³	#10597390	1	1	yes	characteristic
322	C₂³	#10597393	1	1	yes	characteristic
323	C₂³	#10597395	1	1	yes	characteristic
324	C₂³	#10597395	1	1	yes	characteristic
325	C₂³	#10597397	1	1	yes	characteristic
326	C₂³	#10597397	1	1	yes	characteristic
327	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	2	4	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	1	no	—
351	C₂×C₄	—	4	1	no	—
352	C₂×C₄	—	4	1	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	4	1	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	76	4	no	—
361	C₂×C₄	—	76	4	no	—
362	C₂×C₄	—	76	4	no	—
363	C₂×C₄	—	152	2	no	—
364	C₂×C₄	—	152	2	no	—
365	C₂×C₄	—	152	2	no	—
366	C₂×C₄	—	152	2	no	—
367	C₂×C₄	#10597291	1	2	yes	—
368	C₂×C₄	#10597294	1	2	yes	—
369	C₂×C₄	Q₈×Dic₁₉	1	2	yes	—
370	C₂×C₄	#10597392	1	2	yes	—
371	C₈	—	76	4	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	2	1	no	—
377	C₂²	—	2	1	no	—
378	C₂²	—	2	1	no	—
379	C₂²	—	2	1	no	—
380	C₂²	—	2	1	no	—
381	C₂²	—	2	1	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	2	1	no	—
384	C₂²	#11926451	1	1	yes	characteristic
385	C₂²	C₂×#10597291	1	1	yes	characteristic
386	C₂²	#11926518	1	1	yes	characteristic
387	C₂²	#11926545	1	1	yes	characteristic
388	C₂²	#11926545	1	1	yes	characteristic
389	C₂²	C₂×#10597294	1	1	yes	characteristic
390	C₂²	#11926561	1	1	yes	characteristic
391	C₂²	#11926910	1	1	yes	characteristic
392	C₂²	#11926914	1	1	yes	characteristic
393	C₂²	#11926954	1	1	yes	characteristic
394	C₂²	#11926954	1	1	yes	characteristic
395	C₄	—	2	2	no	—
396	C₄	—	2	2	no	—
397	C₄	—	2	2	no	—
398	C₄	—	2	2	no	—
399	C₄	—	4	1	no	—
400	C₄	—	4	1	no	—
401	C₄	—	8	1	no	—
402	C₄	—	8	1	no	—
403	C₄	—	8	1	no	—
404	C₄	—	8	1	no	—
405	C₄	—	152	4	no	—
406	C₂	—	2	1	no	—
407	C₂	—	2	1	no	—
408	C₂	—	2	1	no	—
409	C₂	—	2	1	no	—
410	C₂	#14562139	1	1	yes	characteristic
411	C₂	#14562160	1	1	yes	characteristic
412	C₂	#14562173	1	1	yes	characteristic
413	C₂	#14562178	1	1	yes	characteristic
414	C₂	#14564580	1	1	yes	characteristic
415	C₂	#14564605	1	1	yes	characteristic
416	C₂	#14564621	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₁₉×#2851	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₁₉	C₂×D₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	#2851	D₁₉
hypocenter	C₁₉	#9887
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ #2851

Complements

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

N	H ≅ G/N	type
12. C₂×C₁₉×#125	C₄	semidirect
14. C₁₉×#389	C₄	semidirect
15. C₁₉×#389	C₄	semidirect
20. C₁₉×#382	C₄	semidirect
203. C₂×#125	Dic₁₉	semidirect
208. #389	Dic₁₉	semidirect
209. #389	Dic₁₉	semidirect
214. #382	Dic₁₉	semidirect
266. C₁₉	#9887	semidirect

Maximal subgroups

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

subgroup	index
#14563397	2
#14561865	2
#14561513	2
C₁₉×#2851	2
#9887	19