Subgroups — #18081527

Order 4864.

668 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	C₄×C₂²⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#11926281	C₂	1	2	yes	maximal, complemented
3	C₂×#11926278	C₂	1	2	yes	maximal
4	#14561862	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2850	C₂	1	1	yes	maximal, characteristic
6	C₂×C₂²⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
7	C₂×C₄×C₁₉⋊C₈	—	2	1	no	—
8	C₂×C₁₉⋊#95	—	2	1	no	—
9	C₂×C₁₉⋊#95	—	2	1	no	—
10	C₂×C₁₉⋊#95	C₂²	1	2	yes	—
11	#11926299	—	2	1	no	—
12	#11926281	—	2	4	no	—
13	#11926278	—	2	4	no	—
14	C₂×C₁₉×#124	C₄	1	1	yes	characteristic, complemented
15	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×#391	C₄	1	1	yes	characteristic, complemented
19	C₁₉×#390	C₄	1	1	yes	characteristic, complemented
20	C₁₉×#388	—	2	1	no	—
21	C₁₉×#388	—	2	1	no	—
22	C₁₉×#386	—	2	1	no	—
23	C₁₉×#386	—	2	1	no	—
24	C₁₉×#382	C₄	1	1	yes	characteristic, complemented
25	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₂²×D₄×C₁₉	—	2	1	no	—
27	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
30	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
31	C₂³×Dic₁₉	—	2	2	no	—
32	C₁₉×#124	—	4	2	no	—
33	C₁₉×C₂²⋊Q₈	—	2	2	no	—
34	C₁₉×C₂²⋊Q₈	—	2	2	no	—
35	C₁₉×#121	—	2	2	no	—
36	C₁₉×#121	—	2	2	no	—
37	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
38	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
40	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
41	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
42	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
43	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
44	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
45	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
46	C₂×C₄²×C₁₉	—	4	2	no	—
47	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
50	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
51	C₂²×C₁₉⋊C₈	—	2	2	no	—
52	C₁₉×#95	—	2	1	no	—
53	C₁₉×#95	—	2	1	no	—
54	C₁₉×#95	—	2	1	no	—
55	C₁₉×#95	—	2	1	no	—
56	C₁₉⋊#95	—	2	4	no	—
57	C₁₉⋊#95	—	2	2	no	—
58	C₁₉⋊#95	—	2	2	no	—
59	C₁₉⋊#95	—	4	2	no	—
60	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
61	C₂²⋊(C₁₉⋊C₈)	D₄	1	4	yes	—
62	C₄×C₁₉⋊C₈	—	4	2	no	—
63	C₂⁴×C₁₉	—	2	1	no	—
64	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
65	C₂×Q₈×C₁₉	—	2	2	no	—
66	C₂×Q₈×C₁₉	—	4	1	no	—
67	C₂×Q₈×C₁₉	—	4	1	no	—
68	C₂×D₄×C₁₉	—	2	2	no	—
69	C₂×D₄×C₁₉	—	4	1	no	—
70	C₂×D₄×C₁₉	—	4	1	no	—
71	C₂×D₄×C₁₉	—	4	1	no	—
72	C₂×D₄×C₁₉	—	4	1	no	—
73	C₂×D₄×C₁₉	—	4	2	no	—
74	C₂×D₄×C₁₉	—	4	2	no	—
75	C₂²×C₄×C₁₉	—	2	2	no	—
76	C₂²×C₄×C₁₉	—	2	2	no	—
77	C₂²×C₄×C₁₉	—	2	2	no	—
78	C₂²×C₄×C₁₉	—	2	2	no	—
79	C₂²×C₄×C₁₉	—	2	1	no	—
80	C₂²×C₄×C₁₉	—	2	1	no	—
81	C₂²×C₄×C₁₉	—	2	1	no	—
82	C₂²×C₄×C₁₉	—	4	1	no	—
83	C₂²×C₄×C₁₉	—	4	1	no	—
84	C₂²×C₄×C₁₉	—	4	1	no	—
85	C₂²×C₄×C₁₉	—	4	1	no	—
86	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
92	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₉	#41	1	2	yes	—
94	C₂²×Dic₁₉	—	2	4	no	—
95	C₂²×Dic₁₉	—	4	2	no	—
96	C₂²×Dic₁₉	—	4	2	no	—
97	C₂²×Dic₁₉	—	4	2	no	—
98	C₂²×Dic₁₉	—	4	2	no	—
99	C₂²×Dic₁₉	—	4	2	no	—
100	C₂²×Dic₁₉	—	4	2	no	—
101	C₄⋊C₄×C₁₉	—	2	2	no	—
102	C₄⋊C₄×C₁₉	—	2	2	no	—
103	C₄⋊C₄×C₁₉	—	4	2	no	—
104	C₂²⋊C₄×C₁₉	—	4	2	no	—
105	C₂²⋊C₄×C₁₉	—	4	2	no	—
106	C₂²⋊C₄×C₁₉	—	4	1	no	—
107	C₂²⋊C₄×C₁₉	—	4	1	no	—
108	C₂²⋊C₄×C₁₉	—	4	2	no	—
109	C₂²⋊C₄×C₁₉	—	4	2	no	—
110	C₂²⋊C₄×C₁₉	—	4	2	no	—
111	C₄²×C₁₉	—	2	2	no	—
112	C₄²×C₁₉	—	2	2	no	—
113	C₄²×C₁₉	—	4	1	no	—
114	C₄²×C₁₉	—	4	1	no	—
115	C₂×C₁₉⋊C₈	—	2	4	no	—
116	C₂×C₁₉⋊C₈	—	4	2	no	—
117	C₂×C₁₉⋊C₈	—	4	2	no	—
118	#9681	—	19	1	no	maximal, Sylow
119	C₂³×C₁₉	—	2	1	no	—
120	C₂³×C₁₉	—	2	1	no	—
121	C₂³×C₁₉	—	2	1	no	—
122	C₂³×C₁₉	—	2	1	no	—
123	C₂³×C₁₉	—	4	1	no	—
124	C₂³×C₁₉	—	4	1	no	—
125	C₂³×C₁₉	—	4	1	no	—
126	C₂³×C₁₉	—	4	1	no	—
127	C₂³×C₁₉	—	4	1	no	—
128	C₂³×C₁₉	—	4	1	no	—
129	C₂³×C₁₉	—	4	1	no	—
130	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
131	C₂³×C₁₉	#124	1	1	yes	characteristic
132	C₂³×C₁₉	#127	1	1	yes	characteristic
133	C₂³×C₁₉	#135	1	2	yes	—
134	C₂³×C₁₉	#135	1	2	yes	—
135	Q₈×C₁₉	—	8	2	no	—
136	D₄×C₁₉	—	8	2	no	—
137	D₄×C₁₉	—	8	2	no	—
138	D₄×C₁₉	—	8	2	no	—
139	C₂×C₄×C₁₉	—	2	1	no	—
140	C₂×C₄×C₁₉	—	2	1	no	—
141	C₂×C₄×C₁₉	—	2	1	no	—
142	C₂×C₄×C₁₉	—	2	1	no	—
143	C₂×C₄×C₁₉	—	2	1	no	—
144	C₂×C₄×C₁₉	—	2	1	no	—
145	C₂×C₄×C₁₉	—	2	1	no	—
146	C₂×C₄×C₁₉	—	2	1	no	—
147	C₂×C₄×C₁₉	—	2	1	no	—
148	C₂×C₄×C₁₉	—	2	1	no	—
149	C₂×C₄×C₁₉	—	2	1	no	—
150	C₂×C₄×C₁₉	—	2	1	no	—
151	C₂×C₄×C₁₉	—	2	1	no	—
152	C₂×C₄×C₁₉	—	2	1	no	—
153	C₂×C₄×C₁₉	—	4	2	no	—
154	C₂×C₄×C₁₉	—	4	2	no	—
155	C₂×C₄×C₁₉	—	4	4	no	—
156	C₂×C₄×C₁₉	—	4	4	no	—
157	C₂×C₄×C₁₉	—	4	1	no	—
158	C₂×C₄×C₁₉	—	4	1	no	—
159	C₂×C₄×C₁₉	—	4	1	no	—
160	C₂×C₄×C₁₉	—	4	1	no	—
161	C₂×C₄×C₁₉	—	4	1	no	—
162	C₂×C₄×C₁₉	—	4	1	no	—
163	C₂×C₄×C₁₉	—	4	1	no	—
164	C₂×C₄×C₁₉	—	4	1	no	—
165	C₂×C₄×C₁₉	—	4	1	no	—
166	C₂×C₄×C₁₉	#99	1	2	yes	—
167	C₂×C₄×C₁₉	#104	1	2	yes	—
168	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
169	C₂×C₄×C₁₉	#121	1	2	yes	—
170	C₂×Dic₁₉	—	4	4	no	—
171	C₂×Dic₁₉	—	4	4	no	—
172	C₂×Dic₁₉	—	4	4	no	—
173	C₂×Dic₁₉	—	8	2	no	—
174	C₂×Dic₁₉	—	8	2	no	—
175	C₂×Dic₁₉	—	8	2	no	—
176	C₂×Dic₁₉	—	8	2	no	—
177	C₁₉⋊C₈	—	4	4	no	—
178	#2850	D₁₉	1	1	yes	characteristic
179	C₄×C₂²⋊C₈	—	19	1	no	—
180	C₂×#328	—	19	2	no	—
181	C₂×#327	—	19	2	no	—
182	#1434	—	19	1	no	—
183	C₂²×C₁₉	—	2	1	no	—
184	C₂²×C₁₉	—	2	1	no	—
185	C₂²×C₁₉	—	2	1	no	—
186	C₂²×C₁₉	—	2	1	no	—
187	C₂²×C₁₉	—	2	2	no	—
188	C₂²×C₁₉	—	2	2	no	—
189	C₂²×C₁₉	—	2	2	no	—
190	C₂²×C₁₉	—	2	2	no	—
191	C₂²×C₁₉	—	8	1	no	—
192	C₂²×C₁₉	—	8	1	no	—
193	C₂²×C₁₉	—	8	1	no	—
194	C₂²×C₁₉	—	8	1	no	—
195	C₂²×C₁₉	—	8	1	no	—
196	C₂²×C₁₉	—	8	1	no	—
197	C₂²×C₁₉	—	8	1	no	—
198	C₂²×C₁₉	#390	1	1	yes	characteristic
199	C₂²×C₁₉	C₂×#99	1	1	yes	characteristic
200	C₂²×C₁₉	#410	1	1	yes	characteristic
201	C₂²×C₁₉	#416	1	1	yes	characteristic
202	C₂²×C₁₉	#416	1	1	yes	characteristic
203	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
204	C₂²×C₁₉	#421	1	1	yes	characteristic
205	C₂²×C₁₉	#488	1	2	yes	—
206	C₂²×C₁₉	#495	1	2	yes	—
207	C₄×C₁₉	—	2	2	no	—
208	C₄×C₁₉	—	2	2	no	—
209	C₄×C₁₉	—	2	2	no	—
210	C₄×C₁₉	—	2	2	no	—
211	C₄×C₁₉	—	4	1	no	—
212	C₄×C₁₉	—	4	1	no	—
213	C₄×C₁₉	—	8	1	no	—
214	C₄×C₁₉	—	8	1	no	—
215	C₄×C₁₉	—	8	1	no	—
216	Dic₁₉	—	8	4	no	—
217	C₂×#124	Dic₁₉	1	1	yes	characteristic, complemented
218	C₂×C₂²⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
219	C₂×#121	C₂×D₁₉	1	1	yes	characteristic
220	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
221	C₂×C₂²⋊C₈	—	19	2	no	—
222	C₂×C₄×C₈	—	38	1	no	—
223	#391	Dic₁₉	1	1	yes	characteristic, complemented
224	#390	Dic₁₉	1	1	yes	characteristic, complemented
225	#388	—	2	1	no	—
226	#388	—	2	1	no	—
227	#386	—	2	1	no	—
228	#386	—	2	1	no	—
229	#382	Dic₁₉	1	1	yes	characteristic, complemented
230	C₂×#95	—	19	2	no	—
231	C₂×#95	—	38	1	no	—
232	C₂×#95	—	38	1	no	—
233	#336	—	38	1	no	—
234	#328	—	38	4	no	—
235	#327	—	38	4	no	—
236	C₂×C₁₉	—	2	2	no	—
237	C₂×C₁₉	—	2	2	no	—
238	C₂×C₁₉	—	16	1	no	—
239	C₂×C₁₉	#1500	1	1	yes	characteristic
240	C₂×C₁₉	#1501	1	1	yes	characteristic
241	C₂×C₁₉	#1516	1	1	yes	characteristic
242	C₂×C₁₉	#1521	1	1	yes	characteristic
243	C₂×C₁₉	#1958	1	1	yes	characteristic
244	C₂×C₁₉	#1964	1	1	yes	characteristic
245	C₂×C₁₉	#1980	1	1	yes	characteristic
246	C₂²×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
247	C₂²×D₄	—	2	1	no	—
248	C₂²×D₄	C₂×Dic₁₉	1	1	yes	characteristic
249	C₂³×C₄	—	38	2	no	—
250	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
251	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
252	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
253	C₂²×C₈	—	38	2	no	—
254	#124	—	4	2	no	—
255	C₂²⋊Q₈	—	2	2	no	—
256	C₂²⋊Q₈	—	2	2	no	—
257	#121	—	2	2	no	—
258	#121	—	2	2	no	—
259	C₂×C₄⋊C₄	—	2	1	no	—
260	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
261	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
262	C₂×C₂²⋊C₄	—	2	1	no	—
263	C₂×C₂²⋊C₄	—	2	1	no	—
264	C₂×C₂²⋊C₄	—	2	1	no	—
265	C₂×C₂²⋊C₄	—	2	1	no	—
266	C₂×C₂²⋊C₄	—	2	1	no	—
267	C₂×C₂²⋊C₄	—	2	1	no	—
268	C₂×C₄²	—	4	2	no	—
269	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
270	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
271	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
272	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
273	C₂²⋊C₈	—	19	4	no	—
274	C₂²⋊C₈	—	38	2	no	—
275	C₄×C₈	—	76	2	no	—
276	#95	—	2	1	no	—
277	#95	—	2	1	no	—
278	#95	—	2	1	no	—
279	#95	—	2	1	no	—
280	#95	—	38	4	no	—
281	#95	—	38	2	no	—
282	#95	—	38	2	no	—
283	#95	—	76	2	no	—
284	C₁₉	#9681	1	1	yes	characteristic, complemented, Sylow
285	C₂⁴	—	2	1	no	—
286	C₂⁴	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
287	C₂×Q₈	—	2	2	no	—
288	C₂×Q₈	—	4	1	no	—
289	C₂×Q₈	—	4	1	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	4	1	no	—
292	C₂×D₄	—	4	1	no	—
293	C₂×D₄	—	4	1	no	—
294	C₂×D₄	—	4	1	no	—
295	C₂×D₄	—	4	2	no	—
296	C₂×D₄	—	4	2	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	2	1	no	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	4	1	no	—
305	C₂²×C₄	—	4	1	no	—
306	C₂²×C₄	—	4	1	no	—
307	C₂²×C₄	—	4	1	no	—
308	C₂²×C₄	—	38	4	no	—
309	C₂²×C₄	—	76	2	no	—
310	C₂²×C₄	—	76	2	no	—
311	C₂²×C₄	—	76	2	no	—
312	C₂²×C₄	—	76	2	no	—
313	C₂²×C₄	—	76	2	no	—
314	C₂²×C₄	—	76	2	no	—
315	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
316	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
317	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
318	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
319	C₂²×C₄	D₄×D₁₉	1	2	yes	—
320	C₂²×C₄	#64543	1	2	yes	—
321	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
322	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
323	C₂×C₈	—	38	4	no	—
324	C₂×C₈	—	76	2	no	—
325	C₂×C₈	—	76	2	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	4	2	no	—
329	C₂²⋊C₄	—	4	2	no	—
330	C₂²⋊C₄	—	4	2	no	—
331	C₂²⋊C₄	—	4	1	no	—
332	C₂²⋊C₄	—	4	1	no	—
333	C₂²⋊C₄	—	4	2	no	—
334	C₂²⋊C₄	—	4	2	no	—
335	C₂²⋊C₄	—	4	2	no	—
336	C₄²	—	2	2	no	—
337	C₄²	—	2	2	no	—
338	C₄²	—	4	1	no	—
339	C₄²	—	4	1	no	—
340	C₂³	—	2	1	no	—
341	C₂³	—	2	1	no	—
342	C₂³	—	2	1	no	—
343	C₂³	—	2	1	no	—
344	C₂³	—	4	1	no	—
345	C₂³	—	4	1	no	—
346	C₂³	—	4	1	no	—
347	C₂³	—	4	1	no	—
348	C₂³	—	4	1	no	—
349	C₂³	—	4	1	no	—
350	C₂³	—	4	1	no	—
351	C₂³	#10597382	1	1	yes	characteristic
352	C₂³	#10597386	1	1	yes	characteristic
353	C₂³	#10597396	1	2	yes	—
354	C₂³	#10597396	1	2	yes	—
355	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
356	Q₈	—	8	2	no	—
357	D₄	—	8	2	no	—
358	D₄	—	8	2	no	—
359	D₄	—	8	2	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	4	no	—
377	C₂×C₄	—	4	4	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	76	4	no	—
388	C₂×C₄	—	76	4	no	—
389	C₂×C₄	—	76	4	no	—
390	C₂×C₄	—	152	2	no	—
391	C₂×C₄	—	152	2	no	—
392	C₂×C₄	—	152	2	no	—
393	C₂×C₄	—	152	2	no	—
394	C₂×C₄	#10597291	1	2	yes	—
395	C₂×C₄	#10597294	1	2	yes	—
396	C₂×C₄	D₄×Dic₁₉	1	2	yes	—
397	C₂×C₄	#10597384	1	2	yes	—
398	C₈	—	76	4	no	—
399	C₂²	—	2	2	no	—
400	C₂²	—	2	2	no	—
401	C₂²	—	2	1	no	—
402	C₂²	—	2	1	no	—
403	C₂²	—	2	2	no	—
404	C₂²	—	2	2	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	8	1	no	—
408	C₂²	—	8	1	no	—
409	C₂²	—	8	1	no	—
410	C₂²	—	8	1	no	—
411	C₂²	—	8	1	no	—
412	C₂²	—	8	1	no	—
413	C₂²	—	8	1	no	—
414	C₂²	#11926447	1	1	yes	characteristic
415	C₂²	C₂×#10597291	1	1	yes	characteristic
416	C₂²	#11926518	1	1	yes	characteristic
417	C₂²	#11926540	1	1	yes	characteristic
418	C₂²	#11926540	1	1	yes	characteristic
419	C₂²	C₂×#10597294	1	1	yes	characteristic
420	C₂²	#11926561	1	1	yes	characteristic
421	C₂²	#11926898	1	2	yes	—
422	C₂²	#11926926	1	2	yes	—
423	C₄	—	2	2	no	—
424	C₄	—	2	2	no	—
425	C₄	—	2	2	no	—
426	C₄	—	2	2	no	—
427	C₄	—	4	1	no	—
428	C₄	—	4	1	no	—
429	C₄	—	8	1	no	—
430	C₄	—	8	1	no	—
431	C₄	—	8	1	no	—
432	C₄	—	152	4	no	—
433	C₂	—	2	2	no	—
434	C₂	—	2	2	no	—
435	C₂	—	16	1	no	—
436	C₂	#14562121	1	1	yes	characteristic
437	C₂	#14562126	1	1	yes	characteristic
438	C₂	#14562191	1	1	yes	characteristic
439	C₂	#14562212	1	1	yes	characteristic
440	C₂	#14564447	1	1	yes	characteristic
441	C₂	#14564472	1	1	yes	characteristic
442	C₂	#14564555	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×#2850	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂×C₁₉×#121	C₂²
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	#2850	D₁₉
hypocenter	C₁₉	#9681
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ #2850

Complements

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

N	H ≅ G/N	type
1. C₄×C₂²⋊(C₁₉⋊C₈)	C₂	semidirect
2. C₂×#11926281	C₂	semidirect
4. #14561862	C₂	semidirect
14. C₂×C₁₉×#124	C₄	semidirect
18. C₁₉×#391	C₄	semidirect
19. C₁₉×#390	C₄	semidirect
24. C₁₉×#382	C₄	semidirect
217. C₂×#124	Dic₁₉	semidirect
223. #391	Dic₁₉	semidirect
224. #390	Dic₁₉	semidirect
229. #382	Dic₁₉	semidirect
284. C₁₉	#9681	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₂²⋊(C₁₉⋊C₈)	2
C₂×#11926281	2
C₂×#11926278	2
#14561862	2
C₁₉×#2850	2
#9681	19