Subgroups — #18078245

Order 4864.

752 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926568	C₂	1	1	yes	maximal, characteristic, complemented
2	#14563615	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#11926288	C₂	1	2	yes	maximal, complemented
4	#14561518	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2856	C₂	1	1	yes	maximal, characteristic
6	C₂²×#64520	—	2	1	no	—
7	#11926568	—	2	4	no	—
8	C₂×C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
9	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
10	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
11	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
12	#11926299	—	2	1	no	—
13	#11926288	—	2	4	no	—
14	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×#121	—	2	1	no	—
16	C₂×C₁₉×#121	—	2	1	no	—
17	C₂×C₁₉×#121	C₄	1	2	yes	—
18	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
19	C₁₉×#390	—	2	1	no	—
20	C₁₉×#390	—	2	1	no	—
21	C₁₉×#390	C₄	1	2	yes	—
22	C₁₉×#384	C₂²	1	1	yes	characteristic
23	C₂²×D₄×C₁₉	—	2	2	no	—
24	C₂²×D₄×C₁₉	—	2	1	no	—
25	C₂²×D₄×C₁₉	—	2	1	no	—
26	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
27	C₂³×C₄×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	C₁₉×#127	—	2	2	no	—
31	C₁₉×#127	—	2	2	no	—
32	C₁₉×#121	—	4	4	no	—
33	C₁₉×#121	—	4	2	no	—
34	C₁₉×#121	—	4	2	no	—
35	C₁₉×#121	—	4	4	no	—
36	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
37	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
38	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
39	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
40	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
41	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
42	C₂×C₄²×C₁₉	—	2	2	no	—
43	C₂×C₄²×C₁₉	—	2	2	no	—
44	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
46	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
47	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
48	C₂×#64520	—	2	4	no	—
49	C₂×#64520	—	4	2	no	—
50	C₂×#64520	—	4	2	no	—
51	C₂²×C₁₉⋊C₈	—	2	2	no	—
52	C₂²×C₁₉⋊C₈	—	2	2	no	—
53	C₂²⋊(C₁₉⋊C₈)	—	4	2	no	—
54	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
55	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
56	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
57	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
58	C₄⋊(C₁₉⋊C₈)	D₄	1	4	yes	complemented
59	C₂⁴×C₁₉	—	2	2	no	—
60	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
61	C₂×D₄×C₁₉	—	2	4	no	—
62	C₂×D₄×C₁₉	—	4	2	no	—
63	C₂×D₄×C₁₉	—	4	2	no	—
64	C₂×D₄×C₁₉	—	4	4	no	—
65	C₂×D₄×C₁₉	—	4	4	no	—
66	C₂×D₄×C₁₉	—	4	4	no	—
67	C₂×D₄×C₁₉	—	4	1	no	—
68	C₂×D₄×C₁₉	—	4	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	2	no	—
73	C₂×D₄×C₁₉	—	4	1	no	—
74	C₂×D₄×C₁₉	—	4	1	no	—
75	C₂×D₄×C₁₉	—	4	1	no	—
76	C₂×D₄×C₁₉	—	4	1	no	—
77	C₂²×C₄×C₁₉	—	2	1	no	—
78	C₂²×C₄×C₁₉	—	2	1	no	—
79	C₂²×C₄×C₁₉	—	2	1	no	—
80	C₂²×C₄×C₁₉	—	2	1	no	—
81	C₂²×C₄×C₁₉	—	2	2	no	—
82	C₂²×C₄×C₁₉	—	2	2	no	—
83	C₂²×C₄×C₁₉	—	2	2	no	—
84	C₂²×C₄×C₁₉	—	2	2	no	—
85	C₂²×C₄×C₁₉	—	2	1	no	—
86	C₂²×C₄×C₁₉	—	2	1	no	—
87	C₂²×C₄×C₁₉	—	2	2	no	—
88	C₂²×C₄×C₁₉	—	4	1	no	—
89	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₉	D₈	1	2	yes	—
93	C₂²×C₄×C₁₉	SD₁₆	1	2	yes	—
94	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
97	C₄⋊C₄×C₁₉	—	4	2	no	—
98	C₄⋊C₄×C₁₉	—	4	1	no	—
99	C₄⋊C₄×C₁₉	—	4	1	no	—
100	C₄⋊C₄×C₁₉	—	4	2	no	—
101	C₂²⋊C₄×C₁₉	—	4	4	no	—
102	C₂²⋊C₄×C₁₉	—	4	4	no	—
103	C₂²⋊C₄×C₁₉	—	4	4	no	—
104	C₄²×C₁₉	—	2	2	no	—
105	C₄²×C₁₉	—	2	1	no	—
106	C₄²×C₁₉	—	2	2	no	—
107	C₄²×C₁₉	—	2	1	no	—
108	C₄²×C₁₉	C₂×D₄	1	2	yes	—
109	C₄²×C₁₉	#41	1	2	yes	—
110	#64520	—	4	8	no	—
111	C₂×C₁₉⋊C₈	—	2	4	no	—
112	C₂×C₁₉⋊C₈	—	4	2	no	—
113	C₂×C₁₉⋊C₈	—	4	2	no	—
114	C₂×C₁₉⋊C₈	—	4	2	no	—
115	C₂×C₁₉⋊C₈	—	4	2	no	—
116	C₂×C₁₉⋊C₈	—	4	2	no	—
117	#9141	—	19	1	no	maximal, Sylow
118	C₂³×C₁₉	—	2	1	no	—
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	—	2	1	no	—
124	C₂³×C₁₉	—	4	2	no	—
125	C₂³×C₁₉	—	4	2	no	—
126	C₂³×C₁₉	—	4	2	no	—
127	C₂³×C₁₉	—	4	2	no	—
128	C₂³×C₁₉	—	4	2	no	—
129	C₂³×C₁₉	—	4	2	no	—
130	C₂³×C₁₉	—	4	2	no	—
131	C₂³×C₁₉	#102	1	2	yes	—
132	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
133	D₄×C₁₉	—	8	4	no	—
134	D₄×C₁₉	—	8	8	no	—
135	D₄×C₁₉	—	8	1	no	—
136	D₄×C₁₉	—	8	1	no	—
137	D₄×C₁₉	—	8	2	no	—
138	D₄×C₁₉	—	8	2	no	—
139	D₄×C₁₉	—	8	1	no	—
140	D₄×C₁₉	—	8	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	2	no	—
148	C₂×C₄×C₁₉	—	2	2	no	—
149	C₂×C₄×C₁₉	—	2	2	no	—
150	C₂×C₄×C₁₉	—	2	2	no	—
151	C₂×C₄×C₁₉	—	2	1	no	—
152	C₂×C₄×C₁₉	—	2	1	no	—
153	C₂×C₄×C₁₉	—	2	1	no	—
154	C₂×C₄×C₁₉	—	4	4	no	—
155	C₂×C₄×C₁₉	—	4	2	no	—
156	C₂×C₄×C₁₉	—	4	2	no	—
157	C₂×C₄×C₁₉	—	4	2	no	—
158	C₂×C₄×C₁₉	—	4	2	no	—
159	C₂×C₄×C₁₉	—	4	2	no	—
160	C₂×C₄×C₁₉	#100	1	2	yes	—
161	C₂×C₄×C₁₉	#102	1	2	yes	—
162	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
163	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
164	C₂×C₄×C₁₉	#121	1	2	yes	—
165	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
166	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
167	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
168	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
169	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
170	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
171	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
172	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
173	C₁₉⋊C₈	—	4	4	no	—
174	C₁₉⋊C₈	—	8	2	no	—
175	C₂×#423	—	19	1	no	—
176	#2856	D₁₉	1	1	yes	characteristic
177	#1797	—	19	1	no	—
178	C₂×#331	—	19	2	no	—
179	#1296	—	19	2	no	—
180	C₂²×C₁₉	—	2	2	no	—
181	C₂²×C₁₉	—	2	2	no	—
182	C₂²×C₁₉	—	2	2	no	—
183	C₂²×C₁₉	—	4	1	no	—
184	C₂²×C₁₉	—	4	1	no	—
185	C₂²×C₁₉	—	4	1	no	—
186	C₂²×C₁₉	—	4	1	no	—
187	C₂²×C₁₉	—	8	2	no	—
188	C₂²×C₁₉	—	8	2	no	—
189	C₂²×C₁₉	—	8	2	no	—
190	C₂²×C₁₉	—	8	2	no	—
191	C₂²×C₁₉	—	8	2	no	—
192	C₂²×C₁₉	—	8	2	no	—
193	C₂²×C₁₉	—	8	2	no	—
194	C₂²×C₁₉	#386	1	1	yes	characteristic
195	C₂²×C₁₉	C₂×#100	1	1	yes	characteristic
196	C₂²×C₁₉	#413	1	1	yes	characteristic
197	C₂²×C₁₉	C₂×#102	1	1	yes	characteristic
198	C₂²×C₁₉	#417	1	1	yes	characteristic
199	C₂²×C₁₉	#417	1	1	yes	characteristic
200	C₂²×C₁₉	#418	1	1	yes	characteristic
201	C₄×C₁₉	—	2	2	no	—
202	C₄×C₁₉	—	2	2	no	—
203	C₄×C₁₉	—	2	2	no	—
204	C₄×C₁₉	—	4	1	no	—
205	C₄×C₁₉	—	8	2	no	—
206	C₄×C₁₉	#447	1	1	yes	characteristic
207	C₄×C₁₉	#448	1	1	yes	characteristic
208	C₄×C₁₉	#468	1	2	yes	—
209	C₄×C₁₉	#469	1	2	yes	—
210	C₄×C₁₉	#480	1	1	yes	characteristic
211	C₄×C₁₉	#481	1	1	yes	characteristic
212	C₂²×M₁₆	—	38	1	no	—
213	C₂×#127	C₂×D₁₉	1	1	yes	characteristic
214	C₂×#121	—	2	1	no	—
215	C₂×#121	—	2	1	no	—
216	C₂×#121	Dic₁₉	1	2	yes	—
217	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
218	#423	—	38	4	no	—
219	C₂×C₄⋊C₈	—	19	2	no	—
220	C₂×C₄⋊C₈	—	19	2	no	—
221	C₂×C₄⋊C₈	—	38	1	no	—
222	C₂×C₂²⋊C₈	—	38	1	no	—
223	#390	—	2	1	no	—
224	#390	—	2	1	no	—
225	#390	Dic₁₉	1	2	yes	—
226	#384	C₂×D₁₉	1	1	yes	characteristic
227	#336	—	38	1	no	—
228	#331	—	38	4	no	—
229	C₂×C₁₉	—	4	2	no	—
230	C₂×C₁₉	—	16	2	no	—
231	C₂×C₁₉	#1545	1	1	yes	characteristic
232	C₂×C₁₉	#1547	1	1	yes	characteristic
233	C₂×C₁₉	#1557	1	1	yes	characteristic
234	C₂×C₁₉	#1560	1	1	yes	characteristic
235	C₂×C₁₉	#1874	1	1	yes	characteristic
236	C₂×C₁₉	#1895	1	1	yes	characteristic
237	C₂×C₁₉	#1900	1	1	yes	characteristic
238	C₂²×D₄	—	2	2	no	—
239	C₂²×D₄	—	2	1	no	—
240	C₂²×D₄	—	2	1	no	—
241	C₂²×D₄	C₂×Dic₁₉	1	2	yes	—
242	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
243	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
244	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
245	C₂×M₁₆	—	38	4	no	—
246	C₂×M₁₆	—	76	2	no	—
247	C₂×M₁₆	—	76	2	no	—
248	C₂²×C₈	—	38	2	no	—
249	C₂²×C₈	—	38	2	no	—
250	#127	—	2	2	no	—
251	#127	—	2	2	no	—
252	#121	—	4	4	no	—
253	#121	—	4	2	no	—
254	#121	—	4	2	no	—
255	#121	—	4	4	no	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄⋊C₄	—	2	1	no	—
258	C₂×C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
259	C₂×C₂²⋊C₄	—	2	2	no	—
260	C₂×C₂²⋊C₄	—	2	2	no	—
261	C₂×C₂²⋊C₄	—	2	2	no	—
262	C₂×C₄²	—	2	2	no	—
263	C₂×C₄²	—	2	2	no	—
264	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
265	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
266	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
267	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
268	C₄⋊C₈	—	19	4	no	—
269	C₄⋊C₈	—	38	4	no	—
270	C₄⋊C₈	—	38	2	no	—
271	C₄⋊C₈	—	38	2	no	—
272	C₄⋊C₈	—	38	2	no	—
273	C₂²⋊C₈	—	76	2	no	—
274	C₁₉	#9141	1	1	yes	characteristic, complemented, Sylow
275	C₂⁴	—	2	2	no	—
276	C₂⁴	C₂²⋊Dic₁₉	1	1	yes	characteristic
277	C₂×D₄	—	2	4	no	—
278	C₂×D₄	—	4	2	no	—
279	C₂×D₄	—	4	2	no	—
280	C₂×D₄	—	4	4	no	—
281	C₂×D₄	—	4	4	no	—
282	C₂×D₄	—	4	4	no	—
283	C₂×D₄	—	4	1	no	—
284	C₂×D₄	—	4	2	no	—
285	C₂×D₄	—	4	1	no	—
286	C₂×D₄	—	4	1	no	—
287	C₂×D₄	—	4	1	no	—
288	C₂×D₄	—	4	2	no	—
289	C₂×D₄	—	4	1	no	—
290	C₂×D₄	—	4	1	no	—
291	C₂×D₄	—	4	1	no	—
292	C₂×D₄	—	4	1	no	—
293	C₂²×C₄	—	2	1	no	—
294	C₂²×C₄	—	2	1	no	—
295	C₂²×C₄	—	2	1	no	—
296	C₂²×C₄	—	2	1	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	4	1	no	—
305	C₂²×C₄	#64525	1	2	yes	—
306	C₂²×C₄	#64526	1	2	yes	—
307	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
308	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
309	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
310	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
311	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
312	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
313	M₁₆	—	76	8	no	—
314	C₂×C₈	—	38	4	no	—
315	C₂×C₈	—	76	2	no	—
316	C₂×C₈	—	76	2	no	—
317	C₂×C₈	—	76	2	no	—
318	C₂×C₈	—	76	2	no	—
319	C₂×C₈	—	76	2	no	—
320	C₄⋊C₄	—	4	2	no	—
321	C₄⋊C₄	—	4	1	no	—
322	C₄⋊C₄	—	4	2	no	—
323	C₄⋊C₄	—	4	1	no	—
324	C₂²⋊C₄	—	4	4	no	—
325	C₂²⋊C₄	—	4	4	no	—
326	C₂²⋊C₄	—	4	4	no	—
327	C₄²	—	2	2	no	—
328	C₄²	—	2	1	no	—
329	C₄²	—	2	1	no	—
330	C₄²	—	2	2	no	—
331	C₄²	D₄×D₁₉	1	2	yes	—
332	C₄²	#64543	1	2	yes	—
333	C₂³	—	2	1	no	—
334	C₂³	—	2	1	no	—
335	C₂³	—	2	1	no	—
336	C₂³	—	2	1	no	—
337	C₂³	—	2	1	no	—
338	C₂³	—	2	1	no	—
339	C₂³	—	4	2	no	—
340	C₂³	—	4	2	no	—
341	C₂³	—	4	2	no	—
342	C₂³	—	4	2	no	—
343	C₂³	—	4	2	no	—
344	C₂³	—	4	2	no	—
345	C₂³	—	4	2	no	—
346	C₂³	#10597289	1	2	yes	—
347	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
348	D₄	—	8	4	no	—
349	D₄	—	8	8	no	—
350	D₄	—	8	2	no	—
351	D₄	—	8	2	no	—
352	D₄	—	8	1	no	—
353	D₄	—	8	1	no	—
354	D₄	—	8	1	no	—
355	D₄	—	8	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	4	4	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	#10597289	1	2	yes	—
376	C₂×C₄	#10597290	1	2	yes	—
377	C₂×C₄	C₂×#64525	1	1	yes	characteristic
378	C₂×C₄	#10597378	1	2	yes	—
379	C₂×C₄	C₂×#64526	1	1	yes	characteristic
380	C₂×C₄	D₄×Dic₁₉	1	2	yes	—
381	C₂×C₄	#10597381	1	1	yes	characteristic
382	C₂×C₄	#10597383	1	1	yes	characteristic
383	C₂×C₄	#10597385	1	2	yes	—
384	C₂×C₄	#10597395	1	1	yes	characteristic
385	C₂×C₄	#10597395	1	1	yes	characteristic
386	C₂×C₄	#10597397	1	1	yes	characteristic
387	C₂×C₄	#10597397	1	1	yes	characteristic
388	C₈	—	76	4	no	—
389	C₈	—	152	2	no	—
390	C₂²	—	2	2	no	—
391	C₂²	—	2	2	no	—
392	C₂²	—	2	2	no	—
393	C₂²	—	4	1	no	—
394	C₂²	—	4	1	no	—
395	C₂²	—	4	1	no	—
396	C₂²	—	4	1	no	—
397	C₂²	—	8	2	no	—
398	C₂²	—	8	2	no	—
399	C₂²	—	8	2	no	—
400	C₂²	—	8	2	no	—
401	C₂²	—	8	2	no	—
402	C₂²	—	8	2	no	—
403	C₂²	—	8	2	no	—
404	C₂²	#11926424	1	1	yes	characteristic
405	C₂²	C₂×#10597290	1	1	yes	characteristic
406	C₂²	#11926528	1	1	yes	characteristic
407	C₂²	C₂×#10597289	1	1	yes	characteristic
408	C₂²	#11926545	1	1	yes	characteristic
409	C₂²	#11926545	1	1	yes	characteristic
410	C₂²	#11926549	1	1	yes	characteristic
411	C₄	—	2	2	no	—
412	C₄	—	2	2	no	—
413	C₄	—	2	2	no	—
414	C₄	—	4	1	no	—
415	C₄	—	8	2	no	—
416	C₄	#11926677	1	1	yes	characteristic
417	C₄	#11926682	1	1	yes	characteristic
418	C₄	#11926788	1	2	yes	—
419	C₄	#11926795	1	2	yes	—
420	C₄	#11926855	1	1	yes	characteristic
421	C₄	#11926860	1	1	yes	characteristic
422	C₂	—	4	2	no	—
423	C₂	—	16	2	no	—
424	C₂	#14562303	1	1	yes	characteristic
425	C₂	#14562312	1	1	yes	characteristic
426	C₂	#14562357	1	1	yes	characteristic
427	C₂	#14562370	1	1	yes	characteristic
428	C₂	#14563953	1	1	yes	characteristic
429	C₂	#14564074	1	1	yes	characteristic
430	C₂	#14564099	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting, prime radical	C₁₉×#2856	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#2856	D₁₉
hypocenter	C₁₉	#9141
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ #2856

Complements

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

N	H ≅ G/N	type
1. C₂×#11926568	C₂	semidirect
2. #14563615	C₂	semidirect
3. C₂×#11926288	C₂	semidirect
4. #14561518	C₂	semidirect
58. C₄⋊(C₁₉⋊C₈)	D₄	semidirect
274. C₁₉	#9141	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926568	2
#14563615	2
C₂×#11926288	2
#14561518	2
C₁₉×#2856	2
#9141	19