Subgroups — #18081522

Order 4864.

826 conjugacy classes of subgroups.

The subgroup lattice has 448 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×#11926278	C₂	1	4	yes	maximal, complemented
3	#14561865	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2856	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄⋊Dic₁₉	—	2	1	no	—
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	C₂²	1	2	yes	—
10	#11926299	—	2	1	no	—
11	#11926278	—	2	8	no	—
12	C₂×C₁₉×#127	C₄	1	1	yes	characteristic, complemented
13	C₂×C₁₉×#121	—	2	1	no	—
14	C₂×C₁₉×#121	—	2	1	no	—
15	C₂×C₁₉×#121	C₂²	1	2	yes	—
16	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
17	C₁₉×#390	—	2	1	no	—
18	C₁₉×#390	—	2	1	no	—
19	C₁₉×#390	C₄	1	2	yes	complemented
20	C₁₉×#384	C₄	1	1	yes	characteristic, complemented
21	C₂²×D₄×C₁₉	—	2	2	no	—
22	C₂²×D₄×C₁₉	—	2	1	no	—
23	C₂²×D₄×C₁₉	—	2	1	no	—
24	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
25	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
26	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
27	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
28	C₂³×Dic₁₉	—	2	2	no	—
29	C₁₉×#127	—	4	2	no	—
30	C₁₉×#121	—	2	4	no	—
31	C₁₉×#121	—	2	4	no	—
32	C₁₉×#121	—	4	2	no	—
33	C₁₉×#121	—	4	2	no	—
34	C₁₉×#121	—	4	2	no	—
35	C₁₉×#121	—	4	2	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	—	4	2	no	—
43	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
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×C₄⋊Dic₁₉	—	2	4	no	—
48	C₂×C₄⋊Dic₁₉	—	4	2	no	—
49	C₂×C₄⋊Dic₁₉	—	4	2	no	—
50	C₂²×C₁₉⋊C₈	—	2	2	no	—
51	C₁₉⋊#95	—	2	4	no	—
52	C₁₉⋊#95	—	4	2	no	—
53	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
54	C₂²⋊(C₁₉⋊C₈)	D₄	1	4	yes	complemented
55	C₄×C₁₉⋊C₈	—	4	2	no	—
56	C₂⁴×C₁₉	—	2	2	no	—
57	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
58	C₂×D₄×C₁₉	—	2	4	no	—
59	C₂×D₄×C₁₉	—	4	2	no	—
60	C₂×D₄×C₁₉	—	4	2	no	—
61	C₂×D₄×C₁₉	—	4	2	no	—
62	C₂×D₄×C₁₉	—	4	2	no	—
63	C₂×D₄×C₁₉	—	4	2	no	—
64	C₂×D₄×C₁₉	—	4	2	no	—
65	C₂×D₄×C₁₉	—	4	2	no	—
66	C₂×D₄×C₁₉	—	4	2	no	—
67	C₂×D₄×C₁₉	—	4	2	no	—
68	C₂×D₄×C₁₉	—	4	2	no	—
69	C₂×D₄×C₁₉	—	4	2	no	—
70	C₂×D₄×C₁₉	—	4	2	no	—
71	C₂×D₄×C₁₉	—	4	2	no	—
72	C₂×D₄×C₁₉	—	4	2	no	—
73	C₂²×C₄×C₁₉	—	2	2	no	—
74	C₂²×C₄×C₁₉	—	2	2	no	—
75	C₂²×C₄×C₁₉	—	2	2	no	—
76	C₂²×C₄×C₁₉	—	4	1	no	—
77	C₂²×C₄×C₁₉	—	4	1	no	—
78	C₂²×C₄×C₁₉	—	4	1	no	—
79	C₂²×C₄×C₁₉	—	4	1	no	—
80	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₉	D₈	1	2	yes	—
85	C₂²×C₄×C₁₉	D₈	1	2	yes	—
86	C₂²×C₄×C₁₉	SD₁₆	1	2	yes	—
87	C₂²×C₄×C₁₉	SD₁₆	1	2	yes	—
88	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
90	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₉	#41	1	2	yes	—
92	C₂²×Dic₁₉	—	2	4	no	—
93	C₂²×Dic₁₉	—	4	2	no	—
94	C₂²×Dic₁₉	—	4	2	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	C₄⋊C₄×C₁₉	—	2	4	no	—
100	C₄⋊C₄×C₁₉	—	4	2	no	—
101	C₄⋊C₄×C₁₉	—	4	2	no	—
102	C₂²⋊C₄×C₁₉	—	4	4	no	—
103	C₂²⋊C₄×C₁₉	—	4	4	no	—
104	C₂²⋊C₄×C₁₉	—	4	4	no	—
105	C₄²×C₁₉	—	2	2	no	—
106	C₄²×C₁₉	—	2	2	no	—
107	C₄²×C₁₉	—	4	1	no	—
108	C₄²×C₁₉	—	4	1	no	—
109	C₄⋊Dic₁₉	—	4	8	no	—
110	C₂×C₁₉⋊C₈	—	2	4	no	—
111	C₂×C₁₉⋊C₈	—	4	2	no	—
112	C₂×C₁₉⋊C₈	—	4	2	no	—
113	#9680	—	19	1	no	maximal, Sylow
114	C₂³×C₁₉	—	2	1	no	—
115	C₂³×C₁₉	—	2	1	no	—
116	C₂³×C₁₉	—	2	1	no	—
117	C₂³×C₁₉	—	2	1	no	—
118	C₂³×C₁₉	—	4	2	no	—
119	C₂³×C₁₉	—	4	2	no	—
120	C₂³×C₁₉	—	4	2	no	—
121	C₂³×C₁₉	—	4	2	no	—
122	C₂³×C₁₉	—	4	2	no	—
123	C₂³×C₁₉	—	4	2	no	—
124	C₂³×C₁₉	—	4	2	no	—
125	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
126	C₂³×C₁₉	#124	1	1	yes	characteristic
127	C₂³×C₁₉	#127	1	1	yes	characteristic
128	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
129	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
130	C₂³×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
131	C₂³×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
132	D₄×C₁₉	—	8	4	no	—
133	D₄×C₁₉	—	8	4	no	—
134	D₄×C₁₉	—	8	2	no	—
135	D₄×C₁₉	—	8	2	no	—
136	D₄×C₁₉	—	8	2	no	—
137	D₄×C₁₉	—	8	2	no	—
138	D₄×C₁₉	—	8	4	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	4	no	—
150	C₂×C₄×C₁₉	—	2	4	no	—
151	C₂×C₄×C₁₉	—	4	2	no	—
152	C₂×C₄×C₁₉	—	4	2	no	—
153	C₂×C₄×C₁₉	—	4	2	no	—
154	C₂×C₄×C₁₉	—	4	2	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	#99	1	2	yes	—
159	C₂×C₄×C₁₉	#102	1	2	yes	—
160	C₂×C₄×C₁₉	#102	1	2	yes	—
161	C₂×C₄×C₁₉	#102	1	2	yes	—
162	C₂×C₄×C₁₉	#102	1	2	yes	—
163	C₂×C₄×C₁₉	#104	1	2	yes	—
164	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
165	C₂×C₄×C₁₉	#121	1	2	yes	—
166	C₂×Dic₁₉	—	4	4	no	—
167	C₂×Dic₁₉	—	4	4	no	—
168	C₂×Dic₁₉	—	4	4	no	—
169	C₂×Dic₁₉	—	8	2	no	—
170	C₂×Dic₁₉	—	8	2	no	—
171	C₂×Dic₁₉	—	8	2	no	—
172	C₂×Dic₁₉	—	8	2	no	—
173	C₁₉⋊C₈	—	4	4	no	—
174	#2856	D₁₉	1	1	yes	characteristic
175	C₄×C₂²⋊C₈	—	19	1	no	—
176	C₂×#327	—	19	4	no	—
177	C₄⋊#95	—	19	1	no	—
178	C₂²×C₁₉	—	2	1	no	—
179	C₂²×C₁₉	—	2	1	no	—
180	C₂²×C₁₉	—	2	1	no	—
181	C₂²×C₁₉	—	2	1	no	—
182	C₂²×C₁₉	—	2	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	1	no	—
188	C₂²×C₁₉	—	2	1	no	—
189	C₂²×C₁₉	—	2	1	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	—	8	2	no	—
195	C₂²×C₁₉	—	8	2	no	—
196	C₂²×C₁₉	—	8	2	no	—
197	C₂²×C₁₉	#390	1	1	yes	characteristic
198	C₂²×C₁₉	C₂×#99	1	1	yes	characteristic
199	C₂²×C₁₉	#410	1	1	yes	characteristic
200	C₂²×C₁₉	C₂×#102	1	1	yes	characteristic
201	C₂²×C₁₉	C₂×#102	1	1	yes	characteristic
202	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
203	C₂²×C₁₉	#421	1	1	yes	characteristic
204	C₂²×C₁₉	#486	1	1	yes	characteristic
205	C₂²×C₁₉	#486	1	1	yes	characteristic
206	C₂²×C₁₉	#492	1	1	yes	characteristic
207	C₂²×C₁₉	#493	1	1	yes	characteristic
208	C₄×C₁₉	—	2	2	no	—
209	C₄×C₁₉	—	2	2	no	—
210	C₄×C₁₉	—	2	2	no	—
211	C₄×C₁₉	—	2	2	no	—
212	C₄×C₁₉	—	2	2	no	—
213	C₄×C₁₉	—	8	2	no	—
214	C₄×C₁₉	#327	1	4	yes	complemented
215	Dic₁₉	—	8	4	no	—
216	C₂×#127	Dic₁₉	1	1	yes	characteristic, complemented
217	C₂×#121	—	2	1	no	—
218	C₂×#121	—	2	1	no	—
219	C₂×#121	C₂×D₁₉	1	2	yes	—
220	C₂²×C₄⋊C₄	—	38	1	no	—
221	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
222	C₂×C₂²⋊C₈	—	19	2	no	—
223	C₂×C₄×C₈	—	38	1	no	—
224	#390	—	2	1	no	—
225	#390	—	2	1	no	—
226	#390	Dic₁₉	1	2	yes	complemented
227	#384	Dic₁₉	1	1	yes	characteristic, complemented
228	C₂×#95	—	19	2	no	—
229	C₂×#95	—	38	1	no	—
230	#336	—	38	1	no	—
231	#327	—	38	8	no	—
232	C₂×C₁₉	—	2	1	no	—
233	C₂×C₁₉	—	2	1	no	—
234	C₂×C₁₉	—	2	1	no	—
235	C₂×C₁₉	—	2	1	no	—
236	C₂×C₁₉	—	16	2	no	—
237	C₂×C₁₉	C₂×#327	1	1	yes	characteristic
238	C₂×C₁₉	#1502	1	1	yes	characteristic
239	C₂×C₁₉	#1517	1	1	yes	characteristic
240	C₂×C₁₉	#1519	1	1	yes	characteristic
241	C₂×C₁₉	#1957	1	1	yes	characteristic
242	C₂×C₁₉	#1964	1	1	yes	characteristic
243	C₂×C₁₉	#1980	1	1	yes	characteristic
244	C₂²×D₄	—	2	2	no	—
245	C₂²×D₄	—	2	1	no	—
246	C₂²×D₄	—	2	1	no	—
247	C₂²×D₄	C₂×Dic₁₉	1	2	yes	—
248	C₂³×C₄	—	38	2	no	—
249	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
250	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
251	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
252	C₂²×C₈	—	38	2	no	—
253	#127	—	4	2	no	—
254	#121	—	2	4	no	—
255	#121	—	2	4	no	—
256	#121	—	4	2	no	—
257	#121	—	4	2	no	—
258	#121	—	4	2	no	—
259	#121	—	4	2	no	—
260	C₂×C₄⋊C₄	—	2	1	no	—
261	C₂×C₄⋊C₄	—	2	1	no	—
262	C₂×C₄⋊C₄	—	38	4	no	—
263	C₂×C₄⋊C₄	—	76	2	no	—
264	C₂×C₄⋊C₄	—	76	2	no	—
265	C₂×C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
266	C₂×C₂²⋊C₄	—	2	2	no	—
267	C₂×C₂²⋊C₄	—	2	2	no	—
268	C₂×C₂²⋊C₄	—	2	2	no	—
269	C₂×C₄²	—	4	2	no	—
270	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
271	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
272	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
273	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
274	C₂²⋊C₈	—	19	4	no	—
275	C₂²⋊C₈	—	38	2	no	—
276	C₄×C₈	—	76	2	no	—
277	#95	—	38	4	no	—
278	#95	—	76	2	no	—
279	C₁₉	#9680	1	1	yes	characteristic, complemented, Sylow
280	C₂⁴	—	2	2	no	—
281	C₂⁴	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
282	C₂×D₄	—	2	4	no	—
283	C₂×D₄	—	4	2	no	—
284	C₂×D₄	—	4	2	no	—
285	C₂×D₄	—	4	2	no	—
286	C₂×D₄	—	4	2	no	—
287	C₂×D₄	—	4	2	no	—
288	C₂×D₄	—	4	2	no	—
289	C₂×D₄	—	4	2	no	—
290	C₂×D₄	—	4	2	no	—
291	C₂×D₄	—	4	2	no	—
292	C₂×D₄	—	4	2	no	—
293	C₂×D₄	—	4	2	no	—
294	C₂×D₄	—	4	2	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	—	4	1	no	—
301	C₂²×C₄	—	4	1	no	—
302	C₂²×C₄	—	4	1	no	—
303	C₂²×C₄	—	4	1	no	—
304	C₂²×C₄	—	38	4	no	—
305	C₂²×C₄	—	76	2	no	—
306	C₂²×C₄	—	76	2	no	—
307	C₂²×C₄	—	76	2	no	—
308	C₂²×C₄	—	76	2	no	—
309	C₂²×C₄	—	76	2	no	—
310	C₂²×C₄	—	76	2	no	—
311	C₂²×C₄	#64525	1	2	yes	—
312	C₂²×C₄	#64525	1	2	yes	—
313	C₂²×C₄	#64526	1	2	yes	—
314	C₂²×C₄	#64526	1	2	yes	—
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	4	no	—
327	C₄⋊C₄	—	4	2	no	—
328	C₄⋊C₄	—	4	2	no	—
329	C₄⋊C₄	—	76	8	no	—
330	C₂²⋊C₄	—	4	4	no	—
331	C₂²⋊C₄	—	4	4	no	—
332	C₂²⋊C₄	—	4	4	no	—
333	C₄²	—	2	2	no	—
334	C₄²	—	2	2	no	—
335	C₄²	—	4	1	no	—
336	C₄²	—	4	1	no	—
337	C₂³	—	2	1	no	—
338	C₂³	—	2	1	no	—
339	C₂³	—	2	1	no	—
340	C₂³	—	2	1	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	—	4	2	no	—
347	C₂³	—	4	2	no	—
348	C₂³	C₂×#64525	1	1	yes	characteristic
349	C₂³	C₂×#64525	1	1	yes	characteristic
350	C₂³	C₂×#64526	1	1	yes	characteristic
351	C₂³	C₂×#64526	1	1	yes	characteristic
352	C₂³	#10597382	1	1	yes	characteristic
353	C₂³	#10597386	1	1	yes	characteristic
354	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
355	D₄	—	8	4	no	—
356	D₄	—	8	4	no	—
357	D₄	—	8	2	no	—
358	D₄	—	8	2	no	—
359	D₄	—	8	2	no	—
360	D₄	—	8	2	no	—
361	D₄	—	8	4	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	4	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	76	4	no	—
382	C₂×C₄	—	76	4	no	—
383	C₂×C₄	—	76	4	no	—
384	C₂×C₄	—	152	2	no	—
385	C₂×C₄	—	152	2	no	—
386	C₂×C₄	—	152	2	no	—
387	C₂×C₄	—	152	2	no	—
388	C₂×C₄	#10597289	1	2	yes	—
389	C₂×C₄	#10597289	1	2	yes	—
390	C₂×C₄	#10597289	1	2	yes	—
391	C₂×C₄	#10597289	1	2	yes	—
392	C₂×C₄	#10597291	1	2	yes	—
393	C₂×C₄	#10597294	1	2	yes	—
394	C₂×C₄	D₄×Dic₁₉	1	2	yes	—
395	C₂×C₄	#10597384	1	2	yes	—
396	C₈	—	76	4	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	2	1	no	—
400	C₂²	—	2	1	no	—
401	C₂²	—	2	1	no	—
402	C₂²	—	2	1	no	—
403	C₂²	—	2	1	no	—
404	C₂²	—	2	1	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	2	1	no	—
408	C₂²	—	2	1	no	—
409	C₂²	—	8	2	no	—
410	C₂²	—	8	2	no	—
411	C₂²	—	8	2	no	—
412	C₂²	—	8	2	no	—
413	C₂²	—	8	2	no	—
414	C₂²	—	8	2	no	—
415	C₂²	—	8	2	no	—
416	C₂²	#11926447	1	1	yes	characteristic
417	C₂²	C₂×#10597291	1	1	yes	characteristic
418	C₂²	#11926518	1	1	yes	characteristic
419	C₂²	C₂×#10597289	1	1	yes	characteristic
420	C₂²	C₂×#10597289	1	1	yes	characteristic
421	C₂²	C₂×#10597294	1	1	yes	characteristic
422	C₂²	#11926561	1	1	yes	characteristic
423	C₂²	#11926890	1	1	yes	characteristic
424	C₂²	#11926890	1	1	yes	characteristic
425	C₂²	#11926916	1	1	yes	characteristic
426	C₂²	#11926920	1	1	yes	characteristic
427	C₄	—	2	2	no	—
428	C₄	—	2	2	no	—
429	C₄	—	2	2	no	—
430	C₄	—	2	2	no	—
431	C₄	—	2	2	no	—
432	C₄	—	8	2	no	—
433	C₄	—	152	4	no	—
434	C₄	#11926278	1	4	yes	complemented
435	C₂	—	2	1	no	—
436	C₂	—	2	1	no	—
437	C₂	—	2	1	no	—
438	C₂	—	2	1	no	—
439	C₂	—	16	2	no	—
440	C₂	C₂×#11926278	1	1	yes	characteristic
441	C₂	#14562130	1	1	yes	characteristic
442	C₂	#14562195	1	1	yes	characteristic
443	C₂	#14562203	1	1	yes	characteristic
444	C₂	#14564442	1	1	yes	characteristic
445	C₂	#14564472	1	1	yes	characteristic
446	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, prime radical	C₁₉×#2856	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	#2856	D₁₉
hypocenter	C₁₉	#9680
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. C₄×C₂²⋊(C₁₉⋊C₈)	C₂	semidirect
2. C₂×#11926278	C₂	semidirect
3. #14561865	C₂	semidirect
12. C₂×C₁₉×#127	C₄	semidirect
19. C₁₉×#390	C₄	semidirect
20. C₁₉×#384	C₄	semidirect
54. C₂²⋊(C₁₉⋊C₈)	D₄	semidirect
214. C₄×C₁₉	#327	semidirect
216. C₂×#127	Dic₁₉	semidirect
226. #390	Dic₁₉	semidirect
227. #384	Dic₁₉	semidirect
279. C₁₉	#9680	semidirect
434. C₄	#11926278	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×#11926278	2
#14561865	2
C₁₉×#2856	2
#9680	19