Subgroups — #18075219

Order 4864.

708 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄²×D₇₆	C₂	1	1	yes	maximal, characteristic
2	C₄×C₄⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#11926271	C₂	1	2	yes	maximal
4	#14561474	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1842	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄×D₇₆	C₄	1	1	yes	characteristic
7	C₂×C₄×D₇₆	C₄	1	1	yes	characteristic
8	C₂×C₄×D₇₆	C₂²	1	1	yes	characteristic
9	C₂×C₄²×D₁₉	—	2	1	no	—
10	C₂×C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
11	C₂×C₄×C₁₉⋊C₈	C₂²	1	2	yes	—
12	C₄×C₄⋊Dic₁₉	C₄	1	1	yes	characteristic
13	C₄×C₄⋊Dic₁₉	C₄	1	1	yes	characteristic
14	C₄×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
15	C₄×(C₂×D₁₉)⋊C₄	—	2	1	no	—
16	C₄×(C₂×D₁₉)⋊C₄	—	2	1	no	—
17	C₄×(C₂×D₁₉)⋊C₄	—	2	1	no	—
18	#11926299	—	2	1	no	—
19	#11926271	—	2	4	no	—
20	C₂×C₁₉×C₄⋊C₈	—	2	1	no	—
21	C₂×C₁₉×C₄⋊C₈	—	2	1	no	—
22	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
23	C₄³×C₁₉	C₂²	1	1	yes	characteristic
24	C₂²×D₇₆	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₄×D₁₉	—	2	1	no	—
26	C₂²×C₄×D₁₉	—	2	1	no	—
27	C₂²×C₄×D₁₉	—	2	1	no	—
28	C₂²×C₈×C₁₉	—	2	2	no	—
29	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
30	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
31	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
32	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
33	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
34	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
35	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
36	C₂×(C₂×D₁₉)⋊C₄	—	2	1	no	—
37	C₂×(C₂×D₁₉)⋊C₄	—	2	1	no	—
38	C₂×(C₂×D₁₉)⋊C₄	—	2	1	no	—
39	C₂×C₄⋊Dic₁₉	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄⋊Dic₁₉	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄⋊Dic₁₉	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄×Dic₁₉	—	2	1	no	—
43	C₂×C₄×Dic₁₉	—	2	1	no	—
44	C₂×C₄×Dic₁₉	—	2	1	no	—
45	C₂²×C₁₉⋊C₈	—	2	2	no	—
46	C₄×D₇₆	—	2	2	no	—
47	C₄×D₇₆	—	2	2	no	—
48	C₄×D₇₆	—	2	1	no	—
49	C₄×D₇₆	—	2	1	no	—
50	C₄×D₇₆	—	2	2	no	—
51	C₄×D₇₆	C₈	1	4	yes	complemented
52	C₄×D₇₆	D₄	1	2	yes	—
53	C₄×D₇₆	Q₈	1	2	yes	—
54	C₄²×D₁₉	—	4	2	no	—
55	C₄²×D₁₉	—	4	2	no	—
56	C₁₉×C₄⋊C₈	—	2	2	no	—
57	C₁₉×C₄⋊C₈	—	2	2	no	—
58	C₁₉×C₄⋊C₈	—	4	2	no	—
59	C₁₉×C₄⋊C₈	—	4	2	no	—
60	C₁₉⋊#95	—	2	1	no	—
61	C₁₉⋊#95	—	2	1	no	—
62	C₁₉⋊#95	—	2	1	no	—
63	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
64	C₄×C₁₉⋊C₈	—	2	2	no	—
65	C₄×C₁₉⋊C₈	—	2	2	no	—
66	C₂³×D₁₉	—	2	1	no	—
67	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
68	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
69	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
71	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
74	C₂²×Dic₁₉	—	2	1	no	—
75	C₂²×Dic₁₉	—	2	1	no	—
76	C₂²×Dic₁₉	—	2	1	no	—
77	C₂×D₇₆	—	2	1	no	—
78	C₂×D₇₆	—	2	1	no	—
79	C₂×D₇₆	—	2	1	no	—
80	C₂×D₇₆	C₄⋊C₄	1	2	yes	—
81	C₂×D₇₆	C₂×C₈	1	2	yes	—
82	C₂×D₇₆	M₁₆	1	2	yes	—
83	C₂×C₄×D₁₉	—	2	4	no	—
84	C₂×C₄×D₁₉	—	2	4	no	—
85	C₂×C₄×D₁₉	—	2	2	no	—
86	C₂×C₄×D₁₉	—	2	2	no	—
87	C₂×C₄×D₁₉	—	4	2	no	—
88	C₂×C₄×D₁₉	—	4	2	no	—
89	C₂×C₄×D₁₉	—	4	2	no	—
90	C₂×C₄×D₁₉	—	4	2	no	—
91	C₂×C₄×D₁₉	—	4	1	no	—
92	C₂×C₄×D₁₉	—	4	1	no	—
93	C₂×C₄×D₁₉	—	4	1	no	—
94	C₂×C₄×D₁₉	—	4	1	no	—
95	C₂×C₈×C₁₉	—	4	2	no	—
96	C₂×C₈×C₁₉	—	4	2	no	—
97	C₂×C₈×C₁₉	—	4	2	no	—
98	C₄²×C₁₉	—	2	2	no	—
99	C₄²×C₁₉	—	2	1	no	—
100	C₄²×C₁₉	—	2	1	no	—
101	C₄²×C₁₉	—	2	1	no	—
102	C₄²×C₁₉	—	2	1	no	—
103	C₄²×C₁₉	—	4	1	no	—
104	C₄²×C₁₉	C₂×C₈	1	2	yes	—
105	C₄²×C₁₉	M₁₆	1	2	yes	—
106	C₄²×C₁₉	D₈	1	2	yes	—
107	C₄²×C₁₉	SD₁₆	1	2	yes	—
108	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
109	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
110	C₄²×C₁₉	#41	1	1	yes	characteristic
111	C₄²×C₁₉	#41	1	1	yes	characteristic
112	(C₂×D₁₉)⋊C₄	—	2	4	no	—
113	(C₂×D₁₉)⋊C₄	—	2	4	no	—
114	(C₂×D₁₉)⋊C₄	—	2	2	no	—
115	(C₂×D₁₉)⋊C₄	—	2	2	no	—
116	C₄⋊Dic₁₉	—	2	1	no	—
117	C₄⋊Dic₁₉	—	2	1	no	—
118	C₄⋊Dic₁₉	—	2	1	no	—
119	C₄⋊Dic₁₉	C₄⋊C₄	1	2	yes	—
120	C₄⋊Dic₁₉	C₂×C₈	1	2	yes	—
121	C₄⋊Dic₁₉	M₁₆	1	2	yes	—
122	C₄×Dic₁₉	—	4	2	no	—
123	C₄×Dic₁₉	—	4	2	no	—
124	C₄×Dic₁₉	—	4	1	no	—
125	C₄×Dic₁₉	—	4	1	no	—
126	C₂×C₁₉⋊C₈	—	2	4	no	—
127	C₂×C₁₉⋊C₈	—	4	2	no	—
128	C₂×C₁₉⋊C₈	—	4	2	no	—
129	#8563	—	19	1	no	maximal, Sylow
130	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
131	C₂²×D₁₉	—	2	2	no	—
132	C₂²×D₁₉	—	2	2	no	—
133	C₂²×D₁₉	—	2	2	no	—
134	C₂²×D₁₉	—	4	1	no	—
135	C₂²×D₁₉	—	4	1	no	—
136	C₂²×D₁₉	—	4	1	no	—
137	C₂²×D₁₉	—	4	1	no	—
138	C₂×C₄×C₁₉	—	2	1	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	C₂²⋊C₈	1	2	yes	—
148	C₂×C₄×C₁₉	C₂²⋊C₈	1	2	yes	—
149	C₂×C₄×C₁₉	#102	1	2	yes	—
150	C₂×C₄×C₁₉	#102	1	2	yes	—
151	C₂×C₄×C₁₉	#104	1	2	yes	—
152	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
154	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
155	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
156	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
157	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
158	C₂×C₄×C₁₉	C₂²×C₈	1	1	yes	characteristic
159	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
160	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
161	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
162	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
163	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
164	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
165	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
166	C₂×Dic₁₉	—	2	2	no	—
167	C₂×Dic₁₉	—	2	2	no	—
168	C₂×Dic₁₉	—	2	2	no	—
169	C₂×Dic₁₉	—	4	1	no	—
170	C₂×Dic₁₉	—	4	1	no	—
171	C₂×Dic₁₉	—	4	1	no	—
172	C₂×Dic₁₉	—	4	1	no	—
173	C₂×Dic₁₉	—	4	1	no	—
174	C₂×Dic₁₉	—	4	1	no	—
175	D₇₆	—	2	2	no	—
176	D₇₆	—	2	2	no	—
177	D₇₆	—	2	2	no	—
178	D₇₆	C₄⋊C₈	1	4	yes	complemented
179	C₄×D₁₉	—	4	8	no	—
180	C₄×D₁₉	—	4	8	no	—
181	C₄×D₁₉	—	4	2	no	—
182	C₄×D₁₉	—	4	2	no	—
183	C₄×D₁₉	—	4	2	no	—
184	C₄×D₁₉	—	4	2	no	—
185	C₈×C₁₉	—	8	2	no	—
186	C₁₉⋊C₈	—	4	4	no	—
187	C₄²×D₄	—	19	1	no	—
188	#1842	D₁₉	1	1	yes	characteristic, complemented
189	C₄×C₄⋊C₈	—	19	1	no	—
190	C₂×D₄⋊C₈	—	19	2	no	—
191	#1279	—	19	2	no	—
192	C₂²×C₁₉	#380	1	1	yes	characteristic
193	C₂²×C₁₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
194	C₂²×C₁₉	#407	1	1	yes	characteristic
195	C₂²×C₁₉	C₂×#102	1	1	yes	characteristic
196	C₂²×C₁₉	#417	1	1	yes	characteristic
197	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
198	C₂²×C₁₉	#421	1	1	yes	characteristic
199	C₂×D₁₉	—	2	4	no	—
200	C₂×D₁₉	—	4	2	no	—
201	C₂×D₁₉	—	4	2	no	—
202	C₂×D₁₉	—	4	2	no	—
203	C₂×D₁₉	—	4	2	no	—
204	C₂×D₁₉	—	4	2	no	—
205	C₂×D₁₉	—	4	2	no	—
206	C₄×C₁₉	—	2	1	no	—
207	C₄×C₁₉	—	2	1	no	—
208	C₄×C₁₉	—	2	2	no	—
209	C₄×C₁₉	—	2	2	no	—
210	C₄×C₁₉	—	4	1	no	—
211	C₄×C₁₉	D₄⋊C₈	1	4	yes	complemented
212	C₄×C₁₉	C₂×C₄⋊C₈	1	1	yes	characteristic
213	C₄×C₁₉	#423	1	1	yes	characteristic
214	C₄×C₁₉	#431	1	1	yes	characteristic
215	C₄×C₁₉	#432	1	1	yes	characteristic
216	C₄×C₁₉	#459	1	1	yes	characteristic
217	C₄×C₁₉	#461	1	1	yes	characteristic
218	C₄×C₁₉	#474	1	1	yes	characteristic
219	C₄×C₁₉	#476	1	1	yes	characteristic
220	Dic₁₉	—	4	2	no	—
221	Dic₁₉	—	4	2	no	—
222	Dic₁₉	—	4	2	no	—
223	C₂×C₄×D₄	—	19	1	no	—
224	C₂×C₄×D₄	—	19	1	no	—
225	C₂×C₄×D₄	—	19	1	no	—
226	C₂²×C₄²	—	38	1	no	—
227	C₂×C₄⋊C₈	—	2	1	no	—
228	C₂×C₄⋊C₈	—	2	1	no	—
229	C₂×C₄⋊C₈	—	38	1	no	—
230	C₂×C₄⋊C₈	C₂×D₁₉	1	2	yes	—
231	C₂×C₄×C₈	—	19	2	no	—
232	C₄×C₄⋊C₄	—	19	1	no	—
233	C₄×C₄⋊C₄	—	19	1	no	—
234	C₄×C₄⋊C₄	—	19	1	no	—
235	C₄×C₂²⋊C₄	—	38	1	no	—
236	C₄×C₂²⋊C₄	—	38	1	no	—
237	C₄×C₂²⋊C₄	—	38	1	no	—
238	C₄³	C₂×D₁₉	1	1	yes	characteristic
239	#336	—	38	1	no	—
240	D₄⋊C₈	—	38	4	no	—
241	C₂×C₁₉	C₂×D₄⋊C₈	1	1	yes	characteristic
242	C₂×C₁₉	#1477	1	1	yes	characteristic
243	C₂×C₁₉	#1486	1	1	yes	characteristic
244	C₂×C₁₉	#1489	1	1	yes	characteristic
245	C₂×C₁₉	#1797	1	1	yes	characteristic
246	C₂×C₁₉	#1802	1	1	yes	characteristic
247	C₂×C₁₉	#1806	1	1	yes	characteristic
248	D₁₉	—	4	4	no	—
249	C₂²×D₄	—	19	1	no	—
250	C₂³×C₄	—	38	1	no	—
251	C₂³×C₄	—	38	1	no	—
252	C₂³×C₄	—	38	1	no	—
253	C₂²×C₈	—	2	2	no	—
254	C₂²×C₈	—	38	2	no	—
255	C₄×D₄	—	19	4	no	—
256	C₄×D₄	—	19	2	no	—
257	C₄×D₄	—	19	2	no	—
258	C₄×D₄	—	38	2	no	—
259	C₄×D₄	—	38	2	no	—
260	C₄×D₄	—	38	2	no	—
261	C₄×D₄	—	38	1	no	—
262	C₄×D₄	—	38	1	no	—
263	C₂×C₄⋊C₄	—	19	1	no	—
264	C₂×C₄⋊C₄	—	19	1	no	—
265	C₂×C₄⋊C₄	—	19	1	no	—
266	C₂×C₂²⋊C₄	—	38	1	no	—
267	C₂×C₂²⋊C₄	—	38	1	no	—
268	C₂×C₂²⋊C₄	—	38	1	no	—
269	C₂×C₄²	—	38	1	no	—
270	C₂×C₄²	—	38	1	no	—
271	C₂×C₄²	—	38	1	no	—
272	C₂×C₄²	—	76	2	no	—
273	C₂×C₄²	—	76	2	no	—
274	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
275	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
276	C₂×C₄²	D₇₆	1	1	yes	characteristic
277	C₂×C₄²	D₇₆	1	1	yes	characteristic
278	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
279	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
280	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
281	C₄⋊C₈	—	2	2	no	—
282	C₄⋊C₈	—	2	2	no	—
283	C₄⋊C₈	—	4	2	no	—
284	C₄⋊C₈	—	4	2	no	—
285	C₄⋊C₈	—	38	4	no	—
286	C₄×C₈	—	38	2	no	—
287	C₄×C₈	—	38	2	no	—
288	#95	—	38	1	no	—
289	#95	—	38	1	no	—
290	#95	—	38	1	no	—
291	C₁₉	#8563	1	1	yes	characteristic, complemented, Sylow
292	C₂⁴	—	38	1	no	—
293	C₂×D₄	—	19	2	no	—
294	C₂×D₄	—	19	2	no	—
295	C₂×D₄	—	19	2	no	—
296	C₂×D₄	—	38	1	no	—
297	C₂×D₄	—	38	1	no	—
298	C₂×D₄	—	38	1	no	—
299	C₂²×C₄	—	38	4	no	—
300	C₂²×C₄	—	38	1	no	—
301	C₂²×C₄	—	38	1	no	—
302	C₂²×C₄	—	38	1	no	—
303	C₂²×C₄	—	38	2	no	—
304	C₂²×C₄	—	38	2	no	—
305	C₂²×C₄	—	38	4	no	—
306	C₂²×C₄	—	76	2	no	—
307	C₂²×C₄	—	76	1	no	—
308	C₂²×C₄	—	76	1	no	—
309	C₂²×C₄	—	76	1	no	—
310	C₂²×C₄	—	76	1	no	—
311	C₂²×C₄	—	76	2	no	—
312	C₂²×C₄	—	76	2	no	—
313	C₂²×C₄	—	76	2	no	—
314	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
315	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
316	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
317	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
318	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
319	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
320	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
321	C₂×C₈	—	4	2	no	—
322	C₂×C₈	—	4	2	no	—
323	C₂×C₈	—	4	2	no	—
324	C₂×C₈	—	38	4	no	—
325	C₂×C₈	—	76	2	no	—
326	C₂×C₈	—	76	2	no	—
327	C₄⋊C₄	—	19	2	no	—
328	C₄⋊C₄	—	19	2	no	—
329	C₄⋊C₄	—	19	2	no	—
330	C₄⋊C₄	—	38	1	no	—
331	C₄⋊C₄	—	38	1	no	—
332	C₄⋊C₄	—	38	1	no	—
333	C₂²⋊C₄	—	38	4	no	—
334	C₂²⋊C₄	—	38	4	no	—
335	C₂²⋊C₄	—	38	2	no	—
336	C₂²⋊C₄	—	38	2	no	—
337	C₄²	—	2	1	no	—
338	C₄²	—	2	1	no	—
339	C₄²	—	2	2	no	—
340	C₄²	—	2	1	no	—
341	C₄²	—	2	1	no	—
342	C₄²	—	4	1	no	—
343	C₄²	—	76	1	no	—
344	C₄²	—	76	1	no	—
345	C₄²	—	76	2	no	—
346	C₄²	—	76	2	no	—
347	C₄²	C₈×D₁₉	1	2	yes	—
348	C₄²	#64515	1	2	yes	—
349	C₄²	#64525	1	2	yes	—
350	C₄²	#64527	1	2	yes	—
351	C₄²	D₄×D₁₉	1	1	yes	characteristic
352	C₄²	#64543	1	1	yes	characteristic
353	C₄²	Q₈×D₁₉	1	1	yes	characteristic
354	C₄²	#64545	1	1	yes	characteristic
355	C₂³	—	38	2	no	—
356	C₂³	—	38	2	no	—
357	C₂³	—	38	2	no	—
358	C₂³	—	76	1	no	—
359	C₂³	—	76	1	no	—
360	C₂³	—	76	1	no	—
361	C₂³	—	76	1	no	—
362	C₂³	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
363	D₄	—	19	4	no	—
364	D₄	—	38	2	no	—
365	D₄	—	38	2	no	—
366	D₄	—	38	2	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	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	38	2	no	—
377	C₂×C₄	—	38	2	no	—
378	C₂×C₄	—	38	2	no	—
379	C₂×C₄	—	76	8	no	—
380	C₂×C₄	—	76	1	no	—
381	C₂×C₄	—	76	1	no	—
382	C₂×C₄	—	76	1	no	—
383	C₂×C₄	—	76	1	no	—
384	C₂×C₄	—	76	1	no	—
385	C₂×C₄	—	76	1	no	—
386	C₂×C₄	—	76	2	no	—
387	C₂×C₄	—	76	2	no	—
388	C₂×C₄	—	76	2	no	—
389	C₂×C₄	—	76	2	no	—
390	C₂×C₄	—	76	8	no	—
391	C₂×C₄	#10597266	1	2	yes	—
392	C₂×C₄	#10597266	1	2	yes	—
393	C₂×C₄	(C₂×D₁₉)⋊C₈	1	2	yes	—
394	C₂×C₄	(C₂×D₁₉)⋊C₈	1	2	yes	—
395	C₂×C₄	#10597282	1	2	yes	—
396	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
397	C₂×C₄	#10597338	1	1	yes	characteristic
398	C₂×C₄	#10597341	1	1	yes	characteristic
399	C₂×C₄	#10597343	1	1	yes	characteristic
400	C₂×C₄	C₂×C₈×D₁₉	1	1	yes	characteristic
401	C₂×C₄	C₂×#64515	1	1	yes	characteristic
402	C₂×C₄	M₁₆×D₁₉	1	1	yes	characteristic
403	C₂×C₄	M₁₆×D₁₉	1	1	yes	characteristic
404	C₂×C₄	C₂×#64525	1	1	yes	characteristic
405	C₂×C₄	#10597378	1	1	yes	characteristic
406	C₂×C₄	#10597384	1	1	yes	characteristic
407	C₂×C₄	C₂×#64527	1	1	yes	characteristic
408	C₂×C₄	#10597388	1	1	yes	characteristic
409	C₂×C₄	#10597392	1	1	yes	characteristic
410	C₈	—	8	2	no	—
411	C₈	—	76	4	no	—
412	C₂²	—	38	4	no	—
413	C₂²	—	76	2	no	—
414	C₂²	—	76	2	no	—
415	C₂²	—	76	2	no	—
416	C₂²	—	76	2	no	—
417	C₂²	—	76	2	no	—
418	C₂²	—	76	2	no	—
419	C₂²	#11926401	1	1	yes	characteristic
420	C₂²	C₂×(C₂×D₁₉)⋊C₈	1	1	yes	characteristic
421	C₂²	#11926507	1	1	yes	characteristic
422	C₂²	C₂×#10597266	1	1	yes	characteristic
423	C₂²	#11926543	1	1	yes	characteristic
424	C₂²	C₂×#10597282	1	1	yes	characteristic
425	C₂²	#11926560	1	1	yes	characteristic
426	C₄	—	2	2	no	—
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	2	2	no	—
430	C₄	—	4	1	no	—
431	C₄	—	76	2	no	—
432	C₄	—	76	2	no	—
433	C₄	—	76	2	no	—
434	C₄	#11926271	1	4	yes	complemented
435	C₄	C₄⋊C₈×D₁₉	1	1	yes	characteristic
436	C₄	#11926566	1	1	yes	characteristic
437	C₄	#11926596	1	1	yes	characteristic
438	C₄	#11926600	1	1	yes	characteristic
439	C₄	#11926736	1	1	yes	characteristic
440	C₄	#11926746	1	1	yes	characteristic
441	C₄	#11926821	1	1	yes	characteristic
442	C₄	#11926831	1	1	yes	characteristic
443	C₂	—	76	4	no	—
444	C₂	C₂×#11926271	1	1	yes	characteristic
445	C₂	#14562020	1	1	yes	characteristic
446	C₂	#14562059	1	1	yes	characteristic
447	C₂	#14562072	1	1	yes	characteristic
448	C₂	#14563612	1	1	yes	characteristic
449	C₂	#14563632	1	1	yes	characteristic
450	C₂	#14563652	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₁₉
commutator	C₂×C₄×C₁₉	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1842	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂²×D₇₆	C₂×C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1842	D₁₉
hypocenter	C₁₉	#8563
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ #1842

Complements

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

N	H ≅ G/N	type
2. C₄×C₄⋊(C₁₉⋊C₈)	C₂	semidirect
4. #14561474	C₂	semidirect
5. C₁₉×#1842	C₂	semidirect
51. C₄×D₇₆	C₈	semidirect
178. D₇₆	C₄⋊C₈	semidirect
188. #1842	D₁₉	semidirect
211. C₄×C₁₉	D₄⋊C₈	semidirect
291. C₁₉	#8563	semidirect
434. C₄	#11926271	semidirect

Maximal subgroups

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

subgroup	index
C₄²×D₇₆	2
C₄×C₄⋊(C₁₉⋊C₈)	2
C₂×#11926271	2
#14561474	2
C₁₉×#1842	2
#8563	19