Subgroups — #18076368

Order 4864.

556 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊C₈×D₁₉	C₂	1	1	yes	maximal, characteristic
2	#14563612	C₂	1	1	yes	maximal, characteristic
3	C₄×(C₂×D₁₉)⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926297	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#11926296	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561469	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1277	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₈×D₁₉	—	2	1	no	—
9	C₂×C₄²×D₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
12	C₂×Dic₁₉⋊C₈	—	2	1	no	—
13	C₄⋊C₈×D₁₉	—	2	2	no	—
14	C₄⋊C₈×D₁₉	—	2	2	no	—
15	C₂×(C₂×D₁₉)⋊C₈	—	2	1	no	—
16	C₂×(C₂×D₁₉)⋊C₈	C₄	1	1	yes	characteristic
17	C₂×(C₂×D₁₉)⋊C₈	C₄	1	1	yes	characteristic
18	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
19	#11926298	—	2	1	no	—
20	#11926298	C₄	1	1	yes	characteristic
21	#11926298	C₄	1	1	yes	characteristic
22	#11926297	—	2	2	no	—
23	#11926296	—	2	2	no	—
24	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
27	C₂²×C₄×D₁₉	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₄×D₁₉	D₄	1	1	yes	characteristic
29	C₂²×C₄×D₁₉	Q₈	1	1	yes	characteristic
30	C₂²×C₈×C₁₉	—	2	1	no	—
31	C₂²×C₈×C₁₉	—	2	1	no	—
32	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
35	C₂×C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
37	C₂×C₄×Dic₁₉	Q₈	1	1	yes	characteristic
38	C₂²×C₁₉⋊C₈	—	2	1	no	—
39	C₂²×C₁₉⋊C₈	—	2	1	no	—
40	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
42	C₂×C₈×D₁₉	—	2	4	no	—
43	C₂×C₈×D₁₉	—	4	2	no	—
44	C₂×C₈×D₁₉	—	4	2	no	—
45	C₄²×D₁₉	—	2	1	no	—
46	C₄²×D₁₉	—	2	1	no	—
47	C₄²×D₁₉	—	2	1	no	—
48	C₄²×D₁₉	—	2	1	no	—
49	C₁₉×C₄⋊C₈	—	2	1	no	—
50	C₁₉×C₄⋊C₈	—	2	1	no	—
51	C₁₉×C₄⋊C₈	—	2	1	no	—
52	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
53	C₄×C₈×C₁₉	—	2	1	no	—
54	C₄×C₈×C₁₉	—	2	1	no	—
55	(C₂×D₁₉)⋊C₈	—	2	2	no	—
56	(C₂×D₁₉)⋊C₈	—	4	2	no	—
57	(C₂×D₁₉)⋊C₈	C₈	1	4	yes	complemented
58	Dic₁₉⋊C₈	—	2	4	no	—
59	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
60	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
61	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
62	C₄⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
63	C₄×C₁₉⋊C₈	—	2	1	no	—
64	C₄×C₁₉⋊C₈	—	2	1	no	—
65	C₂³×D₁₉	C₄⋊C₄	1	1	yes	characteristic
66	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
67	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
68	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
69	C₂²×Dic₁₉	C₄⋊C₄	1	1	yes	characteristic
70	C₂²×Dic₁₉	C₄⋊C₄	1	1	yes	characteristic
71	C₂²×Dic₁₉	C₄⋊C₄	1	1	yes	characteristic
72	C₂×C₄×D₁₉	—	2	1	no	—
73	C₂×C₄×D₁₉	—	2	1	no	—
74	C₂×C₄×D₁₉	—	2	1	no	—
75	C₂×C₄×D₁₉	—	2	1	no	—
76	C₂×C₄×D₁₉	—	2	1	no	—
77	C₂×C₄×D₁₉	—	2	1	no	—
78	C₂×C₄×D₁₉	—	2	1	no	—
79	C₂×C₄×D₁₉	—	2	1	no	—
80	C₂×C₄×D₁₉	—	2	2	no	—
81	C₂×C₄×D₁₉	—	2	1	no	—
82	C₂×C₄×D₁₉	—	2	1	no	—
83	C₂×C₄×D₁₉	—	4	1	no	—
84	C₂×C₄×D₁₉	C₂×C₈	1	2	yes	—
85	C₂×C₄×D₁₉	M₁₆	1	2	yes	—
86	C₂×C₄×D₁₉	D₈	1	2	yes	—
87	C₂×C₄×D₁₉	Q₁₆	1	2	yes	—
88	C₂×C₈×C₁₉	—	2	1	no	—
89	C₂×C₈×C₁₉	—	2	1	no	—
90	C₂×C₈×C₁₉	—	2	1	no	—
91	C₂×C₈×C₁₉	—	2	2	no	—
92	C₂×C₈×C₁₉	—	2	1	no	—
93	C₂×C₈×C₁₉	—	2	1	no	—
94	C₂×C₈×C₁₉	—	4	1	no	—
95	C₂×C₈×C₁₉	—	4	1	no	—
96	C₂×C₈×C₁₉	—	4	1	no	—
97	C₂×C₈×C₁₉	—	4	1	no	—
98	C₂×C₈×C₁₉	—	4	1	no	—
99	C₂×C₈×C₁₉	C₂×C₈	1	2	yes	complemented
100	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
101	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
102	C₄²×C₁₉	#41	1	1	yes	characteristic
103	C₄²×C₁₉	#41	1	1	yes	characteristic
104	C₄×Dic₁₉	—	2	1	no	—
105	C₄×Dic₁₉	—	2	1	no	—
106	C₄×Dic₁₉	—	2	1	no	—
107	C₄×Dic₁₉	—	2	1	no	—
108	C₄×Dic₁₉	—	2	1	no	—
109	C₄×Dic₁₉	—	2	1	no	—
110	C₂×C₁₉⋊C₈	—	2	1	no	—
111	C₂×C₁₉⋊C₈	—	2	1	no	—
112	C₂×C₁₉⋊C₈	—	2	1	no	—
113	C₂×C₁₉⋊C₈	—	2	2	no	—
114	C₂×C₁₉⋊C₈	—	2	1	no	—
115	C₂×C₁₉⋊C₈	—	2	1	no	—
116	C₂×C₁₉⋊C₈	—	4	1	no	—
117	C₂×C₁₉⋊C₈	—	4	1	no	—
118	C₂×C₁₉⋊C₈	—	4	1	no	—
119	C₂×C₁₉⋊C₈	—	4	1	no	—
120	C₂×C₁₉⋊C₈	—	4	1	no	—
121	C₂×C₁₉⋊C₈	C₂×C₈	1	2	yes	complemented
122	C₈×D₁₉	—	4	8	no	—
123	#8829	—	19	1	no	maximal, Sylow
124	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
125	C₂²×D₁₉	—	2	1	no	—
126	C₂²×D₁₉	—	2	1	no	—
127	C₂²×D₁₉	—	2	1	no	—
128	C₂²×D₁₉	—	2	1	no	—
129	C₂²×D₁₉	C₄⋊C₈	1	2	yes	—
130	C₂²×D₁₉	#107	1	2	yes	—
131	C₂²×D₁₉	#108	1	2	yes	—
132	C₂×C₄×C₁₉	—	2	1	no	—
133	C₂×C₄×C₁₉	—	2	1	no	—
134	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
135	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
136	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
137	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
138	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
139	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
140	C₂×C₄×C₁₉	C₂²×C₈	1	1	yes	characteristic
141	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
142	C₂×C₄×C₁₉	#131	1	1	yes	characteristic
143	C₂×C₄×C₁₉	#131	1	1	yes	characteristic
144	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
145	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
146	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
147	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
148	C₂×Dic₁₉	—	2	1	no	—
149	C₂×Dic₁₉	—	2	1	no	—
150	C₂×Dic₁₉	—	2	1	no	—
151	C₂×Dic₁₉	—	2	1	no	—
152	C₂×Dic₁₉	—	2	1	no	—
153	C₂×Dic₁₉	—	2	1	no	—
154	C₂×Dic₁₉	—	2	1	no	—
155	C₂×Dic₁₉	C₄⋊C₈	1	2	yes	—
156	C₂×Dic₁₉	#107	1	2	yes	—
157	C₄×D₁₉	—	2	2	no	—
158	C₄×D₁₉	—	2	2	no	—
159	C₄×D₁₉	—	2	2	no	—
160	C₄×D₁₉	—	2	2	no	—
161	C₄×D₁₉	—	2	2	no	—
162	C₄×D₁₉	—	2	2	no	—
163	C₄×D₁₉	—	2	2	no	—
164	C₄×D₁₉	—	2	2	no	—
165	C₄×D₁₉	—	4	2	no	—
166	C₄×D₁₉	—	4	2	no	—
167	C₈×C₁₉	—	2	2	no	—
168	C₈×C₁₉	—	4	1	no	—
169	C₈×C₁₉	—	4	2	no	—
170	C₈×C₁₉	—	8	1	no	—
171	C₁₉⋊C₈	—	2	2	no	—
172	C₁₉⋊C₈	—	4	1	no	—
173	C₁₉⋊C₈	—	4	2	no	—
174	C₁₉⋊C₈	—	8	1	no	—
175	C₂²×C₄⋊C₈	—	19	1	no	—
176	#1797	—	19	1	no	—
177	C₄×C₂²⋊C₈	—	19	1	no	—
178	C₂×#335	—	19	1	no	—
179	C₂×#335	—	19	1	no	—
180	#1277	—	19	1	no	—
181	#1277	D₁₉	1	1	yes	characteristic, complemented
182	C₂²×C₁₉	#385	1	1	yes	characteristic
183	C₂²×C₁₉	C₂×C₄⋊C₈	1	1	yes	characteristic
184	C₂²×C₁₉	#424	1	1	yes	characteristic
185	C₂²×C₁₉	C₂×#107	1	1	yes	characteristic
186	C₂²×C₁₉	#428	1	1	yes	characteristic
187	C₂²×C₁₉	C₂×#108	1	1	yes	characteristic
188	C₂²×C₁₉	#430	1	1	yes	characteristic
189	C₂×D₁₉	—	2	2	no	—
190	C₂×D₁₉	—	2	2	no	—
191	C₂×D₁₉	—	2	2	no	—
192	C₂×D₁₉	—	2	2	no	—
193	C₂×D₁₉	—	2	2	no	—
194	C₂×D₁₉	—	2	2	no	—
195	C₂×D₁₉	#335	1	4	yes	complemented
196	C₄×C₁₉	—	2	1	no	—
197	C₄×C₁₉	—	2	1	no	—
198	C₄×C₁₉	C₈×D₄	1	1	yes	characteristic
199	C₄×C₁₉	C₈×D₄	1	1	yes	characteristic
200	C₄×C₁₉	#435	1	1	yes	characteristic
201	C₄×C₁₉	#435	1	1	yes	characteristic
202	C₄×C₁₉	#447	1	1	yes	characteristic
203	C₄×C₁₉	#451	1	1	yes	characteristic
204	C₄×C₁₉	#480	1	1	yes	characteristic
205	C₄×C₁₉	#484	1	1	yes	characteristic
206	Dic₁₉	—	2	2	no	—
207	Dic₁₉	—	2	2	no	—
208	Dic₁₉	—	4	1	no	—
209	C₂³×C₈	—	38	1	no	—
210	C₂²×C₄²	—	19	1	no	—
211	C₂×C₄⋊C₈	—	19	1	no	—
212	C₂×C₄⋊C₈	—	19	1	no	—
213	C₂×C₄⋊C₈	—	38	2	no	—
214	C₂×C₄⋊C₈	—	38	1	no	—
215	C₂×C₄⋊C₈	—	38	2	no	—
216	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
217	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
218	C₂×C₂²⋊C₈	—	19	1	no	—
219	C₂×C₂²⋊C₈	—	19	1	no	—
220	C₂×C₂²⋊C₈	—	38	1	no	—
221	C₂×C₄×C₈	—	19	1	no	—
222	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
223	#336	—	19	1	no	—
224	#336	—	19	1	no	—
225	#336	—	38	1	no	—
226	#335	—	38	2	no	—
227	#335	—	38	2	no	—
228	C₂×C₁₉	C₂×#335	1	1	yes	characteristic
229	C₂×C₁₉	#1565	1	1	yes	characteristic
230	C₂×C₁₉	#1571	1	1	yes	characteristic
231	C₂×C₁₉	#1573	1	1	yes	characteristic
232	C₂×C₁₉	#1850	1	1	yes	characteristic
233	C₂×C₁₉	#1852	1	1	yes	characteristic
234	C₂×C₁₉	#1855	1	1	yes	characteristic
235	D₁₉	—	2	4	no	—
236	C₂³×C₄	—	19	1	no	—
237	C₂³×C₄	—	19	1	no	—
238	C₂³×C₄	—	19	1	no	—
239	C₂²×C₈	—	2	1	no	—
240	C₂²×C₈	—	2	1	no	—
241	C₂²×C₈	—	19	1	no	—
242	C₂²×C₈	—	19	1	no	—
243	C₂²×C₈	—	38	4	no	—
244	C₂²×C₈	—	38	1	no	—
245	C₂²×C₈	—	38	1	no	—
246	C₂²×C₈	—	76	2	no	—
247	C₂²×C₈	—	76	2	no	—
248	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
249	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
250	C₂×C₄²	—	19	1	no	—
251	C₂×C₄²	—	19	1	no	—
252	C₂×C₄²	—	19	1	no	—
253	C₂×C₄²	—	38	1	no	—
254	C₂×C₄²	—	38	1	no	—
255	C₂×C₄²	—	38	1	no	—
256	C₂×C₄²	—	38	1	no	—
257	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
258	C₄⋊C₈	—	2	1	no	—
259	C₄⋊C₈	—	2	1	no	—
260	C₄⋊C₈	—	2	1	no	—
261	C₄⋊C₈	—	19	2	no	—
262	C₄⋊C₈	—	38	4	no	—
263	C₄⋊C₈	—	38	1	no	—
264	C₄⋊C₈	—	38	1	no	—
265	C₄⋊C₈	—	38	1	no	—
266	C₄⋊C₈	D₇₆	1	2	yes	—
267	C₂²⋊C₈	—	19	4	no	—
268	C₂²⋊C₈	—	38	2	no	—
269	C₂²⋊C₈	—	76	2	no	—
270	C₄×C₈	—	2	1	no	—
271	C₄×C₈	—	2	1	no	—
272	C₄×C₈	—	38	1	no	—
273	C₄×C₈	—	38	1	no	—
274	C₁₉	#8829	1	1	yes	characteristic, complemented, Sylow
275	C₂⁴	—	19	1	no	—
276	C₂²×C₄	—	19	1	no	—
277	C₂²×C₄	—	19	1	no	—
278	C₂²×C₄	—	19	2	no	—
279	C₂²×C₄	—	19	2	no	—
280	C₂²×C₄	—	19	2	no	—
281	C₂²×C₄	—	19	2	no	—
282	C₂²×C₄	—	19	1	no	—
283	C₂²×C₄	—	38	2	no	—
284	C₂²×C₄	—	38	1	no	—
285	C₂²×C₄	—	38	1	no	—
286	C₂²×C₄	—	38	1	no	—
287	C₂²×C₄	—	38	1	no	—
288	C₂²×C₄	—	38	1	no	—
289	C₂²×C₄	—	38	1	no	—
290	C₂²×C₄	—	38	1	no	—
291	C₂²×C₄	—	38	1	no	—
292	C₂²×C₄	—	38	1	no	—
293	C₂²×C₄	—	38	1	no	—
294	C₂²×C₄	—	76	1	no	—
295	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
296	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
297	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
298	C₂×C₈	—	2	1	no	—
299	C₂×C₈	—	2	1	no	—
300	C₂×C₈	—	2	1	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	1	no	—
303	C₂×C₈	—	2	1	no	—
304	C₂×C₈	—	4	1	no	—
305	C₂×C₈	—	4	1	no	—
306	C₂×C₈	—	4	1	no	—
307	C₂×C₈	—	4	1	no	—
308	C₂×C₈	—	4	1	no	—
309	C₂×C₈	—	19	2	no	—
310	C₂×C₈	—	38	1	no	—
311	C₂×C₈	—	38	1	no	—
312	C₂×C₈	—	38	1	no	—
313	C₂×C₈	—	38	2	no	—
314	C₂×C₈	—	38	1	no	—
315	C₂×C₈	—	38	1	no	—
316	C₂×C₈	—	76	8	no	—
317	C₂×C₈	—	76	1	no	—
318	C₂×C₈	—	76	1	no	—
319	C₂×C₈	—	76	1	no	—
320	C₂×C₈	—	76	1	no	—
321	C₂×C₈	—	76	1	no	—
322	C₂×C₈	C₈×D₁₉	1	2	yes	complemented
323	C₄²	—	38	1	no	—
324	C₄²	—	38	1	no	—
325	C₄²	—	38	1	no	—
326	C₄²	—	38	1	no	—
327	C₄²	—	38	1	no	—
328	C₄²	—	38	1	no	—
329	C₄²	C₂×D₇₆	1	1	yes	characteristic
330	C₄²	#64541	1	1	yes	characteristic
331	C₄²	D₄×D₁₉	1	1	yes	characteristic
332	C₄²	#64543	1	1	yes	characteristic
333	C₂³	—	19	2	no	—
334	C₂³	—	19	2	no	—
335	C₂³	—	19	2	no	—
336	C₂³	—	38	1	no	—
337	C₂³	—	38	1	no	—
338	C₂³	—	38	1	no	—
339	C₂³	—	38	1	no	—
340	C₂³	C₄⋊C₄×D₁₉	1	1	yes	characteristic
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	19	2	no	—
344	C₂×C₄	—	19	2	no	—
345	C₂×C₄	—	38	1	no	—
346	C₂×C₄	—	38	1	no	—
347	C₂×C₄	—	38	1	no	—
348	C₂×C₄	—	38	1	no	—
349	C₂×C₄	—	38	2	no	—
350	C₂×C₄	—	38	2	no	—
351	C₂×C₄	—	38	2	no	—
352	C₂×C₄	—	38	2	no	—
353	C₂×C₄	—	38	2	no	—
354	C₂×C₄	—	38	2	no	—
355	C₂×C₄	—	38	2	no	—
356	C₂×C₄	—	38	2	no	—
357	C₂×C₄	—	38	1	no	—
358	C₂×C₄	—	38	1	no	—
359	C₂×C₄	—	38	1	no	—
360	C₂×C₄	—	76	2	no	—
361	C₂×C₄	—	76	2	no	—
362	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
363	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
364	C₂×C₄	#10597328	1	1	yes	characteristic
365	C₂×C₄	#10597329	1	1	yes	characteristic
366	C₂×C₄	#10597342	1	1	yes	characteristic
367	C₂×C₄	#10597343	1	1	yes	characteristic
368	C₂×C₄	C₂×C₈×D₁₉	1	1	yes	characteristic
369	C₂×C₄	#10597347	1	1	yes	characteristic
370	C₂×C₄	M₁₆×D₁₉	1	1	yes	characteristic
371	C₂×C₄	#10597353	1	1	yes	characteristic
372	C₂×C₄	D₈×D₁₉	1	1	yes	characteristic
373	C₂×C₄	#10597360	1	1	yes	characteristic
374	C₂×C₄	#10597361	1	1	yes	characteristic
375	C₂×C₄	Q₁₆×D₁₉	1	1	yes	characteristic
376	C₈	—	2	2	no	—
377	C₈	—	4	1	no	—
378	C₈	—	4	2	no	—
379	C₈	—	8	1	no	—
380	C₈	—	38	2	no	—
381	C₈	—	76	1	no	—
382	C₈	—	76	2	no	—
383	C₈	—	152	1	no	—
384	C₂²	—	19	4	no	—
385	C₂²	—	38	2	no	—
386	C₂²	—	38	2	no	—
387	C₂²	—	38	2	no	—
388	C₂²	—	38	2	no	—
389	C₂²	—	38	2	no	—
390	C₂²	—	38	2	no	—
391	C₂²	#11926418	1	1	yes	characteristic
392	C₂²	C₄⋊C₈×D₁₉	1	1	yes	characteristic
393	C₂²	#11926569	1	1	yes	characteristic
394	C₂²	#107×D₁₉	1	1	yes	characteristic
395	C₂²	#11926583	1	1	yes	characteristic
396	C₂²	#108×D₁₉	1	1	yes	characteristic
397	C₂²	#11926591	1	1	yes	characteristic
398	C₄	—	2	1	no	—
399	C₄	—	2	1	no	—
400	C₄	—	38	2	no	—
401	C₄	—	38	2	no	—
402	C₄	—	76	1	no	—
403	C₄	(C₂²⋊D₁₉)⋊C₈	1	1	yes	characteristic
404	C₄	C₈×D₇₆	1	1	yes	characteristic
405	C₄	#11926617	1	1	yes	characteristic
406	C₄	#11926618	1	1	yes	characteristic
407	C₄	#11926679	1	1	yes	characteristic
408	C₄	#11926701	1	1	yes	characteristic
409	C₄	#11926856	1	1	yes	characteristic
410	C₄	#11926878	1	1	yes	characteristic
411	C₂	—	38	4	no	—
412	C₂	D₁₉×#335	1	1	yes	characteristic
413	C₂	#14562384	1	1	yes	characteristic
414	C₂	#14562408	1	1	yes	characteristic
415	C₂	#14562417	1	1	yes	characteristic
416	C₂	#14563814	1	1	yes	characteristic
417	C₂	#14563824	1	1	yes	characteristic
418	C₂	#14563841	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₁₉
commutator	C₂×C₄×C₁₉	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1277	C₂
socle	C₂³×C₁₉	C₂×C₄⋊C₄
prime radical	C₂³×D₁₉	C₄⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1277	D₁₉
hypocenter	C₁₉	#8829
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ #1277

Complements

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

N	H ≅ G/N	type
4. C₂×#11926297	C₂	semidirect
5. C₂×#11926296	C₂	semidirect
6. #14561469	C₂	semidirect
7. C₁₉×#1277	C₂	semidirect
57. (C₂×D₁₉)⋊C₈	C₈	semidirect
99. C₂×C₈×C₁₉	C₂×C₈	semidirect
121. C₂×C₁₉⋊C₈	C₂×C₈	semidirect
181. #1277	D₁₉	semidirect
195. C₂×D₁₉	#335	semidirect
274. C₁₉	#8829	semidirect
322. C₂×C₈	C₈×D₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄⋊C₈×D₁₉	2
#14563612	2
C₄×(C₂×D₁₉)⋊C₈	2
C₂×#11926297	2
C₂×#11926296	2
#14561469	2
C₁₉×#1277	2
#8829	19