Subgroups — #18075229

Order 4864.

688 conjugacy classes of subgroups.

The subgroup lattice has 424 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×#1831	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	C₂²	1	2	yes	—
21	C₄³×C₁₉	C₂²	1	1	yes	characteristic
22	C₁₉×#336	—	2	1	no	—
23	C₁₉×#336	—	2	1	no	—
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	4	no	—
55	C₁₉×C₄⋊C₈	—	2	2	no	—
56	C₁₉×C₄⋊C₈	—	2	2	no	—
57	C₁₉⋊#95	—	2	1	no	—
58	C₁₉⋊#95	—	2	1	no	—
59	C₁₉⋊#95	—	2	1	no	—
60	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
61	C₄×C₁₉⋊C₈	—	2	2	no	—
62	C₄×C₁₉⋊C₈	—	2	2	no	—
63	C₂³×D₁₉	—	2	1	no	—
64	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
65	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
66	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
67	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
68	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
69	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
71	C₂²×Dic₁₉	—	2	1	no	—
72	C₂²×Dic₁₉	—	2	1	no	—
73	C₂²×Dic₁₉	—	2	1	no	—
74	C₂×D₇₆	—	2	1	no	—
75	C₂×D₇₆	—	2	1	no	—
76	C₂×D₇₆	—	2	1	no	—
77	C₂×D₇₆	C₄⋊C₄	1	2	yes	—
78	C₂×D₇₆	C₂×C₈	1	2	yes	—
79	C₂×D₇₆	M₁₆	1	2	yes	—
80	C₂×C₄×D₁₉	—	2	4	no	—
81	C₂×C₄×D₁₉	—	2	4	no	—
82	C₂×C₄×D₁₉	—	2	2	no	—
83	C₂×C₄×D₁₉	—	2	2	no	—
84	C₂×C₄×D₁₉	—	4	2	no	—
85	C₂×C₄×D₁₉	—	4	2	no	—
86	C₂×C₄×D₁₉	—	4	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×C₈×C₁₉	—	4	2	no	—
91	C₂×C₈×C₁₉	—	4	2	no	—
92	C₂×C₈×C₁₉	—	4	2	no	—
93	C₄²×C₁₉	—	2	2	no	—
94	C₄²×C₁₉	—	2	1	no	—
95	C₄²×C₁₉	—	2	1	no	—
96	C₄²×C₁₉	—	2	2	no	—
97	C₄²×C₁₉	—	2	2	no	—
98	C₄²×C₁₉	—	4	1	no	—
99	C₄²×C₁₉	C₂×C₈	1	2	yes	—
100	C₄²×C₁₉	M₁₆	1	2	yes	—
101	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
102	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
103	C₄²×C₁₉	#41	1	1	yes	characteristic
104	C₄²×C₁₉	#41	1	1	yes	characteristic
105	(C₂×D₁₉)⋊C₄	—	2	4	no	—
106	(C₂×D₁₉)⋊C₄	—	2	4	no	—
107	(C₂×D₁₉)⋊C₄	—	2	2	no	—
108	(C₂×D₁₉)⋊C₄	—	2	2	no	—
109	C₄⋊Dic₁₉	—	2	1	no	—
110	C₄⋊Dic₁₉	—	2	1	no	—
111	C₄⋊Dic₁₉	—	2	1	no	—
112	C₄⋊Dic₁₉	C₄⋊C₄	1	2	yes	—
113	C₄⋊Dic₁₉	C₂×C₈	1	2	yes	—
114	C₄⋊Dic₁₉	M₁₆	1	2	yes	—
115	C₄×Dic₁₉	—	4	2	no	—
116	C₄×Dic₁₉	—	4	2	no	—
117	C₄×Dic₁₉	—	4	2	no	—
118	C₂×C₁₉⋊C₈	—	2	4	no	—
119	C₂×C₁₉⋊C₈	—	4	2	no	—
120	C₂×C₁₉⋊C₈	—	4	2	no	—
121	#8565	—	19	1	no	maximal, Sylow
122	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
123	C₂²×D₁₉	—	2	2	no	—
124	C₂²×D₁₉	—	2	2	no	—
125	C₂²×D₁₉	—	2	2	no	—
126	C₂²×D₁₉	—	4	1	no	—
127	C₂²×D₁₉	—	4	1	no	—
128	C₂²×D₁₉	—	4	1	no	—
129	C₂²×D₁₉	—	4	1	no	—
130	C₂×C₄×C₁₉	—	2	1	no	—
131	C₂×C₄×C₁₉	—	2	1	no	—
132	C₂×C₄×C₁₉	—	2	1	no	—
133	C₂×C₄×C₁₉	—	2	1	no	—
134	C₂×C₄×C₁₉	—	2	1	no	—
135	C₂×C₄×C₁₉	—	2	1	no	—
136	C₂×C₄×C₁₉	—	2	1	no	—
137	C₂×C₄×C₁₉	—	2	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	C₂²⋊C₈	1	2	yes	—
142	C₂×C₄×C₁₉	C₂²⋊C₈	1	2	yes	—
143	C₂×C₄×C₁₉	#104	1	2	yes	—
144	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
145	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
146	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
147	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
148	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
149	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
150	C₂×C₄×C₁₉	C₂²×C₈	1	1	yes	characteristic
151	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
152	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
153	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
154	C₂×C₄×C₁₉	#135	1	2	yes	—
155	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
156	C₂×Dic₁₉	—	2	2	no	—
157	C₂×Dic₁₉	—	2	2	no	—
158	C₂×Dic₁₉	—	2	2	no	—
159	C₂×Dic₁₉	—	4	1	no	—
160	C₂×Dic₁₉	—	4	1	no	—
161	C₂×Dic₁₉	—	4	1	no	—
162	C₂×Dic₁₉	—	4	1	no	—
163	C₂×Dic₁₉	—	4	1	no	—
164	C₂×Dic₁₉	—	4	1	no	—
165	D₇₆	—	2	2	no	—
166	D₇₆	—	2	2	no	—
167	D₇₆	—	2	2	no	—
168	D₇₆	C₄⋊C₈	1	4	yes	complemented
169	C₄×D₁₉	—	4	8	no	—
170	C₄×D₁₉	—	4	8	no	—
171	C₄×D₁₉	—	4	4	no	—
172	C₄×D₁₉	—	4	4	no	—
173	C₈×C₁₉	—	8	2	no	—
174	C₁₉⋊C₈	—	4	4	no	—
175	C₄²×D₄	—	19	1	no	—
176	#1831	D₁₉	1	1	yes	characteristic, complemented
177	C₄×C₄⋊C₈	—	19	1	no	—
178	C₂×D₄⋊C₈	—	19	2	no	—
179	#1279	—	19	2	no	—
180	C₂²×C₁₉	#380	1	1	yes	characteristic
181	C₂²×C₁₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
182	C₂²×C₁₉	#407	1	1	yes	characteristic
183	C₂²×C₁₉	#416	1	1	yes	characteristic
184	C₂²×C₁₉	#418	1	1	yes	characteristic
185	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
186	C₂²×C₁₉	#421	1	1	yes	characteristic
187	C₂×D₁₉	—	2	4	no	—
188	C₂×D₁₉	—	4	2	no	—
189	C₂×D₁₉	—	4	2	no	—
190	C₂×D₁₉	—	4	2	no	—
191	C₂×D₁₉	—	4	2	no	—
192	C₂×D₁₉	—	4	2	no	—
193	C₂×D₁₉	—	4	2	no	—
194	C₄×C₁₉	—	2	1	no	—
195	C₄×C₁₉	—	2	1	no	—
196	C₄×C₁₉	—	2	2	no	—
197	C₄×C₁₉	—	2	2	no	—
198	C₄×C₁₉	—	2	2	no	—
199	C₄×C₁₉	—	4	1	no	—
200	C₄×C₁₉	C₂×C₄⋊C₈	1	1	yes	characteristic
201	C₄×C₁₉	#423	1	1	yes	characteristic
202	C₄×C₁₉	#431	1	1	yes	characteristic
203	C₄×C₁₉	#432	1	1	yes	characteristic
204	C₄×C₁₉	#463	1	2	yes	—
205	C₄×C₁₉	#478	1	2	yes	—
206	Dic₁₉	—	4	2	no	—
207	Dic₁₉	—	4	2	no	—
208	Dic₁₉	—	4	2	no	—
209	C₂×C₄×D₄	—	19	1	no	—
210	C₂×C₄×D₄	—	19	1	no	—
211	C₂×C₄×D₄	—	19	1	no	—
212	C₂²×C₄²	—	38	1	no	—
213	C₂×C₄⋊C₈	—	38	1	no	—
214	C₂×C₄⋊C₈	C₂×D₁₉	1	2	yes	—
215	C₂×C₄×C₈	—	19	2	no	—
216	C₄×C₄⋊C₄	—	19	1	no	—
217	C₄×C₄⋊C₄	—	19	1	no	—
218	C₄×C₄⋊C₄	—	19	1	no	—
219	C₄×C₂²⋊C₄	—	38	1	no	—
220	C₄×C₂²⋊C₄	—	38	1	no	—
221	C₄×C₂²⋊C₄	—	38	1	no	—
222	C₄³	C₂×D₁₉	1	1	yes	characteristic
223	#336	—	2	1	no	—
224	#336	—	2	1	no	—
225	#336	—	38	1	no	—
226	D₄⋊C₈	—	38	4	no	—
227	C₂×C₁₉	#1476	1	1	yes	characteristic
228	C₂×C₁₉	#1478	1	1	yes	characteristic
229	C₂×C₁₉	#1488	1	1	yes	characteristic
230	C₂×C₁₉	#1490	1	1	yes	characteristic
231	C₂×C₁₉	#1797	1	1	yes	characteristic
232	C₂×C₁₉	#1804	1	1	yes	characteristic
233	C₂×C₁₉	#1806	1	1	yes	characteristic
234	D₁₉	—	4	4	no	—
235	C₂²×D₄	—	19	1	no	—
236	C₂³×C₄	—	38	1	no	—
237	C₂³×C₄	—	38	1	no	—
238	C₂³×C₄	—	38	1	no	—
239	C₂²×C₈	—	2	2	no	—
240	C₂²×C₈	—	38	2	no	—
241	C₄×D₄	—	19	4	no	—
242	C₄×D₄	—	19	2	no	—
243	C₄×D₄	—	19	2	no	—
244	C₄×D₄	—	38	2	no	—
245	C₄×D₄	—	38	2	no	—
246	C₄×D₄	—	38	2	no	—
247	C₄×D₄	—	38	1	no	—
248	C₄×D₄	—	38	1	no	—
249	C₂×C₄⋊C₄	—	19	1	no	—
250	C₂×C₄⋊C₄	—	19	1	no	—
251	C₂×C₄⋊C₄	—	19	1	no	—
252	C₂×C₂²⋊C₄	—	38	1	no	—
253	C₂×C₂²⋊C₄	—	38	1	no	—
254	C₂×C₂²⋊C₄	—	38	1	no	—
255	C₂×C₄²	—	38	1	no	—
256	C₂×C₄²	—	38	1	no	—
257	C₂×C₄²	—	38	1	no	—
258	C₂×C₄²	—	76	4	no	—
259	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
260	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
261	C₂×C₄²	D₇₆	1	1	yes	characteristic
262	C₂×C₄²	D₇₆	1	1	yes	characteristic
263	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
264	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
265	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
266	C₄⋊C₈	—	2	2	no	—
267	C₄⋊C₈	—	2	2	no	—
268	C₄⋊C₈	—	38	4	no	—
269	C₄×C₈	—	38	2	no	—
270	C₄×C₈	—	38	2	no	—
271	#95	—	38	1	no	—
272	#95	—	38	1	no	—
273	#95	—	38	1	no	—
274	C₁₉	#8565	1	1	yes	characteristic, complemented, Sylow
275	C₂⁴	—	38	1	no	—
276	C₂×D₄	—	19	2	no	—
277	C₂×D₄	—	19	2	no	—
278	C₂×D₄	—	19	2	no	—
279	C₂×D₄	—	38	1	no	—
280	C₂×D₄	—	38	1	no	—
281	C₂×D₄	—	38	1	no	—
282	C₂²×C₄	—	38	4	no	—
283	C₂²×C₄	—	38	1	no	—
284	C₂²×C₄	—	38	1	no	—
285	C₂²×C₄	—	38	1	no	—
286	C₂²×C₄	—	38	2	no	—
287	C₂²×C₄	—	38	2	no	—
288	C₂²×C₄	—	38	4	no	—
289	C₂²×C₄	—	76	2	no	—
290	C₂²×C₄	—	76	2	no	—
291	C₂²×C₄	—	76	2	no	—
292	C₂²×C₄	—	76	2	no	—
293	C₂²×C₄	—	76	2	no	—
294	C₂²×C₄	—	76	2	no	—
295	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
296	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
297	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
298	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
299	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
300	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
301	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
302	C₂×C₈	—	4	2	no	—
303	C₂×C₈	—	4	2	no	—
304	C₂×C₈	—	4	2	no	—
305	C₂×C₈	—	38	4	no	—
306	C₂×C₈	—	76	2	no	—
307	C₂×C₈	—	76	2	no	—
308	C₄⋊C₄	—	19	2	no	—
309	C₄⋊C₄	—	19	2	no	—
310	C₄⋊C₄	—	19	2	no	—
311	C₄⋊C₄	—	38	1	no	—
312	C₄⋊C₄	—	38	1	no	—
313	C₄⋊C₄	—	38	1	no	—
314	C₂²⋊C₄	—	38	4	no	—
315	C₂²⋊C₄	—	38	4	no	—
316	C₂²⋊C₄	—	38	2	no	—
317	C₂²⋊C₄	—	38	2	no	—
318	C₄²	—	2	2	no	—
319	C₄²	—	2	2	no	—
320	C₄²	—	2	2	no	—
321	C₄²	—	2	1	no	—
322	C₄²	—	2	1	no	—
323	C₄²	—	4	1	no	—
324	C₄²	—	76	2	no	—
325	C₄²	—	76	2	no	—
326	C₄²	—	76	2	no	—
327	C₄²	C₈×D₁₉	1	2	yes	—
328	C₄²	#64515	1	2	yes	—
329	C₄²	D₄×D₁₉	1	1	yes	characteristic
330	C₄²	#64543	1	1	yes	characteristic
331	C₄²	Q₈×D₁₉	1	1	yes	characteristic
332	C₄²	#64545	1	1	yes	characteristic
333	C₂³	—	38	2	no	—
334	C₂³	—	38	2	no	—
335	C₂³	—	38	2	no	—
336	C₂³	—	76	1	no	—
337	C₂³	—	76	1	no	—
338	C₂³	—	76	1	no	—
339	C₂³	—	76	1	no	—
340	C₂³	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
341	D₄	—	19	4	no	—
342	D₄	—	38	2	no	—
343	D₄	—	38	2	no	—
344	D₄	—	38	2	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	38	2	no	—
357	C₂×C₄	—	38	2	no	—
358	C₂×C₄	—	38	2	no	—
359	C₂×C₄	—	76	8	no	—
360	C₂×C₄	—	76	8	no	—
361	C₂×C₄	—	76	1	no	—
362	C₂×C₄	—	76	1	no	—
363	C₂×C₄	—	76	1	no	—
364	C₂×C₄	—	76	1	no	—
365	C₂×C₄	—	76	1	no	—
366	C₂×C₄	—	76	1	no	—
367	C₂×C₄	—	76	4	no	—
368	C₂×C₄	—	76	4	no	—
369	C₂×C₄	(C₂×D₁₉)⋊C₈	1	2	yes	—
370	C₂×C₄	(C₂×D₁₉)⋊C₈	1	2	yes	—
371	C₂×C₄	#10597282	1	2	yes	—
372	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
373	C₂×C₄	#10597338	1	1	yes	characteristic
374	C₂×C₄	#10597341	1	1	yes	characteristic
375	C₂×C₄	#10597343	1	1	yes	characteristic
376	C₂×C₄	C₂×C₈×D₁₉	1	1	yes	characteristic
377	C₂×C₄	C₂×#64515	1	1	yes	characteristic
378	C₂×C₄	M₁₆×D₁₉	1	1	yes	characteristic
379	C₂×C₄	M₁₆×D₁₉	1	1	yes	characteristic
380	C₂×C₄	#10597384	1	1	yes	characteristic
381	C₂×C₄	#10597392	1	1	yes	characteristic
382	C₂×C₄	#10597395	1	2	yes	—
383	C₂×C₄	#10597396	1	2	yes	—
384	C₈	—	8	2	no	—
385	C₈	—	76	4	no	—
386	C₂²	—	38	4	no	—
387	C₂²	—	76	2	no	—
388	C₂²	—	76	2	no	—
389	C₂²	—	76	2	no	—
390	C₂²	—	76	2	no	—
391	C₂²	—	76	2	no	—
392	C₂²	—	76	2	no	—
393	C₂²	#11926401	1	1	yes	characteristic
394	C₂²	C₂×(C₂×D₁₉)⋊C₈	1	1	yes	characteristic
395	C₂²	#11926507	1	1	yes	characteristic
396	C₂²	#11926538	1	1	yes	characteristic
397	C₂²	#11926548	1	1	yes	characteristic
398	C₂²	C₂×#10597282	1	1	yes	characteristic
399	C₂²	#11926560	1	1	yes	characteristic
400	C₄	—	2	2	no	—
401	C₄	—	2	1	no	—
402	C₄	—	2	1	no	—
403	C₄	—	2	2	no	—
404	C₄	—	2	2	no	—
405	C₄	—	4	1	no	—
406	C₄	—	76	2	no	—
407	C₄	—	76	2	no	—
408	C₄	—	76	2	no	—
409	C₄	C₄⋊C₈×D₁₉	1	1	yes	characteristic
410	C₄	#11926566	1	1	yes	characteristic
411	C₄	#11926596	1	1	yes	characteristic
412	C₄	#11926600	1	1	yes	characteristic
413	C₄	#11926756	1	2	yes	—
414	C₄	#11926841	1	2	yes	—
415	C₂	—	76	4	no	—
416	C₂	#14562015	1	1	yes	characteristic
417	C₂	#14562025	1	1	yes	characteristic
418	C₂	#14562067	1	1	yes	characteristic
419	C₂	#14562077	1	1	yes	characteristic
420	C₂	#14563612	1	1	yes	characteristic
421	C₂	#14563642	1	1	yes	characteristic
422	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×#1831	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂²×D₇₆	C₂×C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1831	D₁₉
hypocenter	C₁₉	#8565
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ #1831

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×#1831	C₂	semidirect
51. C₄×D₇₆	C₈	semidirect
168. D₇₆	C₄⋊C₈	semidirect
176. #1831	D₁₉	semidirect
274. C₁₉	#8565	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×#1831	2
#8565	19