Subgroups — #18073438

Order 4864.

720 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14563397	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926281	C₂	1	2	yes	maximal
3	C₄×C₁₉⋊#95	C₂	1	1	yes	maximal, characteristic
4	#14561513	C₂	1	2	yes	maximal
5	C₄×C₁₉×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄×Dic₁₉	—	2	1	no	—
7	C₂×C₂²⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
8	C₂×#10597260	—	2	1	no	—
9	C₂×C₁₉⋊#95	—	2	1	no	—
10	C₂×C₁₉⋊#95	C₂²	1	2	yes	—
11	#11926299	—	2	1	no	—
12	#11926281	C₄	1	8	yes	complemented
13	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₁₉	C₄	1	1	yes	characteristic, complemented
15	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
16	C₁₉×#391	C₄	1	1	yes	characteristic, complemented
17	C₁₉×#389	C₄	1	1	yes	characteristic, complemented
18	C₁₉×#387	—	2	1	no	—
19	C₁₉×#385	—	2	1	no	—
20	C₁₉×#380	C₂²	1	1	yes	characteristic
21	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
22	C₄×C₄⋊C₄×C₁₉	C₄	1	1	yes	characteristic, complemented
23	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
24	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
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×C₂²⋊Q₈	—	2	2	no	—
30	C₁₉×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
31	C₄×Q₈×C₁₉	—	4	2	no	—
32	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
33	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
34	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
35	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
38	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
39	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
40	C₂×C₄²×C₁₉	—	2	1	no	—
41	C₂×C₄²×C₁₉	—	2	1	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	1	no	—
52	C₁₉×#95	—	2	1	no	—
53	C₁₉×#95	—	2	1	no	—
54	C₁₉×#95	—	2	1	no	—
55	C₁₉×#95	—	2	1	no	—
56	C₁₉⋊#95	—	2	4	no	—
57	C₁₉⋊#95	—	2	2	no	—
58	C₁₉⋊#95	C₂×C₄	1	4	yes	—
59	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
60	C₂²⋊(C₁₉⋊C₈)	C₂×C₄	1	4	yes	—
61	#10597260	—	4	2	no	—
62	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
63	C₂×Q₈×C₁₉	—	2	1	no	—
64	C₂×Q₈×C₁₉	—	4	1	no	—
65	C₂×Q₈×C₁₉	—	4	1	no	—
66	C₂×Q₈×C₁₉	C₄²	1	2	yes	complemented
67	C₂²×C₄×C₁₉	—	2	1	no	—
68	C₂²×C₄×C₁₉	—	2	1	no	—
69	C₂²×C₄×C₁₉	—	2	2	no	—
70	C₂²×C₄×C₁₉	—	2	2	no	—
71	C₂²×C₄×C₁₉	—	2	1	no	—
72	C₂²×C₄×C₁₉	—	2	1	no	—
73	C₂²×C₄×C₁₉	—	2	2	no	—
74	C₂²×C₄×C₁₉	—	2	2	no	—
75	C₂²×C₄×C₁₉	—	2	1	no	—
76	C₂²×C₄×C₁₉	—	2	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	C₂²×C₄	1	2	yes	—
85	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₉	#41	1	2	yes	—
88	C₂²×Dic₁₉	—	2	4	no	—
89	C₂²×Dic₁₉	—	2	4	no	—
90	C₂²×Dic₁₉	—	2	4	no	—
91	C₂²×Dic₁₉	—	4	2	no	—
92	C₂²×Dic₁₉	—	4	2	no	—
93	C₂²×Dic₁₉	—	4	2	no	—
94	C₂²×Dic₁₉	—	4	2	no	—
95	C₄⋊C₄×C₁₉	—	2	1	no	—
96	C₄⋊C₄×C₁₉	—	2	4	no	—
97	C₄⋊C₄×C₁₉	—	4	1	no	—
98	C₄⋊C₄×C₁₉	—	4	1	no	—
99	C₄⋊C₄×C₁₉	—	4	2	no	—
100	C₄⋊C₄×C₁₉	—	4	2	no	—
101	C₄⋊C₄×C₁₉	C₄²	1	2	yes	complemented
102	C₂²⋊C₄×C₁₉	—	2	4	no	—
103	C₂²⋊C₄×C₁₉	—	4	1	no	—
104	C₂²⋊C₄×C₁₉	—	4	1	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	C₄²×C₁₉	—	4	2	no	—
110	C₄²×C₁₉	—	4	2	no	—
111	C₄×Dic₁₉	—	4	8	no	—
112	C₂×C₁₉⋊C₈	—	2	4	no	—
113	C₂×C₁₉⋊C₈	—	4	2	no	—
114	C₂×C₁₉⋊C₈	—	4	2	no	—
115	#8219	—	19	1	no	maximal, Sylow
116	C₂³×C₁₉	—	2	1	no	—
117	C₂³×C₁₉	—	2	1	no	—
118	C₂³×C₁₉	—	2	1	no	—
119	C₂³×C₁₉	—	2	1	no	—
120	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
121	C₂³×C₁₉	C₄×D₄	1	2	yes	—
122	C₂³×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
123	C₂³×C₁₉	#137	1	2	yes	—
124	C₂³×C₁₉	#137	1	1	yes	characteristic
125	Q₈×C₁₉	—	4	2	no	—
126	Q₈×C₁₉	—	4	2	no	—
127	C₂×C₄×C₁₉	—	2	4	no	—
128	C₂×C₄×C₁₉	—	2	4	no	—
129	C₂×C₄×C₁₉	—	2	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	2	no	—
140	C₂×C₄×C₁₉	—	2	2	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	—	4	2	no	—
145	C₂×C₄×C₁₉	—	4	2	no	—
146	C₂×C₄×C₁₉	—	4	4	no	—
147	C₂×C₄×C₁₉	—	4	1	no	—
148	C₂×C₄×C₁₉	—	4	1	no	—
149	C₂×C₄×C₁₉	—	4	1	no	—
150	C₂×C₄×C₁₉	—	4	1	no	—
151	C₂×C₄×C₁₉	—	4	1	no	—
152	C₂×C₄×C₁₉	—	4	1	no	—
153	C₂×C₄×C₁₉	—	4	1	no	—
154	C₂×C₄×C₁₉	—	4	1	no	—
155	C₂×C₄×C₁₉	—	4	1	no	—
156	C₂×C₄×C₁₉	—	4	1	no	—
157	C₂×C₄×C₁₉	#99	1	2	yes	—
158	C₂×C₄×C₁₉	#104	1	2	yes	—
159	C₂×C₄×C₁₉	#104	1	2	yes	—
160	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
161	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
162	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
163	C₂×Dic₁₉	—	2	8	no	—
164	C₂×Dic₁₉	—	4	4	no	—
165	C₂×Dic₁₉	—	4	4	no	—
166	C₂×Dic₁₉	—	4	4	no	—
167	C₂×Dic₁₉	—	4	4	no	—
168	C₂×Dic₁₉	—	4	4	no	—
169	C₂×Dic₁₉	—	4	4	no	—
170	C₁₉⋊C₈	—	4	4	no	—
171	C₄×C₂²⋊Q₈	D₁₉	1	1	yes	characteristic
172	#1749	—	19	1	no	—
173	C₂×#328	—	19	2	no	—
174	C₄×#95	—	19	1	no	—
175	#1294	—	19	2	no	—
176	C₂²×C₁₉	—	2	2	no	—
177	C₂²×C₁₉	—	2	2	no	—
178	C₂²×C₁₉	—	2	1	no	—
179	C₂²×C₁₉	—	2	1	no	—
180	C₂²×C₁₉	—	2	2	no	—
181	C₂²×C₁₉	—	2	2	no	—
182	C₂²×C₁₉	—	2	1	no	—
183	C₂²×C₁₉	—	2	1	no	—
184	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
185	C₂²×C₁₉	C₂×#99	1	1	yes	characteristic
186	C₂²×C₁₉	#410	1	1	yes	characteristic
187	C₂²×C₁₉	#417	1	1	yes	characteristic
188	C₂²×C₁₉	#419	1	1	yes	characteristic
189	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
190	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
191	C₂²×C₁₉	#440	1	2	yes	—
192	C₂²×C₁₉	#441	1	2	yes	—
193	C₄×C₁₉	—	2	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	2	no	—
200	C₄×C₁₉	—	4	2	no	—
201	C₄×C₁₉	—	4	1	no	—
202	C₄×C₁₉	—	8	1	no	—
203	C₄×C₁₉	—	8	1	no	—
204	Dic₁₉	—	4	8	no	—
205	C₂×C₂²⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
206	C₂×C₄×Q₈	Dic₁₉	1	1	yes	characteristic, complemented
207	C₂²×C₄²	—	38	1	no	—
208	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
209	C₂×C₂²⋊C₈	—	19	2	no	—
210	C₂×#97	—	38	1	no	—
211	#391	Dic₁₉	1	1	yes	characteristic, complemented
212	#389	Dic₁₉	1	1	yes	characteristic, complemented
213	#387	—	2	1	no	—
214	#385	—	2	1	no	—
215	#380	C₂×D₁₉	1	1	yes	characteristic
216	C₄×C₄⋊C₄	—	2	1	no	—
217	C₄×C₄⋊C₄	Dic₁₉	1	1	yes	characteristic, complemented
218	C₄×C₂²⋊C₄	—	2	1	no	—
219	C₂×#95	—	19	2	no	—
220	C₂×#95	—	38	1	no	—
221	#336	—	38	1	no	—
222	#328	—	19	8	no	—
223	C₂×C₁₉	—	2	2	no	—
224	C₂×C₁₉	—	2	2	no	—
225	C₂×C₁₉	#1504	1	1	yes	characteristic
226	C₂×C₁₉	#1506	1	1	yes	characteristic
227	C₂×C₁₉	#1508	1	1	yes	characteristic
228	C₂×C₁₉	#1509	1	1	yes	characteristic
229	C₂×C₁₉	C₄×#99	1	1	yes	characteristic
230	C₂×C₁₉	C₄×#104	1	1	yes	characteristic
231	C₂×C₁₉	#1763	1	1	yes	characteristic
232	C₂²×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
233	C₂³×C₄	—	38	2	no	—
234	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
235	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
236	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
237	C₂²×C₈	—	38	2	no	—
238	C₂²⋊Q₈	—	2	2	no	—
239	C₂²⋊Q₈	C₄×D₁₉	1	4	yes	—
240	C₄×Q₈	—	4	2	no	—
241	C₂×C₄⋊C₄	—	2	1	no	—
242	C₂×C₄⋊C₄	—	2	1	no	—
243	C₂×C₄⋊C₄	—	2	1	no	—
244	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
245	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
246	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
247	C₂×C₂²⋊C₄	—	2	1	no	—
248	C₂×C₂²⋊C₄	—	2	1	no	—
249	C₂×C₄²	—	2	1	no	—
250	C₂×C₄²	—	2	1	no	—
251	C₂×C₄²	—	4	2	no	—
252	C₂×C₄²	—	38	4	no	—
253	C₂×C₄²	—	76	2	no	—
254	C₂×C₄²	—	76	2	no	—
255	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
256	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
257	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
258	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
259	C₂²⋊C₈	—	19	4	no	—
260	C₂²⋊C₈	—	38	2	no	—
261	#97	—	76	2	no	—
262	#95	—	2	1	no	—
263	#95	—	2	1	no	—
264	#95	—	2	1	no	—
265	#95	—	2	1	no	—
266	#95	—	2	1	no	—
267	#95	—	19	4	no	—
268	#95	—	38	4	no	—
269	#95	—	38	2	no	—
270	C₁₉	#8219	1	1	yes	characteristic, complemented, Sylow
271	C₂⁴	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
272	C₂×Q₈	—	2	1	no	—
273	C₂×Q₈	—	4	1	no	—
274	C₂×Q₈	—	4	1	no	—
275	C₂×Q₈	C₄×Dic₁₉	1	2	yes	complemented
276	C₂²×C₄	—	2	1	no	—
277	C₂²×C₄	—	2	1	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	1	no	—
282	C₂²×C₄	—	2	1	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	1	no	—
285	C₂²×C₄	—	2	1	no	—
286	C₂²×C₄	—	4	1	no	—
287	C₂²×C₄	—	4	1	no	—
288	C₂²×C₄	—	4	1	no	—
289	C₂²×C₄	—	38	4	no	—
290	C₂²×C₄	—	38	4	no	—
291	C₂²×C₄	—	38	4	no	—
292	C₂²×C₄	—	76	2	no	—
293	C₂²×C₄	—	76	2	no	—
294	C₂²×C₄	—	76	2	no	—
295	C₂²×C₄	—	76	2	no	—
296	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
297	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
298	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
299	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
300	C₂²×C₄	C₂×C₄×D₁₉	1	2	yes	—
301	C₂²×C₄	#64541	1	2	yes	—
302	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
303	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
304	C₂×C₈	—	38	4	no	—
305	C₂×C₈	—	76	2	no	—
306	C₂×C₈	—	76	2	no	—
307	C₄⋊C₄	—	2	1	no	—
308	C₄⋊C₄	—	2	4	no	—
309	C₄⋊C₄	—	4	1	no	—
310	C₄⋊C₄	—	4	1	no	—
311	C₄⋊C₄	—	4	2	no	—
312	C₄⋊C₄	—	4	2	no	—
313	C₄⋊C₄	C₄×Dic₁₉	1	2	yes	complemented
314	C₂²⋊C₄	—	2	4	no	—
315	C₂²⋊C₄	—	4	1	no	—
316	C₂²⋊C₄	—	4	1	no	—
317	C₄²	—	2	2	no	—
318	C₄²	—	2	2	no	—
319	C₄²	—	4	1	no	—
320	C₄²	—	4	1	no	—
321	C₄²	—	4	2	no	—
322	C₄²	—	4	2	no	—
323	C₄²	—	76	8	no	—
324	C₂³	—	2	1	no	—
325	C₂³	—	2	1	no	—
326	C₂³	—	2	1	no	—
327	C₂³	—	2	1	no	—
328	C₂³	C₄×C₂²⋊D₁₉	1	2	yes	—
329	C₂³	#10597388	1	2	yes	—
330	C₂³	#10597395	1	1	yes	characteristic
331	C₂³	#10597397	1	1	yes	characteristic
332	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
333	Q₈	—	4	2	no	—
334	Q₈	—	4	2	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	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	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	4	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	38	8	no	—
366	C₂×C₄	—	76	4	no	—
367	C₂×C₄	—	76	4	no	—
368	C₂×C₄	—	76	4	no	—
369	C₂×C₄	—	76	4	no	—
370	C₂×C₄	—	76	4	no	—
371	C₂×C₄	—	76	4	no	—
372	C₂×C₄	#10597291	1	2	yes	—
373	C₂×C₄	#10597294	1	2	yes	—
374	C₂×C₄	#10597294	1	2	yes	—
375	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
376	C₂×C₄	#10597372	1	1	yes	characteristic
377	C₂×C₄	C₄×C₂²⋊D₁₉	1	2	yes	—
378	C₈	—	76	4	no	—
379	C₂²	—	2	1	no	—
380	C₂²	—	2	1	no	—
381	C₂²	—	2	2	no	—
382	C₂²	—	2	2	no	—
383	C₂²	—	2	2	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	1	no	—
386	C₂²	—	2	2	no	—
387	C₂²	C₄×C₂²⋊Dic₁₉	1	1	yes	characteristic
388	C₂²	C₂×#10597291	1	1	yes	characteristic
389	C₂²	#11926518	1	1	yes	characteristic
390	C₂²	#11926545	1	1	yes	characteristic
391	C₂²	#11926553	1	1	yes	characteristic
392	C₂²	C₂×#10597294	1	1	yes	characteristic
393	C₂²	C₂×#10597294	1	1	yes	characteristic
394	C₂²	#11926642	1	2	yes	—
395	C₂²	#11926649	1	2	yes	—
396	C₄	—	2	2	no	—
397	C₄	—	2	2	no	—
398	C₄	—	2	2	no	—
399	C₄	—	2	1	no	—
400	C₄	—	2	1	no	—
401	C₄	—	2	2	no	—
402	C₄	—	4	2	no	—
403	C₄	—	4	1	no	—
404	C₄	—	4	2	no	—
405	C₄	—	8	1	no	—
406	C₄	—	8	1	no	—
407	C₄	—	76	8	no	—
408	C₂	—	2	2	no	—
409	C₂	—	2	2	no	—
410	C₂	#14562139	1	1	yes	characteristic
411	C₂	#14562147	1	1	yes	characteristic
412	C₂	#14562155	1	1	yes	characteristic
413	C₂	#14562160	1	1	yes	characteristic
414	C₂	C₄×#10597291	1	1	yes	characteristic
415	C₂	C₄×#10597294	1	1	yes	characteristic
416	C₂	#14563465	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₁₉
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₄×C₁₉×C₂²⋊Q₈	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₁₉	C₂×D₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₄×C₂²⋊Q₈	D₁₉
hypocenter	C₁₉	#8219
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₄×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
12. #11926281	C₄	semidirect
14. C₂×C₄×Q₈×C₁₉	C₄	semidirect
16. C₁₉×#391	C₄	semidirect
17. C₁₉×#389	C₄	semidirect
22. C₄×C₄⋊C₄×C₁₉	C₄	semidirect
66. C₂×Q₈×C₁₉	C₄²	semidirect
101. C₄⋊C₄×C₁₉	C₄²	semidirect
206. C₂×C₄×Q₈	Dic₁₉	semidirect
211. #391	Dic₁₉	semidirect
212. #389	Dic₁₉	semidirect
217. C₄×C₄⋊C₄	Dic₁₉	semidirect
270. C₁₉	#8219	semidirect
275. C₂×Q₈	C₄×Dic₁₉	semidirect
313. C₄⋊C₄	C₄×Dic₁₉	semidirect

Maximal subgroups

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

subgroup	index
#14563397	2
C₂×#11926281	2
C₄×C₁₉⋊#95	2
#14561513	2
C₄×C₁₉×C₂²⋊Q₈	2
#8219	19