Subgroups — #18088437

Order 4864.

982 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	C₂²×#10597275	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₈×Dic₁₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926306	C₂	1	2	yes	maximal
4	#14561864	C₂	1	2	yes	maximal
5	C₂²×C₁₉×#107	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
7	C₂²×C₄⋊Dic₁₉	C₂²	1	2	yes	—
8	C₂²×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
9	C₂×#10597275	—	2	2	no	—
10	C₂×#10597275	—	2	2	no	—
11	C₂×#10597275	C₄	1	4	yes	complemented
12	C₂×C₈×Dic₁₉	—	2	2	no	—
13	C₂×C₈×Dic₁₉	—	2	2	no	—
14	C₂×C₈×Dic₁₉	C₄	1	4	yes	complemented
15	C₂×C₁₉⋊#95	—	2	4	no	—
16	#11926306	—	2	4	no	—
17	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
19	C₂×C₁₉×#107	—	2	2	no	—
20	C₂×C₁₉×#107	—	2	2	no	—
21	C₂×C₁₉×#107	C₄	1	4	yes	complemented
22	C₂³×C₄×C₁₉	—	2	2	no	—
23	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
24	C₂³×Dic₁₉	—	2	2	no	—
25	C₂³×Dic₁₉	D₄	1	2	yes	—
26	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
27	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
28	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
29	C₂²×C₈×C₁₉	D₄	1	2	yes	—
30	C₂²×C₈×C₁₉	D₄	1	2	yes	—
31	C₂²×C₈×C₁₉	D₄	1	2	yes	—
32	C₂²×C₈×C₁₉	Q₈	1	2	yes	—
33	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
34	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
35	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
36	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
37	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
38	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
39	C₂×C₄⋊Dic₁₉	—	2	2	no	—
40	C₂×C₄⋊Dic₁₉	—	2	2	no	—
41	C₂×C₄⋊Dic₁₉	—	2	2	no	—
42	C₂×C₄⋊Dic₁₉	—	2	2	no	—
43	C₂×C₄⋊Dic₁₉	—	2	2	no	—
44	C₂×C₄⋊Dic₁₉	C₂×C₄	1	4	yes	—
45	C₂×C₄×Dic₁₉	—	2	1	no	—
46	C₂×C₄×Dic₁₉	—	2	1	no	—
47	C₂×C₄×Dic₁₉	—	2	1	no	—
48	C₂×C₄×Dic₁₉	—	2	1	no	—
49	C₂×C₄×Dic₁₉	C₂×C₄	1	2	yes	—
50	C₂×C₄×Dic₁₉	Q₈	1	2	yes	—
51	C₂²×C₁₉⋊C₈	—	2	1	no	—
52	C₂²×C₁₉⋊C₈	—	2	1	no	—
53	C₂²×C₁₉⋊C₈	—	2	1	no	—
54	C₂²×C₁₉⋊C₈	—	2	1	no	—
55	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
56	C₂²×C₁₉⋊C₈	D₄	1	2	yes	—
57	C₂²×C₁₉⋊C₈	Q₈	1	2	yes	—
58	C₁₉×#107	—	2	8	no	—
59	C₁₉⋊#95	—	4	8	no	—
60	#10597275	—	2	8	no	—
61	C₈×Dic₁₉	—	2	8	no	—
62	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
63	C₂²×C₄×C₁₉	—	2	4	no	—
64	C₂²×C₄×C₁₉	—	4	2	no	—
65	C₂²×C₄×C₁₉	—	4	2	no	—
66	C₂²×C₄×C₁₉	—	4	4	no	—
67	C₂²×C₄×C₁₉	—	4	4	no	—
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	C₂×D₄	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×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
76	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
77	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
78	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
79	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
80	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
81	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
82	C₂²×Dic₁₉	—	2	2	no	—
83	C₂²×Dic₁₉	—	2	2	no	—
84	C₂²×Dic₁₉	—	2	2	no	—
85	C₂²×Dic₁₉	—	2	2	no	—
86	C₂²×Dic₁₉	—	2	4	no	—
87	C₂²×Dic₁₉	—	4	2	no	—
88	C₂²×Dic₁₉	—	4	2	no	—
89	C₂²×Dic₁₉	—	4	4	no	—
90	C₂²×Dic₁₉	—	4	4	no	—
91	C₂²×Dic₁₉	C₄⋊C₄	1	4	yes	—
92	C₂²×Dic₁₉	D₈	1	4	yes	—
93	C₂²×Dic₁₉	Q₁₆	1	4	yes	—
94	C₂×C₈×C₁₉	C₄²	1	4	yes	—
95	C₂×C₈×C₁₉	C₂²⋊C₄	1	4	yes	—
96	C₂×C₈×C₁₉	C₂²⋊C₄	1	4	yes	—
97	C₂×C₈×C₁₉	C₂²⋊C₄	1	4	yes	—
98	C₂×C₈×C₁₉	C₄⋊C₄	1	4	yes	—
99	C₂×C₈×C₁₉	C₄⋊C₄	1	4	yes	—
100	C₂×C₈×C₁₉	C₄⋊C₄	1	4	yes	—
101	C₄⋊C₄×C₁₉	—	2	4	no	—
102	C₄⋊C₄×C₁₉	—	2	4	no	—
103	C₄⋊C₄×C₁₉	—	4	2	no	—
104	C₄⋊C₄×C₁₉	—	4	2	no	—
105	C₄⋊Dic₁₉	—	2	4	no	—
106	C₄⋊Dic₁₉	—	2	4	no	—
107	C₄⋊Dic₁₉	—	4	2	no	—
108	C₄⋊Dic₁₉	—	4	2	no	—
109	C₄×Dic₁₉	—	2	2	no	—
110	C₄×Dic₁₉	—	2	2	no	—
111	C₄×Dic₁₉	—	2	2	no	—
112	C₄×Dic₁₉	—	2	2	no	—
113	C₂×C₁₉⋊C₈	—	2	2	no	—
114	C₂×C₁₉⋊C₈	—	2	2	no	—
115	C₂×C₁₉⋊C₈	—	2	2	no	—
116	C₂×C₁₉⋊C₈	—	2	2	no	—
117	C₂×C₁₉⋊C₈	—	2	2	no	—
118	C₂×C₁₉⋊C₈	—	2	2	no	—
119	C₂×C₁₉⋊C₈	C₄⋊C₄	1	4	yes	—
120	#10862	—	19	1	no	maximal, Sylow
121	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
122	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
123	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
124	C₂³×C₁₉	#121	1	1	yes	characteristic
125	C₂³×C₁₉	#121	1	1	yes	characteristic
126	C₂³×C₁₉	#127	1	1	yes	characteristic
127	C₂³×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
128	C₂³×C₁₉	C₂×D₈	1	2	yes	—
129	C₂³×C₁₉	C₂×Q₁₆	1	2	yes	—
130	C₂³×C₁₉	#135	1	2	yes	—
131	C₂³×C₁₉	#135	1	2	yes	—
132	C₂×C₄×C₁₉	—	4	4	no	—
133	C₂×C₄×C₁₉	—	4	8	no	—
134	C₂×C₄×C₁₉	—	8	4	no	—
135	C₂×C₄×C₁₉	—	8	2	no	—
136	C₂×C₄×C₁₉	—	8	2	no	—
137	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
138	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
139	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
140	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
141	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
142	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
143	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
144	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
145	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
146	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
147	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
148	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
149	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
150	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
151	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
152	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
153	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
154	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
155	C₂×C₄×C₁₉	C₂²⋊Q₈	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⋊Q₈	1	1	yes	characteristic
159	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
160	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
161	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
162	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
163	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
164	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
165	C₂×Dic₁₉	—	2	4	no	—
166	C₂×Dic₁₉	—	2	4	no	—
167	C₂×Dic₁₉	—	2	4	no	—
168	C₂×Dic₁₉	—	2	4	no	—
169	C₂×Dic₁₉	—	2	4	no	—
170	C₂×Dic₁₉	—	2	4	no	—
171	C₂×Dic₁₉	—	4	4	no	—
172	C₂×Dic₁₉	—	4	8	no	—
173	C₂×Dic₁₉	—	8	4	no	—
174	C₂×Dic₁₉	—	8	2	no	—
175	C₂×Dic₁₉	—	8	2	no	—
176	C₂×Dic₁₉	#107	1	8	yes	complemented
177	C₈×C₁₉	#95	1	8	yes	complemented
178	C₁₉⋊C₈	—	2	4	no	—
179	C₂²×#107	—	19	1	no	—
180	C₂²×#107	D₁₉	1	1	yes	characteristic
181	C₂²×C₄×C₈	—	19	1	no	—
182	C₂×#340	—	19	2	no	—
183	C₄⋊#95	—	19	2	no	—
184	C₂²×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
185	C₂²×C₁₉	#380	1	1	yes	characteristic
186	C₂²×C₁₉	#384	1	1	yes	characteristic
187	C₂²×C₁₉	#389	1	1	yes	characteristic
188	C₂²×C₁₉	#389	1	1	yes	characteristic
189	C₂²×C₁₉	#390	1	1	yes	characteristic
190	C₂²×C₁₉	#390	1	1	yes	characteristic
191	C₂²×C₁₉	C₂×#107	1	2	yes	—
192	C₂²×C₁₉	#427	1	2	yes	—
193	C₂²×C₁₉	C₄×D₈	1	2	yes	—
194	C₂²×C₁₉	C₄×D₈	1	2	yes	—
195	C₂²×C₁₉	C₄×Q₁₆	1	2	yes	—
196	C₂²×C₁₉	C₄×Q₁₆	1	2	yes	—
197	C₂²×C₁₉	#466	1	2	yes	—
198	C₂²×C₁₉	#466	1	2	yes	—
199	C₂²×C₁₉	#467	1	2	yes	—
200	C₂²×C₁₉	#467	1	2	yes	—
201	C₂²×C₁₉	#493	1	1	yes	characteristic
202	C₂²×C₁₉	#494	1	1	yes	characteristic
203	C₂²×C₁₉	#495	1	1	yes	characteristic
204	C₂²×C₁₉	#495	1	1	yes	characteristic
205	C₂²×C₁₉	#499	1	2	yes	—
206	C₂²×C₁₉	#500	1	2	yes	—
207	C₄×C₁₉	—	8	4	no	—
208	C₄×C₁₉	C₂×#95	1	1	yes	characteristic
209	C₄×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
210	C₄×C₁₉	#380	1	1	yes	characteristic
211	C₄×C₁₉	#382	1	1	yes	characteristic
212	C₄×C₁₉	#389	1	1	yes	characteristic
213	C₄×C₁₉	#389	1	1	yes	characteristic
214	C₄×C₁₉	#391	1	1	yes	characteristic
215	C₄×C₁₉	#391	1	1	yes	characteristic
216	Dic₁₉	—	2	8	no	—
217	Dic₁₉	—	8	4	no	—
218	C₂³×C₈	—	19	1	no	—
219	C₂³×C₈	C₂×D₁₉	1	1	yes	characteristic
220	C₂²×C₄⋊C₄	—	19	2	no	—
221	C₂²×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
222	C₂²×C₄²	—	19	1	no	—
223	C₂×#107	—	2	2	no	—
224	C₂×#107	—	2	2	no	—
225	C₂×#107	—	19	4	no	—
226	C₂×#107	—	38	2	no	—
227	C₂×#107	—	38	2	no	—
228	C₂×#107	Dic₁₉	1	4	yes	complemented
229	C₂×C₄×C₈	—	19	4	no	—
230	C₂×C₄×C₈	—	38	2	no	—
231	C₂×C₄×C₈	—	38	2	no	—
232	C₂×#95	—	38	4	no	—
233	#340	—	38	4	no	—
234	C₂×C₁₉	C₄⋊#95	1	1	yes	characteristic
235	C₂×C₁₉	C₄×#107	1	2	yes	—
236	C₂×C₁₉	#1808	1	2	yes	—
237	C₂×C₁₉	#1845	1	1	yes	characteristic
238	C₂×C₁₉	#1846	1	1	yes	characteristic
239	C₂×C₁₉	#1942	1	2	yes	—
240	C₂×C₁₉	#1942	1	2	yes	—
241	C₂×C₁₉	#1969	1	1	yes	characteristic
242	C₂×C₁₉	#1969	1	1	yes	characteristic
243	C₂×C₁₉	#1970	1	1	yes	characteristic
244	C₂×C₁₉	#1970	1	1	yes	characteristic
245	C₂³×C₄	—	2	2	no	—
246	C₂³×C₄	—	19	2	no	—
247	C₂³×C₄	—	38	2	no	—
248	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
249	C₂²×C₈	—	19	2	no	—
250	C₂²×C₈	—	19	2	no	—
251	C₂²×C₈	—	19	2	no	—
252	C₂²×C₈	—	38	1	no	—
253	C₂²×C₈	—	38	1	no	—
254	C₂²×C₈	—	38	1	no	—
255	C₂²×C₈	—	38	1	no	—
256	C₂²×C₈	Dic₃₈	1	2	yes	—
257	C₂²×C₈	C₄×D₁₉	1	2	yes	—
258	C₂²×C₈	C₄×D₁₉	1	2	yes	—
259	C₂²×C₈	D₇₆	1	2	yes	—
260	C₂²×C₈	C₂×Dic₁₉	1	2	yes	—
261	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
262	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
263	C₂×C₄⋊C₄	—	2	2	no	—
264	C₂×C₄⋊C₄	—	2	2	no	—
265	C₂×C₄⋊C₄	—	2	2	no	—
266	C₂×C₄⋊C₄	—	2	2	no	—
267	C₂×C₄⋊C₄	—	2	2	no	—
268	C₂×C₄⋊C₄	—	19	4	no	—
269	C₂×C₄⋊C₄	—	38	2	no	—
270	C₂×C₄⋊C₄	—	38	2	no	—
271	C₂×C₄⋊C₄	—	38	2	no	—
272	C₂×C₄⋊C₄	—	38	2	no	—
273	C₂×C₄⋊C₄	—	38	2	no	—
274	C₂×C₄⋊C₄	C₂×Dic₁₉	1	4	yes	—
275	C₂×C₄²	—	19	2	no	—
276	C₂×C₄²	—	19	2	no	—
277	C₂×C₄²	—	38	1	no	—
278	C₂×C₄²	—	38	1	no	—
279	C₂×C₄²	—	38	1	no	—
280	C₂×C₄²	—	38	1	no	—
281	#107	—	2	8	no	—
282	#107	—	38	8	no	—
283	C₄×C₈	—	38	8	no	—
284	#95	—	76	8	no	—
285	C₁₉	#10862	1	1	yes	characteristic, complemented, Sylow
286	C₂⁴	D₄×D₁₉	1	1	yes	characteristic
287	C₂²×C₄	—	2	4	no	—
288	C₂²×C₄	—	4	2	no	—
289	C₂²×C₄	—	4	2	no	—
290	C₂²×C₄	—	4	4	no	—
291	C₂²×C₄	—	4	4	no	—
292	C₂²×C₄	—	19	4	no	—
293	C₂²×C₄	—	19	4	no	—
294	C₂²×C₄	—	19	4	no	—
295	C₂²×C₄	—	38	2	no	—
296	C₂²×C₄	—	38	2	no	—
297	C₂²×C₄	—	38	2	no	—
298	C₂²×C₄	—	38	2	no	—
299	C₂²×C₄	—	38	4	no	—
300	C₂²×C₄	—	76	2	no	—
301	C₂²×C₄	—	76	2	no	—
302	C₂²×C₄	—	76	4	no	—
303	C₂²×C₄	—	76	4	no	—
304	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
305	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
306	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
307	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
308	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
309	C₂²×C₄	#64543	1	1	yes	characteristic
310	C₂²×C₄	#64543	1	1	yes	characteristic
311	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
312	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
313	C₂²×C₄	#64545	1	1	yes	characteristic
314	C₂²×C₄	#64545	1	1	yes	characteristic
315	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
316	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
317	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
318	C₂×C₈	—	19	4	no	—
319	C₂×C₈	—	38	2	no	—
320	C₂×C₈	—	38	2	no	—
321	C₂×C₈	—	38	2	no	—
322	C₂×C₈	—	38	2	no	—
323	C₂×C₈	—	38	2	no	—
324	C₂×C₈	—	38	2	no	—
325	C₂×C₈	C₄×Dic₁₉	1	4	yes	—
326	C₂×C₈	Dic₁₉⋊C₄	1	4	yes	—
327	C₂×C₈	Dic₁₉⋊C₄	1	4	yes	—
328	C₂×C₈	C₄⋊Dic₁₉	1	4	yes	—
329	C₂×C₈	(C₂×D₁₉)⋊C₄	1	4	yes	—
330	C₂×C₈	(C₂×D₁₉)⋊C₄	1	4	yes	—
331	C₂×C₈	C₂²⋊Dic₁₉	1	4	yes	—
332	C₄⋊C₄	—	2	4	no	—
333	C₄⋊C₄	—	2	4	no	—
334	C₄⋊C₄	—	4	2	no	—
335	C₄⋊C₄	—	4	2	no	—
336	C₄⋊C₄	—	38	4	no	—
337	C₄⋊C₄	—	38	4	no	—
338	C₄⋊C₄	—	76	2	no	—
339	C₄⋊C₄	—	76	2	no	—
340	C₄²	—	38	2	no	—
341	C₄²	—	38	2	no	—
342	C₄²	—	38	2	no	—
343	C₄²	—	38	2	no	—
344	C₂³	#10597334	1	1	yes	characteristic
345	C₂³	C₄⋊C₄×D₁₉	1	1	yes	characteristic
346	C₂³	#10597339	1	1	yes	characteristic
347	C₂³	#10597341	1	1	yes	characteristic
348	C₂³	D₈×D₁₉	1	2	yes	—
349	C₂³	#10597358	1	2	yes	—
350	C₂³	Q₁₆×D₁₉	1	2	yes	—
351	C₂³	#10597365	1	2	yes	—
352	C₂³	D₄×Dic₁₉	1	1	yes	characteristic
353	C₂³	#10597384	1	1	yes	characteristic
354	C₂³	#10597386	1	1	yes	characteristic
355	C₂×C₄	—	4	8	no	—
356	C₂×C₄	—	4	4	no	—
357	C₂×C₄	—	8	2	no	—
358	C₂×C₄	—	8	2	no	—
359	C₂×C₄	—	8	4	no	—
360	C₂×C₄	—	19	8	no	—
361	C₂×C₄	—	38	4	no	—
362	C₂×C₄	—	38	4	no	—
363	C₂×C₄	—	38	4	no	—
364	C₂×C₄	—	38	4	no	—
365	C₂×C₄	—	38	4	no	—
366	C₂×C₄	—	38	4	no	—
367	C₂×C₄	—	76	8	no	—
368	C₂×C₄	—	76	4	no	—
369	C₂×C₄	—	152	2	no	—
370	C₂×C₄	—	152	2	no	—
371	C₂×C₄	—	152	4	no	—
372	C₂×C₄	#10597333	1	1	yes	characteristic
373	C₂×C₄	#10597333	1	1	yes	characteristic
374	C₂×C₄	#10597334	1	1	yes	characteristic
375	C₂×C₄	#10597336	1	1	yes	characteristic
376	C₂×C₄	#10597336	1	1	yes	characteristic
377	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
378	C₂×C₄	#10597338	1	1	yes	characteristic
379	C₂×C₄	#10597338	1	1	yes	characteristic
380	C₂×C₄	#10597339	1	1	yes	characteristic
381	C₂×C₄	#10597341	1	1	yes	characteristic
382	C₂×C₄	#10597343	1	1	yes	characteristic
383	C₂×C₄	#10597343	1	1	yes	characteristic
384	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
385	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
386	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
387	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
388	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
389	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
390	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
391	C₂×C₄	#10597382	1	1	yes	characteristic
392	C₂×C₄	#10597384	1	1	yes	characteristic
393	C₂×C₄	#10597390	1	1	yes	characteristic
394	C₂×C₄	Q₈×Dic₁₉	1	1	yes	characteristic
395	C₂×C₄	Q₈×Dic₁₉	1	1	yes	characteristic
396	C₂×C₄	#10597392	1	1	yes	characteristic
397	C₂×C₄	#10597392	1	1	yes	characteristic
398	C₂×C₄	#10597393	1	1	yes	characteristic
399	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
400	C₈	—	38	4	no	—
401	C₈	C₁₉⋊#95	1	8	yes	complemented
402	C₂²	C₄⋊C₄×Dic₁₉	1	1	yes	characteristic
403	C₂²	#11926401	1	1	yes	characteristic
404	C₂²	#11926413	1	1	yes	characteristic
405	C₂²	#11926440	1	1	yes	characteristic
406	C₂²	#11926443	1	1	yes	characteristic
407	C₂²	#11926445	1	1	yes	characteristic
408	C₂²	#11926447	1	1	yes	characteristic
409	C₂²	#107×D₁₉	1	2	yes	—
410	C₂²	#11926581	1	2	yes	—
411	C₂²	#11926626	1	2	yes	—
412	C₂²	D₈×Dic₁₉	1	2	yes	—
413	C₂²	#11926638	1	2	yes	—
414	C₂²	Q₁₆×Dic₁₉	1	2	yes	—
415	C₂²	#11926777	1	2	yes	—
416	C₂²	#11926781	1	2	yes	—
417	C₂²	#11926782	1	2	yes	—
418	C₂²	#11926786	1	2	yes	—
419	C₂²	#11926919	1	1	yes	characteristic
420	C₂²	#11926922	1	1	yes	characteristic
421	C₂²	#11926927	1	1	yes	characteristic
422	C₂²	#11926929	1	1	yes	characteristic
423	C₂²	#11926945	1	2	yes	—
424	C₂²	#11926948	1	2	yes	—
425	C₄	—	8	4	no	—
426	C₄	—	38	8	no	—
427	C₄	—	152	4	no	—
428	C₄	C₂×C₁₉⋊#95	1	1	yes	characteristic
429	C₄	C₄⋊C₄×Dic₁₉	1	1	yes	characteristic
430	C₄	#11926401	1	1	yes	characteristic
431	C₄	#11926409	1	1	yes	characteristic
432	C₄	#11926440	1	1	yes	characteristic
433	C₄	#11926443	1	1	yes	characteristic
434	C₄	#11926449	1	1	yes	characteristic
435	C₄	#11926451	1	1	yes	characteristic
436	C₂	#14561864	1	1	yes	characteristic
437	C₂	#107×Dic₁₉	1	2	yes	—
438	C₂	#14563661	1	2	yes	—
439	C₂	#14563793	1	1	yes	characteristic
440	C₂	#14563798	1	1	yes	characteristic
441	C₂	#14564366	1	2	yes	—
442	C₂	#14564369	1	2	yes	—
443	C₂	#14564494	1	1	yes	characteristic
444	C₂	#14564497	1	1	yes	characteristic
445	C₂	#14564499	1	1	yes	characteristic
446	C₂	#14564502	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	D₄×D₁₉
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂²×C₁₉×#107	C₂
socle, prime radical	C₂⁴×C₁₉	C₂×D₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂²×#107	D₁₉
hypocenter	C₁₉	#10862
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄ ◁ C₂²×#107

Complements

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

N	H ≅ G/N	type
11. C₂×#10597275	C₄	semidirect
14. C₂×C₈×Dic₁₉	C₄	semidirect
21. C₂×C₁₉×#107	C₄	semidirect
176. C₂×Dic₁₉	#107	semidirect
177. C₈×C₁₉	#95	semidirect
228. C₂×#107	Dic₁₉	semidirect
285. C₁₉	#10862	semidirect
401. C₈	C₁₉⋊#95	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#10597275	2
C₂²×C₈×Dic₁₉	2
C₂×#11926306	2
#14561864	2
C₂²×C₁₉×#107	2
#10862	19