Subgroups — #18088442

Order 4864.

942 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#10597264	C₂	1	1	yes	maximal, characteristic
2	C₂²×#10597265	C₂	1	1	yes	maximal, characteristic
3	C₂²×#10597260	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926306	C₂	1	1	yes	maximal, characteristic
5	C₂×#11926306	C₂	1	1	yes	maximal, characteristic
6	#14561865	C₂	1	1	yes	maximal, characteristic
7	C₁₉×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
8	C₂³×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
9	C₂³×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
10	C₂²×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
11	C₂²×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
12	C₂×#10597264	—	2	2	no	—
13	C₂×#10597264	—	2	2	no	—
14	C₂×#10597264	C₄	1	4	yes	complemented
15	C₂×#10597265	—	2	2	no	—
16	C₂×#10597265	—	2	2	no	—
17	C₂×#10597265	C₄	1	4	yes	complemented
18	C₂×#10597260	—	2	2	no	—
19	C₂×#10597260	—	2	2	no	—
20	C₂×#10597260	C₄	1	4	yes	complemented
21	C₂×C₁₉⋊#95	—	2	2	no	—
22	#11926306	—	2	2	no	—
23	#11926306	—	2	2	no	—
24	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
25	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
26	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#95	—	2	2	no	—
28	C₂³×C₄×C₁₉	—	2	1	no	—
29	C₂³×C₄×C₁₉	—	2	1	no	—
30	C₂³×C₄×C₁₉	D₄	1	2	yes	—
31	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
32	C₂³×Dic₁₉	—	2	1	no	—
33	C₂³×Dic₁₉	—	2	1	no	—
34	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
35	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
36	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
37	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
38	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
39	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
40	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
41	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
42	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
43	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
44	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
45	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
46	C₂×C₄²×C₁₉	—	2	1	no	—
47	C₂×C₄²×C₁₉	—	2	1	no	—
48	C₂×C₄²×C₁₉	—	2	1	no	—
49	C₂×C₄²×C₁₉	—	2	1	no	—
50	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
51	C₂×C₄²×C₁₉	Q₈	1	2	yes	—
52	C₂×C₄⋊Dic₁₉	—	2	1	no	—
53	C₂×C₄⋊Dic₁₉	—	2	1	no	—
54	C₂×C₄⋊Dic₁₉	—	2	1	no	—
55	C₂×C₄⋊Dic₁₉	—	2	1	no	—
56	C₂×C₄⋊Dic₁₉	—	2	1	no	—
57	C₂×C₄⋊Dic₁₉	—	2	1	no	—
58	C₂×C₄⋊Dic₁₉	—	2	1	no	—
59	C₂×C₄⋊Dic₁₉	—	2	1	no	—
60	C₂×C₄⋊Dic₁₉	—	2	1	no	—
61	C₂×C₄⋊Dic₁₉	—	2	1	no	—
62	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
63	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
64	C₂²×C₁₉⋊C₈	—	2	1	no	—
65	C₂²×C₁₉⋊C₈	—	2	1	no	—
66	C₂²×C₁₉⋊C₈	—	2	1	no	—
67	C₂²×C₁₉⋊C₈	—	2	1	no	—
68	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
69	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
70	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
71	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
72	C₂²×C₁₉⋊C₈	D₄	1	2	yes	—
73	C₂²×C₁₉⋊C₈	D₄	1	2	yes	—
74	C₂²×C₁₉⋊C₈	D₄	1	2	yes	—
75	C₂²×C₁₉⋊C₈	D₄	1	2	yes	—
76	C₂²×C₁₉⋊C₈	Q₈	1	2	yes	—
77	C₂²×C₁₉⋊C₈	Q₈	1	2	yes	—
78	C₁₉×#95	—	4	4	no	—
79	C₁₉⋊#95	—	4	4	no	—
80	#10597265	—	2	8	no	—
81	#10597264	—	2	8	no	—
82	#10597260	—	2	8	no	—
83	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₉	—	2	2	no	—
85	C₂²×C₄×C₁₉	—	2	2	no	—
86	C₂²×C₄×C₁₉	—	2	2	no	—
87	C₂²×C₄×C₁₉	—	2	2	no	—
88	C₂²×C₄×C₁₉	—	2	2	no	—
89	C₂²×C₄×C₁₉	—	2	2	no	—
90	C₂²×C₄×C₁₉	—	2	2	no	—
91	C₂²×C₄×C₁₉	—	2	2	no	—
92	C₂²×C₄×C₁₉	—	4	1	no	—
93	C₂²×C₄×C₁₉	—	4	1	no	—
94	C₂²×C₄×C₁₉	—	4	1	no	—
95	C₂²×C₄×C₁₉	—	4	1	no	—
96	C₂²×C₄×C₁₉	—	4	2	no	—
97	C₂²×C₄×C₁₉	—	4	2	no	—
98	C₂²×C₄×C₁₉	—	4	2	no	—
99	C₂²×C₄×C₁₉	—	4	2	no	—
100	C₂²×C₄×C₁₉	C₄⋊C₄	1	4	yes	—
101	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
109	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
110	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
111	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
112	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
113	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
114	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
115	C₂²×Dic₁₉	—	2	2	no	—
116	C₂²×Dic₁₉	—	2	2	no	—
117	C₂²×Dic₁₉	—	4	1	no	—
118	C₂²×Dic₁₉	—	4	1	no	—
119	C₂²×Dic₁₉	—	4	1	no	—
120	C₂²×Dic₁₉	—	4	1	no	—
121	C₂²×Dic₁₉	—	4	2	no	—
122	C₂²×Dic₁₉	—	4	2	no	—
123	C₂²×Dic₁₉	—	4	2	no	—
124	C₂²×Dic₁₉	—	4	2	no	—
125	C₄⋊C₄×C₁₉	—	2	2	no	—
126	C₄⋊C₄×C₁₉	—	2	2	no	—
127	C₄⋊C₄×C₁₉	—	2	2	no	—
128	C₄⋊C₄×C₁₉	—	2	2	no	—
129	C₄⋊C₄×C₁₉	—	4	1	no	—
130	C₄⋊C₄×C₁₉	—	4	1	no	—
131	C₄⋊C₄×C₁₉	—	4	1	no	—
132	C₄⋊C₄×C₁₉	—	4	1	no	—
133	C₄²×C₁₉	—	2	2	no	—
134	C₄²×C₁₉	—	2	2	no	—
135	C₄²×C₁₉	—	2	2	no	—
136	C₄²×C₁₉	—	2	2	no	—
137	C₄⋊Dic₁₉	—	2	2	no	—
138	C₄⋊Dic₁₉	—	2	2	no	—
139	C₄⋊Dic₁₉	—	2	2	no	—
140	C₄⋊Dic₁₉	—	2	2	no	—
141	C₄⋊Dic₁₉	—	4	1	no	—
142	C₄⋊Dic₁₉	—	4	1	no	—
143	C₄⋊Dic₁₉	—	4	1	no	—
144	C₄⋊Dic₁₉	—	4	1	no	—
145	C₂×C₁₉⋊C₈	—	2	2	no	—
146	C₂×C₁₉⋊C₈	—	2	2	no	—
147	C₂×C₁₉⋊C₈	—	2	2	no	—
148	C₂×C₁₉⋊C₈	—	2	2	no	—
149	C₂×C₁₉⋊C₈	—	2	2	no	—
150	C₂×C₁₉⋊C₈	—	2	2	no	—
151	C₂×C₁₉⋊C₈	C₄²	1	4	yes	—
152	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	4	yes	—
153	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	4	yes	—
154	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	4	yes	—
155	C₂×C₁₉⋊C₈	C₄⋊C₄	1	4	yes	—
156	C₂×C₁₉⋊C₈	C₄⋊C₄	1	4	yes	—
157	C₂×C₁₉⋊C₈	C₄⋊C₄	1	4	yes	—
158	C₂×C₁₉⋊C₈	C₄⋊C₄	1	4	yes	—
159	#10863	—	19	1	no	maximal, Sylow
160	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
161	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
162	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
163	C₂³×C₁₉	#121	1	1	yes	characteristic
164	C₂³×C₁₉	#121	1	1	yes	characteristic
165	C₂³×C₁₉	#127	1	1	yes	characteristic
166	C₂³×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
167	C₂³×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
168	C₂³×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
169	C₂³×C₁₉	#137	1	2	yes	—
170	C₂³×C₁₉	#137	1	2	yes	—
171	C₂×C₄×C₁₉	—	2	4	no	—
172	C₂×C₄×C₁₉	—	2	4	no	—
173	C₂×C₄×C₁₉	—	2	4	no	—
174	C₂×C₄×C₁₉	—	4	2	no	—
175	C₂×C₄×C₁₉	—	4	2	no	—
176	C₂×C₄×C₁₉	—	4	2	no	—
177	C₂×C₄×C₁₉	—	4	2	no	—
178	C₂×C₄×C₁₉	—	4	2	no	—
179	C₂×C₄×C₁₉	—	4	2	no	—
180	C₂×C₄×C₁₉	—	4	4	no	—
181	C₂×C₄×C₁₉	—	4	4	no	—
182	C₂×C₄×C₁₉	—	8	2	no	—
183	C₂×C₄×C₁₉	—	8	2	no	—
184	C₂×C₄×C₁₉	—	8	1	no	—
185	C₂×C₄×C₁₉	—	8	1	no	—
186	C₂×C₄×C₁₉	—	8	1	no	—
187	C₂×C₄×C₁₉	—	8	1	no	—
188	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
189	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
190	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
191	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
192	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
193	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
194	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
195	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
196	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
197	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
198	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
199	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
200	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
201	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
202	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
203	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
204	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
205	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
206	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
207	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
208	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
209	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
210	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
211	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
212	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
213	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
214	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
215	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
216	C₂×Dic₁₉	—	4	2	no	—
217	C₂×Dic₁₉	—	4	2	no	—
218	C₂×Dic₁₉	—	4	4	no	—
219	C₂×Dic₁₉	—	4	4	no	—
220	C₂×Dic₁₉	—	8	2	no	—
221	C₂×Dic₁₉	—	8	2	no	—
222	C₂×Dic₁₉	—	8	1	no	—
223	C₂×Dic₁₉	—	8	1	no	—
224	C₂×Dic₁₉	—	8	1	no	—
225	C₂×Dic₁₉	—	8	1	no	—
226	C₁₉⋊C₈	—	2	4	no	—
227	C₁₉⋊C₈	#95	1	8	yes	complemented
228	C₂²×#107	—	19	1	no	—
229	C₂²×#106	—	19	1	no	—
230	C₂²×#97	—	19	1	no	—
231	C₂×#340	—	19	1	no	—
232	C₂×#340	—	19	1	no	—
233	C₄⋊#95	—	19	1	no	—
234	C₄⋊#95	D₁₉	1	1	yes	characteristic
235	C₂²×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
236	C₂²×C₁₉	#380	1	1	yes	characteristic
237	C₂²×C₁₉	#384	1	1	yes	characteristic
238	C₂²×C₁₉	#389	1	1	yes	characteristic
239	C₂²×C₁₉	#389	1	1	yes	characteristic
240	C₂²×C₁₉	#390	1	1	yes	characteristic
241	C₂²×C₁₉	#390	1	1	yes	characteristic
242	C₂²×C₁₉	#428	1	2	yes	—
243	C₂²×C₁₉	#428	1	2	yes	—
244	C₂²×C₁₉	#440	1	2	yes	—
245	C₂²×C₁₉	#440	1	2	yes	—
246	C₂²×C₁₉	#441	1	2	yes	—
247	C₂²×C₁₉	#442	1	2	yes	—
248	C₂²×C₁₉	#468	1	2	yes	—
249	C₂²×C₁₉	#468	1	2	yes	—
250	C₂²×C₁₉	#469	1	2	yes	—
251	C₂²×C₁₉	#470	1	2	yes	—
252	C₂²×C₁₉	#496	1	1	yes	characteristic
253	C₂²×C₁₉	#496	1	1	yes	characteristic
254	C₂²×C₁₉	#497	1	1	yes	characteristic
255	C₂²×C₁₉	#497	1	1	yes	characteristic
256	C₂²×C₁₉	#501	1	2	yes	—
257	C₂²×C₁₉	#501	1	2	yes	—
258	C₄×C₁₉	—	4	4	no	—
259	C₄×C₁₉	—	8	2	no	—
260	C₄×C₁₉	—	8	2	no	—
261	C₄×C₁₉	C₂×#95	1	1	yes	characteristic
262	C₄×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
263	C₄×C₁₉	#380	1	1	yes	characteristic
264	C₄×C₁₉	#382	1	1	yes	characteristic
265	C₄×C₁₉	#389	1	1	yes	characteristic
266	C₄×C₁₉	#389	1	1	yes	characteristic
267	C₄×C₁₉	#391	1	1	yes	characteristic
268	C₄×C₁₉	#391	1	1	yes	characteristic
269	Dic₁₉	—	8	2	no	—
270	Dic₁₉	—	8	2	no	—
271	C₂³×C₈	—	19	1	no	—
272	C₂³×C₈	—	19	1	no	—
273	C₂²×C₄⋊C₄	—	19	1	no	—
274	C₂²×C₄⋊C₄	—	19	1	no	—
275	C₂²×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
276	C₂²×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
277	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
278	C₂×#107	—	19	4	no	—
279	C₂×#107	—	38	2	no	—
280	C₂×#107	—	38	2	no	—
281	C₂×#106	—	19	4	no	—
282	C₂×#106	—	38	2	no	—
283	C₂×#106	—	38	2	no	—
284	C₂×#97	—	19	4	no	—
285	C₂×#97	—	38	2	no	—
286	C₂×#97	—	38	2	no	—
287	C₂×#95	—	2	2	no	—
288	C₂×#95	—	38	2	no	—
289	#340	—	38	2	no	—
290	#340	—	38	2	no	—
291	C₂×C₁₉	C₄⋊#95	1	1	yes	characteristic
292	C₂×C₁₉	#1776	1	2	yes	—
293	C₂×C₁₉	#1809	1	2	yes	—
294	C₂×C₁₉	#1847	1	1	yes	characteristic
295	C₂×C₁₉	#1847	1	1	yes	characteristic
296	C₂×C₁₉	#1943	1	2	yes	—
297	C₂×C₁₉	#1944	1	2	yes	—
298	C₂×C₁₉	#1971	1	1	yes	characteristic
299	C₂×C₁₉	#1972	1	1	yes	characteristic
300	C₂×C₁₉	#1973	1	1	yes	characteristic
301	C₂×C₁₉	#1973	1	1	yes	characteristic
302	C₂³×C₄	—	2	1	no	—
303	C₂³×C₄	—	2	1	no	—
304	C₂³×C₄	—	38	1	no	—
305	C₂³×C₄	—	38	1	no	—
306	C₂³×C₄	C₂²⋊D₁₉	1	2	yes	—
307	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
308	C₂²×C₈	—	19	2	no	—
309	C₂²×C₈	—	19	2	no	—
310	C₂²×C₈	—	19	2	no	—
311	C₂²×C₈	—	19	2	no	—
312	C₂²×C₈	—	19	2	no	—
313	C₂²×C₈	—	19	2	no	—
314	C₂²×C₈	—	19	2	no	—
315	C₂²×C₈	—	19	2	no	—
316	C₂²×C₈	—	19	2	no	—
317	C₂²×C₈	—	19	2	no	—
318	C₂²×C₈	—	38	1	no	—
319	C₂²×C₈	—	38	1	no	—
320	C₂²×C₈	—	38	1	no	—
321	C₂²×C₈	—	38	1	no	—
322	C₂×C₄⋊C₄	—	2	1	no	—
323	C₂×C₄⋊C₄	—	2	1	no	—
324	C₂×C₄⋊C₄	—	2	1	no	—
325	C₂×C₄⋊C₄	—	2	1	no	—
326	C₂×C₄⋊C₄	—	2	1	no	—
327	C₂×C₄⋊C₄	—	2	1	no	—
328	C₂×C₄⋊C₄	—	2	1	no	—
329	C₂×C₄⋊C₄	—	2	1	no	—
330	C₂×C₄⋊C₄	—	2	1	no	—
331	C₂×C₄⋊C₄	—	2	1	no	—
332	C₂×C₄⋊C₄	—	19	2	no	—
333	C₂×C₄⋊C₄	—	19	2	no	—
334	C₂×C₄⋊C₄	—	38	1	no	—
335	C₂×C₄⋊C₄	—	38	1	no	—
336	C₂×C₄⋊C₄	—	38	1	no	—
337	C₂×C₄⋊C₄	—	38	1	no	—
338	C₂×C₄⋊C₄	—	38	1	no	—
339	C₂×C₄⋊C₄	—	38	1	no	—
340	C₂×C₄⋊C₄	—	38	1	no	—
341	C₂×C₄⋊C₄	—	38	1	no	—
342	C₂×C₄⋊C₄	—	38	1	no	—
343	C₂×C₄⋊C₄	—	38	1	no	—
344	C₂×C₄⋊C₄	C₄×D₁₉	1	2	yes	—
345	C₂×C₄⋊C₄	C₄×D₁₉	1	2	yes	—
346	C₂×C₄²	—	2	1	no	—
347	C₂×C₄²	—	2	1	no	—
348	C₂×C₄²	—	2	1	no	—
349	C₂×C₄²	—	2	1	no	—
350	C₂×C₄²	Dic₃₈	1	2	yes	—
351	C₂×C₄²	C₄×D₁₉	1	2	yes	—
352	#107	—	38	8	no	—
353	#106	—	38	8	no	—
354	#97	—	38	8	no	—
355	#95	—	4	4	no	—
356	#95	—	76	4	no	—
357	C₁₉	#10863	1	1	yes	characteristic, complemented, Sylow
358	C₂⁴	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	4	2	no	—
368	C₂²×C₄	—	4	2	no	—
369	C₂²×C₄	—	4	1	no	—
370	C₂²×C₄	—	4	1	no	—
371	C₂²×C₄	—	4	1	no	—
372	C₂²×C₄	—	4	1	no	—
373	C₂²×C₄	—	4	2	no	—
374	C₂²×C₄	—	4	2	no	—
375	C₂²×C₄	—	38	2	no	—
376	C₂²×C₄	—	38	2	no	—
377	C₂²×C₄	—	76	2	no	—
378	C₂²×C₄	—	76	1	no	—
379	C₂²×C₄	—	76	1	no	—
380	C₂²×C₄	—	76	1	no	—
381	C₂²×C₄	—	76	1	no	—
382	C₂²×C₄	—	76	2	no	—
383	C₂²×C₄	—	76	2	no	—
384	C₂²×C₄	—	76	2	no	—
385	C₂²×C₄	Dic₁₉⋊C₄	1	4	yes	—
386	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
387	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
388	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
389	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
390	C₂²×C₄	#64541	1	1	yes	characteristic
391	C₂²×C₄	#64541	1	1	yes	characteristic
392	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
393	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
394	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
395	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
396	C₂²×C₄	#64543	1	1	yes	characteristic
397	C₂²×C₄	#64543	1	1	yes	characteristic
398	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
399	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
400	C₂×C₈	—	19	4	no	—
401	C₂×C₈	—	19	4	no	—
402	C₂×C₈	—	19	4	no	—
403	C₂×C₈	—	19	4	no	—
404	C₂×C₈	—	19	4	no	—
405	C₂×C₈	—	19	4	no	—
406	C₂×C₈	—	19	4	no	—
407	C₂×C₈	—	19	4	no	—
408	C₂×C₈	—	38	2	no	—
409	C₂×C₈	—	38	2	no	—
410	C₂×C₈	—	38	2	no	—
411	C₂×C₈	—	38	2	no	—
412	C₂×C₈	—	38	2	no	—
413	C₂×C₈	—	38	2	no	—
414	C₄⋊C₄	—	2	2	no	—
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	—	2	2	no	—
417	C₄⋊C₄	—	2	2	no	—
418	C₄⋊C₄	—	4	1	no	—
419	C₄⋊C₄	—	4	1	no	—
420	C₄⋊C₄	—	4	1	no	—
421	C₄⋊C₄	—	4	1	no	—
422	C₄⋊C₄	—	38	2	no	—
423	C₄⋊C₄	—	38	2	no	—
424	C₄⋊C₄	—	38	2	no	—
425	C₄⋊C₄	—	38	2	no	—
426	C₄⋊C₄	—	76	1	no	—
427	C₄⋊C₄	—	76	1	no	—
428	C₄⋊C₄	—	76	1	no	—
429	C₄⋊C₄	—	76	1	no	—
430	C₄²	—	2	2	no	—
431	C₄²	—	2	2	no	—
432	C₄²	—	2	2	no	—
433	C₄²	—	2	2	no	—
434	C₂³	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
435	C₂³	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
436	C₂³	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
437	C₂³	#10597378	1	2	yes	—
438	C₂³	#10597385	1	1	yes	characteristic
439	C₂³	#10597385	1	1	yes	characteristic
440	C₂³	#10597386	1	1	yes	characteristic
441	C₂³	#10597388	1	2	yes	—
442	C₂³	#10597390	1	1	yes	characteristic
443	C₂³	#10597395	1	2	yes	—
444	C₂³	#10597397	1	2	yes	—
445	C₂×C₄	—	2	4	no	—
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	4	4	no	—
453	C₂×C₄	—	4	4	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	8	2	no	—
457	C₂×C₄	—	8	2	no	—
458	C₂×C₄	—	8	1	no	—
459	C₂×C₄	—	8	1	no	—
460	C₂×C₄	—	8	1	no	—
461	C₂×C₄	—	8	1	no	—
462	C₂×C₄	—	76	4	no	—
463	C₂×C₄	—	76	4	no	—
464	C₂×C₄	—	76	2	no	—
465	C₂×C₄	—	76	2	no	—
466	C₂×C₄	—	152	2	no	—
467	C₂×C₄	—	152	2	no	—
468	C₂×C₄	—	152	1	no	—
469	C₂×C₄	—	152	1	no	—
470	C₂×C₄	—	152	1	no	—
471	C₂×C₄	—	152	1	no	—
472	C₂×C₄	C₄×Dic₃₈	1	1	yes	characteristic
473	C₂×C₄	C₄×Dic₃₈	1	1	yes	characteristic
474	C₂×C₄	C₄²×D₁₉	1	1	yes	characteristic
475	C₂×C₄	#10597318	1	1	yes	characteristic
476	C₂×C₄	#10597323	1	1	yes	characteristic
477	C₂×C₄	#10597324	1	1	yes	characteristic
478	C₂×C₄	#10597324	1	1	yes	characteristic
479	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
480	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
481	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
482	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
483	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
484	C₂×C₄	#10597330	1	1	yes	characteristic
485	C₂×C₄	#10597330	1	1	yes	characteristic
486	C₂×C₄	#10597331	1	1	yes	characteristic
487	C₂×C₄	#10597331	1	1	yes	characteristic
488	C₂×C₄	#10597333	1	1	yes	characteristic
489	C₂×C₄	#10597333	1	1	yes	characteristic
490	C₂×C₄	#10597334	1	1	yes	characteristic
491	C₂×C₄	#10597334	1	1	yes	characteristic
492	C₂×C₄	#10597335	1	1	yes	characteristic
493	C₂×C₄	#10597335	1	1	yes	characteristic
494	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
495	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
496	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
497	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
498	C₂×C₄	#10597342	1	1	yes	characteristic
499	C₂×C₄	#10597342	1	1	yes	characteristic
500	C₈	—	19	8	no	—
501	C₈	—	38	4	no	—
502	C₂²	C₄×Dic₁₉⋊C₄	1	1	yes	characteristic
503	C₂²	#11926402	1	1	yes	characteristic
504	C₂²	#11926413	1	1	yes	characteristic
505	C₂²	#11926439	1	1	yes	characteristic
506	C₂²	#11926439	1	1	yes	characteristic
507	C₂²	#11926444	1	1	yes	characteristic
508	C₂²	#11926444	1	1	yes	characteristic
509	C₂²	#11926584	1	2	yes	—
510	C₂²	#11926587	1	2	yes	—
511	C₂²	#11926642	1	2	yes	—
512	C₂²	#11926644	1	2	yes	—
513	C₂²	#11926649	1	2	yes	—
514	C₂²	#11926654	1	2	yes	—
515	C₂²	#11926788	1	2	yes	—
516	C₂²	#11926792	1	2	yes	—
517	C₂²	#11926795	1	2	yes	—
518	C₂²	#11926800	1	2	yes	—
519	C₂²	#11926931	1	1	yes	characteristic
520	C₂²	#11926934	1	1	yes	characteristic
521	C₂²	#11926936	1	1	yes	characteristic
522	C₂²	#11926939	1	1	yes	characteristic
523	C₂²	#11926950	1	2	yes	—
524	C₂²	#11926954	1	2	yes	—
525	C₄	—	4	4	no	—
526	C₄	—	8	2	no	—
527	C₄	—	8	2	no	—
528	C₄	—	152	2	no	—
529	C₄	—	152	2	no	—
530	C₄	#95×D₁₉	1	1	yes	characteristic
531	C₄	#11926395	1	1	yes	characteristic
532	C₄	#11926403	1	1	yes	characteristic
533	C₄	#11926408	1	1	yes	characteristic
534	C₄	#11926441	1	1	yes	characteristic
535	C₄	#11926441	1	1	yes	characteristic
536	C₄	#11926448	1	1	yes	characteristic
537	C₄	#11926448	1	1	yes	characteristic
538	C₂	Dic₁₉⋊#95	1	1	yes	characteristic
539	C₂	#14563533	1	2	yes	—
540	C₂	#14563666	1	2	yes	—
541	C₂	#14563801	1	1	yes	characteristic
542	C₂	#14563804	1	1	yes	characteristic
543	C₂	#14564370	1	2	yes	—
544	C₂	#14564375	1	2	yes	—
545	C₂	#14564505	1	1	yes	characteristic
546	C₂	#14564510	1	1	yes	characteristic
547	C₂	#14564515	1	1	yes	characteristic
548	C₂	#14564519	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂×C₂²⋊D₁₉
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₁₉×C₄⋊#95	C₂
socle, prime radical	C₂⁴×C₁₉	C₂×D₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₄⋊#95	D₁₉
hypocenter	C₁₉	#10863
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄² ◁ C₄⋊#95

Complements

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

N	H ≅ G/N	type
14. C₂×#10597264	C₄	semidirect
17. C₂×#10597265	C₄	semidirect
20. C₂×#10597260	C₄	semidirect
227. C₁₉⋊C₈	#95	semidirect
357. C₁₉	#10863	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#10597264	2
C₂²×#10597265	2
C₂²×#10597260	2
C₂×#11926306	2
#14561865	2
C₁₉×C₄⋊#95	2
#10863	19