Subgroups — #18088362

Order 4864.

998 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#10597272	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926413	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926409	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926307	C₂	1	1	yes	maximal, characteristic
5	C₂×#11926306	C₂	1	1	yes	maximal, characteristic
6	C₂×#11926306	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₉×#340	C₂	1	1	yes	maximal, characteristic
8	C₂³×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
9	C₂²×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
10	C₂²×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
11	C₂²×Dic₁₉⋊C₄	—	2	2	no	—
12	C₂²×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
13	C₂×#10597272	—	2	2	no	—
14	C₂×#10597272	—	2	2	no	—
15	C₂×#10597272	C₄	1	4	yes	complemented
16	#11926413	—	2	2	no	—
17	#11926413	C₄	1	4	yes	complemented
18	#11926409	—	2	2	no	—
19	#11926409	C₄	1	4	yes	complemented
20	C₂×C₁₉⋊#95	—	2	2	no	—
21	#11926307	—	2	2	no	—
22	#11926306	—	2	2	no	—
23	#11926306	—	2	2	no	—
24	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
25	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
26	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
27	C₁₉×#340	—	2	2	no	—
28	C₂³×C₄×C₁₉	—	2	1	no	—
29	C₂³×C₄×C₁₉	—	2	1	no	—
30	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
31	C₂³×Dic₁₉	—	2	1	no	—
32	C₂³×Dic₁₉	—	2	1	no	—
33	C₂³×Dic₁₉	D₄	1	2	yes	—
34	C₂²×C₈×C₁₉	—	2	1	no	—
35	C₂²×C₈×C₁₉	—	2	1	no	—
36	C₂²×C₈×C₁₉	—	2	1	no	—
37	C₂²×C₈×C₁₉	—	2	1	no	—
38	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
39	C₂²×C₈×C₁₉	D₄	1	2	yes	—
40	C₂²×C₈×C₁₉	Q₈	1	2	yes	—
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	—	2	1	no	—
45	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
46	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
47	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
48	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
49	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
50	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
51	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
52	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
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	—	2	1	no	—
63	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
64	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
65	C₂×Dic₁₉⋊C₄	—	2	8	no	—
66	C₂×Dic₁₉⋊C₄	—	4	4	no	—
67	C₂×Dic₁₉⋊C₄	—	4	4	no	—
68	C₂×C₄×Dic₁₉	C₂×C₄	1	2	yes	—
69	C₂×C₄×Dic₁₉	C₂×C₄	1	2	yes	—
70	C₂×C₄×Dic₁₉	C₂×C₄	1	2	yes	—
71	C₂×C₄×Dic₁₉	D₄	1	2	yes	—
72	C₂×C₄×Dic₁₉	D₄	1	2	yes	—
73	C₂×C₄×Dic₁₉	Q₈	1	2	yes	—
74	C₂²×C₁₉⋊C₈	—	2	1	no	—
75	C₂²×C₁₉⋊C₈	—	2	1	no	—
76	C₂²×C₁₉⋊C₈	—	2	1	no	—
77	C₂²×C₁₉⋊C₈	—	2	1	no	—
78	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
79	C₂²×C₁₉⋊C₈	D₄	1	2	yes	—
80	C₂²×C₁₉⋊C₈	Q₈	1	2	yes	—
81	C₁₉⋊#95	—	2	8	no	—
82	#10597272	—	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	—	4	1	no	—
87	C₂²×C₄×C₁₉	—	4	1	no	—
88	C₂²×C₄×C₁₉	—	4	1	no	—
89	C₂²×C₄×C₁₉	—	4	1	no	—
90	C₂²×C₄×C₁₉	—	4	2	no	—
91	C₂²×C₄×C₁₉	—	4	2	no	—
92	C₂²×C₄×C₁₉	—	4	2	no	—
93	C₂²×C₄×C₁₉	—	4	2	no	—
94	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
102	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
103	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
104	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
105	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
106	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
107	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
108	C₂²×Dic₁₉	—	2	2	no	—
109	C₂²×Dic₁₉	—	2	2	no	—
110	C₂²×Dic₁₉	—	2	2	no	—
111	C₂²×Dic₁₉	—	2	2	no	—
112	C₂²×Dic₁₉	—	2	2	no	—
113	C₂²×Dic₁₉	—	2	2	no	—
114	C₂²×Dic₁₉	—	4	1	no	—
115	C₂²×Dic₁₉	—	4	1	no	—
116	C₂²×Dic₁₉	—	4	1	no	—
117	C₂²×Dic₁₉	—	4	1	no	—
118	C₂²×Dic₁₉	—	4	2	no	—
119	C₂²×Dic₁₉	—	4	2	no	—
120	C₂²×Dic₁₉	—	4	2	no	—
121	C₂²×Dic₁₉	—	4	2	no	—
122	C₂²×Dic₁₉	C₂²⋊C₄	1	4	yes	—
123	C₂²×Dic₁₉	C₂²⋊C₄	1	4	yes	—
124	C₂²×Dic₁₉	C₄⋊C₄	1	4	yes	—
125	C₂×C₈×C₁₉	—	2	2	no	—
126	C₂×C₈×C₁₉	—	2	2	no	—
127	C₂×C₈×C₁₉	—	2	2	no	—
128	C₂×C₈×C₁₉	—	2	2	no	—
129	C₂×C₈×C₁₉	—	2	2	no	—
130	C₂×C₈×C₁₉	—	2	2	no	—
131	C₂×C₈×C₁₉	C₄⋊C₄	1	4	yes	complemented
132	C₄⋊C₄×C₁₉	—	2	2	no	—
133	C₄⋊C₄×C₁₉	—	2	2	no	—
134	C₄⋊C₄×C₁₉	—	2	2	no	—
135	C₄⋊C₄×C₁₉	—	2	2	no	—
136	C₄⋊C₄×C₁₉	—	4	1	no	—
137	C₄⋊C₄×C₁₉	—	4	1	no	—
138	C₄⋊C₄×C₁₉	—	4	1	no	—
139	C₄⋊C₄×C₁₉	—	4	1	no	—
140	C₄⋊Dic₁₉	—	2	2	no	—
141	C₄⋊Dic₁₉	—	2	2	no	—
142	C₄⋊Dic₁₉	—	2	2	no	—
143	C₄⋊Dic₁₉	—	2	2	no	—
144	C₄⋊Dic₁₉	—	4	1	no	—
145	C₄⋊Dic₁₉	—	4	1	no	—
146	C₄⋊Dic₁₉	—	4	1	no	—
147	C₄⋊Dic₁₉	—	4	1	no	—
148	Dic₁₉⋊C₄	—	4	16	no	—
149	C₄×Dic₁₉	C₄²	1	4	yes	—
150	C₄×Dic₁₉	C₂²⋊C₄	1	4	yes	—
151	C₄×Dic₁₉	C₄⋊C₄	1	4	yes	—
152	C₄×Dic₁₉	C₄⋊C₄	1	4	yes	—
153	C₂×C₁₉⋊C₈	—	2	2	no	—
154	C₂×C₁₉⋊C₈	—	2	2	no	—
155	C₂×C₁₉⋊C₈	—	2	2	no	—
156	C₂×C₁₉⋊C₈	—	2	2	no	—
157	C₂×C₁₉⋊C₈	—	2	2	no	—
158	C₂×C₁₉⋊C₈	—	2	2	no	—
159	C₂×C₁₉⋊C₈	C₄⋊C₄	1	4	yes	complemented
160	#10843	—	19	1	no	maximal, Sylow
161	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
162	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
163	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₂³×C₁₉	#124	1	1	yes	characteristic
165	C₂³×C₁₉	#124	1	1	yes	characteristic
166	C₂³×C₁₉	#127	1	1	yes	characteristic
167	C₂³×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
168	C₂³×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
169	C₂³×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
170	C₂³×C₁₉	#137	1	2	yes	—
171	C₂³×C₁₉	#137	1	2	yes	—
172	C₂×C₄×C₁₉	—	4	2	no	—
173	C₂×C₄×C₁₉	—	4	2	no	—
174	C₂×C₄×C₁₉	—	4	4	no	—
175	C₂×C₄×C₁₉	—	4	4	no	—
176	C₂×C₄×C₁₉	—	8	2	no	—
177	C₂×C₄×C₁₉	—	8	2	no	—
178	C₂×C₄×C₁₉	—	8	1	no	—
179	C₂×C₄×C₁₉	—	8	1	no	—
180	C₂×C₄×C₁₉	—	8	1	no	—
181	C₂×C₄×C₁₉	—	8	1	no	—
182	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
183	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
184	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
185	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
186	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
187	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
188	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
189	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
190	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
191	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
192	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
193	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
194	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
195	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
196	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
197	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
198	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
199	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
200	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
201	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
202	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
203	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
204	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
205	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
206	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
207	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
208	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
209	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
210	C₂×Dic₁₉	—	2	4	no	—
211	C₂×Dic₁₉	—	2	4	no	—
212	C₂×Dic₁₉	—	2	4	no	—
213	C₂×Dic₁₉	—	2	4	no	—
214	C₂×Dic₁₉	—	2	4	no	—
215	C₂×Dic₁₉	—	2	4	no	—
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	C₂×Dic₁₉	#95	1	8	yes	—
227	C₈×C₁₉	—	2	4	no	—
228	C₁₉⋊C₈	—	2	4	no	—
229	C₂²×#97	—	19	1	no	—
230	C₂×#384	—	19	1	no	—
231	C₂×#382	—	19	1	no	—
232	C₂×#340	—	19	1	no	—
233	C₂×#340	—	19	1	no	—
234	C₂×#340	—	19	1	no	—
235	C₂×#340	D₁₉	1	1	yes	characteristic
236	C₂²×C₁₉	C₂×#95	1	1	yes	characteristic
237	C₂²×C₁₉	#382	1	1	yes	characteristic
238	C₂²×C₁₉	#384	1	1	yes	characteristic
239	C₂²×C₁₉	#390	1	1	yes	characteristic
240	C₂²×C₁₉	#390	1	1	yes	characteristic
241	C₂²×C₁₉	#391	1	1	yes	characteristic
242	C₂²×C₁₉	#391	1	1	yes	characteristic
243	C₂²×C₁₉	#417	1	2	yes	—
244	C₂²×C₁₉	#417	1	2	yes	—
245	C₂²×C₁₉	#418	1	2	yes	—
246	C₂²×C₁₉	#419	1	2	yes	—
247	C₂²×C₁₉	#428	1	2	yes	—
248	C₂²×C₁₉	#428	1	2	yes	—
249	C₂²×C₁₉	#489	1	2	yes	—
250	C₂²×C₁₉	#489	1	2	yes	—
251	C₂²×C₁₉	#490	1	2	yes	—
252	C₂²×C₁₉	#491	1	2	yes	—
253	C₂²×C₁₉	#496	1	1	yes	characteristic
254	C₂²×C₁₉	#496	1	1	yes	characteristic
255	C₂²×C₁₉	#497	1	1	yes	characteristic
256	C₂²×C₁₉	#497	1	1	yes	characteristic
257	C₂²×C₁₉	#501	1	2	yes	—
258	C₂²×C₁₉	#501	1	2	yes	—
259	C₄×C₁₉	—	8	2	no	—
260	C₄×C₁₉	—	8	2	no	—
261	C₄×C₁₉	C₄×C₄⋊C₄	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	#380	1	1	yes	characteristic
265	C₄×C₁₉	#389	1	1	yes	characteristic
266	C₄×C₁₉	#389	1	1	yes	characteristic
267	C₄×C₁₉	#389	1	1	yes	characteristic
268	C₄×C₁₉	#389	1	1	yes	characteristic
269	Dic₁₉	—	2	8	no	—
270	Dic₁₉	—	8	2	no	—
271	Dic₁₉	—	8	2	no	—
272	C₂³×C₈	—	19	1	no	—
273	C₂³×C₈	C₂×D₁₉	1	1	yes	characteristic
274	C₂²×C₄⋊C₄	—	19	1	no	—
275	C₂²×C₄⋊C₄	—	19	1	no	—
276	C₂²×C₄⋊C₄	—	38	2	no	—
277	C₂²×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
278	C₂²×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
279	C₂²×C₄²	—	19	1	no	—
280	C₂×#97	—	19	4	no	—
281	C₂×#97	—	38	2	no	—
282	C₂×#97	—	38	2	no	—
283	#384	—	19	4	no	—
284	#384	—	38	2	no	—
285	#382	—	19	4	no	—
286	#382	—	38	2	no	—
287	C₂×#95	—	38	2	no	—
288	#340	—	2	2	no	—
289	#340	—	38	2	no	—
290	#340	—	38	2	no	—
291	#340	—	38	2	no	—
292	C₂×C₁₉	C₄⋊#95	1	1	yes	characteristic
293	C₂×C₁₉	#1736	1	2	yes	—
294	C₂×C₁₉	#1836	1	2	yes	—
295	C₂×C₁₉	#1847	1	1	yes	characteristic
296	C₂×C₁₉	#1847	1	1	yes	characteristic
297	C₂×C₁₉	#1959	1	1	yes	characteristic
298	C₂×C₁₉	#1959	1	1	yes	characteristic
299	C₂×C₁₉	#1960	1	1	yes	characteristic
300	C₂×C₁₉	#1961	1	1	yes	characteristic
301	C₂×C₁₉	#1992	1	2	yes	—
302	C₂×C₁₉	#1993	1	2	yes	—
303	C₂³×C₄	—	2	1	no	—
304	C₂³×C₄	—	2	1	no	—
305	C₂³×C₄	—	19	2	no	—
306	C₂³×C₄	—	38	1	no	—
307	C₂³×C₄	—	38	1	no	—
308	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
309	C₂²×C₈	—	2	1	no	—
310	C₂²×C₈	—	2	1	no	—
311	C₂²×C₈	—	2	1	no	—
312	C₂²×C₈	—	2	1	no	—
313	C₂²×C₈	—	19	2	no	—
314	C₂²×C₈	—	19	2	no	—
315	C₂²×C₈	—	19	2	no	—
316	C₂²×C₈	—	38	1	no	—
317	C₂²×C₈	—	38	1	no	—
318	C₂²×C₈	—	38	1	no	—
319	C₂²×C₈	—	38	1	no	—
320	C₂²×C₈	Dic₃₈	1	2	yes	—
321	C₂²×C₈	C₄×D₁₉	1	2	yes	—
322	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
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	—	2	1	no	—
333	C₂×C₄⋊C₄	—	19	2	no	—
334	C₂×C₄⋊C₄	—	19	2	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	8	no	—
344	C₂×C₄⋊C₄	—	38	1	no	—
345	C₂×C₄⋊C₄	—	38	1	no	—
346	C₂×C₄⋊C₄	—	76	4	no	—
347	C₂×C₄⋊C₄	—	76	4	no	—
348	C₂×C₄⋊C₄	C₄×D₁₉	1	2	yes	—
349	C₂×C₄⋊C₄	C₄×D₁₉	1	2	yes	—
350	C₂×C₄²	—	19	2	no	—
351	C₂×C₄²	—	19	2	no	—
352	C₂×C₄²	—	19	2	no	—
353	C₂×C₄²	—	19	2	no	—
354	C₂×C₄²	—	19	2	no	—
355	C₂×C₄²	—	19	2	no	—
356	#97	—	38	8	no	—
357	#95	—	38	8	no	—
358	C₁₉	#10843	1	1	yes	characteristic, complemented, Sylow
359	C₂⁴	D₄×D₁₉	1	1	yes	characteristic
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	4	1	no	—
363	C₂²×C₄	—	4	1	no	—
364	C₂²×C₄	—	4	1	no	—
365	C₂²×C₄	—	4	1	no	—
366	C₂²×C₄	—	4	2	no	—
367	C₂²×C₄	—	4	2	no	—
368	C₂²×C₄	—	4	2	no	—
369	C₂²×C₄	—	4	2	no	—
370	C₂²×C₄	—	19	4	no	—
371	C₂²×C₄	—	19	4	no	—
372	C₂²×C₄	—	19	4	no	—
373	C₂²×C₄	—	38	2	no	—
374	C₂²×C₄	—	38	2	no	—
375	C₂²×C₄	—	38	2	no	—
376	C₂²×C₄	—	38	2	no	—
377	C₂²×C₄	—	38	2	no	—
378	C₂²×C₄	—	38	2	no	—
379	C₂²×C₄	—	76	1	no	—
380	C₂²×C₄	—	76	1	no	—
381	C₂²×C₄	—	76	1	no	—
382	C₂²×C₄	—	76	1	no	—
383	C₂²×C₄	—	76	2	no	—
384	C₂²×C₄	—	76	2	no	—
385	C₂²×C₄	—	76	2	no	—
386	C₂²×C₄	—	76	2	no	—
387	C₂²×C₄	C₂×Dic₃₈	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	C₂×C₄×D₁₉	1	1	yes	characteristic
391	C₂²×C₄	#64541	1	1	yes	characteristic
392	C₂²×C₄	#64541	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	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
401	C₂×C₈	—	2	2	no	—
402	C₂×C₈	—	2	2	no	—
403	C₂×C₈	—	2	2	no	—
404	C₂×C₈	—	2	2	no	—
405	C₂×C₈	—	2	2	no	—
406	C₂×C₈	—	2	2	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	C₂×C₈	Dic₁₉⋊C₄	1	4	yes	complemented
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	—	2	2	no	—
417	C₄⋊C₄	—	2	2	no	—
418	C₄⋊C₄	—	2	2	no	—
419	C₄⋊C₄	—	4	1	no	—
420	C₄⋊C₄	—	4	1	no	—
421	C₄⋊C₄	—	4	1	no	—
422	C₄⋊C₄	—	4	1	no	—
423	C₄⋊C₄	—	38	2	no	—
424	C₄⋊C₄	—	38	2	no	—
425	C₄⋊C₄	—	38	2	no	—
426	C₄⋊C₄	—	38	2	no	—
427	C₄⋊C₄	—	76	16	no	—
428	C₄⋊C₄	—	76	1	no	—
429	C₄⋊C₄	—	76	1	no	—
430	C₄⋊C₄	—	76	1	no	—
431	C₄⋊C₄	—	76	1	no	—
432	C₄²	—	19	4	no	—
433	C₄²	—	19	4	no	—
434	C₄²	—	19	4	no	—
435	C₄²	—	19	4	no	—
436	C₂³	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
437	C₂³	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
438	C₂³	#10597331	1	1	yes	characteristic
439	C₂³	#10597331	1	1	yes	characteristic
440	C₂³	#10597334	1	1	yes	characteristic
441	C₂³	C₄⋊C₄×D₁₉	1	1	yes	characteristic
442	C₂³	#10597357	1	2	yes	—
443	C₂³	#10597360	1	2	yes	—
444	C₂³	#10597361	1	2	yes	—
445	C₂³	#10597364	1	2	yes	—
446	C₂³	#10597386	1	1	yes	characteristic
447	C₂×C₄	—	4	4	no	—
448	C₂×C₄	—	4	4	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	8	2	no	—
452	C₂×C₄	—	8	2	no	—
453	C₂×C₄	—	8	1	no	—
454	C₂×C₄	—	8	1	no	—
455	C₂×C₄	—	8	1	no	—
456	C₂×C₄	—	8	1	no	—
457	C₂×C₄	—	19	8	no	—
458	C₂×C₄	—	38	4	no	—
459	C₂×C₄	—	38	4	no	—
460	C₂×C₄	—	38	4	no	—
461	C₂×C₄	—	38	4	no	—
462	C₂×C₄	—	38	4	no	—
463	C₂×C₄	—	38	4	no	—
464	C₂×C₄	—	76	4	no	—
465	C₂×C₄	—	76	4	no	—
466	C₂×C₄	—	76	2	no	—
467	C₂×C₄	—	76	2	no	—
468	C₂×C₄	—	152	2	no	—
469	C₂×C₄	—	152	2	no	—
470	C₂×C₄	—	152	1	no	—
471	C₂×C₄	—	152	1	no	—
472	C₂×C₄	—	152	1	no	—
473	C₂×C₄	—	152	1	no	—
474	C₂×C₄	C₄×Dic₃₈	1	1	yes	characteristic
475	C₂×C₄	C₄×Dic₃₈	1	1	yes	characteristic
476	C₂×C₄	C₄²×D₁₉	1	1	yes	characteristic
477	C₂×C₄	#10597318	1	1	yes	characteristic
478	C₂×C₄	#10597323	1	1	yes	characteristic
479	C₂×C₄	#10597324	1	1	yes	characteristic
480	C₂×C₄	#10597324	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	#10597333	1	1	yes	characteristic
487	C₂×C₄	#10597333	1	1	yes	characteristic
488	C₂×C₄	#10597334	1	1	yes	characteristic
489	C₂×C₄	#10597335	1	1	yes	characteristic
490	C₂×C₄	#10597335	1	1	yes	characteristic
491	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
492	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
493	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
494	C₂×C₄	#10597342	1	1	yes	characteristic
495	C₂×C₄	#10597342	1	1	yes	characteristic
496	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
497	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
498	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
499	C₂×C₄	#10597385	1	1	yes	characteristic
500	C₂×C₄	#10597385	1	1	yes	characteristic
501	C₂×C₄	#10597390	1	1	yes	characteristic
502	C₈	—	2	4	no	—
503	C₈	—	38	4	no	—
504	C₂²	#95×D₁₉	1	1	yes	characteristic
505	C₂²	#11926408	1	1	yes	characteristic
506	C₂²	#11926413	1	1	yes	characteristic
507	C₂²	#11926444	1	1	yes	characteristic
508	C₂²	#11926444	1	1	yes	characteristic
509	C₂²	#11926448	1	1	yes	characteristic
510	C₂²	#11926448	1	1	yes	characteristic
511	C₂²	#11926542	1	2	yes	—
512	C₂²	#11926544	1	2	yes	—
513	C₂²	#11926547	1	2	yes	—
514	C₂²	#11926551	1	2	yes	—
515	C₂²	#11926583	1	2	yes	—
516	C₂²	#11926585	1	2	yes	—
517	C₂²	#11926902	1	2	yes	—
518	C₂²	#11926905	1	2	yes	—
519	C₂²	#11926907	1	2	yes	—
520	C₂²	#11926911	1	2	yes	—
521	C₂²	#11926930	1	1	yes	characteristic
522	C₂²	#11926932	1	1	yes	characteristic
523	C₂²	#11926935	1	1	yes	characteristic
524	C₂²	#11926937	1	1	yes	characteristic
525	C₂²	#11926951	1	2	yes	—
526	C₂²	#11926952	1	2	yes	—
527	C₄	—	8	2	no	—
528	C₄	—	8	2	no	—
529	C₄	—	38	8	no	—
530	C₄	—	152	2	no	—
531	C₄	—	152	2	no	—
532	C₄	#11926395	1	1	yes	characteristic
533	C₄	C₄×Dic₁₉⋊C₄	1	1	yes	characteristic
534	C₄	#11926402	1	1	yes	characteristic
535	C₄	#11926403	1	1	yes	characteristic
536	C₄	#11926439	1	1	yes	characteristic
537	C₄	#11926439	1	1	yes	characteristic
538	C₄	#11926441	1	1	yes	characteristic
539	C₄	#11926441	1	1	yes	characteristic
540	C₂	Dic₁₉⋊#95	1	1	yes	characteristic
541	C₂	#14563353	1	2	yes	—
542	C₂	#14563767	1	2	yes	—
543	C₂	#14563800	1	1	yes	characteristic
544	C₂	#14563802	1	1	yes	characteristic
545	C₂	#14564448	1	1	yes	characteristic
546	C₂	#14564450	1	1	yes	characteristic
547	C₂	#14564453	1	1	yes	characteristic
548	C₂	#14564457	1	1	yes	characteristic
549	C₂	#14564602	1	2	yes	—
550	C₂	#14564606	1	2	yes	—

	subgroup	G/H
center	C₂⁴	D₄×D₁₉
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#340	C₂
socle, prime radical	C₂⁴×C₁₉	C₂×D₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#340	D₁₉
hypocenter	C₁₉	#10843
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄ ◁ C₂×#340

Complements

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

N	H ≅ G/N	type
15. C₂×#10597272	C₄	semidirect
17. #11926413	C₄	semidirect
19. #11926409	C₄	semidirect
131. C₂×C₈×C₁₉	C₄⋊C₄	semidirect
159. C₂×C₁₉⋊C₈	C₄⋊C₄	semidirect
358. C₁₉	#10843	semidirect
414. C₂×C₈	Dic₁₉⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#10597272	2
C₂×#11926413	2
C₂×#11926409	2
C₂×#11926307	2
C₂×#11926306	2
C₂×C₁₉×#340	2
#10843	19