Subgroups — #18074623

Order 4864.

1048 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14564597	C₂	1	1	yes	maximal, characteristic, complemented
2	#14563635	C₂	1	1	yes	maximal, characteristic, complemented
3	#14563635	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11926290	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₄⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₄⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#547	C₂	1	1	yes	maximal, characteristic
8	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
10	C₂×#10597289	—	2	1	no	—
11	C₂×#10597289	—	2	1	no	—
12	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
13	#11926414	C₂²	1	1	yes	characteristic
14	#11926306	—	2	1	no	—
15	#11926306	—	2	1	no	—
16	#11926306	—	2	2	no	—
17	#11926290	—	2	2	no	—
18	D₄⋊(C₁₉⋊C₈)	—	2	2	no	—
19	D₄⋊(C₁₉⋊C₈)	—	2	2	no	—
20	C₂²×#41×C₁₉	—	2	1	no	—
21	C₁₉×#547	—	2	2	no	—
22	C₁₉×#547	—	2	2	no	—
23	C₁₉×#547	—	2	2	no	—
24	C₁₉×#547	C₄	1	4	yes	complemented
25	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#123	—	2	2	no	—
27	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
28	C₂×C₁₉×#121	—	2	1	no	—
29	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
31	C₂²×C₄⋊C₄×C₁₉	—	2	1	no	—
32	C₂×#41×C₁₉	—	2	4	no	—
33	C₂×#41×C₁₉	—	2	4	no	—
34	C₂×#41×C₁₉	—	4	2	no	—
35	C₂×#41×C₁₉	—	4	2	no	—
36	C₂×#41×C₁₉	—	4	2	no	—
37	C₂×#41×C₁₉	—	4	2	no	—
38	C₂²×Q₈×C₁₉	—	2	1	no	—
39	C₂²×D₄×C₁₉	—	2	2	no	—
40	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
41	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
42	C₂³×C₄×C₁₉	—	2	2	no	—
43	C₂³×C₄×C₁₉	—	2	1	no	—
44	C₂³×C₄×C₁₉	—	2	1	no	—
45	C₁₉×C₄⋊Q₈	—	2	1	no	—
46	C₁₉×C₄⋊Q₈	—	2	1	no	—
47	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
48	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
49	C₁₉×#123	—	2	8	no	—
50	C₁₉×#123	—	2	8	no	—
51	C₁₉×C₂²⋊Q₈	—	2	4	no	—
52	C₁₉×C₂²⋊Q₈	—	2	4	no	—
53	C₁₉×#121	—	2	4	no	—
54	C₁₉×#121	—	2	4	no	—
55	C₄×D₄×C₁₉	—	2	1	no	—
56	C₄×D₄×C₁₉	—	2	1	no	—
57	C₄×D₄×C₁₉	—	2	1	no	—
58	C₄×D₄×C₁₉	—	2	1	no	—
59	C₄×D₄×C₁₉	C₂×C₄	1	2	yes	—
60	C₄×D₄×C₁₉	C₂×C₄	1	2	yes	—
61	C₄×D₄×C₁₉	D₄	1	2	yes	—
62	C₄×D₄×C₁₉	D₄	1	2	yes	—
63	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
64	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
65	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
66	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
67	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
70	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
72	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
73	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
74	C₂×C₄⋊Dic₁₉	—	2	1	no	—
75	C₂×C₄⋊Dic₁₉	—	2	1	no	—
76	C₂×C₄⋊Dic₁₉	—	2	1	no	—
77	C₂²×C₁₉⋊C₈	—	2	1	no	—
78	C₂²×C₁₉⋊C₈	—	2	1	no	—
79	C₂²×C₁₉⋊C₈	—	2	1	no	—
80	#10597289	—	4	2	no	—
81	#10597289	—	4	2	no	—
82	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
83	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
84	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
85	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
86	C₄×C₁₉⋊C₈	—	2	1	no	—
87	C₄×C₁₉⋊C₈	—	2	1	no	—
88	C₂⁴×C₁₉	—	2	1	no	—
89	C₂⁴×C₁₉	—	2	1	no	—
90	#41×C₁₉	—	4	8	no	—
91	#41×C₁₉	—	4	8	no	—
92	#41×C₁₉	—	4	8	no	—
93	#41×C₁₉	—	4	8	no	—
94	C₂×Q₈×C₁₉	—	2	2	no	—
95	C₂×Q₈×C₁₉	—	2	2	no	—
96	C₂×Q₈×C₁₉	—	4	1	no	—
97	C₂×Q₈×C₁₉	—	4	1	no	—
98	C₂×Q₈×C₁₉	—	4	1	no	—
99	C₂×Q₈×C₁₉	—	4	1	no	—
100	C₂×D₄×C₁₉	—	2	8	no	—
101	C₂×D₄×C₁₉	—	2	1	no	—
102	C₂×D₄×C₁₉	—	2	1	no	—
103	C₂×D₄×C₁₉	—	2	1	no	—
104	C₂×D₄×C₁₉	—	2	1	no	—
105	C₂×D₄×C₁₉	—	2	1	no	—
106	C₂×D₄×C₁₉	—	2	1	no	—
107	C₂×D₄×C₁₉	—	2	1	no	—
108	C₂×D₄×C₁₉	—	2	1	no	—
109	C₂×D₄×C₁₉	—	4	4	no	—
110	C₂×D₄×C₁₉	—	4	4	no	—
111	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
112	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
113	C₂×D₄×C₁₉	D₈	1	2	yes	—
114	C₂×D₄×C₁₉	SD₁₆	1	2	yes	—
115	C₂²×C₄×C₁₉	—	2	8	no	—
116	C₂²×C₄×C₁₉	—	2	1	no	—
117	C₂²×C₄×C₁₉	—	2	1	no	—
118	C₂²×C₄×C₁₉	—	2	2	no	—
119	C₂²×C₄×C₁₉	—	2	2	no	—
120	C₂²×C₄×C₁₉	—	2	2	no	—
121	C₂²×C₄×C₁₉	—	2	2	no	—
122	C₂²×C₄×C₁₉	—	2	2	no	—
123	C₂²×C₄×C₁₉	—	4	4	no	—
124	C₂²×C₄×C₁₉	—	4	4	no	—
125	C₂²×C₄×C₁₉	—	4	1	no	—
126	C₂²×C₄×C₁₉	—	4	1	no	—
127	C₂²×C₄×C₁₉	—	4	1	no	—
128	C₂²×C₄×C₁₉	—	4	1	no	—
129	C₂²×C₄×C₁₉	—	4	1	no	—
130	C₂²×C₄×C₁₉	—	4	1	no	—
131	C₂²×C₄×C₁₉	—	4	1	no	—
132	C₂²×C₄×C₁₉	—	4	1	no	—
133	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
136	C₂²×Dic₁₉	—	4	1	no	—
137	C₄⋊C₄×C₁₉	—	2	8	no	—
138	C₄⋊C₄×C₁₉	—	2	2	no	—
139	C₄⋊C₄×C₁₉	—	2	1	no	—
140	C₄⋊C₄×C₁₉	—	2	2	no	—
141	C₄⋊C₄×C₁₉	—	2	1	no	—
142	C₄⋊C₄×C₁₉	—	2	2	no	—
143	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
144	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
145	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
146	C₂²⋊C₄×C₁₉	—	2	8	no	—
147	C₂²⋊C₄×C₁₉	—	2	2	no	—
148	C₂²⋊C₄×C₁₉	—	2	2	no	—
149	C₂²⋊C₄×C₁₉	—	2	2	no	—
150	C₂²⋊C₄×C₁₉	—	2	2	no	—
151	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
152	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
153	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
154	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
155	C₄⋊Dic₁₉	—	4	2	no	—
156	C₄⋊Dic₁₉	—	4	1	no	—
157	C₄⋊Dic₁₉	—	4	1	no	—
158	C₄⋊Dic₁₉	—	4	1	no	—
159	C₄⋊Dic₁₉	—	4	1	no	—
160	C₂×C₁₉⋊C₈	—	2	2	no	—
161	C₂×C₁₉⋊C₈	—	4	1	no	—
162	C₂×C₁₉⋊C₈	—	4	1	no	—
163	C₂×C₁₉⋊C₈	—	4	1	no	—
164	C₂×C₁₉⋊C₈	—	4	1	no	—
165	C₂×C₁₉⋊C₈	—	4	1	no	—
166	C₂×C₁₉⋊C₈	—	4	1	no	—
167	C₂×C₁₉⋊C₈	—	4	1	no	—
168	C₂×C₁₉⋊C₈	—	4	1	no	—
169	#8446	—	19	1	no	maximal, Sylow
170	C₂³×C₁₉	—	2	2	no	—
171	C₂³×C₁₉	—	2	2	no	—
172	C₂³×C₁₉	—	2	2	no	—
173	C₂³×C₁₉	—	2	2	no	—
174	C₂³×C₁₉	—	4	1	no	—
175	C₂³×C₁₉	—	4	1	no	—
176	C₂³×C₁₉	—	4	1	no	—
177	C₂³×C₁₉	—	4	1	no	—
178	C₂³×C₁₉	—	4	1	no	—
179	C₂³×C₁₉	—	4	1	no	—
180	C₂³×C₁₉	—	4	1	no	—
181	C₂³×C₁₉	—	4	1	no	—
182	C₂³×C₁₉	—	4	1	no	—
183	C₂³×C₁₉	—	4	1	no	—
184	C₂³×C₁₉	#120	1	1	yes	characteristic
185	Q₈×C₁₉	—	4	2	no	—
186	Q₈×C₁₉	—	4	2	no	—
187	Q₈×C₁₉	—	4	2	no	—
188	Q₈×C₁₉	—	4	2	no	—
189	D₄×C₁₉	—	2	2	no	—
190	D₄×C₁₉	—	2	2	no	—
191	D₄×C₁₉	—	2	2	no	—
192	D₄×C₁₉	—	2	2	no	—
193	D₄×C₁₉	—	2	2	no	—
194	D₄×C₁₉	—	4	16	no	—
195	D₄×C₁₉	—	4	1	no	—
196	D₄×C₁₉	—	4	1	no	—
197	D₄×C₁₉	#102	1	4	yes	complemented
198	C₂×C₄×C₁₉	—	2	1	no	—
199	C₂×C₄×C₁₉	—	2	1	no	—
200	C₂×C₄×C₁₉	—	2	2	no	—
201	C₂×C₄×C₁₉	—	2	2	no	—
202	C₂×C₄×C₁₉	—	2	4	no	—
203	C₂×C₄×C₁₉	—	4	16	no	—
204	C₂×C₄×C₁₉	—	4	1	no	—
205	C₂×C₄×C₁₉	—	4	2	no	—
206	C₂×C₄×C₁₉	—	4	1	no	—
207	C₂×C₄×C₁₉	—	4	1	no	—
208	C₂×C₄×C₁₉	—	4	2	no	—
209	C₂×C₄×C₁₉	—	4	1	no	—
210	C₂×C₄×C₁₉	—	4	2	no	—
211	C₂×C₄×C₁₉	—	4	2	no	—
212	C₂×C₄×C₁₉	—	4	2	no	—
213	C₂×C₄×C₁₉	—	4	2	no	—
214	C₂×C₄×C₁₉	—	4	2	no	—
215	C₂×C₄×C₁₉	—	4	2	no	—
216	C₂×C₄×C₁₉	—	4	2	no	—
217	C₂×C₄×C₁₉	—	4	2	no	—
218	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
219	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
220	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
221	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
222	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
223	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
224	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
225	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
226	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
227	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
228	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
229	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
230	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
231	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
232	C₂×Dic₁₉	—	8	1	no	—
233	C₂×Dic₁₉	—	8	1	no	—
234	C₂×Dic₁₉	—	8	1	no	—
235	C₁₉⋊C₈	—	4	2	no	—
236	C₁₉⋊C₈	—	8	1	no	—
237	C₁₉⋊C₈	—	8	1	no	—
238	C₂×#547	D₁₉	1	1	yes	characteristic
239	#1990	—	19	1	no	—
240	#1802	—	19	1	no	—
241	#1802	—	19	1	no	—
242	C₂×#332	—	19	1	no	—
243	C₂×D₄⋊C₈	—	19	1	no	—
244	C₂×D₄⋊C₈	—	19	1	no	—
245	C₂²×C₁₉	—	2	4	no	—
246	C₂²×C₁₉	—	4	2	no	—
247	C₂²×C₁₉	—	4	2	no	—
248	C₂²×C₁₉	—	4	2	no	—
249	C₂²×C₁₉	—	4	2	no	—
250	C₂²×C₁₉	—	4	2	no	—
251	C₂²×C₁₉	—	4	2	no	—
252	C₂²×C₁₉	—	4	2	no	—
253	C₂²×C₁₉	—	4	2	no	—
254	C₂²×C₁₉	—	4	2	no	—
255	C₂²×C₁₉	—	8	1	no	—
256	C₂²×C₁₉	—	8	1	no	—
257	C₂²×C₁₉	—	8	1	no	—
258	C₂²×C₁₉	—	8	1	no	—
259	C₂²×C₁₉	#379	1	1	yes	characteristic
260	C₂²×C₁₉	#447	1	1	yes	characteristic
261	C₂²×C₁₉	#449	1	1	yes	characteristic
262	C₂²×C₁₉	#450	1	1	yes	characteristic
263	C₂²×C₁₉	#452	1	1	yes	characteristic
264	C₂²×C₁₉	#454	1	1	yes	characteristic
265	C₂²×C₁₉	#456	1	1	yes	characteristic
266	C₄×C₁₉	—	2	1	no	—
267	C₄×C₁₉	—	2	1	no	—
268	C₄×C₁₉	—	4	2	no	—
269	C₄×C₁₉	—	4	4	no	—
270	C₄×C₁₉	—	4	2	no	—
271	C₄×C₁₉	C₂×#102	1	1	yes	characteristic
272	C₄×C₁₉	#416	1	1	yes	characteristic
273	C₄×C₁₉	#417	1	1	yes	characteristic
274	C₄×C₁₉	#418	1	1	yes	characteristic
275	C₄×C₁₉	#447	1	1	yes	characteristic
276	C₄×C₁₉	#449	1	1	yes	characteristic
277	C₄×C₁₉	#450	1	1	yes	characteristic
278	C₄×C₁₉	#452	1	1	yes	characteristic
279	Dic₁₉	—	16	1	no	—
280	C₂²×#41	—	2	1	no	—
281	#547	—	2	2	no	—
282	#547	—	2	2	no	—
283	#547	—	2	2	no	—
284	#547	Dic₁₉	1	4	yes	complemented
285	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
286	C₂×#123	—	2	2	no	—
287	C₂×C₂²⋊Q₈	—	2	1	no	—
288	C₂×#121	—	2	1	no	—
289	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
290	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
291	C₂²×C₄⋊C₄	—	2	1	no	—
292	C₂×C₄⋊C₈	—	19	1	no	—
293	C₂×C₄⋊C₈	—	19	1	no	—
294	C₂×#102	—	38	1	no	—
295	C₂×#102	—	38	1	no	—
296	C₂×C₄×C₈	—	19	1	no	—
297	#384	—	19	1	no	—
298	#340	—	38	1	no	—
299	#340	—	38	1	no	—
300	#340	—	38	2	no	—
301	#332	—	38	2	no	—
302	D₄⋊C₈	—	38	2	no	—
303	D₄⋊C₈	—	38	2	no	—
304	C₂×C₁₉	—	4	4	no	—
305	C₂×C₁₉	—	8	2	no	—
306	C₂×C₁₉	#1625	1	1	yes	characteristic
307	C₂×C₁₉	#1635	1	1	yes	characteristic
308	C₂×C₁₉	#1647	1	1	yes	characteristic
309	C₂×C₁₉	#1654	1	1	yes	characteristic
310	C₂×C₁₉	#1786	1	1	yes	characteristic
311	C₂×C₁₉	#1788	1	1	yes	characteristic
312	C₂×C₁₉	#1793	1	1	yes	characteristic
313	C₂×#41	—	2	4	no	—
314	C₂×#41	—	2	4	no	—
315	C₂×#41	—	4	2	no	—
316	C₂×#41	—	4	2	no	—
317	C₂×#41	—	4	2	no	—
318	C₂×#41	—	4	2	no	—
319	C₂²×Q₈	—	2	1	no	—
320	C₂²×D₄	—	2	2	no	—
321	C₂²×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
322	C₂²×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
323	C₂³×C₄	—	2	2	no	—
324	C₂³×C₄	—	2	1	no	—
325	C₂³×C₄	—	2	1	no	—
326	C₂²×C₈	—	38	1	no	—
327	C₂²×C₈	—	38	1	no	—
328	C₂²×C₈	—	38	1	no	—
329	C₄⋊Q₈	—	2	1	no	—
330	C₄⋊Q₈	—	2	1	no	—
331	C₄⋊Q₈	C₂×Dic₁₉	1	2	yes	—
332	C₄⋊Q₈	C₂²⋊D₁₉	1	2	yes	—
333	#123	—	2	8	no	—
334	#123	—	2	8	no	—
335	C₂²⋊Q₈	—	2	4	no	—
336	C₂²⋊Q₈	—	2	4	no	—
337	#121	—	2	4	no	—
338	#121	—	2	4	no	—
339	C₄×D₄	—	2	1	no	—
340	C₄×D₄	—	2	1	no	—
341	C₄×D₄	—	2	1	no	—
342	C₄×D₄	—	2	1	no	—
343	C₄×D₄	C₂×Dic₁₉	1	2	yes	—
344	C₄×D₄	C₂×Dic₁₉	1	2	yes	—
345	C₄×D₄	C₂²⋊D₁₉	1	2	yes	—
346	C₄×D₄	C₂²⋊D₁₉	1	2	yes	—
347	C₂×C₄⋊C₄	—	2	2	no	—
348	C₂×C₄⋊C₄	—	2	4	no	—
349	C₂×C₄⋊C₄	—	2	1	no	—
350	C₂×C₄⋊C₄	—	2	4	no	—
351	C₂×C₄⋊C₄	—	38	1	no	—
352	C₂×C₄⋊C₄	—	38	1	no	—
353	C₂×C₄⋊C₄	—	38	1	no	—
354	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
355	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
356	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
357	C₂×C₂²⋊C₄	—	2	2	no	—
358	C₂×C₂²⋊C₄	—	2	1	no	—
359	C₂×C₂²⋊C₄	—	2	1	no	—
360	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
361	C₄⋊C₈	—	38	1	no	—
362	C₄⋊C₈	—	38	1	no	—
363	C₄⋊C₈	—	38	1	no	—
364	C₄⋊C₈	—	38	1	no	—
365	#102	—	76	2	no	—
366	#102	—	76	2	no	—
367	C₄×C₈	—	38	1	no	—
368	C₄×C₈	—	38	1	no	—
369	C₁₉	#8446	1	1	yes	characteristic, complemented, Sylow
370	C₂⁴	—	2	1	no	—
371	C₂⁴	—	2	1	no	—
372	#41	—	4	8	no	—
373	#41	—	4	8	no	—
374	#41	—	4	8	no	—
375	#41	—	4	8	no	—
376	C₂×Q₈	—	2	2	no	—
377	C₂×Q₈	—	2	2	no	—
378	C₂×Q₈	—	4	1	no	—
379	C₂×Q₈	—	4	1	no	—
380	C₂×Q₈	—	4	1	no	—
381	C₂×Q₈	—	4	1	no	—
382	C₂×D₄	—	2	8	no	—
383	C₂×D₄	—	2	1	no	—
384	C₂×D₄	—	2	1	no	—
385	C₂×D₄	—	2	1	no	—
386	C₂×D₄	—	2	1	no	—
387	C₂×D₄	—	2	1	no	—
388	C₂×D₄	—	2	1	no	—
389	C₂×D₄	—	2	1	no	—
390	C₂×D₄	—	2	1	no	—
391	C₂×D₄	—	4	4	no	—
392	C₂×D₄	—	4	4	no	—
393	C₂×D₄	#64525	1	2	yes	—
394	C₂×D₄	#64526	1	2	yes	—
395	C₂×D₄	C₂²⋊Dic₁₉	1	2	yes	—
396	C₂×D₄	C₂²⋊Dic₁₉	1	2	yes	—
397	C₂²×C₄	—	2	8	no	—
398	C₂²×C₄	—	2	1	no	—
399	C₂²×C₄	—	2	1	no	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	4	4	no	—
406	C₂²×C₄	—	4	4	no	—
407	C₂²×C₄	—	4	1	no	—
408	C₂²×C₄	—	4	1	no	—
409	C₂²×C₄	—	4	1	no	—
410	C₂²×C₄	—	4	1	no	—
411	C₂²×C₄	—	4	1	no	—
412	C₂²×C₄	—	4	1	no	—
413	C₂²×C₄	—	4	1	no	—
414	C₂²×C₄	—	4	1	no	—
415	C₂²×C₄	—	76	1	no	—
416	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
417	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
418	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
419	C₂×C₈	—	38	2	no	—
420	C₂×C₈	—	76	1	no	—
421	C₂×C₈	—	76	1	no	—
422	C₂×C₈	—	76	1	no	—
423	C₂×C₈	—	76	1	no	—
424	C₂×C₈	—	76	1	no	—
425	C₂×C₈	—	76	1	no	—
426	C₂×C₈	—	76	1	no	—
427	C₂×C₈	—	76	1	no	—
428	C₄⋊C₄	—	2	8	no	—
429	C₄⋊C₄	—	2	2	no	—
430	C₄⋊C₄	—	2	1	no	—
431	C₄⋊C₄	—	2	2	no	—
432	C₄⋊C₄	—	2	1	no	—
433	C₄⋊C₄	—	2	2	no	—
434	C₄⋊C₄	—	76	2	no	—
435	C₄⋊C₄	—	76	1	no	—
436	C₄⋊C₄	—	76	1	no	—
437	C₄⋊C₄	—	76	1	no	—
438	C₄⋊C₄	—	76	1	no	—
439	C₄⋊C₄	C₂²⋊Dic₁₉	1	2	yes	—
440	C₄⋊C₄	C₂²⋊Dic₁₉	1	2	yes	—
441	C₄⋊C₄	C₂²⋊Dic₁₉	1	4	yes	—
442	C₂²⋊C₄	—	2	8	no	—
443	C₂²⋊C₄	—	2	2	no	—
444	C₂²⋊C₄	—	2	2	no	—
445	C₂²⋊C₄	—	2	2	no	—
446	C₂²⋊C₄	—	2	2	no	—
447	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
448	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
449	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
450	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
451	C₂³	—	2	2	no	—
452	C₂³	—	2	2	no	—
453	C₂³	—	2	2	no	—
454	C₂³	—	2	2	no	—
455	C₂³	—	4	1	no	—
456	C₂³	—	4	1	no	—
457	C₂³	—	4	1	no	—
458	C₂³	—	4	1	no	—
459	C₂³	—	4	1	no	—
460	C₂³	—	4	1	no	—
461	C₂³	—	4	1	no	—
462	C₂³	—	4	1	no	—
463	C₂³	—	4	1	no	—
464	C₂³	—	4	1	no	—
465	C₂³	#10597399	1	1	yes	characteristic
466	Q₈	—	4	2	no	—
467	Q₈	—	4	2	no	—
468	Q₈	—	4	2	no	—
469	Q₈	—	4	2	no	—
470	D₄	—	2	2	no	—
471	D₄	—	2	2	no	—
472	D₄	—	2	2	no	—
473	D₄	—	2	2	no	—
474	D₄	—	2	2	no	—
475	D₄	—	4	16	no	—
476	D₄	—	4	1	no	—
477	D₄	—	4	1	no	—
478	D₄	#10597289	1	4	yes	complemented
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	4	no	—
484	C₂×C₄	—	4	16	no	—
485	C₂×C₄	—	4	1	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	4	1	no	—
488	C₂×C₄	—	4	1	no	—
489	C₂×C₄	—	4	2	no	—
490	C₂×C₄	—	4	1	no	—
491	C₂×C₄	—	4	2	no	—
492	C₂×C₄	—	4	2	no	—
493	C₂×C₄	—	4	2	no	—
494	C₂×C₄	—	4	2	no	—
495	C₂×C₄	—	4	2	no	—
496	C₂×C₄	—	4	2	no	—
497	C₂×C₄	—	4	2	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	—	152	1	no	—
500	C₂×C₄	—	152	1	no	—
501	C₂×C₄	—	152	1	no	—
502	C₂×C₄	C₂×#64525	1	1	yes	characteristic
503	C₂×C₄	#10597378	1	1	yes	characteristic
504	C₂×C₄	#10597378	1	1	yes	characteristic
505	C₂×C₄	C₂×#64526	1	1	yes	characteristic
506	C₂×C₄	#10597395	1	1	yes	characteristic
507	C₂×C₄	#10597396	1	1	yes	characteristic
508	C₂×C₄	#10597396	1	1	yes	characteristic
509	C₂×C₄	#10597397	1	1	yes	characteristic
510	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
511	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
512	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
513	C₂×C₄	#10597399	1	1	yes	characteristic
514	C₂×C₄	#10597399	1	1	yes	characteristic
515	C₂×C₄	#10597399	1	1	yes	characteristic
516	C₈	—	76	2	no	—
517	C₈	—	152	1	no	—
518	C₈	—	152	1	no	—
519	C₂²	—	2	4	no	—
520	C₂²	—	4	2	no	—
521	C₂²	—	4	2	no	—
522	C₂²	—	4	2	no	—
523	C₂²	—	4	2	no	—
524	C₂²	—	4	2	no	—
525	C₂²	—	4	2	no	—
526	C₂²	—	4	2	no	—
527	C₂²	—	4	2	no	—
528	C₂²	—	4	2	no	—
529	C₂²	—	8	1	no	—
530	C₂²	—	8	1	no	—
531	C₂²	—	8	1	no	—
532	C₂²	—	8	1	no	—
533	C₂²	#11926400	1	1	yes	characteristic
534	C₂²	#11926678	1	1	yes	characteristic
535	C₂²	#11926689	1	1	yes	characteristic
536	C₂²	#11926695	1	1	yes	characteristic
537	C₂²	#11926706	1	1	yes	characteristic
538	C₂²	#11926717	1	1	yes	characteristic
539	C₂²	#11926727	1	1	yes	characteristic
540	C₄	—	2	1	no	—
541	C₄	—	2	1	no	—
542	C₄	—	4	2	no	—
543	C₄	—	4	4	no	—
544	C₄	—	4	2	no	—
545	C₄	—	304	1	no	—
546	C₄	C₂×#10597289	1	1	yes	characteristic
547	C₄	#11926540	1	1	yes	characteristic
548	C₄	#11926545	1	1	yes	characteristic
549	C₄	#11926549	1	1	yes	characteristic
550	C₄	#11926678	1	1	yes	characteristic
551	C₄	#11926689	1	1	yes	characteristic
552	C₄	#11926695	1	1	yes	characteristic
553	C₄	#11926706	1	1	yes	characteristic
554	C₂	—	4	4	no	—
555	C₂	—	8	2	no	—
556	C₂	#14562724	1	1	yes	characteristic
557	C₂	#14562786	1	1	yes	characteristic
558	C₂	#14562870	1	1	yes	characteristic
559	C₂	#14562919	1	1	yes	characteristic
560	C₂	#14563566	1	1	yes	characteristic
561	C₂	#14563575	1	1	yes	characteristic
562	C₂	#14563594	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597399
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting, prime radical	C₂×C₁₉×#547	C₂
socle	C₂³×C₁₉	#120
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×#547	D₁₉
hypocenter	C₁₉	#8446
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#547

Complements

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

N	H ≅ G/N	type
1. #14564597	C₂	semidirect
2. #14563635	C₂	semidirect
3. #14563635	C₂	semidirect
4. C₂×#11926290	C₂	semidirect
5. C₂×D₄⋊(C₁₉⋊C₈)	C₂	semidirect
6. C₂×D₄⋊(C₁₉⋊C₈)	C₂	semidirect
24. C₁₉×#547	C₄	semidirect
197. D₄×C₁₉	#102	semidirect
284. #547	Dic₁₉	semidirect
369. C₁₉	#8446	semidirect
478. D₄	#10597289	semidirect

Maximal subgroups

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

subgroup	index
#14564597	2
#14563635	2
C₂×#11926290	2
C₂×D₄⋊(C₁₉⋊C₈)	2
C₂×C₁₉×#547	2
#8446	19