Subgroups — #18074561

Order 4864.

1050 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14563655	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#10597289	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562130	C₂	1	1	yes	maximal, characteristic, complemented
4	#14562086	C₂	1	1	yes	maximal, characteristic, complemented
5	#14562060	C₂	1	1	yes	maximal, characteristic, complemented
6	#14562017	C₂	1	1	yes	maximal, characteristic, complemented
7	D₄×#41×C₁₉	C₂	1	1	yes	maximal, characteristic
8	#11926597	C₂²	1	1	yes	characteristic, complemented
9	#11926568	C₂²	1	1	yes	characteristic, complemented
10	C₂×#10597294	—	2	1	no	—
11	C₂×#10597289	—	2	1	no	—
12	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic, complemented
13	C₄×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic, complemented
14	#11926306	—	2	1	no	—
15	#11926303	—	2	1	no	—
16	#11926278	—	2	2	no	—
17	Q₈⋊(C₁₉⋊C₈)	—	2	1	no	—
18	D₄⋊(C₁₉⋊C₈)	—	2	1	no	—
19	D₄⋊(C₁₉⋊C₈)	—	2	1	no	—
20	D₄⋊(C₁₉⋊C₈)	—	2	2	no	—
21	D₄⋊(C₁₉⋊C₈)	—	2	1	no	—
22	C₂²×#41×C₁₉	—	2	1	no	—
23	C₁₉×#550	C₄	1	1	yes	characteristic, complemented
24	D₄×Q₈×C₁₉	C₄	1	1	yes	characteristic, complemented
25	C₁₉×#548	—	2	1	no	—
26	C₁₉×#547	—	2	1	no	—
27	C₁₉×#547	C₄	1	1	yes	characteristic, complemented
28	C₁₉×#546	—	2	2	no	—
29	C₁₉×#546	—	2	1	no	—
30	D₄²×C₁₉	—	2	1	no	—
31	D₄²×C₁₉	C₄	1	1	yes	characteristic, complemented
32	C₁₉×#532	—	2	1	no	—
33	C₁₉×#532	C₂²	1	1	yes	characteristic
34	C₁₉×#525	—	2	2	no	—
35	C₁₉×#525	—	2	1	no	—
36	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₁₉	—	2	1	no	—
38	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
39	C₂×#41×C₁₉	—	2	2	no	—
40	C₂×#41×C₁₉	—	2	2	no	—
41	C₂×#41×C₁₉	—	2	1	no	—
42	C₂×#41×C₁₉	—	2	1	no	—
43	C₂×#41×C₁₉	—	2	1	no	—
44	C₂×#41×C₁₉	—	4	2	no	—
45	C₂×#41×C₁₉	—	4	2	no	—
46	C₂×#41×C₁₉	—	4	2	no	—
47	C₂×#41×C₁₉	—	4	2	no	—
48	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
49	C₂²×Q₈×C₁₉	—	2	1	no	—
50	C₂²×D₄×C₁₉	—	2	2	no	—
51	C₂²×D₄×C₁₉	—	2	1	no	—
52	C₂²×D₄×C₁₉	—	2	1	no	—
53	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
54	C₂³×C₄×C₁₉	—	2	2	no	—
55	C₂³×C₄×C₁₉	—	2	1	no	—
56	C₁₉×C₄⋊Q₈	—	2	1	no	—
57	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
58	C₁₉×#127	—	2	1	no	—
59	C₁₉×#127	C₂×C₄	1	1	yes	characteristic
60	C₁₉×#124	—	2	2	no	—
61	C₁₉×#124	—	2	1	no	—
62	C₁₉×#123	—	2	2	no	—
63	C₁₉×#123	—	2	2	no	—
64	C₁₉×#123	—	2	2	no	—
65	C₁₉×C₂²⋊Q₈	—	2	2	no	—
66	C₁₉×C₂²⋊Q₈	—	2	1	no	—
67	C₁₉×C₂²⋊Q₈	—	2	2	no	—
68	C₁₉×C₂²⋊Q₈	—	2	1	no	—
69	C₁₉×#121	—	2	2	no	—
70	C₁₉×#121	—	2	2	no	—
71	C₁₉×#121	—	2	2	no	—
72	C₁₉×#121	—	2	1	no	—
73	C₁₉×#121	—	2	1	no	—
74	C₁₉×#121	—	2	1	no	—
75	C₁₉×#121	—	2	1	no	—
76	C₁₉×#121	—	2	1	no	—
77	C₁₉×#121	D₄	1	2	yes	—
78	C₁₉×#120	—	2	2	no	—
79	C₁₉×#120	—	2	2	no	—
80	C₁₉×#120	—	2	2	no	—
81	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
82	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
83	C₄×D₄×C₁₉	—	2	2	no	—
84	C₄×D₄×C₁₉	—	2	2	no	—
85	C₄×D₄×C₁₉	—	2	2	no	—
86	C₄×D₄×C₁₉	—	2	1	no	—
87	C₄×D₄×C₁₉	—	2	1	no	—
88	C₄×D₄×C₁₉	—	2	1	no	—
89	C₄×D₄×C₁₉	—	2	1	no	—
90	C₄×D₄×C₁₉	—	2	1	no	—
91	C₄×D₄×C₁₉	—	2	1	no	—
92	C₄×D₄×C₁₉	—	2	1	no	—
93	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
94	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
95	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
96	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
97	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
98	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
99	C₄×D₄×C₁₉	D₄	1	2	yes	—
100	C₁₉×#117	—	2	1	no	—
101	C₁₉×#117	D₄	1	1	yes	characteristic
102	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
103	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
104	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
105	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
106	C₂×C₄²×C₁₉	—	2	1	no	—
107	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
108	C₂×C₄⋊Dic₁₉	—	2	1	no	—
109	C₂×C₄×Dic₁₉	—	2	1	no	—
110	C₂×#64520	—	2	1	no	—
111	C₂²×C₁₉⋊C₈	—	2	1	no	—
112	#10597294	—	4	2	no	—
113	#10597289	—	2	4	no	—
114	C₁₉⋊#95	—	2	1	no	—
115	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
116	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
117	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
118	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
119	C₄×C₁₉⋊C₈	—	2	1	no	—
120	C₄×C₁₉⋊C₈	—	2	1	no	—
121	C₄×C₁₉⋊C₈	—	2	1	no	—
122	C₂⁴×C₁₉	—	2	2	no	—
123	C₂⁴×C₁₉	—	2	1	no	—
124	#41×C₁₉	—	2	1	no	—
125	#41×C₁₉	—	2	1	no	—
126	#41×C₁₉	—	4	4	no	—
127	#41×C₁₉	—	4	4	no	—
128	#41×C₁₉	—	4	4	no	—
129	#41×C₁₉	—	4	4	no	—
130	#41×C₁₉	—	4	2	no	—
131	#41×C₁₉	—	4	2	no	—
132	#41×C₁₉	—	4	2	no	—
133	#41×C₁₉	—	4	2	no	—
134	#41×C₁₉	—	4	1	no	—
135	#41×C₁₉	—	4	1	no	—
136	#41×C₁₉	—	4	1	no	—
137	#41×C₁₉	—	4	1	no	—
138	#41×C₁₉	D₈	1	2	yes	—
139	#41×C₁₉	SD₁₆	1	2	yes	—
140	C₂×Q₈×C₁₉	—	2	2	no	—
141	C₂×Q₈×C₁₉	—	2	1	no	—
142	C₂×Q₈×C₁₉	—	4	2	no	—
143	C₂×Q₈×C₁₉	—	4	2	no	—
144	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
145	C₂×D₄×C₁₉	—	2	1	no	—
146	C₂×D₄×C₁₉	—	2	2	no	—
147	C₂×D₄×C₁₉	—	2	2	no	—
148	C₂×D₄×C₁₉	—	2	2	no	—
149	C₂×D₄×C₁₉	—	2	2	no	—
150	C₂×D₄×C₁₉	—	2	2	no	—
151	C₂×D₄×C₁₉	—	2	2	no	—
152	C₂×D₄×C₁₉	—	2	2	no	—
153	C₂×D₄×C₁₉	—	2	1	no	—
154	C₂×D₄×C₁₉	—	2	1	no	—
155	C₂×D₄×C₁₉	—	2	1	no	—
156	C₂×D₄×C₁₉	—	4	1	no	—
157	C₂×D₄×C₁₉	—	4	2	no	—
158	C₂×D₄×C₁₉	—	4	4	no	—
159	C₂×D₄×C₁₉	—	4	4	no	—
160	C₂×D₄×C₁₉	—	4	2	no	—
161	C₂×D₄×C₁₉	—	4	2	no	—
162	C₂×D₄×C₁₉	—	4	2	no	—
163	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
164	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
165	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
166	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
167	C₂²×C₄×C₁₉	—	2	1	no	—
168	C₂²×C₄×C₁₉	—	2	2	no	—
169	C₂²×C₄×C₁₉	—	2	2	no	—
170	C₂²×C₄×C₁₉	—	2	2	no	—
171	C₂²×C₄×C₁₉	—	2	1	no	—
172	C₂²×C₄×C₁₉	—	2	1	no	—
173	C₂²×C₄×C₁₉	—	2	1	no	—
174	C₂²×C₄×C₁₉	—	2	1	no	—
175	C₂²×C₄×C₁₉	—	2	1	no	—
176	C₂²×C₄×C₁₉	—	2	2	no	—
177	C₂²×C₄×C₁₉	—	2	1	no	—
178	C₂²×C₄×C₁₉	—	2	1	no	—
179	C₂²×C₄×C₁₉	—	4	4	no	—
180	C₂²×C₄×C₁₉	—	4	4	no	—
181	C₂²×C₄×C₁₉	—	4	1	no	—
182	C₂²×C₄×C₁₉	—	4	1	no	—
183	C₂²×C₄×C₁₉	—	4	1	no	—
184	C₂²×C₄×C₁₉	—	4	1	no	—
185	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
186	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
187	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
188	C₂²×Dic₁₉	—	4	1	no	—
189	C₄⋊C₄×C₁₉	—	2	2	no	—
190	C₄⋊C₄×C₁₉	—	2	2	no	—
191	C₄⋊C₄×C₁₉	—	2	1	no	—
192	C₄⋊C₄×C₁₉	—	2	1	no	—
193	C₄⋊C₄×C₁₉	—	2	1	no	—
194	C₄⋊C₄×C₁₉	—	2	1	no	—
195	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
196	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
197	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
198	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
199	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
200	C₂²⋊C₄×C₁₉	—	2	2	no	—
201	C₂²⋊C₄×C₁₉	—	2	2	no	—
202	C₂²⋊C₄×C₁₉	—	2	2	no	—
203	C₂²⋊C₄×C₁₉	—	2	2	no	—
204	C₂²⋊C₄×C₁₉	—	2	1	no	—
205	C₂²⋊C₄×C₁₉	—	2	1	no	—
206	C₂²⋊C₄×C₁₉	—	2	1	no	—
207	C₂²⋊C₄×C₁₉	—	2	1	no	—
208	C₂²⋊C₄×C₁₉	—	2	1	no	—
209	C₂²⋊C₄×C₁₉	—	2	2	no	—
210	C₂²⋊C₄×C₁₉	—	2	1	no	—
211	C₂²⋊C₄×C₁₉	—	2	1	no	—
212	C₂²⋊C₄×C₁₉	—	2	2	no	—
213	C₄²×C₁₉	—	2	1	no	—
214	C₄²×C₁₉	—	2	1	no	—
215	C₄²×C₁₉	—	2	1	no	—
216	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
217	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
218	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
219	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
220	C₄⋊Dic₁₉	—	2	2	no	—
221	C₄⋊Dic₁₉	—	4	1	no	—
222	C₄×Dic₁₉	—	4	1	no	—
223	C₄×Dic₁₉	—	4	1	no	—
224	#64520	—	4	1	no	—
225	#64520	—	4	1	no	—
226	C₂×C₁₉⋊C₈	—	2	2	no	—
227	C₂×C₁₉⋊C₈	—	4	1	no	—
228	C₂×C₁₉⋊C₈	—	4	1	no	—
229	C₂×C₁₉⋊C₈	—	4	1	no	—
230	C₂×C₁₉⋊C₈	—	4	1	no	—
231	#8436	—	19	1	no	maximal, Sylow
232	C₂³×C₁₉	—	2	1	no	—
233	C₂³×C₁₉	—	2	1	no	—
234	C₂³×C₁₉	—	2	2	no	—
235	C₂³×C₁₉	—	2	1	no	—
236	C₂³×C₁₉	—	4	2	no	—
237	C₂³×C₁₉	—	4	4	no	—
238	C₂³×C₁₉	—	4	4	no	—
239	C₂³×C₁₉	—	4	1	no	—
240	C₂³×C₁₉	—	4	1	no	—
241	C₂³×C₁₉	—	8	1	no	—
242	C₂³×C₁₉	—	8	2	no	—
243	C₂³×C₁₉	#120	1	1	yes	characteristic
244	Q₈×C₁₉	—	2	1	no	—
245	Q₈×C₁₉	—	4	4	no	—
246	Q₈×C₁₉	—	4	1	no	—
247	Q₈×C₁₉	—	4	1	no	—
248	Q₈×C₁₉	#102	1	2	yes	complemented
249	D₄×C₁₉	—	2	2	no	—
250	D₄×C₁₉	—	2	2	no	—
251	D₄×C₁₉	—	2	1	no	—
252	D₄×C₁₉	—	2	1	no	—
253	D₄×C₁₉	—	2	1	no	—
254	D₄×C₁₉	—	2	1	no	—
255	D₄×C₁₉	—	4	2	no	—
256	D₄×C₁₉	—	4	2	no	—
257	D₄×C₁₉	—	4	4	no	—
258	D₄×C₁₉	—	4	4	no	—
259	D₄×C₁₉	—	4	4	no	—
260	D₄×C₁₉	—	4	4	no	—
261	D₄×C₁₉	—	4	2	no	—
262	D₄×C₁₉	—	4	2	no	—
263	D₄×C₁₉	—	4	1	no	—
264	D₄×C₁₉	—	4	1	no	—
265	D₄×C₁₉	—	4	1	no	—
266	D₄×C₁₉	—	4	1	no	—
267	D₄×C₁₉	—	8	2	no	—
268	D₄×C₁₉	#102	1	2	yes	complemented
269	D₄×C₁₉	#104	1	2	yes	complemented
270	C₂×C₄×C₁₉	—	2	1	no	—
271	C₂×C₄×C₁₉	—	2	1	no	—
272	C₂×C₄×C₁₉	—	2	1	no	—
273	C₂×C₄×C₁₉	—	2	2	no	—
274	C₂×C₄×C₁₉	—	2	2	no	—
275	C₂×C₄×C₁₉	—	2	1	no	—
276	C₂×C₄×C₁₉	—	2	1	no	—
277	C₂×C₄×C₁₉	—	2	1	no	—
278	C₂×C₄×C₁₉	—	2	2	no	—
279	C₂×C₄×C₁₉	—	2	1	no	—
280	C₂×C₄×C₁₉	—	4	1	no	—
281	C₂×C₄×C₁₉	—	4	4	no	—
282	C₂×C₄×C₁₉	—	4	4	no	—
283	C₂×C₄×C₁₉	—	4	4	no	—
284	C₂×C₄×C₁₉	—	4	1	no	—
285	C₂×C₄×C₁₉	—	4	1	no	—
286	C₂×C₄×C₁₉	—	4	1	no	—
287	C₂×C₄×C₁₉	—	4	1	no	—
288	C₂×C₄×C₁₉	—	4	1	no	—
289	C₂×C₄×C₁₉	—	4	1	no	—
290	C₂×C₄×C₁₉	—	4	1	no	—
291	C₂×C₄×C₁₉	—	4	1	no	—
292	C₂×C₄×C₁₉	—	4	1	no	—
293	C₂×C₄×C₁₉	—	4	2	no	—
294	C₂×C₄×C₁₉	—	4	1	no	—
295	C₂×C₄×C₁₉	—	4	1	no	—
296	C₂×C₄×C₁₉	—	4	2	no	—
297	C₂×C₄×C₁₉	—	4	1	no	—
298	C₂×C₄×C₁₉	—	8	1	no	—
299	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
300	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
301	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
302	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
303	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
304	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
305	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
306	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
307	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
308	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
309	C₂×Dic₁₉	—	4	2	no	—
310	C₂×Dic₁₉	—	8	1	no	—
311	C₂×Dic₁₉	—	8	1	no	—
312	C₁₉⋊C₈	—	4	2	no	—
313	C₁₉⋊C₈	—	8	1	no	—
314	C₁₉⋊C₈	—	8	1	no	—
315	D₄×#41	D₁₉	1	1	yes	characteristic
316	#1806	—	19	1	no	—
317	C₄×#102	—	19	1	no	—
318	#1502	—	19	1	no	—
319	#1492	—	19	1	no	—
320	#1486	—	19	1	no	—
321	#1476	—	19	1	no	—
322	C₂²×C₁₉	—	2	1	no	—
323	C₂²×C₁₉	—	2	1	no	—
324	C₂²×C₁₉	—	2	2	no	—
325	C₂²×C₁₉	—	2	2	no	—
326	C₂²×C₁₉	—	4	1	no	—
327	C₂²×C₁₉	—	4	1	no	—
328	C₂²×C₁₉	—	4	1	no	—
329	C₂²×C₁₉	—	4	1	no	—
330	C₂²×C₁₉	—	4	2	no	—
331	C₂²×C₁₉	—	4	1	no	—
332	C₂²×C₁₉	—	4	2	no	—
333	C₂²×C₁₉	—	4	1	no	—
334	C₂²×C₁₉	—	4	1	no	—
335	C₂²×C₁₉	—	4	2	no	—
336	C₂²×C₁₉	—	8	2	no	—
337	C₂²×C₁₉	—	8	2	no	—
338	C₂²×C₁₉	—	8	8	no	—
339	C₂²×C₁₉	#379	1	1	yes	characteristic
340	C₂²×C₁₉	#447	1	1	yes	characteristic
341	C₂²×C₁₉	#450	1	1	yes	characteristic
342	C₄×C₁₉	—	2	1	no	—
343	C₄×C₁₉	—	2	1	no	—
344	C₄×C₁₉	—	2	2	no	—
345	C₄×C₁₉	—	2	1	no	—
346	C₄×C₁₉	—	4	1	no	—
347	C₄×C₁₉	—	4	1	no	—
348	C₄×C₁₉	—	4	2	no	—
349	C₄×C₁₉	—	4	1	no	—
350	C₄×C₁₉	—	4	1	no	—
351	C₄×C₁₉	C₂×#102	1	1	yes	characteristic
352	C₄×C₁₉	#418	1	1	yes	characteristic
353	C₄×C₁₉	C₂×#104	1	1	yes	characteristic
354	C₄×C₁₉	#421	1	1	yes	characteristic
355	C₄×C₁₉	#447	1	1	yes	characteristic
356	C₄×C₁₉	#450	1	1	yes	characteristic
357	Dic₁₉	—	8	2	no	—
358	C₂²×#41	—	2	1	no	—
359	#550	Dic₁₉	1	1	yes	characteristic, complemented
360	D₄×Q₈	Dic₁₉	1	1	yes	characteristic, complemented
361	#548	—	2	1	no	—
362	#547	—	2	1	no	—
363	#547	Dic₁₉	1	1	yes	characteristic, complemented
364	#546	—	2	2	no	—
365	#546	—	2	1	no	—
366	D₄²	—	2	1	no	—
367	D₄²	Dic₁₉	1	1	yes	characteristic, complemented
368	#532	—	2	1	no	—
369	#532	C₂×D₁₉	1	1	yes	characteristic
370	#525	—	2	2	no	—
371	#525	—	2	1	no	—
372	C₄×#41	C₂×D₁₉	1	1	yes	characteristic
373	C₂×C₄×D₄	—	2	1	no	—
374	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
375	#431	—	19	1	no	—
376	#423	—	19	1	no	—
377	C₂×#104	—	38	1	no	—
378	C₂×#102	—	38	1	no	—
379	C₂×C₄×C₈	—	19	1	no	—
380	C₄×C₄⋊C₄	—	19	1	no	—
381	#340	—	38	1	no	—
382	#339	—	38	1	no	—
383	#327	—	38	2	no	—
384	Q₈⋊C₈	—	38	1	no	—
385	D₄⋊C₈	—	38	1	no	—
386	D₄⋊C₈	—	38	1	no	—
387	D₄⋊C₈	—	38	1	no	—
388	D₄⋊C₈	—	38	2	no	—
389	C₂×C₁₉	—	2	1	no	—
390	C₂×C₁₉	—	2	1	no	—
391	C₂×C₁₉	—	4	2	no	—
392	C₂×C₁₉	—	4	2	no	—
393	C₂×C₁₉	—	8	2	no	—
394	C₂×C₁₉	—	8	1	no	—
395	C₂×C₁₉	#1786	1	1	yes	characteristic
396	C₂×C₁₉	#1789	1	1	yes	characteristic
397	C₂×C₁₉	#1794	1	1	yes	characteristic
398	C₂×#41	—	2	2	no	—
399	C₂×#41	—	2	2	no	—
400	C₂×#41	—	2	1	no	—
401	C₂×#41	—	2	1	no	—
402	C₂×#41	—	2	1	no	—
403	C₂×#41	—	4	2	no	—
404	C₂×#41	—	4	2	no	—
405	C₂×#41	—	4	2	no	—
406	C₂×#41	—	4	2	no	—
407	C₂×#41	C₂²⋊D₁₉	1	1	yes	characteristic
408	C₂²×Q₈	—	2	1	no	—
409	C₂²×D₄	—	2	2	no	—
410	C₂²×D₄	—	2	1	no	—
411	C₂²×D₄	—	2	1	no	—
412	C₂²×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
413	C₂³×C₄	—	2	2	no	—
414	C₂³×C₄	—	2	1	no	—
415	C₂×M₁₆	—	38	1	no	—
416	C₂²×C₈	—	38	1	no	—
417	C₄⋊Q₈	—	2	1	no	—
418	C₄⋊Q₈	C₂×Dic₁₉	1	1	yes	characteristic
419	#127	—	2	1	no	—
420	#127	C₂×Dic₁₉	1	1	yes	characteristic
421	#124	—	2	2	no	—
422	#124	—	2	1	no	—
423	#123	—	2	2	no	—
424	#123	—	2	2	no	—
425	#123	—	2	2	no	—
426	C₂²⋊Q₈	—	2	2	no	—
427	C₂²⋊Q₈	—	2	1	no	—
428	C₂²⋊Q₈	—	2	2	no	—
429	C₂²⋊Q₈	—	2	1	no	—
430	#121	—	2	2	no	—
431	#121	—	2	2	no	—
432	#121	—	2	2	no	—
433	#121	—	2	1	no	—
434	#121	—	2	1	no	—
435	#121	—	2	1	no	—
436	#121	—	2	1	no	—
437	#121	—	2	1	no	—
438	#121	C₂²⋊D₁₉	1	2	yes	—
439	#120	—	2	2	no	—
440	#120	—	2	2	no	—
441	#120	—	2	2	no	—
442	C₄×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
443	C₄×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
444	C₄×D₄	—	2	2	no	—
445	C₄×D₄	—	2	2	no	—
446	C₄×D₄	—	2	2	no	—
447	C₄×D₄	—	2	1	no	—
448	C₄×D₄	—	2	1	no	—
449	C₄×D₄	—	2	1	no	—
450	C₄×D₄	—	2	1	no	—
451	C₄×D₄	—	2	1	no	—
452	C₄×D₄	—	2	1	no	—
453	C₄×D₄	—	2	1	no	—
454	C₄×D₄	C₂×Dic₁₉	1	1	yes	characteristic
455	C₄×D₄	C₂×Dic₁₉	1	1	yes	characteristic
456	C₄×D₄	C₂×Dic₁₉	1	1	yes	characteristic
457	C₄×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
458	C₄×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
459	C₄×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
460	C₄×D₄	C₂²⋊D₁₉	1	2	yes	—
461	#117	—	2	1	no	—
462	#117	C₂²⋊D₁₉	1	1	yes	characteristic
463	C₂×C₄⋊C₄	—	2	1	no	—
464	C₂×C₄⋊C₄	—	38	1	no	—
465	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
466	C₂×C₂²⋊C₄	—	2	2	no	—
467	C₂×C₂²⋊C₄	—	2	1	no	—
468	C₂×C₄²	—	2	1	no	—
469	C₂×C₄²	—	38	1	no	—
470	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
471	C₄⋊C₈	—	38	1	no	—
472	C₄⋊C₈	—	38	1	no	—
473	C₄⋊C₈	—	38	1	no	—
474	#104	—	76	2	no	—
475	#102	—	38	4	no	—
476	C₂²⋊C₈	—	38	1	no	—
477	C₄×C₈	—	38	1	no	—
478	C₄×C₈	—	38	1	no	—
479	C₄×C₈	—	38	1	no	—
480	#95	—	38	1	no	—
481	C₁₉	#8436	1	1	yes	characteristic, complemented, Sylow
482	C₂⁴	—	2	2	no	—
483	C₂⁴	—	2	1	no	—
484	#41	—	2	1	no	—
485	#41	—	2	1	no	—
486	#41	—	4	4	no	—
487	#41	—	4	4	no	—
488	#41	—	4	4	no	—
489	#41	—	4	4	no	—
490	#41	—	4	2	no	—
491	#41	—	4	2	no	—
492	#41	—	4	2	no	—
493	#41	—	4	2	no	—
494	#41	—	4	1	no	—
495	#41	—	4	1	no	—
496	#41	—	4	1	no	—
497	#41	—	4	1	no	—
498	#41	#64525	1	2	yes	—
499	#41	#64526	1	2	yes	—
500	C₂×Q₈	—	2	2	no	—
501	C₂×Q₈	—	2	1	no	—
502	C₂×Q₈	—	4	2	no	—
503	C₂×Q₈	—	4	2	no	—
504	C₂×Q₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
505	C₂×D₄	—	2	1	no	—
506	C₂×D₄	—	2	2	no	—
507	C₂×D₄	—	2	2	no	—
508	C₂×D₄	—	2	2	no	—
509	C₂×D₄	—	2	2	no	—
510	C₂×D₄	—	2	2	no	—
511	C₂×D₄	—	2	2	no	—
512	C₂×D₄	—	2	2	no	—
513	C₂×D₄	—	2	1	no	—
514	C₂×D₄	—	2	1	no	—
515	C₂×D₄	—	2	1	no	—
516	C₂×D₄	—	4	1	no	—
517	C₂×D₄	—	4	2	no	—
518	C₂×D₄	—	4	4	no	—
519	C₂×D₄	—	4	4	no	—
520	C₂×D₄	—	4	2	no	—
521	C₂×D₄	—	4	2	no	—
522	C₂×D₄	—	4	2	no	—
523	C₂×D₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
524	C₂×D₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
525	C₂×D₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
526	C₂×D₄	C₂²⋊Dic₁₉	1	2	yes	—
527	C₂²×C₄	—	2	1	no	—
528	C₂²×C₄	—	2	2	no	—
529	C₂²×C₄	—	2	2	no	—
530	C₂²×C₄	—	2	2	no	—
531	C₂²×C₄	—	2	1	no	—
532	C₂²×C₄	—	2	1	no	—
533	C₂²×C₄	—	2	1	no	—
534	C₂²×C₄	—	2	1	no	—
535	C₂²×C₄	—	2	1	no	—
536	C₂²×C₄	—	2	2	no	—
537	C₂²×C₄	—	2	1	no	—
538	C₂²×C₄	—	2	1	no	—
539	C₂²×C₄	—	4	4	no	—
540	C₂²×C₄	—	4	4	no	—
541	C₂²×C₄	—	4	1	no	—
542	C₂²×C₄	—	4	1	no	—
543	C₂²×C₄	—	4	1	no	—
544	C₂²×C₄	—	4	1	no	—
545	C₂²×C₄	—	76	1	no	—
546	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
547	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
548	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
549	M₁₆	—	76	1	no	—
550	M₁₆	—	76	1	no	—
551	C₂×C₈	—	38	2	no	—
552	C₂×C₈	—	76	1	no	—
553	C₂×C₈	—	76	1	no	—
554	C₂×C₈	—	76	1	no	—
555	C₂×C₈	—	76	1	no	—
556	C₄⋊C₄	—	2	2	no	—
557	C₄⋊C₄	—	2	2	no	—
558	C₄⋊C₄	—	2	1	no	—
559	C₄⋊C₄	—	2	1	no	—
560	C₄⋊C₄	—	2	1	no	—
561	C₄⋊C₄	—	2	1	no	—
562	C₄⋊C₄	—	38	2	no	—
563	C₄⋊C₄	—	76	1	no	—
564	C₄⋊C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
565	C₄⋊C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
566	C₄⋊C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
567	C₄⋊C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
568	C₄⋊C₄	C₂²⋊Dic₁₉	1	2	yes	—
569	C₂²⋊C₄	—	2	2	no	—
570	C₂²⋊C₄	—	2	2	no	—
571	C₂²⋊C₄	—	2	2	no	—
572	C₂²⋊C₄	—	2	2	no	—
573	C₂²⋊C₄	—	2	1	no	—
574	C₂²⋊C₄	—	2	1	no	—
575	C₂²⋊C₄	—	2	1	no	—
576	C₂²⋊C₄	—	2	1	no	—
577	C₂²⋊C₄	—	2	1	no	—
578	C₂²⋊C₄	—	2	2	no	—
579	C₂²⋊C₄	—	2	1	no	—
580	C₂²⋊C₄	—	2	1	no	—
581	C₂²⋊C₄	—	2	2	no	—
582	C₄²	—	2	1	no	—
583	C₄²	—	2	1	no	—
584	C₄²	—	2	1	no	—
585	C₄²	—	76	1	no	—
586	C₄²	—	76	1	no	—
587	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
588	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
589	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
590	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
591	C₂³	—	2	1	no	—
592	C₂³	—	2	1	no	—
593	C₂³	—	2	2	no	—
594	C₂³	—	2	1	no	—
595	C₂³	—	4	2	no	—
596	C₂³	—	4	4	no	—
597	C₂³	—	4	4	no	—
598	C₂³	—	4	1	no	—
599	C₂³	—	4	1	no	—
600	C₂³	—	8	1	no	—
601	C₂³	—	8	2	no	—
602	C₂³	#10597399	1	1	yes	characteristic
603	Q₈	—	2	1	no	—
604	Q₈	—	4	4	no	—
605	Q₈	—	4	1	no	—
606	Q₈	—	4	1	no	—
607	Q₈	#10597289	1	2	yes	complemented
608	D₄	—	2	2	no	—
609	D₄	—	2	2	no	—
610	D₄	—	2	1	no	—
611	D₄	—	2	1	no	—
612	D₄	—	2	1	no	—
613	D₄	—	2	1	no	—
614	D₄	—	4	2	no	—
615	D₄	—	4	2	no	—
616	D₄	—	4	4	no	—
617	D₄	—	4	4	no	—
618	D₄	—	4	4	no	—
619	D₄	—	4	4	no	—
620	D₄	—	4	2	no	—
621	D₄	—	4	2	no	—
622	D₄	—	4	1	no	—
623	D₄	—	4	1	no	—
624	D₄	—	4	1	no	—
625	D₄	—	4	1	no	—
626	D₄	—	8	2	no	—
627	D₄	#10597289	1	2	yes	complemented
628	D₄	#10597294	1	2	yes	complemented
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	2	no	—
633	C₂×C₄	—	2	2	no	—
634	C₂×C₄	—	2	1	no	—
635	C₂×C₄	—	2	1	no	—
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	1	no	—
639	C₂×C₄	—	4	1	no	—
640	C₂×C₄	—	4	4	no	—
641	C₂×C₄	—	4	4	no	—
642	C₂×C₄	—	4	4	no	—
643	C₂×C₄	—	4	1	no	—
644	C₂×C₄	—	4	1	no	—
645	C₂×C₄	—	4	1	no	—
646	C₂×C₄	—	4	1	no	—
647	C₂×C₄	—	4	1	no	—
648	C₂×C₄	—	4	1	no	—
649	C₂×C₄	—	4	1	no	—
650	C₂×C₄	—	4	1	no	—
651	C₂×C₄	—	4	1	no	—
652	C₂×C₄	—	4	2	no	—
653	C₂×C₄	—	4	1	no	—
654	C₂×C₄	—	4	1	no	—
655	C₂×C₄	—	4	2	no	—
656	C₂×C₄	—	4	1	no	—
657	C₂×C₄	—	8	1	no	—
658	C₂×C₄	—	76	2	no	—
659	C₂×C₄	—	152	1	no	—
660	C₂×C₄	—	152	1	no	—
661	C₂×C₄	C₂×#64525	1	1	yes	characteristic
662	C₂×C₄	#10597378	1	1	yes	characteristic
663	C₂×C₄	#10597378	1	1	yes	characteristic
664	C₂×C₄	C₂×#64526	1	1	yes	characteristic
665	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
666	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
667	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
668	C₂×C₄	#10597399	1	1	yes	characteristic
669	C₂×C₄	#10597399	1	1	yes	characteristic
670	C₂×C₄	#10597399	1	1	yes	characteristic
671	C₈	—	76	2	no	—
672	C₈	—	152	1	no	—
673	C₈	—	152	1	no	—
674	C₂²	—	2	1	no	—
675	C₂²	—	2	1	no	—
676	C₂²	—	2	2	no	—
677	C₂²	—	2	2	no	—
678	C₂²	—	4	1	no	—
679	C₂²	—	4	1	no	—
680	C₂²	—	4	1	no	—
681	C₂²	—	4	1	no	—
682	C₂²	—	4	2	no	—
683	C₂²	—	4	1	no	—
684	C₂²	—	4	2	no	—
685	C₂²	—	4	1	no	—
686	C₂²	—	4	1	no	—
687	C₂²	—	4	2	no	—
688	C₂²	—	8	2	no	—
689	C₂²	—	8	2	no	—
690	C₂²	—	8	8	no	—
691	C₂²	#11926400	1	1	yes	characteristic
692	C₂²	#11926678	1	1	yes	characteristic
693	C₂²	#11926695	1	1	yes	characteristic
694	C₄	—	2	1	no	—
695	C₄	—	2	1	no	—
696	C₄	—	2	2	no	—
697	C₄	—	2	1	no	—
698	C₄	—	4	1	no	—
699	C₄	—	4	1	no	—
700	C₄	—	4	2	no	—
701	C₄	—	4	1	no	—
702	C₄	—	4	1	no	—
703	C₄	—	152	2	no	—
704	C₄	C₂×#10597289	1	1	yes	characteristic
705	C₄	#11926549	1	1	yes	characteristic
706	C₄	C₂×#10597294	1	1	yes	characteristic
707	C₄	#11926561	1	1	yes	characteristic
708	C₄	#11926678	1	1	yes	characteristic
709	C₄	#11926695	1	1	yes	characteristic
710	C₂	—	2	1	no	—
711	C₂	—	2	1	no	—
712	C₂	—	4	2	no	—
713	C₂	—	4	2	no	—
714	C₂	—	8	2	no	—
715	C₂	—	8	1	no	—
716	C₂	#14563566	1	1	yes	characteristic
717	C₂	#14563579	1	1	yes	characteristic
718	C₂	#14563599	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#10597399
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting, prime radical	D₄×#41×C₁₉	C₂
socle	C₂²×C₁₉	#379
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	D₄×#41	D₁₉
hypocenter	C₁₉	#8436
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ D₄×#41

Complements

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

N	H ≅ G/N	type
1. #14563655	C₂	semidirect
2. C₄×#10597289	C₂	semidirect
3. #14562130	C₂	semidirect
4. #14562086	C₂	semidirect
5. #14562060	C₂	semidirect
6. #14562017	C₂	semidirect
8. #11926597	C₂²	semidirect
9. #11926568	C₂²	semidirect
12. C₂×C₄×C₁₉⋊C₈	C₂²	semidirect
13. C₄×C₄⋊Dic₁₉	C₂²	semidirect
23. C₁₉×#550	C₄	semidirect
24. D₄×Q₈×C₁₉	C₄	semidirect
27. C₁₉×#547	C₄	semidirect
31. D₄²×C₁₉	C₄	semidirect
248. Q₈×C₁₉	#102	semidirect
268. D₄×C₁₉	#102	semidirect
269. D₄×C₁₉	#104	semidirect
359. #550	Dic₁₉	semidirect
360. D₄×Q₈	Dic₁₉	semidirect
363. #547	Dic₁₉	semidirect
367. D₄²	Dic₁₉	semidirect
481. C₁₉	#8436	semidirect
607. Q₈	#10597289	semidirect
627. D₄	#10597289	semidirect
628. D₄	#10597294	semidirect

Maximal subgroups

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

subgroup	index
#14563655	2
C₄×#10597289	2
#14562130	2
#14562086	2
#14562060	2
#14562017	2
D₄×#41×C₁₉	2
#8436	19