Subgroups — #18088641

Order 4864.

834 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926587	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926313	C₂	1	1	yes	maximal, characteristic
3	#14563356	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926303	C₂	1	1	yes	maximal, characteristic
5	C₂×#11926303	C₂	1	1	yes	maximal, characteristic
6	#14561864	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#2274	C₂	1	1	yes	maximal, characteristic
8	C₂²×#64520	C₂²	1	1	yes	characteristic
9	C₂²×#64520	C₂²	1	1	yes	characteristic
10	C₂²×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
11	C₂²×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
12	#11926587	—	2	2	no	—
13	#11926587	C₄	1	4	yes	complemented
14	C₂×#10597264	—	2	1	no	—
15	C₂×#10597265	—	2	1	no	—
16	C₂×C₁₉⋊#95	—	2	2	no	—
17	#11926313	C₄	1	4	yes	complemented
18	#11926306	—	2	1	no	—
19	#11926306	—	2	1	no	—
20	#11926303	—	2	2	no	—
21	#11926303	C₄	1	4	yes	complemented
22	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
24	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
25	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
26	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
27	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
28	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
29	C₄×C₂²⋊C₄×C₁₉	—	2	2	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	C₁₉×#117	—	2	1	no	—
35	C₁₉×#117	—	2	1	no	—
36	C₁₉×#117	—	2	1	no	—
37	C₁₉×#117	—	2	1	no	—
38	C₁₉×#117	C₂×C₄	1	2	yes	—
39	C₁₉×#117	C₂×C₄	1	2	yes	—
40	C₁₉×#117	D₄	1	2	yes	—
41	C₁₉×#117	Q₈	1	2	yes	—
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	C₂×C₄	1	2	yes	—
47	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
48	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
49	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
50	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
51	C₂×C₄⋊C₄×C₁₉	Q₈	1	2	yes	—
52	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
53	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
54	C₂×C₄²×C₁₉	—	2	1	no	—
55	C₂×C₄²×C₁₉	—	2	1	no	—
56	C₂×C₄²×C₁₉	—	2	2	no	—
57	C₂×C₄²×C₁₉	—	2	2	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	—	2	1	no	—
65	C₂×C₄×Dic₁₉	—	2	1	no	—
66	C₂×C₄×Dic₁₉	—	2	1	no	—
67	C₂×C₄×Dic₁₉	—	2	1	no	—
68	C₂×C₄×Dic₁₉	—	2	1	no	—
69	C₂×C₄×Dic₁₉	C₂×C₄	1	2	yes	—
70	C₂×#64520	—	2	1	no	—
71	C₂×#64520	—	2	1	no	—
72	C₂×#64520	—	2	1	no	—
73	C₂×#64520	—	2	1	no	—
74	C₂×#64520	—	2	1	no	—
75	C₂×#64520	—	2	1	no	—
76	C₂×#64520	—	2	1	no	—
77	C₂×#64520	—	2	1	no	—
78	C₂×#64520	C₂×C₄	1	2	yes	—
79	C₂×#64520	C₂×C₄	1	2	yes	—
80	C₂×#64520	C₂×C₄	1	2	yes	—
81	C₂×#64520	C₂×C₄	1	2	yes	—
82	C₂²×C₁₉⋊C₈	—	2	1	no	—
83	C₂²×C₁₉⋊C₈	—	2	1	no	—
84	C₁₉×#95	—	2	2	no	—
85	C₁₉×#95	—	2	2	no	—
86	C₁₉⋊#95	—	4	4	no	—
87	#10597265	—	2	4	no	—
88	#10597264	—	2	4	no	—
89	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₉	—	2	1	no	—
91	C₂²×C₄×C₁₉	—	2	1	no	—
92	C₂²×C₄×C₁₉	—	2	1	no	—
93	C₂²×C₄×C₁₉	—	2	1	no	—
94	C₂²×C₄×C₁₉	—	2	2	no	—
95	C₂²×C₄×C₁₉	—	2	2	no	—
96	C₂²×C₄×C₁₉	—	4	2	no	—
97	C₂²×C₄×C₁₉	—	4	2	no	—
98	C₂²×C₄×C₁₉	C₄⋊C₄	1	4	yes	—
99	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
106	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
107	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
108	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
109	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
110	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
111	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
112	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
113	C₂²×Dic₁₉	—	2	2	no	—
114	C₂²×Dic₁₉	—	2	2	no	—
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	1	no	—
124	C₂²×Dic₁₉	—	4	1	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	—	2	1	no	—
130	C₄⋊C₄×C₁₉	—	2	1	no	—
131	C₄⋊C₄×C₁₉	—	2	1	no	—
132	C₄⋊C₄×C₁₉	—	2	1	no	—
133	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
134	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
135	C₄⋊C₄×C₁₉	C₄⋊C₄	1	2	yes	—
136	C₄⋊C₄×C₁₉	C₄⋊C₄	1	2	yes	—
137	C₂²⋊C₄×C₁₉	—	2	2	no	—
138	C₂²⋊C₄×C₁₉	—	2	2	no	—
139	C₂²⋊C₄×C₁₉	—	2	2	no	—
140	C₂²⋊C₄×C₁₉	—	2	2	no	—
141	C₄²×C₁₉	—	2	2	no	—
142	C₄²×C₁₉	—	2	2	no	—
143	C₄²×C₁₉	—	2	2	no	—
144	C₄²×C₁₉	—	2	2	no	—
145	C₄²×C₁₉	—	8	2	no	—
146	C₄²×C₁₉	—	8	2	no	—
147	C₄⋊Dic₁₉	—	2	2	no	—
148	C₄⋊Dic₁₉	—	2	2	no	—
149	C₄⋊Dic₁₉	—	4	1	no	—
150	C₄⋊Dic₁₉	—	4	1	no	—
151	C₄×Dic₁₉	—	2	2	no	—
152	C₄×Dic₁₉	—	2	2	no	—
153	C₄×Dic₁₉	—	4	1	no	—
154	C₄×Dic₁₉	—	4	1	no	—
155	#64520	—	2	2	no	—
156	#64520	—	2	2	no	—
157	#64520	—	2	2	no	—
158	#64520	—	2	2	no	—
159	#64520	—	2	2	no	—
160	#64520	—	4	1	no	—
161	#64520	—	4	1	no	—
162	#64520	C₄²	1	4	yes	complemented
163	C₂×C₁₉⋊C₈	—	2	2	no	—
164	C₂×C₁₉⋊C₈	—	2	2	no	—
165	C₂×C₁₉⋊C₈	—	2	2	no	—
166	C₂×C₁₉⋊C₈	—	2	2	no	—
167	C₂×C₁₉⋊C₈	—	4	1	no	—
168	C₂×C₁₉⋊C₈	—	4	1	no	—
169	#10899	—	19	1	no	maximal, Sylow
170	C₂³×C₁₉	—	2	1	no	—
171	C₂³×C₁₉	—	2	1	no	—
172	C₂³×C₁₉	—	2	1	no	—
173	C₂³×C₁₉	—	2	1	no	—
174	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
175	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
176	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
177	C₂³×C₁₉	#120	1	1	yes	characteristic
178	C₂³×C₁₉	#121	1	1	yes	characteristic
179	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
180	C₂³×C₁₉	#123	1	1	yes	characteristic
181	C₂×C₄×C₁₉	—	2	2	no	—
182	C₂×C₄×C₁₉	—	2	2	no	—
183	C₂×C₄×C₁₉	—	2	4	no	—
184	C₂×C₄×C₁₉	—	2	2	no	—
185	C₂×C₄×C₁₉	—	2	2	no	—
186	C₂×C₄×C₁₉	—	4	1	no	—
187	C₂×C₄×C₁₉	—	4	1	no	—
188	C₂×C₄×C₁₉	—	4	2	no	—
189	C₂×C₄×C₁₉	—	4	1	no	—
190	C₂×C₄×C₁₉	—	4	1	no	—
191	C₂×C₄×C₁₉	—	4	1	no	—
192	C₂×C₄×C₁₉	—	4	1	no	—
193	C₂×C₄×C₁₉	—	4	2	no	—
194	C₂×C₄×C₁₉	—	4	1	no	—
195	C₂×C₄×C₁₉	—	4	1	no	—
196	C₂×C₄×C₁₉	—	4	4	no	—
197	C₂×C₄×C₁₉	—	8	2	no	—
198	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
199	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
200	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
201	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
202	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
203	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
204	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
205	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
206	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
207	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
208	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
209	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
210	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
211	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
212	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
213	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
214	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
215	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
216	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
217	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
218	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
219	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
220	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
221	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
222	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
223	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
224	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
225	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
226	C₂×Dic₁₉	—	2	4	no	—
227	C₂×Dic₁₉	—	4	2	no	—
228	C₂×Dic₁₉	—	4	2	no	—
229	C₂×Dic₁₉	—	4	2	no	—
230	C₂×Dic₁₉	—	4	2	no	—
231	C₂×Dic₁₉	—	4	2	no	—
232	C₂×Dic₁₉	—	4	2	no	—
233	C₂×Dic₁₉	—	4	4	no	—
234	C₂×Dic₁₉	—	4	2	no	—
235	C₂×Dic₁₉	—	8	2	no	—
236	C₂×Dic₁₉	—	8	1	no	—
237	C₂×Dic₁₉	—	8	1	no	—
238	C₁₉⋊C₈	—	2	4	no	—
239	C₁₉⋊C₈	—	4	2	no	—
240	C₂×#428	—	19	1	no	—
241	#2274	D₁₉	1	1	yes	characteristic
242	C₂×#343	—	19	1	no	—
243	#1736	—	19	1	no	—
244	C₂×#339	—	19	1	no	—
245	C₂×#339	—	19	1	no	—
246	C₄⋊#95	—	19	1	no	—
247	C₂²×C₁₉	—	2	1	no	—
248	C₂²×C₁₉	—	2	1	no	—
249	C₂²×C₁₉	—	2	1	no	—
250	C₂²×C₁₉	—	2	1	no	—
251	C₂²×C₁₉	—	2	1	no	—
252	C₂²×C₁₉	—	2	1	no	—
253	C₂²×C₁₉	—	2	1	no	—
254	C₂²×C₁₉	—	2	1	no	—
255	C₂²×C₁₉	—	2	1	no	—
256	C₂²×C₁₉	—	2	1	no	—
257	C₂²×C₁₉	—	2	1	no	—
258	C₂²×C₁₉	—	2	1	no	—
259	C₂²×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
260	C₂²×C₁₉	#385	1	1	yes	characteristic
261	C₂²×C₁₉	#385	1	1	yes	characteristic
262	C₂²×C₁₉	#386	1	1	yes	characteristic
263	C₂²×C₁₉	#387	1	1	yes	characteristic
264	C₂²×C₁₉	#388	1	1	yes	characteristic
265	C₂²×C₁₉	#389	1	1	yes	characteristic
266	C₂²×C₁₉	#453	1	1	yes	characteristic
267	C₂²×C₁₉	#454	1	1	yes	characteristic
268	C₂²×C₁₉	#455	1	1	yes	characteristic
269	C₂²×C₁₉	#456	1	1	yes	characteristic
270	C₄×C₁₉	—	4	4	no	—
271	C₄×C₁₉	—	4	2	no	—
272	C₄×C₁₉	—	4	2	no	—
273	C₄×C₁₉	—	4	2	no	—
274	C₄×C₁₉	—	4	2	no	—
275	C₄×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
276	C₄×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
277	C₄×C₁₉	#387	1	1	yes	characteristic
278	C₄×C₁₉	#387	1	1	yes	characteristic
279	C₄×C₁₉	#387	1	1	yes	characteristic
280	C₄×C₁₉	#388	1	1	yes	characteristic
281	C₄×C₁₉	#389	1	1	yes	characteristic
282	C₄×C₁₉	#391	1	1	yes	characteristic
283	Dic₁₉	—	4	4	no	—
284	Dic₁₉	—	8	2	no	—
285	C₂²×M₁₆	—	19	1	no	—
286	C₂²×M₁₆	—	19	1	no	—
287	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
288	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
289	C₂²×C₄⋊C₄	—	19	1	no	—
290	C₂²×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
291	C₂²×C₄²	—	19	1	no	—
292	#428	—	19	4	no	—
293	#428	—	38	2	no	—
294	C₂×#107	—	38	1	no	—
295	C₂×#106	—	38	1	no	—
296	C₄×C₄⋊C₄	—	2	1	no	—
297	C₄×C₄⋊C₄	—	2	1	no	—
298	C₄×C₄⋊C₄	—	2	1	no	—
299	C₄×C₄⋊C₄	—	2	1	no	—
300	C₄×C₂²⋊C₄	—	2	2	no	—
301	C₂×#95	—	38	2	no	—
302	#343	—	19	4	no	—
303	#340	—	38	1	no	—
304	#340	—	38	1	no	—
305	#339	—	19	4	no	—
306	#339	—	38	2	no	—
307	C₂×C₁₉	—	2	1	no	—
308	C₂×C₁₉	—	2	1	no	—
309	C₂×C₁₉	—	2	1	no	—
310	C₂×C₁₉	—	2	1	no	—
311	C₂×C₁₉	#1436	1	1	yes	characteristic
312	C₂×C₁₉	#1856	1	1	yes	characteristic
313	C₂×C₁₉	#1857	1	1	yes	characteristic
314	C₂×C₁₉	#1859	1	1	yes	characteristic
315	C₂×C₁₉	#1860	1	1	yes	characteristic
316	C₂×C₁₉	#1882	1	1	yes	characteristic
317	C₂×C₁₉	#1883	1	1	yes	characteristic
318	C₂³×C₄	—	38	1	no	—
319	C₂³×C₄	—	38	1	no	—
320	C₂³×C₄	C₂²⋊D₁₉	1	2	yes	—
321	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
322	C₂×M₁₆	—	19	2	no	—
323	C₂×M₁₆	—	19	2	no	—
324	C₂×M₁₆	—	19	2	no	—
325	C₂×M₁₆	—	19	2	no	—
326	C₂×M₁₆	—	38	1	no	—
327	C₂×M₁₆	—	38	1	no	—
328	C₂×M₁₆	—	38	1	no	—
329	C₂×M₁₆	—	38	1	no	—
330	C₂×M₁₆	—	38	1	no	—
331	C₂×M₁₆	—	38	1	no	—
332	C₂×M₁₆	—	38	1	no	—
333	C₂×M₁₆	—	38	1	no	—
334	C₂²×C₈	—	38	1	no	—
335	C₂²×C₈	—	38	1	no	—
336	#117	—	2	1	no	—
337	#117	—	2	1	no	—
338	#117	—	2	1	no	—
339	#117	—	2	1	no	—
340	#117	Dic₃₈	1	2	yes	—
341	#117	C₄×D₁₉	1	2	yes	—
342	#117	C₄×D₁₉	1	2	yes	—
343	#117	D₇₆	1	2	yes	—
344	C₂×C₄⋊C₄	—	2	1	no	—
345	C₂×C₄⋊C₄	—	2	1	no	—
346	C₂×C₄⋊C₄	—	2	1	no	—
347	C₂×C₄⋊C₄	—	2	1	no	—
348	C₂×C₄⋊C₄	—	19	2	no	—
349	C₂×C₄⋊C₄	—	38	1	no	—
350	C₂×C₄⋊C₄	—	38	1	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	Dic₃₈	1	2	yes	—
355	C₂×C₄⋊C₄	C₄×D₁₉	1	2	yes	—
356	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
357	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
358	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
359	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
360	C₂×C₂²⋊C₄	—	2	1	no	—
361	C₂×C₂²⋊C₄	—	2	1	no	—
362	C₂×C₄²	—	2	1	no	—
363	C₂×C₄²	—	2	1	no	—
364	C₂×C₄²	—	2	2	no	—
365	C₂×C₄²	—	2	2	no	—
366	C₂×C₄²	—	19	2	no	—
367	C₂×C₄²	—	38	1	no	—
368	C₂×C₄²	—	38	1	no	—
369	C₂×C₄²	—	38	1	no	—
370	C₂×C₄²	—	38	1	no	—
371	C₂×C₄²	—	38	1	no	—
372	#107	—	38	4	no	—
373	#106	—	38	4	no	—
374	#95	—	2	2	no	—
375	#95	—	2	2	no	—
376	#95	—	76	4	no	—
377	C₁₉	#10899	1	1	yes	characteristic, complemented, Sylow
378	C₂⁴	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	4	2	no	—
386	C₂²×C₄	—	4	2	no	—
387	C₂²×C₄	—	38	2	no	—
388	C₂²×C₄	—	38	2	no	—
389	C₂²×C₄	—	38	2	no	—
390	C₂²×C₄	—	38	2	no	—
391	C₂²×C₄	—	76	1	no	—
392	C₂²×C₄	—	76	1	no	—
393	C₂²×C₄	—	76	1	no	—
394	C₂²×C₄	—	76	1	no	—
395	C₂²×C₄	—	76	2	no	—
396	C₂²×C₄	—	76	2	no	—
397	C₂²×C₄	—	76	1	no	—
398	C₂²×C₄	—	76	1	no	—
399	C₂²×C₄	Dic₁₉⋊C₄	1	4	yes	—
400	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
401	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
402	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
403	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
404	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
405	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
406	C₂²×C₄	#64541	1	1	yes	characteristic
407	C₂²×C₄	#64541	1	1	yes	characteristic
408	C₂²×C₄	#64541	1	1	yes	characteristic
409	C₂²×C₄	#64541	1	1	yes	characteristic
410	C₂²×C₄	#64541	1	1	yes	characteristic
411	C₂²×C₄	#64541	1	1	yes	characteristic
412	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
413	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
414	M₁₆	—	19	4	no	—
415	M₁₆	—	38	2	no	—
416	M₁₆	—	38	2	no	—
417	M₁₆	—	38	2	no	—
418	M₁₆	—	38	2	no	—
419	M₁₆	—	38	2	no	—
420	M₁₆	—	76	1	no	—
421	M₁₆	—	76	1	no	—
422	C₂×C₈	—	38	2	no	—
423	C₂×C₈	—	38	2	no	—
424	C₂×C₈	—	38	2	no	—
425	C₂×C₈	—	38	2	no	—
426	C₂×C₈	—	76	1	no	—
427	C₂×C₈	—	76	1	no	—
428	C₄⋊C₄	—	2	2	no	—
429	C₄⋊C₄	—	2	2	no	—
430	C₄⋊C₄	—	2	2	no	—
431	C₄⋊C₄	—	2	2	no	—
432	C₄⋊C₄	—	2	1	no	—
433	C₄⋊C₄	—	2	1	no	—
434	C₄⋊C₄	—	2	1	no	—
435	C₄⋊C₄	—	2	1	no	—
436	C₄⋊C₄	—	38	2	no	—
437	C₄⋊C₄	—	38	2	no	—
438	C₄⋊C₄	—	76	1	no	—
439	C₄⋊C₄	—	76	1	no	—
440	C₄⋊C₄	Dic₁₉⋊C₄	1	2	yes	—
441	C₄⋊C₄	Dic₁₉⋊C₄	1	2	yes	—
442	C₄⋊C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
443	C₄⋊C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
444	C₂²⋊C₄	—	2	2	no	—
445	C₂²⋊C₄	—	2	2	no	—
446	C₂²⋊C₄	—	2	2	no	—
447	C₂²⋊C₄	—	2	2	no	—
448	C₄²	—	2	2	no	—
449	C₄²	—	2	2	no	—
450	C₄²	—	2	2	no	—
451	C₄²	—	2	2	no	—
452	C₄²	—	8	2	no	—
453	C₄²	—	8	2	no	—
454	C₄²	—	38	2	no	—
455	C₄²	—	38	2	no	—
456	C₄²	—	76	1	no	—
457	C₄²	—	76	1	no	—
458	C₂³	—	2	1	no	—
459	C₂³	—	2	1	no	—
460	C₂³	—	2	1	no	—
461	C₂³	—	2	1	no	—
462	C₂³	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
463	C₂³	#10597370	1	1	yes	characteristic
464	C₂³	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
465	C₂³	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
466	C₂³	#10597375	1	1	yes	characteristic
467	C₂³	#10597376	1	1	yes	characteristic
468	C₂³	#10597399	1	1	yes	characteristic
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	4	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	4	2	no	—
477	C₂×C₄	—	4	1	no	—
478	C₂×C₄	—	4	1	no	—
479	C₂×C₄	—	4	1	no	—
480	C₂×C₄	—	4	1	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	1	no	—
483	C₂×C₄	—	4	1	no	—
484	C₂×C₄	—	4	4	no	—
485	C₂×C₄	—	8	2	no	—
486	C₂×C₄	—	38	4	no	—
487	C₂×C₄	—	76	2	no	—
488	C₂×C₄	—	76	2	no	—
489	C₂×C₄	—	76	2	no	—
490	C₂×C₄	—	76	2	no	—
491	C₂×C₄	—	76	2	no	—
492	C₂×C₄	—	76	2	no	—
493	C₂×C₄	—	76	4	no	—
494	C₂×C₄	—	76	2	no	—
495	C₂×C₄	—	152	2	no	—
496	C₂×C₄	—	152	1	no	—
497	C₂×C₄	—	152	1	no	—
498	C₂×C₄	C₄×Dic₃₈	1	1	yes	characteristic
499	C₂×C₄	C₄×Dic₃₈	1	1	yes	characteristic
500	C₂×C₄	C₄×Dic₃₈	1	1	yes	characteristic
501	C₂×C₄	C₄×Dic₃₈	1	1	yes	characteristic
502	C₂×C₄	#10597315	1	1	yes	characteristic
503	C₂×C₄	#10597316	1	1	yes	characteristic
504	C₂×C₄	#10597316	1	1	yes	characteristic
505	C₂×C₄	C₄²×D₁₉	1	1	yes	characteristic
506	C₂×C₄	#10597318	1	1	yes	characteristic
507	C₂×C₄	#10597318	1	1	yes	characteristic
508	C₂×C₄	#10597318	1	1	yes	characteristic
509	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
510	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
511	C₂×C₄	#10597321	1	1	yes	characteristic
512	C₂×C₄	#10597322	1	1	yes	characteristic
513	C₂×C₄	#10597322	1	1	yes	characteristic
514	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
515	C₂×C₄	#10597370	1	1	yes	characteristic
516	C₂×C₄	#10597370	1	1	yes	characteristic
517	C₂×C₄	#10597370	1	1	yes	characteristic
518	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
519	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
520	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
521	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
522	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
523	C₂×C₄	#10597375	1	1	yes	characteristic
524	C₂×C₄	#10597375	1	1	yes	characteristic
525	C₂×C₄	#10597376	1	1	yes	characteristic
526	C₈	—	38	4	no	—
527	C₈	—	76	2	no	—
528	C₂²	—	2	1	no	—
529	C₂²	—	2	1	no	—
530	C₂²	—	2	1	no	—
531	C₂²	—	2	1	no	—
532	C₂²	—	2	1	no	—
533	C₂²	—	2	1	no	—
534	C₂²	—	2	1	no	—
535	C₂²	—	2	1	no	—
536	C₂²	—	2	1	no	—
537	C₂²	—	2	1	no	—
538	C₂²	—	2	1	no	—
539	C₂²	—	2	1	no	—
540	C₂²	C₄×Dic₁₉⋊C₄	1	1	yes	characteristic
541	C₂²	#11926417	1	1	yes	characteristic
542	C₂²	#11926417	1	1	yes	characteristic
543	C₂²	#11926423	1	1	yes	characteristic
544	C₂²	#11926428	1	1	yes	characteristic
545	C₂²	#11926435	1	1	yes	characteristic
546	C₂²	#11926442	1	1	yes	characteristic
547	C₂²	#11926712	1	1	yes	characteristic
548	C₂²	#11926717	1	1	yes	characteristic
549	C₂²	#11926722	1	1	yes	characteristic
550	C₂²	#11926727	1	1	yes	characteristic
551	C₄	—	4	4	no	—
552	C₄	—	4	2	no	—
553	C₄	—	4	2	no	—
554	C₄	—	4	2	no	—
555	C₄	—	4	2	no	—
556	C₄	—	76	4	no	—
557	C₄	—	152	2	no	—
558	C₄	C₄×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
559	C₄	C₄×Dic₁₉⋊C₄	1	1	yes	characteristic
560	C₄	#11926428	1	1	yes	characteristic
561	C₄	#11926428	1	1	yes	characteristic
562	C₄	#11926428	1	1	yes	characteristic
563	C₄	#11926435	1	1	yes	characteristic
564	C₄	#11926442	1	1	yes	characteristic
565	C₄	#11926450	1	1	yes	characteristic
566	C₂	—	2	1	no	—
567	C₂	—	2	1	no	—
568	C₂	—	2	1	no	—
569	C₂	—	2	1	no	—
570	C₂	#14561868	1	1	yes	characteristic
571	C₂	#14563845	1	1	yes	characteristic
572	C₂	#14563850	1	1	yes	characteristic
573	C₂	#14563861	1	1	yes	characteristic
574	C₂	#14563868	1	1	yes	characteristic
575	C₂	#14564004	1	1	yes	characteristic
576	C₂	#14564011	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597399
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₁₉×#2274	C₂
socle	C₂³×C₁₉	#120
prime radical	C₂⁴×C₁₉	C₂×D₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	#2274	D₁₉
hypocenter	C₁₉	#10899
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ #2274

Complements

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

N	H ≅ G/N	type
13. #11926587	C₄	semidirect
17. #11926313	C₄	semidirect
21. #11926303	C₄	semidirect
162. #64520	C₄²	semidirect
377. C₁₉	#10899	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926587	2
C₂×#11926313	2
#14563356	2
C₂×#11926303	2
#14561864	2
C₁₉×#2274	2
#10899	19