Subgroups — #18088989

Order 4864.

1014 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926553	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926451	C₂	1	1	yes	maximal, characteristic
3	#14565991	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926312	C₂	1	1	yes	maximal, characteristic
5	C₂×#11926305	C₂	1	1	yes	maximal, characteristic
6	C₂×#11926303	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₉×#419	C₂	1	1	yes	maximal, characteristic
8	C₂²×#64520	C₂²	1	1	yes	characteristic
9	C₂×#10597372	C₂²	1	1	yes	characteristic
10	C₂²×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
11	C₂²×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
12	#11926553	—	2	2	no	—
13	#11926553	C₄	1	4	yes	complemented
14	C₂×#10597292	—	2	2	no	—
15	#11926451	—	2	2	no	—
16	#11926451	C₄	1	4	yes	complemented
17	C₄⋊C₄×Dic₁₉	—	2	2	no	—
18	C₄×C₄⋊Dic₁₉	—	2	2	no	—
19	C₂²⋊C₄×Dic₁₉	—	2	2	no	—
20	C₂×C₁₉⋊#95	—	2	2	no	—
21	#11926312	—	2	2	no	—
22	#11926305	—	2	2	no	—
23	#11926303	—	2	2	no	—
24	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
25	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
27	C₁₉×#419	—	2	2	no	—
28	C₁₉×#419	C₄	1	4	yes	complemented
29	C₂×C₁₉×#103	—	2	2	no	—
30	C₂²×Q₈×C₁₉	—	2	1	no	—
31	C₂²×Q₈×C₁₉	—	2	1	no	—
32	C₂²×Q₈×C₁₉	—	2	1	no	—
33	C₂²×Q₈×C₁₉	—	2	1	no	—
34	C₂²×Q₈×C₁₉	—	2	1	no	—
35	C₂²×Q₈×C₁₉	—	2	1	no	—
36	C₂²×Q₈×C₁₉	—	2	1	no	—
37	C₂²×Q₈×C₁₉	—	2	1	no	—
38	C₂²×Q₈×C₁₉	—	2	1	no	—
39	C₂²×Q₈×C₁₉	—	2	1	no	—
40	C₂²×Q₈×C₁₉	—	2	1	no	—
41	C₂²×Q₈×C₁₉	C₂×C₄	1	2	yes	—
42	C₂²×Q₈×C₁₉	C₂×C₄	1	2	yes	—
43	C₂²×Q₈×C₁₉	C₂×C₄	1	2	yes	—
44	C₂³×C₄×C₁₉	—	2	1	no	—
45	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
46	C₂³×Dic₁₉	—	2	1	no	—
47	C₂³×Dic₁₉	D₄	1	2	yes	—
48	C₂×M₁₆×C₁₉	—	2	1	no	—
49	C₂×M₁₆×C₁₉	—	2	1	no	—
50	C₂×M₁₆×C₁₉	—	2	1	no	—
51	C₂×M₁₆×C₁₉	—	2	1	no	—
52	C₂×M₁₆×C₁₉	—	2	1	no	—
53	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
54	C₂²×C₈×C₁₉	—	2	1	no	—
55	C₁₉×#117	—	2	1	no	—
56	C₁₉×#117	—	2	1	no	—
57	C₁₉×#117	C₂×C₄	1	2	yes	—
58	C₁₉×#117	D₄	1	2	yes	—
59	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
60	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
61	C₂×C₄²×C₁₉	—	2	1	no	—
62	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
63	#10597372	—	2	1	no	—
64	#10597372	—	2	1	no	—
65	#10597372	C₂×C₄	1	2	yes	—
66	#10597372	D₄	1	2	yes	—
67	C₂×C₄⋊Dic₁₉	—	2	1	no	—
68	C₂×C₄⋊Dic₁₉	—	2	1	no	—
69	C₂×C₄⋊Dic₁₉	—	2	1	no	—
70	C₂×C₄⋊Dic₁₉	—	2	1	no	—
71	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
72	C₂×C₄⋊Dic₁₉	D₄	1	2	yes	—
73	C₂×C₄⋊Dic₁₉	D₄	1	2	yes	—
74	C₂×C₄×Dic₁₉	—	2	1	no	—
75	C₂×C₄×Dic₁₉	—	2	1	no	—
76	C₂×C₄×Dic₁₉	—	2	1	no	—
77	C₂×C₄×Dic₁₉	—	2	1	no	—
78	C₂×C₄×Dic₁₉	—	2	1	no	—
79	C₂×C₄×Dic₁₉	—	2	1	no	—
80	C₂×C₄×Dic₁₉	—	2	4	no	—
81	C₂×C₄×Dic₁₉	C₂×C₄	1	2	yes	—
82	C₂×#64520	—	2	1	no	—
83	C₂×#64520	—	2	1	no	—
84	C₂×#64520	—	2	1	no	—
85	C₂×#64520	—	2	1	no	—
86	C₂×#64520	—	2	1	no	—
87	C₂×#64520	C₂×C₄	1	2	yes	—
88	C₂²×C₁₉⋊C₈	—	2	1	no	—
89	C₁₉×#103	—	2	8	no	—
90	#10597292	—	2	8	no	—
91	C₁₉⋊#95	—	2	4	no	—
92	C₁₉⋊#95	—	2	8	no	—
93	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
94	C₂×Q₈×C₁₉	—	2	2	no	—
95	C₂×Q₈×C₁₉	—	2	2	no	—
96	C₂×Q₈×C₁₉	—	2	2	no	—
97	C₂×Q₈×C₁₉	—	2	2	no	—
98	C₂×Q₈×C₁₉	—	2	2	no	—
99	C₂×Q₈×C₁₉	—	2	2	no	—
100	C₂×Q₈×C₁₉	—	2	2	no	—
101	C₂×Q₈×C₁₉	—	2	2	no	—
102	C₂×Q₈×C₁₉	—	2	2	no	—
103	C₂×Q₈×C₁₉	—	2	2	no	—
104	C₂×Q₈×C₁₉	—	2	2	no	—
105	C₂×Q₈×C₁₉	—	2	2	no	—
106	C₂×Q₈×C₁₉	—	2	2	no	—
107	C₂×Q₈×C₁₉	—	2	2	no	—
108	C₂×Q₈×C₁₉	—	2	2	no	—
109	C₂×Q₈×C₁₉	—	4	1	no	—
110	C₂×Q₈×C₁₉	—	4	1	no	—
111	C₂×Q₈×C₁₉	—	4	1	no	—
112	C₂×Q₈×C₁₉	—	4	1	no	—
113	C₂×Q₈×C₁₉	—	4	1	no	—
114	C₂×Q₈×C₁₉	—	4	1	no	—
115	C₂×Q₈×C₁₉	—	4	1	no	—
116	C₂×Q₈×C₁₉	—	4	1	no	—
117	C₂×Q₈×C₁₉	—	4	1	no	—
118	C₂×Q₈×C₁₉	—	4	1	no	—
119	C₂×Q₈×C₁₉	—	4	1	no	—
120	C₂×Q₈×C₁₉	—	4	1	no	—
121	C₂×Q₈×C₁₉	C₄²	1	4	yes	complemented
122	C₂²×C₄×C₁₉	—	2	2	no	—
123	C₂²×C₄×C₁₉	—	2	2	no	—
124	C₂²×C₄×C₁₉	—	2	2	no	—
125	C₂²×C₄×C₁₉	—	2	2	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	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
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×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
139	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
140	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
141	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
142	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
143	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
144	C₂²×Dic₁₉	—	2	4	no	—
145	C₂²×Dic₁₉	—	2	2	no	—
146	C₂²×Dic₁₉	—	2	2	no	—
147	C₂²×Dic₁₉	—	2	2	no	—
148	C₂²×Dic₁₉	—	2	2	no	—
149	C₂²×Dic₁₉	—	4	2	no	—
150	C₂²×Dic₁₉	—	4	1	no	—
151	C₂²×Dic₁₉	—	4	1	no	—
152	C₂²×Dic₁₉	—	4	4	no	—
153	C₂²×Dic₁₉	C₂²⋊C₄	1	4	yes	—
154	M₁₆×C₁₉	—	2	2	no	—
155	M₁₆×C₁₉	—	2	2	no	—
156	M₁₆×C₁₉	—	4	1	no	—
157	M₁₆×C₁₉	—	4	1	no	—
158	C₂×C₈×C₁₉	—	2	2	no	—
159	C₂×C₈×C₁₉	—	4	1	no	—
160	C₂×C₈×C₁₉	—	4	1	no	—
161	C₄⋊C₄×C₁₉	—	2	2	no	—
162	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
163	C₂²⋊C₄×C₁₉	—	2	2	no	—
164	C₂²⋊C₄×C₁₉	—	2	2	no	—
165	C₄²×C₁₉	—	2	2	no	—
166	C₄²×C₁₉	—	2	2	no	—
167	C₂²⋊Dic₁₉	—	2	2	no	—
168	C₂²⋊Dic₁₉	—	2	2	no	—
169	C₄⋊Dic₁₉	—	2	2	no	—
170	C₄⋊Dic₁₉	—	2	2	no	—
171	C₄⋊Dic₁₉	—	2	2	no	—
172	C₄⋊Dic₁₉	—	2	2	no	—
173	C₄⋊Dic₁₉	—	2	2	no	—
174	C₄⋊Dic₁₉	C₂²⋊C₄	1	4	yes	—
175	C₄×Dic₁₉	—	2	2	no	—
176	C₄×Dic₁₉	—	2	2	no	—
177	C₄×Dic₁₉	—	2	2	no	—
178	C₄×Dic₁₉	—	2	2	no	—
179	C₄×Dic₁₉	—	4	1	no	—
180	C₄×Dic₁₉	—	4	1	no	—
181	C₄×Dic₁₉	—	8	4	no	—
182	#64520	—	2	2	no	—
183	#64520	—	2	2	no	—
184	#64520	—	4	1	no	—
185	#64520	—	4	1	no	—
186	C₂×C₁₉⋊C₈	—	2	2	no	—
187	C₂×C₁₉⋊C₈	—	4	1	no	—
188	C₂×C₁₉⋊C₈	—	4	1	no	—
189	#10957	—	19	1	no	maximal, Sylow
190	C₂³×C₁₉	—	2	2	no	—
191	C₂³×C₁₉	—	2	2	no	—
192	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
193	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
194	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
195	C₂³×C₁₉	#120	1	1	yes	characteristic
196	C₂³×C₁₉	#121	1	1	yes	characteristic
197	C₂³×C₁₉	#121	1	1	yes	characteristic
198	C₂³×C₁₉	#123	1	1	yes	characteristic
199	Q₈×C₁₉	—	2	4	no	—
200	Q₈×C₁₉	—	2	4	no	—
201	Q₈×C₁₉	—	4	2	no	—
202	Q₈×C₁₉	—	4	2	no	—
203	Q₈×C₁₉	—	4	2	no	—
204	Q₈×C₁₉	—	4	2	no	—
205	Q₈×C₁₉	—	4	2	no	—
206	Q₈×C₁₉	—	4	2	no	—
207	C₂×C₄×C₁₉	—	2	4	no	—
208	C₂×C₄×C₁₉	—	2	4	no	—
209	C₂×C₄×C₁₉	—	4	2	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	C₂×C₄²	1	1	yes	characteristic
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	#117	1	1	yes	characteristic
221	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
222	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
223	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
224	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
225	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
226	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
227	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
228	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
229	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
230	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
231	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
232	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
233	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
234	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
235	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
236	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
237	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
238	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
239	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
240	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
241	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
242	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
243	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
244	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
245	C₂×Dic₁₉	—	2	4	no	—
246	C₂×Dic₁₉	—	2	4	no	—
247	C₂×Dic₁₉	—	2	4	no	—
248	C₂×Dic₁₉	—	4	4	no	—
249	C₂×Dic₁₉	—	4	4	no	—
250	C₂×Dic₁₉	—	4	2	no	—
251	C₂×Dic₁₉	—	4	2	no	—
252	C₂×Dic₁₉	—	4	2	no	—
253	C₂×Dic₁₉	—	4	4	no	—
254	C₂×Dic₁₉	—	4	2	no	—
255	C₂×Dic₁₉	—	4	4	no	—
256	C₂×Dic₁₉	—	8	2	no	—
257	C₈×C₁₉	—	4	2	no	—
258	C₁₉⋊C₈	—	4	2	no	—
259	C₂×#419	—	19	1	no	—
260	C₂×#419	D₁₉	1	1	yes	characteristic
261	C₂×#391	—	19	1	no	—
262	#2274	—	19	1	no	—
263	C₂×#343	—	19	1	no	—
264	C₂×#339	—	19	1	no	—
265	C₂×#339	—	19	1	no	—
266	C₂²×C₁₉	—	2	2	no	—
267	C₂²×C₁₉	—	2	2	no	—
268	C₂²×C₁₉	—	2	2	no	—
269	C₂²×C₁₉	—	2	2	no	—
270	C₂²×C₁₉	—	2	1	no	—
271	C₂²×C₁₉	—	2	1	no	—
272	C₂²×C₁₉	—	2	1	no	—
273	C₂²×C₁₉	—	2	1	no	—
274	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
275	C₂²×C₁₉	#386	1	1	yes	characteristic
276	C₂²×C₁₉	#386	1	1	yes	characteristic
277	C₂²×C₁₉	#386	1	1	yes	characteristic
278	C₂²×C₁₉	#388	1	1	yes	characteristic
279	C₂²×C₁₉	#388	1	1	yes	characteristic
280	C₂²×C₁₉	#390	1	1	yes	characteristic
281	C₂²×C₁₉	#455	1	2	yes	—
282	C₂²×C₁₉	#456	1	2	yes	—
283	C₄×C₁₉	—	4	4	no	—
284	C₄×C₁₉	—	4	4	no	—
285	C₄×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
286	C₄×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
287	C₄×C₁₉	#388	1	1	yes	characteristic
288	C₄×C₁₉	#388	1	1	yes	characteristic
289	C₄×C₁₉	#388	1	1	yes	characteristic
290	C₄×C₁₉	#388	1	1	yes	characteristic
291	C₄×C₁₉	#390	1	1	yes	characteristic
292	C₄×C₁₉	#390	1	1	yes	characteristic
293	Dic₁₉	—	4	4	no	—
294	Dic₁₉	—	4	4	no	—
295	Dic₁₉	—	4	4	no	—
296	C₂³×Q₈	C₂×D₁₉	1	1	yes	characteristic
297	C₂²×M₁₆	—	19	1	no	—
298	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
299	C₂×#117	—	19	1	no	—
300	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
301	C₂²×C₄⋊C₄	—	19	1	no	—
302	C₂²×C₄²	—	19	1	no	—
303	#419	—	2	2	no	—
304	#419	—	19	4	no	—
305	#419	—	38	2	no	—
306	#419	Dic₁₉	1	4	yes	complemented
307	C₂×#103	—	2	2	no	—
308	C₂×#103	—	38	2	no	—
309	#391	—	19	4	no	—
310	#391	—	38	2	no	—
311	C₄×C₄⋊C₄	—	38	2	no	—
312	C₄×C₄⋊C₄	—	38	2	no	—
313	C₄×C₂²⋊C₄	—	38	2	no	—
314	C₂×#95	—	38	2	no	—
315	#343	—	38	2	no	—
316	#339	—	38	2	no	—
317	#339	—	38	2	no	—
318	C₂×C₁₉	—	2	1	no	—
319	C₂×C₁₉	—	2	1	no	—
320	C₂×C₁₉	—	2	1	no	—
321	C₂×C₁₉	—	2	1	no	—
322	C₂×C₁₉	#1437	1	1	yes	characteristic
323	C₂×C₁₉	#1882	1	2	yes	—
324	C₂×C₁₉	#1882	1	2	yes	—
325	C₂×C₁₉	#1885	1	1	yes	characteristic
326	C₂×C₁₉	#1886	1	1	yes	characteristic
327	C₂²×Q₈	—	2	1	no	—
328	C₂²×Q₈	—	2	1	no	—
329	C₂²×Q₈	—	2	1	no	—
330	C₂²×Q₈	—	2	1	no	—
331	C₂²×Q₈	—	2	1	no	—
332	C₂²×Q₈	—	2	1	no	—
333	C₂²×Q₈	—	2	1	no	—
334	C₂²×Q₈	—	2	1	no	—
335	C₂²×Q₈	—	2	1	no	—
336	C₂²×Q₈	—	2	1	no	—
337	C₂²×Q₈	—	2	1	no	—
338	C₂²×Q₈	C₄×D₁₉	1	2	yes	—
339	C₂²×Q₈	C₄×D₁₉	1	2	yes	—
340	C₂²×Q₈	C₂×Dic₁₉	1	2	yes	—
341	C₂³×C₄	—	2	1	no	—
342	C₂³×C₄	—	19	2	no	—
343	C₂³×C₄	—	38	1	no	—
344	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
345	C₂×M₁₆	—	2	1	no	—
346	C₂×M₁₆	—	2	1	no	—
347	C₂×M₁₆	—	2	1	no	—
348	C₂×M₁₆	—	2	1	no	—
349	C₂×M₁₆	—	2	1	no	—
350	C₂×M₁₆	—	19	2	no	—
351	C₂×M₁₆	—	38	1	no	—
352	C₂×M₁₆	—	38	1	no	—
353	C₂×M₁₆	—	38	1	no	—
354	C₂×M₁₆	—	38	1	no	—
355	C₂×M₁₆	—	38	1	no	—
356	C₂×M₁₆	C₂×Dic₁₉	1	2	yes	—
357	C₂²×C₈	—	2	1	no	—
358	C₂²×C₈	—	38	1	no	—
359	#117	—	2	1	no	—
360	#117	—	2	1	no	—
361	#117	—	19	2	no	—
362	#117	—	19	2	no	—
363	#117	—	38	1	no	—
364	#117	—	38	1	no	—
365	#117	C₂×Dic₁₉	1	2	yes	—
366	#117	C₂²⋊D₁₉	1	2	yes	—
367	C₂×C₄⋊C₄	—	19	2	no	—
368	C₂×C₄⋊C₄	—	19	2	no	—
369	C₂×C₄⋊C₄	—	19	2	no	—
370	C₂×C₄⋊C₄	—	38	1	no	—
371	C₂×C₄⋊C₄	—	38	1	no	—
372	C₂×C₄⋊C₄	—	38	1	no	—
373	C₂×C₄⋊C₄	—	38	1	no	—
374	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
375	C₂×C₂²⋊C₄	—	2	1	no	—
376	C₂×C₂²⋊C₄	—	38	1	no	—
377	C₂×C₄²	—	2	1	no	—
378	C₂×C₄²	—	19	2	no	—
379	C₂×C₄²	—	38	1	no	—
380	C₂×C₄²	—	38	1	no	—
381	C₂×C₄²	—	38	1	no	—
382	C₂×C₄²	—	38	1	no	—
383	C₂×C₄²	—	38	1	no	—
384	C₂×C₄²	—	38	1	no	—
385	C₂×C₄²	—	38	4	no	—
386	#103	—	2	8	no	—
387	#103	—	38	8	no	—
388	#95	—	38	8	no	—
389	#95	—	38	4	no	—
390	C₁₉	#10957	1	1	yes	characteristic, complemented, Sylow
391	C₂⁴	D₄×D₁₉	1	1	yes	characteristic
392	C₂×Q₈	—	2	2	no	—
393	C₂×Q₈	—	2	2	no	—
394	C₂×Q₈	—	2	2	no	—
395	C₂×Q₈	—	2	2	no	—
396	C₂×Q₈	—	2	2	no	—
397	C₂×Q₈	—	2	2	no	—
398	C₂×Q₈	—	2	2	no	—
399	C₂×Q₈	—	2	2	no	—
400	C₂×Q₈	—	2	2	no	—
401	C₂×Q₈	—	2	2	no	—
402	C₂×Q₈	—	2	2	no	—
403	C₂×Q₈	—	2	2	no	—
404	C₂×Q₈	—	2	2	no	—
405	C₂×Q₈	—	2	2	no	—
406	C₂×Q₈	—	2	2	no	—
407	C₂×Q₈	—	4	1	no	—
408	C₂×Q₈	—	4	1	no	—
409	C₂×Q₈	—	4	1	no	—
410	C₂×Q₈	—	4	1	no	—
411	C₂×Q₈	—	4	1	no	—
412	C₂×Q₈	—	4	1	no	—
413	C₂×Q₈	—	4	1	no	—
414	C₂×Q₈	—	4	1	no	—
415	C₂×Q₈	—	4	1	no	—
416	C₂×Q₈	—	4	1	no	—
417	C₂×Q₈	—	4	1	no	—
418	C₂×Q₈	—	4	1	no	—
419	C₂×Q₈	C₄×Dic₁₉	1	4	yes	complemented
420	C₂²×C₄	—	2	2	no	—
421	C₂²×C₄	—	2	2	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	—	4	1	no	—
425	C₂²×C₄	—	4	1	no	—
426	C₂²×C₄	—	4	1	no	—
427	C₂²×C₄	—	4	1	no	—
428	C₂²×C₄	—	19	4	no	—
429	C₂²×C₄	—	38	4	no	—
430	C₂²×C₄	—	38	2	no	—
431	C₂²×C₄	—	38	2	no	—
432	C₂²×C₄	—	38	2	no	—
433	C₂²×C₄	—	38	2	no	—
434	C₂²×C₄	—	76	2	no	—
435	C₂²×C₄	—	76	1	no	—
436	C₂²×C₄	—	76	1	no	—
437	C₂²×C₄	—	76	4	no	—
438	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
439	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
440	C₂²×C₄	#64541	1	1	yes	characteristic
441	C₂²×C₄	#64541	1	1	yes	characteristic
442	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
443	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
444	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
445	C₂²×C₄	#64543	1	1	yes	characteristic
446	C₂²×C₄	#64543	1	1	yes	characteristic
447	C₂²×C₄	#64543	1	1	yes	characteristic
448	C₂²×C₄	#64543	1	1	yes	characteristic
449	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
450	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
451	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
452	M₁₆	—	2	2	no	—
453	M₁₆	—	2	2	no	—
454	M₁₆	—	4	1	no	—
455	M₁₆	—	4	1	no	—
456	M₁₆	—	38	2	no	—
457	M₁₆	—	38	2	no	—
458	M₁₆	—	76	1	no	—
459	M₁₆	—	76	1	no	—
460	C₂×C₈	—	2	2	no	—
461	C₂×C₈	—	4	1	no	—
462	C₂×C₈	—	4	1	no	—
463	C₂×C₈	—	38	2	no	—
464	C₂×C₈	—	76	1	no	—
465	C₂×C₈	—	76	1	no	—
466	C₄⋊C₄	—	2	2	no	—
467	C₄⋊C₄	—	19	4	no	—
468	C₄⋊C₄	—	38	2	no	—
469	C₄⋊C₄	—	38	2	no	—
470	C₄⋊C₄	—	38	2	no	—
471	C₄⋊C₄	—	38	2	no	—
472	C₄⋊C₄	—	38	2	no	—
473	C₄⋊C₄	C₂²⋊Dic₁₉	1	4	yes	—
474	C₂²⋊C₄	—	2	2	no	—
475	C₂²⋊C₄	—	2	2	no	—
476	C₂²⋊C₄	—	38	2	no	—
477	C₂²⋊C₄	—	38	2	no	—
478	C₄²	—	2	2	no	—
479	C₄²	—	2	2	no	—
480	C₄²	—	38	2	no	—
481	C₄²	—	38	2	no	—
482	C₄²	—	38	2	no	—
483	C₄²	—	38	2	no	—
484	C₄²	—	76	1	no	—
485	C₄²	—	76	1	no	—
486	C₄²	—	152	4	no	—
487	C₂³	—	2	2	no	—
488	C₂³	—	2	2	no	—
489	C₂³	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
490	C₂³	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
491	C₂³	#10597329	1	1	yes	characteristic
492	C₂³	#10597330	1	1	yes	characteristic
493	C₂³	D₄×Dic₁₉	1	1	yes	characteristic
494	C₂³	#10597383	1	1	yes	characteristic
495	C₂³	#10597385	1	1	yes	characteristic
496	Q₈	—	2	4	no	—
497	Q₈	—	2	4	no	—
498	Q₈	—	4	2	no	—
499	Q₈	—	4	2	no	—
500	Q₈	—	4	2	no	—
501	Q₈	—	4	2	no	—
502	Q₈	—	4	2	no	—
503	Q₈	—	4	2	no	—
504	C₂×C₄	—	2	4	no	—
505	C₂×C₄	—	2	4	no	—
506	C₂×C₄	—	4	2	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	4	2	no	—
510	C₂×C₄	—	4	2	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	—	4	2	no	—
513	C₂×C₄	—	4	2	no	—
514	C₂×C₄	—	38	4	no	—
515	C₂×C₄	—	38	4	no	—
516	C₂×C₄	—	38	4	no	—
517	C₂×C₄	—	76	4	no	—
518	C₂×C₄	—	76	4	no	—
519	C₂×C₄	—	76	2	no	—
520	C₂×C₄	—	76	2	no	—
521	C₂×C₄	—	76	2	no	—
522	C₂×C₄	—	76	4	no	—
523	C₂×C₄	—	76	2	no	—
524	C₂×C₄	—	76	4	no	—
525	C₂×C₄	—	152	2	no	—
526	C₂×C₄	#10597323	1	1	yes	characteristic
527	C₂×C₄	#10597323	1	1	yes	characteristic
528	C₂×C₄	#10597325	1	1	yes	characteristic
529	C₂×C₄	#10597325	1	1	yes	characteristic
530	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
531	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
532	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
533	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
534	C₂×C₄	#10597329	1	1	yes	characteristic
535	C₂×C₄	#10597330	1	1	yes	characteristic
536	C₂×C₄	#10597331	1	1	yes	characteristic
537	C₂×C₄	#10597331	1	1	yes	characteristic
538	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
539	C₂×C₄	#10597372	1	1	yes	characteristic
540	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
541	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
542	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
543	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
544	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
545	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
546	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
547	C₂×C₄	#10597381	1	1	yes	characteristic
548	C₂×C₄	#10597382	1	1	yes	characteristic
549	C₂×C₄	#10597384	1	1	yes	characteristic
550	C₂×C₄	#10597384	1	1	yes	characteristic
551	C₂×C₄	#10597385	1	1	yes	characteristic
552	C₂×C₄	#10597386	1	1	yes	characteristic
553	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
554	C₈	—	4	2	no	—
555	C₈	—	76	2	no	—
556	C₂²	—	2	2	no	—
557	C₂²	—	2	2	no	—
558	C₂²	—	2	2	no	—
559	C₂²	—	2	2	no	—
560	C₂²	—	2	1	no	—
561	C₂²	—	2	1	no	—
562	C₂²	—	2	1	no	—
563	C₂²	—	2	1	no	—
564	C₂²	C₂²⋊C₄×Dic₁₉	1	1	yes	characteristic
565	C₂²	#11926420	1	1	yes	characteristic
566	C₂²	#11926420	1	1	yes	characteristic
567	C₂²	#11926424	1	1	yes	characteristic
568	C₂²	#11926437	1	1	yes	characteristic
569	C₂²	#11926438	1	1	yes	characteristic
570	C₂²	#11926444	1	1	yes	characteristic
571	C₂²	#11926720	1	2	yes	—
572	C₂²	#11926725	1	2	yes	—
573	C₄	—	4	4	no	—
574	C₄	—	4	4	no	—
575	C₄	—	76	4	no	—
576	C₄	—	76	4	no	—
577	C₄	—	76	4	no	—
578	C₄	C₄×C₂²⋊Dic₁₉	1	1	yes	characteristic
579	C₄	C₂²⋊C₄×Dic₁₉	1	1	yes	characteristic
580	C₄	#11926432	1	1	yes	characteristic
581	C₄	#11926432	1	1	yes	characteristic
582	C₄	#11926437	1	1	yes	characteristic
583	C₄	#11926438	1	1	yes	characteristic
584	C₄	#11926444	1	1	yes	characteristic
585	C₄	#11926447	1	1	yes	characteristic
586	C₂	—	2	1	no	—
587	C₂	—	2	1	no	—
588	C₂	—	2	1	no	—
589	C₂	—	2	1	no	—
590	C₂	#14561872	1	1	yes	characteristic
591	C₂	#14564001	1	2	yes	—
592	C₂	#14564006	1	2	yes	—
593	C₂	#14564020	1	1	yes	characteristic
594	C₂	#14564025	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597383
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#419	C₂
socle	C₂³×C₁₉	#120
prime radical	C₂⁴×C₁₉	C₂×D₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#419	D₁₉
hypocenter	C₁₉	#10957
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂×#419

Complements

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

N	H ≅ G/N	type
13. #11926553	C₄	semidirect
16. #11926451	C₄	semidirect
28. C₁₉×#419	C₄	semidirect
121. C₂×Q₈×C₁₉	C₄²	semidirect
306. #419	Dic₁₉	semidirect
390. C₁₉	#10957	semidirect
419. C₂×Q₈	C₄×Dic₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926553	2
C₂×#11926451	2
#14565991	2
C₂×#11926312	2
C₂×#11926305	2
C₂×#11926303	2
C₂×C₁₉×#419	2
#10957	19