Subgroups — #18089021

Order 4864.

978 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#10597293	C₂	1	1	yes	maximal, characteristic
2	C₂×M₁₆×Dic₁₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926451	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926312	C₂	1	1	yes	maximal, characteristic
5	C₂×#11926312	C₂	1	1	yes	maximal, characteristic
6	#14563328	C₂	1	1	yes	maximal, characteristic
7	C₂²×C₁₉×#101	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	C₂×#10597293	—	2	2	no	—
13	C₂×#10597293	—	2	2	no	—
14	C₂×#10597293	C₄	1	4	yes	complemented
15	M₁₆×Dic₁₉	—	2	2	no	—
16	M₁₆×Dic₁₉	—	2	2	no	—
17	C₂×#10597272	—	2	1	no	—
18	C₂×C₈×Dic₁₉	—	2	1	no	—
19	#11926451	—	2	2	no	—
20	#11926451	—	2	1	no	—
21	#11926451	—	2	1	no	—
22	C₂×C₁₉⋊#95	C₄	1	4	yes	—
23	#11926312	—	2	2	no	—
24	#11926312	—	2	2	no	—
25	#11926298	—	2	2	no	—
26	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
27	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
28	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×#101	—	2	2	no	—
30	C₂×C₁₉×#101	—	2	2	no	—
31	C₂×C₁₉×#101	C₄	1	4	yes	complemented
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	—	2	1	no	—
42	C₂²×Q₈×C₁₉	—	2	1	no	—
43	C₂²×Q₈×C₁₉	—	2	1	no	—
44	C₂²×Q₈×C₁₉	C₂×C₄	1	2	yes	—
45	C₂²×Q₈×C₁₉	C₂×C₄	1	2	yes	—
46	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
47	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
48	C₂³×Dic₁₉	C₂×C₄	1	2	yes	—
49	C₂³×Dic₁₉	C₂×C₄	1	2	yes	—
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	—	2	1	no	—
54	C₂×M₁₆×C₁₉	—	2	1	no	—
55	C₂×M₁₆×C₁₉	—	2	1	no	—
56	C₂×M₁₆×C₁₉	—	2	1	no	—
57	C₂×M₁₆×C₁₉	—	2	1	no	—
58	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
59	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
60	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
61	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
62	C₂²×C₈×C₁₉	—	2	1	no	—
63	C₂²×C₈×C₁₉	—	2	1	no	—
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	—	2	1	no	—
70	C₂×C₄×Dic₁₉	—	2	1	no	—
71	C₂×C₄×Dic₁₉	—	2	1	no	—
72	C₂×C₄×Dic₁₉	—	2	1	no	—
73	C₂×C₄×Dic₁₉	—	2	1	no	—
74	C₂×C₄×Dic₁₉	D₄	1	2	yes	—
75	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
76	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
77	C₂×#64520	—	2	1	no	—
78	C₂×#64520	—	2	1	no	—
79	C₂×#64520	—	2	1	no	—
80	C₂×#64520	—	2	1	no	—
81	C₂×#64520	—	2	1	no	—
82	C₂×#64520	—	2	1	no	—
83	C₂×#64520	—	2	1	no	—
84	C₂×#64520	—	2	1	no	—
85	C₂×#64520	C₂×C₄	1	2	yes	—
86	C₂×#64520	C₂×C₄	1	2	yes	—
87	C₂×#64520	D₄	1	2	yes	—
88	C₂×#64520	D₄	1	2	yes	—
89	C₂²×C₁₉⋊C₈	—	2	1	no	—
90	C₂²×C₁₉⋊C₈	—	2	1	no	—
91	C₁₉×#101	—	2	8	no	—
92	#10597293	—	2	8	no	—
93	C₁₉⋊#95	—	2	4	no	—
94	C₁₉⋊#95	—	2	4	no	—
95	#10597272	—	2	4	no	—
96	C₈×Dic₁₉	—	2	4	no	—
97	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
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	—	2	2	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	—	4	1	no	—
122	C₂×Q₈×C₁₉	—	4	1	no	—
123	C₂×Q₈×C₁₉	—	4	1	no	—
124	C₂×Q₈×C₁₉	—	4	1	no	—
125	C₂×Q₈×C₁₉	—	4	1	no	—
126	C₂²×C₄×C₁₉	—	2	2	no	—
127	C₂²×C₄×C₁₉	—	2	2	no	—
128	C₂²×C₄×C₁₉	—	2	2	no	—
129	C₂²×C₄×C₁₉	—	2	2	no	—
130	C₂²×C₄×C₁₉	—	2	2	no	—
131	C₂²×C₄×C₁₉	—	2	2	no	—
132	C₂²×C₄×C₁₉	C₄²	1	4	yes	—
133	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₉	C₂²×C₄	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	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₉	C₂×D₄	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×C₄×C₁₉	#41	1	1	yes	characteristic
145	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
146	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
147	C₂²×Dic₁₉	—	2	2	no	—
148	C₂²×Dic₁₉	—	2	2	no	—
149	C₂²×Dic₁₉	—	2	4	no	—
150	C₂²×Dic₁₉	—	2	2	no	—
151	C₂²×Dic₁₉	—	2	2	no	—
152	C₂²×Dic₁₉	—	2	2	no	—
153	C₂²×Dic₁₉	—	4	2	no	—
154	C₂²×Dic₁₉	—	4	4	no	—
155	C₂²×Dic₁₉	C₂²⋊C₄	1	2	yes	—
156	C₂²×Dic₁₉	C₂²⋊C₄	1	2	yes	—
157	M₁₆×C₁₉	—	2	2	no	—
158	M₁₆×C₁₉	—	2	2	no	—
159	M₁₆×C₁₉	—	2	2	no	—
160	M₁₆×C₁₉	—	2	2	no	—
161	M₁₆×C₁₉	—	2	2	no	—
162	M₁₆×C₁₉	—	4	1	no	—
163	M₁₆×C₁₉	—	4	1	no	—
164	M₁₆×C₁₉	C₂²⋊C₄	1	4	yes	—
165	C₂×C₈×C₁₉	—	2	2	no	—
166	C₂×C₈×C₁₉	—	2	2	no	—
167	C₂×C₈×C₁₉	—	2	2	no	—
168	C₂×C₈×C₁₉	—	2	2	no	—
169	C₂×C₈×C₁₉	—	4	1	no	—
170	C₂×C₈×C₁₉	—	4	1	no	—
171	C₄⋊Dic₁₉	—	4	1	no	—
172	C₄⋊Dic₁₉	—	4	1	no	—
173	C₄⋊Dic₁₉	—	4	1	no	—
174	C₄⋊Dic₁₉	—	4	1	no	—
175	C₄×Dic₁₉	—	2	1	no	—
176	C₄×Dic₁₉	—	2	1	no	—
177	C₄×Dic₁₉	—	2	2	no	—
178	C₄×Dic₁₉	—	2	2	no	—
179	C₄×Dic₁₉	—	2	1	no	—
180	C₄×Dic₁₉	—	2	1	no	—
181	#64520	—	2	2	no	—
182	#64520	—	2	2	no	—
183	#64520	—	2	2	no	—
184	#64520	—	2	2	no	—
185	#64520	—	2	2	no	—
186	#64520	—	4	1	no	—
187	#64520	—	4	1	no	—
188	#64520	C₂²⋊C₄	1	4	yes	—
189	C₂×C₁₉⋊C₈	—	2	2	no	—
190	C₂×C₁₉⋊C₈	—	2	2	no	—
191	C₂×C₁₉⋊C₈	—	2	2	no	—
192	C₂×C₁₉⋊C₈	—	2	2	no	—
193	C₂×C₁₉⋊C₈	—	4	1	no	—
194	C₂×C₁₉⋊C₈	—	4	1	no	—
195	#10963	—	19	1	no	maximal, Sylow
196	C₂³×C₁₉	—	2	2	no	—
197	C₂³×C₁₉	—	2	2	no	—
198	C₂³×C₁₉	C₂×C₄²	1	1	yes	characteristic
199	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
200	C₂³×C₁₉	#117	1	1	yes	characteristic
201	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
202	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
203	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
204	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
205	Q₈×C₁₉	—	4	2	no	—
206	Q₈×C₁₉	—	4	2	no	—
207	Q₈×C₁₉	—	4	2	no	—
208	Q₈×C₁₉	—	4	2	no	—
209	Q₈×C₁₉	—	4	2	no	—
210	Q₈×C₁₉	—	4	2	no	—
211	Q₈×C₁₉	—	4	2	no	—
212	Q₈×C₁₉	—	4	2	no	—
213	C₂×C₄×C₁₉	—	2	4	no	—
214	C₂×C₄×C₁₉	—	2	4	no	—
215	C₂×C₄×C₁₉	—	2	4	no	—
216	C₂×C₄×C₁₉	—	4	2	no	—
217	C₂×C₄×C₁₉	—	4	2	no	—
218	C₂×C₄×C₁₉	—	4	2	no	—
219	C₂×C₄×C₁₉	—	4	2	no	—
220	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
221	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
222	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
223	C₂×C₄×C₁₉	#117	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	#120	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	#121	1	1	yes	characteristic
238	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
239	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
240	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
241	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
242	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
243	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
244	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
245	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
246	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
247	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
248	C₂×Dic₁₉	—	2	2	no	—
249	C₂×Dic₁₉	—	2	2	no	—
250	C₂×Dic₁₉	—	2	2	no	—
251	C₂×Dic₁₉	—	2	2	no	—
252	C₂×Dic₁₉	—	2	2	no	—
253	C₂×Dic₁₉	—	4	4	no	—
254	C₂×Dic₁₉	—	4	4	no	—
255	C₂×Dic₁₉	—	4	2	no	—
256	C₂×Dic₁₉	—	4	4	no	—
257	C₂×Dic₁₉	—	8	2	no	—
258	C₂×Dic₁₉	—	8	2	no	—
259	C₂×Dic₁₉	#101	1	4	yes	complemented
260	C₈×C₁₉	—	2	4	no	—
261	C₈×C₁₉	—	4	2	no	—
262	C₁₉⋊C₈	—	2	4	no	—
263	C₁₉⋊C₈	—	4	2	no	—
264	C₂²×#101	—	19	1	no	—
265	C₂²×#101	D₁₉	1	1	yes	characteristic
266	C₂×C₄×M₁₆	—	19	1	no	—
267	C₂×#391	—	19	1	no	—
268	C₂×#343	—	19	1	no	—
269	C₂×#343	—	19	1	no	—
270	#1728	—	19	1	no	—
271	C₂²×C₁₉	—	2	2	no	—
272	C₂²×C₁₉	—	2	2	no	—
273	C₂²×C₁₉	—	2	1	no	—
274	C₂²×C₁₉	—	2	1	no	—
275	C₂²×C₁₉	—	2	1	no	—
276	C₂²×C₁₉	—	2	1	no	—
277	C₂²×C₁₉	—	2	2	no	—
278	C₂²×C₁₉	—	2	2	no	—
279	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
280	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
281	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
282	C₂²×C₁₉	#386	1	1	yes	characteristic
283	C₂²×C₁₉	#388	1	1	yes	characteristic
284	C₂²×C₁₉	#388	1	1	yes	characteristic
285	C₂²×C₁₉	#390	1	1	yes	characteristic
286	C₂²×C₁₉	C₂×#101	1	2	yes	—
287	C₂²×C₁₉	#413	1	2	yes	—
288	C₄×C₁₉	—	4	4	no	—
289	C₄×C₁₉	#386	1	1	yes	characteristic
290	C₄×C₁₉	#386	1	1	yes	characteristic
291	C₄×C₁₉	#388	1	1	yes	characteristic
292	C₄×C₁₉	#388	1	1	yes	characteristic
293	C₄×C₁₉	#388	1	1	yes	characteristic
294	C₄×C₁₉	#388	1	1	yes	characteristic
295	C₄×C₁₉	#390	1	1	yes	characteristic
296	C₄×C₁₉	#390	1	1	yes	characteristic
297	Dic₁₉	—	2	4	no	—
298	Dic₁₉	—	4	2	no	—
299	Dic₁₉	—	8	2	no	—
300	C₂³×Q₈	C₂×D₁₉	1	1	yes	characteristic
301	C₂²×M₁₆	—	19	1	no	—
302	C₂²×M₁₆	—	19	1	no	—
303	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
304	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
305	C₂²×C₄⋊C₄	—	19	1	no	—
306	C₂²×C₄²	—	19	1	no	—
307	C₂×#101	—	2	2	no	—
308	C₂×#101	—	2	2	no	—
309	C₂×#101	—	19	4	no	—
310	C₂×#101	—	38	2	no	—
311	C₂×#101	—	38	2	no	—
312	C₂×#101	Dic₁₉	1	4	yes	complemented
313	C₄×M₁₆	—	38	2	no	—
314	C₄×M₁₆	—	38	2	no	—
315	C₂×#97	—	38	1	no	—
316	C₂×C₄×C₈	—	38	1	no	—
317	#391	—	38	2	no	—
318	#391	—	38	1	no	—
319	#391	—	38	1	no	—
320	C₂×#95	—	19	4	no	—
321	#343	—	38	2	no	—
322	#343	—	38	2	no	—
323	#336	—	38	2	no	—
324	C₂×C₁₉	—	2	1	no	—
325	C₂×C₁₉	—	2	1	no	—
326	C₂×C₁₉	—	2	1	no	—
327	C₂×C₁₉	—	2	1	no	—
328	C₂×C₁₉	#1437	1	1	yes	characteristic
329	C₂×C₁₉	C₄×#101	1	2	yes	—
330	C₂×C₁₉	#1901	1	2	yes	—
331	C₂×C₁₉	#1966	1	1	yes	characteristic
332	C₂×C₁₉	#1967	1	1	yes	characteristic
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	—	2	1	no	—
339	C₂²×Q₈	—	2	1	no	—
340	C₂²×Q₈	—	2	1	no	—
341	C₂²×Q₈	—	2	1	no	—
342	C₂²×Q₈	—	2	1	no	—
343	C₂²×Q₈	—	2	1	no	—
344	C₂²×Q₈	—	2	1	no	—
345	C₂²×Q₈	C₄×D₁₉	1	2	yes	—
346	C₂²×Q₈	C₂×Dic₁₉	1	2	yes	—
347	C₂³×C₄	—	19	2	no	—
348	C₂³×C₄	—	19	2	no	—
349	C₂³×C₄	C₄×D₁₉	1	2	yes	—
350	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
351	C₂×M₁₆	—	2	1	no	—
352	C₂×M₁₆	—	2	1	no	—
353	C₂×M₁₆	—	2	1	no	—
354	C₂×M₁₆	—	2	1	no	—
355	C₂×M₁₆	—	2	1	no	—
356	C₂×M₁₆	—	2	1	no	—
357	C₂×M₁₆	—	2	1	no	—
358	C₂×M₁₆	—	2	1	no	—
359	C₂×M₁₆	—	19	2	no	—
360	C₂×M₁₆	—	19	2	no	—
361	C₂×M₁₆	—	19	2	no	—
362	C₂×M₁₆	—	19	2	no	—
363	C₂×M₁₆	—	38	1	no	—
364	C₂×M₁₆	—	38	1	no	—
365	C₂×M₁₆	—	38	1	no	—
366	C₂×M₁₆	—	38	1	no	—
367	C₂×M₁₆	—	38	1	no	—
368	C₂×M₁₆	—	38	1	no	—
369	C₂×M₁₆	—	38	1	no	—
370	C₂×M₁₆	—	38	1	no	—
371	C₂×M₁₆	C₂×Dic₁₉	1	2	yes	—
372	C₂×M₁₆	C₂×Dic₁₉	1	2	yes	—
373	C₂×M₁₆	C₂²⋊D₁₉	1	2	yes	—
374	C₂×M₁₆	C₂²⋊D₁₉	1	2	yes	—
375	C₂²×C₈	—	2	1	no	—
376	C₂²×C₈	—	2	1	no	—
377	C₂²×C₈	—	38	1	no	—
378	C₂²×C₈	—	38	1	no	—
379	C₂×C₄⋊C₄	—	38	1	no	—
380	C₂×C₄⋊C₄	—	38	1	no	—
381	C₂×C₄⋊C₄	—	38	1	no	—
382	C₂×C₄⋊C₄	—	38	1	no	—
383	C₂×C₄⋊C₄	—	38	1	no	—
384	C₂×C₄⋊C₄	—	38	1	no	—
385	C₂×C₄²	—	19	2	no	—
386	C₂×C₄²	—	19	1	no	—
387	C₂×C₄²	—	19	1	no	—
388	C₂×C₄²	—	38	1	no	—
389	C₂×C₄²	—	38	1	no	—
390	C₂×C₄²	—	38	1	no	—
391	C₂×C₄²	—	38	1	no	—
392	#101	—	2	8	no	—
393	#101	—	38	8	no	—
394	#97	—	38	4	no	—
395	C₄×C₈	—	38	4	no	—
396	#95	—	38	4	no	—
397	#95	—	38	4	no	—
398	C₁₉	#10963	1	1	yes	characteristic, complemented, Sylow
399	C₂⁴	C₂×C₄×D₁₉	1	1	yes	characteristic
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	—	2	2	no	—
408	C₂×Q₈	—	2	2	no	—
409	C₂×Q₈	—	2	2	no	—
410	C₂×Q₈	—	2	2	no	—
411	C₂×Q₈	—	2	2	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	—	4	1	no	—
420	C₂×Q₈	—	4	1	no	—
421	C₂×Q₈	—	4	1	no	—
422	C₂×Q₈	—	4	1	no	—
423	C₂×Q₈	—	4	1	no	—
424	C₂×Q₈	—	4	1	no	—
425	C₂×Q₈	—	4	1	no	—
426	C₂×Q₈	—	4	1	no	—
427	C₂×Q₈	—	4	1	no	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	—	2	2	no	—
432	C₂²×C₄	—	2	2	no	—
433	C₂²×C₄	—	2	2	no	—
434	C₂²×C₄	—	19	2	no	—
435	C₂²×C₄	—	19	2	no	—
436	C₂²×C₄	—	38	4	no	—
437	C₂²×C₄	—	38	2	no	—
438	C₂²×C₄	—	38	2	no	—
439	C₂²×C₄	—	38	2	no	—
440	C₂²×C₄	—	38	2	no	—
441	C₂²×C₄	—	38	2	no	—
442	C₂²×C₄	—	76	2	no	—
443	C₂²×C₄	—	76	4	no	—
444	C₂²×C₄	C₄×Dic₁₉	1	4	yes	—
445	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
446	C₂²×C₄	#64541	1	1	yes	characteristic
447	C₂²×C₄	#64541	1	1	yes	characteristic
448	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
449	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
450	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
451	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
452	C₂²×C₄	#64543	1	1	yes	characteristic
453	C₂²×C₄	#64543	1	1	yes	characteristic
454	C₂²×C₄	#64543	1	1	yes	characteristic
455	C₂²×C₄	#64543	1	1	yes	characteristic
456	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
457	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
458	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
459	M₁₆	—	2	2	no	—
460	M₁₆	—	2	2	no	—
461	M₁₆	—	2	2	no	—
462	M₁₆	—	2	2	no	—
463	M₁₆	—	2	2	no	—
464	M₁₆	—	4	1	no	—
465	M₁₆	—	4	1	no	—
466	M₁₆	—	19	4	no	—
467	M₁₆	—	38	2	no	—
468	M₁₆	—	38	2	no	—
469	M₁₆	—	38	2	no	—
470	M₁₆	—	38	2	no	—
471	M₁₆	—	38	2	no	—
472	M₁₆	—	76	1	no	—
473	M₁₆	—	76	1	no	—
474	M₁₆	C₂²⋊Dic₁₉	1	4	yes	—
475	C₂×C₈	—	2	2	no	—
476	C₂×C₈	—	2	2	no	—
477	C₂×C₈	—	2	2	no	—
478	C₂×C₈	—	2	2	no	—
479	C₂×C₈	—	4	1	no	—
480	C₂×C₈	—	4	1	no	—
481	C₂×C₈	—	38	2	no	—
482	C₂×C₈	—	38	2	no	—
483	C₂×C₈	—	38	2	no	—
484	C₂×C₈	—	38	2	no	—
485	C₂×C₈	—	76	1	no	—
486	C₂×C₈	—	76	1	no	—
487	C₄⋊C₄	—	76	1	no	—
488	C₄⋊C₄	—	76	1	no	—
489	C₄⋊C₄	—	76	1	no	—
490	C₄⋊C₄	—	76	1	no	—
491	C₄²	—	38	1	no	—
492	C₄²	—	38	1	no	—
493	C₄²	—	38	2	no	—
494	C₄²	—	38	1	no	—
495	C₄²	—	38	1	no	—
496	C₄²	—	38	2	no	—
497	C₂³	—	2	2	no	—
498	C₂³	—	2	2	no	—
499	C₂³	#10597323	1	1	yes	characteristic
500	C₂³	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
501	C₂³	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
502	C₂³	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
503	C₂³	C₂×C₄×Dic₁₉	1	1	yes	characteristic
504	C₂³	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
505	C₂³	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
506	Q₈	—	4	2	no	—
507	Q₈	—	4	2	no	—
508	Q₈	—	4	2	no	—
509	Q₈	—	4	2	no	—
510	Q₈	—	4	2	no	—
511	Q₈	—	4	2	no	—
512	Q₈	—	4	2	no	—
513	Q₈	—	4	2	no	—
514	C₂×C₄	—	2	4	no	—
515	C₂×C₄	—	2	4	no	—
516	C₂×C₄	—	2	4	no	—
517	C₂×C₄	—	4	2	no	—
518	C₂×C₄	—	4	2	no	—
519	C₂×C₄	—	4	2	no	—
520	C₂×C₄	—	4	2	no	—
521	C₂×C₄	—	19	4	no	—
522	C₂×C₄	—	38	2	no	—
523	C₂×C₄	—	38	2	no	—
524	C₂×C₄	—	38	2	no	—
525	C₂×C₄	—	38	2	no	—
526	C₂×C₄	—	38	2	no	—
527	C₂×C₄	—	76	4	no	—
528	C₂×C₄	—	76	4	no	—
529	C₂×C₄	—	76	2	no	—
530	C₂×C₄	—	76	4	no	—
531	C₂×C₄	—	152	2	no	—
532	C₂×C₄	—	152	2	no	—
533	C₂×C₄	#10597323	1	1	yes	characteristic
534	C₂×C₄	#10597325	1	1	yes	characteristic
535	C₂×C₄	#10597325	1	1	yes	characteristic
536	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
537	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
538	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
539	C₂×C₄	#10597329	1	1	yes	characteristic
540	C₂×C₄	#10597329	1	1	yes	characteristic
541	C₂×C₄	#10597330	1	1	yes	characteristic
542	C₂×C₄	#10597330	1	1	yes	characteristic
543	C₂×C₄	#10597331	1	1	yes	characteristic
544	C₂×C₄	#10597331	1	1	yes	characteristic
545	C₂×C₄	#10597372	1	1	yes	characteristic
546	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
547	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
548	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
549	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
550	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
551	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
552	C₂×C₄	#10597381	1	1	yes	characteristic
553	C₂×C₄	#10597382	1	1	yes	characteristic
554	C₂×C₄	#10597383	1	1	yes	characteristic
555	C₂×C₄	#10597384	1	1	yes	characteristic
556	C₂×C₄	#10597384	1	1	yes	characteristic
557	C₂×C₄	#10597385	1	1	yes	characteristic
558	C₂×C₄	#10597385	1	1	yes	characteristic
559	C₂×C₄	#10597386	1	1	yes	characteristic
560	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
561	C₈	—	2	4	no	—
562	C₈	—	4	2	no	—
563	C₈	—	38	4	no	—
564	C₈	—	76	2	no	—
565	C₂²	—	2	2	no	—
566	C₂²	—	2	2	no	—
567	C₂²	—	2	2	no	—
568	C₂²	—	2	2	no	—
569	C₂²	—	2	1	no	—
570	C₂²	—	2	1	no	—
571	C₂²	—	2	1	no	—
572	C₂²	—	2	1	no	—
573	C₂²	C₄×C₂²⋊Dic₁₉	1	1	yes	characteristic
574	C₂²	C₂²⋊C₄×Dic₁₉	1	1	yes	characteristic
575	C₂²	C₂²⋊C₄×Dic₁₉	1	1	yes	characteristic
576	C₂²	#11926420	1	1	yes	characteristic
577	C₂²	#11926432	1	1	yes	characteristic
578	C₂²	#11926438	1	1	yes	characteristic
579	C₂²	#11926444	1	1	yes	characteristic
580	C₂²	#101×D₁₉	1	2	yes	—
581	C₂²	#11926527	1	2	yes	—
582	C₄	—	4	4	no	—
583	C₄	—	38	4	no	—
584	C₄	—	76	2	no	—
585	C₄	—	152	2	no	—
586	C₄	#11926420	1	1	yes	characteristic
587	C₄	#11926424	1	1	yes	characteristic
588	C₄	#11926432	1	1	yes	characteristic
589	C₄	#11926437	1	1	yes	characteristic
590	C₄	#11926437	1	1	yes	characteristic
591	C₄	#11926438	1	1	yes	characteristic
592	C₄	#11926444	1	1	yes	characteristic
593	C₄	#11926447	1	1	yes	characteristic
594	C₂	—	2	1	no	—
595	C₂	—	2	1	no	—
596	C₂	—	2	1	no	—
597	C₂	—	2	1	no	—
598	C₂	#14561872	1	1	yes	characteristic
599	C₂	#101×Dic₁₉	1	2	yes	—
600	C₂	#14564100	1	2	yes	—
601	C₂	#14564477	1	1	yes	characteristic
602	C₂	#14564483	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²⋊C₄×D₁₉
commutator	C₂³×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂²×C₁₉×#101	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₁₉	C₂²×C₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂²×#101	D₁₉
hypocenter	C₁₉	#10963
LCS	G ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂²×#101

Complements

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

N	H ≅ G/N	type
14. C₂×#10597293	C₄	semidirect
31. C₂×C₁₉×#101	C₄	semidirect
259. C₂×Dic₁₉	#101	semidirect
312. C₂×#101	Dic₁₉	semidirect
398. C₁₉	#10963	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#10597293	2
C₂×M₁₆×Dic₁₉	2
C₂×#11926451	2
C₂×#11926312	2
#14563328	2
C₂²×C₁₉×#101	2
#10963	19