Subgroups — #14578236

Order 2432.

912 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉⋊#564	C₂	1	2	yes	maximal, complemented
2	#11927296	C₂	1	2	yes	maximal, complemented
3	#11927273	C₂	1	1	yes	maximal, characteristic, complemented
4	#11927271	C₂	1	1	yes	maximal, characteristic, complemented
5	#11927252	C₂	1	1	yes	maximal, characteristic, complemented
6	#11927251	C₂	1	1	yes	maximal, characteristic, complemented
7	#11927236	C₂	1	1	yes	maximal, characteristic, complemented
8	#11927233	C₂	1	1	yes	maximal, characteristic, complemented
9	#11927231	C₂	1	2	yes	maximal, complemented
10	#11927229	C₂	1	1	yes	maximal, characteristic, complemented
11	#11927227	C₂	1	2	yes	maximal, complemented
12	#11927174	C₂	1	1	yes	maximal, characteristic, complemented
13	#11927172	C₂	1	2	yes	maximal, complemented
14	#11927172	C₂	1	1	yes	maximal, characteristic, complemented
15	#11927157	C₂	1	2	yes	maximal, complemented
16	#11927154	C₂	1	1	yes	maximal, characteristic, complemented
17	#11927152	C₂	1	1	yes	maximal, characteristic, complemented
18	#11927151	C₂	1	2	yes	maximal, complemented
19	#11927138	C₂	1	2	yes	maximal
20	#11927096	C₂	1	1	yes	maximal, characteristic, complemented
21	#11927074	C₂	1	1	yes	maximal, characteristic
22	C₂×#10597336	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₉×#552	C₂	1	1	yes	maximal, characteristic, complemented
24	C₁₉×#126	C₂²	1	2	yes	—
25	C₁₉×#125	C₂²	1	2	yes	—
26	C₁₉×#125	C₂²	1	1	yes	characteristic
27	C₁₉×#123	C₂²	1	2	yes	—
28	C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
29	C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
30	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
31	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
32	C₁₉×#117	C₂²	1	2	yes	—
33	C₁₉×#117	C₂²	1	1	yes	characteristic
34	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
35	#10597392	C₂²	1	1	yes	characteristic
36	Q₈×Dic₁₉	C₂²	1	1	yes	characteristic
37	Q₈×Dic₁₉	C₂²	1	1	yes	characteristic
38	#10597390	C₂²	1	1	yes	characteristic
39	#10597385	C₂²	1	1	yes	characteristic
40	#10597381	C₂²	1	1	yes	characteristic
41	D₄×Dic₁₉	C₂²	1	2	yes	—
42	#10597375	C₂²	1	2	yes	—
43	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
44	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
45	#10597372	C₂²	1	1	yes	characteristic
46	#10597372	C₂²	1	2	yes	—
47	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
48	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
49	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
50	#10597370	C₂²	1	1	yes	characteristic
51	#10597370	C₂²	1	1	yes	characteristic
52	C₂×Dic₁₉⋊C₄	C₂²	1	2	yes	—
53	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
54	#10597344	C₂²	1	2	yes	—
55	#10597344	C₂²	1	1	yes	characteristic
56	#10597344	C₂²	1	2	yes	—
57	#10597344	C₂²	1	2	yes	—
58	#10597343	C₂²	1	2	yes	—
59	#10597343	C₂²	1	2	yes	—
60	#10597343	C₂²	1	1	yes	characteristic
61	#10597342	C₂²	1	2	yes	—
62	#10597338	C₂²	1	1	yes	characteristic
63	C₄⋊C₄×D₁₉	C₂²	1	1	yes	characteristic
64	#10597336	C₂²	1	2	yes	—
65	#10597336	C₂²	1	2	yes	—
66	#10597336	C₂²	1	2	yes	—
67	#10597336	C₂²	1	2	yes	—
68	#10597336	C₂²	1	2	yes	—
69	#10597336	C₂²	1	1	yes	characteristic
70	#10597336	C₂²	1	1	yes	characteristic
71	#10597336	C₂²	1	1	yes	characteristic
72	#10597336	C₂²	1	1	yes	characteristic
73	#10597336	C₂²	1	2	yes	—
74	#10597336	C₂²	1	2	yes	—
75	#10597336	C₂²	1	1	yes	characteristic
76	#10597335	C₂²	1	2	yes	—
77	#10597335	C₂²	1	1	yes	characteristic
78	#10597335	C₂²	1	2	yes	—
79	#10597335	C₂²	1	2	yes	—
80	#10597335	C₂²	1	2	yes	—
81	#10597335	C₂²	1	2	yes	—
82	#10597335	C₂²	1	2	yes	—
83	#10597335	C₂²	1	2	yes	—
84	#10597335	C₂²	1	2	yes	—
85	#10597334	C₂²	1	2	yes	—
86	#10597334	C₂²	1	1	yes	characteristic
87	#10597334	C₂²	1	2	yes	—
88	#10597334	C₂²	1	1	yes	characteristic
89	#10597333	C₂²	1	2	yes	—
90	#10597333	C₂²	1	1	yes	characteristic
91	#10597333	C₂²	1	1	yes	characteristic
92	#10597333	C₂²	1	2	yes	—
93	#10597332	C₂²	1	2	yes	—
94	#10597332	C₂²	1	1	yes	characteristic
95	#10597331	C₂²	1	1	yes	characteristic
96	#10597329	C₂²	1	2	yes	—
97	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	—
98	#10597325	C₂²	1	2	yes	—
99	#10597325	C₂²	1	1	yes	characteristic
100	#10597325	C₂²	1	2	yes	—
101	#10597325	C₂²	1	2	yes	—
102	#10597324	C₂²	1	2	yes	—
103	#10597324	C₂²	1	2	yes	—
104	#10597324	C₂²	1	1	yes	characteristic
105	#10597324	C₂²	1	2	yes	—
106	#10597324	C₂²	1	2	yes	—
107	#10597324	C₂²	1	2	yes	—
108	#10597324	C₂²	1	2	yes	—
109	#10597323	C₂²	1	2	yes	—
110	#10597323	C₂²	1	2	yes	—
111	#10597322	C₂²	1	2	yes	—
112	#10597318	C₂²	1	1	yes	characteristic
113	#10597318	C₂²	1	2	yes	—
114	#10597316	C₂²	1	2	yes	—
115	#10597316	C₂²	1	2	yes	—
116	#10597316	C₂²	1	2	yes	—
117	#10597315	C₂²	1	2	yes	—
118	#10597315	C₂²	1	2	yes	—
119	#10597315	C₂²	1	1	yes	characteristic
120	C₄×Dic₃₈	C₂²	1	1	yes	characteristic
121	C₄×Dic₃₈	C₂²	1	2	yes	—
122	C₄×Dic₃₈	C₂²	1	1	yes	characteristic
123	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
124	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
125	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
126	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
127	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
128	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
129	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
130	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
131	C₂²×Dic₁₉	C₂³	1	2	yes	—
132	C₂²×Dic₁₉	C₂³	1	2	yes	—
133	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
134	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
135	C₂×C₄×D₁₉	C₂³	1	2	yes	—
136	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
137	C₂×Dic₃₈	C₂³	1	2	yes	—
138	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
139	C₂×Dic₃₈	C₂³	1	2	yes	—
140	C₂×Dic₃₈	C₂³	1	2	yes	—
141	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
142	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
143	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
144	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
145	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
146	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
147	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
148	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
149	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
150	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
151	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
152	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
153	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
154	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
155	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
156	C₄²×C₁₉	C₂³	1	2	yes	—
157	C₄²×C₁₉	C₂³	1	2	yes	—
158	C₄²×C₁₉	C₂³	1	1	yes	characteristic
159	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
160	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
161	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
162	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
163	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
164	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
165	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
166	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
167	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
168	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
169	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
170	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
171	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
172	C₄⋊Dic₁₉	C₂³	1	2	yes	—
173	C₄⋊Dic₁₉	C₂³	1	2	yes	—
174	C₄⋊Dic₁₉	C₂³	1	2	yes	—
175	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
176	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
177	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
178	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
179	C₄⋊Dic₁₉	C₂³	1	2	yes	—
180	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
181	C₄⋊Dic₁₉	C₂³	1	2	yes	—
182	C₄⋊Dic₁₉	C₂³	1	2	yes	—
183	C₄⋊Dic₁₉	C₂³	1	2	yes	—
184	C₄⋊Dic₁₉	C₂³	1	2	yes	—
185	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
186	C₄⋊Dic₁₉	C₂³	1	2	yes	—
187	C₄⋊Dic₁₉	C₂³	1	2	yes	—
188	C₄⋊Dic₁₉	C₂³	1	2	yes	—
189	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
190	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
191	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
192	Dic₁₉⋊C₄	C₂³	1	2	yes	—
193	Dic₁₉⋊C₄	C₂³	1	2	yes	—
194	Dic₁₉⋊C₄	C₂³	1	2	yes	—
195	Dic₁₉⋊C₄	C₂³	1	2	yes	—
196	Dic₁₉⋊C₄	C₂³	1	2	yes	—
197	Dic₁₉⋊C₄	C₂³	1	2	yes	—
198	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
199	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
200	Dic₁₉⋊C₄	C₂³	1	2	yes	—
201	Dic₁₉⋊C₄	C₂³	1	2	yes	—
202	Dic₁₉⋊C₄	C₂³	1	2	yes	—
203	Dic₁₉⋊C₄	C₂³	1	2	yes	—
204	Dic₁₉⋊C₄	C₂³	1	2	yes	—
205	Dic₁₉⋊C₄	C₂³	1	2	yes	—
206	Dic₁₉⋊C₄	C₂³	1	2	yes	—
207	Dic₁₉⋊C₄	C₂³	1	2	yes	—
208	Dic₁₉⋊C₄	C₂³	1	2	yes	—
209	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
210	Dic₁₉⋊C₄	C₂³	1	2	yes	—
211	C₄×Dic₁₉	C₂³	1	2	yes	—
212	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
213	C₄×Dic₁₉	C₂³	1	2	yes	—
214	C₄×Dic₁₉	C₂³	1	2	yes	—
215	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
216	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
217	C₄×Dic₁₉	C₂³	1	2	yes	—
218	C₄×Dic₁₉	C₂³	1	2	yes	—
219	C₄×Dic₁₉	C₂³	1	2	yes	—
220	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
221	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
222	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
223	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
224	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
225	Q₈×C₁₉	—	2	2	no	—
226	D₄×C₁₉	—	2	2	no	—
227	C₂×C₄×C₁₉	—	2	4	no	—
228	C₂×C₄×C₁₉	—	2	2	no	—
229	C₂×C₄×C₁₉	—	2	2	no	—
230	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
231	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
232	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
233	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
234	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
235	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
236	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
237	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
238	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
239	C₂²⋊D₁₉	—	2	2	no	—
240	C₂²⋊D₁₉	—	4	1	no	—
241	C₂×Dic₁₉	—	2	2	no	—
242	C₂×Dic₁₉	—	4	2	no	—
243	C₂×Dic₁₉	—	4	1	no	—
244	C₂×Dic₁₉	—	4	2	no	—
245	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
246	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
247	C₂×Dic₁₉	C₂⁴	1	2	yes	—
248	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
249	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
250	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
251	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
252	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
253	C₂×Dic₁₉	C₂⁴	1	2	yes	—
254	C₂×Dic₁₉	C₂⁴	1	2	yes	—
255	C₂×Dic₁₉	C₂⁴	1	2	yes	—
256	C₄×D₁₉	—	2	2	no	—
257	C₄×D₁₉	—	4	2	no	—
258	Dic₃₈	—	2	2	no	—
259	Dic₃₈	—	4	2	no	—
260	Dic₃₈	—	4	1	no	—
261	Dic₃₈	—	4	2	no	—
262	Dic₃₈	—	4	2	no	—
263	#3563	—	19	1	no	maximal, Sylow
264	C₂²×C₁₉	—	2	1	no	—
265	C₂²×C₁₉	—	2	1	no	—
266	C₂²×C₁₉	—	2	1	no	—
267	C₂²×C₁₉	—	2	1	no	—
268	C₂²×C₁₉	—	2	1	no	—
269	C₂²×C₁₉	2₋¹⁺⁴	1	2	yes	—
270	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
271	C₂×D₁₉	—	2	1	no	—
272	C₂×D₁₉	—	2	1	no	—
273	C₂×D₁₉	—	2	1	no	—
274	C₄×C₁₉	—	2	2	no	—
275	C₄×C₁₉	—	2	2	no	—
276	C₄×C₁₉	—	2	1	no	—
277	C₄×C₁₉	—	2	1	no	—
278	C₄×C₁₉	—	2	1	no	—
279	C₄×C₁₉	—	2	2	no	—
280	C₄×C₁₉	—	2	1	no	—
281	C₄×C₁₉	—	2	2	no	—
282	C₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
283	Dic₁₉	—	2	2	no	—
284	Dic₁₉	—	2	1	no	—
285	Dic₁₉	—	2	1	no	—
286	Dic₁₉	—	2	1	no	—
287	Dic₁₉	—	2	1	no	—
288	Dic₁₉	—	2	1	no	—
289	Dic₁₉	—	2	1	no	—
290	Dic₁₉	—	2	2	no	—
291	Dic₁₉	—	2	2	no	—
292	Dic₁₉	—	2	2	no	—
293	Dic₁₉	—	2	1	no	—
294	#564	—	19	2	no	—
295	#563	—	19	2	no	—
296	#557	—	19	1	no	—
297	#557	—	19	1	no	—
298	#554	—	19	1	no	—
299	#554	—	19	1	no	—
300	#552	—	19	2	no	—
301	#552	—	19	1	no	—
302	#552	—	19	2	no	—
303	#552	—	19	1	no	—
304	#552	—	19	1	no	—
305	#552	D₁₉	1	1	yes	characteristic, complemented
306	#544	—	19	1	no	—
307	#544	—	19	2	no	—
308	#544	—	19	1	no	—
309	#541	—	19	2	no	—
310	#541	—	19	2	no	—
311	#541	—	19	1	no	—
312	#541	—	19	1	no	—
313	#539	—	19	2	no	—
314	#533	—	19	1	no	—
315	#529	—	19	1	no	—
316	C₂×#125	—	19	1	no	—
317	C₂×C₁₉	—	2	2	no	—
318	C₂×C₁₉	—	4	1	no	—
319	C₂×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
320	C₂×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
321	C₂×C₁₉	#585	1	1	yes	characteristic
322	D₁₉	—	4	1	no	—
323	C₄⋊Q₈	—	19	1	no	—
324	C₄⋊Q₈	—	19	1	no	—
325	C₄⋊Q₈	—	19	2	no	—
326	C₄⋊Q₈	—	19	1	no	—
327	C₄⋊Q₈	—	19	2	no	—
328	C₄⋊Q₈	—	19	2	no	—
329	C₄⋊Q₈	—	19	1	no	—
330	C₄⋊Q₈	—	19	2	no	—
331	#126	—	19	1	no	—
332	#126	—	19	2	no	—
333	#126	—	19	2	no	—
334	#126	—	19	2	no	—
335	#126	—	19	1	no	—
336	#126	—	19	2	no	—
337	#126	—	19	2	no	—
338	#126	—	19	2	no	—
339	#126	—	19	2	no	—
340	#126	C₂×D₁₉	1	2	yes	—
341	#125	—	19	2	no	—
342	#125	—	19	1	no	—
343	#125	—	19	1	no	—
344	#125	—	19	1	no	—
345	#125	—	19	1	no	—
346	#125	—	19	2	no	—
347	#125	—	19	1	no	—
348	#125	—	19	2	no	—
349	#125	—	19	2	no	—
350	#125	—	19	2	no	—
351	#125	—	19	2	no	—
352	#125	—	19	2	no	—
353	#125	—	19	2	no	—
354	#125	—	19	2	no	—
355	#125	—	19	2	no	—
356	#125	—	19	2	no	—
357	#125	—	19	2	no	—
358	#125	—	19	2	no	—
359	#125	—	19	1	no	—
360	#125	—	19	2	no	—
361	#125	—	19	2	no	—
362	#125	—	19	2	no	—
363	#125	—	19	2	no	—
364	#125	—	19	2	no	—
365	#125	C₂×D₁₉	1	2	yes	—
366	#125	C₂×D₁₉	1	1	yes	characteristic
367	#124	—	19	1	no	—
368	#123	—	19	1	no	—
369	#123	—	19	2	no	—
370	#123	—	19	1	no	—
371	#123	—	19	2	no	—
372	#123	—	19	2	no	—
373	#123	C₂×D₁₉	1	2	yes	—
374	C₂²⋊Q₈	—	19	1	no	—
375	C₂²⋊Q₈	—	19	1	no	—
376	C₂²⋊Q₈	—	19	1	no	—
377	C₂²⋊Q₈	—	19	2	no	—
378	C₂²⋊Q₈	—	19	1	no	—
379	C₂²⋊Q₈	—	19	2	no	—
380	C₂²⋊Q₈	—	19	2	no	—
381	C₂²⋊Q₈	—	19	1	no	—
382	C₂²⋊Q₈	—	19	2	no	—
383	C₂²⋊Q₈	—	19	2	no	—
384	C₂²⋊Q₈	—	19	2	no	—
385	C₂²⋊Q₈	—	19	2	no	—
386	C₂²⋊Q₈	—	19	2	no	—
387	C₂²⋊Q₈	—	19	2	no	—
388	C₂²⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
389	C₂²⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
390	#121	—	19	1	no	—
391	C₄×Q₈	—	19	1	no	—
392	C₄×Q₈	—	19	1	no	—
393	C₄×Q₈	—	19	2	no	—
394	C₄×Q₈	—	19	1	no	—
395	C₄×Q₈	—	19	2	no	—
396	C₄×Q₈	—	19	1	no	—
397	C₄×Q₈	—	19	1	no	—
398	C₄×Q₈	—	19	2	no	—
399	C₄×Q₈	—	19	1	no	—
400	C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
401	C₄×D₄	—	19	2	no	—
402	C₄×D₄	—	19	1	no	—
403	C₄×D₄	—	19	1	no	—
404	C₄×D₄	—	19	2	no	—
405	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
406	#117	—	19	1	no	—
407	#117	—	19	2	no	—
408	#117	—	19	1	no	—
409	#117	—	19	2	no	—
410	#117	—	19	2	no	—
411	#117	—	19	1	no	—
412	#117	—	19	2	no	—
413	#117	C₂×D₁₉	1	1	yes	characteristic
414	#117	C₂×D₁₉	1	2	yes	—
415	C₂×C₄⋊C₄	—	19	2	no	—
416	C₂×C₄⋊C₄	—	19	2	no	—
417	C₂×C₄⋊C₄	—	19	1	no	—
418	C₂×C₄⋊C₄	—	19	1	no	—
419	C₂×C₄⋊C₄	—	19	1	no	—
420	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
421	C₂×C₄²	—	19	1	no	—
422	C₁₉	#3563	1	1	yes	characteristic, complemented, Sylow
423	C₂×Q₈	—	19	1	no	—
424	C₂×Q₈	—	19	2	no	—
425	C₂×Q₈	—	19	2	no	—
426	C₂×Q₈	—	19	2	no	—
427	C₂×Q₈	—	19	1	no	—
428	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
429	C₂×D₄	—	19	1	no	—
430	C₂×D₄	—	19	1	no	—
431	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
432	C₂²×C₄	—	19	1	no	—
433	C₂²×C₄	—	19	1	no	—
434	C₂²×C₄	—	19	2	no	—
435	C₂²×C₄	—	19	2	no	—
436	C₂²×C₄	—	19	1	no	—
437	C₂²×C₄	—	19	2	no	—
438	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
439	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
440	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
441	C₄⋊C₄	—	19	2	no	—
442	C₄⋊C₄	—	19	2	no	—
443	C₄⋊C₄	—	19	2	no	—
444	C₄⋊C₄	—	19	2	no	—
445	C₄⋊C₄	—	19	2	no	—
446	C₄⋊C₄	—	19	2	no	—
447	C₄⋊C₄	—	19	2	no	—
448	C₄⋊C₄	—	19	2	no	—
449	C₄⋊C₄	—	19	1	no	—
450	C₄⋊C₄	—	19	1	no	—
451	C₄⋊C₄	—	19	2	no	—
452	C₄⋊C₄	—	19	1	no	—
453	C₄⋊C₄	—	19	2	no	—
454	C₄⋊C₄	—	19	1	no	—
455	C₄⋊C₄	—	19	1	no	—
456	C₄⋊C₄	—	19	1	no	—
457	C₄⋊C₄	—	19	2	no	—
458	C₄⋊C₄	—	19	2	no	—
459	C₄⋊C₄	—	19	2	no	—
460	C₄⋊C₄	—	19	2	no	—
461	C₄⋊C₄	—	19	2	no	—
462	C₄⋊C₄	—	19	2	no	—
463	C₄⋊C₄	—	19	1	no	—
464	C₄⋊C₄	—	19	1	no	—
465	C₄⋊C₄	—	19	1	no	—
466	C₄⋊C₄	—	19	2	no	—
467	C₄⋊C₄	—	19	2	no	—
468	C₄⋊C₄	—	19	2	no	—
469	C₄⋊C₄	—	19	2	no	—
470	C₄⋊C₄	—	19	2	no	—
471	C₄⋊C₄	—	19	2	no	—
472	C₄⋊C₄	—	19	2	no	—
473	C₄⋊C₄	—	19	1	no	—
474	C₄⋊C₄	—	19	2	no	—
475	C₄⋊C₄	—	19	1	no	—
476	C₄⋊C₄	—	19	2	no	—
477	C₄⋊C₄	—	19	1	no	—
478	C₄⋊C₄	—	19	2	no	—
479	C₄⋊C₄	—	19	2	no	—
480	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
481	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
482	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
483	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
484	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
485	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
486	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
487	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
488	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
489	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
490	C₂²⋊C₄	—	19	2	no	—
491	C₂²⋊C₄	—	19	1	no	—
492	C₂²⋊C₄	—	19	1	no	—
493	C₂²⋊C₄	—	19	1	no	—
494	C₂²⋊C₄	—	19	1	no	—
495	C₂²⋊C₄	—	19	2	no	—
496	C₂²⋊C₄	—	19	1	no	—
497	C₂²⋊C₄	—	19	1	no	—
498	C₂²⋊C₄	—	19	2	no	—
499	C₂²⋊C₄	—	19	1	no	—
500	C₂²⋊C₄	—	19	2	no	—
501	C₂²⋊C₄	—	19	2	no	—
502	C₂²⋊C₄	—	19	1	no	—
503	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
504	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
505	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
506	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
507	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
508	C₄²	—	19	1	no	—
509	C₄²	—	19	1	no	—
510	C₄²	—	19	1	no	—
511	C₄²	—	19	1	no	—
512	C₄²	—	19	2	no	—
513	C₄²	—	19	2	no	—
514	C₄²	—	19	2	no	—
515	C₄²	—	19	1	no	—
516	C₄²	—	19	2	no	—
517	C₄²	—	19	2	no	—
518	C₄²	—	19	2	no	—
519	C₄²	C₂²×D₁₉	1	2	yes	—
520	C₄²	C₂²×D₁₉	1	1	yes	characteristic
521	C₄²	C₂²×D₁₉	1	2	yes	—
522	C₂³	—	19	1	no	—
523	C₂³	C₂³×D₁₉	1	1	yes	characteristic
524	C₂³	C₂³×D₁₉	1	1	yes	characteristic
525	Q₈	—	2	2	no	—
526	Q₈	—	38	2	no	—
527	Q₈	—	76	2	no	—
528	Q₈	—	76	2	no	—
529	Q₈	—	76	2	no	—
530	Q₈	—	76	1	no	—
531	D₄	—	2	2	no	—
532	D₄	—	38	2	no	—
533	D₄	—	76	1	no	—
534	C₂×C₄	—	2	4	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	19	1	no	—
538	C₂×C₄	—	19	2	no	—
539	C₂×C₄	—	19	1	no	—
540	C₂×C₄	—	19	1	no	—
541	C₂×C₄	—	19	1	no	—
542	C₂×C₄	—	19	1	no	—
543	C₂×C₄	—	19	1	no	—
544	C₂×C₄	—	19	2	no	—
545	C₂×C₄	—	19	1	no	—
546	C₂×C₄	—	19	2	no	—
547	C₂×C₄	—	19	2	no	—
548	C₂×C₄	—	38	2	no	—
549	C₂×C₄	—	38	2	no	—
550	C₂×C₄	—	76	2	no	—
551	C₂×C₄	—	76	2	no	—
552	C₂×C₄	—	76	2	no	—
553	C₂×C₄	—	76	1	no	—
554	C₂×C₄	C₂³×D₁₉	1	2	yes	—
555	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
556	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
557	C₂×C₄	C₂³×D₁₉	1	2	yes	—
558	C₂×C₄	C₂³×D₁₉	1	2	yes	—
559	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
560	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
561	C₂×C₄	C₂³×D₁₉	1	2	yes	—
562	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
563	C₂²	—	2	1	no	—
564	C₂²	—	2	1	no	—
565	C₂²	—	2	1	no	—
566	C₂²	—	2	1	no	—
567	C₂²	—	2	1	no	—
568	C₂²	—	38	1	no	—
569	C₂²	—	38	1	no	—
570	C₂²	—	38	1	no	—
571	C₂²	#10597436	1	2	yes	—
572	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
573	C₄	—	2	2	no	—
574	C₄	—	2	2	no	—
575	C₄	—	2	1	no	—
576	C₄	—	2	1	no	—
577	C₄	—	2	1	no	—
578	C₄	—	2	2	no	—
579	C₄	—	2	2	no	—
580	C₄	—	2	1	no	—
581	C₄	—	38	1	no	—
582	C₄	—	38	1	no	—
583	C₄	—	38	1	no	—
584	C₄	—	38	1	no	—
585	C₄	—	38	2	no	—
586	C₄	—	38	2	no	—
587	C₄	—	38	2	no	—
588	C₄	—	38	1	no	—
589	C₄	—	38	1	no	—
590	C₄	—	38	2	no	—
591	C₄	—	38	1	no	—
592	C₄	#10597436	1	2	yes	—
593	C₂	—	2	2	no	—
594	C₂	—	4	1	no	—
595	C₂	—	76	1	no	—
596	C₂	C₂×#10597436	1	1	yes	characteristic
597	C₂	C₂×#10597436	1	1	yes	characteristic
598	C₂	#11927381	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Fitting	C₁₉×#552	C₂
prime radical	#10597385	C₂²
hypercenter	#552	D₁₉
hypocenter	C₁₉	#3563
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ #552

Complements

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

N	H ≅ G/N	type
1. C₁₉⋊#564	C₂	semidirect
2. #11927296	C₂	semidirect
3. #11927273	C₂	semidirect
4. #11927271	C₂	semidirect
5. #11927252	C₂	semidirect
6. #11927251	C₂	semidirect
7. #11927236	C₂	semidirect
8. #11927233	C₂	semidirect
9. #11927231	C₂	semidirect
10. #11927229	C₂	semidirect
11. #11927227	C₂	semidirect
12. #11927174	C₂	semidirect
13. #11927172	C₂	semidirect
14. #11927172	C₂	semidirect
15. #11927157	C₂	semidirect
16. #11927154	C₂	semidirect
17. #11927152	C₂	semidirect
18. #11927151	C₂	semidirect
20. #11927096	C₂	semidirect
22. C₂×#10597336	C₂	semidirect
23. C₁₉×#552	C₂	semidirect
305. #552	D₁₉	semidirect
422. C₁₉	#3563	semidirect

Maximal subgroups

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

subgroup	index
C₁₉⋊#564	2
#11927296	2
#11927273	2
#11927271	2
#11927252	2
#11927251	2
#11927236	2
#11927233	2
#11927231	2
#11927229	2
#11927227	2
#11927174	2
#11927172	2
#11927157	2
#11927154	2
#11927152	2
#11927151	2
#11927138	2
#11927096	2
#11927074	2
C₂×#10597336	2
C₁₉×#552	2
#3563	19