Subgroups — #14577383

Order 2432.

1022 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927268	C₂	1	1	yes	maximal, characteristic, complemented
2	#11927265	C₂	1	1	yes	maximal, characteristic, complemented
3	#11927249	C₂	1	1	yes	maximal, characteristic, complemented
4	#11927236	C₂	1	1	yes	maximal, characteristic, complemented
5	#11927235	C₂	1	1	yes	maximal, characteristic, complemented
6	#11927234	C₂	1	1	yes	maximal, characteristic, complemented
7	#11927229	C₂	1	1	yes	maximal, characteristic, complemented
8	#11927228	C₂	1	2	yes	maximal, complemented
9	#11927226	C₂	1	2	yes	maximal, complemented
10	#11927223	C₂	1	2	yes	maximal, complemented
11	#11927221	C₂	1	2	yes	maximal, complemented
12	#11927171	C₂	1	1	yes	maximal, characteristic, complemented
13	#11927164	C₂	1	2	yes	maximal, complemented
14	#11927153	C₂	1	2	yes	maximal, complemented
15	#11927117	C₂	1	1	yes	maximal, characteristic, complemented
16	#11927096	C₂	1	2	yes	maximal, complemented
17	#11927074	C₂	1	2	yes	maximal, complemented
18	#11927053	C₂	1	1	yes	maximal, characteristic
19	C₂²⋊Q₈×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
20	#11927025	C₂	1	1	yes	maximal, characteristic, complemented
21	#11927020	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#10597338	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₉×#554	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×Q₈×D₁₉	C₂²	1	1	yes	characteristic
25	C₂×#64541	C₂²	1	1	yes	characteristic
26	C₂²×C₄×D₁₉	C₂²	1	1	yes	characteristic
27	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
28	C₁₉×#125	C₂²	1	2	yes	complemented
29	C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
30	C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
31	C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
32	C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	complemented
33	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
34	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
35	C₄×D₄×C₁₉	C₂²	1	2	yes	—
36	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
37	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
38	#10597393	C₂²	1	2	yes	—
39	#10597392	C₂²	1	2	yes	—
40	#10597392	C₂²	1	1	yes	characteristic
41	#10597392	C₂²	1	1	yes	characteristic, complemented
42	Q₈×Dic₁₉	C₂²	1	2	yes	complemented
43	Q₈×Dic₁₉	C₂²	1	1	yes	characteristic, complemented
44	#10597390	C₂²	1	2	yes	complemented
45	#10597385	C₂²	1	1	yes	characteristic
46	#10597383	C₂²	1	1	yes	characteristic
47	#10597381	C₂²	1	2	yes	—
48	#10597375	C₂²	1	2	yes	—
49	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
50	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
51	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	—
52	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	—
53	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	complemented
54	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	2	yes	—
55	#10597372	C₂²	1	2	yes	complemented
56	#10597372	C₂²	1	1	yes	characteristic, complemented
57	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
58	#10597370	C₂²	1	2	yes	—
59	#10597370	C₂²	1	1	yes	characteristic
60	#10597370	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₄×Dic₁₉	C₂²	1	2	yes	—
62	#10597344	C₂²	1	2	yes	—
63	#10597344	C₂²	1	2	yes	—
64	#10597344	C₂²	1	2	yes	—
65	#10597344	C₂²	1	2	yes	complemented
66	#10597344	C₂²	1	2	yes	complemented
67	#10597343	C₂²	1	1	yes	characteristic
68	#10597343	C₂²	1	1	yes	characteristic, complemented
69	#10597342	C₂²	1	1	yes	characteristic
70	#10597342	C₂²	1	2	yes	—
71	#10597342	C₂²	1	2	yes	—
72	#10597342	C₂²	1	2	yes	complemented
73	#10597340	C₂²	1	1	yes	characteristic
74	#10597340	C₂²	1	2	yes	—
75	#10597340	C₂²	1	2	yes	—
76	#10597339	C₂²	1	2	yes	—
77	#10597338	C₂²	1	1	yes	characteristic
78	#10597338	C₂²	1	2	yes	—
79	#10597338	C₂²	1	2	yes	—
80	#10597338	C₂²	1	2	yes	—
81	#10597338	C₂²	1	1	yes	characteristic
82	#10597338	C₂²	1	1	yes	characteristic
83	#10597338	C₂²	1	1	yes	characteristic
84	#10597338	C₂²	1	1	yes	characteristic, complemented
85	C₄⋊C₄×D₁₉	C₂²	1	1	yes	characteristic
86	C₄⋊C₄×D₁₉	C₂²	1	2	yes	—
87	C₄⋊C₄×D₁₉	C₂²	1	1	yes	characteristic, complemented
88	#10597336	C₂²	1	2	yes	complemented
89	#10597336	C₂²	1	1	yes	characteristic, complemented
90	#10597335	C₂²	1	2	yes	complemented
91	#10597335	C₂²	1	2	yes	complemented
92	#10597335	C₂²	1	2	yes	complemented
93	#10597335	C₂²	1	2	yes	complemented
94	#10597335	C₂²	1	2	yes	complemented
95	#10597334	C₂²	1	2	yes	complemented
96	#10597334	C₂²	1	1	yes	characteristic, complemented
97	#10597333	C₂²	1	2	yes	complemented
98	#10597333	C₂²	1	2	yes	complemented
99	#10597333	C₂²	1	2	yes	complemented
100	#10597333	C₂²	1	1	yes	characteristic, complemented
101	#10597332	C₂²	1	2	yes	—
102	#10597331	C₂²	1	2	yes	—
103	#10597331	C₂²	1	2	yes	complemented
104	#10597330	C₂²	1	1	yes	characteristic
105	#10597329	C₂²	1	1	yes	characteristic
106	#10597329	C₂²	1	2	yes	—
107	#10597328	C₂²	1	1	yes	characteristic
108	C₂²⋊C₄×D₁₉	C₂²	1	2	yes	—
109	#10597325	C₂²	1	2	yes	complemented
110	#10597325	C₂²	1	2	yes	complemented
111	#10597324	C₂²	1	1	yes	characteristic
112	#10597324	C₂²	1	2	yes	—
113	#10597323	C₂²	1	2	yes	—
114	#10597323	C₂²	1	2	yes	—
115	#10597322	C₂²	1	2	yes	—
116	C₄×D₇₆	C₂²	1	1	yes	characteristic
117	#10597318	C₂²	1	1	yes	characteristic
118	#10597318	C₂²	1	2	yes	—
119	#10597318	C₂²	1	2	yes	complemented
120	#10597316	C₂²	1	1	yes	characteristic, complemented
121	C₄×Dic₃₈	C₂²	1	2	yes	complemented
122	C₄×Dic₃₈	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₉	C₂³	1	1	yes	characteristic
124	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
125	C₂×Q₈×C₁₉	C₂³	1	2	yes	—
126	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
127	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
130	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
131	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
132	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
133	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
134	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
135	C₂²×Dic₁₉	C₂³	1	2	yes	—
136	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
137	Q₈×D₁₉	—	2	4	no	—
138	#64541	—	2	4	no	—
139	C₂×D₇₆	C₂³	1	1	yes	characteristic
140	C₂×D₇₆	C₂³	1	1	yes	characteristic
141	C₂×C₄×D₁₉	—	2	4	no	—
142	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
143	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
144	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
145	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
146	C₂×C₄×D₁₉	C₂³	1	2	yes	—
147	C₂×C₄×D₁₉	C₂³	1	2	yes	—
148	C₂×C₄×D₁₉	C₂³	1	2	yes	—
149	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
150	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
151	C₂×Dic₃₈	C₂³	1	2	yes	—
152	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
153	C₂×Dic₃₈	C₂³	1	2	yes	—
154	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
155	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
156	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
157	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
158	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
159	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
160	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
161	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
162	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
163	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
164	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
165	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
166	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
167	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
168	C₄²×C₁₉	C₂³	1	2	yes	—
169	C₄²×C₁₉	C₂³	1	1	yes	characteristic
170	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
171	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
172	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
173	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
174	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
175	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
176	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
177	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
178	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
179	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
180	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
181	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
182	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
183	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
184	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
185	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
186	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
187	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
188	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
189	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
190	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
191	C₄⋊Dic₁₉	C₂³	1	2	yes	—
192	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
193	C₄⋊Dic₁₉	C₂³	1	2	yes	—
194	C₄⋊Dic₁₉	C₂³	1	2	yes	—
195	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
196	C₄⋊Dic₁₉	C₂³	1	2	yes	—
197	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
198	C₄⋊Dic₁₉	C₂³	1	2	yes	—
199	Dic₁₉⋊C₄	C₂³	1	2	yes	—
200	Dic₁₉⋊C₄	C₂³	1	2	yes	—
201	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
202	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
210	Dic₁₉⋊C₄	C₂³	1	2	yes	—
211	Dic₁₉⋊C₄	C₂³	1	2	yes	—
212	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
213	Dic₁₉⋊C₄	C₂³	1	2	yes	—
214	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
215	C₄×Dic₁₉	C₂³	1	2	yes	—
216	C₄×Dic₁₉	C₂³	1	2	yes	—
217	C₄×Dic₁₉	C₂³	1	2	yes	—
218	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
219	C₄×Dic₁₉	C₂³	1	2	yes	—
220	C₄×Dic₁₉	C₂³	1	2	yes	—
221	C₄×Dic₁₉	C₂³	1	2	yes	—
222	C₄×Dic₁₉	C₂³	1	2	yes	—
223	C₄×Dic₁₉	C₂³	1	2	yes	—
224	C₄×Dic₁₉	C₂³	1	2	yes	—
225	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
226	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
227	C₂²×D₁₉	—	2	2	no	—
228	C₂²×D₁₉	—	2	2	no	—
229	C₂²×D₁₉	—	4	1	no	—
230	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
231	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
232	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
233	Q₈×C₁₉	—	2	2	no	—
234	Q₈×C₁₉	—	4	2	no	—
235	D₄×C₁₉	—	2	2	no	—
236	C₂×C₄×C₁₉	—	2	2	no	—
237	C₂×C₄×C₁₉	—	2	2	no	—
238	C₂×C₄×C₁₉	—	4	2	no	—
239	C₂×C₄×C₁₉	—	4	2	no	—
240	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
241	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
242	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
243	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
244	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
245	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
246	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
247	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
248	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
249	C₂²⋊D₁₉	—	2	2	no	—
250	C₂²⋊D₁₉	—	2	2	no	—
251	C₂²⋊D₁₉	—	2	2	no	—
252	C₂²⋊D₁₉	—	4	1	no	—
253	C₂×Dic₁₉	—	2	4	no	—
254	C₂×Dic₁₉	—	2	2	no	—
255	C₂×Dic₁₉	C₂⁴	1	2	yes	—
256	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
257	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
258	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
259	C₂×Dic₁₉	C₂⁴	1	2	yes	—
260	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
261	C₂×Dic₁₉	C₂⁴	1	2	yes	—
262	C₂×Dic₁₉	C₂⁴	1	2	yes	—
263	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
264	D₇₆	—	2	2	no	—
265	D₇₆	—	4	1	no	—
266	C₄×D₁₉	—	2	2	no	—
267	C₄×D₁₉	—	2	4	no	—
268	C₄×D₁₉	—	2	2	no	—
269	C₄×D₁₉	—	2	2	no	—
270	C₄×D₁₉	—	2	2	no	—
271	C₄×D₁₉	—	4	2	no	—
272	C₄×D₁₉	—	4	2	no	—
273	C₄×D₁₉	#41	1	4	yes	—
274	Dic₃₈	—	2	2	no	—
275	Dic₃₈	—	2	2	no	—
276	Dic₃₈	—	2	4	no	—
277	Dic₃₈	—	4	2	no	—
278	#3495	—	19	1	no	maximal, Sylow
279	C₂²×C₁₉	—	2	1	no	—
280	C₂²×C₁₉	—	2	1	no	—
281	C₂²×C₁₉	—	2	1	no	—
282	C₂²×C₁₉	—	2	1	no	—
283	C₂²×C₁₉	—	2	1	no	—
284	C₂²×C₁₉	2₋¹⁺⁴	1	2	yes	—
285	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
286	C₂×D₁₉	—	2	1	no	—
287	C₂×D₁₉	—	2	1	no	—
288	C₂×D₁₉	—	2	1	no	—
289	C₂×D₁₉	—	2	1	no	—
290	C₂×D₁₉	—	2	1	no	—
291	C₂×D₁₉	—	2	1	no	—
292	C₂×D₁₉	—	2	1	no	—
293	C₂×D₁₉	—	2	1	no	—
294	C₂×D₁₉	—	4	4	no	—
295	C₂×D₁₉	C₂×#41	1	2	yes	—
296	C₄×C₁₉	—	2	2	no	—
297	C₄×C₁₉	—	2	1	no	—
298	C₄×C₁₉	—	2	1	no	—
299	C₄×C₁₉	—	2	1	no	—
300	C₄×C₁₉	—	2	2	no	—
301	C₄×C₁₉	—	2	2	no	—
302	C₄×C₁₉	—	2	2	no	—
303	C₄×C₁₉	—	2	1	no	—
304	C₄×C₁₉	C₂×#41	1	2	yes	—
305	Dic₁₉	—	2	2	no	—
306	Dic₁₉	—	2	1	no	—
307	Dic₁₉	—	2	1	no	—
308	Dic₁₉	—	2	2	no	—
309	Dic₁₉	—	2	2	no	—
310	Dic₁₉	—	2	1	no	—
311	Dic₁₉	—	2	1	no	—
312	Dic₁₉	—	2	2	no	—
313	Dic₁₉	C₂×#41	1	2	yes	—
314	#556	—	19	1	no	—
315	#556	—	19	1	no	—
316	#554	—	19	1	no	—
317	#554	D₁₉	1	1	yes	characteristic, complemented
318	#552	—	19	2	no	—
319	#552	—	19	1	no	—
320	#552	—	19	2	no	—
321	#552	—	19	1	no	—
322	#552	—	19	1	no	—
323	#552	—	19	1	no	—
324	#551	—	19	2	no	—
325	#551	—	19	2	no	—
326	#544	—	19	1	no	—
327	#542	—	19	2	no	—
328	#541	—	19	2	no	—
329	#536	—	19	1	no	—
330	#533	—	19	2	no	—
331	#529	—	19	2	no	—
332	#525	—	19	1	no	—
333	C₂×C₂²⋊Q₈	—	19	1	no	—
334	#520	—	19	1	no	—
335	#519	—	19	1	no	—
336	C₂×#117	—	19	1	no	—
337	C₂×C₁₉	—	2	2	no	—
338	C₂×C₁₉	—	4	1	no	—
339	C₂×C₁₉	C₂²×#41	1	1	yes	characteristic
340	C₂×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
341	C₂×C₁₉	#585	1	1	yes	characteristic
342	D₁₉	—	2	2	no	—
343	D₁₉	—	4	1	no	—
344	D₁₉	—	4	1	no	—
345	C₂×#41	—	19	1	no	—
346	C₂²×Q₈	—	19	1	no	—
347	C₂³×C₄	—	19	1	no	—
348	C₄⋊Q₈	—	19	2	no	—
349	C₄⋊Q₈	—	19	2	no	—
350	C₄⋊Q₈	—	19	1	no	—
351	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
352	#126	—	19	2	no	—
353	#126	—	19	2	no	—
354	#126	—	19	2	no	—
355	#126	—	19	2	no	—
356	#126	—	19	2	no	—
357	#126	—	19	2	no	—
358	#126	—	19	2	no	—
359	#126	—	19	2	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	—	19	2	no	—
366	#125	—	19	1	no	—
367	#125	—	19	1	no	—
368	#125	C₂×D₁₉	1	2	yes	complemented
369	#124	—	19	2	no	—
370	#124	—	19	2	no	—
371	#124	—	19	2	no	—
372	#123	—	19	2	no	—
373	#123	—	19	2	no	—
374	#123	—	19	1	no	—
375	#123	—	19	2	no	—
376	#123	—	19	2	no	—
377	#123	—	19	1	no	—
378	#123	—	19	2	no	—
379	#123	—	19	2	no	—
380	C₂²⋊Q₈	—	19	1	no	—
381	C₂²⋊Q₈	—	19	2	no	—
382	C₂²⋊Q₈	—	19	1	no	—
383	C₂²⋊Q₈	—	19	1	no	—
384	C₂²⋊Q₈	—	19	2	no	—
385	C₂²⋊Q₈	—	19	1	no	—
386	C₂²⋊Q₈	—	19	2	no	—
387	C₂²⋊Q₈	—	19	1	no	—
388	C₂²⋊Q₈	—	19	1	no	—
389	C₂²⋊Q₈	—	19	1	no	—
390	C₂²⋊Q₈	—	19	2	no	—
391	C₂²⋊Q₈	—	19	2	no	—
392	C₂²⋊Q₈	—	19	2	no	—
393	C₂²⋊Q₈	—	19	1	no	—
394	C₂²⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
395	C₂²⋊Q₈	C₂×D₁₉	1	2	yes	—
396	C₂²⋊Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
397	C₂²⋊Q₈	C₂×D₁₉	1	2	yes	complemented
398	#121	—	19	1	no	—
399	#121	—	19	1	no	—
400	#120	—	19	1	no	—
401	#120	—	19	1	no	—
402	C₄×Q₈	—	19	1	no	—
403	C₄×Q₈	—	19	2	no	—
404	C₄×Q₈	—	19	2	no	—
405	C₄×Q₈	—	19	1	no	—
406	C₄×Q₈	—	19	2	no	—
407	C₄×Q₈	—	19	2	no	—
408	C₄×Q₈	—	19	2	no	—
409	C₄×Q₈	—	19	1	no	—
410	C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
411	C₄×D₄	—	19	2	no	—
412	C₄×D₄	—	19	2	no	—
413	C₄×D₄	—	19	1	no	—
414	C₄×D₄	—	19	1	no	—
415	C₄×D₄	—	19	2	no	—
416	C₄×D₄	—	19	2	no	—
417	C₄×D₄	—	19	1	no	—
418	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
419	C₄×D₄	C₂×D₁₉	1	2	yes	—
420	#117	—	19	1	no	—
421	#117	—	19	2	no	—
422	#117	—	19	1	no	—
423	#117	—	19	1	no	—
424	#117	—	19	2	no	—
425	#117	—	19	1	no	—
426	#117	—	19	2	no	—
427	#117	—	19	1	no	—
428	#117	—	19	2	no	—
429	#117	—	19	1	no	—
430	#117	—	19	2	no	—
431	#117	—	19	2	no	—
432	#117	—	19	1	no	—
433	#117	—	19	2	no	—
434	#117	—	19	2	no	—
435	C₂×C₄⋊C₄	—	19	1	no	—
436	C₂×C₄⋊C₄	—	19	1	no	—
437	C₂×C₄⋊C₄	—	19	1	no	—
438	C₂×C₄⋊C₄	—	19	2	no	—
439	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
440	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic, complemented
441	C₂×C₂²⋊C₄	—	19	2	no	—
442	C₂×C₂²⋊C₄	—	19	2	no	—
443	C₂×C₄²	—	19	2	no	—
444	C₁₉	#3495	1	1	yes	characteristic, complemented, Sylow
445	C₂⁴	—	19	1	no	—
446	#41	—	38	4	no	—
447	C₂×Q₈	—	19	1	no	—
448	C₂×Q₈	—	19	2	no	—
449	C₂×Q₈	—	19	1	no	—
450	C₂×Q₈	—	19	2	no	—
451	C₂×Q₈	—	38	4	no	—
452	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
453	C₂×Q₈	C₂²×D₁₉	1	2	yes	—
454	C₂×D₄	—	19	1	no	—
455	C₂×D₄	—	19	1	no	—
456	C₂×D₄	—	19	1	no	—
457	C₂×D₄	—	19	1	no	—
458	C₂×D₄	—	19	1	no	—
459	C₂×D₄	—	19	1	no	—
460	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
461	C₂²×C₄	—	19	1	no	—
462	C₂²×C₄	—	19	1	no	—
463	C₂²×C₄	—	19	2	no	—
464	C₂²×C₄	—	19	2	no	—
465	C₂²×C₄	—	19	1	no	—
466	C₂²×C₄	—	19	1	no	—
467	C₂²×C₄	—	19	1	no	—
468	C₂²×C₄	—	19	1	no	—
469	C₂²×C₄	—	19	2	no	—
470	C₂²×C₄	—	19	2	no	—
471	C₂²×C₄	—	38	4	no	—
472	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
473	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
474	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
475	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
476	C₄⋊C₄	—	19	2	no	—
477	C₄⋊C₄	—	19	2	no	—
478	C₄⋊C₄	—	19	2	no	—
479	C₄⋊C₄	—	19	2	no	—
480	C₄⋊C₄	—	19	1	no	—
481	C₄⋊C₄	—	19	1	no	—
482	C₄⋊C₄	—	19	2	no	—
483	C₄⋊C₄	—	19	2	no	—
484	C₄⋊C₄	—	19	2	no	—
485	C₄⋊C₄	—	19	2	no	—
486	C₄⋊C₄	—	19	2	no	—
487	C₄⋊C₄	—	19	2	no	—
488	C₄⋊C₄	—	19	2	no	—
489	C₄⋊C₄	—	19	1	no	—
490	C₄⋊C₄	—	19	1	no	—
491	C₄⋊C₄	—	19	2	no	—
492	C₄⋊C₄	—	19	1	no	—
493	C₄⋊C₄	—	19	1	no	—
494	C₄⋊C₄	—	19	1	no	—
495	C₄⋊C₄	—	19	2	no	—
496	C₄⋊C₄	—	19	2	no	—
497	C₄⋊C₄	—	19	2	no	—
498	C₄⋊C₄	—	19	2	no	—
499	C₄⋊C₄	—	19	1	no	—
500	C₄⋊C₄	—	19	2	no	—
501	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
502	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
503	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
504	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
505	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
506	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
507	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
508	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
509	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
510	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
511	C₂²⋊C₄	—	19	2	no	—
512	C₂²⋊C₄	—	19	1	no	—
513	C₂²⋊C₄	—	19	1	no	—
514	C₂²⋊C₄	—	19	2	no	—
515	C₂²⋊C₄	—	19	2	no	—
516	C₂²⋊C₄	—	19	2	no	—
517	C₂²⋊C₄	—	19	2	no	—
518	C₂²⋊C₄	—	19	2	no	—
519	C₂²⋊C₄	—	19	2	no	—
520	C₂²⋊C₄	—	19	2	no	—
521	C₂²⋊C₄	—	19	2	no	—
522	C₂²⋊C₄	—	19	1	no	—
523	C₂²⋊C₄	—	19	1	no	—
524	C₂²⋊C₄	—	19	1	no	—
525	C₂²⋊C₄	—	19	2	no	—
526	C₂²⋊C₄	—	19	2	no	—
527	C₂²⋊C₄	—	19	1	no	—
528	C₂²⋊C₄	—	19	1	no	—
529	C₂²⋊C₄	—	19	1	no	—
530	C₂²⋊C₄	—	19	2	no	—
531	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
532	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
533	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
534	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
535	C₄²	—	19	2	no	—
536	C₄²	—	19	2	no	—
537	C₄²	—	19	2	no	—
538	C₄²	—	19	2	no	—
539	C₄²	—	19	2	no	—
540	C₄²	—	19	2	no	—
541	C₄²	—	19	2	no	—
542	C₄²	—	19	2	no	—
543	C₄²	—	19	2	no	—
544	C₄²	—	19	1	no	—
545	C₄²	C₂²×D₁₉	1	2	yes	—
546	C₄²	C₂²×D₁₉	1	1	yes	characteristic
547	C₂³	—	19	1	no	—
548	C₂³	—	19	1	no	—
549	C₂³	—	19	1	no	—
550	C₂³	—	38	2	no	—
551	C₂³	—	38	2	no	—
552	C₂³	—	76	1	no	—
553	C₂³	C₂³×D₁₉	1	1	yes	characteristic
554	C₂³	C₂³×D₁₉	1	1	yes	characteristic
555	Q₈	—	2	2	no	—
556	Q₈	—	4	2	no	—
557	Q₈	—	38	4	no	—
558	Q₈	—	38	2	no	—
559	Q₈	—	38	2	no	—
560	Q₈	—	76	2	no	—
561	D₄	—	2	2	no	—
562	D₄	—	38	2	no	—
563	D₄	—	38	2	no	—
564	D₄	—	38	2	no	—
565	D₄	—	38	2	no	—
566	D₄	—	76	1	no	—
567	D₄	—	76	1	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	4	2	no	—
571	C₂×C₄	—	4	2	no	—
572	C₂×C₄	—	19	1	no	—
573	C₂×C₄	—	19	4	no	—
574	C₂×C₄	—	19	2	no	—
575	C₂×C₄	—	19	1	no	—
576	C₂×C₄	—	19	1	no	—
577	C₂×C₄	—	19	1	no	—
578	C₂×C₄	—	19	2	no	—
579	C₂×C₄	—	19	2	no	—
580	C₂×C₄	—	19	1	no	—
581	C₂×C₄	—	19	2	no	—
582	C₂×C₄	—	38	2	no	—
583	C₂×C₄	—	38	2	no	—
584	C₂×C₄	—	38	4	no	—
585	C₂×C₄	—	38	2	no	—
586	C₂×C₄	—	38	4	no	—
587	C₂×C₄	—	38	2	no	—
588	C₂×C₄	—	38	2	no	—
589	C₂×C₄	—	76	2	no	—
590	C₂×C₄	—	76	2	no	—
591	C₂×C₄	C₂³×D₁₉	1	2	yes	—
592	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
593	C₂×C₄	C₂³×D₁₉	1	2	yes	—
594	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
595	C₂×C₄	C₂³×D₁₉	1	2	yes	—
596	C₂×C₄	C₂³×D₁₉	1	2	yes	—
597	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
598	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
599	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
600	C₂²	—	2	1	no	—
601	C₂²	—	2	1	no	—
602	C₂²	—	2	1	no	—
603	C₂²	—	2	1	no	—
604	C₂²	—	2	1	no	—
605	C₂²	—	19	2	no	—
606	C₂²	—	38	1	no	—
607	C₂²	—	38	1	no	—
608	C₂²	—	38	1	no	—
609	C₂²	—	38	1	no	—
610	C₂²	—	38	1	no	—
611	C₂²	—	38	1	no	—
612	C₂²	—	38	1	no	—
613	C₂²	—	38	1	no	—
614	C₂²	—	76	4	no	—
615	C₂²	#10597433	1	2	yes	—
616	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
617	C₄	—	2	1	no	—
618	C₄	—	2	1	no	—
619	C₄	—	2	2	no	—
620	C₄	—	2	1	no	—
621	C₄	—	2	2	no	—
622	C₄	—	2	2	no	—
623	C₄	—	2	2	no	—
624	C₄	—	2	1	no	—
625	C₄	—	19	2	no	—
626	C₄	—	38	1	no	—
627	C₄	—	38	1	no	—
628	C₄	—	38	2	no	—
629	C₄	—	38	2	no	—
630	C₄	—	38	2	no	—
631	C₄	—	38	1	no	—
632	C₄	—	38	2	no	—
633	C₄	—	38	1	no	—
634	C₄	#41×D₁₉	1	2	yes	—
635	C₂	—	2	2	no	—
636	C₂	—	4	1	no	—
637	C₂	—	38	2	no	—
638	C₂	—	76	1	no	—
639	C₂	—	76	1	no	—
640	C₂	C₂×#41×D₁₉	1	1	yes	characteristic
641	C₂	C₂×#10597433	1	1	yes	characteristic
642	C₂	#11927379	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Fitting	C₁₉×#554	C₂
prime radical	#11927053	C₂
hypercenter	#554	D₁₉
hypocenter	C₁₉	#3495
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ #554

Complements

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

N	H ≅ G/N	type
1. #11927268	C₂	semidirect
2. #11927265	C₂	semidirect
3. #11927249	C₂	semidirect
4. #11927236	C₂	semidirect
5. #11927235	C₂	semidirect
6. #11927234	C₂	semidirect
7. #11927229	C₂	semidirect
8. #11927228	C₂	semidirect
9. #11927226	C₂	semidirect
10. #11927223	C₂	semidirect
11. #11927221	C₂	semidirect
12. #11927171	C₂	semidirect
13. #11927164	C₂	semidirect
14. #11927153	C₂	semidirect
15. #11927117	C₂	semidirect
16. #11927096	C₂	semidirect
17. #11927074	C₂	semidirect
19. C₂²⋊Q₈×D₁₉	C₂	semidirect
20. #11927025	C₂	semidirect
21. #11927020	C₂	semidirect
22. C₂×#10597338	C₂	semidirect
23. C₁₉×#554	C₂	semidirect
27. C₁₉×C₄⋊Q₈	C₂²	semidirect
28. C₁₉×#125	C₂²	semidirect
31. C₁₉×C₂²⋊Q₈	C₂²	semidirect
32. C₁₉×C₂²⋊Q₈	C₂²	semidirect
33. C₄×Q₈×C₁₉	C₂²	semidirect
37. C₂×C₄⋊C₄×C₁₉	C₂²	semidirect
41. #10597392	C₂²	semidirect
42. Q₈×Dic₁₉	C₂²	semidirect
43. Q₈×Dic₁₉	C₂²	semidirect
44. #10597390	C₂²	semidirect
53. C₄×C₂²⋊D₁₉	C₂²	semidirect
55. #10597372	C₂²	semidirect
56. #10597372	C₂²	semidirect
60. #10597370	C₂²	semidirect
65. #10597344	C₂²	semidirect
66. #10597344	C₂²	semidirect
68. #10597343	C₂²	semidirect
72. #10597342	C₂²	semidirect
84. #10597338	C₂²	semidirect
87. C₄⋊C₄×D₁₉	C₂²	semidirect
88. #10597336	C₂²	semidirect
89. #10597336	C₂²	semidirect
90. #10597335	C₂²	semidirect
91. #10597335	C₂²	semidirect
92. #10597335	C₂²	semidirect
93. #10597335	C₂²	semidirect
94. #10597335	C₂²	semidirect
95. #10597334	C₂²	semidirect
96. #10597334	C₂²	semidirect
97. #10597333	C₂²	semidirect
98. #10597333	C₂²	semidirect
99. #10597333	C₂²	semidirect
100. #10597333	C₂²	semidirect
103. #10597331	C₂²	semidirect
109. #10597325	C₂²	semidirect
110. #10597325	C₂²	semidirect
119. #10597318	C₂²	semidirect
120. #10597316	C₂²	semidirect
121. C₄×Dic₃₈	C₂²	semidirect
122. C₄×Dic₃₈	C₂²	semidirect
317. #554	D₁₉	semidirect
351. C₄⋊Q₈	C₂×D₁₉	semidirect
368. #125	C₂×D₁₉	semidirect
396. C₂²⋊Q₈	C₂×D₁₉	semidirect
397. C₂²⋊Q₈	C₂×D₁₉	semidirect
410. C₄×Q₈	C₂×D₁₉	semidirect
440. C₂×C₄⋊C₄	C₂×D₁₉	semidirect
444. C₁₉	#3495	semidirect

Maximal subgroups

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

subgroup	index
#11927268	2
#11927265	2
#11927249	2
#11927236	2
#11927235	2
#11927234	2
#11927229	2
#11927228	2
#11927226	2
#11927223	2
#11927221	2
#11927171	2
#11927164	2
#11927153	2
#11927117	2
#11927096	2
#11927074	2
#11927053	2
C₂²⋊Q₈×D₁₉	2
#11927025	2
#11927020	2
C₂×#10597338	2
C₁₉×#554	2
#3495	19