Subgroups — #14577876

Order 2432.

1014 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927295	C₂	1	2	yes	maximal, complemented
2	#11927293	C₂	1	2	yes	maximal, complemented
3	#11927236	C₂	1	1	yes	maximal, characteristic, complemented
4	#11927235	C₂	1	1	yes	maximal, characteristic, complemented
5	#11927234	C₂	1	1	yes	maximal, characteristic, complemented
6	#11927228	C₂	1	1	yes	maximal, characteristic, complemented
7	#11927223	C₂	1	2	yes	maximal, complemented
8	#11927221	C₂	1	2	yes	maximal, complemented
9	#11927209	C₂	1	1	yes	maximal, characteristic, complemented
10	Q₈×C₂²⋊D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
11	Q₈×C₂²⋊D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#11927173	C₂	1	2	yes	maximal, complemented
13	#11927171	C₂	1	2	yes	maximal, complemented
14	#11927155	C₂	1	1	yes	maximal, characteristic, complemented
15	#11927152	C₂	1	1	yes	maximal, characteristic, complemented
16	#11927140	C₂	1	2	yes	maximal, complemented
17	#11927136	C₂	1	2	yes	maximal, complemented
18	#11927118	C₂	1	1	yes	maximal, characteristic, complemented
19	#11927117	C₂	1	1	yes	maximal, characteristic, complemented
20	#11927053	C₂	1	1	yes	maximal, characteristic
21	C₂×#10597392	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂²⋊Q₈×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
23	D₄×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×Q₈×C₁₉	C₂²	1	1	yes	characteristic
25	C₂²×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
26	C₂×Q₈×D₁₉	C₂²	1	1	yes	characteristic
27	C₂×Q₈×D₁₉	C₂²	1	1	yes	characteristic, complemented
28	C₂×#64541	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₁₉	C₂²	1	1	yes	characteristic
30	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₁₉×C₄⋊Q₈	C₂²	1	2	yes	complemented
32	C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
33	C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
34	C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
35	C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	complemented
36	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
37	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
38	C₄×D₄×C₁₉	C₂²	1	2	yes	—
39	#10597393	C₂²	1	2	yes	—
40	#10597392	C₂²	1	1	yes	characteristic
41	#10597392	C₂²	1	1	yes	characteristic
42	#10597392	C₂²	1	1	yes	characteristic
43	#10597392	C₂²	1	2	yes	—
44	#10597392	C₂²	1	2	yes	—
45	#10597392	C₂²	1	1	yes	characteristic
46	#10597392	C₂²	1	1	yes	characteristic
47	#10597392	C₂²	1	2	yes	—
48	#10597392	C₂²	1	1	yes	characteristic, complemented
49	#10597392	C₂²	1	1	yes	characteristic, complemented
50	#10597392	C₂²	1	2	yes	complemented
51	Q₈×Dic₁₉	C₂²	1	1	yes	characteristic, complemented
52	Q₈×Dic₁₉	C₂²	1	1	yes	characteristic, complemented
53	#10597390	C₂²	1	2	yes	complemented
54	#10597390	C₂²	1	1	yes	characteristic, complemented
55	#10597390	C₂²	1	2	yes	complemented
56	#10597390	C₂²	1	2	yes	complemented
57	#10597385	C₂²	1	1	yes	characteristic
58	#10597383	C₂²	1	1	yes	characteristic
59	#10597381	C₂²	1	2	yes	—
60	#10597375	C₂²	1	2	yes	—
61	#10597375	C₂²	1	2	yes	complemented
62	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
63	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
64	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	—
65	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	—
66	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	2	yes	—
67	#10597372	C₂²	1	1	yes	characteristic, complemented
68	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
69	#10597370	C₂²	1	2	yes	—
70	#10597370	C₂²	1	1	yes	characteristic
71	#10597370	C₂²	1	1	yes	characteristic, complemented
72	#10597370	C₂²	1	2	yes	complemented
73	C₂×Dic₁₉⋊C₄	C₂²	1	2	yes	—
74	#10597344	C₂²	1	2	yes	—
75	#10597344	C₂²	1	2	yes	—
76	#10597344	C₂²	1	2	yes	—
77	#10597344	C₂²	1	2	yes	complemented
78	#10597343	C₂²	1	1	yes	characteristic
79	#10597342	C₂²	1	1	yes	characteristic
80	#10597342	C₂²	1	2	yes	—
81	#10597342	C₂²	1	2	yes	—
82	#10597342	C₂²	1	2	yes	complemented
83	#10597340	C₂²	1	1	yes	characteristic
84	#10597340	C₂²	1	2	yes	—
85	#10597340	C₂²	1	2	yes	—
86	#10597339	C₂²	1	2	yes	—
87	#10597338	C₂²	1	2	yes	—
88	#10597338	C₂²	1	1	yes	characteristic, complemented
89	C₄⋊C₄×D₁₉	C₂²	1	2	yes	—
90	C₄⋊C₄×D₁₉	C₂²	1	1	yes	characteristic
91	#10597336	C₂²	1	1	yes	characteristic, complemented
92	#10597336	C₂²	1	2	yes	complemented
93	#10597335	C₂²	1	2	yes	complemented
94	#10597335	C₂²	1	2	yes	complemented
95	#10597335	C₂²	1	2	yes	complemented
96	#10597335	C₂²	1	2	yes	complemented
97	#10597335	C₂²	1	2	yes	complemented
98	#10597335	C₂²	1	2	yes	complemented
99	#10597334	C₂²	1	2	yes	complemented
100	#10597334	C₂²	1	2	yes	complemented
101	#10597332	C₂²	1	2	yes	—
102	#10597331	C₂²	1	2	yes	—
103	#10597330	C₂²	1	1	yes	characteristic
104	#10597329	C₂²	1	1	yes	characteristic
105	#10597329	C₂²	1	2	yes	—
106	#10597329	C₂²	1	2	yes	complemented
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	#10597322	C₂²	1	2	yes	complemented
117	C₄×D₇₆	C₂²	1	1	yes	characteristic
118	#10597318	C₂²	1	1	yes	characteristic
119	#10597318	C₂²	1	2	yes	—
120	#10597316	C₂²	1	2	yes	complemented
121	#10597316	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₃₈	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₉	C₂³	1	1	yes	characteristic
124	C₂×Q₈×C₁₉	—	4	2	no	—
125	C₂×Q₈×C₁₉	—	4	2	no	—
126	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
127	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
128	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
129	C₂×Q₈×C₁₉	C₂³	1	2	yes	—
130	C₂×Q₈×C₁₉	C₂³	1	2	yes	—
131	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
132	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
133	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
134	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
135	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
137	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
138	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
139	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
140	C₂²×Dic₁₉	C₂³	1	2	yes	—
141	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
142	Q₈×D₁₉	—	4	2	no	—
143	Q₈×D₁₉	—	4	2	no	—
144	#64541	—	4	2	no	—
145	C₂×D₇₆	C₂³	1	1	yes	characteristic
146	C₂×D₇₆	C₂³	1	1	yes	characteristic
147	C₂×C₄×D₁₉	—	4	2	no	—
148	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
149	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
151	C₂×C₄×D₁₉	C₂³	1	2	yes	—
152	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
153	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
154	C₂×C₄×D₁₉	C₂³	1	2	yes	—
155	C₂×C₄×D₁₉	C₂³	1	2	yes	—
156	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
157	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
158	C₂×Dic₃₈	C₂³	1	2	yes	—
159	C₂×Dic₃₈	C₂³	1	2	yes	—
160	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
161	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
162	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
163	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
164	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
165	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
166	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
167	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
168	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
169	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
170	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
171	C₄²×C₁₉	C₂³	1	1	yes	characteristic
172	C₄²×C₁₉	C₂³	1	2	yes	—
173	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
174	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
175	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
176	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
177	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
178	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
179	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
180	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
181	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
182	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
183	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
190	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
191	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
192	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
193	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
194	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
195	C₄⋊Dic₁₉	C₂³	1	2	yes	—
196	C₄⋊Dic₁₉	C₂³	1	2	yes	—
197	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
198	C₄⋊Dic₁₉	C₂³	1	2	yes	—
199	C₄⋊Dic₁₉	C₂³	1	2	yes	—
200	C₄⋊Dic₁₉	C₂³	1	2	yes	—
201	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
202	Dic₁₉⋊C₄	C₂³	1	2	yes	—
203	Dic₁₉⋊C₄	C₂³	1	2	yes	—
204	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
209	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
210	Dic₁₉⋊C₄	C₂³	1	2	yes	—
211	Dic₁₉⋊C₄	C₂³	1	2	yes	—
212	Dic₁₉⋊C₄	C₂³	1	2	yes	—
213	Dic₁₉⋊C₄	C₂³	1	2	yes	—
214	Dic₁₉⋊C₄	C₂³	1	2	yes	—
215	Dic₁₉⋊C₄	C₂³	1	2	yes	—
216	Dic₁₉⋊C₄	C₂³	1	2	yes	—
217	Dic₁₉⋊C₄	C₂³	1	2	yes	—
218	Dic₁₉⋊C₄	C₂³	1	2	yes	—
219	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
220	Dic₁₉⋊C₄	C₂³	1	2	yes	—
221	Dic₁₉⋊C₄	C₂³	1	2	yes	—
222	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
223	C₄×Dic₁₉	C₂³	1	2	yes	—
224	C₄×Dic₁₉	C₂³	1	2	yes	—
225	C₄×Dic₁₉	C₂³	1	2	yes	—
226	C₄×Dic₁₉	C₂³	1	2	yes	—
227	C₄×Dic₁₉	C₂³	1	2	yes	—
228	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
229	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
230	C₂²×D₁₉	—	2	2	no	—
231	C₂²×D₁₉	—	2	2	no	—
232	C₂²×D₁₉	—	4	1	no	—
233	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
234	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
235	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
236	Q₈×C₁₉	—	2	2	no	—
237	Q₈×C₁₉	—	2	2	no	—
238	Q₈×C₁₉	—	2	2	no	—
239	Q₈×C₁₉	—	4	2	no	—
240	Q₈×C₁₉	—	4	2	no	—
241	D₄×C₁₉	—	2	2	no	—
242	C₂×C₄×C₁₉	—	2	2	no	—
243	C₂×C₄×C₁₉	—	2	2	no	—
244	C₂×C₄×C₁₉	—	4	2	no	—
245	C₂×C₄×C₁₉	—	4	2	no	—
246	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
247	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
248	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
249	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
250	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
251	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
252	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
253	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
254	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
255	C₂²⋊D₁₉	—	2	2	no	—
256	C₂²⋊D₁₉	—	2	2	no	—
257	C₂²⋊D₁₉	—	4	1	no	—
258	C₂²⋊D₁₉	—	4	1	no	—
259	C₂×Dic₁₉	—	2	4	no	—
260	C₂×Dic₁₉	—	4	1	no	—
261	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
262	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
263	C₂×Dic₁₉	C₂⁴	1	2	yes	—
264	C₂×Dic₁₉	C₂⁴	1	2	yes	—
265	C₂×Dic₁₉	C₂⁴	1	2	yes	—
266	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
267	C₂×Dic₁₉	C₂⁴	1	2	yes	—
268	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
269	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
270	D₇₆	—	2	2	no	—
271	D₇₆	—	4	1	no	—
272	C₄×D₁₉	—	2	4	no	—
273	C₄×D₁₉	—	2	2	no	—
274	C₄×D₁₉	—	2	2	no	—
275	C₄×D₁₉	—	2	2	no	—
276	C₄×D₁₉	—	4	1	no	—
277	C₄×D₁₉	—	4	1	no	—
278	C₄×D₁₉	—	4	2	no	—
279	C₄×D₁₉	—	4	2	no	—
280	Dic₃₈	—	2	2	no	—
281	Dic₃₈	—	4	1	no	—
282	Dic₃₈	—	4	2	no	—
283	Dic₃₈	—	4	2	no	—
284	#3538	—	19	1	no	maximal, Sylow
285	C₂²×C₁₉	—	2	1	no	—
286	C₂²×C₁₉	—	2	1	no	—
287	C₂²×C₁₉	—	2	1	no	—
288	C₂²×C₁₉	—	2	1	no	—
289	C₂²×C₁₉	—	2	1	no	—
290	C₂²×C₁₉	2₋¹⁺⁴	1	2	yes	—
291	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
292	C₂×D₁₉	—	2	1	no	—
293	C₂×D₁₉	—	2	1	no	—
294	C₂×D₁₉	—	2	1	no	—
295	C₂×D₁₉	—	2	1	no	—
296	C₂×D₁₉	—	2	1	no	—
297	C₂×D₁₉	—	2	1	no	—
298	C₂×D₁₉	—	2	1	no	—
299	C₂×D₁₉	—	2	1	no	—
300	C₂×D₁₉	—	4	4	no	—
301	C₂×D₁₉	2₋¹⁺⁴	1	2	yes	—
302	C₄×C₁₉	—	2	2	no	—
303	C₄×C₁₉	—	2	2	no	—
304	C₄×C₁₉	—	2	1	no	—
305	C₄×C₁₉	—	2	1	no	—
306	C₄×C₁₉	—	2	2	no	—
307	C₄×C₁₉	—	2	2	no	—
308	C₄×C₁₉	—	2	1	no	—
309	C₄×C₁₉	—	2	1	no	—
310	C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
311	Dic₁₉	—	2	2	no	—
312	Dic₁₉	—	2	1	no	—
313	Dic₁₉	—	2	1	no	—
314	Dic₁₉	—	2	1	no	—
315	Dic₁₉	—	2	2	no	—
316	Dic₁₉	—	2	2	no	—
317	Dic₁₉	—	2	2	no	—
318	Dic₁₉	—	2	1	no	—
319	Dic₁₉	—	2	1	no	—
320	#563	—	19	2	no	—
321	#563	—	19	2	no	—
322	#552	—	19	1	no	—
323	#552	—	19	1	no	—
324	#552	—	19	1	no	—
325	#552	—	19	1	no	—
326	#551	—	19	2	no	—
327	#551	—	19	2	no	—
328	D₄×Q₈	—	19	1	no	—
329	D₄×Q₈	—	19	1	no	—
330	D₄×Q₈	—	19	1	no	—
331	D₄×Q₈	D₁₉	1	1	yes	characteristic, complemented
332	#544	—	19	2	no	—
333	#544	—	19	2	no	—
334	#541	—	19	1	no	—
335	#541	—	19	1	no	—
336	#539	—	19	2	no	—
337	#539	—	19	2	no	—
338	#536	—	19	1	no	—
339	#536	—	19	1	no	—
340	#525	—	19	1	no	—
341	C₂×C₂²⋊Q₈	—	19	1	no	—
342	C₂×C₂²⋊Q₈	—	19	1	no	—
343	C₂×C₁₉	—	2	2	no	—
344	C₂×C₁₉	—	4	1	no	—
345	C₂×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
346	C₂×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
347	C₂×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
348	D₁₉	—	2	2	no	—
349	D₁₉	—	4	1	no	—
350	D₁₉	—	4	1	no	—
351	C₂×#41	—	19	1	no	—
352	C₂²×Q₈	—	19	1	no	—
353	C₂²×Q₈	—	19	1	no	—
354	C₂²×Q₈	C₂×D₁₉	1	1	yes	characteristic
355	C₂²×Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
356	C₂³×C₄	—	19	1	no	—
357	C₄⋊Q₈	—	19	2	no	—
358	C₄⋊Q₈	—	19	1	no	—
359	C₄⋊Q₈	—	19	2	no	—
360	C₄⋊Q₈	—	19	2	no	—
361	C₄⋊Q₈	—	19	2	no	—
362	C₄⋊Q₈	—	19	2	no	—
363	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
364	C₄⋊Q₈	C₂×D₁₉	1	2	yes	complemented
365	#126	—	19	2	no	—
366	#126	—	19	2	no	—
367	#126	—	19	2	no	—
368	#126	—	19	2	no	—
369	#126	—	19	2	no	—
370	#126	—	19	2	no	—
371	#126	—	19	2	no	—
372	#126	—	19	2	no	—
373	#125	—	19	2	no	—
374	#125	—	19	2	no	—
375	#125	—	19	2	no	—
376	#125	—	19	1	no	—
377	#125	—	19	2	no	—
378	#125	—	19	2	no	—
379	#125	—	19	2	no	—
380	#125	—	19	2	no	—
381	#125	—	19	2	no	—
382	#125	—	19	1	no	—
383	#124	—	19	2	no	—
384	#124	—	19	2	no	—
385	#123	—	19	2	no	—
386	#123	—	19	2	no	—
387	#123	—	19	2	no	—
388	#123	—	19	1	no	—
389	#123	—	19	2	no	—
390	#123	—	19	2	no	—
391	#123	—	19	1	no	—
392	#123	—	19	2	no	—
393	#123	—	19	2	no	—
394	#123	—	19	2	no	—
395	C₂²⋊Q₈	—	19	1	no	—
396	C₂²⋊Q₈	—	19	1	no	—
397	C₂²⋊Q₈	—	19	1	no	—
398	C₂²⋊Q₈	—	19	2	no	—
399	C₂²⋊Q₈	—	19	1	no	—
400	C₂²⋊Q₈	—	19	1	no	—
401	C₂²⋊Q₈	—	19	2	no	—
402	C₂²⋊Q₈	—	19	2	no	—
403	C₂²⋊Q₈	—	19	1	no	—
404	C₂²⋊Q₈	—	19	1	no	—
405	C₂²⋊Q₈	—	19	2	no	—
406	C₂²⋊Q₈	—	19	1	no	—
407	C₂²⋊Q₈	—	19	1	no	—
408	C₂²⋊Q₈	—	19	2	no	—
409	C₂²⋊Q₈	—	19	2	no	—
410	C₂²⋊Q₈	—	19	1	no	—
411	C₂²⋊Q₈	—	19	2	no	—
412	C₂²⋊Q₈	—	19	1	no	—
413	C₂²⋊Q₈	—	19	2	no	—
414	C₂²⋊Q₈	—	19	2	no	—
415	C₂²⋊Q₈	—	19	2	no	—
416	C₂²⋊Q₈	—	19	1	no	—
417	C₂²⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
418	C₂²⋊Q₈	C₂×D₁₉	1	2	yes	—
419	C₂²⋊Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
420	C₂²⋊Q₈	C₂×D₁₉	1	2	yes	complemented
421	#121	—	19	1	no	—
422	#121	—	19	1	no	—
423	#120	—	19	1	no	—
424	#120	—	19	1	no	—
425	C₄×Q₈	—	19	1	no	—
426	C₄×Q₈	—	19	1	no	—
427	C₄×Q₈	—	19	1	no	—
428	C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
429	C₄×D₄	—	19	1	no	—
430	C₄×D₄	—	19	1	no	—
431	C₄×D₄	—	19	2	no	—
432	C₄×D₄	—	19	2	no	—
433	C₄×D₄	—	19	2	no	—
434	C₄×D₄	—	19	1	no	—
435	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
436	C₄×D₄	C₂×D₁₉	1	2	yes	—
437	#117	—	19	1	no	—
438	#117	—	19	1	no	—
439	#117	—	19	2	no	—
440	#117	—	19	2	no	—
441	#117	—	19	2	no	—
442	#117	—	19	1	no	—
443	#117	—	19	2	no	—
444	C₂×C₄⋊C₄	—	19	2	no	—
445	C₂×C₄⋊C₄	—	19	1	no	—
446	C₂×C₄⋊C₄	—	19	2	no	—
447	C₂×C₄⋊C₄	—	19	1	no	—
448	C₂×C₂²⋊C₄	—	19	2	no	—
449	C₂×C₂²⋊C₄	—	19	2	no	—
450	C₁₉	#3538	1	1	yes	characteristic, complemented, Sylow
451	C₂⁴	—	19	1	no	—
452	#41	—	76	2	no	—
453	C₂×Q₈	—	4	2	no	—
454	C₂×Q₈	—	4	2	no	—
455	C₂×Q₈	—	19	1	no	—
456	C₂×Q₈	—	19	2	no	—
457	C₂×Q₈	—	19	2	no	—
458	C₂×Q₈	—	19	1	no	—
459	C₂×Q₈	—	76	2	no	—
460	C₂×Q₈	—	76	2	no	—
461	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
462	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
463	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
464	C₂×Q₈	C₂²×D₁₉	1	2	yes	—
465	C₂×Q₈	C₂²×D₁₉	1	2	yes	—
466	C₂×D₄	—	19	1	no	—
467	C₂×D₄	—	19	1	no	—
468	C₂×D₄	—	19	1	no	—
469	C₂×D₄	—	19	1	no	—
470	C₂×D₄	—	19	1	no	—
471	C₂×D₄	—	19	1	no	—
472	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
473	C₂²×C₄	—	19	2	no	—
474	C₂²×C₄	—	19	1	no	—
475	C₂²×C₄	—	19	2	no	—
476	C₂²×C₄	—	19	1	no	—
477	C₂²×C₄	—	19	1	no	—
478	C₂²×C₄	—	19	1	no	—
479	C₂²×C₄	—	19	2	no	—
480	C₂²×C₄	—	19	1	no	—
481	C₂²×C₄	—	19	2	no	—
482	C₂²×C₄	—	19	1	no	—
483	C₂²×C₄	—	76	2	no	—
484	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
485	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
486	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
487	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
488	C₄⋊C₄	—	19	2	no	—
489	C₄⋊C₄	—	19	2	no	—
490	C₄⋊C₄	—	19	2	no	—
491	C₄⋊C₄	—	19	2	no	—
492	C₄⋊C₄	—	19	2	no	—
493	C₄⋊C₄	—	19	2	no	—
494	C₄⋊C₄	—	19	2	no	—
495	C₄⋊C₄	—	19	1	no	—
496	C₄⋊C₄	—	19	1	no	—
497	C₄⋊C₄	—	19	2	no	—
498	C₄⋊C₄	—	19	2	no	—
499	C₄⋊C₄	—	19	2	no	—
500	C₄⋊C₄	—	19	2	no	—
501	C₄⋊C₄	—	19	2	no	—
502	C₄⋊C₄	—	19	2	no	—
503	C₄⋊C₄	—	19	2	no	—
504	C₄⋊C₄	—	19	2	no	—
505	C₄⋊C₄	—	19	1	no	—
506	C₄⋊C₄	—	19	1	no	—
507	C₄⋊C₄	—	19	2	no	—
508	C₄⋊C₄	—	19	1	no	—
509	C₄⋊C₄	—	19	1	no	—
510	C₄⋊C₄	—	19	1	no	—
511	C₄⋊C₄	—	19	2	no	—
512	C₄⋊C₄	—	19	2	no	—
513	C₄⋊C₄	—	19	2	no	—
514	C₄⋊C₄	—	19	1	no	—
515	C₄⋊C₄	—	19	2	no	—
516	C₄⋊C₄	—	19	2	no	—
517	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
518	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
519	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
520	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
521	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
522	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
523	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
524	C₂²⋊C₄	—	19	2	no	—
525	C₂²⋊C₄	—	19	1	no	—
526	C₂²⋊C₄	—	19	2	no	—
527	C₂²⋊C₄	—	19	1	no	—
528	C₂²⋊C₄	—	19	2	no	—
529	C₂²⋊C₄	—	19	2	no	—
530	C₂²⋊C₄	—	19	2	no	—
531	C₂²⋊C₄	—	19	2	no	—
532	C₂²⋊C₄	—	19	2	no	—
533	C₂²⋊C₄	—	19	2	no	—
534	C₂²⋊C₄	—	19	2	no	—
535	C₂²⋊C₄	—	19	1	no	—
536	C₂²⋊C₄	—	19	1	no	—
537	C₂²⋊C₄	—	19	1	no	—
538	C₂²⋊C₄	—	19	1	no	—
539	C₂²⋊C₄	—	19	2	no	—
540	C₂²⋊C₄	—	19	1	no	—
541	C₂²⋊C₄	—	19	1	no	—
542	C₂²⋊C₄	—	19	2	no	—
543	C₂²⋊C₄	—	19	2	no	—
544	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
545	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
546	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
547	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
548	C₄²	—	19	2	no	—
549	C₄²	—	19	2	no	—
550	C₄²	—	19	1	no	—
551	C₄²	—	19	2	no	—
552	C₄²	—	19	2	no	—
553	C₄²	—	19	2	no	—
554	C₄²	C₂²×D₁₉	1	1	yes	characteristic
555	C₄²	C₂²×D₁₉	1	2	yes	—
556	C₂³	—	19	1	no	—
557	C₂³	—	19	1	no	—
558	C₂³	—	19	1	no	—
559	C₂³	—	38	2	no	—
560	C₂³	—	38	2	no	—
561	C₂³	—	76	1	no	—
562	C₂³	C₂³×D₁₉	1	1	yes	characteristic
563	C₂³	C₂³×D₁₉	1	1	yes	characteristic
564	Q₈	—	2	2	no	—
565	Q₈	—	2	2	no	—
566	Q₈	—	2	2	no	—
567	Q₈	—	4	2	no	—
568	Q₈	—	4	2	no	—
569	Q₈	—	38	2	no	—
570	Q₈	—	76	2	no	—
571	Q₈	—	76	2	no	—
572	Q₈	—	76	1	no	—
573	D₄	—	2	2	no	—
574	D₄	—	38	2	no	—
575	D₄	—	38	2	no	—
576	D₄	—	38	2	no	—
577	D₄	—	76	1	no	—
578	D₄	—	76	1	no	—
579	D₄	—	76	1	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	4	2	no	—
583	C₂×C₄	—	4	2	no	—
584	C₂×C₄	—	19	1	no	—
585	C₂×C₄	—	19	1	no	—
586	C₂×C₄	—	19	2	no	—
587	C₂×C₄	—	19	2	no	—
588	C₂×C₄	—	19	2	no	—
589	C₂×C₄	—	19	1	no	—
590	C₂×C₄	—	19	2	no	—
591	C₂×C₄	—	19	1	no	—
592	C₂×C₄	—	19	1	no	—
593	C₂×C₄	—	38	4	no	—
594	C₂×C₄	—	38	4	no	—
595	C₂×C₄	—	38	2	no	—
596	C₂×C₄	—	38	2	no	—
597	C₂×C₄	—	38	2	no	—
598	C₂×C₄	—	76	1	no	—
599	C₂×C₄	—	76	1	no	—
600	C₂×C₄	—	76	2	no	—
601	C₂×C₄	—	76	2	no	—
602	C₂×C₄	—	76	1	no	—
603	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
604	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
605	C₂×C₄	C₂³×D₁₉	1	2	yes	—
606	C₂×C₄	C₂³×D₁₉	1	2	yes	—
607	C₂×C₄	C₂³×D₁₉	1	2	yes	—
608	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
609	C₂×C₄	C₂³×D₁₉	1	2	yes	—
610	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
611	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
612	C₂²	—	2	1	no	—
613	C₂²	—	2	1	no	—
614	C₂²	—	2	1	no	—
615	C₂²	—	2	1	no	—
616	C₂²	—	2	1	no	—
617	C₂²	—	19	2	no	—
618	C₂²	—	38	1	no	—
619	C₂²	—	38	1	no	—
620	C₂²	—	38	1	no	—
621	C₂²	—	38	1	no	—
622	C₂²	—	38	1	no	—
623	C₂²	—	38	1	no	—
624	C₂²	—	38	1	no	—
625	C₂²	—	38	1	no	—
626	C₂²	—	76	4	no	—
627	C₂²	#10597433	1	2	yes	—
628	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
629	C₄	—	2	1	no	—
630	C₄	—	2	1	no	—
631	C₄	—	2	2	no	—
632	C₄	—	2	2	no	—
633	C₄	—	2	2	no	—
634	C₄	—	2	2	no	—
635	C₄	—	2	1	no	—
636	C₄	—	2	1	no	—
637	C₄	—	38	1	no	—
638	C₄	—	38	1	no	—
639	C₄	—	38	1	no	—
640	C₄	—	38	2	no	—
641	C₄	—	38	2	no	—
642	C₄	—	38	1	no	—
643	C₄	—	38	2	no	—
644	C₄	—	38	2	no	—
645	C₄	—	38	1	no	—
646	C₄	#10597430	1	2	yes	—
647	C₂	—	2	2	no	—
648	C₂	—	4	1	no	—
649	C₂	—	38	2	no	—
650	C₂	—	76	1	no	—
651	C₂	—	76	1	no	—
652	C₂	C₂×#10597430	1	1	yes	characteristic
653	C₂	2₋¹⁺⁴×D₁₉	1	1	yes	characteristic
654	C₂	C₂×#10597433	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Fitting	D₄×Q₈×C₁₉	C₂
prime radical	#11927053	C₂
hypercenter	D₄×Q₈	D₁₉
hypocenter	C₁₉	#3538
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ D₄×Q₈

Complements

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

N	H ≅ G/N	type
1. #11927295	C₂	semidirect
2. #11927293	C₂	semidirect
3. #11927236	C₂	semidirect
4. #11927235	C₂	semidirect
5. #11927234	C₂	semidirect
6. #11927228	C₂	semidirect
7. #11927223	C₂	semidirect
8. #11927221	C₂	semidirect
9. #11927209	C₂	semidirect
10. Q₈×C₂²⋊D₁₉	C₂	semidirect
11. Q₈×C₂²⋊D₁₉	C₂	semidirect
12. #11927173	C₂	semidirect
13. #11927171	C₂	semidirect
14. #11927155	C₂	semidirect
15. #11927152	C₂	semidirect
16. #11927140	C₂	semidirect
17. #11927136	C₂	semidirect
18. #11927118	C₂	semidirect
19. #11927117	C₂	semidirect
21. C₂×#10597392	C₂	semidirect
22. C₂²⋊Q₈×D₁₉	C₂	semidirect
23. D₄×Q₈×C₁₉	C₂	semidirect
25. C₂²×Q₈×C₁₉	C₂²	semidirect
27. C₂×Q₈×D₁₉	C₂²	semidirect
30. C₁₉×C₄⋊Q₈	C₂²	semidirect
31. C₁₉×C₄⋊Q₈	C₂²	semidirect
34. C₁₉×C₂²⋊Q₈	C₂²	semidirect
35. C₁₉×C₂²⋊Q₈	C₂²	semidirect
36. C₄×Q₈×C₁₉	C₂²	semidirect
48. #10597392	C₂²	semidirect
49. #10597392	C₂²	semidirect
50. #10597392	C₂²	semidirect
51. Q₈×Dic₁₉	C₂²	semidirect
52. Q₈×Dic₁₉	C₂²	semidirect
53. #10597390	C₂²	semidirect
54. #10597390	C₂²	semidirect
55. #10597390	C₂²	semidirect
56. #10597390	C₂²	semidirect
61. #10597375	C₂²	semidirect
67. #10597372	C₂²	semidirect
71. #10597370	C₂²	semidirect
72. #10597370	C₂²	semidirect
77. #10597344	C₂²	semidirect
82. #10597342	C₂²	semidirect
88. #10597338	C₂²	semidirect
91. #10597336	C₂²	semidirect
92. #10597336	C₂²	semidirect
93. #10597335	C₂²	semidirect
94. #10597335	C₂²	semidirect
95. #10597335	C₂²	semidirect
96. #10597335	C₂²	semidirect
97. #10597335	C₂²	semidirect
98. #10597335	C₂²	semidirect
99. #10597334	C₂²	semidirect
100. #10597334	C₂²	semidirect
106. #10597329	C₂²	semidirect
109. #10597325	C₂²	semidirect
110. #10597325	C₂²	semidirect
116. #10597322	C₂²	semidirect
120. #10597316	C₂²	semidirect
121. #10597316	C₂²	semidirect
122. C₄×Dic₃₈	C₂²	semidirect
331. D₄×Q₈	D₁₉	semidirect
355. C₂²×Q₈	C₂×D₁₉	semidirect
363. C₄⋊Q₈	C₂×D₁₉	semidirect
364. C₄⋊Q₈	C₂×D₁₉	semidirect
419. C₂²⋊Q₈	C₂×D₁₉	semidirect
420. C₂²⋊Q₈	C₂×D₁₉	semidirect
428. C₄×Q₈	C₂×D₁₉	semidirect
450. C₁₉	#3538	semidirect

Maximal subgroups

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

subgroup	index
#11927295	2
#11927293	2
#11927236	2
#11927235	2
#11927234	2
#11927228	2
#11927223	2
#11927221	2
#11927209	2
Q₈×C₂²⋊D₁₉	2
#11927173	2
#11927171	2
#11927155	2
#11927152	2
#11927140	2
#11927136	2
#11927118	2
#11927117	2
#11927053	2
C₂×#10597392	2
C₂²⋊Q₈×D₁₉	2
D₄×Q₈×C₁₉	2
#3538	19