Subgroups — #14577926

Order 2432.

1032 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927294	C₂	1	2	yes	maximal, complemented
2	#11927289	C₂	1	2	yes	maximal, complemented
3	#11927264	C₂	1	1	yes	maximal, characteristic, complemented
4	#11927254	C₂	1	1	yes	maximal, characteristic, complemented
5	#11927248	C₂	1	2	yes	maximal, complemented
6	#11927244	C₂	1	2	yes	maximal, complemented
7	#11927241	C₂	1	1	yes	maximal, characteristic, complemented
8	#11927228	C₂	1	1	yes	maximal, characteristic, complemented
9	Q₈×C₂²⋊D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#11927202	C₂	1	1	yes	maximal, characteristic, complemented
11	#11927193	C₂	1	1	yes	maximal, characteristic, complemented
12	#11927164	C₂	1	2	yes	maximal, complemented
13	#11927163	C₂	1	1	yes	maximal, characteristic, complemented
14	#11927152	C₂	1	1	yes	maximal, characteristic, complemented
15	#11927136	C₂	1	2	yes	maximal, complemented
16	#11927128	C₂	1	2	yes	maximal, complemented
17	#11927126	C₂	1	2	yes	maximal, complemented
18	#11927123	C₂	1	1	yes	maximal, characteristic, complemented
19	#11927118	C₂	1	1	yes	maximal, characteristic, complemented
20	#11927053	C₂	1	1	yes	maximal, characteristic, complemented
21	#11927051	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂²⋊Q₈×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₉×#548	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#41×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×#64543	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×#124	C₂²	1	2	yes	—
31	C₁₉×#124	C₂²	1	1	yes	characteristic, complemented
32	C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
33	C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	complemented
34	C₁₉×#121	C₂²	1	2	yes	—
35	C₁₉×#121	C₂²	1	1	yes	characteristic, 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	complemented
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	1	yes	characteristic, complemented
45	#10597392	C₂²	1	1	yes	characteristic, complemented
46	Q₈×Dic₁₉	C₂²	1	1	yes	characteristic, complemented
47	#10597390	C₂²	1	2	yes	complemented
48	#10597390	C₂²	1	1	yes	characteristic, complemented
49	#10597390	C₂²	1	2	yes	complemented
50	#10597385	C₂²	1	1	yes	characteristic
51	#10597385	C₂²	1	2	yes	—
52	#10597385	C₂²	1	2	yes	—
53	#10597384	C₂²	1	1	yes	characteristic
54	#10597384	C₂²	1	1	yes	characteristic
55	#10597384	C₂²	1	2	yes	—
56	#10597384	C₂²	1	2	yes	complemented
57	#10597383	C₂²	1	2	yes	—
58	#10597383	C₂²	1	1	yes	characteristic
59	#10597382	C₂²	1	2	yes	—
60	#10597381	C₂²	1	2	yes	—
61	#10597381	C₂²	1	2	yes	—
62	#10597381	C₂²	1	2	yes	complemented
63	D₄×Dic₁₉	C₂²	1	1	yes	characteristic, complemented
64	#10597375	C₂²	1	2	yes	—
65	#10597375	C₂²	1	2	yes	complemented
66	#10597375	C₂²	1	2	yes	complemented
67	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	—
68	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	—
69	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
70	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
71	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	—
72	#10597372	C₂²	1	1	yes	characteristic
73	#10597372	C₂²	1	1	yes	characteristic, complemented
74	#10597370	C₂²	1	1	yes	characteristic
75	#10597370	C₂²	1	1	yes	characteristic, complemented
76	#10597370	C₂²	1	2	yes	complemented
77	C₂×Dic₁₉⋊C₄	C₂²	1	2	yes	complemented
78	#10597344	C₂²	1	2	yes	—
79	#10597343	C₂²	1	1	yes	characteristic
80	#10597342	C₂²	1	1	yes	characteristic
81	#10597342	C₂²	1	2	yes	—
82	#10597342	C₂²	1	2	yes	—
83	#10597342	C₂²	1	2	yes	complemented
84	#10597340	C₂²	1	1	yes	characteristic
85	#10597338	C₂²	1	2	yes	complemented
86	C₄⋊C₄×D₁₉	C₂²	1	1	yes	characteristic
87	C₄⋊C₄×D₁₉	C₂²	1	2	yes	—
88	C₄⋊C₄×D₁₉	C₂²	1	1	yes	characteristic, complemented
89	#10597336	C₂²	1	1	yes	characteristic, complemented
90	#10597335	C₂²	1	2	yes	complemented
91	#10597335	C₂²	1	2	yes	complemented
92	#10597333	C₂²	1	2	yes	complemented
93	#10597332	C₂²	1	2	yes	—
94	#10597331	C₂²	1	2	yes	—
95	#10597331	C₂²	1	2	yes	complemented
96	#10597330	C₂²	1	1	yes	characteristic
97	#10597330	C₂²	1	2	yes	—
98	#10597330	C₂²	1	2	yes	—
99	#10597329	C₂²	1	1	yes	characteristic
100	#10597329	C₂²	1	2	yes	—
101	#10597328	C₂²	1	1	yes	characteristic
102	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	—
103	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	—
104	C₂²⋊C₄×D₁₉	C₂²	1	2	yes	—
105	#10597325	C₂²	1	2	yes	—
106	#10597325	C₂²	1	2	yes	—
107	#10597325	C₂²	1	2	yes	complemented
108	#10597325	C₂²	1	2	yes	complemented
109	#10597325	C₂²	1	2	yes	complemented
110	#10597324	C₂²	1	1	yes	characteristic
111	#10597324	C₂²	1	2	yes	—
112	#10597324	C₂²	1	2	yes	complemented
113	#10597324	C₂²	1	2	yes	complemented
114	#10597324	C₂²	1	2	yes	complemented
115	#10597322	C₂²	1	2	yes	—
116	C₄×D₇₆	C₂²	1	1	yes	characteristic
117	C₄×D₇₆	C₂²	1	2	yes	—
118	#10597318	C₂²	1	1	yes	characteristic
119	#10597316	C₂²	1	2	yes	complemented
120	#10597316	C₂²	1	2	yes	complemented
121	#10597315	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₃₈	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₉	C₂³	1	1	yes	characteristic
124	#41×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	2	yes	—
129	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
130	C₂×D₄×C₁₉	C₂³	1	2	yes	—
131	C₂×D₄×C₁₉	C₂³	1	2	yes	—
132	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
133	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
134	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
135	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
136	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
139	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
141	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
142	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
144	C₂²×Dic₁₉	C₂³	1	2	yes	—
145	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
146	C₂²×Dic₁₉	C₂³	1	2	yes	—
147	Q₈×D₁₉	—	4	2	no	—
148	#64543	—	4	2	no	—
149	#64541	—	4	2	no	—
150	C₂×D₇₆	C₂³	1	1	yes	characteristic
151	C₂×D₇₆	C₂³	1	1	yes	characteristic
152	C₂×C₄×D₁₉	—	4	2	no	—
153	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
154	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
155	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
156	C₂×C₄×D₁₉	C₂³	1	2	yes	—
157	C₂×C₄×D₁₉	C₂³	1	2	yes	—
158	C₂×C₄×D₁₉	C₂³	1	2	yes	—
159	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
160	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
161	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
162	C₂×Dic₃₈	C₂³	1	2	yes	—
163	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
164	C₂×Dic₃₈	C₂³	1	2	yes	—
165	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
166	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
167	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
168	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
169	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
170	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
171	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
172	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
173	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
174	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
175	C₄²×C₁₉	C₂³	1	1	yes	characteristic
176	C₄²×C₁₉	C₂³	1	2	yes	—
177	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
178	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
179	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
180	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
181	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
182	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
183	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
184	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
185	C₂²⋊Dic₁₉	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	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
191	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
192	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
193	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
194	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
195	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
196	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
197	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
198	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
199	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
200	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
201	C₄⋊Dic₁₉	C₂³	1	2	yes	—
202	C₄⋊Dic₁₉	C₂³	1	2	yes	—
203	C₄⋊Dic₁₉	C₂³	1	2	yes	—
204	C₄⋊Dic₁₉	C₂³	1	2	yes	—
205	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
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	2	yes	—
213	Dic₁₉⋊C₄	C₂³	1	2	yes	—
214	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
215	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
220	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
221	Dic₁₉⋊C₄	C₂³	1	2	yes	—
222	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
223	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
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	C₂³×C₁₉	C₂⁴	1	2	yes	—
231	C₂²×D₁₉	—	2	2	no	—
232	C₂²×D₁₉	—	4	1	no	—
233	C₂²×D₁₉	—	4	1	no	—
234	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
235	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
236	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
237	Q₈×C₁₉	—	2	2	no	—
238	Q₈×C₁₉	—	2	2	no	—
239	Q₈×C₁₉	—	4	2	no	—
240	D₄×C₁₉	—	2	2	no	—
241	D₄×C₁₉	—	4	1	no	—
242	D₄×C₁₉	—	4	2	no	—
243	D₄×C₁₉	—	4	2	no	—
244	C₂×C₄×C₁₉	—	2	2	no	—
245	C₂×C₄×C₁₉	—	2	2	no	—
246	C₂×C₄×C₁₉	—	4	2	no	—
247	C₂×C₄×C₁₉	—	4	2	no	—
248	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
249	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
250	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
251	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
252	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
253	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
254	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
255	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
256	C₂²⋊D₁₉	—	2	4	no	—
257	C₂²⋊D₁₉	—	2	2	no	—
258	C₂²⋊D₁₉	—	4	1	no	—
259	C₂²⋊D₁₉	—	4	1	no	—
260	C₂²⋊D₁₉	—	4	2	no	—
261	C₂²⋊D₁₉	—	4	2	no	—
262	C₂²⋊D₁₉	—	4	1	no	—
263	C₂×Dic₁₉	—	4	1	no	—
264	C₂×Dic₁₉	—	4	2	no	—
265	C₂×Dic₁₉	—	4	2	no	—
266	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
267	C₂×Dic₁₉	C₂⁴	1	2	yes	—
268	C₂×Dic₁₉	C₂⁴	1	2	yes	—
269	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
270	C₂×Dic₁₉	C₂⁴	1	2	yes	—
271	C₂×Dic₁₉	C₂⁴	1	2	yes	—
272	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
273	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
274	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
275	D₇₆	—	2	2	no	—
276	D₇₆	—	4	1	no	—
277	C₄×D₁₉	—	2	2	no	—
278	C₄×D₁₉	—	2	2	no	—
279	C₄×D₁₉	—	2	2	no	—
280	C₄×D₁₉	—	4	1	no	—
281	C₄×D₁₉	—	4	1	no	—
282	C₄×D₁₉	—	4	2	no	—
283	C₄×D₁₉	—	4	2	no	—
284	C₄×D₁₉	—	4	2	no	—
285	Dic₃₈	—	2	2	no	—
286	Dic₃₈	—	4	2	no	—
287	Dic₃₈	—	4	1	no	—
288	Dic₃₈	—	4	2	no	—
289	#3541	—	19	1	no	maximal, Sylow
290	C₂²×C₁₉	—	2	2	no	—
291	C₂²×C₁₉	—	2	1	no	—
292	C₂²×C₁₉	—	2	1	no	—
293	C₂²×C₁₉	—	2	1	no	—
294	C₂²×C₁₉	—	2	2	no	—
295	C₂²×C₁₉	—	2	1	no	—
296	C₂²×C₁₉	—	2	2	no	—
297	C₂²×C₁₉	—	2	1	no	—
298	C₂²×C₁₉	—	2	1	no	—
299	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
300	C₂×D₁₉	—	2	1	no	—
301	C₂×D₁₉	—	2	1	no	—
302	C₂×D₁₉	—	2	1	no	—
303	C₂×D₁₉	—	2	1	no	—
304	C₂×D₁₉	—	2	1	no	—
305	C₂×D₁₉	—	2	1	no	—
306	C₂×D₁₉	—	2	1	no	—
307	C₂×D₁₉	—	2	1	no	—
308	C₂×D₁₉	—	4	4	no	—
309	C₂×D₁₉	2₋¹⁺⁴	1	2	yes	—
310	C₄×C₁₉	—	2	2	no	—
311	C₄×C₁₉	—	2	1	no	—
312	C₄×C₁₉	—	2	1	no	—
313	C₄×C₁₉	—	2	2	no	—
314	C₄×C₁₉	—	2	1	no	—
315	C₄×C₁₉	—	2	1	no	—
316	C₄×C₁₉	—	2	2	no	—
317	C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
318	Dic₁₉	—	2	2	no	—
319	Dic₁₉	—	2	1	no	—
320	Dic₁₉	—	2	1	no	—
321	Dic₁₉	—	2	1	no	—
322	Dic₁₉	—	2	1	no	—
323	Dic₁₉	—	2	2	no	—
324	Dic₁₉	—	2	2	no	—
325	Dic₁₉	—	2	2	no	—
326	Dic₁₉	—	2	1	no	—
327	#563	—	19	2	no	—
328	#562	—	19	2	no	—
329	#556	—	19	1	no	—
330	#554	—	19	2	no	—
331	#554	—	19	1	no	—
332	#553	—	19	1	no	—
333	#553	—	19	2	no	—
334	#552	—	19	1	no	—
335	D₄×Q₈	—	19	1	no	—
336	#548	—	19	1	no	—
337	#548	D₁₉	1	1	yes	characteristic, complemented
338	#547	—	19	1	no	—
339	#542	—	19	1	no	—
340	#542	—	19	2	no	—
341	#541	—	19	1	no	—
342	#539	—	19	2	no	—
343	#538	—	19	2	no	—
344	#538	—	19	2	no	—
345	#537	—	19	1	no	—
346	#536	—	19	1	no	—
347	#525	—	19	1	no	—
348	#525	—	19	1	no	—
349	C₂×C₂²⋊Q₈	—	19	1	no	—
350	C₂×C₁₉	—	4	1	no	—
351	C₂×C₁₉	—	4	2	no	—
352	C₂×C₁₉	—	4	1	no	—
353	C₂×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
354	C₂×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
355	C₂×C₁₉	#585	1	1	yes	characteristic
356	D₁₉	—	2	2	no	—
357	D₁₉	—	4	1	no	—
358	D₁₉	—	4	1	no	—
359	C₂×#41	—	19	1	no	—
360	C₂×#41	—	19	1	no	—
361	C₂×#41	C₂×D₁₉	1	1	yes	characteristic
362	C₂²×Q₈	—	19	1	no	—
363	C₂²×Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
364	C₂³×C₄	—	19	1	no	—
365	C₄⋊Q₈	—	19	2	no	—
366	C₄⋊Q₈	—	19	1	no	—
367	C₄⋊Q₈	—	19	2	no	—
368	C₄⋊Q₈	—	19	1	no	—
369	#126	—	19	2	no	—
370	#126	—	19	2	no	—
371	#126	—	19	2	no	—
372	#126	—	19	2	no	—
373	#126	—	19	2	no	—
374	#126	—	19	2	no	—
375	#126	—	19	2	no	—
376	#125	—	19	2	no	—
377	#125	—	19	1	no	—
378	#125	—	19	2	no	—
379	#125	—	19	2	no	—
380	#125	—	19	2	no	—
381	#124	—	19	2	no	—
382	#124	—	19	2	no	—
383	#124	—	19	2	no	—
384	#124	—	19	2	no	—
385	#124	C₂×D₁₉	1	2	yes	—
386	#124	C₂×D₁₉	1	1	yes	characteristic, complemented
387	#123	—	19	2	no	—
388	#123	—	19	2	no	—
389	#123	—	19	2	no	—
390	#123	—	19	2	no	—
391	#123	—	19	2	no	—
392	#123	—	19	2	no	—
393	#123	—	19	1	no	—
394	#123	—	19	1	no	—
395	#123	—	19	2	no	—
396	#123	—	19	2	no	—
397	C₂²⋊Q₈	—	19	1	no	—
398	C₂²⋊Q₈	—	19	1	no	—
399	C₂²⋊Q₈	—	19	1	no	—
400	C₂²⋊Q₈	—	19	2	no	—
401	C₂²⋊Q₈	—	19	1	no	—
402	C₂²⋊Q₈	—	19	1	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	2	no	—
408	C₂²⋊Q₈	—	19	1	no	—
409	C₂²⋊Q₈	—	19	2	no	—
410	C₂²⋊Q₈	—	19	2	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	C₂×D₁₉	1	1	yes	characteristic
417	C₂²⋊Q₈	C₂×D₁₉	1	2	yes	complemented
418	#121	—	19	1	no	—
419	#121	—	19	1	no	—
420	#121	—	19	2	no	—
421	#121	—	19	2	no	—
422	#121	—	19	1	no	—
423	#121	—	19	2	no	—
424	#121	—	19	2	no	—
425	#121	—	19	1	no	—
426	#121	—	19	2	no	—
427	#121	—	19	2	no	—
428	#121	C₂×D₁₉	1	2	yes	—
429	#121	C₂×D₁₉	1	1	yes	characteristic, complemented
430	#120	—	19	2	no	—
431	#120	—	19	1	no	—
432	#120	—	19	1	no	—
433	C₄×Q₈	—	19	1	no	—
434	C₄×Q₈	—	19	2	no	—
435	C₄×Q₈	—	19	1	no	—
436	C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
437	C₄×D₄	—	19	1	no	—
438	C₄×D₄	—	19	2	no	—
439	C₄×D₄	—	19	1	no	—
440	C₄×D₄	—	19	1	no	—
441	C₄×D₄	—	19	2	no	—
442	C₄×D₄	—	19	2	no	—
443	C₄×D₄	—	19	2	no	—
444	C₄×D₄	—	19	2	no	—
445	C₄×D₄	—	19	1	no	—
446	C₄×D₄	—	19	2	no	—
447	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
448	C₄×D₄	C₂×D₁₉	1	2	yes	complemented
449	#117	—	19	1	no	—
450	#117	—	19	1	no	—
451	#117	—	19	2	no	—
452	#117	—	19	1	no	—
453	C₂×C₄⋊C₄	—	19	2	no	—
454	C₂×C₄⋊C₄	—	19	2	no	—
455	C₂×C₄⋊C₄	—	19	1	no	—
456	C₂×C₄⋊C₄	—	19	1	no	—
457	C₂×C₂²⋊C₄	—	19	2	no	—
458	C₁₉	#3541	1	1	yes	characteristic, complemented, Sylow
459	C₂⁴	—	19	1	no	—
460	#41	—	4	2	no	—
461	#41	—	76	2	no	—
462	#41	—	76	2	no	—
463	C₂×Q₈	—	4	2	no	—
464	C₂×Q₈	—	19	1	no	—
465	C₂×Q₈	—	19	2	no	—
466	C₂×Q₈	—	19	2	no	—
467	C₂×Q₈	—	19	1	no	—
468	C₂×Q₈	—	76	2	no	—
469	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
470	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
471	C₂×Q₈	C₂²×D₁₉	1	2	yes	—
472	C₂×D₄	—	19	1	no	—
473	C₂×D₄	—	19	2	no	—
474	C₂×D₄	—	19	1	no	—
475	C₂×D₄	—	19	2	no	—
476	C₂×D₄	—	19	1	no	—
477	C₂×D₄	—	19	1	no	—
478	C₂×D₄	—	19	2	no	—
479	C₂×D₄	—	19	1	no	—
480	C₂×D₄	—	19	1	no	—
481	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
482	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
483	C₂×D₄	C₂²×D₁₉	1	2	yes	—
484	C₂×D₄	C₂²×D₁₉	1	2	yes	—
485	C₂²×C₄	—	19	2	no	—
486	C₂²×C₄	—	19	2	no	—
487	C₂²×C₄	—	19	1	no	—
488	C₂²×C₄	—	19	1	no	—
489	C₂²×C₄	—	19	1	no	—
490	C₂²×C₄	—	19	1	no	—
491	C₂²×C₄	—	19	2	no	—
492	C₂²×C₄	—	19	2	no	—
493	C₂²×C₄	—	19	1	no	—
494	C₂²×C₄	—	19	2	no	—
495	C₂²×C₄	—	19	1	no	—
496	C₂²×C₄	—	76	2	no	—
497	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
498	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
499	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
500	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
501	C₄⋊C₄	—	19	1	no	—
502	C₄⋊C₄	—	19	2	no	—
503	C₄⋊C₄	—	19	2	no	—
504	C₄⋊C₄	—	19	2	no	—
505	C₄⋊C₄	—	19	2	no	—
506	C₄⋊C₄	—	19	2	no	—
507	C₄⋊C₄	—	19	2	no	—
508	C₄⋊C₄	—	19	1	no	—
509	C₄⋊C₄	—	19	1	no	—
510	C₄⋊C₄	—	19	2	no	—
511	C₄⋊C₄	—	19	2	no	—
512	C₄⋊C₄	—	19	2	no	—
513	C₄⋊C₄	—	19	1	no	—
514	C₄⋊C₄	—	19	2	no	—
515	C₄⋊C₄	—	19	2	no	—
516	C₄⋊C₄	—	19	2	no	—
517	C₄⋊C₄	—	19	2	no	—
518	C₄⋊C₄	—	19	1	no	—
519	C₄⋊C₄	—	19	1	no	—
520	C₄⋊C₄	—	19	2	no	—
521	C₄⋊C₄	—	19	1	no	—
522	C₄⋊C₄	—	19	2	no	—
523	C₄⋊C₄	—	19	1	no	—
524	C₄⋊C₄	—	19	2	no	—
525	C₄⋊C₄	—	19	2	no	—
526	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
527	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
528	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
529	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
530	C₂²⋊C₄	—	19	2	no	—
531	C₂²⋊C₄	—	19	2	no	—
532	C₂²⋊C₄	—	19	2	no	—
533	C₂²⋊C₄	—	19	1	no	—
534	C₂²⋊C₄	—	19	2	no	—
535	C₂²⋊C₄	—	19	2	no	—
536	C₂²⋊C₄	—	19	1	no	—
537	C₂²⋊C₄	—	19	2	no	—
538	C₂²⋊C₄	—	19	2	no	—
539	C₂²⋊C₄	—	19	2	no	—
540	C₂²⋊C₄	—	19	2	no	—
541	C₂²⋊C₄	—	19	1	no	—
542	C₂²⋊C₄	—	19	1	no	—
543	C₂²⋊C₄	—	19	1	no	—
544	C₂²⋊C₄	—	19	2	no	—
545	C₂²⋊C₄	—	19	2	no	—
546	C₂²⋊C₄	—	19	1	no	—
547	C₂²⋊C₄	—	19	1	no	—
548	C₂²⋊C₄	—	19	2	no	—
549	C₂²⋊C₄	—	19	2	no	—
550	C₂²⋊C₄	—	19	1	no	—
551	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
552	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
553	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
554	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
555	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
556	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
557	C₄²	—	19	2	no	—
558	C₄²	—	19	1	no	—
559	C₄²	—	19	2	no	—
560	C₄²	—	19	2	no	—
561	C₄²	—	19	2	no	—
562	C₄²	C₂²×D₁₉	1	1	yes	characteristic
563	C₄²	C₂²×D₁₉	1	2	yes	—
564	C₂³	—	19	1	no	—
565	C₂³	—	19	1	no	—
566	C₂³	—	19	1	no	—
567	C₂³	—	38	2	no	—
568	C₂³	—	76	1	no	—
569	C₂³	—	76	1	no	—
570	C₂³	C₂³×D₁₉	1	1	yes	characteristic
571	C₂³	C₂³×D₁₉	1	1	yes	characteristic
572	C₂³	C₂³×D₁₉	1	2	yes	—
573	Q₈	—	2	2	no	—
574	Q₈	—	2	2	no	—
575	Q₈	—	4	2	no	—
576	Q₈	—	38	2	no	—
577	Q₈	—	76	2	no	—
578	Q₈	—	76	1	no	—
579	Q₈	—	76	2	no	—
580	D₄	—	2	2	no	—
581	D₄	—	4	2	no	—
582	D₄	—	4	2	no	—
583	D₄	—	4	1	no	—
584	D₄	—	38	2	no	—
585	D₄	—	38	2	no	—
586	D₄	—	38	4	no	—
587	D₄	—	76	1	no	—
588	D₄	—	76	1	no	—
589	D₄	—	76	1	no	—
590	D₄	—	76	2	no	—
591	D₄	—	76	1	no	—
592	D₄	—	76	2	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	4	2	no	—
596	C₂×C₄	—	4	2	no	—
597	C₂×C₄	—	19	2	no	—
598	C₂×C₄	—	19	1	no	—
599	C₂×C₄	—	19	2	no	—
600	C₂×C₄	—	19	2	no	—
601	C₂×C₄	—	19	1	no	—
602	C₂×C₄	—	19	2	no	—
603	C₂×C₄	—	19	1	no	—
604	C₂×C₄	—	19	1	no	—
605	C₂×C₄	—	19	1	no	—
606	C₂×C₄	—	38	2	no	—
607	C₂×C₄	—	38	2	no	—
608	C₂×C₄	—	38	2	no	—
609	C₂×C₄	—	76	1	no	—
610	C₂×C₄	—	76	1	no	—
611	C₂×C₄	—	76	2	no	—
612	C₂×C₄	—	76	2	no	—
613	C₂×C₄	—	76	2	no	—
614	C₂×C₄	—	76	1	no	—
615	C₂×C₄	—	76	2	no	—
616	C₂×C₄	—	76	2	no	—
617	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
618	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
619	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
620	C₂×C₄	C₂³×D₁₉	1	2	yes	—
621	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
622	C₂×C₄	C₂³×D₁₉	1	2	yes	—
623	C₂×C₄	C₂³×D₁₉	1	2	yes	—
624	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
625	C₂²	—	2	1	no	—
626	C₂²	—	2	1	no	—
627	C₂²	—	2	2	no	—
628	C₂²	—	2	1	no	—
629	C₂²	—	2	2	no	—
630	C₂²	—	2	1	no	—
631	C₂²	—	2	2	no	—
632	C₂²	—	2	1	no	—
633	C₂²	—	2	1	no	—
634	C₂²	—	19	2	no	—
635	C₂²	—	38	1	no	—
636	C₂²	—	38	1	no	—
637	C₂²	—	38	1	no	—
638	C₂²	—	38	1	no	—
639	C₂²	—	38	1	no	—
640	C₂²	—	38	1	no	—
641	C₂²	—	38	1	no	—
642	C₂²	—	38	1	no	—
643	C₂²	—	76	4	no	—
644	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
645	C₄	—	2	1	no	—
646	C₄	—	2	1	no	—
647	C₄	—	2	2	no	—
648	C₄	—	2	2	no	—
649	C₄	—	2	1	no	—
650	C₄	—	2	2	no	—
651	C₄	—	2	1	no	—
652	C₄	—	38	1	no	—
653	C₄	—	38	1	no	—
654	C₄	—	38	1	no	—
655	C₄	—	38	2	no	—
656	C₄	—	38	2	no	—
657	C₄	—	38	1	no	—
658	C₄	—	38	1	no	—
659	C₄	—	38	2	no	—
660	C₄	—	38	2	no	—
661	C₄	#10597430	1	2	yes	—
662	C₂	—	4	1	no	—
663	C₂	—	4	1	no	—
664	C₂	—	4	2	no	—
665	C₂	—	38	2	no	—
666	C₂	—	76	1	no	—
667	C₂	—	76	1	no	—
668	C₂	C₂×#10597430	1	1	yes	characteristic
669	C₂	2₋¹⁺⁴×D₁₉	1	1	yes	characteristic
670	C₂	#11927380	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Fitting	C₁₉×#548	C₂
hypercenter	#548	D₁₉
hypocenter	C₁₉	#3541
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ #548

Complements

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

N	H ≅ G/N	type
1. #11927294	C₂	semidirect
2. #11927289	C₂	semidirect
3. #11927264	C₂	semidirect
4. #11927254	C₂	semidirect
5. #11927248	C₂	semidirect
6. #11927244	C₂	semidirect
7. #11927241	C₂	semidirect
8. #11927228	C₂	semidirect
9. Q₈×C₂²⋊D₁₉	C₂	semidirect
10. #11927202	C₂	semidirect
11. #11927193	C₂	semidirect
12. #11927164	C₂	semidirect
13. #11927163	C₂	semidirect
14. #11927152	C₂	semidirect
15. #11927136	C₂	semidirect
16. #11927128	C₂	semidirect
17. #11927126	C₂	semidirect
18. #11927123	C₂	semidirect
19. #11927118	C₂	semidirect
20. #11927053	C₂	semidirect
21. #11927051	C₂	semidirect
22. C₂²⋊Q₈×D₁₉	C₂	semidirect
23. C₁₉×#548	C₂	semidirect
25. C₂²×Q₈×C₁₉	C₂²	semidirect
27. C₂×#64543	C₂²	semidirect
31. C₁₉×#124	C₂²	semidirect
33. C₁₉×C₂²⋊Q₈	C₂²	semidirect
35. C₁₉×#121	C₂²	semidirect
36. C₄×Q₈×C₁₉	C₂²	semidirect
38. C₄×D₄×C₁₉	C₂²	semidirect
44. #10597392	C₂²	semidirect
45. #10597392	C₂²	semidirect
46. Q₈×Dic₁₉	C₂²	semidirect
47. #10597390	C₂²	semidirect
48. #10597390	C₂²	semidirect
49. #10597390	C₂²	semidirect
56. #10597384	C₂²	semidirect
62. #10597381	C₂²	semidirect
63. D₄×Dic₁₉	C₂²	semidirect
65. #10597375	C₂²	semidirect
66. #10597375	C₂²	semidirect
73. #10597372	C₂²	semidirect
75. #10597370	C₂²	semidirect
76. #10597370	C₂²	semidirect
77. C₂×Dic₁₉⋊C₄	C₂²	semidirect
83. #10597342	C₂²	semidirect
85. #10597338	C₂²	semidirect
88. C₄⋊C₄×D₁₉	C₂²	semidirect
89. #10597336	C₂²	semidirect
90. #10597335	C₂²	semidirect
91. #10597335	C₂²	semidirect
92. #10597333	C₂²	semidirect
95. #10597331	C₂²	semidirect
107. #10597325	C₂²	semidirect
108. #10597325	C₂²	semidirect
109. #10597325	C₂²	semidirect
112. #10597324	C₂²	semidirect
113. #10597324	C₂²	semidirect
114. #10597324	C₂²	semidirect
119. #10597316	C₂²	semidirect
120. #10597316	C₂²	semidirect
121. #10597315	C₂²	semidirect
122. C₄×Dic₃₈	C₂²	semidirect
337. #548	D₁₉	semidirect
363. C₂²×Q₈	C₂×D₁₉	semidirect
386. #124	C₂×D₁₉	semidirect
417. C₂²⋊Q₈	C₂×D₁₉	semidirect
429. #121	C₂×D₁₉	semidirect
436. C₄×Q₈	C₂×D₁₉	semidirect
448. C₄×D₄	C₂×D₁₉	semidirect
458. C₁₉	#3541	semidirect

Maximal subgroups

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

subgroup	index
#11927294	2
#11927289	2
#11927264	2
#11927254	2
#11927248	2
#11927244	2
#11927241	2
#11927228	2
Q₈×C₂²⋊D₁₉	2
#11927202	2
#11927193	2
#11927164	2
#11927163	2
#11927152	2
#11927136	2
#11927128	2
#11927126	2
#11927123	2
#11927118	2
#11927053	2
#11927051	2
C₂²⋊Q₈×D₁₉	2
C₁₉×#548	2
#3541	19