Subgroups — #14577688

Order 2432.

1042 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927264	C₂	1	1	yes	maximal, characteristic, complemented
2	#11927263	C₂	1	1	yes	maximal, characteristic, complemented
3	#11927251	C₂	1	1	yes	maximal, characteristic, complemented
4	#11927246	C₂	1	2	yes	maximal, complemented
5	#11927241	C₂	1	1	yes	maximal, characteristic, complemented
6	#11927231	C₂	1	2	yes	maximal, complemented
7	#11927228	C₂	1	1	yes	maximal, characteristic, complemented
8	#11927225	C₂	1	2	yes	maximal, complemented
9	#11927220	C₂	1	2	yes	maximal, complemented
10	#11927193	C₂	1	1	yes	maximal, characteristic, complemented
11	#11927188	C₂	1	1	yes	maximal, characteristic, complemented
12	#11927163	C₂	1	1	yes	maximal, characteristic, complemented
13	#11927154	C₂	1	1	yes	maximal, characteristic, complemented
14	#11927139	C₂	1	2	yes	maximal, complemented
15	#11927129	C₂	1	2	yes	maximal, complemented
16	#11927075	C₂	1	1	yes	maximal, characteristic, complemented
17	#11927074	C₂	1	1	yes	maximal, characteristic, complemented
18	#11927071	C₂	1	2	yes	maximal, complemented
19	C₂×#10597325	C₂	1	2	yes	maximal, complemented
20	#11927023	C₂	1	1	yes	maximal, characteristic, complemented
21	#11927019	C₂	1	1	yes	maximal, characteristic, complemented
22	#41×Dic₁₉	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₉×#546	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#41×C₁₉	C₂²	1	1	yes	characteristic
25	C₂²×D₄×C₁₉	C₂²	1	1	yes	characteristic
26	C₂×#64543	C₂²	1	1	yes	characteristic
27	C₁₉×#124	C₂²	1	1	yes	characteristic
28	C₁₉×#123	C₂²	1	2	yes	—
29	C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
30	C₁₉×#121	C₂²	1	1	yes	characteristic
31	C₁₉×#121	C₂²	1	2	yes	—
32	C₁₉×#120	C₂²	1	2	yes	—
33	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
34	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
35	C₂×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
36	#10597399	C₂²	1	2	yes	—
37	C₂×C₂²⋊Dic₁₉	C₂²	1	2	yes	—
38	C₂×C₂²⋊Dic₁₉	C₂²	1	2	yes	—
39	C₂×C₂²⋊Dic₁₉	C₂²	1	2	yes	—
40	#10597392	C₂²	1	1	yes	characteristic, complemented
41	Q₈×Dic₁₉	C₂²	1	1	yes	characteristic, complemented
42	Q₈×Dic₁₉	C₂²	1	1	yes	characteristic, complemented
43	#10597390	C₂²	1	1	yes	characteristic, complemented
44	#10597385	C₂²	1	2	yes	—
45	#10597385	C₂²	1	1	yes	characteristic
46	#10597385	C₂²	1	2	yes	complemented
47	#10597384	C₂²	1	1	yes	characteristic
48	#10597384	C₂²	1	2	yes	complemented
49	#10597382	C₂²	1	1	yes	characteristic
50	#10597382	C₂²	1	2	yes	—
51	#10597381	C₂²	1	1	yes	characteristic
52	#10597381	C₂²	1	2	yes	—
53	#10597381	C₂²	1	2	yes	complemented
54	#10597381	C₂²	1	2	yes	complemented
55	#10597381	C₂²	1	2	yes	complemented
56	D₄×Dic₁₉	C₂²	1	2	yes	—
57	D₄×Dic₁₉	C₂²	1	1	yes	characteristic
58	D₄×Dic₁₉	C₂²	1	1	yes	characteristic
59	D₄×Dic₁₉	C₂²	1	1	yes	characteristic
60	D₄×Dic₁₉	C₂²	1	2	yes	—
61	D₄×Dic₁₉	C₂²	1	1	yes	characteristic
62	D₄×Dic₁₉	C₂²	1	1	yes	characteristic
63	D₄×Dic₁₉	C₂²	1	2	yes	complemented
64	D₄×Dic₁₉	C₂²	1	2	yes	complemented
65	D₄×Dic₁₉	C₂²	1	2	yes	complemented
66	#10597375	C₂²	1	2	yes	complemented
67	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
68	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic, complemented
69	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	complemented
70	#10597372	C₂²	1	1	yes	characteristic
71	#10597372	C₂²	1	1	yes	characteristic
72	#10597372	C₂²	1	2	yes	complemented
73	#10597372	C₂²	1	1	yes	characteristic, complemented
74	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	complemented
75	#10597370	C₂²	1	1	yes	characteristic
76	#10597370	C₂²	1	1	yes	characteristic, complemented
77	#10597370	C₂²	1	2	yes	complemented
78	C₂×Dic₁₉⋊C₄	C₂²	1	2	yes	complemented
79	C₂×Dic₁₉⋊C₄	C₂²	1	2	yes	complemented
80	C₂×C₄×Dic₁₉	C₂²	1	2	yes	complemented
81	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic, complemented
82	#10597344	C₂²	1	1	yes	characteristic, complemented
83	#10597338	C₂²	1	2	yes	complemented
84	C₄⋊C₄×D₁₉	C₂²	1	1	yes	characteristic, complemented
85	#10597336	C₂²	1	1	yes	characteristic, complemented
86	#10597336	C₂²	1	2	yes	complemented
87	#10597336	C₂²	1	1	yes	characteristic, complemented
88	#10597335	C₂²	1	2	yes	complemented
89	#10597335	C₂²	1	1	yes	characteristic, complemented
90	#10597335	C₂²	1	2	yes	complemented
91	#10597333	C₂²	1	2	yes	complemented
92	#10597333	C₂²	1	1	yes	characteristic, complemented
93	#10597332	C₂²	1	1	yes	characteristic, complemented
94	#10597332	C₂²	1	2	yes	complemented
95	#10597331	C₂²	1	1	yes	characteristic
96	#10597331	C₂²	1	2	yes	complemented
97	#10597329	C₂²	1	2	yes	—
98	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	complemented
99	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	complemented
100	#10597325	C₂²	1	1	yes	characteristic
101	#10597325	C₂²	1	2	yes	—
102	#10597325	C₂²	1	2	yes	—
103	#10597325	C₂²	1	2	yes	—
104	#10597325	C₂²	1	2	yes	—
105	#10597325	C₂²	1	2	yes	complemented
106	#10597325	C₂²	1	2	yes	complemented
107	#10597325	C₂²	1	2	yes	complemented
108	#10597325	C₂²	1	2	yes	complemented
109	#10597325	C₂²	1	2	yes	complemented
110	#10597325	C₂²	1	2	yes	complemented
111	#10597324	C₂²	1	2	yes	complemented
112	#10597324	C₂²	1	1	yes	characteristic, complemented
113	#10597324	C₂²	1	2	yes	complemented
114	#10597324	C₂²	1	2	yes	complemented
115	#10597324	C₂²	1	2	yes	complemented
116	#10597323	C₂²	1	2	yes	complemented
117	#10597323	C₂²	1	2	yes	complemented
118	#10597323	C₂²	1	2	yes	complemented
119	#10597318	C₂²	1	1	yes	characteristic, complemented
120	#10597315	C₂²	1	1	yes	characteristic, complemented
121	C₄×Dic₃₈	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₃₈	C₂²	1	1	yes	characteristic, complemented
123	C₂⁴×C₁₉	C₂³	1	2	yes	—
124	#41×C₁₉	—	2	4	no	—
125	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
126	C₂×D₄×C₁₉	—	2	4	no	—
127	C₂×D₄×C₁₉	C₂³	1	2	yes	—
128	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
129	C₂×D₄×C₁₉	C₂³	1	2	yes	—
130	C₂×D₄×C₁₉	C₂³	1	2	yes	—
131	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
132	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
133	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
134	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
135	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
136	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
140	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
141	C₂²×Dic₁₉	C₂³	1	2	yes	—
142	C₂²×Dic₁₉	C₂³	1	2	yes	—
143	C₂²×Dic₁₉	C₂³	1	2	yes	—
144	C₂²×Dic₁₉	C₂³	1	2	yes	—
145	C₂²×Dic₁₉	C₂³	1	2	yes	—
146	C₂²×Dic₁₉	C₂³	1	2	yes	—
147	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
148	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
149	#64543	—	2	4	no	—
150	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
151	C₂×C₄×D₁₉	C₂³	1	2	yes	—
152	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
153	C₂×Dic₃₈	C₂³	1	2	yes	—
154	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
155	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
156	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
157	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
158	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
159	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
160	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
161	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
162	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
163	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
164	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
165	C₄²×C₁₉	C₂³	1	1	yes	characteristic
166	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
167	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
168	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
169	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
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	2	yes	—
174	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
175	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
176	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
177	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
182	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
183	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
184	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
185	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
186	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
187	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
188	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
189	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
190	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
191	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
192	C₄⋊Dic₁₉	C₂³	1	2	yes	—
193	C₄⋊Dic₁₉	C₂³	1	2	yes	—
194	C₄⋊Dic₁₉	C₂³	1	2	yes	—
195	C₄⋊Dic₁₉	C₂³	1	2	yes	—
196	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
197	C₄⋊Dic₁₉	C₂³	1	2	yes	—
198	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
199	Dic₁₉⋊C₄	C₂³	1	2	yes	—
200	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
201	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
209	Dic₁₉⋊C₄	C₂³	1	2	yes	—
210	Dic₁₉⋊C₄	C₂³	1	2	yes	—
211	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
212	Dic₁₉⋊C₄	C₂³	1	2	yes	—
213	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
214	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
215	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
216	C₄×Dic₁₉	C₂³	1	2	yes	—
217	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
218	C₄×Dic₁₉	C₂³	1	2	yes	—
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	1	yes	characteristic
223	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
224	C₄×Dic₁₉	C₂³	1	2	yes	—
225	C₂³×C₁₉	—	2	4	no	—
226	C₂³×C₁₉	—	4	2	no	—
227	C₂³×C₁₉	—	4	2	no	—
228	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
229	C₂³×C₁₉	C₂⁴	1	2	yes	—
230	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
231	C₂³×C₁₉	C₂⁴	1	2	yes	—
232	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
233	Q₈×C₁₉	—	2	2	no	—
234	D₄×C₁₉	—	2	4	no	—
235	D₄×C₁₉	—	2	4	no	—
236	D₄×C₁₉	—	2	2	no	—
237	D₄×C₁₉	—	4	1	no	—
238	D₄×C₁₉	—	4	2	no	—
239	D₄×C₁₉	#41	1	4	yes	—
240	C₂×C₄×C₁₉	—	2	4	no	—
241	C₂×C₄×C₁₉	—	2	2	no	—
242	C₂×C₄×C₁₉	—	2	2	no	—
243	C₂×C₄×C₁₉	—	4	2	no	—
244	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
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	2	yes	—
249	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
250	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
251	C₂²⋊D₁₉	—	2	4	no	—
252	C₂²⋊D₁₉	—	4	1	no	—
253	C₂²⋊D₁₉	—	4	2	no	—
254	C₂²⋊D₁₉	—	4	1	no	—
255	C₂×Dic₁₉	—	2	4	no	—
256	C₂×Dic₁₉	—	4	2	no	—
257	C₂×Dic₁₉	—	4	2	no	—
258	C₂×Dic₁₉	—	4	2	no	—
259	C₂×Dic₁₉	—	4	2	no	—
260	C₂×Dic₁₉	—	4	1	no	—
261	C₂×Dic₁₉	—	4	2	no	—
262	C₂×Dic₁₉	—	4	1	no	—
263	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
264	C₂×Dic₁₉	C₂⁴	1	2	yes	—
265	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
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	2	yes	—
270	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
271	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
272	C₂×Dic₁₉	C₂⁴	1	2	yes	—
273	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
274	C₄×D₁₉	—	2	2	no	—
275	C₄×D₁₉	—	4	2	no	—
276	Dic₃₈	—	2	2	no	—
277	Dic₃₈	—	4	2	no	—
278	Dic₃₈	—	4	1	no	—
279	#3521	—	19	1	no	maximal, Sylow
280	C₂²×C₁₉	—	2	2	no	—
281	C₂²×C₁₉	—	2	2	no	—
282	C₂²×C₁₉	—	2	1	no	—
283	C₂²×C₁₉	—	2	1	no	—
284	C₂²×C₁₉	—	2	2	no	—
285	C₂²×C₁₉	—	2	1	no	—
286	C₂²×C₁₉	—	2	2	no	—
287	C₂²×C₁₉	—	2	1	no	—
288	C₂²×C₁₉	—	2	2	no	—
289	C₂²×C₁₉	—	2	1	no	—
290	C₂²×C₁₉	—	2	1	no	—
291	C₂²×C₁₉	—	8	4	no	—
292	C₂²×C₁₉	C₂×#41	1	4	yes	—
293	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
294	C₂×D₁₉	—	2	1	no	—
295	C₂×D₁₉	—	2	1	no	—
296	C₂×D₁₉	—	2	1	no	—
297	C₄×C₁₉	—	2	1	no	—
298	C₄×C₁₉	—	2	1	no	—
299	C₄×C₁₉	—	2	2	no	—
300	C₄×C₁₉	—	2	1	no	—
301	C₄×C₁₉	—	2	1	no	—
302	C₄×C₁₉	—	2	2	no	—
303	C₄×C₁₉	C₂×#41	1	2	yes	—
304	Dic₁₉	—	2	2	no	—
305	Dic₁₉	—	2	1	no	—
306	Dic₁₉	—	2	1	no	—
307	Dic₁₉	—	2	2	no	—
308	Dic₁₉	—	2	1	no	—
309	Dic₁₉	—	2	2	no	—
310	Dic₁₉	—	2	2	no	—
311	Dic₁₉	—	2	1	no	—
312	Dic₁₉	—	2	1	no	—
313	Dic₁₉	—	2	1	no	—
314	Dic₁₉	—	2	1	no	—
315	#556	—	19	1	no	—
316	#556	—	19	1	no	—
317	#554	—	19	1	no	—
318	#553	—	19	1	no	—
319	#553	—	19	2	no	—
320	#552	—	19	2	no	—
321	#552	—	19	1	no	—
322	#551	—	19	2	no	—
323	#551	—	19	2	no	—
324	#547	—	19	1	no	—
325	#546	—	19	1	no	—
326	#546	D₁₉	1	1	yes	characteristic, complemented
327	#542	—	19	1	no	—
328	#541	—	19	1	no	—
329	#539	—	19	2	no	—
330	#538	—	19	2	no	—
331	#529	—	19	2	no	—
332	#529	—	19	1	no	—
333	#529	—	19	1	no	—
334	C₂×#126	—	19	2	no	—
335	#520	—	19	1	no	—
336	#518	—	19	1	no	—
337	C₄×#41	—	19	1	no	—
338	C₂×C₁₉	—	2	4	no	—
339	C₂×C₁₉	—	4	1	no	—
340	C₂×C₁₉	—	4	2	no	—
341	C₂×C₁₉	—	4	1	no	—
342	C₂×C₁₉	C₂²×#41	1	1	yes	characteristic
343	C₂×C₁₉	#585	1	1	yes	characteristic
344	C₂×C₁₉	#585	1	1	yes	characteristic
345	D₁₉	—	4	1	no	—
346	C₂×#41	—	19	1	no	—
347	C₂×#41	C₂×D₁₉	1	1	yes	characteristic
348	C₂²×D₄	C₂×D₁₉	1	1	yes	characteristic
349	C₄⋊Q₈	—	19	1	no	—
350	C₄⋊Q₈	—	19	1	no	—
351	#126	—	19	1	no	—
352	#126	—	19	1	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	#126	—	19	2	no	—
361	#126	—	19	2	no	—
362	#126	—	19	2	no	—
363	#125	—	19	2	no	—
364	#125	—	19	1	no	—
365	#125	—	19	1	no	—
366	#125	—	19	2	no	—
367	#125	—	19	2	no	—
368	#125	—	19	1	no	—
369	#124	—	19	1	no	—
370	#124	—	19	2	no	—
371	#124	—	19	2	no	—
372	#124	—	19	1	no	—
373	#124	C₂×D₁₉	1	1	yes	characteristic
374	#123	—	19	1	no	—
375	#123	—	19	2	no	—
376	#123	—	19	2	no	—
377	#123	—	19	2	no	—
378	#123	—	19	2	no	—
379	#123	—	19	2	no	—
380	#123	—	19	1	no	—
381	#123	—	19	2	no	—
382	#123	—	19	2	no	—
383	#123	C₂×D₁₉	1	2	yes	—
384	C₂²⋊Q₈	—	19	1	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	2	no	—
390	C₂²⋊Q₈	—	19	2	no	—
391	C₂²⋊Q₈	—	19	2	no	—
392	C₂²⋊Q₈	—	19	2	no	—
393	C₂²⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
394	#121	—	19	1	no	—
395	#121	—	19	2	no	—
396	#121	—	19	1	no	—
397	#121	—	19	2	no	—
398	#121	—	19	2	no	—
399	#121	C₂×D₁₉	1	1	yes	characteristic
400	#121	C₂×D₁₉	1	2	yes	—
401	#120	—	19	2	no	—
402	#120	C₂×D₁₉	1	2	yes	—
403	C₄×Q₈	—	19	1	no	—
404	C₄×Q₈	—	19	1	no	—
405	C₄×Q₈	—	19	1	no	—
406	C₄×Q₈	—	19	2	no	—
407	C₄×Q₈	—	19	1	no	—
408	C₄×Q₈	—	19	1	no	—
409	C₄×D₄	—	19	1	no	—
410	C₄×D₄	—	19	1	no	—
411	C₄×D₄	—	19	2	no	—
412	C₄×D₄	—	19	1	no	—
413	C₄×D₄	—	19	1	no	—
414	C₄×D₄	—	19	2	no	—
415	C₄×D₄	—	19	1	no	—
416	C₄×D₄	—	19	2	no	—
417	C₄×D₄	—	19	2	no	—
418	C₄×D₄	—	19	2	no	—
419	C₄×D₄	—	19	2	no	—
420	C₄×D₄	—	19	1	no	—
421	C₄×D₄	—	19	1	no	—
422	C₄×D₄	—	19	2	no	—
423	C₄×D₄	—	19	2	no	—
424	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
425	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
426	#117	—	19	2	no	—
427	#117	—	19	1	no	—
428	#117	—	19	1	no	—
429	#117	—	19	1	no	—
430	#117	—	19	2	no	—
431	#117	—	19	2	no	—
432	#117	—	19	2	no	—
433	#117	—	19	2	no	—
434	#117	—	19	1	no	—
435	C₂×C₄⋊C₄	—	19	2	no	—
436	C₂×C₄⋊C₄	—	19	2	no	—
437	C₂×C₄⋊C₄	—	19	2	no	—
438	C₂×C₄⋊C₄	—	19	1	no	—
439	C₂×C₂²⋊C₄	—	19	2	no	—
440	C₂×C₂²⋊C₄	—	19	2	no	—
441	C₂×C₂²⋊C₄	—	19	2	no	—
442	C₂×C₂²⋊C₄	C₂×D₁₉	1	2	yes	—
443	C₂×C₄²	—	19	2	no	—
444	C₂×C₄²	—	19	1	no	—
445	C₁₉	#3521	1	1	yes	characteristic, complemented, Sylow
446	C₂⁴	C₂²×D₁₉	1	2	yes	—
447	#41	—	2	4	no	—
448	#41	—	38	4	no	—
449	C₂×Q₈	—	19	1	no	—
450	C₂×Q₈	—	19	1	no	—
451	C₂×Q₈	—	19	2	no	—
452	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
453	C₂×D₄	—	2	4	no	—
454	C₂×D₄	—	19	2	no	—
455	C₂×D₄	—	19	1	no	—
456	C₂×D₄	—	19	2	no	—
457	C₂×D₄	—	19	1	no	—
458	C₂×D₄	C₂²×D₁₉	1	2	yes	—
459	C₂×D₄	C₂²×D₁₉	1	2	yes	—
460	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
461	C₂×D₄	C₂²×D₁₉	1	2	yes	—
462	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
463	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
464	C₂²×C₄	—	19	2	no	—
465	C₂²×C₄	—	19	2	no	—
466	C₂²×C₄	—	19	2	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	—	19	2	no	—
472	C₂²×C₄	—	19	1	no	—
473	C₂²×C₄	—	19	2	no	—
474	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
475	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
476	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
477	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
478	C₄⋊C₄	—	19	1	no	—
479	C₄⋊C₄	—	19	2	no	—
480	C₄⋊C₄	—	19	1	no	—
481	C₄⋊C₄	—	19	2	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	1	no	—
487	C₄⋊C₄	—	19	1	no	—
488	C₄⋊C₄	—	19	2	no	—
489	C₄⋊C₄	—	19	2	no	—
490	C₄⋊C₄	—	19	2	no	—
491	C₄⋊C₄	—	19	1	no	—
492	C₄⋊C₄	—	19	1	no	—
493	C₄⋊C₄	—	19	2	no	—
494	C₄⋊C₄	—	19	1	no	—
495	C₄⋊C₄	—	19	1	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	1	no	—
501	C₄⋊C₄	—	19	1	no	—
502	C₄⋊C₄	—	19	1	no	—
503	C₄⋊C₄	—	19	2	no	—
504	C₄⋊C₄	—	19	2	no	—
505	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
506	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
507	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
508	C₂²⋊C₄	—	19	1	no	—
509	C₂²⋊C₄	—	19	1	no	—
510	C₂²⋊C₄	—	19	2	no	—
511	C₂²⋊C₄	—	19	1	no	—
512	C₂²⋊C₄	—	19	2	no	—
513	C₂²⋊C₄	—	19	2	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	2	no	—
523	C₂²⋊C₄	—	19	1	no	—
524	C₂²⋊C₄	—	19	1	no	—
525	C₂²⋊C₄	—	19	1	no	—
526	C₂²⋊C₄	—	19	1	no	—
527	C₂²⋊C₄	—	19	2	no	—
528	C₂²⋊C₄	—	19	1	no	—
529	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
530	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
531	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
532	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
533	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
534	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
535	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
536	C₄²	—	19	1	no	—
537	C₄²	—	19	1	no	—
538	C₄²	—	19	1	no	—
539	C₄²	—	19	2	no	—
540	C₄²	—	19	2	no	—
541	C₄²	—	19	1	no	—
542	C₄²	—	19	2	no	—
543	C₄²	—	19	2	no	—
544	C₄²	—	19	2	no	—
545	C₄²	—	19	2	no	—
546	C₄²	—	19	1	no	—
547	C₄²	C₂²×D₁₉	1	1	yes	characteristic
548	C₂³	—	2	4	no	—
549	C₂³	—	4	2	no	—
550	C₂³	—	4	2	no	—
551	C₂³	—	19	1	no	—
552	C₂³	C₂³×D₁₉	1	1	yes	characteristic
553	C₂³	C₂³×D₁₉	1	2	yes	—
554	C₂³	C₂³×D₁₉	1	1	yes	characteristic
555	C₂³	C₂³×D₁₉	1	2	yes	—
556	Q₈	—	2	2	no	—
557	Q₈	—	38	2	no	—
558	Q₈	—	76	1	no	—
559	Q₈	—	76	2	no	—
560	D₄	—	2	4	no	—
561	D₄	—	2	4	no	—
562	D₄	—	2	2	no	—
563	D₄	—	4	2	no	—
564	D₄	—	4	1	no	—
565	D₄	—	38	4	no	—
566	D₄	—	76	1	no	—
567	D₄	—	76	1	no	—
568	D₄	—	76	2	no	—
569	D₄	#64543	1	4	yes	—
570	C₂×C₄	—	2	4	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	4	2	no	—
574	C₂×C₄	—	19	1	no	—
575	C₂×C₄	—	19	2	no	—
576	C₂×C₄	—	19	1	no	—
577	C₂×C₄	—	19	1	no	—
578	C₂×C₄	—	19	2	no	—
579	C₂×C₄	—	19	1	no	—
580	C₂×C₄	—	19	2	no	—
581	C₂×C₄	—	19	1	no	—
582	C₂×C₄	—	19	2	no	—
583	C₂×C₄	—	19	1	no	—
584	C₂×C₄	—	19	1	no	—
585	C₂×C₄	—	38	4	no	—
586	C₂×C₄	—	38	2	no	—
587	C₂×C₄	—	76	2	no	—
588	C₂×C₄	—	76	2	no	—
589	C₂×C₄	—	76	2	no	—
590	C₂×C₄	—	76	1	no	—
591	C₂×C₄	—	76	1	no	—
592	C₂×C₄	—	76	2	no	—
593	C₂×C₄	—	76	2	no	—
594	C₂×C₄	—	76	2	no	—
595	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
596	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
597	C₂×C₄	C₂³×D₁₉	1	2	yes	—
598	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
599	C₂×C₄	C₂³×D₁₉	1	2	yes	—
600	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
601	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
602	C₂²	—	2	2	no	—
603	C₂²	—	2	2	no	—
604	C₂²	—	2	1	no	—
605	C₂²	—	2	1	no	—
606	C₂²	—	2	2	no	—
607	C₂²	—	2	1	no	—
608	C₂²	—	2	2	no	—
609	C₂²	—	2	1	no	—
610	C₂²	—	2	1	no	—
611	C₂²	—	2	2	no	—
612	C₂²	—	2	1	no	—
613	C₂²	—	8	4	no	—
614	C₂²	—	38	1	no	—
615	C₂²	—	38	1	no	—
616	C₂²	—	38	1	no	—
617	C₂²	C₂×#64543	1	4	yes	—
618	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
619	C₄	—	2	1	no	—
620	C₄	—	2	1	no	—
621	C₄	—	2	2	no	—
622	C₄	—	2	1	no	—
623	C₄	—	2	2	no	—
624	C₄	—	2	1	no	—
625	C₄	—	38	1	no	—
626	C₄	—	38	2	no	—
627	C₄	—	38	2	no	—
628	C₄	—	38	1	no	—
629	C₄	—	38	1	no	—
630	C₄	—	38	1	no	—
631	C₄	—	38	1	no	—
632	C₄	—	38	1	no	—
633	C₄	—	38	1	no	—
634	C₄	—	38	2	no	—
635	C₄	—	38	2	no	—
636	C₄	C₂×#64543	1	2	yes	—
637	C₂	—	2	4	no	—
638	C₂	—	4	1	no	—
639	C₂	—	4	2	no	—
640	C₂	—	4	1	no	—
641	C₂	—	76	1	no	—
642	C₂	C₂²×#64543	1	1	yes	characteristic
643	C₂	#11927379	1	1	yes	characteristic
644	C₂	#11927380	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Fitting	C₁₉×#546	C₂
hypercenter	#546	D₁₉
hypocenter	C₁₉	#3521
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ #546

Complements

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

N	H ≅ G/N	type
1. #11927264	C₂	semidirect
2. #11927263	C₂	semidirect
3. #11927251	C₂	semidirect
4. #11927246	C₂	semidirect
5. #11927241	C₂	semidirect
6. #11927231	C₂	semidirect
7. #11927228	C₂	semidirect
8. #11927225	C₂	semidirect
9. #11927220	C₂	semidirect
10. #11927193	C₂	semidirect
11. #11927188	C₂	semidirect
12. #11927163	C₂	semidirect
13. #11927154	C₂	semidirect
14. #11927139	C₂	semidirect
15. #11927129	C₂	semidirect
16. #11927075	C₂	semidirect
17. #11927074	C₂	semidirect
18. #11927071	C₂	semidirect
19. C₂×#10597325	C₂	semidirect
20. #11927023	C₂	semidirect
21. #11927019	C₂	semidirect
22. #41×Dic₁₉	C₂	semidirect
23. C₁₉×#546	C₂	semidirect
40. #10597392	C₂²	semidirect
41. Q₈×Dic₁₉	C₂²	semidirect
42. Q₈×Dic₁₉	C₂²	semidirect
43. #10597390	C₂²	semidirect
46. #10597385	C₂²	semidirect
48. #10597384	C₂²	semidirect
53. #10597381	C₂²	semidirect
54. #10597381	C₂²	semidirect
55. #10597381	C₂²	semidirect
63. D₄×Dic₁₉	C₂²	semidirect
64. D₄×Dic₁₉	C₂²	semidirect
65. D₄×Dic₁₉	C₂²	semidirect
66. #10597375	C₂²	semidirect
68. C₄×C₂²⋊D₁₉	C₂²	semidirect
69. C₄×C₂²⋊D₁₉	C₂²	semidirect
72. #10597372	C₂²	semidirect
73. #10597372	C₂²	semidirect
74. C₂×C₄⋊Dic₁₉	C₂²	semidirect
76. #10597370	C₂²	semidirect
77. #10597370	C₂²	semidirect
78. C₂×Dic₁₉⋊C₄	C₂²	semidirect
79. C₂×Dic₁₉⋊C₄	C₂²	semidirect
80. C₂×C₄×Dic₁₉	C₂²	semidirect
81. C₂×C₄×Dic₁₉	C₂²	semidirect
82. #10597344	C₂²	semidirect
83. #10597338	C₂²	semidirect
84. C₄⋊C₄×D₁₉	C₂²	semidirect
85. #10597336	C₂²	semidirect
86. #10597336	C₂²	semidirect
87. #10597336	C₂²	semidirect
88. #10597335	C₂²	semidirect
89. #10597335	C₂²	semidirect
90. #10597335	C₂²	semidirect
91. #10597333	C₂²	semidirect
92. #10597333	C₂²	semidirect
93. #10597332	C₂²	semidirect
94. #10597332	C₂²	semidirect
96. #10597331	C₂²	semidirect
98. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
99. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
105. #10597325	C₂²	semidirect
106. #10597325	C₂²	semidirect
107. #10597325	C₂²	semidirect
108. #10597325	C₂²	semidirect
109. #10597325	C₂²	semidirect
110. #10597325	C₂²	semidirect
111. #10597324	C₂²	semidirect
112. #10597324	C₂²	semidirect
113. #10597324	C₂²	semidirect
114. #10597324	C₂²	semidirect
115. #10597324	C₂²	semidirect
116. #10597323	C₂²	semidirect
117. #10597323	C₂²	semidirect
118. #10597323	C₂²	semidirect
119. #10597318	C₂²	semidirect
120. #10597315	C₂²	semidirect
121. C₄×Dic₃₈	C₂²	semidirect
122. C₄×Dic₃₈	C₂²	semidirect
326. #546	D₁₉	semidirect
445. C₁₉	#3521	semidirect

Maximal subgroups

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

subgroup	index
#11927264	2
#11927263	2
#11927251	2
#11927246	2
#11927241	2
#11927231	2
#11927228	2
#11927225	2
#11927220	2
#11927193	2
#11927188	2
#11927163	2
#11927154	2
#11927139	2
#11927129	2
#11927075	2
#11927074	2
#11927071	2
C₂×#10597325	2
#11927023	2
#11927019	2
#41×Dic₁₉	2
C₁₉×#546	2
#3521	19