Subgroups — #14577583

Order 2432.

1142 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927276	C₂	1	1	yes	maximal, characteristic, complemented
2	#11927265	C₂	1	1	yes	maximal, characteristic, complemented
3	#11927259	C₂	1	1	yes	maximal, characteristic, complemented
4	#11927258	C₂	1	1	yes	maximal, characteristic, complemented
5	#11927220	C₂	1	2	yes	maximal, complemented
6	#11927217	C₂	1	2	yes	maximal, complemented
7	D₄×Dic₃₈	C₂	1	1	yes	maximal, characteristic, complemented
8	#11927200	C₂	1	2	yes	maximal, complemented
9	#11927182	C₂	1	1	yes	maximal, characteristic, complemented
10	#11927181	C₂	1	2	yes	maximal, complemented
11	D₄×C₂²⋊D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#11927167	C₂	1	1	yes	maximal, characteristic, complemented
13	#11927163	C₂	1	1	yes	maximal, characteristic, complemented
14	#11927131	C₂	1	2	yes	maximal, complemented
15	#11927129	C₂	1	2	yes	maximal, complemented
16	#11927089	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×#10597331	C₂	1	2	yes	maximal, complemented
20	#11927019	C₂	1	1	yes	maximal, characteristic, complemented
21	#11927016	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	C₂²×C₂²⋊D₁₉	C₂²	1	2	yes	—
27	C₂×#64543	C₂²	1	2	yes	complemented
28	C₂×D₄×D₁₉	C₂²	1	1	yes	characteristic
29	C₂²×Dic₃₈	C₂²	1	2	yes	complemented
30	C₁₉×#124	C₂²	1	1	yes	characteristic, complemented
31	C₁₉×#123	C₂²	1	2	yes	complemented
32	C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
33	C₁₉×#121	C₂²	1	1	yes	characteristic, complemented
34	C₁₉×#121	C₂²	1	2	yes	complemented
35	C₁₉×#120	C₂²	1	2	yes	complemented
36	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
37	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	complemented
39	#10597399	C₂²	1	2	yes	—
40	C₂×C₂²⋊Dic₁₉	C₂²	1	2	yes	complemented
41	C₂×C₂²⋊Dic₁₉	C₂²	1	2	yes	complemented
42	#10597393	C₂²	1	1	yes	characteristic, complemented
43	#10597392	C₂²	1	1	yes	characteristic, complemented
44	Q₈×Dic₁₉	C₂²	1	1	yes	characteristic, complemented
45	Q₈×Dic₁₉	C₂²	1	1	yes	characteristic, complemented
46	#10597386	C₂²	1	1	yes	characteristic
47	#10597385	C₂²	1	2	yes	—
48	#10597385	C₂²	1	1	yes	characteristic
49	#10597385	C₂²	1	2	yes	complemented
50	#10597385	C₂²	1	2	yes	complemented
51	#10597385	C₂²	1	2	yes	complemented
52	#10597384	C₂²	1	1	yes	characteristic
53	#10597384	C₂²	1	2	yes	complemented
54	#10597383	C₂²	1	2	yes	—
55	#10597383	C₂²	1	2	yes	complemented
56	#10597382	C₂²	1	2	yes	complemented
57	#10597381	C₂²	1	1	yes	characteristic, complemented
58	D₄×Dic₁₉	C₂²	1	1	yes	characteristic
59	D₄×Dic₁₉	C₂²	1	1	yes	characteristic
60	D₄×Dic₁₉	C₂²	1	1	yes	characteristic
61	D₄×Dic₁₉	C₂²	1	2	yes	complemented
62	D₄×Dic₁₉	C₂²	1	1	yes	characteristic, complemented
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	D₄×Dic₁₉	C₂²	1	1	yes	characteristic, complemented
67	#10597376	C₂²	1	1	yes	characteristic
68	#10597376	C₂²	1	1	yes	characteristic, complemented
69	#10597375	C₂²	1	2	yes	complemented
70	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
71	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic, complemented
72	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	complemented
73	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	2	yes	complemented
74	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	2	yes	complemented
75	#10597372	C₂²	1	1	yes	characteristic, complemented
76	#10597372	C₂²	1	2	yes	complemented
77	#10597372	C₂²	1	1	yes	characteristic, complemented
78	#10597372	C₂²	1	1	yes	characteristic, complemented
79	#10597370	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	2	yes	complemented
83	#10597344	C₂²	1	1	yes	characteristic, complemented
84	#10597344	C₂²	1	2	yes	complemented
85	#10597343	C₂²	1	2	yes	complemented
86	#10597339	C₂²	1	1	yes	characteristic, complemented
87	#10597338	C₂²	1	2	yes	complemented
88	#10597338	C₂²	1	1	yes	characteristic, complemented
89	#10597335	C₂²	1	1	yes	characteristic, complemented
90	#10597334	C₂²	1	1	yes	characteristic, complemented
91	#10597334	C₂²	1	1	yes	characteristic, complemented
92	#10597333	C₂²	1	2	yes	complemented
93	#10597332	C₂²	1	1	yes	characteristic, complemented
94	#10597332	C₂²	1	2	yes	complemented
95	#10597332	C₂²	1	2	yes	complemented
96	#10597331	C₂²	1	1	yes	characteristic
97	#10597331	C₂²	1	2	yes	—
98	#10597331	C₂²	1	2	yes	complemented
99	#10597331	C₂²	1	2	yes	complemented
100	#10597331	C₂²	1	2	yes	complemented
101	#10597331	C₂²	1	2	yes	complemented
102	#10597331	C₂²	1	2	yes	complemented
103	#10597331	C₂²	1	2	yes	complemented
104	#10597331	C₂²	1	2	yes	complemented
105	#10597329	C₂²	1	2	yes	complemented
106	#10597329	C₂²	1	2	yes	complemented
107	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	complemented
108	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	complemented
109	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	complemented
110	C₂²⋊C₄×D₁₉	C₂²	1	2	yes	complemented
111	#10597325	C₂²	1	2	yes	complemented
112	#10597325	C₂²	1	1	yes	characteristic, complemented
113	#10597325	C₂²	1	2	yes	complemented
114	#10597324	C₂²	1	2	yes	complemented
115	#10597324	C₂²	1	1	yes	characteristic, complemented
116	#10597324	C₂²	1	2	yes	complemented
117	#10597324	C₂²	1	2	yes	complemented
118	#10597323	C₂²	1	2	yes	complemented
119	C₄×D₇₆	C₂²	1	1	yes	characteristic, complemented
120	#10597318	C₂²	1	1	yes	characteristic, complemented
121	#10597315	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₃₈	C₂²	1	1	yes	characteristic, complemented
123	C₂⁴×C₁₉	C₂³	1	2	yes	—
124	C₂³×D₁₉	C₂³	1	2	yes	—
125	#41×C₁₉	—	2	4	no	—
126	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
127	C₂×D₄×C₁₉	—	2	4	no	—
128	C₂×D₄×C₁₉	C₂³	1	2	yes	—
129	C₂×D₄×C₁₉	C₂³	1	2	yes	—
130	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
131	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
132	C₂×D₄×C₁₉	C₂³	1	2	yes	—
133	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
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	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₁₉	—	4	4	no	—
139	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
142	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
144	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
145	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
146	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
147	C₂²×Dic₁₉	C₂³	1	2	yes	—
148	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
149	C₂²×Dic₁₉	C₂³	1	2	yes	—
150	C₂²×Dic₁₉	C₂³	1	2	yes	—
151	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
152	C₂²×Dic₁₉	C₂³	1	2	yes	—
153	C₂²×Dic₁₉	C₂³	1	2	yes	—
154	#64543	—	4	4	no	—
155	D₄×D₁₉	—	2	4	no	—
156	C₂×D₇₆	C₂³	1	1	yes	characteristic
157	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
158	C₂×C₄×D₁₉	C₂³	1	2	yes	—
159	C₂×C₄×D₁₉	C₂³	1	2	yes	—
160	C₂×Dic₃₈	—	4	4	no	—
161	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
162	C₂×Dic₃₈	C₂³	1	2	yes	—
163	C₂×Dic₃₈	C₂³	1	2	yes	—
164	C₂×Dic₃₈	C₂³	1	2	yes	—
165	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
166	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
167	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
168	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
169	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
170	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
171	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
172	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
173	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
174	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
175	C₄²×C₁₉	C₂³	1	1	yes	characteristic
176	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
177	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
178	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
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	1	yes	characteristic
183	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
184	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
185	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
186	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
187	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
188	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
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	(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	2	yes	—
197	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
198	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
199	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
200	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
201	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
202	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
203	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
204	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
205	C₄⋊Dic₁₉	C₂³	1	2	yes	—
206	C₄⋊Dic₁₉	C₂³	1	2	yes	—
207	C₄⋊Dic₁₉	C₂³	1	2	yes	—
208	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
209	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
210	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
211	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
212	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
217	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
218	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
219	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
220	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
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	C₄×Dic₁₉	C₂³	1	2	yes	—
226	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
227	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
228	C₂³×C₁₉	—	2	4	no	—
229	C₂³×C₁₉	—	4	2	no	—
230	C₂³×C₁₉	—	4	2	no	—
231	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
232	C₂³×C₁₉	C₂⁴	1	2	yes	—
233	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
234	C₂³×C₁₉	C₂⁴	1	2	yes	—
235	C₂²×D₁₉	—	2	4	no	—
236	C₂²×D₁₉	—	4	2	no	—
237	C₂²×D₁₉	—	4	2	no	—
238	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
239	C₂²×D₁₉	C₂⁴	1	2	yes	—
240	Q₈×C₁₉	—	2	2	no	—
241	D₄×C₁₉	—	2	4	no	—
242	D₄×C₁₉	—	2	4	no	—
243	D₄×C₁₉	—	2	2	no	—
244	D₄×C₁₉	—	4	2	no	—
245	D₄×C₁₉	—	4	1	no	—
246	D₄×C₁₉	#41	1	4	yes	complemented
247	C₂×C₄×C₁₉	—	2	4	no	—
248	C₂×C₄×C₁₉	—	2	2	no	—
249	C₂×C₄×C₁₉	—	2	2	no	—
250	C₂×C₄×C₁₉	—	4	2	no	—
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	2	yes	—
255	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
256	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
257	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
258	C₂²⋊D₁₉	—	2	4	no	—
259	C₂²⋊D₁₉	—	2	4	no	—
260	C₂²⋊D₁₉	—	2	2	no	—
261	C₂²⋊D₁₉	—	4	2	no	—
262	C₂²⋊D₁₉	—	4	2	no	—
263	C₂²⋊D₁₉	—	4	2	no	—
264	C₂²⋊D₁₉	—	4	1	no	—
265	C₂²⋊D₁₉	—	4	2	no	—
266	C₂×Dic₁₉	—	2	4	no	—
267	C₂×Dic₁₉	—	2	2	no	—
268	C₂×Dic₁₉	—	4	2	no	—
269	C₂×Dic₁₉	—	4	2	no	—
270	C₂×Dic₁₉	—	4	2	no	—
271	C₂×Dic₁₉	—	4	2	no	—
272	C₂×Dic₁₉	—	4	1	no	—
273	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
274	C₂×Dic₁₉	C₂⁴	1	2	yes	—
275	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
276	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
277	C₂×Dic₁₉	C₂⁴	1	2	yes	—
278	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
279	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
280	C₂×Dic₁₉	C₂⁴	1	2	yes	—
281	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
282	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
283	D₇₆	—	2	2	no	—
284	C₄×D₁₉	—	2	2	no	—
285	C₄×D₁₉	—	4	2	no	—
286	C₄×D₁₉	—	4	2	no	—
287	Dic₃₈	—	2	2	no	—
288	Dic₃₈	—	2	4	no	—
289	Dic₃₈	—	4	2	no	—
290	Dic₃₈	—	4	2	no	—
291	#3514	—	19	1	no	maximal, Sylow
292	C₂²×C₁₉	—	2	2	no	—
293	C₂²×C₁₉	—	2	2	no	—
294	C₂²×C₁₉	—	2	1	no	—
295	C₂²×C₁₉	—	2	1	no	—
296	C₂²×C₁₉	—	2	2	no	—
297	C₂²×C₁₉	—	2	1	no	—
298	C₂²×C₁₉	—	2	2	no	—
299	C₂²×C₁₉	—	2	1	no	—
300	C₂²×C₁₉	—	2	1	no	—
301	C₂²×C₁₉	—	2	2	no	—
302	C₂²×C₁₉	—	2	1	no	—
303	C₂²×C₁₉	—	8	4	no	—
304	C₂²×C₁₉	C₂×#41	1	4	yes	—
305	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
306	C₂×D₁₉	—	2	1	no	—
307	C₂×D₁₉	—	2	2	no	—
308	C₂×D₁₉	—	2	2	no	—
309	C₂×D₁₉	—	2	1	no	—
310	C₂×D₁₉	—	2	2	no	—
311	C₂×D₁₉	—	2	1	no	—
312	C₂×D₁₉	—	8	4	no	—
313	C₄×C₁₉	—	2	1	no	—
314	C₄×C₁₉	—	2	1	no	—
315	C₄×C₁₉	—	2	2	no	—
316	C₄×C₁₉	—	2	1	no	—
317	C₄×C₁₉	—	2	2	no	—
318	C₄×C₁₉	—	2	1	no	—
319	C₄×C₁₉	C₂×#41	1	2	yes	—
320	Dic₁₉	—	2	1	no	—
321	Dic₁₉	—	2	1	no	—
322	Dic₁₉	—	2	2	no	—
323	Dic₁₉	—	2	2	no	—
324	Dic₁₉	—	2	1	no	—
325	Dic₁₉	—	2	2	no	—
326	Dic₁₉	—	2	1	no	—
327	Dic₁₉	—	2	1	no	—
328	Dic₁₉	—	2	1	no	—
329	Dic₁₉	H(5,𝔽₂)	1	2	yes	—
330	#559	—	19	1	no	—
331	#556	—	19	1	no	—
332	#555	—	19	1	no	—
333	#555	—	19	1	no	—
334	#551	—	19	2	no	—
335	#551	—	19	2	no	—
336	D₄×Q₈	—	19	1	no	—
337	#548	—	19	2	no	—
338	#546	—	19	1	no	—
339	#546	—	19	2	no	—
340	#546	D₁₉	1	1	yes	characteristic, complemented
341	D₄²	—	19	1	no	—
342	#542	—	19	1	no	—
343	#542	—	19	1	no	—
344	#538	—	19	2	no	—
345	#538	—	19	2	no	—
346	#532	—	19	1	no	—
347	#529	—	19	2	no	—
348	#529	—	19	1	no	—
349	C₂×#124	—	19	2	no	—
350	#518	—	19	1	no	—
351	#518	—	19	1	no	—
352	C₄×#41	—	19	1	no	—
353	C₂×C₁₉	—	2	4	no	—
354	C₂×C₁₉	—	4	1	no	—
355	C₂×C₁₉	—	4	2	no	—
356	C₂×C₁₉	—	4	1	no	—
357	C₂×C₁₉	C₂²×#41	1	1	yes	characteristic
358	C₂×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
359	C₂×C₁₉	#585	1	1	yes	characteristic
360	D₁₉	—	4	2	no	—
361	D₁₉	—	4	1	no	—
362	C₂×#41	—	19	2	no	—
363	C₂×#41	C₂×D₁₉	1	1	yes	characteristic
364	C₂²×Q₈	—	19	2	no	—
365	C₂²×D₄	—	19	2	no	—
366	C₂²×D₄	—	19	1	no	—
367	C₂²×D₄	C₂×D₁₉	1	1	yes	characteristic
368	C₄⋊Q₈	—	19	1	no	—
369	C₄⋊Q₈	—	19	1	no	—
370	C₄⋊Q₈	—	19	1	no	—
371	#127	—	19	1	no	—
372	#126	—	19	2	no	—
373	#126	—	19	1	no	—
374	#126	—	19	2	no	—
375	#126	—	19	2	no	—
376	#126	—	19	1	no	—
377	#126	—	19	2	no	—
378	#125	—	19	1	no	—
379	#124	—	19	1	no	—
380	#124	—	19	2	no	—
381	#124	—	19	1	no	—
382	#124	—	19	2	no	—
383	#124	—	19	2	no	—
384	#124	—	19	2	no	—
385	#124	—	19	2	no	—
386	#124	—	19	2	no	—
387	#124	—	19	2	no	—
388	#124	—	19	2	no	—
389	#124	—	19	2	no	—
390	#124	C₂×D₁₉	1	1	yes	characteristic, complemented
391	#123	—	19	1	no	—
392	#123	—	19	2	no	—
393	#123	—	19	1	no	—
394	#123	—	19	2	no	—
395	#123	—	19	2	no	—
396	#123	—	19	2	no	—
397	#123	—	19	2	no	—
398	#123	C₂×D₁₉	1	2	yes	complemented
399	C₂²⋊Q₈	—	19	1	no	—
400	C₂²⋊Q₈	—	19	2	no	—
401	C₂²⋊Q₈	—	19	2	no	—
402	C₂²⋊Q₈	—	19	2	no	—
403	C₂²⋊Q₈	—	19	1	no	—
404	C₂²⋊Q₈	—	19	2	no	—
405	C₂²⋊Q₈	—	19	2	no	—
406	C₂²⋊Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
407	#121	—	19	1	no	—
408	#121	—	19	2	no	—
409	#121	—	19	2	no	—
410	#121	—	19	1	no	—
411	#121	—	19	2	no	—
412	#121	—	19	2	no	—
413	#121	—	19	2	no	—
414	#121	—	19	1	no	—
415	#121	—	19	1	no	—
416	#121	C₂×D₁₉	1	1	yes	characteristic, complemented
417	#121	C₂×D₁₉	1	2	yes	complemented
418	#120	—	19	2	no	—
419	#120	—	19	2	no	—
420	#120	—	19	2	no	—
421	#120	C₂×D₁₉	1	2	yes	complemented
422	C₄×Q₈	—	19	1	no	—
423	C₄×Q₈	—	19	1	no	—
424	C₄×Q₈	—	19	2	no	—
425	C₄×Q₈	—	19	1	no	—
426	C₄×D₄	—	19	1	no	—
427	C₄×D₄	—	19	1	no	—
428	C₄×D₄	—	19	1	no	—
429	C₄×D₄	—	19	2	no	—
430	C₄×D₄	—	19	2	no	—
431	C₄×D₄	—	19	2	no	—
432	C₄×D₄	—	19	1	no	—
433	C₄×D₄	—	19	2	no	—
434	C₄×D₄	—	19	1	no	—
435	C₄×D₄	—	19	2	no	—
436	C₄×D₄	—	19	1	no	—
437	C₄×D₄	—	19	1	no	—
438	C₄×D₄	—	19	1	no	—
439	C₄×D₄	—	19	2	no	—
440	C₄×D₄	—	19	2	no	—
441	C₄×D₄	—	19	2	no	—
442	C₄×D₄	—	19	1	no	—
443	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
444	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic, complemented
445	#117	—	19	2	no	—
446	#117	—	19	1	no	—
447	#117	—	19	1	no	—
448	#117	—	19	1	no	—
449	#117	—	19	1	no	—
450	#117	—	19	2	no	—
451	#117	—	19	2	no	—
452	#117	—	19	1	no	—
453	C₂×C₂²⋊C₄	—	19	2	no	—
454	C₂×C₂²⋊C₄	—	19	2	no	—
455	C₂×C₂²⋊C₄	—	19	2	no	—
456	C₂×C₂²⋊C₄	—	19	2	no	—
457	C₂×C₂²⋊C₄	—	19	2	no	—
458	C₂×C₂²⋊C₄	C₂×D₁₉	1	2	yes	complemented
459	C₂×C₄²	—	19	2	no	—
460	C₂×C₄²	—	19	1	no	—
461	C₁₉	#3514	1	1	yes	characteristic, complemented, Sylow
462	C₂⁴	—	19	2	no	—
463	C₂⁴	C₂²×D₁₉	1	2	yes	—
464	#41	—	2	4	no	—
465	#41	—	76	4	no	—
466	C₂×Q₈	—	19	1	no	—
467	C₂×Q₈	—	19	2	no	—
468	C₂×Q₈	—	19	2	no	—
469	C₂×Q₈	—	19	2	no	—
470	C₂×Q₈	—	76	4	no	—
471	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
472	C₂×D₄	—	2	4	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	2	no	—
478	C₂×D₄	—	19	2	no	—
479	C₂×D₄	—	19	2	no	—
480	C₂×D₄	—	19	2	no	—
481	C₂×D₄	—	19	1	no	—
482	C₂×D₄	—	38	4	no	—
483	C₂×D₄	—	76	4	no	—
484	C₂×D₄	C₂²×D₁₉	1	2	yes	—
485	C₂×D₄	C₂²×D₁₉	1	2	yes	—
486	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
487	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
488	C₂×D₄	C₂²×D₁₉	1	2	yes	—
489	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
490	C₂²×C₄	—	19	2	no	—
491	C₂²×C₄	—	19	1	no	—
492	C₂²×C₄	—	19	2	no	—
493	C₂²×C₄	—	19	1	no	—
494	C₂²×C₄	—	19	2	no	—
495	C₂²×C₄	—	19	2	no	—
496	C₂²×C₄	—	19	2	no	—
497	C₂²×C₄	—	19	1	no	—
498	C₂²×C₄	—	19	2	no	—
499	C₂²×C₄	—	19	2	no	—
500	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
501	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
502	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
503	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
504	C₄⋊C₄	—	19	1	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	2	no	—
511	C₄⋊C₄	—	19	2	no	—
512	C₄⋊C₄	—	19	1	no	—
513	C₄⋊C₄	—	19	1	no	—
514	C₄⋊C₄	—	19	1	no	—
515	C₄⋊C₄	—	19	1	no	—
516	C₄⋊C₄	—	19	1	no	—
517	C₄⋊C₄	—	19	1	no	—
518	C₄⋊C₄	—	19	2	no	—
519	C₄⋊C₄	—	19	2	no	—
520	C₄⋊C₄	—	19	2	no	—
521	C₄⋊C₄	—	19	1	no	—
522	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
523	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
524	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
525	C₂²⋊C₄	—	19	2	no	—
526	C₂²⋊C₄	—	19	1	no	—
527	C₂²⋊C₄	—	19	2	no	—
528	C₂²⋊C₄	—	19	1	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	2	no	—
539	C₂²⋊C₄	—	19	1	no	—
540	C₂²⋊C₄	—	19	1	no	—
541	C₂²⋊C₄	—	19	2	no	—
542	C₂²⋊C₄	—	19	2	no	—
543	C₂²⋊C₄	—	19	2	no	—
544	C₂²⋊C₄	—	19	2	no	—
545	C₂²⋊C₄	—	19	2	no	—
546	C₂²⋊C₄	—	19	2	no	—
547	C₂²⋊C₄	—	19	1	no	—
548	C₂²⋊C₄	—	19	2	no	—
549	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
550	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
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	2	yes	—
555	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
556	C₄²	—	19	1	no	—
557	C₄²	—	19	2	no	—
558	C₄²	—	19	1	no	—
559	C₄²	—	19	1	no	—
560	C₄²	—	19	2	no	—
561	C₄²	—	19	1	no	—
562	C₄²	—	19	2	no	—
563	C₄²	—	19	2	no	—
564	C₄²	—	19	2	no	—
565	C₄²	—	19	1	no	—
566	C₄²	C₂²×D₁₉	1	1	yes	characteristic
567	C₂³	—	2	4	no	—
568	C₂³	—	4	2	no	—
569	C₂³	—	4	2	no	—
570	C₂³	—	19	1	no	—
571	C₂³	—	19	2	no	—
572	C₂³	—	38	4	no	—
573	C₂³	—	76	2	no	—
574	C₂³	—	76	2	no	—
575	C₂³	C₂³×D₁₉	1	1	yes	characteristic
576	C₂³	C₂³×D₁₉	1	2	yes	—
577	C₂³	C₂³×D₁₉	1	1	yes	characteristic
578	C₂³	C₂³×D₁₉	1	2	yes	—
579	Q₈	—	2	2	no	—
580	Q₈	—	38	2	no	—
581	Q₈	—	38	4	no	—
582	Q₈	—	76	2	no	—
583	Q₈	—	76	2	no	—
584	D₄	—	2	4	no	—
585	D₄	—	2	4	no	—
586	D₄	—	2	2	no	—
587	D₄	—	4	2	no	—
588	D₄	—	4	1	no	—
589	D₄	—	38	2	no	—
590	D₄	—	38	4	no	—
591	D₄	—	38	4	no	—
592	D₄	—	38	2	no	—
593	D₄	—	76	2	no	—
594	D₄	—	76	2	no	—
595	D₄	—	76	2	no	—
596	D₄	—	76	1	no	—
597	D₄	—	76	2	no	—
598	D₄	#64543	1	4	yes	complemented
599	C₂×C₄	—	2	4	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	4	2	no	—
603	C₂×C₄	—	19	1	no	—
604	C₂×C₄	—	19	1	no	—
605	C₂×C₄	—	19	2	no	—
606	C₂×C₄	—	19	1	no	—
607	C₂×C₄	—	19	1	no	—
608	C₂×C₄	—	19	1	no	—
609	C₂×C₄	—	19	2	no	—
610	C₂×C₄	—	19	1	no	—
611	C₂×C₄	—	19	1	no	—
612	C₂×C₄	—	19	2	no	—
613	C₂×C₄	—	38	4	no	—
614	C₂×C₄	—	38	2	no	—
615	C₂×C₄	—	38	2	no	—
616	C₂×C₄	—	76	2	no	—
617	C₂×C₄	—	76	2	no	—
618	C₂×C₄	—	76	2	no	—
619	C₂×C₄	—	76	2	no	—
620	C₂×C₄	—	76	2	no	—
621	C₂×C₄	—	76	2	no	—
622	C₂×C₄	—	76	1	no	—
623	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
624	C₂×C₄	C₂³×D₁₉	1	2	yes	—
625	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
626	C₂×C₄	C₂³×D₁₉	1	2	yes	—
627	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
628	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
629	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
630	C₂²	—	2	2	no	—
631	C₂²	—	2	2	no	—
632	C₂²	—	2	1	no	—
633	C₂²	—	2	1	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	2	1	no	—
636	C₂²	—	2	2	no	—
637	C₂²	—	2	1	no	—
638	C₂²	—	2	1	no	—
639	C₂²	—	2	2	no	—
640	C₂²	—	2	1	no	—
641	C₂²	—	8	4	no	—
642	C₂²	—	38	1	no	—
643	C₂²	—	38	2	no	—
644	C₂²	—	38	2	no	—
645	C₂²	—	38	1	no	—
646	C₂²	—	38	2	no	—
647	C₂²	—	38	1	no	—
648	C₂²	—	152	4	no	—
649	C₂²	C₂×#64543	1	4	yes	—
650	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
651	C₄	—	2	1	no	—
652	C₄	—	2	1	no	—
653	C₄	—	2	2	no	—
654	C₄	—	2	1	no	—
655	C₄	—	2	2	no	—
656	C₄	—	2	1	no	—
657	C₄	—	19	2	no	—
658	C₄	—	38	1	no	—
659	C₄	—	38	1	no	—
660	C₄	—	38	2	no	—
661	C₄	—	38	2	no	—
662	C₄	—	38	1	no	—
663	C₄	—	38	2	no	—
664	C₄	—	38	1	no	—
665	C₄	—	38	1	no	—
666	C₄	—	38	1	no	—
667	C₄	C₂×#64543	1	2	yes	—
668	C₂	—	2	4	no	—
669	C₂	—	4	1	no	—
670	C₂	—	4	2	no	—
671	C₂	—	4	1	no	—
672	C₂	—	76	1	no	—
673	C₂	—	76	2	no	—
674	C₂	C₂²×#64543	1	1	yes	characteristic
675	C₂	H(5,𝔽₂)×D₁₉	1	1	yes	characteristic
676	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	#3514
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. #11927276	C₂	semidirect
2. #11927265	C₂	semidirect
3. #11927259	C₂	semidirect
4. #11927258	C₂	semidirect
5. #11927220	C₂	semidirect
6. #11927217	C₂	semidirect
7. D₄×Dic₃₈	C₂	semidirect
8. #11927200	C₂	semidirect
9. #11927182	C₂	semidirect
10. #11927181	C₂	semidirect
11. D₄×C₂²⋊D₁₉	C₂	semidirect
12. #11927167	C₂	semidirect
13. #11927163	C₂	semidirect
14. #11927131	C₂	semidirect
15. #11927129	C₂	semidirect
16. #11927089	C₂	semidirect
17. #11927074	C₂	semidirect
18. #11927071	C₂	semidirect
19. C₂×#10597331	C₂	semidirect
20. #11927019	C₂	semidirect
21. #11927016	C₂	semidirect
22. #41×Dic₁₉	C₂	semidirect
23. C₁₉×#546	C₂	semidirect
27. C₂×#64543	C₂²	semidirect
29. C₂²×Dic₃₈	C₂²	semidirect
30. C₁₉×#124	C₂²	semidirect
31. C₁₉×#123	C₂²	semidirect
32. C₁₉×C₂²⋊Q₈	C₂²	semidirect
33. C₁₉×#121	C₂²	semidirect
34. C₁₉×#121	C₂²	semidirect
35. C₁₉×#120	C₂²	semidirect
37. C₄×D₄×C₁₉	C₂²	semidirect
38. C₂×C₂²⋊C₄×C₁₉	C₂²	semidirect
40. C₂×C₂²⋊Dic₁₉	C₂²	semidirect
41. C₂×C₂²⋊Dic₁₉	C₂²	semidirect
42. #10597393	C₂²	semidirect
43. #10597392	C₂²	semidirect
44. Q₈×Dic₁₉	C₂²	semidirect
45. Q₈×Dic₁₉	C₂²	semidirect
49. #10597385	C₂²	semidirect
50. #10597385	C₂²	semidirect
51. #10597385	C₂²	semidirect
53. #10597384	C₂²	semidirect
55. #10597383	C₂²	semidirect
56. #10597382	C₂²	semidirect
57. #10597381	C₂²	semidirect
61. D₄×Dic₁₉	C₂²	semidirect
62. D₄×Dic₁₉	C₂²	semidirect
63. D₄×Dic₁₉	C₂²	semidirect
64. D₄×Dic₁₉	C₂²	semidirect
65. D₄×Dic₁₉	C₂²	semidirect
66. D₄×Dic₁₉	C₂²	semidirect
68. #10597376	C₂²	semidirect
69. #10597375	C₂²	semidirect
71. C₄×C₂²⋊D₁₉	C₂²	semidirect
72. C₄×C₂²⋊D₁₉	C₂²	semidirect
73. C₂×(C₂×D₁₉)⋊C₄	C₂²	semidirect
74. C₂×(C₂×D₁₉)⋊C₄	C₂²	semidirect
75. #10597372	C₂²	semidirect
76. #10597372	C₂²	semidirect
77. #10597372	C₂²	semidirect
78. #10597372	C₂²	semidirect
79. #10597370	C₂²	semidirect
80. C₂×C₄×Dic₁₉	C₂²	semidirect
81. C₂×C₄×Dic₁₉	C₂²	semidirect
82. #10597344	C₂²	semidirect
83. #10597344	C₂²	semidirect
84. #10597344	C₂²	semidirect
85. #10597343	C₂²	semidirect
86. #10597339	C₂²	semidirect
87. #10597338	C₂²	semidirect
88. #10597338	C₂²	semidirect
89. #10597335	C₂²	semidirect
90. #10597334	C₂²	semidirect
91. #10597334	C₂²	semidirect
92. #10597333	C₂²	semidirect
93. #10597332	C₂²	semidirect
94. #10597332	C₂²	semidirect
95. #10597332	C₂²	semidirect
98. #10597331	C₂²	semidirect
99. #10597331	C₂²	semidirect
100. #10597331	C₂²	semidirect
101. #10597331	C₂²	semidirect
102. #10597331	C₂²	semidirect
103. #10597331	C₂²	semidirect
104. #10597331	C₂²	semidirect
105. #10597329	C₂²	semidirect
106. #10597329	C₂²	semidirect
107. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
108. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
109. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
110. C₂²⋊C₄×D₁₉	C₂²	semidirect
111. #10597325	C₂²	semidirect
112. #10597325	C₂²	semidirect
113. #10597325	C₂²	semidirect
114. #10597324	C₂²	semidirect
115. #10597324	C₂²	semidirect
116. #10597324	C₂²	semidirect
117. #10597324	C₂²	semidirect
118. #10597323	C₂²	semidirect
119. C₄×D₇₆	C₂²	semidirect
120. #10597318	C₂²	semidirect
121. #10597315	C₂²	semidirect
122. C₄×Dic₃₈	C₂²	semidirect
246. D₄×C₁₉	#41	semidirect
340. #546	D₁₉	semidirect
390. #124	C₂×D₁₉	semidirect
398. #123	C₂×D₁₉	semidirect
406. C₂²⋊Q₈	C₂×D₁₉	semidirect
416. #121	C₂×D₁₉	semidirect
417. #121	C₂×D₁₉	semidirect
421. #120	C₂×D₁₉	semidirect
444. C₄×D₄	C₂×D₁₉	semidirect
458. C₂×C₂²⋊C₄	C₂×D₁₉	semidirect
461. C₁₉	#3514	semidirect
598. D₄	#64543	semidirect

Maximal subgroups

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

subgroup	index
#11927276	2
#11927265	2
#11927259	2
#11927258	2
#11927220	2
#11927217	2
D₄×Dic₃₈	2
#11927200	2
#11927182	2
#11927181	2
D₄×C₂²⋊D₁₉	2
#11927167	2
#11927163	2
#11927131	2
#11927129	2
#11927089	2
#11927074	2
#11927071	2
C₂×#10597331	2
#11927019	2
#11927016	2
#41×Dic₁₉	2
C₁₉×#546	2
#3514	19