Subgroups — #14577560

Order 2432.

1152 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	#11927280	C₂	1	1	yes	maximal, characteristic, complemented
2	#11927253	C₂	1	1	yes	maximal, characteristic, complemented
3	#11927241	C₂	1	1	yes	maximal, characteristic, complemented
4	#11927237	C₂	1	2	yes	maximal, complemented
5	#11927234	C₂	1	1	yes	maximal, characteristic, complemented
6	#11927225	C₂	1	2	yes	maximal, complemented
7	#11927225	C₂	1	2	yes	maximal, complemented
8	#11927194	C₂	1	1	yes	maximal, characteristic, complemented
9	#11927188	C₂	1	1	yes	maximal, characteristic, complemented
10	#11927188	C₂	1	1	yes	maximal, characteristic, complemented
11	#11927188	C₂	1	2	yes	maximal, complemented
12	#11927161	C₂	1	1	yes	maximal, characteristic, complemented
13	#11927148	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	#11927050	C₂	1	2	yes	maximal, complemented
19	C₂×#10597381	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	C₂×D₄×Dic₁₉	C₂	1	1	yes	maximal, characteristic, complemented
23	D₄²×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×D₄×C₁₉	C₂²	1	1	yes	characteristic
25	C₂²×D₄×C₁₉	C₂²	1	1	yes	characteristic
26	C₂²×D₄×C₁₉	C₂²	1	2	yes	—
27	C₂³×Dic₁₉	C₂²	1	2	yes	complemented
28	C₂×#64543	C₂²	1	1	yes	characteristic
29	C₂×#64543	C₂²	1	2	yes	complemented
30	C₁₉×#127	C₂²	1	1	yes	characteristic
31	C₁₉×#121	C₂²	1	1	yes	characteristic
32	C₁₉×#121	C₂²	1	2	yes	—
33	C₁₉×#121	C₂²	1	1	yes	characteristic
34	C₁₉×#120	C₂²	1	2	yes	—
35	C₁₉×#120	C₂²	1	2	yes	—
36	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
37	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
38	#10597399	C₂²	1	2	yes	complemented
39	#10597399	C₂²	1	2	yes	complemented
40	C₂×C₂²⋊Dic₁₉	C₂²	1	2	yes	complemented
41	C₂×C₂²⋊Dic₁₉	C₂²	1	2	yes	complemented
42	C₂×C₂²⋊Dic₁₉	C₂²	1	2	yes	complemented
43	C₂×C₂²⋊Dic₁₉	C₂²	1	2	yes	complemented
44	C₂×C₂²⋊Dic₁₉	C₂²	1	2	yes	complemented
45	#10597385	C₂²	1	1	yes	characteristic
46	#10597385	C₂²	1	2	yes	complemented
47	#10597385	C₂²	1	2	yes	complemented
48	#10597385	C₂²	1	2	yes	complemented
49	#10597385	C₂²	1	2	yes	complemented
50	#10597384	C₂²	1	2	yes	complemented
51	#10597384	C₂²	1	1	yes	characteristic, complemented
52	#10597384	C₂²	1	1	yes	characteristic, complemented
53	#10597382	C₂²	1	1	yes	characteristic, complemented
54	#10597382	C₂²	1	2	yes	complemented
55	#10597382	C₂²	1	2	yes	complemented
56	#10597382	C₂²	1	1	yes	characteristic, complemented
57	#10597381	C₂²	1	1	yes	characteristic
58	#10597381	C₂²	1	2	yes	—
59	#10597381	C₂²	1	2	yes	complemented
60	#10597381	C₂²	1	2	yes	complemented
61	#10597381	C₂²	1	2	yes	complemented
62	#10597381	C₂²	1	2	yes	complemented
63	#10597381	C₂²	1	2	yes	complemented
64	#10597381	C₂²	1	2	yes	complemented
65	#10597381	C₂²	1	2	yes	complemented
66	#10597381	C₂²	1	2	yes	complemented
67	#10597381	C₂²	1	2	yes	complemented
68	#10597381	C₂²	1	2	yes	complemented
69	D₄×Dic₁₉	C₂²	1	1	yes	characteristic
70	D₄×Dic₁₉	C₂²	1	1	yes	characteristic
71	D₄×Dic₁₉	C₂²	1	1	yes	characteristic
72	D₄×Dic₁₉	C₂²	1	2	yes	complemented
73	D₄×Dic₁₉	C₂²	1	2	yes	complemented
74	D₄×Dic₁₉	C₂²	1	1	yes	characteristic, complemented
75	D₄×Dic₁₉	C₂²	1	2	yes	complemented
76	D₄×Dic₁₉	C₂²	1	2	yes	complemented
77	D₄×Dic₁₉	C₂²	1	1	yes	characteristic, complemented
78	D₄×Dic₁₉	C₂²	1	1	yes	characteristic, complemented
79	D₄×Dic₁₉	C₂²	1	2	yes	complemented
80	D₄×Dic₁₉	C₂²	1	2	yes	complemented
81	D₄×Dic₁₉	C₂²	1	1	yes	characteristic, complemented
82	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic, complemented
83	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic, complemented
84	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	complemented
85	#10597372	C₂²	1	1	yes	characteristic, complemented
86	#10597372	C₂²	1	1	yes	characteristic, complemented
87	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic, complemented
88	#10597370	C₂²	1	1	yes	characteristic, complemented
89	#10597370	C₂²	1	2	yes	complemented
90	#10597370	C₂²	1	1	yes	characteristic, complemented
91	C₂×Dic₁₉⋊C₄	C₂²	1	2	yes	complemented
92	C₂×Dic₁₉⋊C₄	C₂²	1	2	yes	complemented
93	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic, complemented
94	#10597344	C₂²	1	1	yes	characteristic, complemented
95	C₄⋊C₄×D₁₉	C₂²	1	1	yes	characteristic, complemented
96	#10597336	C₂²	1	1	yes	characteristic, complemented
97	#10597335	C₂²	1	1	yes	characteristic, complemented
98	#10597335	C₂²	1	2	yes	complemented
99	#10597334	C₂²	1	1	yes	characteristic, complemented
100	#10597333	C₂²	1	1	yes	characteristic, complemented
101	#10597332	C₂²	1	1	yes	characteristic, complemented
102	#10597331	C₂²	1	1	yes	characteristic, complemented
103	#10597329	C₂²	1	2	yes	complemented
104	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	complemented
105	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	complemented
106	#10597325	C₂²	1	1	yes	characteristic, 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	2	yes	complemented
113	#10597324	C₂²	1	1	yes	characteristic, 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	#10597316	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	C₂⁴×C₁₉	C₂³	1	2	yes	—
125	C₂×D₄×C₁₉	—	2	4	no	—
126	C₂×D₄×C₁₉	—	2	4	no	—
127	C₂×D₄×C₁₉	—	4	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	C₂×D₄×C₁₉	C₂³	1	2	yes	—
135	C₂×D₄×C₁₉	C₂³	1	2	yes	—
136	C₂×D₄×C₁₉	C₂³	1	2	yes	—
137	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
138	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
139	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
140	C₂²×C₄×C₁₉	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	1	yes	characteristic
144	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
145	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
146	C₂²×Dic₁₉	—	4	4	no	—
147	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
148	C₂²×Dic₁₉	C₂³	1	2	yes	—
149	C₂²×Dic₁₉	C₂³	1	2	yes	—
150	C₂²×Dic₁₉	C₂³	1	2	yes	—
151	C₂²×Dic₁₉	C₂³	1	2	yes	—
152	C₂²×Dic₁₉	C₂³	1	2	yes	—
153	C₂²×Dic₁₉	C₂³	1	2	yes	—
154	C₂²×Dic₁₉	C₂³	1	2	yes	—
155	C₂²×Dic₁₉	C₂³	1	2	yes	—
156	C₂²×Dic₁₉	C₂³	1	2	yes	—
157	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
158	#64543	—	2	4	no	—
159	#64543	—	4	4	no	—
160	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
161	C₂×C₄×D₁₉	C₂³	1	2	yes	—
162	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
172	C₄²×C₁₉	C₂³	1	1	yes	characteristic
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	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	2	yes	—
183	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
184	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
185	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
186	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
187	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
188	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
189	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
190	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
191	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
192	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
193	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
194	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
195	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
196	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
197	C₄⋊Dic₁₉	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	1	yes	characteristic
202	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
203	C₄⋊Dic₁₉	C₂³	1	2	yes	—
204	C₄⋊Dic₁₉	C₂³	1	2	yes	—
205	Dic₁₉⋊C₄	C₂³	1	2	yes	—
206	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
207	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
208	Dic₁₉⋊C₄	C₂³	1	2	yes	—
209	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
210	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
211	Dic₁₉⋊C₄	C₂³	1	2	yes	—
212	Dic₁₉⋊C₄	C₂³	1	2	yes	—
213	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
214	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
220	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
221	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
222	C₄×Dic₁₉	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	1	yes	characteristic
226	C₄×Dic₁₉	C₂³	1	2	yes	—
227	C₄×Dic₁₉	C₂³	1	2	yes	—
228	C₂³×C₁₉	—	2	4	no	—
229	C₂³×C₁₉	—	2	4	no	—
230	C₂³×C₁₉	—	2	4	no	—
231	C₂³×C₁₉	—	4	2	no	—
232	C₂³×C₁₉	—	4	2	no	—
233	C₂³×C₁₉	—	4	2	no	—
234	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
235	C₂³×C₁₉	C₂⁴	1	2	yes	—
236	C₂³×C₁₉	C₂⁴	1	2	yes	—
237	C₂³×C₁₉	C₂⁴	1	2	yes	—
238	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
239	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
240	D₄×C₁₉	—	2	4	no	—
241	D₄×C₁₉	—	2	4	no	—
242	D₄×C₁₉	—	2	4	no	—
243	D₄×C₁₉	—	2	2	no	—
244	D₄×C₁₉	—	2	2	no	—
245	D₄×C₁₉	—	2	2	no	—
246	D₄×C₁₉	—	4	2	no	—
247	D₄×C₁₉	—	4	2	no	—
248	D₄×C₁₉	—	4	2	no	—
249	D₄×C₁₉	#41	1	4	yes	complemented
250	C₂×C₄×C₁₉	—	2	2	no	—
251	C₂×C₄×C₁₉	—	2	2	no	—
252	C₂×C₄×C₁₉	—	4	2	no	—
253	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
254	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
255	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
256	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
257	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
258	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
259	C₂²⋊D₁₉	—	2	4	no	—
260	C₂²⋊D₁₉	—	2	2	no	—
261	C₂²⋊D₁₉	—	4	2	no	—
262	C₂²⋊D₁₉	—	4	1	no	—
263	C₂²⋊D₁₉	—	4	2	no	—
264	C₂×Dic₁₉	—	2	4	no	—
265	C₂×Dic₁₉	—	2	4	no	—
266	C₂×Dic₁₉	—	2	2	no	—
267	C₂×Dic₁₉	—	4	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	2	no	—
273	C₂×Dic₁₉	—	4	1	no	—
274	C₂×Dic₁₉	—	4	2	no	—
275	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
276	C₂×Dic₁₉	C₂⁴	1	2	yes	—
277	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
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	2	yes	—
282	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
283	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
284	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
285	C₂×Dic₁₉	C₂⁴	1	2	yes	—
286	C₄×D₁₉	—	2	2	no	—
287	C₄×D₁₉	—	4	2	no	—
288	Dic₃₈	—	2	2	no	—
289	Dic₃₈	—	4	1	no	—
290	Dic₃₈	—	4	2	no	—
291	#3513	—	19	1	no	maximal, Sylow
292	C₂²×C₁₉	—	2	1	no	—
293	C₂²×C₁₉	—	2	2	no	—
294	C₂²×C₁₉	—	2	1	no	—
295	C₂²×C₁₉	—	2	2	no	—
296	C₂²×C₁₉	—	2	1	no	—
297	C₂²×C₁₉	—	2	2	no	—
298	C₂²×C₁₉	—	2	2	no	—
299	C₂²×C₁₉	—	2	2	no	—
300	C₂²×C₁₉	—	2	2	no	—
301	C₂²×C₁₉	—	2	1	no	—
302	C₂²×C₁₉	—	2	2	no	—
303	C₂²×C₁₉	—	2	2	no	—
304	C₂²×C₁₉	—	2	1	no	—
305	C₂²×C₁₉	—	4	8	no	—
306	C₂²×C₁₉	—	8	4	no	—
307	C₂²×C₁₉	C₂×#41	1	4	yes	—
308	C₂²×C₁₉	H(5,𝔽₂)	1	2	yes	—
309	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
310	C₂×D₁₉	—	2	1	no	—
311	C₂×D₁₉	—	2	1	no	—
312	C₂×D₁₉	—	2	1	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	1	no	—
318	C₄×C₁₉	C₂×#41	1	2	yes	—
319	Dic₁₉	—	2	2	no	—
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	1	no	—
326	Dic₁₉	—	2	1	no	—
327	Dic₁₉	—	2	1	no	—
328	Dic₁₉	—	2	1	no	—
329	Dic₁₉	—	2	2	no	—
330	#559	—	19	1	no	—
331	#554	—	19	1	no	—
332	#553	—	19	2	no	—
333	#553	—	19	1	no	—
334	#552	—	19	1	no	—
335	#551	—	19	2	no	—
336	#551	—	19	2	no	—
337	#547	—	19	1	no	—
338	#546	—	19	2	no	—
339	#546	—	19	1	no	—
340	#546	—	19	1	no	—
341	D₄²	D₁₉	1	1	yes	characteristic, complemented
342	#542	—	19	1	no	—
343	#540	—	19	1	no	—
344	#539	—	19	2	no	—
345	#538	—	19	2	no	—
346	#529	—	19	1	no	—
347	#529	—	19	1	no	—
348	#525	—	19	2	no	—
349	C₂×#123	—	19	2	no	—
350	#520	—	19	1	no	—
351	#518	—	19	1	no	—
352	C₂×C₄×D₄	—	19	1	no	—
353	C₂×C₁₉	—	2	2	no	—
354	C₂×C₁₉	—	2	4	no	—
355	C₂×C₁₉	—	4	2	no	—
356	C₂×C₁₉	—	4	2	no	—
357	C₂×C₁₉	—	4	1	no	—
358	C₂×C₁₉	C₂²×#41	1	1	yes	characteristic
359	C₂×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
360	C₂×C₁₉	#585	1	1	yes	characteristic
361	D₁₉	—	4	1	no	—
362	C₂×#41	—	19	1	no	—
363	C₂×#41	—	19	2	no	—
364	C₂²×D₄	C₂×D₁₉	1	1	yes	characteristic
365	C₂²×D₄	C₂×D₁₉	1	1	yes	characteristic
366	C₂²×D₄	C₂×D₁₉	1	2	yes	—
367	C₂³×C₄	—	19	2	no	—
368	C₄⋊Q₈	—	19	1	no	—
369	#127	C₂×D₁₉	1	1	yes	characteristic
370	#126	—	19	1	no	—
371	#126	—	19	2	no	—
372	#126	—	19	1	no	—
373	#126	—	19	2	no	—
374	#126	—	19	2	no	—
375	#126	—	19	2	no	—
376	#125	—	19	1	no	—
377	#125	—	19	1	no	—
378	#125	—	19	2	no	—
379	#125	—	19	1	no	—
380	#124	—	19	1	no	—
381	#124	—	19	2	no	—
382	#124	—	19	2	no	—
383	#124	—	19	1	no	—
384	#124	—	19	1	no	—
385	#123	—	19	1	no	—
386	#123	—	19	2	no	—
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	2	no	—
394	#123	—	19	2	no	—
395	#123	—	19	2	no	—
396	#123	—	19	2	no	—
397	#123	—	19	1	no	—
398	#123	—	19	2	no	—
399	C₂²⋊Q₈	—	19	1	no	—
400	C₂²⋊Q₈	—	19	2	no	—
401	C₂²⋊Q₈	—	19	1	no	—
402	C₂²⋊Q₈	—	19	2	no	—
403	C₂²⋊Q₈	—	19	2	no	—
404	C₂²⋊Q₈	—	19	1	no	—
405	C₂²⋊Q₈	—	19	2	no	—
406	C₂²⋊Q₈	—	19	2	no	—
407	#121	—	19	2	no	—
408	#121	—	19	1	no	—
409	#121	—	19	1	no	—
410	#121	—	19	1	no	—
411	#121	—	19	2	no	—
412	#121	—	19	2	no	—
413	#121	—	19	2	no	—
414	#121	—	19	2	no	—
415	#121	C₂×D₁₉	1	1	yes	characteristic
416	#121	C₂×D₁₉	1	2	yes	—
417	#121	C₂×D₁₉	1	1	yes	characteristic
418	#120	—	19	2	no	—
419	#120	—	19	2	no	—
420	#120	C₂×D₁₉	1	2	yes	—
421	#120	C₂×D₁₉	1	2	yes	—
422	C₄×Q₈	—	19	1	no	—
423	C₄×Q₈	—	19	1	no	—
424	C₄×Q₈	—	19	1	no	—
425	C₄×D₄	—	19	1	no	—
426	C₄×D₄	—	19	1	no	—
427	C₄×D₄	—	19	2	no	—
428	C₄×D₄	—	19	1	no	—
429	C₄×D₄	—	19	2	no	—
430	C₄×D₄	—	19	1	no	—
431	C₄×D₄	—	19	1	no	—
432	C₄×D₄	—	19	2	no	—
433	C₄×D₄	—	19	1	no	—
434	C₄×D₄	—	19	1	no	—
435	C₄×D₄	—	19	2	no	—
436	C₄×D₄	—	19	2	no	—
437	C₄×D₄	—	19	2	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	C₂×D₁₉	1	1	yes	characteristic
444	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
445	#117	—	19	1	no	—
446	#117	—	19	1	no	—
447	#117	—	19	2	no	—
448	#117	—	19	2	no	—
449	#117	—	19	2	no	—
450	#117	—	19	1	no	—
451	C₂×C₄⋊C₄	—	19	1	no	—
452	C₂×C₄⋊C₄	—	19	2	no	—
453	C₂×C₄⋊C₄	—	19	2	no	—
454	C₂×C₄⋊C₄	—	19	1	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	—	19	2	no	—
459	C₂×C₂²⋊C₄	—	19	2	no	—
460	C₂×C₄²	—	19	1	no	—
461	C₁₉	#3513	1	1	yes	characteristic, complemented, Sylow
462	C₂⁴	C₂²×D₁₉	1	2	yes	—
463	C₂⁴	C₂²×D₁₉	1	2	yes	—
464	#41	—	38	4	no	—
465	#41	—	76	4	no	—
466	C₂×Q₈	—	19	1	no	—
467	C₂×Q₈	—	19	1	no	—
468	C₂×Q₈	—	19	2	no	—
469	C₂×D₄	—	2	4	no	—
470	C₂×D₄	—	2	4	no	—
471	C₂×D₄	—	4	4	no	—
472	C₂×D₄	—	19	2	no	—
473	C₂×D₄	—	19	1	no	—
474	C₂×D₄	—	19	1	no	—
475	C₂×D₄	—	19	2	no	—
476	C₂×D₄	—	19	2	no	—
477	C₂×D₄	C₂²×D₁₉	1	2	yes	—
478	C₂×D₄	C₂²×D₁₉	1	2	yes	—
479	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
480	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
481	C₂×D₄	C₂²×D₁₉	1	2	yes	—
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	C₂×D₄	C₂²×D₁₉	1	2	yes	—
486	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
487	C₂²×C₄	—	19	1	no	—
488	C₂²×C₄	—	19	2	no	—
489	C₂²×C₄	—	19	2	no	—
490	C₂²×C₄	—	19	1	no	—
491	C₂²×C₄	—	19	2	no	—
492	C₂²×C₄	—	19	2	no	—
493	C₂²×C₄	—	19	2	no	—
494	C₂²×C₄	—	19	2	no	—
495	C₂²×C₄	—	19	2	no	—
496	C₂²×C₄	—	19	2	no	—
497	C₂²×C₄	—	19	2	no	—
498	C₂²×C₄	—	19	1	no	—
499	C₂²×C₄	—	19	2	no	—
500	C₂²×C₄	—	76	4	no	—
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	2	no	—
505	C₄⋊C₄	—	19	1	no	—
506	C₄⋊C₄	—	19	1	no	—
507	C₄⋊C₄	—	19	2	no	—
508	C₄⋊C₄	—	19	2	no	—
509	C₄⋊C₄	—	19	2	no	—
510	C₄⋊C₄	—	19	2	no	—
511	C₄⋊C₄	—	19	2	no	—
512	C₄⋊C₄	—	19	1	no	—
513	C₄⋊C₄	—	19	2	no	—
514	C₄⋊C₄	—	19	2	no	—
515	C₄⋊C₄	—	19	2	no	—
516	C₄⋊C₄	—	19	1	no	—
517	C₄⋊C₄	—	19	1	no	—
518	C₄⋊C₄	—	19	1	no	—
519	C₄⋊C₄	—	19	1	no	—
520	C₄⋊C₄	—	19	1	no	—
521	C₄⋊C₄	—	19	2	no	—
522	C₄⋊C₄	—	19	1	no	—
523	C₄⋊C₄	—	19	1	no	—
524	C₄⋊C₄	—	19	1	no	—
525	C₄⋊C₄	—	19	1	no	—
526	C₄⋊C₄	—	19	2	no	—
527	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
528	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
529	C₂²⋊C₄	—	19	2	no	—
530	C₂²⋊C₄	—	19	2	no	—
531	C₂²⋊C₄	—	19	1	no	—
532	C₂²⋊C₄	—	19	1	no	—
533	C₂²⋊C₄	—	19	1	no	—
534	C₂²⋊C₄	—	19	1	no	—
535	C₂²⋊C₄	—	19	2	no	—
536	C₂²⋊C₄	—	19	2	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	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	2	no	—
548	C₂²⋊C₄	—	19	2	no	—
549	C₂²⋊C₄	—	19	1	no	—
550	C₂²⋊C₄	—	19	1	no	—
551	C₂²⋊C₄	—	19	1	no	—
552	C₂²⋊C₄	—	19	1	no	—
553	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
554	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
555	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
556	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
557	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
558	C₄²	—	19	1	no	—
559	C₄²	—	19	1	no	—
560	C₄²	—	19	1	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	—	2	4	no	—
569	C₂³	—	2	4	no	—
570	C₂³	—	4	2	no	—
571	C₂³	—	4	2	no	—
572	C₂³	—	4	2	no	—
573	C₂³	—	19	1	no	—
574	C₂³	C₂³×D₁₉	1	1	yes	characteristic
575	C₂³	C₂³×D₁₉	1	2	yes	—
576	C₂³	C₂³×D₁₉	1	2	yes	—
577	C₂³	C₂³×D₁₉	1	2	yes	—
578	C₂³	C₂³×D₁₉	1	1	yes	characteristic
579	Q₈	—	38	2	no	—
580	Q₈	—	76	2	no	—
581	Q₈	—	76	1	no	—
582	D₄	—	2	4	no	—
583	D₄	—	2	4	no	—
584	D₄	—	2	2	no	—
585	D₄	—	2	4	no	—
586	D₄	—	2	2	no	—
587	D₄	—	2	2	no	—
588	D₄	—	4	2	no	—
589	D₄	—	4	2	no	—
590	D₄	—	4	2	no	—
591	D₄	—	38	4	no	—
592	D₄	—	38	2	no	—
593	D₄	—	76	2	no	—
594	D₄	—	76	2	no	—
595	D₄	—	76	1	no	—
596	D₄	#64543	1	4	yes	complemented
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	4	2	no	—
600	C₂×C₄	—	19	1	no	—
601	C₂×C₄	—	19	2	no	—
602	C₂×C₄	—	19	1	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	2	no	—
608	C₂×C₄	—	19	1	no	—
609	C₂×C₄	—	19	1	no	—
610	C₂×C₄	—	19	2	no	—
611	C₂×C₄	—	38	4	no	—
612	C₂×C₄	—	38	2	no	—
613	C₂×C₄	—	38	4	no	—
614	C₂×C₄	—	38	2	no	—
615	C₂×C₄	—	76	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	—	76	2	no	—
624	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
625	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
626	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
627	C₂×C₄	C₂³×D₁₉	1	2	yes	—
628	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
629	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
630	C₂²	—	2	1	no	—
631	C₂²	—	2	2	no	—
632	C₂²	—	2	1	no	—
633	C₂²	—	2	2	no	—
634	C₂²	—	2	1	no	—
635	C₂²	—	2	2	no	—
636	C₂²	—	2	2	no	—
637	C₂²	—	2	2	no	—
638	C₂²	—	2	2	no	—
639	C₂²	—	2	1	no	—
640	C₂²	—	2	2	no	—
641	C₂²	—	2	2	no	—
642	C₂²	—	2	1	no	—
643	C₂²	—	4	8	no	—
644	C₂²	—	8	4	no	—
645	C₂²	—	38	1	no	—
646	C₂²	—	38	1	no	—
647	C₂²	—	38	1	no	—
648	C₂²	C₂×#64543	1	4	yes	—
649	C₂²	#10597430	1	2	yes	—
650	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
651	C₄	—	2	1	no	—
652	C₄	—	2	1	no	—
653	C₄	—	2	1	no	—
654	C₄	—	2	2	no	—
655	C₄	—	2	1	no	—
656	C₄	—	38	1	no	—
657	C₄	—	38	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	1	no	—
664	C₄	—	38	2	no	—
665	C₄	—	38	1	no	—
666	C₄	—	38	1	no	—
667	C₄	C₂×#64543	1	2	yes	—
668	C₂	—	2	2	no	—
669	C₂	—	2	4	no	—
670	C₂	—	4	2	no	—
671	C₂	—	4	1	no	—
672	C₂	—	4	2	no	—
673	C₂	—	76	1	no	—
674	C₂	C₂²×#64543	1	1	yes	characteristic
675	C₂	C₂×#10597430	1	1	yes	characteristic
676	C₂	#11927379	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Fitting	D₄²×C₁₉	C₂
hypercenter	D₄²	D₁₉
hypocenter	C₁₉	#3513
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ D₄²

Complements

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

N	H ≅ G/N	type
1. #11927280	C₂	semidirect
2. #11927253	C₂	semidirect
3. #11927241	C₂	semidirect
4. #11927237	C₂	semidirect
5. #11927234	C₂	semidirect
6. #11927225	C₂	semidirect
7. #11927225	C₂	semidirect
8. #11927194	C₂	semidirect
9. #11927188	C₂	semidirect
10. #11927188	C₂	semidirect
11. #11927188	C₂	semidirect
12. #11927161	C₂	semidirect
13. #11927148	C₂	semidirect
14. #11927139	C₂	semidirect
15. #11927129	C₂	semidirect
16. #11927075	C₂	semidirect
17. #11927074	C₂	semidirect
18. #11927050	C₂	semidirect
19. C₂×#10597381	C₂	semidirect
20. #11927023	C₂	semidirect
21. #11927019	C₂	semidirect
22. C₂×D₄×Dic₁₉	C₂	semidirect
23. D₄²×C₁₉	C₂	semidirect
27. C₂³×Dic₁₉	C₂²	semidirect
29. C₂×#64543	C₂²	semidirect
38. #10597399	C₂²	semidirect
39. #10597399	C₂²	semidirect
40. C₂×C₂²⋊Dic₁₉	C₂²	semidirect
41. C₂×C₂²⋊Dic₁₉	C₂²	semidirect
42. C₂×C₂²⋊Dic₁₉	C₂²	semidirect
43. C₂×C₂²⋊Dic₁₉	C₂²	semidirect
44. C₂×C₂²⋊Dic₁₉	C₂²	semidirect
46. #10597385	C₂²	semidirect
47. #10597385	C₂²	semidirect
48. #10597385	C₂²	semidirect
49. #10597385	C₂²	semidirect
50. #10597384	C₂²	semidirect
51. #10597384	C₂²	semidirect
52. #10597384	C₂²	semidirect
53. #10597382	C₂²	semidirect
54. #10597382	C₂²	semidirect
55. #10597382	C₂²	semidirect
56. #10597382	C₂²	semidirect
59. #10597381	C₂²	semidirect
60. #10597381	C₂²	semidirect
61. #10597381	C₂²	semidirect
62. #10597381	C₂²	semidirect
63. #10597381	C₂²	semidirect
64. #10597381	C₂²	semidirect
65. #10597381	C₂²	semidirect
66. #10597381	C₂²	semidirect
67. #10597381	C₂²	semidirect
68. #10597381	C₂²	semidirect
72. D₄×Dic₁₉	C₂²	semidirect
73. D₄×Dic₁₉	C₂²	semidirect
74. D₄×Dic₁₉	C₂²	semidirect
75. D₄×Dic₁₉	C₂²	semidirect
76. D₄×Dic₁₉	C₂²	semidirect
77. D₄×Dic₁₉	C₂²	semidirect
78. D₄×Dic₁₉	C₂²	semidirect
79. D₄×Dic₁₉	C₂²	semidirect
80. D₄×Dic₁₉	C₂²	semidirect
81. D₄×Dic₁₉	C₂²	semidirect
82. C₄×C₂²⋊D₁₉	C₂²	semidirect
83. C₄×C₂²⋊D₁₉	C₂²	semidirect
84. C₄×C₂²⋊D₁₉	C₂²	semidirect
85. #10597372	C₂²	semidirect
86. #10597372	C₂²	semidirect
87. C₂×C₄⋊Dic₁₉	C₂²	semidirect
88. #10597370	C₂²	semidirect
89. #10597370	C₂²	semidirect
90. #10597370	C₂²	semidirect
91. C₂×Dic₁₉⋊C₄	C₂²	semidirect
92. C₂×Dic₁₉⋊C₄	C₂²	semidirect
93. C₂×C₄×Dic₁₉	C₂²	semidirect
94. #10597344	C₂²	semidirect
95. C₄⋊C₄×D₁₉	C₂²	semidirect
96. #10597336	C₂²	semidirect
97. #10597335	C₂²	semidirect
98. #10597335	C₂²	semidirect
99. #10597334	C₂²	semidirect
100. #10597333	C₂²	semidirect
101. #10597332	C₂²	semidirect
102. #10597331	C₂²	semidirect
103. #10597329	C₂²	semidirect
104. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
105. (C₂²⋊D₁₉)⋊C₄	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. #10597316	C₂²	semidirect
121. C₄×Dic₃₈	C₂²	semidirect
122. C₄×Dic₃₈	C₂²	semidirect
249. D₄×C₁₉	#41	semidirect
341. D₄²	D₁₉	semidirect
461. C₁₉	#3513	semidirect
596. D₄	#64543	semidirect

Maximal subgroups

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

subgroup	index
#11927280	2
#11927253	2
#11927241	2
#11927237	2
#11927234	2
#11927225	2
#11927194	2
#11927188	2
#11927161	2
#11927148	2
#11927139	2
#11927129	2
#11927075	2
#11927074	2
#11927050	2
C₂×#10597381	2
#11927023	2
#11927019	2
C₂×D₄×Dic₁₉	2
D₄²×C₁₉	2
#3513	19