Subgroups — #14577351

Order 2432.

1040 conjugacy classes of subgroups.

The subgroup lattice has 660 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	#11927262	C₂	1	1	yes	maximal, characteristic, complemented
3	#11927261	C₂	1	2	yes	maximal, complemented
4	#11927259	C₂	1	1	yes	maximal, characteristic, complemented
5	#11927258	C₂	1	2	yes	maximal, complemented
6	#11927258	C₂	1	1	yes	maximal, characteristic, complemented
7	#11927243	C₂	1	2	yes	maximal, complemented
8	#11927241	C₂	1	1	yes	maximal, characteristic, complemented
9	#11927232	C₂	1	1	yes	maximal, characteristic, complemented
10	#11927231	C₂	1	2	yes	maximal, complemented
11	#11927229	C₂	1	1	yes	maximal, characteristic, complemented
12	#11927174	C₂	1	1	yes	maximal, characteristic, complemented
13	#11927130	C₂	1	2	yes	maximal, complemented
14	#11927126	C₂	1	2	yes	maximal, complemented
15	#11927123	C₂	1	1	yes	maximal, characteristic, complemented
16	#11927077	C₂	1	2	yes	maximal, complemented
17	#11927076	C₂	1	2	yes	maximal, complemented
18	#11927054	C₂	1	1	yes	maximal, characteristic, complemented
19	#11927053	C₂	1	1	yes	maximal, characteristic, complemented
20	#11927025	C₂	1	1	yes	maximal, characteristic, complemented
21	#11927023	C₂	1	1	yes	maximal, characteristic, complemented
22	#117×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₉×#553	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#64543	C₂²	1	1	yes	characteristic
25	C₂×#64541	C₂²	1	1	yes	characteristic
26	C₂²×C₄×D₁₉	C₂²	1	1	yes	characteristic
27	C₁₉×#126	C₂²	1	2	yes	complemented
28	C₁₉×#125	C₂²	1	1	yes	characteristic, complemented
29	C₁₉×#123	C₂²	1	2	yes	—
30	C₁₉×#121	C₂²	1	1	yes	characteristic
31	C₁₉×#121	C₂²	1	2	yes	—
32	C₁₉×#121	C₂²	1	1	yes	characteristic, complemented
33	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
34	C₄×D₄×C₁₉	C₂²	1	2	yes	complemented
35	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
36	C₁₉×#117	C₂²	1	1	yes	characteristic
37	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
38	#10597385	C₂²	1	1	yes	characteristic
39	#10597385	C₂²	1	2	yes	—
40	#10597385	C₂²	1	2	yes	complemented
41	#10597384	C₂²	1	1	yes	characteristic
42	#10597384	C₂²	1	2	yes	—
43	#10597384	C₂²	1	2	yes	—
44	#10597384	C₂²	1	1	yes	characteristic, complemented
45	#10597383	C₂²	1	1	yes	characteristic
46	#10597383	C₂²	1	2	yes	—
47	#10597382	C₂²	1	2	yes	—
48	#10597382	C₂²	1	2	yes	complemented
49	#10597381	C₂²	1	2	yes	—
50	D₄×Dic₁₉	C₂²	1	2	yes	—
51	D₄×Dic₁₉	C₂²	1	1	yes	characteristic, complemented
52	#10597376	C₂²	1	2	yes	—
53	#10597375	C₂²	1	2	yes	—
54	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
55	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
56	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	—
57	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	—
58	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	complemented
59	#10597372	C₂²	1	1	yes	characteristic
60	#10597372	C₂²	1	2	yes	complemented
61	#10597372	C₂²	1	2	yes	complemented
62	#10597372	C₂²	1	1	yes	characteristic, complemented
63	#10597370	C₂²	1	1	yes	characteristic
64	#10597370	C₂²	1	1	yes	characteristic, complemented
65	C₂×Dic₁₉⋊C₄	C₂²	1	2	yes	complemented
66	#10597344	C₂²	1	2	yes	—
67	#10597344	C₂²	1	2	yes	—
68	#10597343	C₂²	1	1	yes	characteristic
69	#10597343	C₂²	1	2	yes	—
70	#10597343	C₂²	1	1	yes	characteristic, complemented
71	#10597342	C₂²	1	1	yes	characteristic
72	#10597342	C₂²	1	2	yes	—
73	#10597340	C₂²	1	1	yes	characteristic
74	#10597340	C₂²	1	2	yes	—
75	#10597339	C₂²	1	2	yes	—
76	#10597338	C₂²	1	1	yes	characteristic
77	#10597338	C₂²	1	1	yes	characteristic
78	#10597338	C₂²	1	1	yes	characteristic
79	#10597338	C₂²	1	2	yes	complemented
80	#10597338	C₂²	1	1	yes	characteristic, complemented
81	C₄⋊C₄×D₁₉	C₂²	1	1	yes	characteristic
82	C₄⋊C₄×D₁₉	C₂²	1	1	yes	characteristic
83	C₄⋊C₄×D₁₉	C₂²	1	1	yes	characteristic, complemented
84	#10597336	C₂²	1	2	yes	complemented
85	#10597336	C₂²	1	1	yes	characteristic, complemented
86	#10597335	C₂²	1	2	yes	complemented
87	#10597335	C₂²	1	2	yes	complemented
88	#10597334	C₂²	1	2	yes	complemented
89	#10597334	C₂²	1	1	yes	characteristic, complemented
90	#10597333	C₂²	1	2	yes	complemented
91	#10597333	C₂²	1	1	yes	characteristic, complemented
92	#10597333	C₂²	1	2	yes	complemented
93	#10597331	C₂²	1	2	yes	—
94	#10597331	C₂²	1	2	yes	—
95	#10597331	C₂²	1	2	yes	—
96	#10597331	C₂²	1	2	yes	complemented
97	#10597330	C₂²	1	1	yes	characteristic
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⋊D₁₉)⋊C₄	C₂²	1	2	yes	complemented
105	C₂²⋊C₄×D₁₉	C₂²	1	2	yes	—
106	#10597325	C₂²	1	2	yes	—
107	#10597325	C₂²	1	2	yes	—
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	complemented
112	#10597323	C₂²	1	2	yes	—
113	#10597323	C₂²	1	2	yes	complemented
114	#10597323	C₂²	1	2	yes	complemented
115	#10597322	C₂²	1	2	yes	complemented
116	C₄×D₇₆	C₂²	1	1	yes	characteristic
117	#10597318	C₂²	1	1	yes	characteristic
118	#10597318	C₂²	1	2	yes	—
119	C₄²×D₁₉	C₂²	1	2	yes	—
120	#10597315	C₂²	1	1	yes	characteristic, complemented
121	C₄×Dic₃₈	C₂²	1	2	yes	complemented
122	C₄×Dic₃₈	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₉	C₂³	1	1	yes	characteristic
124	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
125	C₂×D₄×C₁₉	C₂³	1	2	yes	—
126	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
127	C₂×D₄×C₁₉	C₂³	1	2	yes	—
128	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
130	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
131	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
133	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
138	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
139	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
140	C₂²×Dic₁₉	C₂³	1	2	yes	—
141	C₂²×Dic₁₉	C₂³	1	2	yes	—
142	#64543	—	2	4	no	—
143	#64541	—	2	4	no	—
144	C₂×D₇₆	C₂³	1	1	yes	characteristic
145	C₂×D₇₆	C₂³	1	1	yes	characteristic
146	C₂×C₄×D₁₉	—	2	4	no	—
147	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
148	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
149	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
151	C₂×C₄×D₁₉	C₂³	1	2	yes	—
152	C₂×C₄×D₁₉	C₂³	1	2	yes	—
153	C₂×C₄×D₁₉	C₂³	1	2	yes	—
154	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
155	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
156	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
157	C₂×Dic₃₈	C₂³	1	2	yes	—
158	C₂×Dic₃₈	C₂³	1	2	yes	—
159	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
160	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
161	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
162	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
163	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
164	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
165	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
166	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
167	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
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	C₄²×C₁₉	C₂³	1	2	yes	—
173	C₄²×C₁₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
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	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
193	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
194	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
195	C₄⋊Dic₁₉	C₂³	1	2	yes	—
196	C₄⋊Dic₁₉	C₂³	1	2	yes	—
197	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
198	C₄⋊Dic₁₉	C₂³	1	2	yes	—
199	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
200	C₄⋊Dic₁₉	C₂³	1	2	yes	—
201	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
202	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
203	Dic₁₉⋊C₄	C₂³	1	2	yes	—
204	Dic₁₉⋊C₄	C₂³	1	2	yes	—
205	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
212	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
213	Dic₁₉⋊C₄	C₂³	1	2	yes	—
214	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
215	Dic₁₉⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
223	C₄×Dic₁₉	C₂³	1	2	yes	—
224	C₄×Dic₁₉	C₂³	1	2	yes	—
225	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
226	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
227	C₂³×C₁₉	C₂⁴	1	2	yes	—
228	C₂²×D₁₉	—	2	2	no	—
229	C₂²×D₁₉	—	4	1	no	—
230	C₂²×D₁₉	—	4	1	no	—
231	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
232	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
233	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
234	D₄×C₁₉	—	2	2	no	—
235	D₄×C₁₉	—	4	1	no	—
236	D₄×C₁₉	—	4	2	no	—
237	D₄×C₁₉	—	4	2	no	—
238	C₂×C₄×C₁₉	—	2	2	no	—
239	C₂×C₄×C₁₉	—	2	2	no	—
240	C₂×C₄×C₁₉	—	4	2	no	—
241	C₂×C₄×C₁₉	—	4	2	no	—
242	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
243	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
244	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
245	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
246	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
247	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
248	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
249	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
250	C₂²⋊D₁₉	—	2	2	no	—
251	C₂²⋊D₁₉	—	2	4	no	—
252	C₂²⋊D₁₉	—	2	2	no	—
253	C₂²⋊D₁₉	—	4	1	no	—
254	C₂²⋊D₁₉	—	4	2	no	—
255	C₂²⋊D₁₉	—	4	2	no	—
256	C₂²⋊D₁₉	—	4	1	no	—
257	C₂×Dic₁₉	—	2	2	no	—
258	C₂×Dic₁₉	—	2	4	no	—
259	C₂×Dic₁₉	—	4	2	no	—
260	C₂×Dic₁₉	C₂⁴	1	2	yes	—
261	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
262	C₂×Dic₁₉	C₂⁴	1	2	yes	—
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	2	yes	—
267	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
268	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
269	D₇₆	—	2	2	no	—
270	D₇₆	—	4	1	no	—
271	C₄×D₁₉	—	2	2	no	—
272	C₄×D₁₉	—	2	2	no	—
273	C₄×D₁₉	—	2	2	no	—
274	C₄×D₁₉	—	2	2	no	—
275	C₄×D₁₉	—	4	2	no	—
276	C₄×D₁₉	—	4	2	no	—
277	C₄×D₁₉	—	4	2	no	—
278	C₄×D₁₉	#41	1	4	yes	—
279	Dic₃₈	—	2	2	no	—
280	Dic₃₈	—	2	2	no	—
281	Dic₃₈	—	4	2	no	—
282	Dic₃₈	—	4	2	no	—
283	#3493	—	19	1	no	maximal, Sylow
284	C₂²×C₁₉	—	2	2	no	—
285	C₂²×C₁₉	—	2	1	no	—
286	C₂²×C₁₉	—	2	1	no	—
287	C₂²×C₁₉	—	2	2	no	—
288	C₂²×C₁₉	—	2	2	no	—
289	C₂²×C₁₉	—	2	1	no	—
290	C₂²×C₁₉	—	2	1	no	—
291	C₂²×C₁₉	—	2	1	no	—
292	C₂²×C₁₉	—	2	1	no	—
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	C₂×D₁₉	—	2	1	no	—
298	C₂×D₁₉	—	2	1	no	—
299	C₂×D₁₉	—	2	1	no	—
300	C₂×D₁₉	—	2	1	no	—
301	C₂×D₁₉	—	2	1	no	—
302	C₂×D₁₉	—	4	4	no	—
303	C₂×D₁₉	C₂×#41	1	2	yes	—
304	C₄×C₁₉	—	2	1	no	—
305	C₄×C₁₉	—	2	1	no	—
306	C₄×C₁₉	—	2	1	no	—
307	C₄×C₁₉	—	2	2	no	—
308	C₄×C₁₉	—	2	2	no	—
309	C₄×C₁₉	—	2	2	no	—
310	C₄×C₁₉	—	2	1	no	—
311	C₄×C₁₉	C₂×#41	1	2	yes	—
312	Dic₁₉	—	2	1	no	—
313	Dic₁₉	—	2	2	no	—
314	Dic₁₉	—	2	1	no	—
315	Dic₁₉	—	2	1	no	—
316	Dic₁₉	—	2	2	no	—
317	Dic₁₉	—	2	2	no	—
318	Dic₁₉	—	2	2	no	—
319	Dic₁₉	—	2	1	no	—
320	Dic₁₉	C₂×#41	1	2	yes	—
321	#556	—	19	2	no	—
322	#556	—	19	1	no	—
323	#556	—	19	1	no	—
324	#555	—	19	2	no	—
325	#555	—	19	1	no	—
326	#555	—	19	1	no	—
327	#553	—	19	1	no	—
328	#553	—	19	2	no	—
329	#553	D₁₉	1	1	yes	characteristic, complemented
330	#552	—	19	1	no	—
331	#552	—	19	2	no	—
332	#552	—	19	1	no	—
333	#544	—	19	1	no	—
334	#538	—	19	2	no	—
335	#538	—	19	2	no	—
336	#537	—	19	1	no	—
337	#529	—	19	2	no	—
338	#529	—	19	2	no	—
339	#525	—	19	1	no	—
340	#525	—	19	1	no	—
341	#520	—	19	1	no	—
342	#520	—	19	1	no	—
343	C₂×#117	—	19	1	no	—
344	C₂×C₁₉	—	4	1	no	—
345	C₂×C₁₉	—	4	2	no	—
346	C₂×C₁₉	—	4	1	no	—
347	C₂×C₁₉	C₂²×#41	1	1	yes	characteristic
348	C₂×C₁₉	#585	1	1	yes	characteristic
349	C₂×C₁₉	#585	1	1	yes	characteristic
350	D₁₉	—	2	2	no	—
351	D₁₉	—	4	1	no	—
352	D₁₉	—	4	1	no	—
353	C₂×#41	—	19	1	no	—
354	C₂×#41	—	19	1	no	—
355	C₂³×C₄	—	19	1	no	—
356	C₄⋊Q₈	—	19	2	no	—
357	C₄⋊Q₈	—	19	1	no	—
358	C₄⋊Q₈	—	19	1	no	—
359	#126	—	19	2	no	—
360	#126	—	19	2	no	—
361	#126	—	19	2	no	—
362	#126	—	19	2	no	—
363	#126	—	19	2	no	—
364	#126	—	19	2	no	—
365	#126	—	19	2	no	—
366	#126	C₂×D₁₉	1	2	yes	complemented
367	#125	—	19	2	no	—
368	#125	—	19	2	no	—
369	#125	—	19	2	no	—
370	#125	—	19	1	no	—
371	#125	C₂×D₁₉	1	1	yes	characteristic, complemented
372	#124	—	19	2	no	—
373	#124	—	19	2	no	—
374	#124	—	19	2	no	—
375	#124	—	19	2	no	—
376	#124	—	19	2	no	—
377	#124	—	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	—	19	1	no	—
384	#123	C₂×D₁₉	1	2	yes	—
385	C₂²⋊Q₈	—	19	1	no	—
386	C₂²⋊Q₈	—	19	1	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	1	no	—
392	C₂²⋊Q₈	—	19	1	no	—
393	C₂²⋊Q₈	—	19	2	no	—
394	#121	—	19	1	no	—
395	#121	—	19	2	no	—
396	#121	—	19	2	no	—
397	#121	—	19	1	no	—
398	#121	—	19	1	no	—
399	#121	—	19	2	no	—
400	#121	—	19	2	no	—
401	#121	—	19	2	no	—
402	#121	—	19	1	no	—
403	#121	—	19	2	no	—
404	#121	C₂×D₁₉	1	1	yes	characteristic
405	#121	C₂×D₁₉	1	2	yes	—
406	#121	C₂×D₁₉	1	1	yes	characteristic, complemented
407	#120	—	19	1	no	—
408	#120	—	19	2	no	—
409	#120	—	19	1	no	—
410	C₄×Q₈	—	19	2	no	—
411	C₄×Q₈	—	19	1	no	—
412	C₄×Q₈	—	19	2	no	—
413	C₄×Q₈	—	19	1	no	—
414	C₄×Q₈	—	19	2	no	—
415	C₄×D₄	—	19	2	no	—
416	C₄×D₄	—	19	1	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	—	19	2	no	—
425	C₄×D₄	—	19	2	no	—
426	C₄×D₄	—	19	1	no	—
427	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
428	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic, complemented
429	C₄×D₄	C₂×D₁₉	1	2	yes	complemented
430	#117	—	19	1	no	—
431	#117	—	19	1	no	—
432	#117	—	19	2	no	—
433	#117	—	19	2	no	—
434	#117	—	19	1	no	—
435	#117	—	19	1	no	—
436	#117	—	19	1	no	—
437	#117	—	19	1	no	—
438	#117	—	19	2	no	—
439	#117	—	19	2	no	—
440	#117	—	19	2	no	—
441	#117	—	19	2	no	—
442	#117	—	19	2	no	—
443	#117	—	19	1	no	—
444	#117	C₂×D₁₉	1	1	yes	characteristic
445	C₂×C₄⋊C₄	—	19	2	no	—
446	C₂×C₄⋊C₄	—	19	1	no	—
447	C₂×C₄⋊C₄	—	19	1	no	—
448	C₂×C₄⋊C₄	—	19	1	no	—
449	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic, complemented
450	C₂×C₂²⋊C₄	—	19	2	no	—
451	C₂×C₄²	—	19	2	no	—
452	C₁₉	#3493	1	1	yes	characteristic, complemented, Sylow
453	C₂⁴	—	19	1	no	—
454	#41	—	38	4	no	—
455	#41	—	38	4	no	—
456	C₂×Q₈	—	19	1	no	—
457	C₂×Q₈	—	19	1	no	—
458	C₂×Q₈	—	19	2	no	—
459	C₂×Q₈	—	19	2	no	—
460	C₂×D₄	—	19	1	no	—
461	C₂×D₄	—	19	2	no	—
462	C₂×D₄	—	19	1	no	—
463	C₂×D₄	—	19	1	no	—
464	C₂×D₄	—	19	2	no	—
465	C₂×D₄	—	19	1	no	—
466	C₂×D₄	—	19	2	no	—
467	C₂×D₄	—	19	1	no	—
468	C₂×D₄	—	19	1	no	—
469	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
470	C₂×D₄	C₂²×D₁₉	1	2	yes	—
471	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
472	C₂×D₄	C₂²×D₁₉	1	2	yes	—
473	C₂²×C₄	—	19	1	no	—
474	C₂²×C₄	—	19	2	no	—
475	C₂²×C₄	—	19	1	no	—
476	C₂²×C₄	—	19	2	no	—
477	C₂²×C₄	—	19	1	no	—
478	C₂²×C₄	—	19	1	no	—
479	C₂²×C₄	—	19	1	no	—
480	C₂²×C₄	—	19	1	no	—
481	C₂²×C₄	—	19	2	no	—
482	C₂²×C₄	—	19	2	no	—
483	C₂²×C₄	—	19	2	no	—
484	C₂²×C₄	—	38	4	no	—
485	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
486	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
487	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
488	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
489	C₄⋊C₄	—	19	2	no	—
490	C₄⋊C₄	—	19	1	no	—
491	C₄⋊C₄	—	19	2	no	—
492	C₄⋊C₄	—	19	2	no	—
493	C₄⋊C₄	—	19	2	no	—
494	C₄⋊C₄	—	19	2	no	—
495	C₄⋊C₄	—	19	1	no	—
496	C₄⋊C₄	—	19	1	no	—
497	C₄⋊C₄	—	19	2	no	—
498	C₄⋊C₄	—	19	1	no	—
499	C₄⋊C₄	—	19	2	no	—
500	C₄⋊C₄	—	19	2	no	—
501	C₄⋊C₄	—	19	2	no	—
502	C₄⋊C₄	—	19	1	no	—
503	C₄⋊C₄	—	19	1	no	—
504	C₄⋊C₄	—	19	1	no	—
505	C₄⋊C₄	—	19	2	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	C₂²×D₁₉	1	1	yes	characteristic
511	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
512	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
513	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
514	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
515	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
516	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
517	C₂²⋊C₄	—	19	2	no	—
518	C₂²⋊C₄	—	19	1	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	2	no	—
524	C₂²⋊C₄	—	19	1	no	—
525	C₂²⋊C₄	—	19	2	no	—
526	C₂²⋊C₄	—	19	2	no	—
527	C₂²⋊C₄	—	19	2	no	—
528	C₂²⋊C₄	—	19	1	no	—
529	C₂²⋊C₄	—	19	2	no	—
530	C₂²⋊C₄	—	19	1	no	—
531	C₂²⋊C₄	—	19	1	no	—
532	C₂²⋊C₄	—	19	2	no	—
533	C₂²⋊C₄	—	19	2	no	—
534	C₂²⋊C₄	—	19	1	no	—
535	C₂²⋊C₄	—	19	2	no	—
536	C₂²⋊C₄	—	19	1	no	—
537	C₂²⋊C₄	—	19	1	no	—
538	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
539	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
540	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
541	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
542	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
543	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
544	C₄²	—	19	2	no	—
545	C₄²	—	19	2	no	—
546	C₄²	—	19	2	no	—
547	C₄²	—	19	2	no	—
548	C₄²	—	19	2	no	—
549	C₄²	—	19	2	no	—
550	C₄²	—	19	2	no	—
551	C₄²	—	19	2	no	—
552	C₄²	—	19	1	no	—
553	C₄²	C₂²×D₁₉	1	2	yes	—
554	C₄²	C₂²×D₁₉	1	1	yes	characteristic
555	C₂³	—	19	1	no	—
556	C₂³	—	19	1	no	—
557	C₂³	—	19	1	no	—
558	C₂³	—	38	2	no	—
559	C₂³	—	76	1	no	—
560	C₂³	—	76	1	no	—
561	C₂³	C₂³×D₁₉	1	1	yes	characteristic
562	C₂³	C₂³×D₁₉	1	1	yes	characteristic
563	C₂³	C₂³×D₁₉	1	2	yes	—
564	Q₈	—	38	2	no	—
565	Q₈	—	38	2	no	—
566	Q₈	—	76	2	no	—
567	Q₈	—	76	2	no	—
568	D₄	—	2	2	no	—
569	D₄	—	4	2	no	—
570	D₄	—	4	2	no	—
571	D₄	—	4	1	no	—
572	D₄	—	38	2	no	—
573	D₄	—	38	2	no	—
574	D₄	—	38	2	no	—
575	D₄	—	38	4	no	—
576	D₄	—	76	1	no	—
577	D₄	—	76	1	no	—
578	D₄	—	76	2	no	—
579	D₄	—	76	2	no	—
580	D₄	—	76	1	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	4	2	no	—
584	C₂×C₄	—	4	2	no	—
585	C₂×C₄	—	19	1	no	—
586	C₂×C₄	—	19	4	no	—
587	C₂×C₄	—	19	1	no	—
588	C₂×C₄	—	19	2	no	—
589	C₂×C₄	—	19	1	no	—
590	C₂×C₄	—	19	2	no	—
591	C₂×C₄	—	19	1	no	—
592	C₂×C₄	—	19	2	no	—
593	C₂×C₄	—	19	2	no	—
594	C₂×C₄	—	19	1	no	—
595	C₂×C₄	—	38	2	no	—
596	C₂×C₄	—	38	2	no	—
597	C₂×C₄	—	38	2	no	—
598	C₂×C₄	—	38	4	no	—
599	C₂×C₄	—	38	2	no	—
600	C₂×C₄	—	38	2	no	—
601	C₂×C₄	—	76	2	no	—
602	C₂×C₄	—	76	2	no	—
603	C₂×C₄	—	76	2	no	—
604	C₂×C₄	—	76	2	no	—
605	C₂×C₄	C₂³×D₁₉	1	2	yes	—
606	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
607	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
608	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
609	C₂×C₄	C₂³×D₁₉	1	2	yes	—
610	C₂×C₄	C₂³×D₁₉	1	2	yes	—
611	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
612	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
613	C₂²	—	2	1	no	—
614	C₂²	—	2	1	no	—
615	C₂²	—	2	2	no	—
616	C₂²	—	2	1	no	—
617	C₂²	—	2	2	no	—
618	C₂²	—	2	1	no	—
619	C₂²	—	2	1	no	—
620	C₂²	—	2	2	no	—
621	C₂²	—	2	1	no	—
622	C₂²	—	19	2	no	—
623	C₂²	—	38	1	no	—
624	C₂²	—	38	1	no	—
625	C₂²	—	38	1	no	—
626	C₂²	—	38	1	no	—
627	C₂²	—	38	1	no	—
628	C₂²	—	38	1	no	—
629	C₂²	—	38	1	no	—
630	C₂²	—	38	1	no	—
631	C₂²	—	76	4	no	—
632	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
633	C₄	—	2	1	no	—
634	C₄	—	2	1	no	—
635	C₄	—	2	2	no	—
636	C₄	—	2	1	no	—
637	C₄	—	2	2	no	—
638	C₄	—	2	2	no	—
639	C₄	—	2	1	no	—
640	C₄	—	19	2	no	—
641	C₄	—	38	1	no	—
642	C₄	—	38	2	no	—
643	C₄	—	38	1	no	—
644	C₄	—	38	2	no	—
645	C₄	—	38	1	no	—
646	C₄	—	38	2	no	—
647	C₄	—	38	1	no	—
648	C₄	—	38	2	no	—
649	C₄	#41×D₁₉	1	2	yes	—
650	C₂	—	4	1	no	—
651	C₂	—	4	1	no	—
652	C₂	—	4	2	no	—
653	C₂	—	38	2	no	—
654	C₂	—	76	1	no	—
655	C₂	—	76	1	no	—
656	C₂	C₂×#41×D₁₉	1	1	yes	characteristic
657	C₂	#11927379	1	1	yes	characteristic
658	C₂	#11927380	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Fitting	C₁₉×#553	C₂
hypercenter	#553	D₁₉
hypocenter	C₁₉	#3493
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ #553

Complements

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

N	H ≅ G/N	type
1. #11927264	C₂	semidirect
2. #11927262	C₂	semidirect
3. #11927261	C₂	semidirect
4. #11927259	C₂	semidirect
5. #11927258	C₂	semidirect
6. #11927258	C₂	semidirect
7. #11927243	C₂	semidirect
8. #11927241	C₂	semidirect
9. #11927232	C₂	semidirect
10. #11927231	C₂	semidirect
11. #11927229	C₂	semidirect
12. #11927174	C₂	semidirect
13. #11927130	C₂	semidirect
14. #11927126	C₂	semidirect
15. #11927123	C₂	semidirect
16. #11927077	C₂	semidirect
17. #11927076	C₂	semidirect
18. #11927054	C₂	semidirect
19. #11927053	C₂	semidirect
20. #11927025	C₂	semidirect
21. #11927023	C₂	semidirect
22. #117×D₁₉	C₂	semidirect
23. C₁₉×#553	C₂	semidirect
27. C₁₉×#126	C₂²	semidirect
28. C₁₉×#125	C₂²	semidirect
32. C₁₉×#121	C₂²	semidirect
34. C₄×D₄×C₁₉	C₂²	semidirect
35. C₄×D₄×C₁₉	C₂²	semidirect
37. C₂×C₄⋊C₄×C₁₉	C₂²	semidirect
40. #10597385	C₂²	semidirect
44. #10597384	C₂²	semidirect
48. #10597382	C₂²	semidirect
51. D₄×Dic₁₉	C₂²	semidirect
58. C₄×C₂²⋊D₁₉	C₂²	semidirect
60. #10597372	C₂²	semidirect
61. #10597372	C₂²	semidirect
62. #10597372	C₂²	semidirect
64. #10597370	C₂²	semidirect
65. C₂×Dic₁₉⋊C₄	C₂²	semidirect
70. #10597343	C₂²	semidirect
79. #10597338	C₂²	semidirect
80. #10597338	C₂²	semidirect
83. C₄⋊C₄×D₁₉	C₂²	semidirect
84. #10597336	C₂²	semidirect
85. #10597336	C₂²	semidirect
86. #10597335	C₂²	semidirect
87. #10597335	C₂²	semidirect
88. #10597334	C₂²	semidirect
89. #10597334	C₂²	semidirect
90. #10597333	C₂²	semidirect
91. #10597333	C₂²	semidirect
92. #10597333	C₂²	semidirect
96. #10597331	C₂²	semidirect
104. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
108. #10597325	C₂²	semidirect
109. #10597325	C₂²	semidirect
111. #10597324	C₂²	semidirect
113. #10597323	C₂²	semidirect
114. #10597323	C₂²	semidirect
115. #10597322	C₂²	semidirect
120. #10597315	C₂²	semidirect
121. C₄×Dic₃₈	C₂²	semidirect
122. C₄×Dic₃₈	C₂²	semidirect
329. #553	D₁₉	semidirect
366. #126	C₂×D₁₉	semidirect
371. #125	C₂×D₁₉	semidirect
406. #121	C₂×D₁₉	semidirect
428. C₄×D₄	C₂×D₁₉	semidirect
429. C₄×D₄	C₂×D₁₉	semidirect
449. C₂×C₄⋊C₄	C₂×D₁₉	semidirect
452. C₁₉	#3493	semidirect

Maximal subgroups

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

subgroup	index
#11927264	2
#11927262	2
#11927261	2
#11927259	2
#11927258	2
#11927243	2
#11927241	2
#11927232	2
#11927231	2
#11927229	2
#11927174	2
#11927130	2
#11927126	2
#11927123	2
#11927077	2
#11927076	2
#11927054	2
#11927053	2
#11927025	2
#11927023	2
#117×D₁₉	2
C₁₉×#553	2
#3493	19