Subgroups — #14577327

Order 2432.

1052 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927235	C₂	1	2	yes	maximal, complemented
2	#11927233	C₂	1	2	yes	maximal, complemented
3	#11927230	C₂	1	2	yes	maximal, complemented
4	#11927226	C₂	1	2	yes	maximal, complemented
5	#11927224	C₂	1	2	yes	maximal, complemented
6	#11927223	C₂	1	2	yes	maximal, complemented
7	#11927219	C₂	1	2	yes	maximal, complemented
8	#11927218	C₂	1	2	yes	maximal, complemented
9	#11927169	C₂	1	1	yes	maximal, characteristic, complemented
10	#11927143	C₂	1	1	yes	maximal, characteristic, complemented
11	#11927139	C₂	1	1	yes	maximal, characteristic, complemented
12	#11927136	C₂	1	2	yes	maximal, complemented
13	#11927102	C₂	1	1	yes	maximal, characteristic
14	#11927078	C₂	1	1	yes	maximal, characteristic, complemented
15	#11927071	C₂	1	2	yes	maximal, complemented
16	#123×D₁₉	C₂	1	2	yes	maximal, complemented
17	#11927016	C₂	1	2	yes	maximal, complemented
18	C₂×#10597318	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₉×#529	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×D₄×D₁₉	C₂²	1	2	yes	—
21	C₂²×C₄×D₁₉	C₂²	1	1	yes	characteristic
22	C₁₉×#126	C₂²	1	2	yes	complemented
23	C₁₉×#125	C₂²	1	1	yes	characteristic, complemented
24	C₁₉×#124	C₂²	1	1	yes	characteristic, complemented
25	C₁₉×#123	C₂²	1	2	yes	complemented
26	C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
27	C₁₉×#121	C₂²	1	1	yes	characteristic
28	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
29	C₄×D₄×C₁₉	C₂²	1	2	yes	complemented
30	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
31	C₁₉×#117	C₂²	1	2	yes	complemented
32	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic, complemented
33	#10597392	C₂²	1	2	yes	complemented
34	#10597392	C₂²	1	2	yes	complemented
35	#10597385	C₂²	1	2	yes	—
36	#10597383	C₂²	1	2	yes	—
37	#10597381	C₂²	1	2	yes	complemented
38	#10597381	C₂²	1	2	yes	complemented
39	D₄×Dic₁₉	C₂²	1	2	yes	complemented
40	#10597376	C₂²	1	1	yes	characteristic
41	#10597375	C₂²	1	2	yes	complemented
42	#10597375	C₂²	1	2	yes	complemented
43	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	—
44	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	complemented
45	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	1	yes	characteristic
46	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	1	yes	characteristic
47	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	2	yes	complemented
48	#10597370	C₂²	1	1	yes	characteristic, complemented
49	#10597370	C₂²	1	2	yes	complemented
50	C₂×Dic₁₉⋊C₄	C₂²	1	1	yes	characteristic, complemented
51	C₂×Dic₁₉⋊C₄	C₂²	1	1	yes	characteristic, complemented
52	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic, complemented
53	#10597344	C₂²	1	2	yes	complemented
54	#10597344	C₂²	1	2	yes	complemented
55	#10597343	C₂²	1	2	yes	complemented
56	#10597342	C₂²	1	2	yes	complemented
57	#10597342	C₂²	1	2	yes	complemented
58	#10597342	C₂²	1	2	yes	complemented
59	#10597340	C₂²	1	2	yes	—
60	#10597340	C₂²	1	2	yes	—
61	#10597340	C₂²	1	2	yes	—
62	#10597340	C₂²	1	2	yes	complemented
63	#10597339	C₂²	1	2	yes	—
64	#10597338	C₂²	1	2	yes	complemented
65	#10597338	C₂²	1	2	yes	complemented
66	C₄⋊C₄×D₁₉	C₂²	1	2	yes	complemented
67	C₄⋊C₄×D₁₉	C₂²	1	2	yes	complemented
68	#10597336	C₂²	1	2	yes	complemented
69	#10597335	C₂²	1	2	yes	complemented
70	#10597335	C₂²	1	2	yes	complemented
71	#10597335	C₂²	1	2	yes	complemented
72	#10597333	C₂²	1	2	yes	complemented
73	#10597332	C₂²	1	2	yes	complemented
74	#10597331	C₂²	1	2	yes	complemented
75	#10597329	C₂²	1	2	yes	—
76	#10597329	C₂²	1	2	yes	—
77	#10597329	C₂²	1	2	yes	—
78	#10597329	C₂²	1	2	yes	complemented
79	#10597328	C₂²	1	2	yes	—
80	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	—
81	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	complemented
82	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	complemented
83	C₂²⋊C₄×D₁₉	C₂²	1	2	yes	—
84	C₂²⋊C₄×D₁₉	C₂²	1	2	yes	complemented
85	C₂²⋊C₄×D₁₉	C₂²	1	2	yes	complemented
86	C₂²⋊C₄×D₁₉	C₂²	1	2	yes	complemented
87	#10597325	C₂²	1	2	yes	complemented
88	#10597325	C₂²	1	2	yes	complemented
89	#10597325	C₂²	1	2	yes	complemented
90	#10597324	C₂²	1	2	yes	complemented
91	#10597324	C₂²	1	2	yes	complemented
92	#10597323	C₂²	1	2	yes	complemented
93	#10597322	C₂²	1	2	yes	complemented
94	#10597322	C₂²	1	2	yes	complemented
95	#10597321	C₂²	1	1	yes	characteristic, complemented
96	C₄×D₇₆	C₂²	1	2	yes	—
97	C₄×D₇₆	C₂²	1	1	yes	characteristic, complemented
98	#10597318	C₂²	1	2	yes	complemented
99	#10597318	C₂²	1	2	yes	complemented
100	#10597318	C₂²	1	2	yes	complemented
101	#10597318	C₂²	1	2	yes	complemented
102	#10597318	C₂²	1	2	yes	complemented
103	#10597318	C₂²	1	2	yes	complemented
104	#10597316	C₂²	1	1	yes	characteristic, complemented
105	#10597316	C₂²	1	2	yes	complemented
106	C₄×Dic₃₈	C₂²	1	1	yes	characteristic, complemented
107	C₂³×D₁₉	C₂³	1	2	yes	—
108	C₂³×D₁₉	C₂³	1	1	yes	characteristic
109	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
110	C₂×D₄×C₁₉	C₂³	1	2	yes	—
111	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
112	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
113	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
114	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
115	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
116	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
117	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
118	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
119	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
120	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
121	C₂²×Dic₁₉	C₂³	1	2	yes	—
122	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
123	D₄×D₁₉	—	2	8	no	—
124	C₂×D₇₆	C₂³	1	2	yes	—
125	C₂×D₇₆	C₂³	1	1	yes	characteristic
126	C₂×C₄×D₁₉	—	2	4	no	—
127	C₂×C₄×D₁₉	C₂³	1	2	yes	—
128	C₂×C₄×D₁₉	C₂³	1	2	yes	—
129	C₂×C₄×D₁₉	C₂³	1	2	yes	—
130	C₂×C₄×D₁₉	C₂³	1	2	yes	—
131	C₂×C₄×D₁₉	C₂³	1	2	yes	—
132	C₂×C₄×D₁₉	C₂³	1	2	yes	—
133	C₂×C₄×D₁₉	C₂³	1	2	yes	—
134	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
135	C₂×Dic₃₈	C₂³	1	2	yes	—
136	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
137	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
138	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
139	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
140	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
141	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
142	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
143	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
144	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
145	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
146	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
147	C₄²×C₁₉	C₂³	1	1	yes	characteristic
148	C₄²×C₁₉	C₂³	1	1	yes	characteristic
149	C₄²×C₁₉	C₂³	1	1	yes	characteristic
150	C₄²×C₁₉	C₂³	1	1	yes	characteristic
151	C₄²×C₁₉	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	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
158	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
159	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
160	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
161	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
162	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
163	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
164	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
165	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
166	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
167	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
168	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
169	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
170	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
171	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
172	C₄⋊Dic₁₉	C₂³	1	2	yes	—
173	C₄⋊Dic₁₉	C₂³	1	2	yes	—
174	C₄⋊Dic₁₉	C₂³	1	2	yes	—
175	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
176	C₄⋊Dic₁₉	C₂³	1	2	yes	—
177	Dic₁₉⋊C₄	C₂³	1	2	yes	—
178	Dic₁₉⋊C₄	C₂³	1	2	yes	—
179	Dic₁₉⋊C₄	C₂³	1	2	yes	—
180	Dic₁₉⋊C₄	C₂³	1	2	yes	—
181	Dic₁₉⋊C₄	C₂³	1	2	yes	—
182	Dic₁₉⋊C₄	C₂³	1	2	yes	—
183	Dic₁₉⋊C₄	C₂³	1	2	yes	—
184	Dic₁₉⋊C₄	C₂³	1	2	yes	—
185	Dic₁₉⋊C₄	C₂³	1	2	yes	—
186	Dic₁₉⋊C₄	C₂³	1	2	yes	—
187	Dic₁₉⋊C₄	C₂³	1	2	yes	—
188	Dic₁₉⋊C₄	C₂³	1	2	yes	—
189	Dic₁₉⋊C₄	C₂³	1	2	yes	—
190	Dic₁₉⋊C₄	C₂³	1	2	yes	—
191	C₄×Dic₁₉	C₂³	1	2	yes	—
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	C₂³×C₁₉	C₂⁴	1	2	yes	—
197	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
198	C₂²×D₁₉	—	2	4	no	—
199	C₂²×D₁₉	—	4	1	no	—
200	C₂²×D₁₉	—	4	1	no	—
201	C₂²×D₁₉	—	4	2	no	—
202	C₂²×D₁₉	—	4	2	no	—
203	C₂²×D₁₉	#41	1	4	yes	—
204	C₂²×D₁₉	C₂⁴	1	2	yes	—
205	C₂²×D₁₉	C₂⁴	1	2	yes	—
206	Q₈×C₁₉	—	4	1	no	—
207	D₄×C₁₉	—	2	4	no	—
208	D₄×C₁₉	—	4	1	no	—
209	C₂×C₄×C₁₉	—	2	2	no	—
210	C₂×C₄×C₁₉	—	4	2	no	—
211	C₂×C₄×C₁₉	—	4	1	no	—
212	C₂×C₄×C₁₉	—	4	1	no	—
213	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
214	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
215	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
216	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
217	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
218	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
219	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
220	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
221	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
222	C₂²⋊D₁₉	—	2	4	no	—
223	C₂²⋊D₁₉	—	2	4	no	—
224	C₂²⋊D₁₉	—	4	2	no	—
225	C₂×Dic₁₉	—	2	2	no	—
226	C₂×Dic₁₉	—	4	2	no	—
227	C₂×Dic₁₉	—	4	1	no	—
228	C₂×Dic₁₉	—	4	1	no	—
229	C₂×Dic₁₉	C₂⁴	1	2	yes	—
230	C₂×Dic₁₉	C₂⁴	1	2	yes	—
231	C₂×Dic₁₉	C₂⁴	1	2	yes	—
232	C₂×Dic₁₉	C₂⁴	1	2	yes	—
233	C₂×Dic₁₉	C₂⁴	1	2	yes	—
234	C₂×Dic₁₉	C₂⁴	1	2	yes	—
235	D₇₆	—	2	4	no	—
236	D₇₆	—	4	1	no	—
237	C₄×D₁₉	—	2	4	no	—
238	C₄×D₁₉	—	2	4	no	—
239	C₄×D₁₉	—	2	4	no	—
240	C₄×D₁₉	—	4	2	no	—
241	C₄×D₁₉	—	4	2	no	—
242	C₄×D₁₉	—	4	2	no	—
243	C₄×D₁₉	—	4	2	no	—
244	Dic₃₈	—	4	2	no	—
245	Dic₃₈	—	4	1	no	—
246	#3491	—	19	1	no	maximal, Sylow
247	C₂²×C₁₉	—	2	1	no	—
248	C₂²×C₁₉	—	2	1	no	—
249	C₂²×C₁₉	—	2	2	no	—
250	C₂²×C₁₉	—	2	2	no	—
251	C₂²×C₁₉	—	2	2	no	—
252	C₂²×C₁₉	C₂×#41	1	2	yes	—
253	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
254	C₂×D₁₉	—	2	2	no	—
255	C₂×D₁₉	—	2	2	no	—
256	C₂×D₁₉	—	2	2	no	—
257	C₂×D₁₉	—	2	2	no	—
258	C₂×D₁₉	—	2	2	no	—
259	C₂×D₁₉	—	4	4	no	—
260	C₂×D₁₉	—	8	4	no	—
261	C₂×D₁₉	C₂×#41	1	4	yes	—
262	C₄×C₁₉	—	2	1	no	—
263	C₄×C₁₉	—	2	1	no	—
264	C₄×C₁₉	—	2	2	no	—
265	C₄×C₁₉	—	2	2	no	—
266	C₄×C₁₉	—	2	1	no	—
267	C₄×C₁₉	—	2	1	no	—
268	C₄×C₁₉	—	2	2	no	—
269	C₄×C₁₉	—	2	1	no	—
270	C₄×C₁₉	—	2	1	no	—
271	Dic₁₉	—	2	2	no	—
272	Dic₁₉	—	2	2	no	—
273	Dic₁₉	—	2	2	no	—
274	Dic₁₉	—	2	2	no	—
275	Dic₁₉	—	2	2	no	—
276	Dic₁₉	—	2	2	no	—
277	#552	—	19	2	no	—
278	#552	—	19	2	no	—
279	#552	—	19	2	no	—
280	#552	—	19	2	no	—
281	#551	—	19	2	no	—
282	#551	—	19	2	no	—
283	#551	—	19	2	no	—
284	#551	—	19	2	no	—
285	#543	—	19	1	no	—
286	#539	—	19	1	no	—
287	#539	—	19	1	no	—
288	#539	—	19	2	no	—
289	#534	—	19	1	no	—
290	#529	—	19	2	no	—
291	#529	—	19	1	no	—
292	#529	D₁₉	1	1	yes	characteristic, complemented
293	C₂×#123	—	19	2	no	—
294	#518	—	19	2	no	—
295	C₂×#117	—	19	1	no	—
296	C₂×C₁₉	—	2	2	no	—
297	C₂×C₁₉	—	4	2	no	—
298	C₂×C₁₉	C₂²×#41	1	1	yes	characteristic
299	C₂×C₁₉	#585	1	1	yes	characteristic
300	C₂×C₁₉	#585	1	1	yes	characteristic
301	D₁₉	—	2	4	no	—
302	D₁₉	—	4	2	no	—
303	C₂²×D₄	—	19	2	no	—
304	C₂³×C₄	—	19	1	no	—
305	#126	—	19	2	no	—
306	#126	—	19	2	no	—
307	#126	—	19	2	no	—
308	#126	—	19	2	no	—
309	#126	—	19	2	no	—
310	#126	—	19	2	no	—
311	#126	—	19	2	no	—
312	#126	C₂×D₁₉	1	2	yes	complemented
313	#125	—	19	2	no	—
314	#125	—	19	2	no	—
315	#125	—	19	2	no	—
316	#125	—	19	2	no	—
317	#125	—	19	1	no	—
318	#125	—	19	2	no	—
319	#125	C₂×D₁₉	1	1	yes	characteristic, complemented
320	#124	—	19	2	no	—
321	#124	—	19	1	no	—
322	#124	C₂×D₁₉	1	1	yes	characteristic, complemented
323	#123	—	19	2	no	—
324	#123	—	19	2	no	—
325	#123	—	19	2	no	—
326	#123	—	19	2	no	—
327	#123	—	19	2	no	—
328	#123	—	19	2	no	—
329	#123	—	19	2	no	—
330	#123	—	19	2	no	—
331	#123	—	19	2	no	—
332	#123	—	19	2	no	—
333	#123	—	19	2	no	—
334	#123	—	19	2	no	—
335	#123	—	19	2	no	—
336	#123	C₂×D₁₉	1	2	yes	complemented
337	C₂²⋊Q₈	—	19	2	no	—
338	C₂²⋊Q₈	—	19	2	no	—
339	C₂²⋊Q₈	—	19	1	no	—
340	C₂²⋊Q₈	—	19	2	no	—
341	C₂²⋊Q₈	—	19	2	no	—
342	C₂²⋊Q₈	—	19	2	no	—
343	C₂²⋊Q₈	—	19	2	no	—
344	C₂²⋊Q₈	—	19	2	no	—
345	C₂²⋊Q₈	—	19	2	no	—
346	C₂²⋊Q₈	—	19	2	no	—
347	C₂²⋊Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
348	#121	—	19	2	no	—
349	#121	—	19	1	no	—
350	#121	C₂×D₁₉	1	1	yes	characteristic
351	#120	—	19	2	no	—
352	#120	—	19	2	no	—
353	C₄×Q₈	—	19	2	no	—
354	C₄×Q₈	—	19	1	no	—
355	C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
356	C₄×D₄	—	19	2	no	—
357	C₄×D₄	—	19	2	no	—
358	C₄×D₄	—	19	2	no	—
359	C₄×D₄	—	19	2	no	—
360	C₄×D₄	—	19	2	no	—
361	C₄×D₄	—	19	2	no	—
362	C₄×D₄	—	19	2	no	—
363	C₄×D₄	—	19	2	no	—
364	C₄×D₄	—	19	1	no	—
365	C₄×D₄	C₂×D₁₉	1	2	yes	complemented
366	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic, complemented
367	#117	—	19	2	no	—
368	#117	—	19	2	no	—
369	#117	—	19	2	no	—
370	#117	—	19	2	no	—
371	#117	—	19	2	no	—
372	#117	—	19	2	no	—
373	#117	—	19	2	no	—
374	#117	—	19	2	no	—
375	#117	—	19	2	no	—
376	#117	C₂×D₁₉	1	2	yes	complemented
377	C₂×C₄⋊C₄	—	19	1	no	—
378	C₂×C₄⋊C₄	—	19	1	no	—
379	C₂×C₄⋊C₄	—	19	2	no	—
380	C₂×C₄⋊C₄	—	19	2	no	—
381	C₂×C₂²⋊C₄	—	19	1	no	—
382	C₂×C₂²⋊C₄	—	19	1	no	—
383	C₂×C₂²⋊C₄	—	19	2	no	—
384	C₂×C₂²⋊C₄	—	19	2	no	—
385	C₂×C₂²⋊C₄	—	19	2	no	—
386	C₂×C₂²⋊C₄	—	19	2	no	—
387	C₂×C₂²⋊C₄	—	19	2	no	—
388	C₂×C₄²	—	19	1	no	—
389	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic, complemented
390	C₁₉	#3491	1	1	yes	characteristic, complemented, Sylow
391	C₂⁴	—	19	1	no	—
392	C₂⁴	—	19	2	no	—
393	C₂×Q₈	—	19	2	no	—
394	C₂×Q₈	—	19	1	no	—
395	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
396	C₂×D₄	—	19	2	no	—
397	C₂×D₄	—	19	2	no	—
398	C₂×D₄	—	19	2	no	—
399	C₂×D₄	—	19	2	no	—
400	C₂×D₄	—	19	1	no	—
401	C₂×D₄	—	38	8	no	—
402	C₂×D₄	C₂²×D₁₉	1	2	yes	—
403	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
404	C₂²×C₄	—	19	1	no	—
405	C₂²×C₄	—	19	1	no	—
406	C₂²×C₄	—	19	1	no	—
407	C₂²×C₄	—	19	2	no	—
408	C₂²×C₄	—	19	2	no	—
409	C₂²×C₄	—	19	2	no	—
410	C₂²×C₄	—	19	2	no	—
411	C₂²×C₄	—	19	2	no	—
412	C₂²×C₄	—	19	2	no	—
413	C₂²×C₄	—	19	2	no	—
414	C₂²×C₄	—	19	2	no	—
415	C₂²×C₄	—	38	4	no	—
416	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
417	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
418	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
419	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
420	C₄⋊C₄	—	19	2	no	—
421	C₄⋊C₄	—	19	2	no	—
422	C₄⋊C₄	—	19	2	no	—
423	C₄⋊C₄	—	19	2	no	—
424	C₄⋊C₄	—	19	2	no	—
425	C₄⋊C₄	—	19	2	no	—
426	C₄⋊C₄	—	19	2	no	—
427	C₄⋊C₄	—	19	2	no	—
428	C₄⋊C₄	—	19	2	no	—
429	C₄⋊C₄	—	19	2	no	—
430	C₄⋊C₄	—	19	2	no	—
431	C₄⋊C₄	—	19	2	no	—
432	C₄⋊C₄	—	19	2	no	—
433	C₄⋊C₄	—	19	2	no	—
434	C₄⋊C₄	—	19	2	no	—
435	C₄⋊C₄	—	19	2	no	—
436	C₄⋊C₄	—	19	2	no	—
437	C₄⋊C₄	—	19	2	no	—
438	C₄⋊C₄	—	19	1	no	—
439	C₄⋊C₄	—	19	1	no	—
440	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
441	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
442	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
443	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
444	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
445	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
446	C₂²⋊C₄	—	19	2	no	—
447	C₂²⋊C₄	—	19	2	no	—
448	C₂²⋊C₄	—	19	2	no	—
449	C₂²⋊C₄	—	19	2	no	—
450	C₂²⋊C₄	—	19	2	no	—
451	C₂²⋊C₄	—	19	2	no	—
452	C₂²⋊C₄	—	19	2	no	—
453	C₂²⋊C₄	—	19	2	no	—
454	C₂²⋊C₄	—	19	2	no	—
455	C₂²⋊C₄	—	19	2	no	—
456	C₂²⋊C₄	—	19	2	no	—
457	C₂²⋊C₄	—	19	2	no	—
458	C₂²⋊C₄	—	19	2	no	—
459	C₂²⋊C₄	—	19	2	no	—
460	C₂²⋊C₄	—	19	2	no	—
461	C₂²⋊C₄	—	19	2	no	—
462	C₂²⋊C₄	—	19	2	no	—
463	C₂²⋊C₄	—	19	2	no	—
464	C₂²⋊C₄	—	19	2	no	—
465	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
466	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
467	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
468	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
469	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
470	C₄²	—	19	2	no	—
471	C₄²	—	19	2	no	—
472	C₄²	—	19	2	no	—
473	C₄²	—	19	2	no	—
474	C₄²	—	19	2	no	—
475	C₄²	C₂²×D₁₉	1	1	yes	characteristic
476	C₄²	C₂²×D₁₉	1	1	yes	characteristic
477	C₄²	C₂²×D₁₉	1	1	yes	characteristic
478	C₄²	C₂²×D₁₉	1	1	yes	characteristic
479	C₄²	C₂²×D₁₉	1	2	yes	—
480	C₂³	—	19	2	no	—
481	C₂³	—	19	4	no	—
482	C₂³	—	19	2	no	—
483	C₂³	—	38	4	no	—
484	C₂³	—	76	1	no	—
485	C₂³	—	76	1	no	—
486	C₂³	—	76	2	no	—
487	C₂³	—	76	2	no	—
488	C₂³	C₂³×D₁₉	1	2	yes	—
489	C₂³	C₂³×D₁₉	1	1	yes	characteristic
490	Q₈	—	4	1	no	—
491	Q₈	—	76	2	no	—
492	Q₈	—	76	1	no	—
493	D₄	—	2	4	no	—
494	D₄	—	4	1	no	—
495	D₄	—	38	4	no	—
496	D₄	—	38	4	no	—
497	D₄	—	38	4	no	—
498	D₄	—	76	1	no	—
499	D₄	—	76	2	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	4	1	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	19	2	no	—
505	C₂×C₄	—	19	2	no	—
506	C₂×C₄	—	19	2	no	—
507	C₂×C₄	—	19	2	no	—
508	C₂×C₄	—	19	2	no	—
509	C₂×C₄	—	19	2	no	—
510	C₂×C₄	—	38	4	no	—
511	C₂×C₄	—	38	4	no	—
512	C₂×C₄	—	38	4	no	—
513	C₂×C₄	—	38	2	no	—
514	C₂×C₄	—	76	2	no	—
515	C₂×C₄	—	76	2	no	—
516	C₂×C₄	—	76	2	no	—
517	C₂×C₄	—	76	2	no	—
518	C₂×C₄	—	76	1	no	—
519	C₂×C₄	—	76	2	no	—
520	C₂×C₄	—	76	1	no	—
521	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
522	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
523	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
524	C₂×C₄	C₂³×D₁₉	1	2	yes	—
525	C₂×C₄	C₂³×D₁₉	1	2	yes	—
526	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
527	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
528	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
529	C₂×C₄	C₂³×D₁₉	1	2	yes	—
530	C₂²	—	2	1	no	—
531	C₂²	—	2	1	no	—
532	C₂²	—	2	2	no	—
533	C₂²	—	2	2	no	—
534	C₂²	—	2	2	no	—
535	C₂²	—	19	4	no	—
536	C₂²	—	38	2	no	—
537	C₂²	—	38	2	no	—
538	C₂²	—	38	2	no	—
539	C₂²	—	38	2	no	—
540	C₂²	—	38	2	no	—
541	C₂²	—	76	4	no	—
542	C₂²	—	152	4	no	—
543	C₂²	#41×D₁₉	1	2	yes	—
544	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
545	C₄	—	2	1	no	—
546	C₄	—	2	1	no	—
547	C₄	—	2	2	no	—
548	C₄	—	2	1	no	—
549	C₄	—	2	1	no	—
550	C₄	—	2	2	no	—
551	C₄	—	2	1	no	—
552	C₄	—	2	1	no	—
553	C₄	—	2	2	no	—
554	C₄	—	38	2	no	—
555	C₄	—	38	2	no	—
556	C₄	—	38	2	no	—
557	C₄	—	38	2	no	—
558	C₄	—	38	2	no	—
559	C₄	—	38	2	no	—
560	C₂	—	2	2	no	—
561	C₂	—	4	2	no	—
562	C₂	—	38	4	no	—
563	C₂	—	76	2	no	—
564	C₂	C₂×#41×D₁₉	1	1	yes	characteristic
565	C₂	#11927380	1	1	yes	characteristic
566	C₂	#11927380	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Fitting	C₁₉×#529	C₂
prime radical	#11927102	C₂
hypercenter	#529	D₁₉
hypocenter	C₁₉	#3491
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ #529

Complements

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

N	H ≅ G/N	type
1. #11927235	C₂	semidirect
2. #11927233	C₂	semidirect
3. #11927230	C₂	semidirect
4. #11927226	C₂	semidirect
5. #11927224	C₂	semidirect
6. #11927223	C₂	semidirect
7. #11927219	C₂	semidirect
8. #11927218	C₂	semidirect
9. #11927169	C₂	semidirect
10. #11927143	C₂	semidirect
11. #11927139	C₂	semidirect
12. #11927136	C₂	semidirect
14. #11927078	C₂	semidirect
15. #11927071	C₂	semidirect
16. #123×D₁₉	C₂	semidirect
17. #11927016	C₂	semidirect
18. C₂×#10597318	C₂	semidirect
19. C₁₉×#529	C₂	semidirect
22. C₁₉×#126	C₂²	semidirect
23. C₁₉×#125	C₂²	semidirect
24. C₁₉×#124	C₂²	semidirect
25. C₁₉×#123	C₂²	semidirect
26. C₁₉×C₂²⋊Q₈	C₂²	semidirect
28. C₄×Q₈×C₁₉	C₂²	semidirect
29. C₄×D₄×C₁₉	C₂²	semidirect
30. C₄×D₄×C₁₉	C₂²	semidirect
31. C₁₉×#117	C₂²	semidirect
32. C₂×C₄²×C₁₉	C₂²	semidirect
33. #10597392	C₂²	semidirect
34. #10597392	C₂²	semidirect
37. #10597381	C₂²	semidirect
38. #10597381	C₂²	semidirect
39. D₄×Dic₁₉	C₂²	semidirect
41. #10597375	C₂²	semidirect
42. #10597375	C₂²	semidirect
44. C₄×C₂²⋊D₁₉	C₂²	semidirect
47. C₂×(C₂×D₁₉)⋊C₄	C₂²	semidirect
48. #10597370	C₂²	semidirect
49. #10597370	C₂²	semidirect
50. C₂×Dic₁₉⋊C₄	C₂²	semidirect
51. C₂×Dic₁₉⋊C₄	C₂²	semidirect
52. C₂×C₄×Dic₁₉	C₂²	semidirect
53. #10597344	C₂²	semidirect
54. #10597344	C₂²	semidirect
55. #10597343	C₂²	semidirect
56. #10597342	C₂²	semidirect
57. #10597342	C₂²	semidirect
58. #10597342	C₂²	semidirect
62. #10597340	C₂²	semidirect
64. #10597338	C₂²	semidirect
65. #10597338	C₂²	semidirect
66. C₄⋊C₄×D₁₉	C₂²	semidirect
67. C₄⋊C₄×D₁₉	C₂²	semidirect
68. #10597336	C₂²	semidirect
69. #10597335	C₂²	semidirect
70. #10597335	C₂²	semidirect
71. #10597335	C₂²	semidirect
72. #10597333	C₂²	semidirect
73. #10597332	C₂²	semidirect
74. #10597331	C₂²	semidirect
78. #10597329	C₂²	semidirect
81. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
82. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
84. C₂²⋊C₄×D₁₉	C₂²	semidirect
85. C₂²⋊C₄×D₁₉	C₂²	semidirect
86. C₂²⋊C₄×D₁₉	C₂²	semidirect
87. #10597325	C₂²	semidirect
88. #10597325	C₂²	semidirect
89. #10597325	C₂²	semidirect
90. #10597324	C₂²	semidirect
91. #10597324	C₂²	semidirect
92. #10597323	C₂²	semidirect
93. #10597322	C₂²	semidirect
94. #10597322	C₂²	semidirect
95. #10597321	C₂²	semidirect
97. C₄×D₇₆	C₂²	semidirect
98. #10597318	C₂²	semidirect
99. #10597318	C₂²	semidirect
100. #10597318	C₂²	semidirect
101. #10597318	C₂²	semidirect
102. #10597318	C₂²	semidirect
103. #10597318	C₂²	semidirect
104. #10597316	C₂²	semidirect
105. #10597316	C₂²	semidirect
106. C₄×Dic₃₈	C₂²	semidirect
292. #529	D₁₉	semidirect
312. #126	C₂×D₁₉	semidirect
319. #125	C₂×D₁₉	semidirect
322. #124	C₂×D₁₉	semidirect
336. #123	C₂×D₁₉	semidirect
347. C₂²⋊Q₈	C₂×D₁₉	semidirect
355. C₄×Q₈	C₂×D₁₉	semidirect
365. C₄×D₄	C₂×D₁₉	semidirect
366. C₄×D₄	C₂×D₁₉	semidirect
376. #117	C₂×D₁₉	semidirect
389. C₂×C₄²	C₂×D₁₉	semidirect
390. C₁₉	#3491	semidirect

Maximal subgroups

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

subgroup	index
#11927235	2
#11927233	2
#11927230	2
#11927226	2
#11927224	2
#11927223	2
#11927219	2
#11927218	2
#11927169	2
#11927143	2
#11927139	2
#11927136	2
#11927102	2
#11927078	2
#11927071	2
#123×D₁₉	2
#11927016	2
C₂×#10597318	2
C₁₉×#529	2
#3491	19