Subgroups — #14578263

Order 2432.

936 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927293	C₂	1	2	yes	maximal, complemented
2	#11927293	C₂	1	2	yes	maximal, complemented
3	#11927266	C₂	1	2	yes	maximal, complemented
4	#11927248	C₂	1	2	yes	maximal, complemented
5	#11927235	C₂	1	2	yes	maximal, complemented
6	#11927227	C₂	1	2	yes	maximal, complemented
7	#11927221	C₂	1	2	yes	maximal, complemented
8	#11927218	C₂	1	2	yes	maximal, complemented
9	#11927173	C₂	1	1	yes	maximal, characteristic, complemented
10	#11927169	C₂	1	1	yes	maximal, characteristic, complemented
11	#11927166	C₂	1	2	yes	maximal, complemented
12	#11927153	C₂	1	2	yes	maximal, complemented
13	#11927152	C₂	1	2	yes	maximal, complemented
14	#11927143	C₂	1	1	yes	maximal, characteristic, complemented
15	#11927142	C₂	1	2	yes	maximal, complemented
16	#11927134	C₂	1	1	yes	maximal, characteristic
17	#11927078	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#10597322	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₉×#533	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
21	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
22	C₁₉×#125	C₂²	1	2	yes	complemented
23	C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
24	C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
25	C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
26	C₄×Q₈×C₁₉	C₂²	1	2	yes	complemented
27	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
28	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
29	C₁₉×#117	C₂²	1	2	yes	—
30	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
31	#10597393	C₂²	1	2	yes	—
32	#10597393	C₂²	1	2	yes	—
33	#10597392	C₂²	1	2	yes	—
34	#10597392	C₂²	1	2	yes	—
35	#10597392	C₂²	1	2	yes	complemented
36	#10597392	C₂²	1	2	yes	complemented
37	#10597390	C₂²	1	2	yes	complemented
38	#10597390	C₂²	1	2	yes	complemented
39	#10597376	C₂²	1	1	yes	characteristic
40	#10597375	C₂²	1	2	yes	—
41	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	—
42	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	1	yes	characteristic
43	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	1	yes	characteristic
44	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	1	yes	characteristic
45	#10597370	C₂²	1	1	yes	characteristic
46	C₂×Dic₁₉⋊C₄	C₂²	1	1	yes	characteristic
47	C₂×Dic₁₉⋊C₄	C₂²	1	1	yes	characteristic
48	C₂×Dic₁₉⋊C₄	C₂²	1	1	yes	characteristic
49	#10597344	C₂²	1	2	yes	—
50	#10597344	C₂²	1	2	yes	—
51	#10597344	C₂²	1	2	yes	—
52	#10597344	C₂²	1	2	yes	—
53	#10597344	C₂²	1	2	yes	complemented
54	#10597344	C₂²	1	2	yes	complemented
55	#10597343	C₂²	1	2	yes	—
56	#10597342	C₂²	1	2	yes	—
57	#10597342	C₂²	1	2	yes	—
58	#10597342	C₂²	1	2	yes	—
59	#10597342	C₂²	1	2	yes	complemented
60	#10597342	C₂²	1	2	yes	complemented
61	#10597342	C₂²	1	2	yes	complemented
62	#10597341	C₂²	1	2	yes	—
63	#10597340	C₂²	1	2	yes	—
64	#10597340	C₂²	1	2	yes	—
65	#10597340	C₂²	1	2	yes	—
66	#10597340	C₂²	1	2	yes	—
67	#10597340	C₂²	1	2	yes	—
68	#10597340	C₂²	1	2	yes	complemented
69	#10597339	C₂²	1	2	yes	—
70	#10597338	C₂²	1	2	yes	—
71	C₄⋊C₄×D₁₉	C₂²	1	2	yes	complemented
72	#10597336	C₂²	1	2	yes	complemented
73	#10597335	C₂²	1	2	yes	complemented
74	#10597335	C₂²	1	2	yes	complemented
75	#10597335	C₂²	1	2	yes	complemented
76	#10597335	C₂²	1	2	yes	complemented
77	#10597335	C₂²	1	2	yes	complemented
78	#10597335	C₂²	1	2	yes	complemented
79	#10597334	C₂²	1	2	yes	complemented
80	#10597333	C₂²	1	2	yes	complemented
81	#10597332	C₂²	1	2	yes	—
82	#10597328	C₂²	1	2	yes	—
83	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	—
84	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	—
85	C₂²⋊C₄×D₁₉	C₂²	1	2	yes	—
86	#10597324	C₂²	1	2	yes	—
87	#10597324	C₂²	1	2	yes	—
88	#10597323	C₂²	1	2	yes	—
89	#10597322	C₂²	1	2	yes	—
90	#10597322	C₂²	1	2	yes	—
91	#10597322	C₂²	1	2	yes	—
92	#10597322	C₂²	1	2	yes	—
93	#10597322	C₂²	1	2	yes	—
94	#10597322	C₂²	1	2	yes	complemented
95	#10597322	C₂²	1	2	yes	complemented
96	#10597321	C₂²	1	2	yes	—
97	#10597321	C₂²	1	1	yes	characteristic, complemented
98	C₄×D₇₆	C₂²	1	2	yes	—
99	C₄×D₇₆	C₂²	1	1	yes	characteristic, complemented
100	#10597318	C₂²	1	2	yes	—
101	#10597318	C₂²	1	2	yes	complemented
102	#10597318	C₂²	1	2	yes	complemented
103	#10597316	C₂²	1	1	yes	characteristic, complemented
104	#10597316	C₂²	1	2	yes	complemented
105	C₄×Dic₃₈	C₂²	1	1	yes	characteristic, complemented
106	C₄×Dic₃₈	C₂²	1	2	yes	complemented
107	C₂³×D₁₉	C₂³	1	1	yes	characteristic
108	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
109	C₂×Q₈×C₁₉	C₂³	1	2	yes	—
110	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
111	C₂²×C₄×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	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
115	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
116	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
117	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
118	C₂×D₇₆	C₂³	1	1	yes	characteristic
119	C₂×D₇₆	C₂³	1	2	yes	—
120	C₂×D₇₆	C₂³	1	2	yes	—
121	C₂×C₄×D₁₉	C₂³	1	2	yes	—
122	C₂×C₄×D₁₉	C₂³	1	2	yes	—
123	C₂×C₄×D₁₉	C₂³	1	2	yes	—
124	C₂×C₄×D₁₉	C₂³	1	2	yes	—
125	C₂×C₄×D₁₉	C₂³	1	2	yes	—
126	C₂×Dic₃₈	C₂³	1	2	yes	—
127	C₂×Dic₃₈	C₂³	1	2	yes	—
128	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
129	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
130	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
131	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
132	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
133	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
134	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
135	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
136	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
137	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
138	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
139	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
140	C₄²×C₁₉	C₂³	1	1	yes	characteristic
141	C₄²×C₁₉	C₂³	1	1	yes	characteristic
142	C₄²×C₁₉	C₂³	1	1	yes	characteristic
143	C₄²×C₁₉	C₂³	1	1	yes	characteristic
144	C₄²×C₁₉	C₂³	1	2	yes	—
145	C₄²×C₁₉	C₂³	1	2	yes	—
146	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
147	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
148	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
149	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
150	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
151	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
152	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
153	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
154	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
155	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
156	(C₂×D₁₉)⋊C₄	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	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
166	C₄⋊Dic₁₉	C₂³	1	2	yes	—
167	C₄⋊Dic₁₉	C₂³	1	2	yes	—
168	C₄⋊Dic₁₉	C₂³	1	2	yes	—
169	C₄⋊Dic₁₉	C₂³	1	2	yes	—
170	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
171	Dic₁₉⋊C₄	C₂³	1	2	yes	—
172	Dic₁₉⋊C₄	C₂³	1	2	yes	—
173	Dic₁₉⋊C₄	C₂³	1	2	yes	—
174	Dic₁₉⋊C₄	C₂³	1	2	yes	—
175	Dic₁₉⋊C₄	C₂³	1	2	yes	—
176	Dic₁₉⋊C₄	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	C₄×Dic₁₉	C₂³	1	2	yes	—
190	C₄×Dic₁₉	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	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
195	C₂²×D₁₉	—	2	2	no	—
196	C₂²×D₁₉	—	4	1	no	—
197	C₂²×D₁₉	—	4	1	no	—
198	C₂²×D₁₉	C₂⁴	1	2	yes	—
199	C₂²×D₁₉	C₂⁴	1	2	yes	—
200	Q₈×C₁₉	—	4	2	no	—
201	Q₈×C₁₉	—	4	1	no	—
202	Q₈×C₁₉	—	4	1	no	—
203	C₂×C₄×C₁₉	—	2	2	no	—
204	C₂×C₄×C₁₉	—	4	1	no	—
205	C₂×C₄×C₁₉	—	4	1	no	—
206	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
207	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
208	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
209	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
210	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
211	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
212	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
213	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
214	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
215	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
216	C₂²⋊D₁₉	—	2	4	no	—
217	C₂×Dic₁₉	—	2	2	no	—
218	C₂×Dic₁₉	—	4	1	no	—
219	C₂×Dic₁₉	—	4	1	no	—
220	C₂×Dic₁₉	C₂⁴	1	2	yes	—
221	C₂×Dic₁₉	C₂⁴	1	2	yes	—
222	C₂×Dic₁₉	C₂⁴	1	2	yes	—
223	C₂×Dic₁₉	C₂⁴	1	2	yes	—
224	C₂×Dic₁₉	C₂⁴	1	2	yes	—
225	C₂×Dic₁₉	C₂⁴	1	2	yes	—
226	D₇₆	—	4	1	no	—
227	D₇₆	—	4	2	no	—
228	D₇₆	—	4	2	no	—
229	C₄×D₁₉	—	4	2	no	—
230	C₄×D₁₉	—	4	2	no	—
231	C₄×D₁₉	—	4	2	no	—
232	C₄×D₁₉	—	4	2	no	—
233	C₄×D₁₉	—	4	2	no	—
234	Dic₃₈	—	4	1	no	—
235	Dic₃₈	—	4	2	no	—
236	Dic₃₈	—	4	2	no	—
237	#3564	—	19	1	no	maximal, Sylow
238	C₂²×C₁₉	—	2	1	no	—
239	C₂²×C₁₉	—	2	1	no	—
240	C₂²×C₁₉	2₋¹⁺⁴	1	2	yes	—
241	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
242	C₂×D₁₉	—	2	2	no	—
243	C₂×D₁₉	—	2	2	no	—
244	C₂×D₁₉	—	2	2	no	—
245	C₂×D₁₉	—	2	2	no	—
246	C₂×D₁₉	—	2	2	no	—
247	C₂×D₁₉	—	2	2	no	—
248	C₂×D₁₉	—	8	2	no	—
249	C₄×C₁₉	—	2	1	no	—
250	C₄×C₁₉	—	2	1	no	—
251	C₄×C₁₉	—	2	2	no	—
252	C₄×C₁₉	—	2	1	no	—
253	C₄×C₁₉	—	2	2	no	—
254	C₄×C₁₉	—	2	1	no	—
255	C₄×C₁₉	—	2	2	no	—
256	C₄×C₁₉	—	2	2	no	—
257	C₄×C₁₉	—	2	1	no	—
258	C₄×C₁₉	—	2	1	no	—
259	Dic₁₉	—	2	2	no	—
260	Dic₁₉	—	2	2	no	—
261	Dic₁₉	—	2	2	no	—
262	Dic₁₉	—	2	2	no	—
263	Dic₁₉	—	2	2	no	—
264	Dic₁₉	—	2	2	no	—
265	#563	—	19	2	no	—
266	#563	—	19	2	no	—
267	#556	—	19	2	no	—
268	#554	—	19	2	no	—
269	#552	—	19	2	no	—
270	#552	—	19	2	no	—
271	#551	—	19	2	no	—
272	#551	—	19	2	no	—
273	#544	—	19	1	no	—
274	#543	—	19	1	no	—
275	#542	—	19	2	no	—
276	#541	—	19	2	no	—
277	#541	—	19	2	no	—
278	#539	—	19	2	no	—
279	#539	—	19	1	no	—
280	#538	—	19	1	no	—
281	#533	D₁₉	1	1	yes	characteristic, complemented
282	#529	—	19	1	no	—
283	C₂×#126	—	19	1	no	—
284	C₂×C₁₉	—	2	2	no	—
285	C₂×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
286	C₂×C₁₉	#585	1	1	yes	characteristic
287	C₂×C₁₉	#585	1	1	yes	characteristic
288	D₁₉	—	4	2	no	—
289	D₁₉	—	4	2	no	—
290	C₄⋊Q₈	—	19	2	no	—
291	C₄⋊Q₈	—	19	2	no	—
292	C₄⋊Q₈	—	19	2	no	—
293	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
294	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
295	#126	—	19	2	no	—
296	#126	—	19	2	no	—
297	#126	—	19	2	no	—
298	#126	—	19	2	no	—
299	#126	—	19	2	no	—
300	#126	—	19	2	no	—
301	#126	—	19	2	no	—
302	#126	—	19	2	no	—
303	#126	—	19	2	no	—
304	#126	—	19	2	no	—
305	#126	—	19	2	no	—
306	#126	—	19	2	no	—
307	#126	—	19	2	no	—
308	#125	—	19	2	no	—
309	#125	—	19	2	no	—
310	#125	—	19	2	no	—
311	#125	—	19	2	no	—
312	#125	—	19	2	no	—
313	#125	—	19	2	no	—
314	#125	—	19	2	no	—
315	#125	—	19	1	no	—
316	#125	—	19	2	no	—
317	#125	C₂×D₁₉	1	2	yes	complemented
318	#124	—	19	2	no	—
319	#124	—	19	2	no	—
320	#124	—	19	1	no	—
321	#124	—	19	2	no	—
322	#123	—	19	2	no	—
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	C₂²⋊Q₈	—	19	2	no	—
331	C₂²⋊Q₈	—	19	2	no	—
332	C₂²⋊Q₈	—	19	2	no	—
333	C₂²⋊Q₈	—	19	2	no	—
334	C₂²⋊Q₈	—	19	1	no	—
335	C₂²⋊Q₈	—	19	2	no	—
336	C₂²⋊Q₈	—	19	2	no	—
337	C₂²⋊Q₈	—	19	2	no	—
338	C₂²⋊Q₈	—	19	2	no	—
339	C₂²⋊Q₈	—	19	2	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	C₂×D₁₉	1	1	yes	characteristic
345	C₂²⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
346	C₂²⋊Q₈	C₂×D₁₉	1	2	yes	—
347	#121	—	19	1	no	—
348	#121	—	19	2	no	—
349	#120	—	19	2	no	—
350	C₄×Q₈	—	19	2	no	—
351	C₄×Q₈	—	19	1	no	—
352	C₄×Q₈	—	19	2	no	—
353	C₄×Q₈	C₂×D₁₉	1	2	yes	complemented
354	C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
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	1	no	—
361	C₄×D₄	—	19	2	no	—
362	#117	—	19	2	no	—
363	#117	—	19	2	no	—
364	#117	—	19	2	no	—
365	#117	—	19	2	no	—
366	#117	—	19	2	no	—
367	#117	C₂×D₁₉	1	2	yes	—
368	C₂×C₄⋊C₄	—	19	1	no	—
369	C₂×C₄⋊C₄	—	19	1	no	—
370	C₂×C₄⋊C₄	—	19	1	no	—
371	C₂×C₄⋊C₄	—	19	2	no	—
372	C₂×C₂²⋊C₄	—	19	1	no	—
373	C₂×C₂²⋊C₄	—	19	1	no	—
374	C₂×C₂²⋊C₄	—	19	1	no	—
375	C₂×C₂²⋊C₄	—	19	2	no	—
376	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
377	C₁₉	#3564	1	1	yes	characteristic, complemented, Sylow
378	C₂⁴	—	19	1	no	—
379	C₂×Q₈	—	19	2	no	—
380	C₂×Q₈	—	19	1	no	—
381	C₂×Q₈	—	19	2	no	—
382	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
383	C₂×Q₈	C₂²×D₁₉	1	2	yes	—
384	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
385	C₂×D₄	—	19	2	no	—
386	C₂×D₄	—	19	2	no	—
387	C₂×D₄	—	19	2	no	—
388	C₂×D₄	—	19	1	no	—
389	C₂²×C₄	—	19	1	no	—
390	C₂²×C₄	—	19	1	no	—
391	C₂²×C₄	—	19	1	no	—
392	C₂²×C₄	—	19	2	no	—
393	C₂²×C₄	—	19	2	no	—
394	C₂²×C₄	—	19	2	no	—
395	C₂²×C₄	—	19	2	no	—
396	C₂²×C₄	—	19	2	no	—
397	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
398	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
399	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
400	C₄⋊C₄	—	19	2	no	—
401	C₄⋊C₄	—	19	2	no	—
402	C₄⋊C₄	—	19	2	no	—
403	C₄⋊C₄	—	19	2	no	—
404	C₄⋊C₄	—	19	2	no	—
405	C₄⋊C₄	—	19	2	no	—
406	C₄⋊C₄	—	19	2	no	—
407	C₄⋊C₄	—	19	2	no	—
408	C₄⋊C₄	—	19	2	no	—
409	C₄⋊C₄	—	19	2	no	—
410	C₄⋊C₄	—	19	2	no	—
411	C₄⋊C₄	—	19	2	no	—
412	C₄⋊C₄	—	19	2	no	—
413	C₄⋊C₄	—	19	2	no	—
414	C₄⋊C₄	—	19	2	no	—
415	C₄⋊C₄	—	19	2	no	—
416	C₄⋊C₄	—	19	2	no	—
417	C₄⋊C₄	—	19	2	no	—
418	C₄⋊C₄	—	19	2	no	—
419	C₄⋊C₄	—	19	2	no	—
420	C₄⋊C₄	—	19	1	no	—
421	C₄⋊C₄	—	19	2	no	—
422	C₄⋊C₄	—	19	1	no	—
423	C₄⋊C₄	—	19	2	no	—
424	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
425	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
426	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
427	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
428	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
429	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
430	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
431	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
432	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
433	C₂²⋊C₄	—	19	2	no	—
434	C₂²⋊C₄	—	19	2	no	—
435	C₂²⋊C₄	—	19	2	no	—
436	C₂²⋊C₄	—	19	2	no	—
437	C₂²⋊C₄	—	19	2	no	—
438	C₂²⋊C₄	—	19	2	no	—
439	C₂²⋊C₄	—	19	2	no	—
440	C₂²⋊C₄	—	19	2	no	—
441	C₂²⋊C₄	—	19	2	no	—
442	C₂²⋊C₄	—	19	2	no	—
443	C₂²⋊C₄	—	19	2	no	—
444	C₂²⋊C₄	—	19	2	no	—
445	C₂²⋊C₄	—	19	2	no	—
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	C₂²×D₁₉	1	2	yes	—
453	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
454	C₄²	—	19	2	no	—
455	C₄²	—	19	2	no	—
456	C₄²	—	19	2	no	—
457	C₄²	—	19	2	no	—
458	C₄²	—	19	2	no	—
459	C₄²	C₂²×D₁₉	1	1	yes	characteristic
460	C₄²	C₂²×D₁₉	1	1	yes	characteristic
461	C₄²	C₂²×D₁₉	1	1	yes	characteristic
462	C₄²	C₂²×D₁₉	1	1	yes	characteristic
463	C₄²	C₂²×D₁₉	1	2	yes	—
464	C₄²	C₂²×D₁₉	1	2	yes	—
465	C₂³	—	19	2	no	—
466	C₂³	—	19	2	no	—
467	C₂³	—	38	2	no	—
468	C₂³	—	76	1	no	—
469	C₂³	—	76	1	no	—
470	C₂³	C₂³×D₁₉	1	1	yes	characteristic
471	Q₈	—	4	1	no	—
472	Q₈	—	4	2	no	—
473	Q₈	—	4	1	no	—
474	Q₈	—	76	1	no	—
475	Q₈	—	76	2	no	—
476	Q₈	—	76	2	no	—
477	D₄	—	38	4	no	—
478	D₄	—	76	1	no	—
479	D₄	—	76	2	no	—
480	D₄	—	76	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	4	1	no	—
483	C₂×C₄	—	4	1	no	—
484	C₂×C₄	—	19	2	no	—
485	C₂×C₄	—	19	2	no	—
486	C₂×C₄	—	19	2	no	—
487	C₂×C₄	—	19	2	no	—
488	C₂×C₄	—	19	2	no	—
489	C₂×C₄	—	19	2	no	—
490	C₂×C₄	—	38	2	no	—
491	C₂×C₄	—	76	2	no	—
492	C₂×C₄	—	76	2	no	—
493	C₂×C₄	—	76	2	no	—
494	C₂×C₄	—	76	2	no	—
495	C₂×C₄	—	76	2	no	—
496	C₂×C₄	—	76	1	no	—
497	C₂×C₄	—	76	1	no	—
498	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
499	C₂×C₄	C₂³×D₁₉	1	2	yes	—
500	C₂×C₄	C₂³×D₁₉	1	2	yes	—
501	C₂×C₄	C₂³×D₁₉	1	2	yes	—
502	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
503	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
504	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
505	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
506	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
507	C₂×C₄	C₂³×D₁₉	1	2	yes	—
508	C₂²	—	2	1	no	—
509	C₂²	—	2	1	no	—
510	C₂²	—	38	2	no	—
511	C₂²	—	38	2	no	—
512	C₂²	—	38	2	no	—
513	C₂²	—	38	2	no	—
514	C₂²	—	38	2	no	—
515	C₂²	—	38	2	no	—
516	C₂²	—	152	2	no	—
517	C₂²	#10597433	1	2	yes	—
518	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
519	C₄	—	2	1	no	—
520	C₄	—	2	1	no	—
521	C₄	—	2	1	no	—
522	C₄	—	2	1	no	—
523	C₄	—	2	1	no	—
524	C₄	—	2	1	no	—
525	C₄	—	2	2	no	—
526	C₄	—	2	2	no	—
527	C₄	—	2	2	no	—
528	C₄	—	2	2	no	—
529	C₄	—	38	2	no	—
530	C₄	—	38	2	no	—
531	C₄	—	38	2	no	—
532	C₄	—	38	2	no	—
533	C₄	—	38	2	no	—
534	C₄	—	38	2	no	—
535	C₂	—	2	2	no	—
536	C₂	—	76	2	no	—
537	C₂	—	76	2	no	—
538	C₂	C₂×#10597433	1	1	yes	characteristic
539	C₂	#11927380	1	1	yes	characteristic
540	C₂	#11927380	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Fitting	C₁₉×#533	C₂
prime radical	#11927134	C₂
hypercenter	#533	D₁₉
hypocenter	C₁₉	#3564
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ #533

Complements

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

N	H ≅ G/N	type
1. #11927293	C₂	semidirect
2. #11927293	C₂	semidirect
3. #11927266	C₂	semidirect
4. #11927248	C₂	semidirect
5. #11927235	C₂	semidirect
6. #11927227	C₂	semidirect
7. #11927221	C₂	semidirect
8. #11927218	C₂	semidirect
9. #11927173	C₂	semidirect
10. #11927169	C₂	semidirect
11. #11927166	C₂	semidirect
12. #11927153	C₂	semidirect
13. #11927152	C₂	semidirect
14. #11927143	C₂	semidirect
15. #11927142	C₂	semidirect
17. #11927078	C₂	semidirect
18. C₂×#10597322	C₂	semidirect
19. C₁₉×#533	C₂	semidirect
20. C₁₉×C₄⋊Q₈	C₂²	semidirect
21. C₁₉×C₄⋊Q₈	C₂²	semidirect
22. C₁₉×#125	C₂²	semidirect
26. C₄×Q₈×C₁₉	C₂²	semidirect
27. C₄×Q₈×C₁₉	C₂²	semidirect
28. C₄×Q₈×C₁₉	C₂²	semidirect
35. #10597392	C₂²	semidirect
36. #10597392	C₂²	semidirect
37. #10597390	C₂²	semidirect
38. #10597390	C₂²	semidirect
53. #10597344	C₂²	semidirect
54. #10597344	C₂²	semidirect
59. #10597342	C₂²	semidirect
60. #10597342	C₂²	semidirect
61. #10597342	C₂²	semidirect
68. #10597340	C₂²	semidirect
71. C₄⋊C₄×D₁₉	C₂²	semidirect
72. #10597336	C₂²	semidirect
73. #10597335	C₂²	semidirect
74. #10597335	C₂²	semidirect
75. #10597335	C₂²	semidirect
76. #10597335	C₂²	semidirect
77. #10597335	C₂²	semidirect
78. #10597335	C₂²	semidirect
79. #10597334	C₂²	semidirect
80. #10597333	C₂²	semidirect
94. #10597322	C₂²	semidirect
95. #10597322	C₂²	semidirect
97. #10597321	C₂²	semidirect
99. C₄×D₇₆	C₂²	semidirect
101. #10597318	C₂²	semidirect
102. #10597318	C₂²	semidirect
103. #10597316	C₂²	semidirect
104. #10597316	C₂²	semidirect
105. C₄×Dic₃₈	C₂²	semidirect
106. C₄×Dic₃₈	C₂²	semidirect
281. #533	D₁₉	semidirect
293. C₄⋊Q₈	C₂×D₁₉	semidirect
294. C₄⋊Q₈	C₂×D₁₉	semidirect
317. #125	C₂×D₁₉	semidirect
353. C₄×Q₈	C₂×D₁₉	semidirect
354. C₄×Q₈	C₂×D₁₉	semidirect
355. C₄×Q₈	C₂×D₁₉	semidirect
377. C₁₉	#3564	semidirect

Maximal subgroups

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

subgroup	index
#11927293	2
#11927266	2
#11927248	2
#11927235	2
#11927227	2
#11927221	2
#11927218	2
#11927173	2
#11927169	2
#11927166	2
#11927153	2
#11927152	2
#11927143	2
#11927142	2
#11927134	2
#11927078	2
C₂×#10597322	2
C₁₉×#533	2
#3564	19