Subgroups — #14578331

Order 2432.

958 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927298	C₂	1	1	yes	maximal, characteristic, complemented
2	#11927298	C₂	1	1	yes	maximal, characteristic, complemented
3	#11927294	C₂	1	1	yes	maximal, characteristic, complemented
4	#11927286	C₂	1	1	yes	maximal, characteristic, complemented
5	#11927266	C₂	1	2	yes	maximal, complemented
6	#11927262	C₂	1	2	yes	maximal, complemented
7	#11927261	C₂	1	2	yes	maximal, complemented
8	#11927223	C₂	1	2	yes	maximal, complemented
9	#11927219	C₂	1	2	yes	maximal, complemented
10	#11927218	C₂	1	2	yes	maximal, complemented
11	#11927164	C₂	1	2	yes	maximal, complemented
12	#11927162	C₂	1	2	yes	maximal, complemented
13	#11927159	C₂	1	2	yes	maximal, complemented
14	#11927130	C₂	1	2	yes	maximal, complemented
15	#11927127	C₂	1	2	yes	maximal, complemented
16	#11927126	C₂	1	2	yes	maximal, complemented
17	#11927078	C₂	1	1	yes	maximal, characteristic, complemented
18	#11927078	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₉×#529	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₉×#126	C₂²	1	2	yes	complemented
21	C₁₉×#125	C₂²	1	1	yes	characteristic, complemented
22	C₁₉×#124	C₂²	1	1	yes	characteristic
23	C₁₉×#123	C₂²	1	2	yes	complemented
24	C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
25	C₁₉×#121	C₂²	1	1	yes	characteristic
26	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
27	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
28	C₄×D₄×C₁₉	C₂²	1	2	yes	complemented
29	C₁₉×#117	C₂²	1	2	yes	complemented
30	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic, complemented
31	#10597393	C₂²	1	2	yes	—
32	#10597390	C₂²	1	2	yes	complemented
33	#10597385	C₂²	1	2	yes	—
34	#10597384	C₂²	1	2	yes	—
35	#10597383	C₂²	1	2	yes	—
36	#10597383	C₂²	1	2	yes	complemented
37	#10597382	C₂²	1	2	yes	complemented
38	#10597381	C₂²	1	2	yes	—
39	#10597376	C₂²	1	1	yes	characteristic
40	#10597376	C₂²	1	1	yes	characteristic
41	#10597375	C₂²	1	2	yes	—
42	#10597375	C₂²	1	2	yes	complemented
43	#10597375	C₂²	1	2	yes	complemented
44	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	—
45	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	complemented
46	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	complemented
47	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	2	yes	complemented
48	#10597370	C₂²	1	1	yes	characteristic, complemented
49	#10597370	C₂²	1	1	yes	characteristic, complemented
50	#10597370	C₂²	1	2	yes	complemented
51	#10597344	C₂²	1	2	yes	complemented
52	#10597344	C₂²	1	2	yes	complemented
53	#10597344	C₂²	1	2	yes	complemented
54	#10597344	C₂²	1	2	yes	complemented
55	#10597344	C₂²	1	2	yes	complemented
56	#10597343	C₂²	1	2	yes	complemented
57	#10597343	C₂²	1	2	yes	complemented
58	#10597342	C₂²	1	2	yes	complemented
59	#10597342	C₂²	1	2	yes	complemented
60	#10597342	C₂²	1	2	yes	complemented
61	#10597342	C₂²	1	2	yes	complemented
62	#10597340	C₂²	1	2	yes	—
63	#10597340	C₂²	1	2	yes	—
64	#10597340	C₂²	1	2	yes	—
65	#10597339	C₂²	1	2	yes	—
66	#10597338	C₂²	1	2	yes	complemented
67	#10597334	C₂²	1	2	yes	complemented
68	#10597334	C₂²	1	2	yes	complemented
69	#10597333	C₂²	1	2	yes	complemented
70	#10597333	C₂²	1	2	yes	complemented
71	#10597331	C₂²	1	2	yes	—
72	#10597331	C₂²	1	2	yes	—
73	#10597331	C₂²	1	2	yes	—
74	#10597331	C₂²	1	2	yes	—
75	#10597331	C₂²	1	2	yes	complemented
76	#10597331	C₂²	1	2	yes	complemented
77	#10597330	C₂²	1	2	yes	—
78	#10597329	C₂²	1	2	yes	—
79	#10597328	C₂²	1	2	yes	—
80	#10597328	C₂²	1	2	yes	—
81	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	—
82	C₂²⋊C₄×D₁₉	C₂²	1	2	yes	complemented
83	C₂²⋊C₄×D₁₉	C₂²	1	2	yes	complemented
84	#10597325	C₂²	1	2	yes	complemented
85	#10597325	C₂²	1	2	yes	complemented
86	#10597325	C₂²	1	2	yes	complemented
87	#10597325	C₂²	1	2	yes	complemented
88	#10597324	C₂²	1	2	yes	complemented
89	#10597324	C₂²	1	2	yes	complemented
90	#10597323	C₂²	1	2	yes	complemented
91	#10597322	C₂²	1	2	yes	complemented
92	#10597322	C₂²	1	2	yes	complemented
93	#10597322	C₂²	1	2	yes	complemented
94	#10597321	C₂²	1	1	yes	characteristic
95	#10597321	C₂²	1	1	yes	characteristic
96	#10597321	C₂²	1	2	yes	—
97	C₄×D₇₆	C₂²	1	1	yes	characteristic
98	C₄×D₇₆	C₂²	1	1	yes	characteristic
99	#10597318	C₂²	1	2	yes	complemented
100	#10597318	C₂²	1	2	yes	complemented
101	#10597318	C₂²	1	2	yes	complemented
102	#10597316	C₂²	1	1	yes	characteristic, complemented
103	#10597316	C₂²	1	1	yes	characteristic, complemented
104	C₄×Dic₃₈	C₂²	1	1	yes	characteristic, complemented
105	C₄×Dic₃₈	C₂²	1	1	yes	characteristic, complemented
106	C₄×Dic₃₈	C₂²	1	2	yes	complemented
107	C₂³×D₁₉	C₂³	1	2	yes	—
108	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
109	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
110	C₂×D₄×C₁₉	C₂³	1	2	yes	—
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	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
115	C₂×C₂²⋊D₁₉	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	2	yes	—
120	C₂×D₇₆	C₂³	1	1	yes	characteristic
121	C₂×D₇₆	C₂³	1	1	yes	characteristic
122	C₂×D₇₆	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×C₄×D₁₉	C₂³	1	2	yes	—
127	C₂×Dic₃₈	C₂³	1	2	yes	—
128	C₂×Dic₃₈	C₂³	1	2	yes	—
129	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
130	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
131	C₂×Dic₃₈	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	1	yes	characteristic
135	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
136	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
137	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
138	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
139	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
140	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
141	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
142	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
143	C₄²×C₁₉	C₂³	1	1	yes	characteristic
144	C₄²×C₁₉	C₂³	1	1	yes	characteristic
145	C₄²×C₁₉	C₂³	1	1	yes	characteristic
146	C₄²×C₁₉	C₂³	1	1	yes	characteristic
147	C₄²×C₁₉	C₂³	1	2	yes	—
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	(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	(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	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
171	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
172	C₄⋊Dic₁₉	C₂³	1	2	yes	—
173	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
174	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
175	C₄⋊Dic₁₉	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	C₄×Dic₁₉	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	2	yes	—
195	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
196	C₂²×D₁₉	—	4	2	no	—
197	C₂²×D₁₉	—	4	2	no	—
198	C₂²×D₁₉	—	4	2	no	—
199	C₂²×D₁₉	C₂⁴	1	2	yes	—
200	C₂²×D₁₉	C₂⁴	1	2	yes	—
201	Q₈×C₁₉	—	4	1	no	—
202	D₄×C₁₉	—	4	2	no	—
203	D₄×C₁₉	—	4	1	no	—
204	C₂×C₄×C₁₉	—	4	2	no	—
205	C₂×C₄×C₁₉	—	4	1	no	—
206	C₂×C₄×C₁₉	—	4	1	no	—
207	C₂×C₄×C₁₉	—	4	1	no	—
208	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
209	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
210	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
211	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
212	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
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	1	yes	characteristic
217	C₂²⋊D₁₉	—	4	2	no	—
218	C₂²⋊D₁₉	—	4	2	no	—
219	C₂²⋊D₁₉	—	4	2	no	—
220	C₂²⋊D₁₉	—	4	2	no	—
221	C₂×Dic₁₉	—	4	2	no	—
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	C₂×Dic₁₉	C₂⁴	1	2	yes	—
227	C₂×Dic₁₉	C₂⁴	1	2	yes	—
228	D₇₆	—	4	1	no	—
229	D₇₆	—	4	1	no	—
230	D₇₆	—	4	2	no	—
231	C₄×D₁₉	—	4	2	no	—
232	C₄×D₁₉	—	4	2	no	—
233	C₄×D₁₉	—	4	2	no	—
234	C₄×D₁₉	—	4	2	no	—
235	Dic₃₈	—	4	1	no	—
236	Dic₃₈	—	4	1	no	—
237	Dic₃₈	—	4	2	no	—
238	Dic₃₈	—	4	2	no	—
239	Dic₃₈	—	4	2	no	—
240	#3568	—	19	1	no	maximal, Sylow
241	C₂²×C₁₉	—	2	2	no	—
242	C₂²×C₁₉	—	2	1	no	—
243	C₂²×C₁₉	—	2	1	no	—
244	C₂²×C₁₉	—	2	2	no	—
245	C₂²×C₁₉	—	2	2	no	—
246	C₂²×C₁₉	—	2	1	no	—
247	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
248	C₂×D₁₉	—	2	2	no	—
249	C₂×D₁₉	—	2	2	no	—
250	C₂×D₁₉	—	2	2	no	—
251	C₂×D₁₉	—	2	2	no	—
252	C₂×D₁₉	—	2	2	no	—
253	C₂×D₁₉	—	2	2	no	—
254	C₂×D₁₉	—	8	4	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	C₄×C₁₉	—	2	2	no	—
260	C₄×C₁₉	—	2	1	no	—
261	C₄×C₁₉	—	2	1	no	—
262	C₄×C₁₉	—	2	1	no	—
263	C₄×C₁₉	—	2	1	no	—
264	Dic₁₉	—	2	2	no	—
265	Dic₁₉	—	2	2	no	—
266	Dic₁₉	—	2	2	no	—
267	Dic₁₉	—	2	2	no	—
268	Dic₁₉	—	2	2	no	—
269	Dic₁₉	—	2	2	no	—
270	#563	—	19	1	no	—
271	#563	—	19	1	no	—
272	#563	—	19	1	no	—
273	H(3,𝔽₄)	—	19	1	no	—
274	#556	—	19	2	no	—
275	#556	—	19	2	no	—
276	#556	—	19	2	no	—
277	#551	—	19	2	no	—
278	#551	—	19	2	no	—
279	#551	—	19	2	no	—
280	#542	—	19	2	no	—
281	#542	—	19	2	no	—
282	#542	—	19	2	no	—
283	#538	—	19	2	no	—
284	#538	—	19	2	no	—
285	#538	—	19	2	no	—
286	#529	—	19	1	no	—
287	#529	—	19	1	no	—
288	#529	D₁₉	1	1	yes	characteristic, complemented
289	C₂×C₁₉	—	4	2	no	—
290	C₂×C₁₉	—	4	1	no	—
291	C₂×C₁₉	#585	1	1	yes	characteristic
292	C₂×C₁₉	#585	1	1	yes	characteristic
293	C₂×C₁₉	#585	1	1	yes	characteristic
294	D₁₉	—	4	2	no	—
295	D₁₉	—	4	2	no	—
296	C₄⋊Q₈	—	19	2	no	—
297	C₄⋊Q₈	—	19	2	no	—
298	C₄⋊Q₈	—	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	#126	—	19	2	no	—
309	#126	—	19	2	no	—
310	#126	—	19	2	no	—
311	#126	C₂×D₁₉	1	2	yes	complemented
312	#125	—	19	1	no	—
313	#125	—	19	1	no	—
314	#125	C₂×D₁₉	1	1	yes	characteristic, complemented
315	#124	—	19	2	no	—
316	#124	—	19	2	no	—
317	#124	—	19	2	no	—
318	#124	—	19	2	no	—
319	#124	—	19	2	no	—
320	#124	—	19	2	no	—
321	#124	—	19	2	no	—
322	#124	—	19	2	no	—
323	#124	—	19	1	no	—
324	#124	—	19	1	no	—
325	#124	—	19	2	no	—
326	#124	C₂×D₁₉	1	1	yes	characteristic
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	C₂×D₁₉	1	2	yes	complemented
336	C₂²⋊Q₈	—	19	1	no	—
337	C₂²⋊Q₈	—	19	1	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	—	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	2	no	—
350	#121	—	19	1	no	—
351	#121	—	19	1	no	—
352	#121	—	19	2	no	—
353	#121	C₂×D₁₉	1	1	yes	characteristic
354	#120	—	19	2	no	—
355	#120	—	19	2	no	—
356	#120	—	19	2	no	—
357	#120	—	19	2	no	—
358	C₄×Q₈	—	19	2	no	—
359	C₄×Q₈	—	19	2	no	—
360	C₄×Q₈	—	19	1	no	—
361	C₄×Q₈	—	19	1	no	—
362	C₄×Q₈	—	19	2	no	—
363	C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
364	C₄×D₄	—	19	2	no	—
365	C₄×D₄	—	19	2	no	—
366	C₄×D₄	—	19	2	no	—
367	C₄×D₄	—	19	2	no	—
368	C₄×D₄	—	19	2	no	—
369	C₄×D₄	—	19	1	no	—
370	C₄×D₄	—	19	1	no	—
371	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
372	C₄×D₄	C₂×D₁₉	1	2	yes	complemented
373	#117	—	19	2	no	—
374	#117	—	19	2	no	—
375	#117	—	19	2	no	—
376	#117	—	19	2	no	—
377	#117	—	19	2	no	—
378	#117	C₂×D₁₉	1	2	yes	complemented
379	C₂×C₂²⋊C₄	—	19	2	no	—
380	C₂×C₂²⋊C₄	—	19	2	no	—
381	C₂×C₂²⋊C₄	—	19	2	no	—
382	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic, complemented
383	C₁₉	#3568	1	1	yes	characteristic, complemented, Sylow
384	C₂⁴	—	19	2	no	—
385	C₂×Q₈	—	19	2	no	—
386	C₂×Q₈	—	19	2	no	—
387	C₂×Q₈	—	19	2	no	—
388	C₂×Q₈	—	19	1	no	—
389	C₂×Q₈	—	19	1	no	—
390	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
391	C₂×D₄	—	19	2	no	—
392	C₂×D₄	—	19	2	no	—
393	C₂×D₄	—	19	2	no	—
394	C₂×D₄	—	19	2	no	—
395	C₂×D₄	—	19	1	no	—
396	C₂×D₄	—	19	1	no	—
397	C₂×D₄	—	19	2	no	—
398	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
399	C₂×D₄	C₂²×D₁₉	1	2	yes	—
400	C₂²×C₄	—	19	2	no	—
401	C₂²×C₄	—	19	2	no	—
402	C₂²×C₄	—	19	2	no	—
403	C₂²×C₄	—	19	2	no	—
404	C₂²×C₄	—	19	2	no	—
405	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
406	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
407	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
408	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
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	2	no	—
421	C₄⋊C₄	—	19	2	no	—
422	C₄⋊C₄	—	19	1	no	—
423	C₄⋊C₄	—	19	1	no	—
424	C₄⋊C₄	—	19	1	no	—
425	C₄⋊C₄	—	19	1	no	—
426	C₄⋊C₄	—	19	2	no	—
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	—	19	2	no	—
453	C₂²⋊C₄	—	19	2	no	—
454	C₂²⋊C₄	—	19	2	no	—
455	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
456	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
457	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
458	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
459	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
460	C₄²	—	19	2	no	—
461	C₄²	—	19	2	no	—
462	C₄²	—	19	2	no	—
463	C₄²	—	19	2	no	—
464	C₄²	—	19	2	no	—
465	C₄²	—	19	2	no	—
466	C₄²	C₂²×D₁₉	1	1	yes	characteristic
467	C₄²	C₂²×D₁₉	1	1	yes	characteristic
468	C₄²	C₂²×D₁₉	1	1	yes	characteristic
469	C₄²	C₂²×D₁₉	1	1	yes	characteristic
470	C₄²	C₂²×D₁₉	1	2	yes	—
471	C₂³	—	19	2	no	—
472	C₂³	—	19	2	no	—
473	C₂³	—	76	2	no	—
474	C₂³	—	76	2	no	—
475	C₂³	—	76	2	no	—
476	C₂³	C₂³×D₁₉	1	2	yes	—
477	C₂³	C₂³×D₁₉	1	1	yes	characteristic
478	Q₈	—	4	1	no	—
479	Q₈	—	76	2	no	—
480	Q₈	—	76	1	no	—
481	Q₈	—	76	1	no	—
482	Q₈	—	76	2	no	—
483	Q₈	—	76	2	no	—
484	D₄	—	4	1	no	—
485	D₄	—	4	2	no	—
486	D₄	—	76	1	no	—
487	D₄	—	76	1	no	—
488	D₄	—	76	2	no	—
489	D₄	—	76	2	no	—
490	D₄	—	76	2	no	—
491	D₄	—	76	2	no	—
492	D₄	—	76	2	no	—
493	C₂×C₄	—	4	2	no	—
494	C₂×C₄	—	4	1	no	—
495	C₂×C₄	—	4	1	no	—
496	C₂×C₄	—	4	1	no	—
497	C₂×C₄	—	19	2	no	—
498	C₂×C₄	—	19	2	no	—
499	C₂×C₄	—	19	2	no	—
500	C₂×C₄	—	19	2	no	—
501	C₂×C₄	—	19	2	no	—
502	C₂×C₄	—	19	2	no	—
503	C₂×C₄	—	76	2	no	—
504	C₂×C₄	—	76	2	no	—
505	C₂×C₄	—	76	2	no	—
506	C₂×C₄	—	76	2	no	—
507	C₂×C₄	—	76	2	no	—
508	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
509	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
510	C₂×C₄	C₂³×D₁₉	1	2	yes	—
511	C₂×C₄	C₂³×D₁₉	1	2	yes	—
512	C₂×C₄	C₂³×D₁₉	1	2	yes	—
513	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
514	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
515	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
516	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
517	C₂²	—	2	1	no	—
518	C₂²	—	2	1	no	—
519	C₂²	—	2	1	no	—
520	C₂²	—	2	2	no	—
521	C₂²	—	2	2	no	—
522	C₂²	—	2	2	no	—
523	C₂²	—	38	2	no	—
524	C₂²	—	38	2	no	—
525	C₂²	—	38	2	no	—
526	C₂²	—	38	2	no	—
527	C₂²	—	38	2	no	—
528	C₂²	—	38	2	no	—
529	C₂²	—	152	4	no	—
530	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
531	C₄	—	2	1	no	—
532	C₄	—	2	1	no	—
533	C₄	—	2	1	no	—
534	C₄	—	2	2	no	—
535	C₄	—	2	1	no	—
536	C₄	—	2	1	no	—
537	C₄	—	2	1	no	—
538	C₄	—	2	2	no	—
539	C₄	—	2	2	no	—
540	C₄	—	38	2	no	—
541	C₄	—	38	2	no	—
542	C₄	—	38	2	no	—
543	C₄	—	38	2	no	—
544	C₄	—	38	2	no	—
545	C₄	—	38	2	no	—
546	C₂	—	4	2	no	—
547	C₂	—	4	1	no	—
548	C₂	—	76	2	no	—
549	C₂	—	76	2	no	—
550	C₂	#11927380	1	1	yes	characteristic
551	C₂	#11927380	1	1	yes	characteristic
552	C₂	#11927380	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Fitting	C₁₉×#529	C₂
hypercenter	#529	D₁₉
hypocenter	C₁₉	#3568
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. #11927298	C₂	semidirect
2. #11927298	C₂	semidirect
3. #11927294	C₂	semidirect
4. #11927286	C₂	semidirect
5. #11927266	C₂	semidirect
6. #11927262	C₂	semidirect
7. #11927261	C₂	semidirect
8. #11927223	C₂	semidirect
9. #11927219	C₂	semidirect
10. #11927218	C₂	semidirect
11. #11927164	C₂	semidirect
12. #11927162	C₂	semidirect
13. #11927159	C₂	semidirect
14. #11927130	C₂	semidirect
15. #11927127	C₂	semidirect
16. #11927126	C₂	semidirect
17. #11927078	C₂	semidirect
18. #11927078	C₂	semidirect
19. C₁₉×#529	C₂	semidirect
20. C₁₉×#126	C₂²	semidirect
21. C₁₉×#125	C₂²	semidirect
23. C₁₉×#123	C₂²	semidirect
24. C₁₉×C₂²⋊Q₈	C₂²	semidirect
26. C₄×Q₈×C₁₉	C₂²	semidirect
28. C₄×D₄×C₁₉	C₂²	semidirect
29. C₁₉×#117	C₂²	semidirect
30. C₂×C₄²×C₁₉	C₂²	semidirect
32. #10597390	C₂²	semidirect
36. #10597383	C₂²	semidirect
37. #10597382	C₂²	semidirect
42. #10597375	C₂²	semidirect
43. #10597375	C₂²	semidirect
45. C₄×C₂²⋊D₁₉	C₂²	semidirect
46. C₄×C₂²⋊D₁₉	C₂²	semidirect
47. C₂×(C₂×D₁₉)⋊C₄	C₂²	semidirect
48. #10597370	C₂²	semidirect
49. #10597370	C₂²	semidirect
50. #10597370	C₂²	semidirect
51. #10597344	C₂²	semidirect
52. #10597344	C₂²	semidirect
53. #10597344	C₂²	semidirect
54. #10597344	C₂²	semidirect
55. #10597344	C₂²	semidirect
56. #10597343	C₂²	semidirect
57. #10597343	C₂²	semidirect
58. #10597342	C₂²	semidirect
59. #10597342	C₂²	semidirect
60. #10597342	C₂²	semidirect
61. #10597342	C₂²	semidirect
66. #10597338	C₂²	semidirect
67. #10597334	C₂²	semidirect
68. #10597334	C₂²	semidirect
69. #10597333	C₂²	semidirect
70. #10597333	C₂²	semidirect
75. #10597331	C₂²	semidirect
76. #10597331	C₂²	semidirect
82. C₂²⋊C₄×D₁₉	C₂²	semidirect
83. C₂²⋊C₄×D₁₉	C₂²	semidirect
84. #10597325	C₂²	semidirect
85. #10597325	C₂²	semidirect
86. #10597325	C₂²	semidirect
87. #10597325	C₂²	semidirect
88. #10597324	C₂²	semidirect
89. #10597324	C₂²	semidirect
90. #10597323	C₂²	semidirect
91. #10597322	C₂²	semidirect
92. #10597322	C₂²	semidirect
93. #10597322	C₂²	semidirect
99. #10597318	C₂²	semidirect
100. #10597318	C₂²	semidirect
101. #10597318	C₂²	semidirect
102. #10597316	C₂²	semidirect
103. #10597316	C₂²	semidirect
104. C₄×Dic₃₈	C₂²	semidirect
105. C₄×Dic₃₈	C₂²	semidirect
106. C₄×Dic₃₈	C₂²	semidirect
288. #529	D₁₉	semidirect
311. #126	C₂×D₁₉	semidirect
314. #125	C₂×D₁₉	semidirect
335. #123	C₂×D₁₉	semidirect
347. C₂²⋊Q₈	C₂×D₁₉	semidirect
363. C₄×Q₈	C₂×D₁₉	semidirect
372. C₄×D₄	C₂×D₁₉	semidirect
378. #117	C₂×D₁₉	semidirect
382. C₂×C₄²	C₂×D₁₉	semidirect
383. C₁₉	#3568	semidirect

Maximal subgroups

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

subgroup	index
#11927298	2
#11927294	2
#11927286	2
#11927266	2
#11927262	2
#11927261	2
#11927223	2
#11927219	2
#11927218	2
#11927164	2
#11927162	2
#11927159	2
#11927130	2
#11927127	2
#11927126	2
#11927078	2
C₁₉×#529	2
#3568	19