Subgroups — #14577504

Order 2432.

1232 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927277	C₂	1	2	yes	maximal, complemented
2	#11927276	C₂	1	2	yes	maximal, complemented
3	#11927213	C₂	1	2	yes	maximal, complemented
4	#11927212	C₂	1	2	yes	maximal, complemented
5	#11927191	C₂	1	2	yes	maximal, complemented
6	#11927189	C₂	1	2	yes	maximal, complemented
7	#11927187	C₂	1	2	yes	maximal, complemented
8	#11927182	C₂	1	2	yes	maximal, complemented
9	#11927147	C₂	1	2	yes	maximal, complemented
10	#11927145	C₂	1	2	yes	maximal, complemented
11	#11927110	C₂	1	2	yes	maximal, complemented
12	#11927099	C₂	1	1	yes	maximal, characteristic, complemented
13	#11927095	C₂	1	1	yes	maximal, characteristic, complemented
14	#11927094	C₂	1	1	yes	maximal, characteristic, complemented
15	#11927092	C₂	1	1	yes	maximal, characteristic, complemented
16	#127×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
17	#11927016	C₂	1	2	yes	maximal, complemented
18	C₄×#64541	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₉×#532	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#41×C₁₉	C₂²	1	2	yes	complemented
21	C₂×#64545	C₂²	1	2	yes	complemented
22	C₂×#64543	C₂²	1	2	yes	complemented
23	C₂×D₄×D₁₉	C₂²	1	2	yes	—
24	C₂×D₄×D₁₉	C₂²	1	2	yes	—
25	C₂×D₄×D₁₉	C₂²	1	2	yes	—
26	C₂×#64541	C₂²	1	1	yes	characteristic
27	C₂×#64541	C₂²	1	2	yes	complemented
28	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
29	C₁₉×#127	C₂²	1	1	yes	characteristic
30	C₁₉×#124	C₂²	1	2	yes	complemented
31	C₁₉×#121	C₂²	1	2	yes	complemented
32	C₁₉×#121	C₂²	1	2	yes	complemented
33	C₄×D₄×C₁₉	C₂²	1	2	yes	complemented
34	C₄×D₄×C₁₉	C₂²	1	2	yes	complemented
35	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic, complemented
36	#10597393	C₂²	1	2	yes	complemented
37	#10597392	C₂²	1	2	yes	—
38	Q₈×Dic₁₉	C₂²	1	2	yes	complemented
39	#10597386	C₂²	1	2	yes	—
40	#10597386	C₂²	1	2	yes	—
41	#10597386	C₂²	1	2	yes	—
42	#10597386	C₂²	1	4	yes	complemented
43	#10597385	C₂²	1	4	yes	complemented
44	#10597384	C₂²	1	2	yes	complemented
45	#10597384	C₂²	1	2	yes	complemented
46	#10597384	C₂²	1	4	yes	complemented
47	#10597383	C₂²	1	4	yes	—
48	#10597382	C₂²	1	2	yes	complemented
49	D₄×Dic₁₉	C₂²	1	2	yes	complemented
50	D₄×Dic₁₉	C₂²	1	2	yes	complemented
51	#10597376	C₂²	1	2	yes	complemented
52	#10597376	C₂²	1	2	yes	complemented
53	#10597376	C₂²	1	4	yes	complemented
54	#10597375	C₂²	1	4	yes	complemented
55	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
56	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
57	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic, complemented
58	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic, complemented
59	C₄×C₂²⋊D₁₉	C₂²	1	4	yes	complemented
60	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	4	yes	—
61	#10597372	C₂²	1	1	yes	characteristic, complemented
62	#10597343	C₂²	1	2	yes	—
63	#10597341	C₂²	1	2	yes	complemented
64	#10597341	C₂²	1	2	yes	complemented
65	#10597339	C₂²	1	2	yes	complemented
66	#10597339	C₂²	1	2	yes	complemented
67	#10597338	C₂²	1	2	yes	—
68	#10597336	C₂²	1	2	yes	complemented
69	#10597333	C₂²	1	2	yes	complemented
70	#10597332	C₂²	1	4	yes	complemented
71	#10597331	C₂²	1	4	yes	complemented
72	#10597330	C₂²	1	4	yes	complemented
73	#10597329	C₂²	1	4	yes	complemented
74	#10597329	C₂²	1	4	yes	complemented
75	#10597328	C₂²	1	4	yes	—
76	(C₂²⋊D₁₉)⋊C₄	C₂²	1	4	yes	complemented
77	C₂²⋊C₄×D₁₉	C₂²	1	4	yes	—
78	#10597321	C₂²	1	2	yes	complemented
79	#10597320	C₂²	1	1	yes	characteristic
80	C₄×D₇₆	C₂²	1	1	yes	characteristic
81	C₄×D₇₆	C₂²	1	1	yes	characteristic
82	C₄×D₇₆	C₂²	1	2	yes	complemented
83	C₄×D₇₆	C₂²	1	2	yes	complemented
84	#10597318	C₂²	1	1	yes	characteristic
85	#10597318	C₂²	1	1	yes	characteristic, complemented
86	C₄²×D₁₉	C₂²	1	1	yes	characteristic
87	C₄²×D₁₉	C₂²	1	1	yes	characteristic, complemented
88	#10597315	C₂²	1	1	yes	characteristic, complemented
89	C₄×Dic₃₈	C₂²	1	1	yes	characteristic, complemented
90	C₄×Dic₃₈	C₂²	1	1	yes	characteristic, complemented
91	C₂³×D₁₉	C₂³	1	4	yes	—
92	#41×C₁₉	—	4	4	no	—
93	C₂×Q₈×C₁₉	C₂³	1	2	yes	—
94	C₂×D₄×C₁₉	C₂³	1	2	yes	—
95	C₂×D₄×C₁₉	C₂³	1	2	yes	—
96	C₂×D₄×C₁₉	C₂³	1	2	yes	—
97	C₂×D₄×C₁₉	C₂³	1	4	yes	—
98	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
99	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
100	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
101	C₂²×C₄×C₁₉	C₂³	1	4	yes	—
102	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
103	C₂×C₂²⋊D₁₉	C₂³	1	4	yes	—
104	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
105	C₂×C₂²⋊D₁₉	C₂³	1	4	yes	—
106	C₂×C₂²⋊D₁₉	C₂³	1	4	yes	—
107	C₂×C₂²⋊D₁₉	C₂³	1	4	yes	—
108	C₂×C₂²⋊D₁₉	C₂³	1	4	yes	—
109	C₂²×Dic₁₉	C₂³	1	4	yes	—
110	#64545	—	4	4	no	—
111	#64543	—	4	4	no	—
112	D₄×D₁₉	—	2	8	no	—
113	D₄×D₁₉	—	4	4	no	—
114	D₄×D₁₉	—	4	4	no	—
115	#64541	—	2	4	no	—
116	#64541	—	4	4	no	—
117	C₂×D₇₆	C₂³	1	2	yes	—
118	C₂×D₇₆	C₂³	1	2	yes	—
119	C₂×D₇₆	C₂³	1	2	yes	—
120	C₂×D₇₆	C₂³	1	1	yes	characteristic
121	C₂×D₇₆	C₂³	1	4	yes	—
122	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
123	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
124	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
125	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
126	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
127	C₂×C₄×D₁₉	C₂³	1	4	yes	—
128	C₂×C₄×D₁₉	C₂³	1	4	yes	—
129	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
130	C₂×Dic₃₈	C₂³	1	2	yes	—
131	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
132	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
133	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
134	C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
135	C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
136	C₄²×C₁₉	C₂³	1	1	yes	characteristic
137	C₄²×C₁₉	C₂³	1	1	yes	characteristic
138	C₄²×C₁₉	C₂³	1	1	yes	characteristic
139	C₄²×C₁₉	C₂³	1	1	yes	characteristic
140	C₂²⋊Dic₁₉	C₂³	1	4	yes	—
141	C₂²⋊Dic₁₉	C₂³	1	4	yes	—
142	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
143	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
144	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
145	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
146	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
147	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
148	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
149	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
150	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
151	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
152	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
153	C₄⋊Dic₁₉	C₂³	1	2	yes	—
154	C₄⋊Dic₁₉	C₂³	1	2	yes	—
155	C₄⋊Dic₁₉	C₂³	1	4	yes	—
156	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
157	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
158	Dic₁₉⋊C₄	C₂³	1	4	yes	—
159	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
160	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
161	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
162	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
163	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
164	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
165	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
166	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
167	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
168	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
169	C₄×Dic₁₉	C₂³	1	4	yes	—
170	C₂³×C₁₉	C₂⁴	1	4	yes	—
171	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
172	C₂²×D₁₉	—	2	8	no	—
173	C₂²×D₁₉	—	4	4	no	—
174	C₂²×D₁₉	—	4	4	no	—
175	C₂²×D₁₉	C₂⁴	1	4	yes	—
176	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
177	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
178	Q₈×C₁₉	—	2	4	no	—
179	D₄×C₁₉	—	2	4	no	—
180	D₄×C₁₉	—	2	4	no	—
181	D₄×C₁₉	—	2	4	no	—
182	D₄×C₁₉	—	4	4	no	—
183	C₂×C₄×C₁₉	—	2	2	no	—
184	C₂×C₄×C₁₉	—	2	2	no	—
185	C₂×C₄×C₁₉	—	2	2	no	—
186	C₂×C₄×C₁₉	—	4	4	no	—
187	C₂×C₄×C₁₉	C₂⁴	1	4	yes	—
188	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
189	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
190	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
191	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
192	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
193	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
194	C₂²⋊D₁₉	—	2	2	no	—
195	C₂²⋊D₁₉	—	2	2	no	—
196	C₂²⋊D₁₉	—	2	8	no	—
197	C₂²⋊D₁₉	—	4	4	no	—
198	C₂²⋊D₁₉	—	4	4	no	—
199	C₂²⋊D₁₉	—	4	4	no	—
200	C₂²⋊D₁₉	—	4	4	no	—
201	C₂×Dic₁₉	—	4	4	no	—
202	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
203	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
204	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
205	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
206	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
207	C₂×Dic₁₉	C₂⁴	1	4	yes	—
208	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
209	D₇₆	—	2	2	no	—
210	D₇₆	—	2	4	no	—
211	D₇₆	—	2	4	no	—
212	D₇₆	—	2	4	no	—
213	D₇₆	—	4	4	no	—
214	C₄×D₁₉	—	2	2	no	—
215	C₄×D₁₉	—	2	2	no	—
216	C₄×D₁₉	—	2	2	no	—
217	C₄×D₁₉	—	2	2	no	—
218	C₄×D₁₉	—	2	2	no	—
219	C₄×D₁₉	—	4	4	no	—
220	C₄×D₁₉	—	4	4	no	—
221	C₄×D₁₉	#41	1	4	yes	complemented
222	Dic₃₈	—	2	4	no	—
223	Dic₃₈	—	2	2	no	—
224	#3508	—	19	1	no	maximal, Sylow
225	C₂²×C₁₉	—	2	1	no	—
226	C₂²×C₁₉	—	2	4	no	—
227	C₂²×C₁₉	—	2	4	no	—
228	C₂²×C₁₉	—	2	1	no	—
229	C₂²×C₁₉	—	2	4	no	—
230	C₂²×C₁₉	—	2	1	no	—
231	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
232	C₂×D₁₉	—	2	1	no	—
233	C₂×D₁₉	—	2	1	no	—
234	C₂×D₁₉	—	2	1	no	—
235	C₂×D₁₉	—	2	4	no	—
236	C₂×D₁₉	—	2	1	no	—
237	C₂×D₁₉	—	2	1	no	—
238	C₂×D₁₉	—	2	4	no	—
239	C₂×D₁₉	—	2	4	no	—
240	C₂×D₁₉	—	8	8	no	—
241	C₂×D₁₉	C₂×#41	1	2	yes	—
242	C₄×C₁₉	—	2	1	no	—
243	C₄×C₁₉	—	2	1	no	—
244	C₄×C₁₉	—	2	4	no	—
245	C₄×C₁₉	—	2	1	no	—
246	C₄×C₁₉	C₂×#41	1	2	yes	—
247	C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
248	C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
249	Dic₁₉	—	2	1	no	—
250	Dic₁₉	—	2	4	no	—
251	Dic₁₉	—	2	1	no	—
252	Dic₁₉	—	2	1	no	—
253	Dic₁₉	—	2	1	no	—
254	Dic₁₉	—	2	1	no	—
255	Dic₁₉	C₂×#41	1	2	yes	—
256	#559	—	19	2	no	—
257	#559	—	19	2	no	—
258	#550	—	19	2	no	—
259	#550	—	19	2	no	—
260	#546	—	19	2	no	—
261	#546	—	19	2	no	—
262	#546	—	19	2	no	—
263	#546	—	19	2	no	—
264	#540	—	19	2	no	—
265	#540	—	19	2	no	—
266	#535	—	19	2	no	—
267	#533	—	19	1	no	—
268	#532	—	19	1	no	—
269	#532	—	19	1	no	—
270	#532	—	19	1	no	—
271	#532	D₁₉	1	1	yes	characteristic, complemented
272	C₂×#127	—	19	1	no	—
273	#518	—	19	2	no	—
274	C₄×#41	—	19	1	no	—
275	C₂×C₁₉	—	4	4	no	—
276	C₂×C₁₉	—	4	1	no	—
277	C₂×C₁₉	C₂²×#41	1	1	yes	characteristic
278	C₂×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
279	C₂×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
280	D₁₉	—	2	2	no	—
281	D₁₉	—	4	1	no	—
282	D₁₉	—	4	4	no	—
283	C₂×#41	—	19	2	no	—
284	C₂×#41	—	19	2	no	—
285	C₂×#41	—	19	1	no	—
286	C₂×#41	—	19	2	no	—
287	C₂×#41	C₂×D₁₉	1	2	yes	complemented
288	C₂²×D₄	—	19	2	no	—
289	C₂²×D₄	—	19	2	no	—
290	C₂²×D₄	—	19	2	no	—
291	C₄⋊Q₈	—	19	1	no	—
292	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
293	#127	—	19	2	no	—
294	#127	—	19	2	no	—
295	#127	—	19	2	no	—
296	#127	—	19	4	no	—
297	#127	—	19	1	no	—
298	#127	C₂×D₁₉	1	1	yes	characteristic
299	#125	—	19	2	no	—
300	#124	—	19	2	no	—
301	#124	—	19	2	no	—
302	#124	—	19	4	no	—
303	#124	—	19	2	no	—
304	#124	C₂×D₁₉	1	2	yes	complemented
305	#123	—	19	4	no	—
306	#123	—	19	4	no	—
307	#123	—	19	4	no	—
308	#123	—	19	4	no	—
309	C₂²⋊Q₈	—	19	2	no	—
310	C₂²⋊Q₈	—	19	2	no	—
311	#121	—	19	2	no	—
312	#121	—	19	2	no	—
313	#121	—	19	4	no	—
314	#121	—	19	4	no	—
315	#121	—	19	2	no	—
316	#121	—	19	2	no	—
317	#121	—	19	4	no	—
318	#121	—	19	2	no	—
319	#121	—	19	2	no	—
320	#121	—	19	4	no	—
321	#121	C₂×D₁₉	1	2	yes	complemented
322	#121	C₂×D₁₉	1	2	yes	complemented
323	#120	—	19	4	no	—
324	#120	—	19	4	no	—
325	C₄×Q₈	—	19	2	no	—
326	C₄×Q₈	—	19	2	no	—
327	C₄×Q₈	—	19	1	no	—
328	C₄×Q₈	—	19	1	no	—
329	C₄×D₄	—	19	2	no	—
330	C₄×D₄	—	19	2	no	—
331	C₄×D₄	—	19	1	no	—
332	C₄×D₄	—	19	1	no	—
333	C₄×D₄	—	19	1	no	—
334	C₄×D₄	—	19	1	no	—
335	C₄×D₄	—	19	4	no	—
336	C₄×D₄	—	19	2	no	—
337	C₄×D₄	—	19	2	no	—
338	C₄×D₄	—	19	4	no	—
339	C₄×D₄	—	19	1	no	—
340	C₄×D₄	—	19	1	no	—
341	C₄×D₄	—	19	2	no	—
342	C₄×D₄	—	19	2	no	—
343	C₄×D₄	C₂×D₁₉	1	2	yes	complemented
344	C₄×D₄	C₂×D₁₉	1	2	yes	complemented
345	#117	—	19	1	no	—
346	#117	—	19	2	no	—
347	#117	—	19	1	no	—
348	#117	—	19	1	no	—
349	C₂×C₂²⋊C₄	—	19	4	no	—
350	C₂×C₂²⋊C₄	—	19	4	no	—
351	C₂×C₄²	—	19	1	no	—
352	C₂×C₄²	—	19	1	no	—
353	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic, complemented
354	C₁₉	#3508	1	1	yes	characteristic, complemented, Sylow
355	C₂⁴	—	19	4	no	—
356	#41	—	4	4	no	—
357	#41	—	38	4	no	—
358	#41	—	76	4	no	—
359	#41	—	76	4	no	—
360	#41	—	76	4	no	—
361	C₂×Q₈	—	19	1	no	—
362	C₂×Q₈	—	19	2	no	—
363	C₂×Q₈	C₂²×D₁₉	1	2	yes	—
364	C₂×D₄	—	19	1	no	—
365	C₂×D₄	—	19	4	no	—
366	C₂×D₄	—	19	1	no	—
367	C₂×D₄	—	19	4	no	—
368	C₂×D₄	—	19	4	no	—
369	C₂×D₄	—	19	4	no	—
370	C₂×D₄	—	19	4	no	—
371	C₂×D₄	—	19	1	no	—
372	C₂×D₄	—	19	2	no	—
373	C₂×D₄	—	19	2	no	—
374	C₂×D₄	—	19	2	no	—
375	C₂×D₄	—	19	4	no	—
376	C₂×D₄	—	38	8	no	—
377	C₂×D₄	—	76	4	no	—
378	C₂×D₄	—	76	4	no	—
379	C₂×D₄	C₂²×D₁₉	1	2	yes	—
380	C₂×D₄	C₂²×D₁₉	1	2	yes	—
381	C₂×D₄	C₂²×D₁₉	1	2	yes	—
382	C₂×D₄	C₂²×D₁₉	1	4	yes	—
383	C₂²×C₄	—	19	1	no	—
384	C₂²×C₄	—	19	4	no	—
385	C₂²×C₄	—	19	1	no	—
386	C₂²×C₄	—	19	1	no	—
387	C₂²×C₄	—	19	1	no	—
388	C₂²×C₄	—	19	1	no	—
389	C₂²×C₄	—	19	1	no	—
390	C₂²×C₄	—	19	4	no	—
391	C₂²×C₄	—	19	4	no	—
392	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
393	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
394	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
395	C₂²×C₄	C₂²×D₁₉	1	4	yes	—
396	C₄⋊C₄	—	19	1	no	—
397	C₄⋊C₄	—	19	1	no	—
398	C₄⋊C₄	—	19	1	no	—
399	C₄⋊C₄	—	19	1	no	—
400	C₄⋊C₄	—	19	4	no	—
401	C₄⋊C₄	—	19	2	no	—
402	C₄⋊C₄	—	19	1	no	—
403	C₄⋊C₄	—	19	1	no	—
404	C₄⋊C₄	—	19	2	no	—
405	C₄⋊C₄	—	19	4	no	—
406	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
407	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
408	C₂²⋊C₄	—	19	4	no	—
409	C₂²⋊C₄	—	19	1	no	—
410	C₂²⋊C₄	—	19	1	no	—
411	C₂²⋊C₄	—	19	4	no	—
412	C₂²⋊C₄	—	19	1	no	—
413	C₂²⋊C₄	—	19	1	no	—
414	C₂²⋊C₄	—	19	4	no	—
415	C₂²⋊C₄	—	19	4	no	—
416	C₂²⋊C₄	—	19	4	no	—
417	C₂²⋊C₄	—	19	1	no	—
418	C₂²⋊C₄	—	19	1	no	—
419	C₂²⋊C₄	—	19	4	no	—
420	C₂²⋊C₄	—	19	4	no	—
421	C₂²⋊C₄	C₂²×D₁₉	1	4	yes	—
422	C₂²⋊C₄	C₂²×D₁₉	1	4	yes	—
423	C₄²	—	19	1	no	—
424	C₄²	—	19	1	no	—
425	C₄²	—	19	1	no	—
426	C₄²	—	19	1	no	—
427	C₄²	—	19	1	no	—
428	C₄²	—	19	1	no	—
429	C₄²	—	19	4	no	—
430	C₄²	C₂²×D₁₉	1	1	yes	characteristic
431	C₄²	C₂²×D₁₉	1	1	yes	characteristic
432	C₄²	C₂²×D₁₉	1	1	yes	characteristic
433	C₄²	C₂²×D₁₉	1	1	yes	characteristic
434	C₂³	—	19	1	no	—
435	C₂³	—	19	4	no	—
436	C₂³	—	19	1	no	—
437	C₂³	—	38	8	no	—
438	C₂³	—	76	4	no	—
439	C₂³	—	76	4	no	—
440	C₂³	C₂³×D₁₉	1	4	yes	—
441	C₂³	C₂³×D₁₉	1	1	yes	characteristic
442	Q₈	—	2	4	no	—
443	Q₈	—	38	2	no	—
444	Q₈	—	38	4	no	—
445	D₄	—	2	4	no	—
446	D₄	—	2	4	no	—
447	D₄	—	2	4	no	—
448	D₄	—	4	4	no	—
449	D₄	—	38	2	no	—
450	D₄	—	38	8	no	—
451	D₄	—	38	2	no	—
452	D₄	—	38	2	no	—
453	D₄	—	38	4	no	—
454	D₄	—	38	4	no	—
455	D₄	—	38	4	no	—
456	D₄	—	76	4	no	—
457	D₄	—	76	4	no	—
458	D₄	—	76	4	no	—
459	D₄	—	76	4	no	—
460	D₄	—	76	4	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	4	4	no	—
465	C₂×C₄	—	19	1	no	—
466	C₂×C₄	—	19	4	no	—
467	C₂×C₄	—	19	1	no	—
468	C₂×C₄	—	19	1	no	—
469	C₂×C₄	—	19	1	no	—
470	C₂×C₄	—	19	1	no	—
471	C₂×C₄	—	19	1	no	—
472	C₂×C₄	—	19	4	no	—
473	C₂×C₄	—	38	2	no	—
474	C₂×C₄	—	38	2	no	—
475	C₂×C₄	—	38	2	no	—
476	C₂×C₄	—	38	2	no	—
477	C₂×C₄	—	38	2	no	—
478	C₂×C₄	—	76	4	no	—
479	C₂×C₄	—	76	4	no	—
480	C₂×C₄	—	76	4	no	—
481	C₂×C₄	C₂³×D₁₉	1	4	yes	—
482	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
483	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
484	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
485	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
486	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
487	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
488	C₂²	—	2	1	no	—
489	C₂²	—	2	4	no	—
490	C₂²	—	2	1	no	—
491	C₂²	—	2	4	no	—
492	C₂²	—	2	1	no	—
493	C₂²	—	2	4	no	—
494	C₂²	—	19	2	no	—
495	C₂²	—	38	1	no	—
496	C₂²	—	38	1	no	—
497	C₂²	—	38	1	no	—
498	C₂²	—	38	4	no	—
499	C₂²	—	38	1	no	—
500	C₂²	—	38	4	no	—
501	C₂²	—	38	1	no	—
502	C₂²	—	38	4	no	—
503	C₂²	—	152	8	no	—
504	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
505	C₄	—	2	1	no	—
506	C₄	—	2	1	no	—
507	C₄	—	2	4	no	—
508	C₄	—	2	1	no	—
509	C₄	—	19	2	no	—
510	C₄	—	38	1	no	—
511	C₄	—	38	1	no	—
512	C₄	—	38	1	no	—
513	C₄	—	38	1	no	—
514	C₄	—	38	1	no	—
515	C₄	—	38	4	no	—
516	C₄	#10597430	1	2	yes	—
517	C₄	#41×D₁₉	1	2	yes	—
518	C₄	#10597435	1	2	yes	—
519	C₂	—	4	4	no	—
520	C₂	—	4	1	no	—
521	C₂	—	38	2	no	—
522	C₂	—	76	4	no	—
523	C₂	—	76	1	no	—
524	C₂	C₂×#41×D₁₉	1	1	yes	characteristic
525	C₂	C₂×#10597430	1	1	yes	characteristic
526	C₂	C₂×#10597435	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Fitting	C₁₉×#532	C₂
hypercenter	#532	D₁₉
hypocenter	C₁₉	#3508
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ #532

Complements

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

N	H ≅ G/N	type
1. #11927277	C₂	semidirect
2. #11927276	C₂	semidirect
3. #11927213	C₂	semidirect
4. #11927212	C₂	semidirect
5. #11927191	C₂	semidirect
6. #11927189	C₂	semidirect
7. #11927187	C₂	semidirect
8. #11927182	C₂	semidirect
9. #11927147	C₂	semidirect
10. #11927145	C₂	semidirect
11. #11927110	C₂	semidirect
12. #11927099	C₂	semidirect
13. #11927095	C₂	semidirect
14. #11927094	C₂	semidirect
15. #11927092	C₂	semidirect
16. #127×D₁₉	C₂	semidirect
17. #11927016	C₂	semidirect
18. C₄×#64541	C₂	semidirect
19. C₁₉×#532	C₂	semidirect
20. C₂×#41×C₁₉	C₂²	semidirect
21. C₂×#64545	C₂²	semidirect
22. C₂×#64543	C₂²	semidirect
27. C₂×#64541	C₂²	semidirect
28. C₁₉×C₄⋊Q₈	C₂²	semidirect
30. C₁₉×#124	C₂²	semidirect
31. C₁₉×#121	C₂²	semidirect
32. C₁₉×#121	C₂²	semidirect
33. C₄×D₄×C₁₉	C₂²	semidirect
34. C₄×D₄×C₁₉	C₂²	semidirect
35. C₂×C₄²×C₁₉	C₂²	semidirect
36. #10597393	C₂²	semidirect
38. Q₈×Dic₁₉	C₂²	semidirect
42. #10597386	C₂²	semidirect
43. #10597385	C₂²	semidirect
44. #10597384	C₂²	semidirect
45. #10597384	C₂²	semidirect
46. #10597384	C₂²	semidirect
48. #10597382	C₂²	semidirect
49. D₄×Dic₁₉	C₂²	semidirect
50. D₄×Dic₁₉	C₂²	semidirect
51. #10597376	C₂²	semidirect
52. #10597376	C₂²	semidirect
53. #10597376	C₂²	semidirect
54. #10597375	C₂²	semidirect
57. C₄×C₂²⋊D₁₉	C₂²	semidirect
58. C₄×C₂²⋊D₁₉	C₂²	semidirect
59. C₄×C₂²⋊D₁₉	C₂²	semidirect
61. #10597372	C₂²	semidirect
63. #10597341	C₂²	semidirect
64. #10597341	C₂²	semidirect
65. #10597339	C₂²	semidirect
66. #10597339	C₂²	semidirect
68. #10597336	C₂²	semidirect
69. #10597333	C₂²	semidirect
70. #10597332	C₂²	semidirect
71. #10597331	C₂²	semidirect
72. #10597330	C₂²	semidirect
73. #10597329	C₂²	semidirect
74. #10597329	C₂²	semidirect
76. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
78. #10597321	C₂²	semidirect
82. C₄×D₇₆	C₂²	semidirect
83. C₄×D₇₆	C₂²	semidirect
85. #10597318	C₂²	semidirect
87. C₄²×D₁₉	C₂²	semidirect
88. #10597315	C₂²	semidirect
89. C₄×Dic₃₈	C₂²	semidirect
90. C₄×Dic₃₈	C₂²	semidirect
221. C₄×D₁₉	#41	semidirect
271. #532	D₁₉	semidirect
287. C₂×#41	C₂×D₁₉	semidirect
292. C₄⋊Q₈	C₂×D₁₉	semidirect
304. #124	C₂×D₁₉	semidirect
321. #121	C₂×D₁₉	semidirect
322. #121	C₂×D₁₉	semidirect
343. C₄×D₄	C₂×D₁₉	semidirect
344. C₄×D₄	C₂×D₁₉	semidirect
353. C₂×C₄²	C₂×D₁₉	semidirect
354. C₁₉	#3508	semidirect

Maximal subgroups

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

subgroup	index
#11927277	2
#11927276	2
#11927213	2
#11927212	2
#11927191	2
#11927189	2
#11927187	2
#11927182	2
#11927147	2
#11927145	2
#11927110	2
#11927099	2
#11927095	2
#11927094	2
#11927092	2
#127×D₁₉	2
#11927016	2
C₄×#64541	2
C₁₉×#532	2
#3508	19