Subgroups — #14578062

Order 2432.

1050 conjugacy classes of subgroups.

The subgroup lattice has 428 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	#11927281	C₂	1	2	yes	maximal, complemented
3	#11927256	C₂	1	2	yes	maximal, complemented
4	#11927240	C₂	1	2	yes	maximal, complemented
5	#11927234	C₂	1	2	yes	maximal, complemented
6	#11927224	C₂	1	2	yes	maximal, complemented
7	#11927203	C₂	1	2	yes	maximal, complemented
8	#11927190	C₂	1	2	yes	maximal, complemented
9	#11927144	C₂	1	4	yes	maximal, complemented
10	#11927126	C₂	1	4	yes	maximal, complemented
11	#11927122	C₂	1	2	yes	maximal, complemented
12	#11927115	C₂	1	1	yes	maximal, characteristic, complemented
13	#11927108	C₂	1	1	yes	maximal, characteristic, complemented
14	#11927078	C₂	1	2	yes	maximal, complemented
15	C₁₉×#532	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#41×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×#41×C₁₉	C₂²	1	1	yes	characteristic, complemented
18	C₂×#64541	C₂²	1	2	yes	—
19	C₂²×D₇₆	C₂²	1	1	yes	characteristic
20	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic, complemented
21	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
22	C₁₉×#127	C₂²	1	1	yes	characteristic
23	C₁₉×#124	C₂²	1	1	yes	characteristic
24	C₁₉×#124	C₂²	1	1	yes	characteristic, complemented
25	C₁₉×#121	C₂²	1	2	yes	—
26	C₁₉×#121	C₂²	1	2	yes	complemented
27	C₄×D₄×C₁₉	C₂²	1	2	yes	—
28	C₄×D₄×C₁₉	C₂²	1	2	yes	complemented
29	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic, complemented
30	#10597393	C₂²	1	2	yes	—
31	#10597392	C₂²	1	4	yes	complemented
32	#10597390	C₂²	1	2	yes	complemented
33	#10597386	C₂²	1	2	yes	—
34	#10597385	C₂²	1	4	yes	complemented
35	#10597385	C₂²	1	4	yes	complemented
36	#10597385	C₂²	1	4	yes	complemented
37	#10597385	C₂²	1	4	yes	complemented
38	#10597384	C₂²	1	4	yes	complemented
39	#10597383	C₂²	1	2	yes	—
40	#10597383	C₂²	1	2	yes	—
41	#10597383	C₂²	1	4	yes	—
42	#10597382	C₂²	1	2	yes	—
43	#10597381	C₂²	1	2	yes	—
44	#10597381	C₂²	1	4	yes	—
45	#10597381	C₂²	1	2	yes	complemented
46	#10597376	C₂²	1	2	yes	—
47	#10597376	C₂²	1	2	yes	—
48	#10597376	C₂²	1	2	yes	—
49	#10597375	C₂²	1	4	yes	complemented
50	C₄×C₂²⋊D₁₉	C₂²	1	4	yes	complemented
51	#10597372	C₂²	1	1	yes	characteristic
52	#10597372	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	complemented
54	#10597370	C₂²	1	2	yes	—
55	#10597370	C₂²	1	2	yes	complemented
56	#10597370	C₂²	1	2	yes	complemented
57	#10597344	C₂²	1	4	yes	complemented
58	#10597342	C₂²	1	4	yes	complemented
59	#10597340	C₂²	1	4	yes	—
60	#10597335	C₂²	1	4	yes	complemented
61	#10597331	C₂²	1	4	yes	complemented
62	#10597330	C₂²	1	4	yes	—
63	#10597329	C₂²	1	4	yes	complemented
64	(C₂²⋊D₁₉)⋊C₄	C₂²	1	4	yes	complemented
65	(C₂²⋊D₁₉)⋊C₄	C₂²	1	4	yes	complemented
66	C₂²⋊C₄×D₁₉	C₂²	1	4	yes	—
67	#10597325	C₂²	1	4	yes	—
68	#10597323	C₂²	1	4	yes	complemented
69	#10597322	C₂²	1	4	yes	complemented
70	#10597321	C₂²	1	2	yes	—
71	C₄×D₇₆	C₂²	1	2	yes	—
72	#10597318	C₂²	1	4	yes	complemented
73	#10597316	C₂²	1	2	yes	complemented
74	C₄×Dic₃₈	C₂²	1	2	yes	complemented
75	C₂³×D₁₉	C₂³	1	2	yes	—
76	#41×C₁₉	—	4	2	no	—
77	#41×C₁₉	—	4	2	no	—
78	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
79	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
80	C₂×D₄×C₁₉	C₂³	1	2	yes	—
81	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
82	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
83	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
84	C₂×D₄×C₁₉	C₂³	1	2	yes	—
85	C₂×D₄×C₁₉	C₂³	1	2	yes	—
86	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
87	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
88	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
89	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
90	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
91	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
92	C₂×C₂²⋊D₁₉	C₂³	1	4	yes	—
93	C₂×C₂²⋊D₁₉	C₂³	1	4	yes	—
94	C₂×C₂²⋊D₁₉	C₂³	1	4	yes	—
95	C₂×C₂²⋊D₁₉	C₂³	1	4	yes	—
96	C₂²×Dic₁₉	C₂³	1	2	yes	—
97	C₂²×Dic₁₉	C₂³	1	4	yes	—
98	#64541	—	4	4	no	—
99	C₂×D₇₆	—	4	2	no	—
100	C₂×D₇₆	C₂³	1	2	yes	—
101	C₂×D₇₆	C₂³	1	2	yes	—
102	C₂×C₄×D₁₉	C₂³	1	4	yes	—
103	C₂×C₄×D₁₉	C₂³	1	4	yes	—
104	C₂×Dic₃₈	—	4	2	no	—
105	C₂×Dic₃₈	C₂³	1	2	yes	—
106	C₂×Dic₃₈	C₂³	1	2	yes	—
107	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
108	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
109	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
110	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
111	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
112	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
113	C₄²×C₁₉	C₂³	1	2	yes	—
114	C₄²×C₁₉	C₂³	1	1	yes	characteristic
115	C₄²×C₁₉	C₂³	1	1	yes	characteristic
116	C₂²⋊Dic₁₉	C₂³	1	4	yes	—
117	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
118	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
119	C₂²⋊Dic₁₉	C₂³	1	4	yes	—
120	C₂²⋊Dic₁₉	C₂³	1	4	yes	—
121	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
122	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
123	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
124	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
125	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
126	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
127	C₄⋊Dic₁₉	C₂³	1	2	yes	—
128	C₄⋊Dic₁₉	C₂³	1	2	yes	—
129	C₄⋊Dic₁₉	C₂³	1	4	yes	—
130	Dic₁₉⋊C₄	C₂³	1	4	yes	—
131	Dic₁₉⋊C₄	C₂³	1	4	yes	—
132	Dic₁₉⋊C₄	C₂³	1	4	yes	—
133	Dic₁₉⋊C₄	C₂³	1	4	yes	—
134	Dic₁₉⋊C₄	C₂³	1	4	yes	—
135	Dic₁₉⋊C₄	C₂³	1	4	yes	—
136	C₄×Dic₁₉	C₂³	1	2	yes	—
137	C₄×Dic₁₉	C₂³	1	2	yes	—
138	C₄×Dic₁₉	C₂³	1	4	yes	—
139	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
140	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
141	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
142	C₂³×C₁₉	C₂⁴	1	2	yes	—
143	C₂²×D₁₉	—	4	2	no	—
144	C₂²×D₁₉	—	4	4	no	—
145	C₂²×D₁₉	C₂⁴	1	4	yes	—
146	Q₈×C₁₉	—	4	1	no	—
147	Q₈×C₁₉	—	4	1	no	—
148	D₄×C₁₉	—	4	2	no	—
149	D₄×C₁₉	—	4	2	no	—
150	D₄×C₁₉	—	4	1	no	—
151	D₄×C₁₉	—	4	2	no	—
152	D₄×C₁₉	—	4	1	no	—
153	D₄×C₁₉	—	4	1	no	—
154	D₄×C₁₉	—	4	1	no	—
155	C₂×C₄×C₁₉	—	2	2	no	—
156	C₂×C₄×C₁₉	—	2	2	no	—
157	C₂×C₄×C₁₉	—	2	4	no	—
158	C₂×C₄×C₁₉	—	2	2	no	—
159	C₂×C₄×C₁₉	—	4	2	no	—
160	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
161	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
162	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
163	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
164	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
165	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
166	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
167	C₂²⋊D₁₉	—	4	4	no	—
168	C₂²⋊D₁₉	—	4	4	no	—
169	C₂²⋊D₁₉	—	4	4	no	—
170	C₂²⋊D₁₉	—	4	4	no	—
171	C₂×Dic₁₉	—	4	2	no	—
172	C₂×Dic₁₉	—	4	4	no	—
173	C₂×Dic₁₉	C₂⁴	1	4	yes	—
174	C₂×Dic₁₉	C₂⁴	1	4	yes	—
175	C₂×Dic₁₉	C₂⁴	1	4	yes	—
176	D₇₆	—	2	4	no	—
177	D₇₆	—	4	2	no	—
178	C₄×D₁₉	—	4	4	no	—
179	C₄×D₁₉	—	4	4	no	—
180	Dic₃₈	—	2	4	no	—
181	Dic₃₈	—	4	2	no	—
182	#3551	—	19	1	no	maximal, Sylow
183	C₂²×C₁₉	—	2	1	no	—
184	C₂²×C₁₉	—	2	2	no	—
185	C₂²×C₁₉	—	2	1	no	—
186	C₂²×C₁₉	—	2	1	no	—
187	C₂²×C₁₉	—	2	2	no	—
188	C₂²×C₁₉	—	2	2	no	—
189	C₂²×C₁₉	—	2	2	no	—
190	C₂²×C₁₉	—	2	2	no	—
191	C₂²×C₁₉	—	2	2	no	—
192	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
193	C₂×D₁₉	—	2	4	no	—
194	C₂×D₁₉	—	2	4	no	—
195	C₂×D₁₉	—	2	4	no	—
196	C₂×D₁₉	—	8	4	no	—
197	C₄×C₁₉	—	2	1	no	—
198	C₄×C₁₉	—	2	2	no	—
199	C₄×C₁₉	—	2	1	no	—
200	C₄×C₁₉	—	2	1	no	—
201	C₄×C₁₉	—	2	2	no	—
202	C₄×C₁₉	—	2	2	no	—
203	C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
204	Dic₁₉	—	2	4	no	—
205	Dic₁₉	—	2	4	no	—
206	Dic₁₉	—	2	4	no	—
207	#563	—	19	2	no	—
208	#560	—	19	2	no	—
209	#555	—	19	2	no	—
210	#553	—	19	2	no	—
211	#552	—	19	2	no	—
212	#551	—	19	2	no	—
213	#548	—	19	2	no	—
214	#546	—	19	2	no	—
215	#540	—	19	4	no	—
216	#538	—	19	4	no	—
217	#537	—	19	2	no	—
218	#536	—	19	1	no	—
219	#535	—	19	1	no	—
220	#532	D₁₉	1	1	yes	characteristic, complemented
221	#529	—	19	2	no	—
222	C₂×C₁₉	—	4	1	no	—
223	C₂×C₁₉	—	4	1	no	—
224	C₂×C₁₉	—	4	2	no	—
225	C₂×C₁₉	—	4	1	no	—
226	C₂×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
227	C₂×C₁₉	#585	1	2	yes	—
228	D₁₉	—	4	4	no	—
229	C₂×#41	—	19	2	no	—
230	C₂×#41	C₂×D₁₉	1	1	yes	characteristic
231	C₂×#41	C₂×D₁₉	1	1	yes	characteristic, complemented
232	C₂²×Q₈	—	19	1	no	—
233	C₂²×D₄	—	19	1	no	—
234	C₄⋊Q₈	—	19	2	no	—
235	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
236	#127	—	19	2	no	—
237	#127	C₂×D₁₉	1	1	yes	characteristic
238	#126	—	19	4	no	—
239	#126	—	19	4	no	—
240	#126	—	19	4	no	—
241	#125	—	19	4	no	—
242	#125	—	19	2	no	—
243	#124	—	19	2	no	—
244	#124	—	19	2	no	—
245	#124	—	19	4	no	—
246	#124	—	19	2	no	—
247	#124	C₂×D₁₉	1	1	yes	characteristic
248	#124	C₂×D₁₉	1	1	yes	characteristic, complemented
249	#123	—	19	2	no	—
250	#123	—	19	4	no	—
251	#123	—	19	2	no	—
252	#123	—	19	4	no	—
253	#123	—	19	4	no	—
254	#123	—	19	4	no	—
255	C₂²⋊Q₈	—	19	4	no	—
256	C₂²⋊Q₈	—	19	2	no	—
257	C₂²⋊Q₈	—	19	2	no	—
258	C₂²⋊Q₈	—	19	2	no	—
259	C₂²⋊Q₈	—	19	4	no	—
260	#121	—	19	4	no	—
261	#121	—	19	4	no	—
262	#121	—	19	4	no	—
263	#121	—	19	4	no	—
264	#121	—	19	4	no	—
265	#121	—	19	2	no	—
266	#121	—	19	2	no	—
267	#121	—	19	2	no	—
268	#121	—	19	4	no	—
269	#121	C₂×D₁₉	1	2	yes	—
270	#121	C₂×D₁₉	1	2	yes	complemented
271	#120	—	19	2	no	—
272	#120	—	19	2	no	—
273	#120	—	19	4	no	—
274	C₄×Q₈	—	19	2	no	—
275	C₄×D₄	—	19	4	no	—
276	C₄×D₄	—	19	4	no	—
277	C₄×D₄	—	19	4	no	—
278	C₄×D₄	—	19	2	no	—
279	C₄×D₄	C₂×D₁₉	1	2	yes	—
280	C₄×D₄	C₂×D₁₉	1	2	yes	complemented
281	#117	—	19	1	no	—
282	#117	—	19	1	no	—
283	#117	—	19	4	no	—
284	#117	—	19	4	no	—
285	C₂×C₄⋊C₄	—	19	2	no	—
286	C₂×C₂²⋊C₄	—	19	4	no	—
287	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic, complemented
288	C₁₉	#3551	1	1	yes	characteristic, complemented, Sylow
289	C₂⁴	—	19	2	no	—
290	#41	—	4	2	no	—
291	#41	—	4	2	no	—
292	#41	—	76	4	no	—
293	C₂×Q₈	—	19	2	no	—
294	C₂×Q₈	—	19	2	no	—
295	C₂×Q₈	—	76	2	no	—
296	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
297	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
298	C₂×D₄	—	19	4	no	—
299	C₂×D₄	—	19	4	no	—
300	C₂×D₄	—	19	4	no	—
301	C₂×D₄	—	19	4	no	—
302	C₂×D₄	—	19	2	no	—
303	C₂×D₄	—	19	2	no	—
304	C₂×D₄	—	76	2	no	—
305	C₂×D₄	C₂²×D₁₉	1	2	yes	—
306	C₂×D₄	C₂²×D₁₉	1	2	yes	—
307	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
308	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
309	C₂×D₄	C₂²×D₁₉	1	2	yes	—
310	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
311	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
312	C₂²×C₄	—	19	4	no	—
313	C₂²×C₄	—	19	2	no	—
314	C₂²×C₄	—	19	4	no	—
315	C₂²×C₄	—	19	4	no	—
316	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
317	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
318	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
319	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
320	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
321	C₄⋊C₄	—	19	4	no	—
322	C₄⋊C₄	—	19	4	no	—
323	C₄⋊C₄	—	19	4	no	—
324	C₄⋊C₄	—	19	4	no	—
325	C₄⋊C₄	—	19	4	no	—
326	C₄⋊C₄	—	19	4	no	—
327	C₄⋊C₄	—	19	2	no	—
328	C₄⋊C₄	—	19	2	no	—
329	C₄⋊C₄	—	19	4	no	—
330	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
331	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
332	C₂²⋊C₄	—	19	4	no	—
333	C₂²⋊C₄	—	19	2	no	—
334	C₂²⋊C₄	—	19	4	no	—
335	C₂²⋊C₄	—	19	2	no	—
336	C₂²⋊C₄	—	19	4	no	—
337	C₂²⋊C₄	—	19	4	no	—
338	C₂²⋊C₄	—	19	4	no	—
339	C₂²⋊C₄	—	19	4	no	—
340	C₂²⋊C₄	—	19	4	no	—
341	C₂²⋊C₄	—	19	4	no	—
342	C₂²⋊C₄	—	19	4	no	—
343	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
344	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
345	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
346	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
347	C₄²	—	19	2	no	—
348	C₄²	—	19	4	no	—
349	C₄²	—	19	2	no	—
350	C₄²	C₂²×D₁₉	1	1	yes	characteristic
351	C₄²	C₂²×D₁₉	1	2	yes	—
352	C₄²	C₂²×D₁₉	1	1	yes	characteristic
353	C₂³	—	19	4	no	—
354	C₂³	—	76	2	no	—
355	C₂³	—	76	4	no	—
356	C₂³	C₂³×D₁₉	1	1	yes	characteristic
357	C₂³	C₂³×D₁₉	1	1	yes	characteristic
358	C₂³	C₂³×D₁₉	1	1	yes	characteristic
359	C₂³	C₂³×D₁₉	1	2	yes	—
360	Q₈	—	4	1	no	—
361	Q₈	—	4	1	no	—
362	Q₈	—	38	4	no	—
363	Q₈	—	76	2	no	—
364	D₄	—	4	2	no	—
365	D₄	—	4	1	no	—
366	D₄	—	4	1	no	—
367	D₄	—	4	1	no	—
368	D₄	—	4	1	no	—
369	D₄	—	4	2	no	—
370	D₄	—	4	2	no	—
371	D₄	—	38	4	no	—
372	D₄	—	76	2	no	—
373	D₄	—	76	4	no	—
374	D₄	—	76	4	no	—
375	D₄	—	76	4	no	—
376	D₄	—	76	4	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	19	4	no	—
383	C₂×C₄	—	19	4	no	—
384	C₂×C₄	—	19	4	no	—
385	C₂×C₄	—	76	4	no	—
386	C₂×C₄	—	76	4	no	—
387	C₂×C₄	—	76	2	no	—
388	C₂×C₄	—	76	4	no	—
389	C₂×C₄	C₂³×D₁₉	1	2	yes	—
390	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
391	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
392	C₂×C₄	C₂³×D₁₉	1	2	yes	—
393	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
394	C₂×C₄	C₂³×D₁₉	1	2	yes	—
395	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
396	C₂²	—	2	1	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	2	2	no	—
399	C₂²	—	2	1	no	—
400	C₂²	—	2	2	no	—
401	C₂²	—	2	2	no	—
402	C₂²	—	2	2	no	—
403	C₂²	—	2	2	no	—
404	C₂²	—	2	2	no	—
405	C₂²	—	38	4	no	—
406	C₂²	—	38	4	no	—
407	C₂²	—	38	4	no	—
408	C₂²	—	152	4	no	—
409	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
410	C₄	—	2	2	no	—
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	2	no	—
415	C₄	—	2	2	no	—
416	C₄	—	38	4	no	—
417	C₄	—	38	4	no	—
418	C₄	—	38	4	no	—
419	C₄	#10597430	1	2	yes	—
420	C₂	—	4	1	no	—
421	C₂	—	4	1	no	—
422	C₂	—	4	1	no	—
423	C₂	—	4	2	no	—
424	C₂	—	76	4	no	—
425	C₂	C₂×#10597430	1	1	yes	characteristic
426	C₂	#11927380	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Fitting	C₁₉×#532	C₂
hypercenter	#532	D₁₉
hypocenter	C₁₉	#3551
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. #11927293	C₂	semidirect
2. #11927281	C₂	semidirect
3. #11927256	C₂	semidirect
4. #11927240	C₂	semidirect
5. #11927234	C₂	semidirect
6. #11927224	C₂	semidirect
7. #11927203	C₂	semidirect
8. #11927190	C₂	semidirect
9. #11927144	C₂	semidirect
10. #11927126	C₂	semidirect
11. #11927122	C₂	semidirect
12. #11927115	C₂	semidirect
13. #11927108	C₂	semidirect
14. #11927078	C₂	semidirect
15. C₁₉×#532	C₂	semidirect
17. C₂×#41×C₁₉	C₂²	semidirect
20. C₂²×Dic₃₈	C₂²	semidirect
21. C₁₉×C₄⋊Q₈	C₂²	semidirect
24. C₁₉×#124	C₂²	semidirect
26. C₁₉×#121	C₂²	semidirect
28. C₄×D₄×C₁₉	C₂²	semidirect
29. C₂×C₄²×C₁₉	C₂²	semidirect
31. #10597392	C₂²	semidirect
32. #10597390	C₂²	semidirect
34. #10597385	C₂²	semidirect
35. #10597385	C₂²	semidirect
36. #10597385	C₂²	semidirect
37. #10597385	C₂²	semidirect
38. #10597384	C₂²	semidirect
45. #10597381	C₂²	semidirect
49. #10597375	C₂²	semidirect
50. C₄×C₂²⋊D₁₉	C₂²	semidirect
52. #10597372	C₂²	semidirect
53. C₂×C₄⋊Dic₁₉	C₂²	semidirect
55. #10597370	C₂²	semidirect
56. #10597370	C₂²	semidirect
57. #10597344	C₂²	semidirect
58. #10597342	C₂²	semidirect
60. #10597335	C₂²	semidirect
61. #10597331	C₂²	semidirect
63. #10597329	C₂²	semidirect
64. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
65. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
68. #10597323	C₂²	semidirect
69. #10597322	C₂²	semidirect
72. #10597318	C₂²	semidirect
73. #10597316	C₂²	semidirect
74. C₄×Dic₃₈	C₂²	semidirect
220. #532	D₁₉	semidirect
231. C₂×#41	C₂×D₁₉	semidirect
235. C₄⋊Q₈	C₂×D₁₉	semidirect
248. #124	C₂×D₁₉	semidirect
270. #121	C₂×D₁₉	semidirect
280. C₄×D₄	C₂×D₁₉	semidirect
287. C₂×C₄²	C₂×D₁₉	semidirect
288. C₁₉	#3551	semidirect

Maximal subgroups

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

subgroup	index
#11927293	2
#11927281	2
#11927256	2
#11927240	2
#11927234	2
#11927224	2
#11927203	2
#11927190	2
#11927144	2
#11927126	2
#11927122	2
#11927115	2
#11927108	2
#11927078	2
C₁₉×#532	2
#3551	19