Subgroups — #14578158

Order 2432.

1160 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927288	C₂	1	2	yes	maximal, complemented
2	#11927286	C₂	1	2	yes	maximal, complemented
3	#11927277	C₂	1	2	yes	maximal, complemented
4	#11927200	C₂	1	2	yes	maximal, complemented
5	#11927189	C₂	1	2	yes	maximal, complemented
6	#11927182	C₂	1	4	yes	maximal, complemented
7	#11927178	C₂	1	2	yes	maximal, complemented
8	#11927168	C₂	1	2	yes	maximal, complemented
9	#11927131	C₂	1	2	yes	maximal, complemented
10	#11927127	C₂	1	4	yes	maximal, complemented
11	#11927107	C₂	1	2	yes	maximal, complemented
12	#11927102	C₂	1	2	yes	maximal, complemented
13	#11927078	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#10597321	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#532	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#41×C₁₉	C₂²	1	2	yes	complemented
17	C₂×#64543	C₂²	1	2	yes	complemented
18	C₂×D₄×D₁₉	C₂²	1	4	yes	complemented
19	C₂×D₄×D₁₉	C₂²	1	2	yes	complemented
20	C₂²×D₇₆	C₂²	1	1	yes	characteristic
21	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic, complemented
22	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
23	C₁₉×#127	C₂²	1	1	yes	characteristic, complemented
24	C₁₉×#124	C₂²	1	2	yes	complemented
25	C₁₉×#121	C₂²	1	2	yes	complemented
26	C₁₉×#121	C₂²	1	2	yes	complemented
27	C₄×D₄×C₁₉	C₂²	1	2	yes	complemented
28	C₄×D₄×C₁₉	C₂²	1	2	yes	complemented
29	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic, complemented
30	#10597393	C₂²	1	4	yes	complemented
31	#10597392	C₂²	1	4	yes	complemented
32	#10597386	C₂²	1	2	yes	—
33	#10597385	C₂²	1	4	yes	complemented
34	#10597385	C₂²	1	4	yes	complemented
35	#10597385	C₂²	1	4	yes	complemented
36	#10597383	C₂²	1	4	yes	complemented
37	#10597383	C₂²	1	4	yes	complemented
38	#10597383	C₂²	1	4	yes	complemented
39	#10597382	C₂²	1	2	yes	complemented
40	D₄×Dic₁₉	C₂²	1	4	yes	complemented
41	#10597376	C₂²	1	1	yes	characteristic
42	#10597376	C₂²	1	4	yes	complemented
43	#10597375	C₂²	1	2	yes	complemented
44	#10597375	C₂²	1	4	yes	complemented
45	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	complemented
46	C₄×C₂²⋊D₁₉	C₂²	1	4	yes	complemented
47	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	2	yes	complemented
48	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	2	yes	complemented
49	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	4	yes	complemented
50	#10597370	C₂²	1	1	yes	characteristic, complemented
51	#10597344	C₂²	1	4	yes	complemented
52	#10597343	C₂²	1	2	yes	complemented
53	#10597341	C₂²	1	2	yes	—
54	#10597340	C₂²	1	4	yes	complemented
55	#10597339	C₂²	1	2	yes	complemented
56	#10597333	C₂²	1	2	yes	complemented
57	#10597332	C₂²	1	4	yes	complemented
58	#10597331	C₂²	1	4	yes	complemented
59	#10597331	C₂²	1	4	yes	complemented
60	#10597330	C₂²	1	4	yes	complemented
61	#10597329	C₂²	1	4	yes	complemented
62	#10597328	C₂²	1	4	yes	complemented
63	#10597328	C₂²	1	4	yes	complemented
64	#10597324	C₂²	1	4	yes	complemented
65	#10597322	C₂²	1	2	yes	complemented
66	#10597321	C₂²	1	2	yes	complemented
67	#10597321	C₂²	1	2	yes	complemented
68	#10597321	C₂²	1	2	yes	complemented
69	#10597321	C₂²	1	2	yes	complemented
70	#10597321	C₂²	1	1	yes	characteristic, complemented
71	C₄×D₇₆	C₂²	1	1	yes	characteristic, complemented
72	#10597318	C₂²	1	2	yes	complemented
73	#10597316	C₂²	1	1	yes	characteristic, complemented
74	C₄×Dic₃₈	C₂²	1	1	yes	characteristic, complemented
75	C₂³×D₁₉	C₂³	1	2	yes	—
76	C₂³×D₁₉	C₂³	1	4	yes	—
77	#41×C₁₉	—	4	4	no	—
78	C₂×Q₈×C₁₉	C₂³	1	2	yes	—
79	C₂×D₄×C₁₉	C₂³	1	4	yes	—
80	C₂×D₄×C₁₉	C₂³	1	2	yes	—
81	C₂×D₄×C₁₉	C₂³	1	2	yes	—
82	C₂×D₄×C₁₉	C₂³	1	2	yes	—
83	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
84	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
85	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
86	C₂²×C₄×C₁₉	C₂³	1	4	yes	—
87	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
88	C₂×C₂²⋊D₁₉	C₂³	1	4	yes	—
89	C₂×C₂²⋊D₁₉	C₂³	1	4	yes	—
90	C₂×C₂²⋊D₁₉	C₂³	1	4	yes	—
91	C₂×C₂²⋊D₁₉	C₂³	1	4	yes	—
92	C₂²×Dic₁₉	C₂³	1	2	yes	—
93	C₂²×Dic₁₉	C₂³	1	4	yes	—
94	#64543	—	4	4	no	—
95	D₄×D₁₉	—	4	4	no	—
96	D₄×D₁₉	—	4	8	no	—
97	C₂×D₇₆	—	4	2	no	—
98	C₂×D₇₆	C₂³	1	2	yes	—
99	C₂×D₇₆	C₂³	1	1	yes	characteristic
100	C₂×D₇₆	C₂³	1	4	yes	—
101	C₂×D₇₆	C₂³	1	2	yes	—
102	C₂×C₄×D₁₉	C₂³	1	2	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	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
108	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
109	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
110	C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
111	C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
112	C₄²×C₁₉	C₂³	1	1	yes	characteristic
113	C₄²×C₁₉	C₂³	1	1	yes	characteristic
114	C₄²×C₁₉	C₂³	1	1	yes	characteristic
115	C₄²×C₁₉	C₂³	1	1	yes	characteristic
116	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
117	C₂²⋊Dic₁₉	C₂³	1	4	yes	—
118	C₂²⋊Dic₁₉	C₂³	1	4	yes	—
119	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
120	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
121	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
122	(C₂×D₁₉)⋊C₄	C₂³	1	2	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	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
128	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
129	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
130	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
131	C₄⋊Dic₁₉	C₂³	1	4	yes	—
132	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
133	Dic₁₉⋊C₄	C₂³	1	2	yes	—
134	Dic₁₉⋊C₄	C₂³	1	2	yes	—
135	Dic₁₉⋊C₄	C₂³	1	4	yes	—
136	Dic₁₉⋊C₄	C₂³	1	2	yes	—
137	Dic₁₉⋊C₄	C₂³	1	2	yes	—
138	C₄×Dic₁₉	C₂³	1	4	yes	—
139	C₄×Dic₁₉	C₂³	1	2	yes	—
140	C₂³×C₁₉	C₂⁴	1	4	yes	—
141	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
142	C₂²×D₁₉	—	2	4	no	—
143	C₂²×D₁₉	—	4	2	no	—
144	C₂²×D₁₉	—	4	4	no	—
145	C₂²×D₁₉	—	4	4	no	—
146	C₂²×D₁₉	—	4	4	no	—
147	C₂²×D₁₉	—	4	2	no	—
148	C₂²×D₁₉	C₂⁴	1	2	yes	—
149	C₂²×D₁₉	C₂⁴	1	4	yes	—
150	Q₈×C₁₉	—	4	2	no	—
151	D₄×C₁₉	—	2	8	no	—
152	D₄×C₁₉	—	2	4	no	—
153	D₄×C₁₉	—	4	2	no	—
154	D₄×C₁₉	—	4	2	no	—
155	C₂×C₄×C₁₉	—	2	2	no	—
156	C₂×C₄×C₁₉	—	2	2	no	—
157	C₂×C₄×C₁₉	—	4	1	no	—
158	C₂×C₄×C₁₉	—	4	4	no	—
159	C₂×C₄×C₁₉	C₂⁴	1	4	yes	—
160	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
161	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
162	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
163	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
164	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
165	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
166	C₂²⋊D₁₉	—	2	4	no	—
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	2	yes	—
174	C₂×Dic₁₉	C₂⁴	1	2	yes	—
175	C₂×Dic₁₉	C₂⁴	1	4	yes	—
176	C₂×Dic₁₉	C₂⁴	1	2	yes	—
177	D₇₆	—	2	4	no	—
178	D₇₆	—	4	2	no	—
179	D₇₆	—	4	1	no	—
180	D₇₆	—	4	4	no	—
181	C₄×D₁₉	—	2	4	no	—
182	C₄×D₁₉	—	4	4	no	—
183	Dic₃₈	—	2	4	no	—
184	Dic₃₈	—	4	2	no	—
185	Dic₃₈	—	4	1	no	—
186	#3558	—	19	1	no	maximal, Sylow
187	C₂²×C₁₉	—	2	1	no	—
188	C₂²×C₁₉	—	2	1	no	—
189	C₂²×C₁₉	—	2	4	no	—
190	C₂²×C₁₉	—	2	4	no	—
191	C₂²×C₁₉	—	2	4	no	—
192	C₂²×C₁₉	H(5,𝔽₂)	1	2	yes	—
193	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
194	C₂×D₁₉	—	2	2	no	—
195	C₂×D₁₉	—	2	4	no	—
196	C₂×D₁₉	—	2	4	no	—
197	C₂×D₁₉	—	2	2	no	—
198	C₂×D₁₉	—	2	2	no	—
199	C₂×D₁₉	—	2	4	no	—
200	C₂×D₁₉	—	8	4	no	—
201	C₂×D₁₉	—	8	8	no	—
202	C₄×C₁₉	—	2	1	no	—
203	C₄×C₁₉	—	2	4	no	—
204	C₄×C₁₉	—	2	1	no	—
205	C₄×C₁₉	—	2	1	no	—
206	C₄×C₁₉	—	2	1	no	—
207	C₄×C₁₉	—	2	1	no	—
208	C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
209	Dic₁₉	—	2	4	no	—
210	Dic₁₉	—	2	2	no	—
211	Dic₁₉	—	2	2	no	—
212	Dic₁₉	—	2	2	no	—
213	#562	—	19	2	no	—
214	H(3,𝔽₄)	—	19	2	no	—
215	#559	—	19	2	no	—
216	#548	—	19	2	no	—
217	#546	—	19	4	no	—
218	#546	—	19	2	no	—
219	D₄²	—	19	2	no	—
220	#542	—	19	2	no	—
221	#538	—	19	2	no	—
222	#538	—	19	4	no	—
223	#535	—	19	2	no	—
224	#534	—	19	2	no	—
225	#532	D₁₉	1	1	yes	characteristic, complemented
226	#529	—	19	1	no	—
227	C₂×#124	—	19	1	no	—
228	C₂×C₁₉	—	2	2	no	—
229	C₂×C₁₉	—	4	4	no	—
230	C₂×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
231	C₂×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
232	C₂×C₁₉	#585	1	1	yes	characteristic
233	D₁₉	—	4	2	no	—
234	D₁₉	—	4	4	no	—
235	C₂×#41	—	19	2	no	—
236	C₂×#41	C₂×D₁₉	1	2	yes	complemented
237	C₂²×Q₈	—	19	1	no	—
238	C₂²×D₄	—	19	4	no	—
239	C₂²×D₄	—	19	2	no	—
240	C₂²×D₄	—	19	1	no	—
241	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
242	#127	—	19	2	no	—
243	#127	C₂×D₁₉	1	1	yes	characteristic, complemented
244	#126	—	19	4	no	—
245	#126	—	19	2	no	—
246	#125	—	19	1	no	—
247	#124	—	19	4	no	—
248	#124	—	19	2	no	—
249	#124	—	19	4	no	—
250	#124	—	19	4	no	—
251	#124	—	19	2	no	—
252	#124	—	19	2	no	—
253	#124	—	19	2	no	—
254	#124	—	19	2	no	—
255	#124	—	19	1	no	—
256	#124	C₂×D₁₉	1	2	yes	complemented
257	#123	—	19	2	no	—
258	#123	—	19	4	no	—
259	#123	—	19	4	no	—
260	#123	—	19	4	no	—
261	#123	—	19	4	no	—
262	C₂²⋊Q₈	—	19	4	no	—
263	C₂²⋊Q₈	—	19	1	no	—
264	C₂²⋊Q₈	—	19	2	no	—
265	C₂²⋊Q₈	—	19	4	no	—
266	#121	—	19	4	no	—
267	#121	—	19	4	no	—
268	#121	—	19	4	no	—
269	#121	—	19	1	no	—
270	#121	—	19	4	no	—
271	#121	—	19	2	no	—
272	#121	—	19	4	no	—
273	#121	C₂×D₁₉	1	2	yes	complemented
274	#121	C₂×D₁₉	1	2	yes	complemented
275	#120	—	19	4	no	—
276	#120	—	19	4	no	—
277	#120	—	19	4	no	—
278	#120	—	19	4	no	—
279	#120	—	19	4	no	—
280	C₄×Q₈	—	19	2	no	—
281	C₄×Q₈	—	19	1	no	—
282	C₄×D₄	—	19	4	no	—
283	C₄×D₄	—	19	2	no	—
284	C₄×D₄	—	19	4	no	—
285	C₄×D₄	—	19	2	no	—
286	C₄×D₄	—	19	1	no	—
287	C₄×D₄	C₂×D₁₉	1	2	yes	complemented
288	C₄×D₄	C₂×D₁₉	1	2	yes	complemented
289	#117	—	19	2	no	—
290	C₂×C₂²⋊C₄	—	19	2	no	—
291	C₂×C₂²⋊C₄	—	19	2	no	—
292	C₂×C₂²⋊C₄	—	19	4	no	—
293	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic, complemented
294	C₁₉	#3558	1	1	yes	characteristic, complemented, Sylow
295	C₂⁴	—	19	2	no	—
296	C₂⁴	—	19	4	no	—
297	#41	—	4	4	no	—
298	#41	—	76	4	no	—
299	C₂×Q₈	—	19	2	no	—
300	C₂×Q₈	—	19	1	no	—
301	C₂×Q₈	—	19	2	no	—
302	C₂×Q₈	—	76	2	no	—
303	C₂×Q₈	C₂²×D₁₉	1	2	yes	—
304	C₂×D₄	—	19	2	no	—
305	C₂×D₄	—	19	4	no	—
306	C₂×D₄	—	19	4	no	—
307	C₂×D₄	—	19	4	no	—
308	C₂×D₄	—	19	4	no	—
309	C₂×D₄	—	19	2	no	—
310	C₂×D₄	—	19	1	no	—
311	C₂×D₄	—	19	4	no	—
312	C₂×D₄	—	19	2	no	—
313	C₂×D₄	—	76	2	no	—
314	C₂×D₄	—	76	4	no	—
315	C₂×D₄	—	76	8	no	—
316	C₂×D₄	C₂²×D₁₉	1	4	yes	—
317	C₂×D₄	C₂²×D₁₉	1	2	yes	—
318	C₂×D₄	C₂²×D₁₉	1	2	yes	—
319	C₂×D₄	C₂²×D₁₉	1	2	yes	—
320	C₂²×C₄	—	19	2	no	—
321	C₂²×C₄	—	19	4	no	—
322	C₂²×C₄	—	19	2	no	—
323	C₂²×C₄	—	19	4	no	—
324	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
325	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
326	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
327	C₂²×C₄	C₂²×D₁₉	1	4	yes	—
328	C₄⋊C₄	—	19	2	no	—
329	C₄⋊C₄	—	19	2	no	—
330	C₄⋊C₄	—	19	2	no	—
331	C₄⋊C₄	—	19	2	no	—
332	C₄⋊C₄	—	19	4	no	—
333	C₄⋊C₄	—	19	4	no	—
334	C₄⋊C₄	—	19	1	no	—
335	C₄⋊C₄	—	19	1	no	—
336	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
337	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
338	C₂²⋊C₄	—	19	2	no	—
339	C₂²⋊C₄	—	19	4	no	—
340	C₂²⋊C₄	—	19	4	no	—
341	C₂²⋊C₄	—	19	2	no	—
342	C₂²⋊C₄	—	19	4	no	—
343	C₂²⋊C₄	—	19	4	no	—
344	C₂²⋊C₄	—	19	4	no	—
345	C₂²⋊C₄	—	19	4	no	—
346	C₂²⋊C₄	—	19	4	no	—
347	C₂²⋊C₄	—	19	4	no	—
348	C₂²⋊C₄	—	19	2	no	—
349	C₂²⋊C₄	—	19	2	no	—
350	C₂²⋊C₄	—	19	4	no	—
351	C₂²⋊C₄	—	19	2	no	—
352	C₂²⋊C₄	C₂²×D₁₉	1	4	yes	—
353	C₂²⋊C₄	C₂²×D₁₉	1	4	yes	—
354	C₄²	—	19	2	no	—
355	C₄²	—	19	4	no	—
356	C₄²	C₂²×D₁₉	1	1	yes	characteristic
357	C₄²	C₂²×D₁₉	1	1	yes	characteristic
358	C₄²	C₂²×D₁₉	1	1	yes	characteristic
359	C₄²	C₂²×D₁₉	1	1	yes	characteristic
360	C₂³	—	19	4	no	—
361	C₂³	—	19	2	no	—
362	C₂³	—	38	4	no	—
363	C₂³	—	76	2	no	—
364	C₂³	—	76	4	no	—
365	C₂³	—	76	4	no	—
366	C₂³	—	76	2	no	—
367	C₂³	—	76	4	no	—
368	C₂³	C₂³×D₁₉	1	4	yes	—
369	C₂³	C₂³×D₁₉	1	1	yes	characteristic
370	Q₈	—	4	2	no	—
371	Q₈	—	38	4	no	—
372	Q₈	—	76	2	no	—
373	Q₈	—	76	1	no	—
374	D₄	—	2	8	no	—
375	D₄	—	2	4	no	—
376	D₄	—	4	2	no	—
377	D₄	—	4	2	no	—
378	D₄	—	38	4	no	—
379	D₄	—	38	4	no	—
380	D₄	—	76	4	no	—
381	D₄	—	76	2	no	—
382	D₄	—	76	1	no	—
383	D₄	—	76	4	no	—
384	D₄	—	76	4	no	—
385	D₄	—	76	4	no	—
386	D₄	—	76	4	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	4	4	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	19	2	no	—
392	C₂×C₄	—	19	4	no	—
393	C₂×C₄	—	19	2	no	—
394	C₂×C₄	—	19	2	no	—
395	C₂×C₄	—	38	4	no	—
396	C₂×C₄	—	76	4	no	—
397	C₂×C₄	—	76	2	no	—
398	C₂×C₄	—	76	4	no	—
399	C₂×C₄	C₂³×D₁₉	1	4	yes	—
400	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
401	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
402	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
403	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
404	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
405	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
406	C₂²	—	2	1	no	—
407	C₂²	—	2	1	no	—
408	C₂²	—	2	4	no	—
409	C₂²	—	2	4	no	—
410	C₂²	—	2	4	no	—
411	C₂²	—	38	4	no	—
412	C₂²	—	38	2	no	—
413	C₂²	—	38	2	no	—
414	C₂²	—	38	4	no	—
415	C₂²	—	38	2	no	—
416	C₂²	—	38	4	no	—
417	C₂²	—	152	4	no	—
418	C₂²	—	152	8	no	—
419	C₂²	#10597430	1	2	yes	—
420	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
421	C₄	—	2	1	no	—
422	C₄	—	2	1	no	—
423	C₄	—	2	4	no	—
424	C₄	—	2	1	no	—
425	C₄	—	2	1	no	—
426	C₄	—	2	1	no	—
427	C₄	—	38	2	no	—
428	C₄	—	38	2	no	—
429	C₄	—	38	4	no	—
430	C₄	—	38	2	no	—
431	C₄	#10597435	1	2	yes	—
432	C₂	—	2	2	no	—
433	C₂	—	4	4	no	—
434	C₂	—	76	4	no	—
435	C₂	—	76	2	no	—
436	C₂	C₂×#10597430	1	1	yes	characteristic
437	C₂	C₂×#10597435	1	1	yes	characteristic
438	C₂	#11927380	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	#3558
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. #11927288	C₂	semidirect
2. #11927286	C₂	semidirect
3. #11927277	C₂	semidirect
4. #11927200	C₂	semidirect
5. #11927189	C₂	semidirect
6. #11927182	C₂	semidirect
7. #11927178	C₂	semidirect
8. #11927168	C₂	semidirect
9. #11927131	C₂	semidirect
10. #11927127	C₂	semidirect
11. #11927107	C₂	semidirect
12. #11927102	C₂	semidirect
13. #11927078	C₂	semidirect
14. C₂×#10597321	C₂	semidirect
15. C₁₉×#532	C₂	semidirect
16. C₂×#41×C₁₉	C₂²	semidirect
17. C₂×#64543	C₂²	semidirect
18. C₂×D₄×D₁₉	C₂²	semidirect
19. C₂×D₄×D₁₉	C₂²	semidirect
21. C₂²×Dic₃₈	C₂²	semidirect
22. C₁₉×C₄⋊Q₈	C₂²	semidirect
23. C₁₉×#127	C₂²	semidirect
24. C₁₉×#124	C₂²	semidirect
25. C₁₉×#121	C₂²	semidirect
26. C₁₉×#121	C₂²	semidirect
27. C₄×D₄×C₁₉	C₂²	semidirect
28. C₄×D₄×C₁₉	C₂²	semidirect
29. C₂×C₄²×C₁₉	C₂²	semidirect
30. #10597393	C₂²	semidirect
31. #10597392	C₂²	semidirect
33. #10597385	C₂²	semidirect
34. #10597385	C₂²	semidirect
35. #10597385	C₂²	semidirect
36. #10597383	C₂²	semidirect
37. #10597383	C₂²	semidirect
38. #10597383	C₂²	semidirect
39. #10597382	C₂²	semidirect
40. D₄×Dic₁₉	C₂²	semidirect
42. #10597376	C₂²	semidirect
43. #10597375	C₂²	semidirect
44. #10597375	C₂²	semidirect
45. C₄×C₂²⋊D₁₉	C₂²	semidirect
46. C₄×C₂²⋊D₁₉	C₂²	semidirect
47. C₂×(C₂×D₁₉)⋊C₄	C₂²	semidirect
48. C₂×(C₂×D₁₉)⋊C₄	C₂²	semidirect
49. C₂×(C₂×D₁₉)⋊C₄	C₂²	semidirect
50. #10597370	C₂²	semidirect
51. #10597344	C₂²	semidirect
52. #10597343	C₂²	semidirect
54. #10597340	C₂²	semidirect
55. #10597339	C₂²	semidirect
56. #10597333	C₂²	semidirect
57. #10597332	C₂²	semidirect
58. #10597331	C₂²	semidirect
59. #10597331	C₂²	semidirect
60. #10597330	C₂²	semidirect
61. #10597329	C₂²	semidirect
62. #10597328	C₂²	semidirect
63. #10597328	C₂²	semidirect
64. #10597324	C₂²	semidirect
65. #10597322	C₂²	semidirect
66. #10597321	C₂²	semidirect
67. #10597321	C₂²	semidirect
68. #10597321	C₂²	semidirect
69. #10597321	C₂²	semidirect
70. #10597321	C₂²	semidirect
71. C₄×D₇₆	C₂²	semidirect
72. #10597318	C₂²	semidirect
73. #10597316	C₂²	semidirect
74. C₄×Dic₃₈	C₂²	semidirect
225. #532	D₁₉	semidirect
236. C₂×#41	C₂×D₁₉	semidirect
241. C₄⋊Q₈	C₂×D₁₉	semidirect
243. #127	C₂×D₁₉	semidirect
256. #124	C₂×D₁₉	semidirect
273. #121	C₂×D₁₉	semidirect
274. #121	C₂×D₁₉	semidirect
287. C₄×D₄	C₂×D₁₉	semidirect
288. C₄×D₄	C₂×D₁₉	semidirect
293. C₂×C₄²	C₂×D₁₉	semidirect
294. C₁₉	#3558	semidirect

Maximal subgroups

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

subgroup	index
#11927288	2
#11927286	2
#11927277	2
#11927200	2
#11927189	2
#11927182	2
#11927178	2
#11927168	2
#11927131	2
#11927127	2
#11927107	2
#11927102	2
#11927078	2
C₂×#10597321	2
C₁₉×#532	2
#3558	19