Subgroups — #14570672

Order 2432.

552 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11926480	C₂	1	1	yes	maximal, characteristic, complemented
2	#11926472	C₂	1	1	yes	maximal, characteristic, complemented
3	#11926472	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926469	C₂	1	1	yes	maximal, characteristic, complemented
5	#11926467	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926467	C₂	1	1	yes	maximal, characteristic, complemented
7	#11926438	C₂	1	1	yes	maximal, characteristic, complemented
8	#11926438	C₂	1	1	yes	maximal, characteristic, complemented
9	#11926437	C₂	1	1	yes	maximal, characteristic, complemented
10	#11926437	C₂	1	1	yes	maximal, characteristic, complemented
11	#11926432	C₂	1	1	yes	maximal, characteristic, complemented
12	#11926432	C₂	1	1	yes	maximal, characteristic, complemented
13	#11926400	C₂	1	1	yes	maximal, characteristic
14	#11926400	C₂	1	1	yes	maximal, characteristic
15	C₁₉×#379	C₂	1	1	yes	maximal, characteristic
16	C₂⁵×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
18	C₂×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₂×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
20	C₂×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
21	C₂×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
22	C₂×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
23	C₂×C₂²⋊Dic₁₉	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊Dic₁₉	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊Dic₁₉	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊Dic₁₉	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊Dic₁₉	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊Dic₁₉	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊Dic₁₉	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊Dic₁₉	C₂²	1	1	yes	characteristic
31	C₂×C₂²⋊Dic₁₉	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊Dic₁₉	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊Dic₁₉	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊Dic₁₉	C₂²	1	1	yes	characteristic
35	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic, complemented
37	C₂×Dic₁₉⋊C₄	C₂²	1	1	yes	characteristic, complemented
38	C₂×Dic₁₉⋊C₄	C₂²	1	1	yes	characteristic, complemented
39	C₂×Dic₁₉⋊C₄	C₂²	1	1	yes	characteristic, complemented
40	C₂×Dic₁₉⋊C₄	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic, complemented
43	C₁₉⋊#95	C₂²	1	1	yes	characteristic, complemented
44	C₁₉⋊#95	C₂²	1	1	yes	characteristic, complemented
45	C₁₉⋊#95	C₂²	1	1	yes	characteristic, complemented
46	C₁₉⋊#95	C₂²	1	1	yes	characteristic, complemented
47	C₁₉⋊#95	C₂²	1	1	yes	characteristic, complemented
48	C₁₉⋊#95	C₂²	1	1	yes	characteristic, complemented
49	C₁₉⋊#95	C₂²	1	1	yes	characteristic, complemented
50	C₁₉⋊#95	C₂²	1	1	yes	characteristic, complemented
51	C₂⁴×C₁₉	—	2	2	no	—
52	C₂⁴×C₁₉	—	2	2	no	—
53	C₂⁴×C₁₉	—	2	2	no	—
54	C₂⁴×C₁₉	—	4	1	no	—
55	C₂⁴×C₁₉	—	4	1	no	—
56	C₂⁴×C₁₉	—	4	1	no	—
57	C₂⁴×C₁₉	—	4	1	no	—
58	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
59	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
60	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
61	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
62	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
63	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
64	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
65	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
66	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
67	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
68	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
69	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
70	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
71	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
72	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
73	C₂²⋊C₄×C₁₉	—	2	2	no	—
74	C₂²⋊C₄×C₁₉	—	2	2	no	—
75	C₂²⋊C₄×C₁₉	—	4	1	no	—
76	C₂²⋊C₄×C₁₉	—	4	1	no	—
77	C₂²⋊C₄×C₁₉	—	4	1	no	—
78	C₂²⋊C₄×C₁₉	—	4	1	no	—
79	C₂²⋊Dic₁₉	—	2	2	no	—
80	C₂²⋊Dic₁₉	—	2	2	no	—
81	C₂²⋊Dic₁₉	—	2	2	no	—
82	C₂²⋊Dic₁₉	—	2	2	no	—
83	C₂²⋊Dic₁₉	—	4	1	no	—
84	C₂²⋊Dic₁₉	—	4	1	no	—
85	C₂²⋊Dic₁₉	—	4	1	no	—
86	C₂²⋊Dic₁₉	—	4	1	no	—
87	C₂²⋊Dic₁₉	—	4	1	no	—
88	C₂²⋊Dic₁₉	—	4	1	no	—
89	C₂²⋊Dic₁₉	—	4	1	no	—
90	C₂²⋊Dic₁₉	—	4	1	no	—
91	C₄⋊Dic₁₉	—	4	1	no	—
92	C₄⋊Dic₁₉	—	4	1	no	—
93	Dic₁₉⋊C₄	—	4	1	no	—
94	Dic₁₉⋊C₄	—	4	1	no	—
95	Dic₁₉⋊C₄	—	4	1	no	—
96	Dic₁₉⋊C₄	—	4	1	no	—
97	C₄×Dic₁₉	—	4	1	no	—
98	C₄×Dic₁₉	—	4	1	no	—
99	C₂³×C₁₉	—	2	1	no	—
100	C₂³×C₁₉	—	2	1	no	—
101	C₂³×C₁₉	—	2	1	no	—
102	C₂³×C₁₉	—	2	1	no	—
103	C₂³×C₁₉	—	2	1	no	—
104	C₂³×C₁₉	—	2	1	no	—
105	C₂³×C₁₉	—	2	1	no	—
106	C₂³×C₁₉	—	2	1	no	—
107	C₂³×C₁₉	—	2	1	no	—
108	C₂³×C₁₉	—	2	1	no	—
109	C₂³×C₁₉	—	2	1	no	—
110	C₂³×C₁₉	—	2	1	no	—
111	C₂³×C₁₉	—	2	1	no	—
112	C₂³×C₁₉	—	2	1	no	—
113	C₂³×C₁₉	—	2	1	no	—
114	C₂³×C₁₉	—	2	1	no	—
115	C₂³×C₁₉	—	2	1	no	—
116	C₂³×C₁₉	—	2	1	no	—
117	C₂³×C₁₉	—	4	4	no	—
118	C₂³×C₁₉	—	4	4	no	—
119	C₂³×C₁₉	—	4	4	no	—
120	C₂³×C₁₉	—	4	4	no	—
121	C₂³×C₁₉	—	4	4	no	—
122	C₂³×C₁₉	—	4	4	no	—
123	C₂³×C₁₉	—	4	4	no	—
124	C₂³×C₁₉	#41	1	2	yes	—
125	C₂³×C₁₉	#41	1	2	yes	—
126	C₂³×C₁₉	#41	1	2	yes	—
127	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
128	C₂×C₄×C₁₉	—	2	1	no	—
129	C₂×C₄×C₁₉	—	2	1	no	—
130	C₂×C₄×C₁₉	—	2	1	no	—
131	C₂×C₄×C₁₉	—	2	1	no	—
132	C₂×C₄×C₁₉	—	2	1	no	—
133	C₂×C₄×C₁₉	—	2	1	no	—
134	C₂×C₄×C₁₉	—	2	1	no	—
135	C₂×C₄×C₁₉	—	2	1	no	—
136	C₂×C₄×C₁₉	—	2	1	no	—
137	C₂×C₄×C₁₉	—	2	1	no	—
138	C₂×C₄×C₁₉	—	2	1	no	—
139	C₂×C₄×C₁₉	—	2	1	no	—
140	C₂×Dic₁₉	—	2	1	no	—
141	C₂×Dic₁₉	—	2	1	no	—
142	C₂×Dic₁₉	—	2	1	no	—
143	C₂×Dic₁₉	—	2	1	no	—
144	C₂×Dic₁₉	—	2	1	no	—
145	C₂×Dic₁₉	—	2	1	no	—
146	C₂×Dic₁₉	—	2	1	no	—
147	C₂×Dic₁₉	—	2	1	no	—
148	C₂×Dic₁₉	—	2	1	no	—
149	C₂×Dic₁₉	—	2	1	no	—
150	C₂×Dic₁₉	—	2	1	no	—
151	C₂×Dic₁₉	—	2	1	no	—
152	C₂×Dic₁₉	—	2	1	no	—
153	C₂×Dic₁₉	—	2	1	no	—
154	C₂×Dic₁₉	—	2	1	no	—
155	C₂×Dic₁₉	—	2	1	no	—
156	C₂×Dic₁₉	—	2	1	no	—
157	C₂×Dic₁₉	—	2	1	no	—
158	C₂×Dic₁₉	—	2	1	no	—
159	C₂×Dic₁₉	—	2	1	no	—
160	C₂×Dic₁₉	—	2	1	no	—
161	C₂×Dic₁₉	—	2	1	no	—
162	C₂×Dic₁₉	—	2	1	no	—
163	C₂×Dic₁₉	—	2	1	no	—
164	#2735	—	19	1	no	maximal, Sylow
165	C₂²×C₁₉	—	2	2	no	—
166	C₂²×C₁₉	—	2	2	no	—
167	C₂²×C₁₉	—	2	2	no	—
168	C₂²×C₁₉	—	2	2	no	—
169	C₂²×C₁₉	—	2	2	no	—
170	C₂²×C₁₉	—	2	2	no	—
171	C₂²×C₁₉	—	2	2	no	—
172	C₂²×C₁₉	—	2	2	no	—
173	C₂²×C₁₉	—	2	2	no	—
174	C₂²×C₁₉	—	4	16	no	—
175	C₂²×C₁₉	—	4	1	no	—
176	C₂²×C₁₉	—	4	1	no	—
177	C₂²×C₁₉	—	4	1	no	—
178	C₂²×C₁₉	—	4	1	no	—
179	C₂²×C₁₉	—	4	1	no	—
180	C₂²×C₁₉	—	4	1	no	—
181	C₂²×C₁₉	—	4	1	no	—
182	C₂²×C₁₉	—	4	1	no	—
183	C₂²×C₁₉	—	4	1	no	—
184	C₂²×C₁₉	—	4	1	no	—
185	C₂²×C₁₉	—	4	1	no	—
186	C₂²×C₁₉	—	4	1	no	—
187	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
188	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
189	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
190	C₂²×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
191	C₂²×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
192	C₂²×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
193	C₂²×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
194	C₄×C₁₉	—	4	1	no	—
195	C₄×C₁₉	—	4	1	no	—
196	C₄×C₁₉	—	4	1	no	—
197	C₄×C₁₉	—	4	1	no	—
198	Dic₁₉	—	4	1	no	—
199	Dic₁₉	—	4	1	no	—
200	Dic₁₉	—	4	1	no	—
201	Dic₁₉	—	4	1	no	—
202	Dic₁₉	—	4	1	no	—
203	Dic₁₉	—	4	1	no	—
204	Dic₁₉	—	4	1	no	—
205	Dic₁₉	—	4	1	no	—
206	#399	—	19	1	no	—
207	#397	—	19	1	no	—
208	#397	—	19	1	no	—
209	#397	—	19	1	no	—
210	#396	—	19	1	no	—
211	#396	—	19	1	no	—
212	#388	—	19	1	no	—
213	#388	—	19	1	no	—
214	#388	—	19	1	no	—
215	#388	—	19	1	no	—
216	#388	—	19	1	no	—
217	#388	—	19	1	no	—
218	#379	—	19	1	no	—
219	#379	—	19	1	no	—
220	#379	D₁₉	1	1	yes	characteristic
221	C₂×C₁₉	—	4	2	no	—
222	C₂×C₁₉	—	4	2	no	—
223	C₂×C₁₉	—	4	2	no	—
224	C₂×C₁₉	#538	1	1	yes	characteristic
225	C₂×C₁₉	#538	1	1	yes	characteristic
226	C₂×C₁₉	#538	1	1	yes	characteristic
227	C₂×C₁₉	#551	1	1	yes	characteristic
228	C₂×C₁₉	#551	1	1	yes	characteristic
229	C₂×C₁₉	#551	1	1	yes	characteristic
230	C₂×C₁₉	#560	1	1	yes	characteristic
231	C₂⁵	C₂×D₁₉	1	1	yes	characteristic
232	C₂×C₄⋊C₄	—	19	1	no	—
233	C₂×C₄⋊C₄	—	19	1	no	—
234	C₂×C₄⋊C₄	—	19	1	no	—
235	C₂×C₄⋊C₄	—	19	1	no	—
236	C₂×C₄⋊C₄	—	19	1	no	—
237	C₂×C₄⋊C₄	—	19	1	no	—
238	C₂×C₂²⋊C₄	—	19	1	no	—
239	C₂×C₂²⋊C₄	—	19	1	no	—
240	C₂×C₂²⋊C₄	—	19	1	no	—
241	C₂×C₂²⋊C₄	—	19	1	no	—
242	C₂×C₂²⋊C₄	—	19	1	no	—
243	C₂×C₂²⋊C₄	—	19	1	no	—
244	C₂×C₂²⋊C₄	—	19	1	no	—
245	C₂×C₂²⋊C₄	—	19	1	no	—
246	C₂×C₂²⋊C₄	—	19	1	no	—
247	C₂×C₂²⋊C₄	—	19	1	no	—
248	C₂×C₂²⋊C₄	—	19	1	no	—
249	C₂×C₂²⋊C₄	—	19	1	no	—
250	C₂×C₂²⋊C₄	C₂×D₁₉	1	1	yes	characteristic
251	C₂×C₂²⋊C₄	C₂×D₁₉	1	1	yes	characteristic
252	C₂×C₂²⋊C₄	C₂×D₁₉	1	1	yes	characteristic
253	C₂×C₂²⋊C₄	C₂×D₁₉	1	1	yes	characteristic
254	C₂×C₂²⋊C₄	C₂×D₁₉	1	1	yes	characteristic
255	C₂×C₂²⋊C₄	C₂×D₁₉	1	1	yes	characteristic
256	C₂×C₄²	—	19	1	no	—
257	C₂×C₄²	—	19	1	no	—
258	#95	—	19	1	no	—
259	#95	—	19	1	no	—
260	#95	—	19	1	no	—
261	#95	—	19	1	no	—
262	#95	—	19	1	no	—
263	#95	—	19	1	no	—
264	#95	—	19	1	no	—
265	#95	—	19	1	no	—
266	C₁₉	#2735	1	1	yes	characteristic, complemented, Sylow
267	C₂⁴	—	2	2	no	—
268	C₂⁴	—	2	2	no	—
269	C₂⁴	—	2	2	no	—
270	C₂⁴	—	4	1	no	—
271	C₂⁴	—	4	1	no	—
272	C₂⁴	—	4	1	no	—
273	C₂⁴	—	4	1	no	—
274	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
275	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
276	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
277	C₂²×C₄	—	19	1	no	—
278	C₂²×C₄	—	19	1	no	—
279	C₂²×C₄	—	19	1	no	—
280	C₂²×C₄	—	19	1	no	—
281	C₂²×C₄	—	19	1	no	—
282	C₂²×C₄	—	19	1	no	—
283	C₂²×C₄	—	19	1	no	—
284	C₂²×C₄	—	19	1	no	—
285	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
286	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
287	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
288	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
289	C₄⋊C₄	—	76	1	no	—
290	C₄⋊C₄	—	76	1	no	—
291	C₄⋊C₄	—	76	1	no	—
292	C₄⋊C₄	—	76	1	no	—
293	C₄⋊C₄	—	76	1	no	—
294	C₄⋊C₄	—	76	1	no	—
295	C₂²⋊C₄	—	2	2	no	—
296	C₂²⋊C₄	—	2	2	no	—
297	C₂²⋊C₄	—	4	1	no	—
298	C₂²⋊C₄	—	4	1	no	—
299	C₂²⋊C₄	—	4	1	no	—
300	C₂²⋊C₄	—	4	1	no	—
301	C₂²⋊C₄	—	38	2	no	—
302	C₂²⋊C₄	—	38	2	no	—
303	C₂²⋊C₄	—	38	2	no	—
304	C₂²⋊C₄	—	38	2	no	—
305	C₂²⋊C₄	—	76	1	no	—
306	C₂²⋊C₄	—	76	1	no	—
307	C₂²⋊C₄	—	76	1	no	—
308	C₂²⋊C₄	—	76	1	no	—
309	C₂²⋊C₄	—	76	1	no	—
310	C₂²⋊C₄	—	76	1	no	—
311	C₂²⋊C₄	—	76	1	no	—
312	C₂²⋊C₄	—	76	1	no	—
313	C₄²	—	76	1	no	—
314	C₄²	—	76	1	no	—
315	C₂³	—	2	1	no	—
316	C₂³	—	2	1	no	—
317	C₂³	—	2	1	no	—
318	C₂³	—	2	1	no	—
319	C₂³	—	2	1	no	—
320	C₂³	—	2	1	no	—
321	C₂³	—	2	1	no	—
322	C₂³	—	2	1	no	—
323	C₂³	—	2	1	no	—
324	C₂³	—	2	1	no	—
325	C₂³	—	2	1	no	—
326	C₂³	—	2	1	no	—
327	C₂³	—	2	1	no	—
328	C₂³	—	2	1	no	—
329	C₂³	—	2	1	no	—
330	C₂³	—	2	1	no	—
331	C₂³	—	2	1	no	—
332	C₂³	—	2	1	no	—
333	C₂³	—	4	4	no	—
334	C₂³	—	4	4	no	—
335	C₂³	—	4	4	no	—
336	C₂³	—	4	4	no	—
337	C₂³	—	4	4	no	—
338	C₂³	—	4	4	no	—
339	C₂³	—	4	4	no	—
340	C₂³	#64541	1	2	yes	—
341	C₂³	#64543	1	2	yes	—
342	C₂³	#64543	1	2	yes	—
343	C₂³	C₂³×D₁₉	1	1	yes	characteristic
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	38	1	no	—
357	C₂×C₄	—	38	1	no	—
358	C₂×C₄	—	38	1	no	—
359	C₂×C₄	—	38	1	no	—
360	C₂×C₄	—	38	1	no	—
361	C₂×C₄	—	38	1	no	—
362	C₂×C₄	—	38	1	no	—
363	C₂×C₄	—	38	1	no	—
364	C₂×C₄	—	38	1	no	—
365	C₂×C₄	—	38	1	no	—
366	C₂×C₄	—	38	1	no	—
367	C₂×C₄	—	38	1	no	—
368	C₂×C₄	—	38	1	no	—
369	C₂×C₄	—	38	1	no	—
370	C₂×C₄	—	38	1	no	—
371	C₂×C₄	—	38	1	no	—
372	C₂×C₄	—	38	1	no	—
373	C₂×C₄	—	38	1	no	—
374	C₂×C₄	—	38	1	no	—
375	C₂×C₄	—	38	1	no	—
376	C₂×C₄	—	38	1	no	—
377	C₂×C₄	—	38	1	no	—
378	C₂×C₄	—	38	1	no	—
379	C₂×C₄	—	38	1	no	—
380	C₂²	—	2	2	no	—
381	C₂²	—	2	2	no	—
382	C₂²	—	2	2	no	—
383	C₂²	—	2	2	no	—
384	C₂²	—	2	2	no	—
385	C₂²	—	2	2	no	—
386	C₂²	—	2	2	no	—
387	C₂²	—	2	2	no	—
388	C₂²	—	2	2	no	—
389	C₂²	—	4	16	no	—
390	C₂²	—	4	1	no	—
391	C₂²	—	4	1	no	—
392	C₂²	—	4	1	no	—
393	C₂²	—	4	1	no	—
394	C₂²	—	4	1	no	—
395	C₂²	—	4	1	no	—
396	C₂²	—	4	1	no	—
397	C₂²	—	4	1	no	—
398	C₂²	—	4	1	no	—
399	C₂²	—	4	1	no	—
400	C₂²	—	4	1	no	—
401	C₂²	—	4	1	no	—
402	C₂²	C₂×#64541	1	1	yes	characteristic
403	C₂²	C₂×#64543	1	1	yes	characteristic
404	C₂²	C₂×#64543	1	1	yes	characteristic
405	C₂²	#10597430	1	1	yes	characteristic
406	C₂²	#10597430	1	1	yes	characteristic
407	C₂²	#10597430	1	1	yes	characteristic
408	C₂²	#10597430	1	1	yes	characteristic
409	C₄	—	4	1	no	—
410	C₄	—	4	1	no	—
411	C₄	—	4	1	no	—
412	C₄	—	4	1	no	—
413	C₄	—	76	1	no	—
414	C₄	—	76	1	no	—
415	C₄	—	76	1	no	—
416	C₄	—	76	1	no	—
417	C₄	—	76	1	no	—
418	C₄	—	76	1	no	—
419	C₄	—	76	1	no	—
420	C₄	—	76	1	no	—
421	C₂	—	4	2	no	—
422	C₂	—	4	2	no	—
423	C₂	—	4	2	no	—
424	C₂	#11927129	1	1	yes	characteristic
425	C₂	#11927129	1	1	yes	characteristic
426	C₂	#11927132	1	1	yes	characteristic
427	C₂	#11927220	1	1	yes	characteristic
428	C₂	#11927220	1	1	yes	characteristic
429	C₂	#11927225	1	1	yes	characteristic
430	C₂	#11927283	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₁₉×#379	C₂
prime radical	C₂⁵×C₁₉	C₂²
hypercenter	#379	D₁₉
hypocenter	C₁₉	#2735
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ #379

Complements

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

N	H ≅ G/N	type
1. #11926480	C₂	semidirect
2. #11926472	C₂	semidirect
3. #11926472	C₂	semidirect
4. #11926469	C₂	semidirect
5. #11926467	C₂	semidirect
6. #11926467	C₂	semidirect
7. #11926438	C₂	semidirect
8. #11926438	C₂	semidirect
9. #11926437	C₂	semidirect
10. #11926437	C₂	semidirect
11. #11926432	C₂	semidirect
12. #11926432	C₂	semidirect
35. C₂×C₄⋊Dic₁₉	C₂²	semidirect
36. C₂×C₄⋊Dic₁₉	C₂²	semidirect
37. C₂×Dic₁₉⋊C₄	C₂²	semidirect
38. C₂×Dic₁₉⋊C₄	C₂²	semidirect
39. C₂×Dic₁₉⋊C₄	C₂²	semidirect
40. C₂×Dic₁₉⋊C₄	C₂²	semidirect
41. C₂×C₄×Dic₁₉	C₂²	semidirect
42. C₂×C₄×Dic₁₉	C₂²	semidirect
43. C₁₉⋊#95	C₂²	semidirect
44. C₁₉⋊#95	C₂²	semidirect
45. C₁₉⋊#95	C₂²	semidirect
46. C₁₉⋊#95	C₂²	semidirect
47. C₁₉⋊#95	C₂²	semidirect
48. C₁₉⋊#95	C₂²	semidirect
49. C₁₉⋊#95	C₂²	semidirect
50. C₁₉⋊#95	C₂²	semidirect
266. C₁₉	#2735	semidirect

Maximal subgroups

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

subgroup	index
#11926480	2
#11926472	2
#11926469	2
#11926467	2
#11926438	2
#11926437	2
#11926432	2
#11926400	2
C₁₉×#379	2
#2735	19