Subgroups — #14577505

Order 2432.

1232 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927280	C₂	1	1	yes	maximal, characteristic, complemented
2	#11927279	C₂	1	1	yes	maximal, characteristic, complemented
3	#11927277	C₂	1	2	yes	maximal, complemented
4	#11927215	C₂	1	1	yes	maximal, characteristic, complemented
5	#11927214	C₂	1	2	yes	maximal, complemented
6	#11927191	C₂	1	2	yes	maximal, complemented
7	#11927183	C₂	1	4	yes	maximal, complemented
8	#11927182	C₂	1	2	yes	maximal, complemented
9	#11927144	C₂	1	4	yes	maximal, complemented
10	#11927107	C₂	1	2	yes	maximal, complemented
11	#11927098	C₂	1	1	yes	maximal, characteristic, complemented
12	#11927090	C₂	1	2	yes	maximal, complemented
13	#11927089	C₂	1	2	yes	maximal, complemented
14	#127×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#11927016	C₂	1	2	yes	maximal, complemented
16	C₄×#64543	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₉×#550	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#41×C₁₉	C₂²	1	2	yes	complemented
19	C₂×#64543	C₂²	1	1	yes	characteristic
20	C₂×#64543	C₂²	1	4	yes	complemented
21	C₂×D₄×D₁₉	C₂²	1	2	yes	—
22	C₂×D₄×D₁₉	C₂²	1	2	yes	—
23	C₂×D₄×D₁₉	C₂²	1	2	yes	—
24	C₂×#64541	C₂²	1	2	yes	complemented
25	C₁₉×#127	C₂²	1	1	yes	characteristic
26	C₁₉×#127	C₂²	1	2	yes	complemented
27	C₁₉×#121	C₂²	1	2	yes	complemented
28	C₁₉×#121	C₂²	1	4	yes	complemented
29	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
30	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
31	C₄×D₄×C₁₉	C₂²	1	2	yes	complemented
32	#10597393	C₂²	1	2	yes	complemented
33	#10597392	C₂²	1	1	yes	characteristic
34	#10597390	C₂²	1	1	yes	characteristic, complemented
35	#10597386	C₂²	1	2	yes	—
36	#10597386	C₂²	1	2	yes	—
37	#10597386	C₂²	1	2	yes	—
38	#10597386	C₂²	1	2	yes	complemented
39	#10597385	C₂²	1	4	yes	complemented
40	#10597385	C₂²	1	4	yes	complemented
41	#10597385	C₂²	1	4	yes	complemented
42	#10597385	C₂²	1	4	yes	complemented
43	#10597384	C₂²	1	4	yes	complemented
44	#10597383	C₂²	1	4	yes	—
45	#10597383	C₂²	1	4	yes	—
46	#10597382	C₂²	1	2	yes	complemented
47	#10597382	C₂²	1	2	yes	complemented
48	#10597381	C₂²	1	4	yes	complemented
49	D₄×Dic₁₉	C₂²	1	2	yes	complemented
50	D₄×Dic₁₉	C₂²	1	1	yes	characteristic, complemented
51	D₄×Dic₁₉	C₂²	1	2	yes	complemented
52	#10597376	C₂²	1	2	yes	complemented
53	#10597375	C₂²	1	4	yes	complemented
54	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	—
55	C₄×C₂²⋊D₁₉	C₂²	1	4	yes	complemented
56	C₄×C₂²⋊D₁₉	C₂²	1	4	yes	complemented
57	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	4	yes	—
58	C₂×C₄×Dic₁₉	C₂²	1	2	yes	complemented
59	#10597343	C₂²	1	1	yes	characteristic
60	#10597342	C₂²	1	2	yes	—
61	#10597340	C₂²	1	4	yes	complemented
62	#10597339	C₂²	1	2	yes	complemented
63	#10597339	C₂²	1	2	yes	complemented
64	#10597338	C₂²	1	1	yes	characteristic
65	#10597335	C₂²	1	2	yes	complemented
66	#10597334	C₂²	1	1	yes	characteristic, complemented
67	#10597333	C₂²	1	1	yes	characteristic, complemented
68	#10597331	C₂²	1	4	yes	complemented
69	#10597330	C₂²	1	4	yes	complemented
70	#10597329	C₂²	1	4	yes	complemented
71	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	—
72	(C₂²⋊D₁₉)⋊C₄	C₂²	1	4	yes	complemented
73	C₂²⋊C₄×D₁₉	C₂²	1	4	yes	—
74	#10597323	C₂²	1	2	yes	complemented
75	#10597321	C₂²	1	2	yes	complemented
76	#10597320	C₂²	1	1	yes	characteristic
77	C₄×D₇₆	C₂²	1	2	yes	complemented
78	#10597318	C₂²	1	2	yes	—
79	C₄²×D₁₉	C₂²	1	1	yes	characteristic
80	C₄×Dic₃₈	C₂²	1	2	yes	complemented
81	C₄×Dic₃₈	C₂²	1	1	yes	characteristic, complemented
82	C₄×Dic₃₈	C₂²	1	1	yes	characteristic, complemented
83	C₂³×D₁₉	C₂³	1	4	yes	—
84	#41×C₁₉	—	4	4	no	—
85	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
86	C₂×D₄×C₁₉	C₂³	1	2	yes	—
87	C₂×D₄×C₁₉	C₂³	1	2	yes	—
88	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
89	C₂×D₄×C₁₉	C₂³	1	2	yes	—
90	C₂×D₄×C₁₉	C₂³	1	4	yes	—
91	C₂×D₄×C₁₉	C₂³	1	4	yes	—
92	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
93	C₂²×C₄×C₁₉	C₂³	1	4	yes	—
94	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
95	C₂×C₂²⋊D₁₉	C₂³	1	4	yes	—
96	C₂×C₂²⋊D₁₉	C₂³	1	4	yes	—
97	C₂×C₂²⋊D₁₉	C₂³	1	4	yes	—
98	C₂×C₂²⋊D₁₉	C₂³	1	4	yes	—
99	C₂×C₂²⋊D₁₉	C₂³	1	4	yes	—
100	C₂²×Dic₁₉	C₂³	1	2	yes	—
101	C₂²×Dic₁₉	C₂³	1	2	yes	—
102	C₂²×Dic₁₉	C₂³	1	4	yes	—
103	#64543	—	2	4	no	—
104	#64543	—	4	8	no	—
105	D₄×D₁₉	—	2	8	no	—
106	D₄×D₁₉	—	4	4	no	—
107	D₄×D₁₉	—	4	4	no	—
108	#64541	—	4	4	no	—
109	C₂×D₇₆	C₂³	1	2	yes	—
110	C₂×D₇₆	C₂³	1	2	yes	—
111	C₂×D₇₆	C₂³	1	2	yes	—
112	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
113	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
114	C₂×C₄×D₁₉	C₂³	1	4	yes	—
115	C₂×C₄×D₁₉	C₂³	1	4	yes	—
116	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
117	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
118	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
119	C₂×Dic₃₈	C₂³	1	2	yes	—
120	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
121	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
122	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
123	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
124	C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
125	C₄²×C₁₉	C₂³	1	1	yes	characteristic
126	C₄²×C₁₉	C₂³	1	2	yes	—
127	C₂²⋊Dic₁₉	C₂³	1	4	yes	—
128	C₂²⋊Dic₁₉	C₂³	1	4	yes	—
129	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
130	C₂²⋊Dic₁₉	C₂³	1	4	yes	—
131	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
132	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
133	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
134	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
135	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
136	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
137	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
138	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
139	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
140	C₄⋊Dic₁₉	C₂³	1	2	yes	—
141	Dic₁₉⋊C₄	C₂³	1	2	yes	—
142	Dic₁₉⋊C₄	C₂³	1	2	yes	—
143	Dic₁₉⋊C₄	C₂³	1	2	yes	—
144	Dic₁₉⋊C₄	C₂³	1	2	yes	—
145	Dic₁₉⋊C₄	C₂³	1	2	yes	—
146	Dic₁₉⋊C₄	C₂³	1	2	yes	—
147	Dic₁₉⋊C₄	C₂³	1	2	yes	—
148	C₄×Dic₁₉	C₂³	1	2	yes	—
149	C₄×Dic₁₉	C₂³	1	2	yes	—
150	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
151	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
152	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
153	C₄×Dic₁₉	C₂³	1	2	yes	—
154	C₄×Dic₁₉	C₂³	1	2	yes	—
155	C₂³×C₁₉	C₂⁴	1	4	yes	—
156	C₂³×C₁₉	C₂⁴	1	2	yes	—
157	C₂²×D₁₉	—	2	8	no	—
158	C₂²×D₁₉	—	4	4	no	—
159	C₂²×D₁₉	—	4	4	no	—
160	C₂²×D₁₉	C₂⁴	1	4	yes	—
161	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
162	Q₈×C₁₉	—	2	2	no	—
163	D₄×C₁₉	—	2	4	no	—
164	D₄×C₁₉	—	2	2	no	—
165	D₄×C₁₉	—	2	4	no	—
166	D₄×C₁₉	—	4	2	no	—
167	D₄×C₁₉	—	4	4	no	—
168	D₄×C₁₉	—	4	4	no	—
169	C₂×C₄×C₁₉	—	2	4	no	—
170	C₂×C₄×C₁₉	—	4	4	no	—
171	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
172	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
173	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
174	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
175	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
176	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
177	C₂²⋊D₁₉	—	2	4	no	—
178	C₂²⋊D₁₉	—	2	8	no	—
179	C₂²⋊D₁₉	—	2	8	no	—
180	C₂²⋊D₁₉	—	4	4	no	—
181	C₂²⋊D₁₉	—	4	4	no	—
182	C₂²⋊D₁₉	—	4	4	no	—
183	C₂×Dic₁₉	—	2	4	no	—
184	C₂×Dic₁₉	—	2	4	no	—
185	C₂×Dic₁₉	—	4	4	no	—
186	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
187	C₂×Dic₁₉	C₂⁴	1	2	yes	—
188	C₂×Dic₁₉	C₂⁴	1	2	yes	—
189	C₂×Dic₁₉	C₂⁴	1	2	yes	—
190	C₂×Dic₁₉	C₂⁴	1	2	yes	—
191	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
192	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
193	D₇₆	—	2	4	no	—
194	D₇₆	—	2	4	no	—
195	D₇₆	—	4	2	no	—
196	C₄×D₁₉	—	2	2	no	—
197	C₄×D₁₉	—	2	2	no	—
198	C₄×D₁₉	—	4	4	no	—
199	C₄×D₁₉	—	4	4	no	—
200	C₄×D₁₉	#41	1	4	yes	complemented
201	Dic₃₈	—	2	2	no	—
202	Dic₃₈	—	2	2	no	—
203	Dic₃₈	—	2	4	no	—
204	#3508	—	19	1	no	maximal, Sylow
205	C₂²×C₁₉	—	2	2	no	—
206	C₂²×C₁₉	—	2	4	no	—
207	C₂²×C₁₉	—	2	2	no	—
208	C₂²×C₁₉	—	2	4	no	—
209	C₂²×C₁₉	—	2	2	no	—
210	C₂²×C₁₉	—	2	4	no	—
211	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
212	C₂×D₁₉	—	2	1	no	—
213	C₂×D₁₉	—	2	1	no	—
214	C₂×D₁₉	—	2	4	no	—
215	C₂×D₁₉	—	2	4	no	—
216	C₂×D₁₉	—	2	4	no	—
217	C₂×D₁₉	—	8	8	no	—
218	C₂×D₁₉	C₂×#41	1	2	yes	—
219	C₄×C₁₉	—	2	2	no	—
220	C₄×C₁₉	—	2	1	no	—
221	C₄×C₁₉	—	2	2	no	—
222	C₄×C₁₉	—	2	2	no	—
223	C₄×C₁₉	C₂×#41	1	2	yes	—
224	C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
225	Dic₁₉	—	2	2	no	—
226	Dic₁₉	—	2	2	no	—
227	Dic₁₉	—	2	2	no	—
228	Dic₁₉	—	2	1	no	—
229	Dic₁₉	—	2	2	no	—
230	Dic₁₉	C₂×#41	1	2	yes	—
231	Dic₁₉	H(5,𝔽₂)	1	2	yes	—
232	#559	—	19	1	no	—
233	#559	—	19	1	no	—
234	#559	—	19	2	no	—
235	#550	—	19	2	no	—
236	#550	—	19	1	no	—
237	#550	D₁₉	1	1	yes	characteristic, complemented
238	#546	—	19	2	no	—
239	#546	—	19	4	no	—
240	#546	—	19	2	no	—
241	#540	—	19	4	no	—
242	#535	—	19	2	no	—
243	#533	—	19	1	no	—
244	#532	—	19	2	no	—
245	#532	—	19	2	no	—
246	C₂×#127	—	19	1	no	—
247	#518	—	19	2	no	—
248	C₄×#41	—	19	1	no	—
249	C₂×C₁₉	—	4	4	no	—
250	C₂×C₁₉	—	4	2	no	—
251	C₂×C₁₉	C₂²×#41	1	1	yes	characteristic
252	C₂×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
253	C₂×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
254	D₁₉	—	2	2	no	—
255	D₁₉	—	4	4	no	—
256	C₂×#41	—	19	1	no	—
257	C₂×#41	—	19	4	no	—
258	C₂×#41	—	19	2	no	—
259	C₂×#41	C₂×D₁₉	1	2	yes	complemented
260	C₂²×D₄	—	19	2	no	—
261	C₂²×D₄	—	19	2	no	—
262	C₂²×D₄	—	19	2	no	—
263	C₄⋊Q₈	—	19	1	no	—
264	C₄⋊Q₈	—	19	1	no	—
265	#127	—	19	2	no	—
266	#127	—	19	2	no	—
267	#127	—	19	2	no	—
268	#127	—	19	2	no	—
269	#127	—	19	1	no	—
270	#127	C₂×D₁₉	1	1	yes	characteristic
271	#127	C₂×D₁₉	1	2	yes	complemented
272	#125	—	19	2	no	—
273	#124	—	19	2	no	—
274	#124	—	19	2	no	—
275	#124	—	19	2	no	—
276	#124	—	19	4	no	—
277	#124	—	19	2	no	—
278	#123	—	19	4	no	—
279	#123	—	19	4	no	—
280	#123	—	19	4	no	—
281	#123	—	19	4	no	—
282	C₂²⋊Q₈	—	19	1	no	—
283	C₂²⋊Q₈	—	19	2	no	—
284	C₂²⋊Q₈	—	19	1	no	—
285	#121	—	19	4	no	—
286	#121	—	19	4	no	—
287	#121	—	19	4	no	—
288	#121	—	19	4	no	—
289	#121	—	19	4	no	—
290	#121	—	19	2	no	—
291	#121	—	19	4	no	—
292	#121	C₂×D₁₉	1	2	yes	complemented
293	#121	C₂×D₁₉	1	4	yes	complemented
294	#120	—	19	4	no	—
295	#120	—	19	4	no	—
296	C₄×Q₈	—	19	1	no	—
297	C₄×Q₈	—	19	1	no	—
298	C₄×Q₈	—	19	2	no	—
299	C₄×Q₈	—	19	1	no	—
300	C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
301	C₄×D₄	—	19	1	no	—
302	C₄×D₄	—	19	2	no	—
303	C₄×D₄	—	19	2	no	—
304	C₄×D₄	—	19	2	no	—
305	C₄×D₄	—	19	4	no	—
306	C₄×D₄	—	19	4	no	—
307	C₄×D₄	—	19	2	no	—
308	C₄×D₄	—	19	2	no	—
309	C₄×D₄	—	19	2	no	—
310	C₄×D₄	—	19	4	no	—
311	C₄×D₄	—	19	2	no	—
312	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic, complemented
313	C₄×D₄	C₂×D₁₉	1	2	yes	complemented
314	#117	—	19	1	no	—
315	#117	—	19	2	no	—
316	#117	—	19	2	no	—
317	C₂×C₂²⋊C₄	—	19	4	no	—
318	C₂×C₂²⋊C₄	—	19	4	no	—
319	C₂×C₄²	—	19	2	no	—
320	C₂×C₄²	—	19	1	no	—
321	C₁₉	#3508	1	1	yes	characteristic, complemented, Sylow
322	C₂⁴	—	19	4	no	—
323	#41	—	4	4	no	—
324	#41	—	38	4	no	—
325	#41	—	76	4	no	—
326	#41	—	76	8	no	—
327	C₂×Q₈	—	19	1	no	—
328	C₂×Q₈	—	19	2	no	—
329	C₂×Q₈	—	19	1	no	—
330	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
331	C₂×D₄	—	19	2	no	—
332	C₂×D₄	—	19	4	no	—
333	C₂×D₄	—	19	4	no	—
334	C₂×D₄	—	19	4	no	—
335	C₂×D₄	—	19	4	no	—
336	C₂×D₄	—	19	4	no	—
337	C₂×D₄	—	19	2	no	—
338	C₂×D₄	—	19	2	no	—
339	C₂×D₄	—	19	2	no	—
340	C₂×D₄	—	38	8	no	—
341	C₂×D₄	—	76	4	no	—
342	C₂×D₄	—	76	4	no	—
343	C₂×D₄	C₂²×D₁₉	1	2	yes	—
344	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
345	C₂×D₄	C₂²×D₁₉	1	2	yes	—
346	C₂×D₄	C₂²×D₁₉	1	4	yes	—
347	C₂×D₄	C₂²×D₁₉	1	4	yes	—
348	C₂×D₄	C₂²×D₁₉	1	2	yes	—
349	C₂²×C₄	—	19	1	no	—
350	C₂²×C₄	—	19	2	no	—
351	C₂²×C₄	—	19	2	no	—
352	C₂²×C₄	—	19	4	no	—
353	C₂²×C₄	—	19	1	no	—
354	C₂²×C₄	—	19	1	no	—
355	C₂²×C₄	—	19	4	no	—
356	C₂²×C₄	—	19	4	no	—
357	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
358	C₂²×C₄	C₂²×D₁₉	1	4	yes	—
359	C₄⋊C₄	—	19	2	no	—
360	C₄⋊C₄	—	19	2	no	—
361	C₄⋊C₄	—	19	2	no	—
362	C₄⋊C₄	—	19	2	no	—
363	C₄⋊C₄	—	19	2	no	—
364	C₄⋊C₄	—	19	2	no	—
365	C₄⋊C₄	—	19	2	no	—
366	C₄⋊C₄	—	19	1	no	—
367	C₄⋊C₄	—	19	1	no	—
368	C₄⋊C₄	—	19	2	no	—
369	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
370	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
371	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
372	C₂²⋊C₄	—	19	4	no	—
373	C₂²⋊C₄	—	19	2	no	—
374	C₂²⋊C₄	—	19	4	no	—
375	C₂²⋊C₄	—	19	4	no	—
376	C₂²⋊C₄	—	19	2	no	—
377	C₂²⋊C₄	—	19	2	no	—
378	C₂²⋊C₄	—	19	2	no	—
379	C₂²⋊C₄	—	19	4	no	—
380	C₂²⋊C₄	—	19	4	no	—
381	C₂²⋊C₄	—	19	4	no	—
382	C₂²⋊C₄	—	19	4	no	—
383	C₂²⋊C₄	C₂²×D₁₉	1	4	yes	—
384	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
385	C₄²	—	19	1	no	—
386	C₄²	—	19	2	no	—
387	C₄²	—	19	1	no	—
388	C₄²	—	19	2	no	—
389	C₄²	—	19	2	no	—
390	C₄²	—	19	1	no	—
391	C₄²	—	19	2	no	—
392	C₄²	C₂²×D₁₉	1	1	yes	characteristic
393	C₄²	C₂²×D₁₉	1	2	yes	—
394	C₂³	—	19	1	no	—
395	C₂³	—	19	4	no	—
396	C₂³	—	38	8	no	—
397	C₂³	—	76	4	no	—
398	C₂³	—	76	4	no	—
399	C₂³	C₂³×D₁₉	1	4	yes	—
400	C₂³	C₂³×D₁₉	1	2	yes	—
401	Q₈	—	2	2	no	—
402	Q₈	—	38	4	no	—
403	Q₈	—	38	2	no	—
404	Q₈	—	38	2	no	—
405	D₄	—	2	4	no	—
406	D₄	—	2	4	no	—
407	D₄	—	2	2	no	—
408	D₄	—	4	2	no	—
409	D₄	—	4	4	no	—
410	D₄	—	4	4	no	—
411	D₄	—	38	8	no	—
412	D₄	—	38	8	no	—
413	D₄	—	38	4	no	—
414	D₄	—	38	4	no	—
415	D₄	—	38	4	no	—
416	D₄	—	76	2	no	—
417	D₄	—	76	4	no	—
418	D₄	—	76	4	no	—
419	D₄	—	76	4	no	—
420	C₂×C₄	—	2	4	no	—
421	C₂×C₄	—	4	4	no	—
422	C₂×C₄	—	19	1	no	—
423	C₂×C₄	—	19	1	no	—
424	C₂×C₄	—	19	4	no	—
425	C₂×C₄	—	19	2	no	—
426	C₂×C₄	—	19	2	no	—
427	C₂×C₄	—	19	1	no	—
428	C₂×C₄	—	19	2	no	—
429	C₂×C₄	—	19	2	no	—
430	C₂×C₄	—	38	2	no	—
431	C₂×C₄	—	38	4	no	—
432	C₂×C₄	—	38	4	no	—
433	C₂×C₄	—	38	2	no	—
434	C₂×C₄	—	76	4	no	—
435	C₂×C₄	—	76	4	no	—
436	C₂×C₄	—	76	4	no	—
437	C₂×C₄	C₂³×D₁₉	1	2	yes	—
438	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
439	C₂×C₄	C₂³×D₁₉	1	2	yes	—
440	C₂×C₄	C₂³×D₁₉	1	2	yes	—
441	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
442	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
443	C₂²	—	2	2	no	—
444	C₂²	—	2	4	no	—
445	C₂²	—	2	2	no	—
446	C₂²	—	2	4	no	—
447	C₂²	—	2	2	no	—
448	C₂²	—	2	4	no	—
449	C₂²	—	19	2	no	—
450	C₂²	—	38	1	no	—
451	C₂²	—	38	1	no	—
452	C₂²	—	38	4	no	—
453	C₂²	—	38	4	no	—
454	C₂²	—	38	4	no	—
455	C₂²	—	152	8	no	—
456	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
457	C₄	—	2	1	no	—
458	C₄	—	2	2	no	—
459	C₄	—	2	2	no	—
460	C₄	—	2	2	no	—
461	C₄	—	19	2	no	—
462	C₄	—	19	2	no	—
463	C₄	—	38	2	no	—
464	C₄	—	38	2	no	—
465	C₄	—	38	2	no	—
466	C₄	—	38	1	no	—
467	C₄	—	38	2	no	—
468	C₄	#10597430	1	2	yes	—
469	C₄	#41×D₁₉	1	2	yes	—
470	C₂	—	4	4	no	—
471	C₂	—	4	2	no	—
472	C₂	—	38	2	no	—
473	C₂	—	76	4	no	—
474	C₂	C₂×#41×D₁₉	1	1	yes	characteristic
475	C₂	H(5,𝔽₂)×D₁₉	1	1	yes	characteristic
476	C₂	C₂×#10597430	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Fitting	C₁₉×#550	C₂
hypercenter	#550	D₁₉
hypocenter	C₁₉	#3508
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ #550

Complements

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

N	H ≅ G/N	type
1. #11927280	C₂	semidirect
2. #11927279	C₂	semidirect
3. #11927277	C₂	semidirect
4. #11927215	C₂	semidirect
5. #11927214	C₂	semidirect
6. #11927191	C₂	semidirect
7. #11927183	C₂	semidirect
8. #11927182	C₂	semidirect
9. #11927144	C₂	semidirect
10. #11927107	C₂	semidirect
11. #11927098	C₂	semidirect
12. #11927090	C₂	semidirect
13. #11927089	C₂	semidirect
14. #127×D₁₉	C₂	semidirect
15. #11927016	C₂	semidirect
16. C₄×#64543	C₂	semidirect
17. C₁₉×#550	C₂	semidirect
18. C₂×#41×C₁₉	C₂²	semidirect
20. C₂×#64543	C₂²	semidirect
24. C₂×#64541	C₂²	semidirect
26. C₁₉×#127	C₂²	semidirect
27. C₁₉×#121	C₂²	semidirect
28. C₁₉×#121	C₂²	semidirect
29. C₄×Q₈×C₁₉	C₂²	semidirect
30. C₄×D₄×C₁₉	C₂²	semidirect
31. C₄×D₄×C₁₉	C₂²	semidirect
32. #10597393	C₂²	semidirect
34. #10597390	C₂²	semidirect
38. #10597386	C₂²	semidirect
39. #10597385	C₂²	semidirect
40. #10597385	C₂²	semidirect
41. #10597385	C₂²	semidirect
42. #10597385	C₂²	semidirect
43. #10597384	C₂²	semidirect
46. #10597382	C₂²	semidirect
47. #10597382	C₂²	semidirect
48. #10597381	C₂²	semidirect
49. D₄×Dic₁₉	C₂²	semidirect
50. D₄×Dic₁₉	C₂²	semidirect
51. D₄×Dic₁₉	C₂²	semidirect
52. #10597376	C₂²	semidirect
53. #10597375	C₂²	semidirect
55. C₄×C₂²⋊D₁₉	C₂²	semidirect
56. C₄×C₂²⋊D₁₉	C₂²	semidirect
58. C₂×C₄×Dic₁₉	C₂²	semidirect
61. #10597340	C₂²	semidirect
62. #10597339	C₂²	semidirect
63. #10597339	C₂²	semidirect
65. #10597335	C₂²	semidirect
66. #10597334	C₂²	semidirect
67. #10597333	C₂²	semidirect
68. #10597331	C₂²	semidirect
69. #10597330	C₂²	semidirect
70. #10597329	C₂²	semidirect
72. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
74. #10597323	C₂²	semidirect
75. #10597321	C₂²	semidirect
77. C₄×D₇₆	C₂²	semidirect
80. C₄×Dic₃₈	C₂²	semidirect
81. C₄×Dic₃₈	C₂²	semidirect
82. C₄×Dic₃₈	C₂²	semidirect
200. C₄×D₁₉	#41	semidirect
237. #550	D₁₉	semidirect
259. C₂×#41	C₂×D₁₉	semidirect
271. #127	C₂×D₁₉	semidirect
292. #121	C₂×D₁₉	semidirect
293. #121	C₂×D₁₉	semidirect
300. C₄×Q₈	C₂×D₁₉	semidirect
312. C₄×D₄	C₂×D₁₉	semidirect
313. C₄×D₄	C₂×D₁₉	semidirect
321. C₁₉	#3508	semidirect

Maximal subgroups

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

subgroup	index
#11927280	2
#11927279	2
#11927277	2
#11927215	2
#11927214	2
#11927191	2
#11927183	2
#11927182	2
#11927144	2
#11927107	2
#11927098	2
#11927090	2
#11927089	2
#127×D₁₉	2
#11927016	2
C₄×#64543	2
C₁₉×#550	2
#3508	19