Subgroups — #14577959

Order 2432.

1260 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927282	C₂	1	4	yes	maximal, complemented
2	#11927279	C₂	1	1	yes	maximal, characteristic, complemented
3	#11927214	C₂	1	1	yes	maximal, characteristic, complemented
4	#11927189	C₂	1	2	yes	maximal, complemented
5	#11927182	C₂	1	2	yes	maximal, complemented
6	D₄×D₇₆	C₂	1	1	yes	maximal, characteristic, complemented
7	#11927179	C₂	1	2	yes	maximal, complemented
8	#11927178	C₂	1	2	yes	maximal, complemented
9	#11927147	C₂	1	2	yes	maximal, complemented
10	#11927145	C₂	1	2	yes	maximal, complemented
11	#11927108	C₂	1	2	yes	maximal, complemented
12	#11927107	C₂	1	2	yes	maximal, complemented
13	#11927102	C₂	1	4	yes	maximal, complemented
14	#127×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#11927081	C₂	1	1	yes	maximal, characteristic, complemented
16	#11927076	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	2	yes	complemented
20	C₂×D₄×D₁₉	C₂²	1	2	yes	complemented
21	C₂×D₄×D₁₉	C₂²	1	2	yes	complemented
22	C₂×D₄×D₁₉	C₂²	1	2	yes	complemented
23	C₂×D₄×D₁₉	C₂²	1	4	yes	complemented
24	C₂×D₄×D₁₉	C₂²	1	2	yes	complemented
25	C₂²×D₇₆	C₂²	1	2	yes	complemented
26	C₁₉×#127	C₂²	1	1	yes	characteristic, complemented
27	C₁₉×#127	C₂²	1	2	yes	complemented
28	C₁₉×#121	C₂²	1	4	yes	complemented
29	C₁₉×#121	C₂²	1	2	yes	complemented
30	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
31	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
32	C₄×D₄×C₁₉	C₂²	1	2	yes	complemented
33	#10597393	C₂²	1	1	yes	characteristic, complemented
34	#10597393	C₂²	1	2	yes	complemented
35	#10597392	C₂²	1	1	yes	characteristic, complemented
36	#10597386	C₂²	1	2	yes	complemented
37	#10597386	C₂²	1	2	yes	complemented
38	#10597386	C₂²	1	2	yes	complemented
39	#10597386	C₂²	1	2	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	1	yes	characteristic
44	#10597384	C₂²	1	2	yes	complemented
45	#10597384	C₂²	1	4	yes	complemented
46	#10597383	C₂²	1	4	yes	complemented
47	#10597383	C₂²	1	4	yes	complemented
48	#10597383	C₂²	1	4	yes	complemented
49	#10597383	C₂²	1	4	yes	complemented
50	#10597382	C₂²	1	1	yes	characteristic, complemented
51	D₄×Dic₁₉	C₂²	1	2	yes	complemented
52	#10597376	C₂²	1	4	yes	complemented
53	#10597376	C₂²	1	4	yes	complemented
54	#10597376	C₂²	1	2	yes	complemented
55	#10597375	C₂²	1	4	yes	complemented
56	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	complemented
57	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	4	yes	complemented
58	#10597372	C₂²	1	2	yes	complemented
59	#10597344	C₂²	1	2	yes	complemented
60	#10597343	C₂²	1	1	yes	characteristic, complemented
61	#10597341	C₂²	1	1	yes	characteristic
62	#10597341	C₂²	1	2	yes	complemented
63	#10597340	C₂²	1	2	yes	complemented
64	#10597340	C₂²	1	4	yes	complemented
65	#10597339	C₂²	1	2	yes	complemented
66	#10597336	C₂²	1	1	yes	characteristic, complemented
67	#10597336	C₂²	1	1	yes	characteristic, complemented
68	#10597332	C₂²	1	4	yes	complemented
69	#10597330	C₂²	1	4	yes	complemented
70	#10597329	C₂²	1	2	yes	complemented
71	#10597329	C₂²	1	4	yes	complemented
72	#10597328	C₂²	1	4	yes	complemented
73	#10597328	C₂²	1	4	yes	complemented
74	#10597325	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	C₄×D₇₆	C₂²	1	1	yes	characteristic, complemented
79	C₄×D₇₆	C₂²	1	2	yes	complemented
80	#10597318	C₂²	1	2	yes	complemented
81	C₄²×D₁₉	C₂²	1	1	yes	characteristic, complemented
82	C₄×Dic₃₈	C₂²	1	1	yes	characteristic, complemented
83	C₂³×D₁₉	C₂³	1	4	yes	—
84	C₂³×D₁₉	C₂³	1	4	yes	—
85	#41×C₁₉	—	4	4	no	—
86	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
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	C₂×D₄×C₁₉	C₂³	1	2	yes	—
93	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
94	C₂²×C₄×C₁₉	C₂³	1	4	yes	—
95	C₂×C₂²⋊D₁₉	C₂³	1	2	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	C₂×C₂²⋊D₁₉	C₂³	1	4	yes	—
101	C₂×C₂²⋊D₁₉	C₂³	1	4	yes	—
102	C₂²×Dic₁₉	C₂³	1	4	yes	—
103	#64543	—	4	4	no	—
104	D₄×D₁₉	—	4	4	no	—
105	D₄×D₁₉	—	4	4	no	—
106	D₄×D₁₉	—	4	4	no	—
107	D₄×D₁₉	—	4	4	no	—
108	D₄×D₁₉	—	4	8	no	—
109	C₂×D₇₆	—	4	4	no	—
110	C₂×D₇₆	C₂³	1	2	yes	—
111	C₂×D₇₆	C₂³	1	1	yes	characteristic
112	C₂×D₇₆	C₂³	1	2	yes	—
113	C₂×D₇₆	C₂³	1	2	yes	—
114	C₂×D₇₆	C₂³	1	4	yes	—
115	C₂×D₇₆	C₂³	1	2	yes	—
116	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
117	C₂×C₄×D₁₉	C₂³	1	2	yes	—
118	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
119	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
120	C₂×C₄×D₁₉	C₂³	1	4	yes	—
121	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
122	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
123	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
124	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
125	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
126	C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
127	C₄²×C₁₉	C₂³	1	1	yes	characteristic
128	C₄²×C₁₉	C₂³	1	2	yes	—
129	C₂²⋊Dic₁₉	C₂³	1	4	yes	—
130	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
131	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
132	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
133	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
134	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
135	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
136	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
137	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
138	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
139	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
140	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
141	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
142	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
143	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
144	C₄⋊Dic₁₉	C₂³	1	2	yes	—
145	C₄⋊Dic₁₉	C₂³	1	2	yes	—
146	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
147	C₄⋊Dic₁₉	C₂³	1	2	yes	—
148	Dic₁₉⋊C₄	C₂³	1	2	yes	—
149	Dic₁₉⋊C₄	C₂³	1	2	yes	—
150	Dic₁₉⋊C₄	C₂³	1	2	yes	—
151	Dic₁₉⋊C₄	C₂³	1	2	yes	—
152	C₄×Dic₁₉	C₂³	1	2	yes	—
153	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
154	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
155	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
156	C₂³×C₁₉	C₂⁴	1	2	yes	—
157	C₂³×C₁₉	C₂⁴	1	4	yes	—
158	C₂²×D₁₉	—	2	8	no	—
159	C₂²×D₁₉	—	4	4	no	—
160	C₂²×D₁₉	—	4	4	no	—
161	C₂²×D₁₉	—	4	4	no	—
162	C₂²×D₁₉	—	4	4	no	—
163	C₂²×D₁₉	—	4	4	no	—
164	C₂²×D₁₉	C₂⁴	1	2	yes	—
165	C₂²×D₁₉	C₂⁴	1	4	yes	—
166	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
167	Q₈×C₁₉	—	2	2	no	—
168	D₄×C₁₉	—	2	2	no	—
169	D₄×C₁₉	—	2	4	no	—
170	D₄×C₁₉	—	2	4	no	—
171	D₄×C₁₉	—	4	2	no	—
172	D₄×C₁₉	—	4	4	no	—
173	D₄×C₁₉	—	4	4	no	—
174	C₂×C₄×C₁₉	—	2	4	no	—
175	C₂×C₄×C₁₉	—	4	4	no	—
176	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
177	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
178	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
179	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
180	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
181	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
182	C₂²⋊D₁₉	—	2	4	no	—
183	C₂²⋊D₁₉	—	4	4	no	—
184	C₂²⋊D₁₉	—	4	4	no	—
185	C₂²⋊D₁₉	—	4	4	no	—
186	C₂²⋊D₁₉	—	4	4	no	—
187	C₂²⋊D₁₉	—	4	4	no	—
188	C₂²⋊D₁₉	—	4	4	no	—
189	C₂×Dic₁₉	—	4	4	no	—
190	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
191	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
192	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
193	C₂×Dic₁₉	C₂⁴	1	2	yes	—
194	C₂×Dic₁₉	C₂⁴	1	2	yes	—
195	C₂×Dic₁₉	C₂⁴	1	2	yes	—
196	D₇₆	—	2	4	no	—
197	D₇₆	—	2	2	no	—
198	D₇₆	—	2	4	no	—
199	D₇₆	—	2	4	no	—
200	D₇₆	—	4	4	no	—
201	D₇₆	—	4	2	no	—
202	C₄×D₁₉	—	2	2	no	—
203	C₄×D₁₉	—	2	2	no	—
204	C₄×D₁₉	—	2	2	no	—
205	C₄×D₁₉	—	2	4	no	—
206	C₄×D₁₉	—	4	4	no	—
207	Dic₃₈	—	2	2	no	—
208	#3543	—	19	1	no	maximal, Sylow
209	C₂²×C₁₉	—	2	4	no	—
210	C₂²×C₁₉	—	2	2	no	—
211	C₂²×C₁₉	—	2	2	no	—
212	C₂²×C₁₉	—	2	4	no	—
213	C₂²×C₁₉	—	2	4	no	—
214	C₂²×C₁₉	—	2	2	no	—
215	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
216	C₂×D₁₉	—	2	1	no	—
217	C₂×D₁₉	—	2	1	no	—
218	C₂×D₁₉	—	2	2	no	—
219	C₂×D₁₉	—	2	4	no	—
220	C₂×D₁₉	—	2	2	no	—
221	C₂×D₁₉	—	2	4	no	—
222	C₂×D₁₉	—	2	2	no	—
223	C₂×D₁₉	—	2	4	no	—
224	C₂×D₁₉	—	8	8	no	—
225	C₂×D₁₉	—	8	8	no	—
226	C₂×D₁₉	H(5,𝔽₂)	1	2	yes	—
227	C₄×C₁₉	—	2	1	no	—
228	C₄×C₁₉	—	2	2	no	—
229	C₄×C₁₉	—	2	2	no	—
230	C₄×C₁₉	—	2	2	no	—
231	C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
232	C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
233	Dic₁₉	—	2	2	no	—
234	Dic₁₉	—	2	2	no	—
235	Dic₁₉	—	2	1	no	—
236	Dic₁₉	—	2	1	no	—
237	Dic₁₉	—	2	1	no	—
238	Dic₁₉	—	2	2	no	—
239	#560	—	19	4	no	—
240	#559	—	19	1	no	—
241	#550	—	19	1	no	—
242	#550	D₁₉	1	1	yes	characteristic, complemented
243	#546	—	19	2	no	—
244	#546	—	19	2	no	—
245	D₄²	—	19	2	no	—
246	D₄²	—	19	2	no	—
247	D₄²	—	19	1	no	—
248	#540	—	19	2	no	—
249	#540	—	19	2	no	—
250	#535	—	19	2	no	—
251	#535	—	19	2	no	—
252	#534	—	19	4	no	—
253	C₂×#127	—	19	1	no	—
254	#529	—	19	1	no	—
255	#529	—	19	1	no	—
256	C₂×C₁₉	—	4	2	no	—
257	C₂×C₁₉	—	4	4	no	—
258	C₂×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
259	C₂×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
260	C₂×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
261	D₁₉	—	2	2	no	—
262	D₁₉	—	4	2	no	—
263	D₁₉	—	4	4	no	—
264	C₂×#41	—	19	2	no	—
265	C₂×#41	C₂×D₁₉	1	2	yes	complemented
266	C₂²×D₄	—	19	2	no	—
267	C₂²×D₄	—	19	2	no	—
268	C₂²×D₄	—	19	2	no	—
269	C₂²×D₄	—	19	4	no	—
270	C₂²×D₄	—	19	2	no	—
271	C₂²×D₄	—	19	2	no	—
272	#127	—	19	2	no	—
273	#127	—	19	2	no	—
274	#127	—	19	2	no	—
275	#127	—	19	2	no	—
276	#127	—	19	1	no	—
277	#127	C₂×D₁₉	1	1	yes	characteristic, complemented
278	#127	C₂×D₁₉	1	2	yes	complemented
279	#126	—	19	2	no	—
280	#126	—	19	2	no	—
281	#125	—	19	1	no	—
282	#125	—	19	1	no	—
283	#124	—	19	1	no	—
284	#124	—	19	2	no	—
285	#124	—	19	1	no	—
286	#124	—	19	2	no	—
287	#123	—	19	4	no	—
288	#123	—	19	2	no	—
289	#123	—	19	4	no	—
290	#123	—	19	2	no	—
291	#123	—	19	4	no	—
292	#123	—	19	4	no	—
293	C₂²⋊Q₈	—	19	1	no	—
294	C₂²⋊Q₈	—	19	1	no	—
295	#121	—	19	1	no	—
296	#121	—	19	2	no	—
297	#121	—	19	4	no	—
298	#121	—	19	4	no	—
299	#121	—	19	4	no	—
300	#121	—	19	4	no	—
301	#121	—	19	4	no	—
302	#121	—	19	4	no	—
303	#121	—	19	2	no	—
304	#121	—	19	1	no	—
305	#121	—	19	2	no	—
306	#121	—	19	4	no	—
307	#121	C₂×D₁₉	1	4	yes	complemented
308	#121	C₂×D₁₉	1	2	yes	complemented
309	#120	—	19	4	no	—
310	#120	—	19	4	no	—
311	#120	—	19	4	no	—
312	#120	—	19	4	no	—
313	#120	—	19	4	no	—
314	#120	—	19	4	no	—
315	C₄×Q₈	—	19	1	no	—
316	C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
317	C₄×D₄	—	19	2	no	—
318	C₄×D₄	—	19	2	no	—
319	C₄×D₄	—	19	2	no	—
320	C₄×D₄	—	19	2	no	—
321	C₄×D₄	—	19	1	no	—
322	C₄×D₄	—	19	2	no	—
323	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic, complemented
324	C₄×D₄	C₂×D₁₉	1	2	yes	complemented
325	#117	—	19	2	no	—
326	#117	—	19	2	no	—
327	C₂×C₂²⋊C₄	—	19	4	no	—
328	C₂×C₄²	—	19	1	no	—
329	C₁₉	#3543	1	1	yes	characteristic, complemented, Sylow
330	C₂⁴	—	19	4	no	—
331	C₂⁴	—	19	4	no	—
332	#41	—	4	4	no	—
333	#41	—	76	4	no	—
334	C₂×Q₈	—	19	1	no	—
335	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
336	C₂×D₄	—	19	2	no	—
337	C₂×D₄	—	19	4	no	—
338	C₂×D₄	—	19	4	no	—
339	C₂×D₄	—	19	4	no	—
340	C₂×D₄	—	19	4	no	—
341	C₂×D₄	—	19	4	no	—
342	C₂×D₄	—	19	4	no	—
343	C₂×D₄	—	19	2	no	—
344	C₂×D₄	—	19	2	no	—
345	C₂×D₄	—	19	1	no	—
346	C₂×D₄	—	19	2	no	—
347	C₂×D₄	—	19	4	no	—
348	C₂×D₄	—	19	2	no	—
349	C₂×D₄	—	76	4	no	—
350	C₂×D₄	—	76	4	no	—
351	C₂×D₄	—	76	4	no	—
352	C₂×D₄	—	76	4	no	—
353	C₂×D₄	—	76	4	no	—
354	C₂×D₄	—	76	8	no	—
355	C₂×D₄	C₂²×D₁₉	1	2	yes	—
356	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
357	C₂×D₄	C₂²×D₁₉	1	2	yes	—
358	C₂×D₄	C₂²×D₁₉	1	4	yes	—
359	C₂×D₄	C₂²×D₁₉	1	4	yes	—
360	C₂×D₄	C₂²×D₁₉	1	2	yes	—
361	C₂²×C₄	—	19	4	no	—
362	C₂²×C₄	—	19	1	no	—
363	C₂²×C₄	—	19	1	no	—
364	C₂²×C₄	—	19	1	no	—
365	C₂²×C₄	—	19	2	no	—
366	C₂²×C₄	—	19	4	no	—
367	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
368	C₂²×C₄	C₂²×D₁₉	1	4	yes	—
369	C₄⋊C₄	—	19	2	no	—
370	C₄⋊C₄	—	19	2	no	—
371	C₄⋊C₄	—	19	2	no	—
372	C₄⋊C₄	—	19	2	no	—
373	C₄⋊C₄	—	19	2	no	—
374	C₄⋊C₄	—	19	2	no	—
375	C₄⋊C₄	—	19	1	no	—
376	C₄⋊C₄	—	19	1	no	—
377	C₄⋊C₄	—	19	2	no	—
378	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
379	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
380	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
381	C₂²⋊C₄	—	19	2	no	—
382	C₂²⋊C₄	—	19	2	no	—
383	C₂²⋊C₄	—	19	2	no	—
384	C₂²⋊C₄	—	19	4	no	—
385	C₂²⋊C₄	—	19	2	no	—
386	C₂²⋊C₄	—	19	2	no	—
387	C₂²⋊C₄	—	19	4	no	—
388	C₂²⋊C₄	—	19	4	no	—
389	C₂²⋊C₄	—	19	2	no	—
390	C₂²⋊C₄	—	19	2	no	—
391	C₂²⋊C₄	—	19	2	no	—
392	C₂²⋊C₄	—	19	2	no	—
393	C₂²⋊C₄	—	19	4	no	—
394	C₂²⋊C₄	—	19	4	no	—
395	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
396	C₂²⋊C₄	C₂²×D₁₉	1	4	yes	—
397	C₄²	—	19	1	no	—
398	C₄²	—	19	1	no	—
399	C₄²	—	19	1	no	—
400	C₄²	—	19	2	no	—
401	C₄²	C₂²×D₁₉	1	1	yes	characteristic
402	C₄²	C₂²×D₁₉	1	2	yes	—
403	C₂³	—	19	1	no	—
404	C₂³	—	19	4	no	—
405	C₂³	—	19	2	no	—
406	C₂³	—	38	8	no	—
407	C₂³	—	76	4	no	—
408	C₂³	—	76	4	no	—
409	C₂³	—	76	4	no	—
410	C₂³	—	76	4	no	—
411	C₂³	—	76	4	no	—
412	C₂³	C₂³×D₁₉	1	2	yes	—
413	C₂³	C₂³×D₁₉	1	4	yes	—
414	Q₈	—	2	2	no	—
415	Q₈	—	38	2	no	—
416	D₄	—	2	4	no	—
417	D₄	—	2	2	no	—
418	D₄	—	2	4	no	—
419	D₄	—	4	2	no	—
420	D₄	—	4	4	no	—
421	D₄	—	4	4	no	—
422	D₄	—	38	4	no	—
423	D₄	—	38	4	no	—
424	D₄	—	38	2	no	—
425	D₄	—	38	4	no	—
426	D₄	—	38	4	no	—
427	D₄	—	76	2	no	—
428	D₄	—	76	4	no	—
429	D₄	—	76	4	no	—
430	D₄	—	76	4	no	—
431	D₄	—	76	4	no	—
432	D₄	—	76	4	no	—
433	D₄	—	76	4	no	—
434	D₄	—	76	4	no	—
435	C₂×C₄	—	2	4	no	—
436	C₂×C₄	—	4	4	no	—
437	C₂×C₄	—	19	1	no	—
438	C₂×C₄	—	19	1	no	—
439	C₂×C₄	—	19	1	no	—
440	C₂×C₄	—	19	2	no	—
441	C₂×C₄	—	19	2	no	—
442	C₂×C₄	—	19	2	no	—
443	C₂×C₄	—	38	2	no	—
444	C₂×C₄	—	38	2	no	—
445	C₂×C₄	—	38	2	no	—
446	C₂×C₄	—	38	4	no	—
447	C₂×C₄	—	76	4	no	—
448	C₂×C₄	—	76	4	no	—
449	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
450	C₂×C₄	C₂³×D₁₉	1	2	yes	—
451	C₂×C₄	C₂³×D₁₉	1	2	yes	—
452	C₂×C₄	C₂³×D₁₉	1	2	yes	—
453	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
454	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
455	C₂²	—	2	2	no	—
456	C₂²	—	2	4	no	—
457	C₂²	—	2	2	no	—
458	C₂²	—	2	4	no	—
459	C₂²	—	2	4	no	—
460	C₂²	—	2	2	no	—
461	C₂²	—	19	2	no	—
462	C₂²	—	38	1	no	—
463	C₂²	—	38	1	no	—
464	C₂²	—	38	4	no	—
465	C₂²	—	38	2	no	—
466	C₂²	—	38	2	no	—
467	C₂²	—	38	4	no	—
468	C₂²	—	38	2	no	—
469	C₂²	—	38	4	no	—
470	C₂²	—	152	8	no	—
471	C₂²	—	152	8	no	—
472	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
473	C₄	—	2	1	no	—
474	C₄	—	2	2	no	—
475	C₄	—	2	2	no	—
476	C₄	—	2	2	no	—
477	C₄	—	38	1	no	—
478	C₄	—	38	2	no	—
479	C₄	—	38	1	no	—
480	C₄	—	38	2	no	—
481	C₄	—	38	1	no	—
482	C₄	—	38	2	no	—
483	C₄	#10597430	1	2	yes	—
484	C₄	#10597435	1	2	yes	—
485	C₂	—	4	2	no	—
486	C₂	—	4	4	no	—
487	C₂	—	38	2	no	—
488	C₂	—	76	4	no	—
489	C₂	—	76	2	no	—
490	C₂	H(5,𝔽₂)×D₁₉	1	1	yes	characteristic
491	C₂	C₂×#10597430	1	1	yes	characteristic
492	C₂	C₂×#10597435	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	#3543
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. #11927282	C₂	semidirect
2. #11927279	C₂	semidirect
3. #11927214	C₂	semidirect
4. #11927189	C₂	semidirect
5. #11927182	C₂	semidirect
6. D₄×D₇₆	C₂	semidirect
7. #11927179	C₂	semidirect
8. #11927178	C₂	semidirect
9. #11927147	C₂	semidirect
10. #11927145	C₂	semidirect
11. #11927108	C₂	semidirect
12. #11927107	C₂	semidirect
13. #11927102	C₂	semidirect
14. #127×D₁₉	C₂	semidirect
15. #11927081	C₂	semidirect
16. #11927076	C₂	semidirect
17. C₁₉×#550	C₂	semidirect
18. C₂×#41×C₁₉	C₂²	semidirect
19. C₂×#64543	C₂²	semidirect
20. C₂×D₄×D₁₉	C₂²	semidirect
21. C₂×D₄×D₁₉	C₂²	semidirect
22. C₂×D₄×D₁₉	C₂²	semidirect
23. C₂×D₄×D₁₉	C₂²	semidirect
24. C₂×D₄×D₁₉	C₂²	semidirect
25. C₂²×D₇₆	C₂²	semidirect
26. C₁₉×#127	C₂²	semidirect
27. C₁₉×#127	C₂²	semidirect
28. C₁₉×#121	C₂²	semidirect
29. C₁₉×#121	C₂²	semidirect
30. C₄×Q₈×C₁₉	C₂²	semidirect
31. C₄×D₄×C₁₉	C₂²	semidirect
32. C₄×D₄×C₁₉	C₂²	semidirect
33. #10597393	C₂²	semidirect
34. #10597393	C₂²	semidirect
35. #10597392	C₂²	semidirect
36. #10597386	C₂²	semidirect
37. #10597386	C₂²	semidirect
38. #10597386	C₂²	semidirect
39. #10597386	C₂²	semidirect
40. #10597385	C₂²	semidirect
41. #10597385	C₂²	semidirect
42. #10597385	C₂²	semidirect
44. #10597384	C₂²	semidirect
45. #10597384	C₂²	semidirect
46. #10597383	C₂²	semidirect
47. #10597383	C₂²	semidirect
48. #10597383	C₂²	semidirect
49. #10597383	C₂²	semidirect
50. #10597382	C₂²	semidirect
51. D₄×Dic₁₉	C₂²	semidirect
52. #10597376	C₂²	semidirect
53. #10597376	C₂²	semidirect
54. #10597376	C₂²	semidirect
55. #10597375	C₂²	semidirect
56. C₄×C₂²⋊D₁₉	C₂²	semidirect
57. C₂×(C₂×D₁₉)⋊C₄	C₂²	semidirect
58. #10597372	C₂²	semidirect
59. #10597344	C₂²	semidirect
60. #10597343	C₂²	semidirect
62. #10597341	C₂²	semidirect
63. #10597340	C₂²	semidirect
64. #10597340	C₂²	semidirect
65. #10597339	C₂²	semidirect
66. #10597336	C₂²	semidirect
67. #10597336	C₂²	semidirect
68. #10597332	C₂²	semidirect
69. #10597330	C₂²	semidirect
70. #10597329	C₂²	semidirect
71. #10597329	C₂²	semidirect
72. #10597328	C₂²	semidirect
73. #10597328	C₂²	semidirect
74. #10597325	C₂²	semidirect
75. #10597321	C₂²	semidirect
77. C₄×D₇₆	C₂²	semidirect
78. C₄×D₇₆	C₂²	semidirect
79. C₄×D₇₆	C₂²	semidirect
80. #10597318	C₂²	semidirect
81. C₄²×D₁₉	C₂²	semidirect
82. C₄×Dic₃₈	C₂²	semidirect
242. #550	D₁₉	semidirect
265. C₂×#41	C₂×D₁₉	semidirect
277. #127	C₂×D₁₉	semidirect
278. #127	C₂×D₁₉	semidirect
307. #121	C₂×D₁₉	semidirect
308. #121	C₂×D₁₉	semidirect
316. C₄×Q₈	C₂×D₁₉	semidirect
323. C₄×D₄	C₂×D₁₉	semidirect
324. C₄×D₄	C₂×D₁₉	semidirect
329. C₁₉	#3543	semidirect

Maximal subgroups

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

subgroup	index
#11927282	2
#11927279	2
#11927214	2
#11927189	2
#11927182	2
D₄×D₇₆	2
#11927179	2
#11927178	2
#11927147	2
#11927145	2
#11927108	2
#11927107	2
#11927102	2
#127×D₁₉	2
#11927081	2
#11927076	2
C₁₉×#550	2
#3543	19