Subgroups — #14577912

Order 2432.

1058 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927286	C₂	1	2	yes	maximal, complemented
2	#11927284	C₂	1	2	yes	maximal, complemented
3	#11927278	C₂	1	2	yes	maximal, complemented
4	#11927265	C₂	1	2	yes	maximal, complemented
5	#11927257	C₂	1	2	yes	maximal, complemented
6	#11927224	C₂	1	2	yes	maximal, complemented
7	#11927205	C₂	1	2	yes	maximal, complemented
8	#11927185	C₂	1	2	yes	maximal, complemented
9	#11927168	C₂	1	4	yes	maximal, complemented
10	#11927167	C₂	1	2	yes	maximal, complemented
11	#11927130	C₂	1	4	yes	maximal, complemented
12	#11927108	C₂	1	1	yes	maximal, characteristic, complemented
13	#11927057	C₂	1	2	yes	maximal, complemented
14	#11927051	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#536	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#41×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
18	C₂×#64545	C₂²	1	2	yes	—
19	C₂²×D₇₆	C₂²	1	1	yes	characteristic, complemented
20	C₂²×C₄×D₁₉	C₂²	1	1	yes	characteristic, complemented
21	C₁₉×C₄⋊Q₈	C₂²	1	2	yes	complemented
22	C₁₉×#124	C₂²	1	2	yes	—
23	C₁₉×#123	C₂²	1	2	yes	complemented
24	C₁₉×#123	C₂²	1	2	yes	complemented
25	C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	complemented
26	C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	complemented
27	C₁₉×#117	C₂²	1	1	yes	characteristic, complemented
28	#10597393	C₂²	1	2	yes	complemented
29	#10597393	C₂²	1	2	yes	complemented
30	#10597393	C₂²	1	4	yes	complemented
31	#10597392	C₂²	1	2	yes	complemented
32	#10597392	C₂²	1	2	yes	complemented
33	#10597392	C₂²	1	4	yes	complemented
34	Q₈×Dic₁₉	C₂²	1	2	yes	complemented
35	#10597386	C₂²	1	2	yes	—
36	#10597384	C₂²	1	2	yes	—
37	#10597383	C₂²	1	1	yes	characteristic
38	#10597383	C₂²	1	2	yes	—
39	#10597383	C₂²	1	1	yes	characteristic, complemented
40	#10597383	C₂²	1	2	yes	complemented
41	#10597381	C₂²	1	1	yes	characteristic
42	#10597381	C₂²	1	1	yes	characteristic, complemented
43	#10597376	C₂²	1	2	yes	—
44	#10597376	C₂²	1	2	yes	complemented
45	#10597376	C₂²	1	4	yes	complemented
46	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	—
47	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	complemented
48	C₄×C₂²⋊D₁₉	C₂²	1	4	yes	complemented
49	#10597372	C₂²	1	1	yes	characteristic, complemented
50	#10597372	C₂²	1	1	yes	characteristic, complemented
51	#10597344	C₂²	1	4	yes	complemented
52	#10597344	C₂²	1	4	yes	complemented
53	#10597343	C₂²	1	4	yes	complemented
54	#10597341	C₂²	1	2	yes	—
55	#10597341	C₂²	1	4	yes	—
56	#10597340	C₂²	1	4	yes	complemented
57	#10597340	C₂²	1	4	yes	complemented
58	#10597339	C₂²	1	4	yes	complemented
59	#10597339	C₂²	1	2	yes	complemented
60	#10597338	C₂²	1	2	yes	complemented
61	#10597334	C₂²	1	2	yes	complemented
62	#10597333	C₂²	1	4	yes	complemented
63	#10597331	C₂²	1	4	yes	—
64	#10597331	C₂²	1	4	yes	complemented
65	#10597331	C₂²	1	4	yes	complemented
66	#10597330	C₂²	1	4	yes	complemented
67	#10597329	C₂²	1	4	yes	complemented
68	#10597328	C₂²	1	4	yes	—
69	#10597328	C₂²	1	4	yes	complemented
70	(C₂²⋊D₁₉)⋊C₄	C₂²	1	4	yes	complemented
71	C₂²⋊C₄×D₁₉	C₂²	1	4	yes	complemented
72	#10597325	C₂²	1	4	yes	complemented
73	#10597321	C₂²	1	4	yes	complemented
74	#10597318	C₂²	1	4	yes	complemented
75	C₂³×D₁₉	C₂³	1	1	yes	characteristic
76	C₂³×D₁₉	C₂³	1	2	yes	—
77	#41×C₁₉	—	4	2	no	—
78	C₂×Q₈×C₁₉	—	4	2	no	—
79	C₂×Q₈×C₁₉	C₂³	1	2	yes	—
80	C₂×Q₈×C₁₉	C₂³	1	2	yes	—
81	C₂×Q₈×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	1	yes	characteristic
85	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
86	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
87	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
88	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
89	C₂×C₂²⋊D₁₉	C₂³	1	4	yes	—
90	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
91	C₂×C₂²⋊D₁₉	C₂³	1	4	yes	—
92	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
93	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
94	#64545	—	4	4	no	—
95	C₂×D₇₆	—	4	2	no	—
96	C₂×D₇₆	C₂³	1	2	yes	—
97	C₂×D₇₆	C₂³	1	4	yes	—
98	C₂×D₇₆	C₂³	1	2	yes	—
99	C₂×D₇₆	C₂³	1	4	yes	—
100	C₂×C₄×D₁₉	—	4	2	no	—
101	C₂×C₄×D₁₉	C₂³	1	2	yes	—
102	C₂×C₄×D₁₉	C₂³	1	2	yes	—
103	C₂×C₄×D₁₉	C₂³	1	4	yes	—
104	C₂×C₄×D₁₉	C₂³	1	4	yes	—
105	C₂×Dic₃₈	C₂³	1	4	yes	—
106	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
107	C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
108	C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
109	C₂²⋊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	2	yes	—
113	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
114	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
115	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
116	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
117	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
118	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
119	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
120	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
121	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
122	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
123	(C₂×D₁₉)⋊C₄	C₂³	1	2	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	C₄⋊Dic₁₉	C₂³	1	2	yes	—
129	C₄⋊Dic₁₉	C₂³	1	4	yes	—
130	C₄⋊Dic₁₉	C₂³	1	2	yes	—
131	Dic₁₉⋊C₄	C₂³	1	2	yes	—
132	Dic₁₉⋊C₄	C₂³	1	2	yes	—
133	Dic₁₉⋊C₄	C₂³	1	4	yes	—
134	Dic₁₉⋊C₄	C₂³	1	4	yes	—
135	C₄×Dic₁₉	C₂³	1	2	yes	—
136	C₄×Dic₁₉	C₂³	1	4	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	C₂²×D₁₉	—	4	1	no	—
143	C₂²×D₁₉	—	4	2	no	—
144	C₂²×D₁₉	—	4	2	no	—
145	C₂²×D₁₉	—	4	4	no	—
146	C₂²×D₁₉	C₂⁴	1	2	yes	—
147	C₂²×D₁₉	C₂⁴	1	4	yes	—
148	Q₈×C₁₉	—	2	4	no	—
149	Q₈×C₁₉	—	4	2	no	—
150	Q₈×C₁₉	—	4	1	no	—
151	D₄×C₁₉	—	4	1	no	—
152	D₄×C₁₉	—	4	1	no	—
153	D₄×C₁₉	—	4	1	no	—
154	C₂×C₄×C₁₉	—	2	2	no	—
155	C₂×C₄×C₁₉	—	2	2	no	—
156	C₂×C₄×C₁₉	—	2	2	no	—
157	C₂×C₄×C₁₉	—	4	2	no	—
158	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
159	C₂×C₄×C₁₉	C₂⁴	1	4	yes	—
160	C₂×C₄×C₁₉	C₂⁴	1	4	yes	—
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	C₂²⋊D₁₉	—	4	2	no	—
165	C₂²⋊D₁₉	—	4	4	no	—
166	C₂²⋊D₁₉	—	4	4	no	—
167	C₂²⋊D₁₉	—	4	2	no	—
168	C₂×Dic₁₉	—	4	1	no	—
169	C₂×Dic₁₉	C₂⁴	1	4	yes	—
170	C₂×Dic₁₉	C₂⁴	1	2	yes	—
171	C₂×Dic₁₉	C₂⁴	1	2	yes	—
172	C₂×Dic₁₉	C₂⁴	1	2	yes	—
173	D₇₆	—	2	4	no	—
174	D₇₆	—	4	2	no	—
175	D₇₆	—	4	4	no	—
176	D₇₆	—	4	4	no	—
177	C₄×D₁₉	—	2	4	no	—
178	C₄×D₁₉	—	4	2	no	—
179	C₄×D₁₉	—	4	4	no	—
180	C₄×D₁₉	—	4	4	no	—
181	Dic₃₈	—	4	4	no	—
182	#3540	—	19	1	no	maximal, Sylow
183	C₂²×C₁₉	—	2	1	no	—
184	C₂²×C₁₉	—	2	1	no	—
185	C₂²×C₁₉	—	2	1	no	—
186	C₂²×C₁₉	—	2	2	no	—
187	C₂²×C₁₉	—	2	2	no	—
188	C₂²×C₁₉	—	2	2	no	—
189	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
190	C₂×D₁₉	—	2	2	no	—
191	C₂×D₁₉	—	2	4	no	—
192	C₂×D₁₉	—	2	4	no	—
193	C₂×D₁₉	—	2	2	no	—
194	C₂×D₁₉	—	2	4	no	—
195	C₂×D₁₉	—	2	2	no	—
196	C₂×D₁₉	—	4	4	no	—
197	C₂×D₁₉	—	8	4	no	—
198	C₄×C₁₉	—	2	1	no	—
199	C₄×C₁₉	—	2	4	no	—
200	C₄×C₁₉	—	2	1	no	—
201	C₄×C₁₉	—	2	1	no	—
202	C₄×C₁₉	—	2	4	no	—
203	C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
204	Dic₁₉	—	2	2	no	—
205	Dic₁₉	—	2	2	no	—
206	Dic₁₉	—	2	4	no	—
207	Dic₁₉	—	2	2	no	—
208	H(3,𝔽₄)	—	19	2	no	—
209	#560	—	19	2	no	—
210	#559	—	19	2	no	—
211	#556	—	19	2	no	—
212	#555	—	19	2	no	—
213	#551	—	19	2	no	—
214	#548	—	19	2	no	—
215	#546	—	19	2	no	—
216	#542	—	19	4	no	—
217	#542	—	19	2	no	—
218	#538	—	19	4	no	—
219	#536	D₁₉	1	1	yes	characteristic, complemented
220	#535	—	19	1	no	—
221	#525	—	19	1	no	—
222	#525	—	19	2	no	—
223	C₂×C₁₉	—	4	1	no	—
224	C₂×C₁₉	—	4	1	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	2	no	—
229	D₁₉	—	4	4	no	—
230	C₂×#41	—	19	2	no	—
231	C₂×#41	C₂×D₁₉	1	1	yes	characteristic
232	C₂²×Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
233	C₂²×D₄	—	19	1	no	—
234	C₂³×C₄	—	19	1	no	—
235	C₄⋊Q₈	—	19	2	no	—
236	C₄⋊Q₈	C₂×D₁₉	1	2	yes	complemented
237	#127	—	19	2	no	—
238	#126	—	19	4	no	—
239	#126	—	19	4	no	—
240	#126	—	19	4	no	—
241	#124	—	19	2	no	—
242	#124	—	19	2	no	—
243	#124	—	19	4	no	—
244	#124	—	19	4	no	—
245	#124	—	19	4	no	—
246	#124	—	19	4	no	—
247	#124	—	19	4	no	—
248	#124	C₂×D₁₉	1	2	yes	—
249	#123	—	19	1	no	—
250	#123	—	19	1	no	—
251	#123	—	19	4	no	—
252	#123	—	19	4	no	—
253	#123	—	19	4	no	—
254	#123	C₂×D₁₉	1	2	yes	complemented
255	#123	C₂×D₁₉	1	2	yes	complemented
256	C₂²⋊Q₈	—	19	2	no	—
257	C₂²⋊Q₈	—	19	2	no	—
258	C₂²⋊Q₈	—	19	4	no	—
259	C₂²⋊Q₈	—	19	4	no	—
260	C₂²⋊Q₈	C₂×D₁₉	1	2	yes	complemented
261	C₂²⋊Q₈	C₂×D₁₉	1	2	yes	complemented
262	#121	—	19	2	no	—
263	#121	—	19	2	no	—
264	#121	—	19	2	no	—
265	#121	—	19	4	no	—
266	#121	—	19	2	no	—
267	#121	—	19	4	no	—
268	#121	—	19	4	no	—
269	#120	—	19	1	no	—
270	#120	—	19	2	no	—
271	#120	—	19	1	no	—
272	#120	—	19	2	no	—
273	#120	—	19	4	no	—
274	#120	—	19	4	no	—
275	C₄×Q₈	—	19	2	no	—
276	C₄×Q₈	—	19	4	no	—
277	C₄×D₄	—	19	2	no	—
278	C₄×D₄	—	19	2	no	—
279	C₄×D₄	—	19	4	no	—
280	C₄×D₄	—	19	4	no	—
281	C₄×D₄	—	19	2	no	—
282	C₄×D₄	—	19	4	no	—
283	#117	—	19	1	no	—
284	#117	—	19	1	no	—
285	#117	—	19	2	no	—
286	#117	—	19	4	no	—
287	#117	C₂×D₁₉	1	1	yes	characteristic, complemented
288	C₂×C₂²⋊C₄	—	19	4	no	—
289	C₁₉	#3540	1	1	yes	characteristic, complemented, Sylow
290	C₂⁴	—	19	2	no	—
291	C₂⁴	—	19	1	no	—
292	#41	—	4	2	no	—
293	#41	—	76	4	no	—
294	C₂×Q₈	—	4	2	no	—
295	C₂×Q₈	—	19	4	no	—
296	C₂×Q₈	C₂²×D₁₉	1	2	yes	—
297	C₂×Q₈	C₂²×D₁₉	1	2	yes	—
298	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
299	C₂×D₄	—	19	2	no	—
300	C₂×D₄	—	19	4	no	—
301	C₂×D₄	—	19	2	no	—
302	C₂×D₄	—	19	4	no	—
303	C₂×D₄	—	19	2	no	—
304	C₂×D₄	—	19	4	no	—
305	C₂×D₄	—	19	4	no	—
306	C₂×D₄	—	19	2	no	—
307	C₂×D₄	—	76	2	no	—
308	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
309	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
310	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
311	C₂²×C₄	—	19	1	no	—
312	C₂²×C₄	—	19	2	no	—
313	C₂²×C₄	—	19	4	no	—
314	C₂²×C₄	—	19	4	no	—
315	C₂²×C₄	—	19	2	no	—
316	C₂²×C₄	—	76	2	no	—
317	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
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	2	no	—
322	C₄⋊C₄	—	19	4	no	—
323	C₄⋊C₄	—	19	4	no	—
324	C₄⋊C₄	—	19	2	no	—
325	C₄⋊C₄	—	19	2	no	—
326	C₄⋊C₄	—	19	2	no	—
327	C₄⋊C₄	—	19	4	no	—
328	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
329	C₄⋊C₄	C₂²×D₁₉	1	4	yes	—
330	C₄⋊C₄	C₂²×D₁₉	1	4	yes	—
331	C₂²⋊C₄	—	19	2	no	—
332	C₂²⋊C₄	—	19	2	no	—
333	C₂²⋊C₄	—	19	1	no	—
334	C₂²⋊C₄	—	19	1	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	2	no	—
341	C₂²⋊C₄	—	19	4	no	—
342	C₂²⋊C₄	—	19	4	no	—
343	C₂²⋊C₄	—	19	4	no	—
344	C₂²⋊C₄	—	19	2	no	—
345	C₂²⋊C₄	—	19	4	no	—
346	C₂²⋊C₄	C₂²×D₁₉	1	4	yes	—
347	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
348	C₂²⋊C₄	C₂²×D₁₉	1	4	yes	—
349	C₄²	—	19	4	no	—
350	C₄²	—	19	2	no	—
351	C₄²	—	19	2	no	—
352	C₄²	—	19	4	no	—
353	C₄²	C₂²×D₁₉	1	2	yes	—
354	C₂³	—	19	2	no	—
355	C₂³	—	19	4	no	—
356	C₂³	—	76	1	no	—
357	C₂³	—	76	2	no	—
358	C₂³	—	76	2	no	—
359	C₂³	—	76	4	no	—
360	C₂³	C₂³×D₁₉	1	1	yes	characteristic
361	C₂³	C₂³×D₁₉	1	1	yes	characteristic
362	C₂³	C₂³×D₁₉	1	1	yes	characteristic
363	Q₈	—	2	4	no	—
364	Q₈	—	4	2	no	—
365	Q₈	—	4	1	no	—
366	Q₈	—	76	4	no	—
367	D₄	—	4	1	no	—
368	D₄	—	4	1	no	—
369	D₄	—	4	1	no	—
370	D₄	—	38	4	no	—
371	D₄	—	76	2	no	—
372	D₄	—	76	4	no	—
373	D₄	—	76	4	no	—
374	D₄	—	76	2	no	—
375	D₄	—	76	4	no	—
376	D₄	—	76	4	no	—
377	D₄	—	76	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	19	2	no	—
383	C₂×C₄	—	19	4	no	—
384	C₂×C₄	—	19	2	no	—
385	C₂×C₄	—	19	2	no	—
386	C₂×C₄	—	38	4	no	—
387	C₂×C₄	—	76	2	no	—
388	C₂×C₄	—	76	4	no	—
389	C₂×C₄	—	76	4	no	—
390	C₂×C₄	—	76	1	no	—
391	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
392	C₂×C₄	C₂³×D₁₉	1	4	yes	—
393	C₂×C₄	C₂³×D₁₉	1	4	yes	—
394	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
395	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
396	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	2	1	no	—
400	C₂²	—	2	2	no	—
401	C₂²	—	2	2	no	—
402	C₂²	—	2	2	no	—
403	C₂²	—	38	2	no	—
404	C₂²	—	38	4	no	—
405	C₂²	—	38	4	no	—
406	C₂²	—	38	2	no	—
407	C₂²	—	38	2	no	—
408	C₂²	—	38	4	no	—
409	C₂²	—	76	4	no	—
410	C₂²	—	152	4	no	—
411	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	2	4	no	—
416	C₄	—	2	4	no	—
417	C₄	—	38	2	no	—
418	C₄	—	38	2	no	—
419	C₄	—	38	4	no	—
420	C₄	—	38	2	no	—
421	C₄	#10597430	1	2	yes	—
422	C₂	—	4	1	no	—
423	C₂	—	4	1	no	—
424	C₂	—	4	1	no	—
425	C₂	—	76	2	no	—
426	C₂	—	76	4	no	—
427	C₂	C₂×#10597430	1	1	yes	characteristic
428	C₂	#11927381	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Fitting	C₁₉×#536	C₂
hypercenter	#536	D₁₉
hypocenter	C₁₉	#3540
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ #536

Complements

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

N	H ≅ G/N	type
1. #11927286	C₂	semidirect
2. #11927284	C₂	semidirect
3. #11927278	C₂	semidirect
4. #11927265	C₂	semidirect
5. #11927257	C₂	semidirect
6. #11927224	C₂	semidirect
7. #11927205	C₂	semidirect
8. #11927185	C₂	semidirect
9. #11927168	C₂	semidirect
10. #11927167	C₂	semidirect
11. #11927130	C₂	semidirect
12. #11927108	C₂	semidirect
13. #11927057	C₂	semidirect
14. #11927051	C₂	semidirect
15. C₁₉×#536	C₂	semidirect
17. C₂²×Q₈×C₁₉	C₂²	semidirect
19. C₂²×D₇₆	C₂²	semidirect
20. C₂²×C₄×D₁₉	C₂²	semidirect
21. C₁₉×C₄⋊Q₈	C₂²	semidirect
23. C₁₉×#123	C₂²	semidirect
24. C₁₉×#123	C₂²	semidirect
25. C₁₉×C₂²⋊Q₈	C₂²	semidirect
26. C₁₉×C₂²⋊Q₈	C₂²	semidirect
27. C₁₉×#117	C₂²	semidirect
28. #10597393	C₂²	semidirect
29. #10597393	C₂²	semidirect
30. #10597393	C₂²	semidirect
31. #10597392	C₂²	semidirect
32. #10597392	C₂²	semidirect
33. #10597392	C₂²	semidirect
34. Q₈×Dic₁₉	C₂²	semidirect
39. #10597383	C₂²	semidirect
40. #10597383	C₂²	semidirect
42. #10597381	C₂²	semidirect
44. #10597376	C₂²	semidirect
45. #10597376	C₂²	semidirect
47. C₄×C₂²⋊D₁₉	C₂²	semidirect
48. C₄×C₂²⋊D₁₉	C₂²	semidirect
49. #10597372	C₂²	semidirect
50. #10597372	C₂²	semidirect
51. #10597344	C₂²	semidirect
52. #10597344	C₂²	semidirect
53. #10597343	C₂²	semidirect
56. #10597340	C₂²	semidirect
57. #10597340	C₂²	semidirect
58. #10597339	C₂²	semidirect
59. #10597339	C₂²	semidirect
60. #10597338	C₂²	semidirect
61. #10597334	C₂²	semidirect
62. #10597333	C₂²	semidirect
64. #10597331	C₂²	semidirect
65. #10597331	C₂²	semidirect
66. #10597330	C₂²	semidirect
67. #10597329	C₂²	semidirect
69. #10597328	C₂²	semidirect
70. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
71. C₂²⋊C₄×D₁₉	C₂²	semidirect
72. #10597325	C₂²	semidirect
73. #10597321	C₂²	semidirect
74. #10597318	C₂²	semidirect
219. #536	D₁₉	semidirect
232. C₂²×Q₈	C₂×D₁₉	semidirect
236. C₄⋊Q₈	C₂×D₁₉	semidirect
254. #123	C₂×D₁₉	semidirect
255. #123	C₂×D₁₉	semidirect
260. C₂²⋊Q₈	C₂×D₁₉	semidirect
261. C₂²⋊Q₈	C₂×D₁₉	semidirect
287. #117	C₂×D₁₉	semidirect
289. C₁₉	#3540	semidirect

Maximal subgroups

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

subgroup	index
#11927286	2
#11927284	2
#11927278	2
#11927265	2
#11927257	2
#11927224	2
#11927205	2
#11927185	2
#11927168	2
#11927167	2
#11927130	2
#11927108	2
#11927057	2
#11927051	2
C₁₉×#536	2
#3540	19