Subgroups — #14577791

Order 2432.

1336 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927286	C₂	1	1	yes	maximal, characteristic, complemented
2	#11927285	C₂	1	2	yes	maximal, complemented
3	#11927284	C₂	1	1	yes	maximal, characteristic, complemented
4	#11927218	C₂	1	2	yes	maximal, complemented
5	#11927186	C₂	1	2	yes	maximal, complemented
6	#11927185	C₂	1	2	yes	maximal, complemented
7	#11927184	C₂	1	2	yes	maximal, complemented
8	D₄×D₇₆	C₂	1	2	yes	maximal, complemented
9	#11927176	C₂	1	1	yes	maximal, characteristic, complemented
10	#11927134	C₂	1	2	yes	maximal, complemented
11	#11927133	C₂	1	2	yes	maximal, complemented
12	#11927127	C₂	1	2	yes	maximal, complemented
13	#11927113	C₂	1	2	yes	maximal, complemented
14	#11927112	C₂	1	1	yes	maximal, characteristic, complemented
15	#11927105	C₂	1	2	yes	maximal, complemented
16	#11927105	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#10597328	C₂	1	2	yes	maximal, complemented
18	#120×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₉×#551	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂⁴×D₁₉	C₂²	1	1	yes	characteristic, complemented
21	C₂²×C₂²⋊D₁₉	C₂²	1	2	yes	complemented
22	C₂×#64545	C₂²	1	1	yes	characteristic, complemented
23	C₂×D₄×D₁₉	C₂²	1	1	yes	characteristic, complemented
24	C₂×D₄×D₁₉	C₂²	1	2	yes	complemented
25	C₂×D₄×D₁₉	C₂²	1	2	yes	complemented
26	C₂×#64541	C₂²	1	2	yes	complemented
27	C₂²×D₇₆	C₂²	1	2	yes	complemented
28	C₂²×D₇₆	C₂²	1	2	yes	complemented
29	C₂²×D₇₆	C₂²	1	1	yes	characteristic, complemented
30	C₁₉×#126	C₂²	1	2	yes	complemented
31	C₁₉×#124	C₂²	1	1	yes	characteristic, complemented
32	C₁₉×#123	C₂²	1	1	yes	characteristic, complemented
33	C₁₉×#123	C₂²	1	2	yes	complemented
34	C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	complemented
35	C₁₉×#120	C₂²	1	1	yes	characteristic
36	C₄×D₄×C₁₉	C₂²	1	2	yes	complemented
37	C₁₉×#117	C₂²	1	2	yes	complemented
38	C₂×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	complemented
39	#10597399	C₂²	1	1	yes	characteristic, complemented
40	#10597393	C₂²	1	1	yes	characteristic, complemented
41	#10597393	C₂²	1	2	yes	complemented
42	#10597386	C₂²	1	1	yes	characteristic, complemented
43	#10597385	C₂²	1	2	yes	complemented
44	#10597383	C₂²	1	2	yes	complemented
45	#10597383	C₂²	1	1	yes	characteristic, complemented
46	#10597383	C₂²	1	1	yes	characteristic, complemented
47	#10597376	C₂²	1	2	yes	complemented
48	#10597376	C₂²	1	2	yes	complemented
49	#10597375	C₂²	1	1	yes	characteristic, complemented
50	#10597375	C₂²	1	2	yes	complemented
51	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	complemented
52	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	2	yes	complemented
53	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	2	yes	complemented
54	#10597344	C₂²	1	2	yes	complemented
55	#10597344	C₂²	1	2	yes	complemented
56	#10597342	C₂²	1	2	yes	complemented
57	#10597341	C₂²	1	2	yes	complemented
58	#10597341	C₂²	1	2	yes	complemented
59	#10597341	C₂²	1	2	yes	complemented
60	#10597341	C₂²	1	2	yes	complemented
61	#10597341	C₂²	1	2	yes	complemented
62	#10597341	C₂²	1	2	yes	complemented
63	#10597341	C₂²	1	2	yes	complemented
64	#10597340	C₂²	1	2	yes	complemented
65	#10597340	C₂²	1	2	yes	complemented
66	#10597340	C₂²	1	2	yes	complemented
67	#10597340	C₂²	1	2	yes	complemented
68	#10597340	C₂²	1	2	yes	complemented
69	#10597339	C₂²	1	2	yes	complemented
70	#10597331	C₂²	1	2	yes	complemented
71	#10597331	C₂²	1	2	yes	complemented
72	#10597330	C₂²	1	2	yes	complemented
73	#10597330	C₂²	1	2	yes	complemented
74	#10597330	C₂²	1	2	yes	complemented
75	#10597330	C₂²	1	2	yes	complemented
76	#10597330	C₂²	1	2	yes	complemented
77	#10597329	C₂²	1	2	yes	complemented
78	#10597328	C₂²	1	2	yes	—
79	#10597328	C₂²	1	2	yes	complemented
80	#10597328	C₂²	1	2	yes	complemented
81	#10597328	C₂²	1	2	yes	complemented
82	#10597328	C₂²	1	2	yes	complemented
83	#10597328	C₂²	1	2	yes	complemented
84	#10597328	C₂²	1	2	yes	complemented
85	#10597328	C₂²	1	1	yes	characteristic, complemented
86	#10597328	C₂²	1	2	yes	complemented
87	#10597328	C₂²	1	2	yes	complemented
88	#10597328	C₂²	1	2	yes	complemented
89	#10597328	C₂²	1	2	yes	complemented
90	#10597328	C₂²	1	2	yes	complemented
91	#10597328	C₂²	1	1	yes	characteristic, complemented
92	#10597328	C₂²	1	2	yes	complemented
93	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	complemented
94	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	complemented
95	C₂²⋊C₄×D₁₉	C₂²	1	1	yes	characteristic, complemented
96	C₂²⋊C₄×D₁₉	C₂²	1	2	yes	complemented
97	C₂²⋊C₄×D₁₉	C₂²	1	1	yes	characteristic, complemented
98	C₂²⋊C₄×D₁₉	C₂²	1	2	yes	complemented
99	#10597324	C₂²	1	2	yes	complemented
100	#10597322	C₂²	1	2	yes	complemented
101	#10597321	C₂²	1	2	yes	complemented
102	#10597321	C₂²	1	2	yes	complemented
103	#10597320	C₂²	1	1	yes	characteristic, complemented
104	#10597320	C₂²	1	2	yes	complemented
105	C₄×D₇₆	C₂²	1	2	yes	complemented
106	#10597318	C₂²	1	1	yes	characteristic, complemented
107	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
108	C₂³×D₁₉	—	4	2	no	—
109	C₂³×D₁₉	—	4	4	no	—
110	C₂³×D₁₉	C₂³	1	2	yes	—
111	C₂³×D₁₉	C₂³	1	2	yes	—
112	C₂³×D₁₉	C₂³	1	2	yes	—
113	C₂³×D₁₉	C₂³	1	1	yes	characteristic
114	C₂³×D₁₉	C₂³	1	1	yes	characteristic
115	C₂³×D₁₉	C₂³	1	1	yes	characteristic
116	C₂³×D₁₉	C₂³	1	1	yes	characteristic, complemented
117	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic, complemented
118	C₂×D₄×C₁₉	C₂³	1	2	yes	—
119	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
120	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
121	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
122	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic, complemented
123	C₂×C₂²⋊D₁₉	—	4	4	no	—
124	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
125	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
126	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
127	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
128	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
129	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
130	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
131	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
132	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	complemented
133	C₂²×Dic₁₉	C₂³	1	2	yes	—
134	#64545	—	4	2	no	—
135	D₄×D₁₉	—	4	2	no	—
136	D₄×D₁₉	—	4	4	no	—
137	D₄×D₁₉	—	4	4	no	—
138	#64541	—	4	4	no	—
139	C₂×D₇₆	—	4	2	no	—
140	C₂×D₇₆	—	4	4	no	—
141	C₂×D₇₆	—	4	4	no	—
142	C₂×D₇₆	C₂³	1	2	yes	—
143	C₂×D₇₆	C₂³	1	2	yes	—
144	C₂×D₇₆	C₂³	1	2	yes	—
145	C₂×D₇₆	C₂³	1	2	yes	—
146	C₂×D₇₆	C₂³	1	1	yes	characteristic
147	C₂×D₇₆	C₂³	1	2	yes	—
148	C₂×D₇₆	C₂³	1	2	yes	—
149	C₂×D₇₆	C₂³	1	2	yes	—
150	C₂×D₇₆	C₂³	1	2	yes	—
151	C₂×D₇₆	C₂³	1	2	yes	—
152	C₂×D₇₆	C₂³	1	2	yes	complemented
153	C₂×D₇₆	C₂³	1	1	yes	characteristic, complemented
154	C₂×D₇₆	C₂³	1	2	yes	complemented
155	C₂×D₇₆	C₂³	1	2	yes	complemented
156	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
157	C₂×C₄×D₁₉	C₂³	1	2	yes	—
158	C₂×C₄×D₁₉	C₂³	1	2	yes	complemented
159	C₂×C₄×D₁₉	C₂³	1	2	yes	complemented
160	C₂×C₄×D₁₉	C₂³	1	2	yes	complemented
161	C₂×C₄×D₁₉	C₂³	1	2	yes	complemented
162	C₂×Dic₃₈	C₂³	1	2	yes	complemented
163	C₄⋊C₄×C₁₉	C₂³	1	2	yes	complemented
164	C₄⋊C₄×C₁₉	C₂³	1	2	yes	complemented
165	C₄⋊C₄×C₁₉	C₂³	1	2	yes	complemented
166	C₄⋊C₄×C₁₉	C₂³	1	2	yes	complemented
167	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
168	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
169	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
170	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
171	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
172	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
173	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	complemented
174	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic, complemented
175	C₄²×C₁₉	C₂³	1	1	yes	characteristic, complemented
176	C₄²×C₁₉	C₂³	1	2	yes	complemented
177	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
178	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
179	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic, complemented
180	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
181	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
182	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
183	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
184	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
185	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
186	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
187	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
188	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
189	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
190	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
191	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	complemented
192	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	complemented
193	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	complemented
194	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	complemented
195	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	complemented
196	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	complemented
197	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	complemented
198	C₄⋊Dic₁₉	C₂³	1	2	yes	complemented
199	Dic₁₉⋊C₄	C₂³	1	2	yes	complemented
200	Dic₁₉⋊C₄	C₂³	1	2	yes	complemented
201	Dic₁₉⋊C₄	C₂³	1	2	yes	complemented
202	Dic₁₉⋊C₄	C₂³	1	2	yes	complemented
203	C₄×Dic₁₉	C₂³	1	1	yes	characteristic, complemented
204	C₄×Dic₁₉	C₂³	1	2	yes	complemented
205	C₂³×C₁₉	—	2	4	no	—
206	C₂³×C₁₉	—	4	1	no	—
207	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
208	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
209	C₂³×C₁₉	C₂⁴	1	2	yes	—
210	C₂²×D₁₉	—	2	4	no	—
211	C₂²×D₁₉	—	2	4	no	—
212	C₂²×D₁₉	—	2	4	no	—
213	C₂²×D₁₉	—	2	4	no	—
214	C₂²×D₁₉	—	2	2	no	—
215	C₂²×D₁₉	—	2	2	no	—
216	C₂²×D₁₉	—	4	2	no	—
217	C₂²×D₁₉	—	4	2	no	—
218	C₂²×D₁₉	—	4	1	no	—
219	C₂²×D₁₉	—	4	2	no	—
220	C₂²×D₁₉	—	4	2	no	—
221	C₂²×D₁₉	—	4	2	no	—
222	C₂²×D₁₉	—	4	2	no	—
223	C₂²×D₁₉	—	4	1	no	—
224	C₂²×D₁₉	—	4	2	no	—
225	C₂²×D₁₉	—	4	2	no	—
226	C₂²×D₁₉	—	4	2	no	—
227	C₂²×D₁₉	—	4	16	no	—
228	C₂²×D₁₉	C₂⁴	1	2	yes	—
229	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
230	C₂²×D₁₉	C₂⁴	1	2	yes	—
231	C₂²×D₁₉	C₂⁴	1	2	yes	—
232	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
233	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
234	Q₈×C₁₉	—	4	1	no	—
235	D₄×C₁₉	—	2	4	no	—
236	D₄×C₁₉	—	4	1	no	—
237	C₂×C₄×C₁₉	—	2	4	no	—
238	C₂×C₄×C₁₉	—	4	2	no	—
239	C₂×C₄×C₁₉	—	4	1	no	—
240	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
241	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
242	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
243	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
244	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
245	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
246	C₂²⋊D₁₉	—	2	4	no	—
247	C₂²⋊D₁₉	—	2	4	no	—
248	C₂²⋊D₁₉	—	2	4	no	—
249	C₂²⋊D₁₉	—	4	2	no	—
250	C₂²⋊D₁₉	—	4	1	no	—
251	C₂²⋊D₁₉	—	4	1	no	—
252	C₂²⋊D₁₉	—	4	2	no	—
253	C₂²⋊D₁₉	—	4	2	no	—
254	C₂²⋊D₁₉	—	4	2	no	—
255	C₂×Dic₁₉	—	4	2	no	—
256	C₂×Dic₁₉	C₂⁴	1	2	yes	—
257	C₂×Dic₁₉	C₂⁴	1	2	yes	—
258	C₂×Dic₁₉	C₂⁴	1	2	yes	—
259	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
260	D₇₆	—	2	4	no	—
261	D₇₆	—	2	4	no	—
262	D₇₆	—	4	2	no	—
263	D₇₆	—	4	2	no	—
264	D₇₆	—	4	2	no	—
265	D₇₆	—	4	2	no	—
266	D₇₆	—	4	2	no	—
267	D₇₆	—	4	2	no	—
268	D₇₆	—	4	2	no	—
269	D₇₆	—	4	1	no	—
270	D₇₆	—	4	2	no	—
271	D₇₆	—	4	2	no	—
272	D₇₆	—	4	2	no	—
273	D₇₆	—	4	1	no	—
274	C₄×D₁₉	—	2	2	no	—
275	C₄×D₁₉	—	4	2	no	—
276	C₄×D₁₉	—	4	2	no	—
277	C₄×D₁₉	—	4	2	no	—
278	C₄×D₁₉	—	4	2	no	—
279	C₄×D₁₉	—	4	2	no	—
280	Dic₃₈	—	4	2	no	—
281	#3532	—	19	1	no	maximal, Sylow
282	C₂²×C₁₉	—	2	2	no	—
283	C₂²×C₁₉	—	2	2	no	—
284	C₂²×C₁₉	—	2	2	no	—
285	C₂²×C₁₉	—	2	2	no	—
286	C₂²×C₁₉	—	2	1	no	—
287	C₂²×C₁₉	—	2	1	no	—
288	C₂²×C₁₉	—	4	4	no	—
289	C₂²×C₁₉	H(5,𝔽₂)	1	4	yes	—
290	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
291	C₂×D₁₉	—	2	2	no	—
292	C₂×D₁₉	—	2	2	no	—
293	C₂×D₁₉	—	2	2	no	—
294	C₂×D₁₉	—	2	2	no	—
295	C₂×D₁₉	—	2	2	no	—
296	C₂×D₁₉	—	2	2	no	—
297	C₂×D₁₉	—	2	1	no	—
298	C₂×D₁₉	—	2	2	no	—
299	C₂×D₁₉	—	2	2	no	—
300	C₂×D₁₉	—	2	2	no	—
301	C₂×D₁₉	—	2	2	no	—
302	C₂×D₁₉	—	2	2	no	—
303	C₂×D₁₉	—	2	1	no	—
304	C₂×D₁₉	—	2	2	no	—
305	C₂×D₁₉	—	4	8	no	—
306	C₂×D₁₉	—	4	4	no	—
307	C₂×D₁₉	—	4	8	no	—
308	C₂×D₁₉	—	4	4	no	—
309	C₂×D₁₉	—	8	2	no	—
310	C₂×D₁₉	—	8	4	no	—
311	C₂×D₁₉	—	8	2	no	—
312	C₂×D₁₉	H(5,𝔽₂)	1	2	yes	—
313	C₄×C₁₉	—	2	2	no	—
314	C₄×C₁₉	—	2	1	no	—
315	C₄×C₁₉	—	2	2	no	—
316	C₄×C₁₉	—	2	2	no	—
317	C₄×C₁₉	—	2	2	no	—
318	C₄×C₁₉	—	2	2	no	—
319	Dic₁₉	—	2	2	no	—
320	Dic₁₉	—	2	2	no	—
321	Dic₁₉	—	2	1	no	—
322	Dic₁₉	—	2	2	no	—
323	H(3,𝔽₄)	—	19	1	no	—
324	#560	—	19	2	no	—
325	#560	—	19	1	no	—
326	#551	—	19	2	no	—
327	#551	D₁₉	1	1	yes	characteristic, complemented
328	#546	—	19	2	no	—
329	#546	—	19	2	no	—
330	#546	—	19	2	no	—
331	D₄²	—	19	1	no	—
332	D₄²	—	19	2	no	—
333	#538	—	19	2	no	—
334	#538	—	19	2	no	—
335	#538	—	19	2	no	—
336	#535	—	19	1	no	—
337	#535	—	19	2	no	—
338	#534	—	19	2	no	—
339	#534	—	19	1	no	—
340	C₂×#120	—	19	1	no	—
341	C₂×#120	—	19	2	no	—
342	C₂×C₁₉	—	2	4	no	—
343	C₂×C₁₉	—	4	1	no	—
344	C₂×C₁₉	—	4	1	no	—
345	C₂×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
346	C₂×C₁₉	C₂×H(5,𝔽₂)	1	2	yes	—
347	D₁₉	—	2	2	no	—
348	D₁₉	—	4	2	no	—
349	D₁₉	—	4	1	no	—
350	D₁₉	—	4	2	no	—
351	D₁₉	—	4	1	no	—
352	D₁₉	—	4	2	no	—
353	C₂⁵	—	19	1	no	—
354	C₂×#41	—	19	1	no	—
355	C₂×#41	—	19	2	no	—
356	C₂²×D₄	—	19	2	no	—
357	C₂²×D₄	—	19	1	no	—
358	C₂²×D₄	—	19	2	no	—
359	C₂²×D₄	—	19	2	no	—
360	C₂²×D₄	—	19	2	no	—
361	C₂²×D₄	—	19	2	no	—
362	C₂²×D₄	—	19	1	no	—
363	#127	—	19	1	no	—
364	#127	—	19	1	no	—
365	#127	—	19	2	no	—
366	#126	—	19	2	no	—
367	#126	—	19	2	no	—
368	#126	—	19	2	no	—
369	#126	C₂×D₁₉	1	2	yes	complemented
370	#124	—	19	1	no	—
371	#124	—	19	2	no	—
372	#124	—	19	2	no	—
373	#124	—	19	2	no	—
374	#124	—	19	2	no	—
375	#124	—	19	2	no	—
376	#124	C₂×D₁₉	1	1	yes	characteristic, complemented
377	#123	—	19	2	no	—
378	#123	—	19	1	no	—
379	#123	—	19	2	no	—
380	#123	—	19	2	no	—
381	#123	—	19	2	no	—
382	#123	—	19	2	no	—
383	#123	—	19	2	no	—
384	#123	—	19	2	no	—
385	#123	C₂×D₁₉	1	1	yes	characteristic, complemented
386	#123	C₂×D₁₉	1	2	yes	complemented
387	C₂²⋊Q₈	—	19	2	no	—
388	C₂²⋊Q₈	—	19	2	no	—
389	C₂²⋊Q₈	C₂×D₁₉	1	2	yes	complemented
390	#121	—	19	2	no	—
391	#121	—	19	2	no	—
392	#121	—	19	2	no	—
393	#121	—	19	2	no	—
394	#121	—	19	2	no	—
395	#121	—	19	2	no	—
396	#121	—	19	2	no	—
397	#121	—	19	2	no	—
398	#121	—	19	2	no	—
399	#121	—	19	2	no	—
400	#121	—	19	2	no	—
401	#121	—	19	2	no	—
402	#121	—	19	2	no	—
403	#121	—	19	2	no	—
404	#121	—	19	2	no	—
405	#120	—	19	1	no	—
406	#120	—	19	2	no	—
407	#120	—	19	1	no	—
408	#120	—	19	1	no	—
409	#120	—	19	2	no	—
410	#120	—	19	2	no	—
411	#120	—	19	2	no	—
412	#120	—	19	2	no	—
413	#120	—	19	2	no	—
414	#120	—	19	2	no	—
415	#120	—	19	2	no	—
416	#120	—	19	2	no	—
417	#120	—	19	1	no	—
418	#120	—	19	2	no	—
419	#120	—	19	2	no	—
420	#120	—	19	2	no	—
421	#120	—	19	1	no	—
422	#120	—	19	2	no	—
423	#120	—	19	2	no	—
424	#120	C₂×D₁₉	1	1	yes	characteristic
425	C₄×D₄	—	19	2	no	—
426	C₄×D₄	—	19	2	no	—
427	C₄×D₄	—	19	2	no	—
428	C₄×D₄	—	19	2	no	—
429	C₄×D₄	—	19	2	no	—
430	C₄×D₄	C₂×D₁₉	1	2	yes	complemented
431	#117	—	19	1	no	—
432	#117	C₂×D₁₉	1	2	yes	complemented
433	C₂×C₂²⋊C₄	—	19	2	no	—
434	C₂×C₂²⋊C₄	—	19	2	no	—
435	C₂×C₂²⋊C₄	—	19	1	no	—
436	C₂×C₂²⋊C₄	—	19	2	no	—
437	C₂×C₂²⋊C₄	—	19	2	no	—
438	C₂×C₂²⋊C₄	—	19	1	no	—
439	C₂×C₂²⋊C₄	C₂×D₁₉	1	2	yes	complemented
440	C₁₉	#3532	1	1	yes	characteristic, complemented, Sylow
441	C₂⁴	—	19	2	no	—
442	C₂⁴	—	19	1	no	—
443	C₂⁴	—	19	2	no	—
444	C₂⁴	—	19	1	no	—
445	C₂⁴	—	19	2	no	—
446	C₂⁴	—	19	1	no	—
447	C₂⁴	—	19	1	no	—
448	C₂⁴	—	76	4	no	—
449	C₂⁴	—	76	2	no	—
450	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
451	#41	—	76	4	no	—
452	#41	—	76	2	no	—
453	C₂×Q₈	—	19	2	no	—
454	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic, complemented
455	C₂×D₄	—	19	2	no	—
456	C₂×D₄	—	19	2	no	—
457	C₂×D₄	—	19	2	no	—
458	C₂×D₄	—	19	1	no	—
459	C₂×D₄	—	19	2	no	—
460	C₂×D₄	—	19	2	no	—
461	C₂×D₄	—	19	1	no	—
462	C₂×D₄	—	19	2	no	—
463	C₂×D₄	—	19	2	no	—
464	C₂×D₄	—	19	2	no	—
465	C₂×D₄	—	19	2	no	—
466	C₂×D₄	—	19	2	no	—
467	C₂×D₄	—	19	2	no	—
468	C₂×D₄	—	19	2	no	—
469	C₂×D₄	—	19	2	no	—
470	C₂×D₄	—	19	2	no	—
471	C₂×D₄	—	19	2	no	—
472	C₂×D₄	—	19	1	no	—
473	C₂×D₄	—	19	2	no	—
474	C₂×D₄	—	19	1	no	—
475	C₂×D₄	—	19	2	no	—
476	C₂×D₄	—	19	2	no	—
477	C₂×D₄	—	19	2	no	—
478	C₂×D₄	—	76	4	no	—
479	C₂×D₄	—	76	4	no	—
480	C₂×D₄	—	76	2	no	—
481	C₂×D₄	—	76	2	no	—
482	C₂×D₄	—	76	4	no	—
483	C₂×D₄	—	76	4	no	—
484	C₂×D₄	—	76	4	no	—
485	C₂×D₄	C₂²×D₁₉	1	2	yes	—
486	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
487	C₂²×C₄	—	19	2	no	—
488	C₂²×C₄	—	19	1	no	—
489	C₂²×C₄	—	19	2	no	—
490	C₂²×C₄	—	19	2	no	—
491	C₂²×C₄	—	19	2	no	—
492	C₂²×C₄	—	19	2	no	—
493	C₂²×C₄	—	19	2	no	—
494	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
495	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
496	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic, complemented
497	C₄⋊C₄	—	19	2	no	—
498	C₄⋊C₄	—	19	2	no	—
499	C₄⋊C₄	—	19	2	no	—
500	C₄⋊C₄	—	19	2	no	—
501	C₄⋊C₄	—	19	2	no	—
502	C₄⋊C₄	C₂²×D₁₉	1	2	yes	complemented
503	C₄⋊C₄	C₂²×D₁₉	1	2	yes	complemented
504	C₄⋊C₄	C₂²×D₁₉	1	2	yes	complemented
505	C₄⋊C₄	C₂²×D₁₉	1	2	yes	complemented
506	C₂²⋊C₄	—	19	2	no	—
507	C₂²⋊C₄	—	19	1	no	—
508	C₂²⋊C₄	—	19	1	no	—
509	C₂²⋊C₄	—	19	2	no	—
510	C₂²⋊C₄	—	19	2	no	—
511	C₂²⋊C₄	—	19	2	no	—
512	C₂²⋊C₄	—	19	2	no	—
513	C₂²⋊C₄	—	19	2	no	—
514	C₂²⋊C₄	—	19	2	no	—
515	C₂²⋊C₄	—	19	2	no	—
516	C₂²⋊C₄	—	19	2	no	—
517	C₂²⋊C₄	—	19	2	no	—
518	C₂²⋊C₄	—	19	2	no	—
519	C₂²⋊C₄	—	19	2	no	—
520	C₂²⋊C₄	—	19	2	no	—
521	C₂²⋊C₄	—	19	2	no	—
522	C₂²⋊C₄	—	19	2	no	—
523	C₂²⋊C₄	—	19	2	no	—
524	C₂²⋊C₄	—	19	2	no	—
525	C₂²⋊C₄	—	19	2	no	—
526	C₂²⋊C₄	—	19	2	no	—
527	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
528	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
529	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
530	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
531	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
532	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
533	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic, complemented
534	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	complemented
535	C₄²	—	19	1	no	—
536	C₄²	—	19	2	no	—
537	C₄²	C₂²×D₁₉	1	1	yes	characteristic, complemented
538	C₄²	C₂²×D₁₉	1	2	yes	complemented
539	C₂³	—	2	4	no	—
540	C₂³	—	4	1	no	—
541	C₂³	—	19	1	no	—
542	C₂³	—	19	2	no	—
543	C₂³	—	19	1	no	—
544	C₂³	—	19	2	no	—
545	C₂³	—	19	2	no	—
546	C₂³	—	19	1	no	—
547	C₂³	—	38	4	no	—
548	C₂³	—	38	2	no	—
549	C₂³	—	38	2	no	—
550	C₂³	—	38	4	no	—
551	C₂³	—	38	4	no	—
552	C₂³	—	38	4	no	—
553	C₂³	—	76	2	no	—
554	C₂³	—	76	2	no	—
555	C₂³	—	76	2	no	—
556	C₂³	—	76	1	no	—
557	C₂³	—	76	2	no	—
558	C₂³	—	76	2	no	—
559	C₂³	—	76	2	no	—
560	C₂³	—	76	2	no	—
561	C₂³	—	76	1	no	—
562	C₂³	—	76	2	no	—
563	C₂³	—	76	2	no	—
564	C₂³	—	76	16	no	—
565	C₂³	C₂³×D₁₉	1	1	yes	characteristic
566	C₂³	C₂³×D₁₉	1	1	yes	characteristic
567	C₂³	C₂³×D₁₉	1	2	yes	—
568	Q₈	—	4	1	no	—
569	Q₈	—	76	2	no	—
570	D₄	—	2	4	no	—
571	D₄	—	4	1	no	—
572	D₄	—	38	4	no	—
573	D₄	—	38	4	no	—
574	D₄	—	38	4	no	—
575	D₄	—	38	4	no	—
576	D₄	—	38	4	no	—
577	D₄	—	76	2	no	—
578	D₄	—	76	2	no	—
579	D₄	—	76	2	no	—
580	D₄	—	76	1	no	—
581	D₄	—	76	2	no	—
582	D₄	—	76	2	no	—
583	D₄	—	76	2	no	—
584	D₄	—	76	2	no	—
585	D₄	—	76	2	no	—
586	D₄	—	76	2	no	—
587	D₄	—	76	1	no	—
588	D₄	—	76	2	no	—
589	D₄	—	76	1	no	—
590	D₄	—	76	1	no	—
591	D₄	—	76	2	no	—
592	D₄	—	76	2	no	—
593	D₄	—	76	2	no	—
594	D₄	—	76	2	no	—
595	C₂×C₄	—	2	4	no	—
596	C₂×C₄	—	4	2	no	—
597	C₂×C₄	—	4	1	no	—
598	C₂×C₄	—	19	2	no	—
599	C₂×C₄	—	19	2	no	—
600	C₂×C₄	—	19	2	no	—
601	C₂×C₄	—	19	1	no	—
602	C₂×C₄	—	38	2	no	—
603	C₂×C₄	—	76	2	no	—
604	C₂×C₄	—	76	2	no	—
605	C₂×C₄	—	76	2	no	—
606	C₂×C₄	—	76	2	no	—
607	C₂×C₄	—	76	2	no	—
608	C₂×C₄	—	76	2	no	—
609	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
610	C₂×C₄	C₂³×D₁₉	1	2	yes	—
611	C₂×C₄	C₂³×D₁₉	1	2	yes	—
612	C₂×C₄	C₂³×D₁₉	1	2	yes	—
613	C₂×C₄	C₂³×D₁₉	1	2	yes	—
614	C₂×C₄	C₂³×D₁₉	1	2	yes	—
615	C₂²	—	2	2	no	—
616	C₂²	—	2	2	no	—
617	C₂²	—	2	1	no	—
618	C₂²	—	2	1	no	—
619	C₂²	—	2	2	no	—
620	C₂²	—	2	2	no	—
621	C₂²	—	4	4	no	—
622	C₂²	—	19	2	no	—
623	C₂²	—	38	2	no	—
624	C₂²	—	38	2	no	—
625	C₂²	—	38	2	no	—
626	C₂²	—	38	1	no	—
627	C₂²	—	38	2	no	—
628	C₂²	—	38	1	no	—
629	C₂²	—	38	2	no	—
630	C₂²	—	38	2	no	—
631	C₂²	—	38	2	no	—
632	C₂²	—	38	2	no	—
633	C₂²	—	38	2	no	—
634	C₂²	—	38	2	no	—
635	C₂²	—	38	2	no	—
636	C₂²	—	38	2	no	—
637	C₂²	—	76	8	no	—
638	C₂²	—	76	8	no	—
639	C₂²	—	76	4	no	—
640	C₂²	—	76	4	no	—
641	C₂²	—	152	4	no	—
642	C₂²	—	152	2	no	—
643	C₂²	—	152	2	no	—
644	C₂²	#10597435	1	4	yes	—
645	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
646	C₄	—	2	2	no	—
647	C₄	—	2	2	no	—
648	C₄	—	2	1	no	—
649	C₄	—	2	2	no	—
650	C₄	—	2	2	no	—
651	C₄	—	2	2	no	—
652	C₄	—	38	1	no	—
653	C₄	—	38	2	no	—
654	C₄	—	38	2	no	—
655	C₄	—	38	2	no	—
656	C₂	—	2	4	no	—
657	C₂	—	4	1	no	—
658	C₂	—	4	1	no	—
659	C₂	—	38	2	no	—
660	C₂	—	76	2	no	—
661	C₂	—	76	1	no	—
662	C₂	—	76	2	no	—
663	C₂	—	76	2	no	—
664	C₂	—	76	1	no	—
665	C₂	H(5,𝔽₂)×D₁₉	1	1	yes	characteristic
666	C₂	C₂×#10597435	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Fitting	C₁₉×#551	C₂
hypercenter	#551	D₁₉
hypocenter	C₁₉	#3532
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ #551

Complements

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

N	H ≅ G/N	type
1. #11927286	C₂	semidirect
2. #11927285	C₂	semidirect
3. #11927284	C₂	semidirect
4. #11927218	C₂	semidirect
5. #11927186	C₂	semidirect
6. #11927185	C₂	semidirect
7. #11927184	C₂	semidirect
8. D₄×D₇₆	C₂	semidirect
9. #11927176	C₂	semidirect
10. #11927134	C₂	semidirect
11. #11927133	C₂	semidirect
12. #11927127	C₂	semidirect
13. #11927113	C₂	semidirect
14. #11927112	C₂	semidirect
15. #11927105	C₂	semidirect
16. #11927105	C₂	semidirect
17. C₂×#10597328	C₂	semidirect
18. #120×D₁₉	C₂	semidirect
19. C₁₉×#551	C₂	semidirect
20. C₂⁴×D₁₉	C₂²	semidirect
21. C₂²×C₂²⋊D₁₉	C₂²	semidirect
22. C₂×#64545	C₂²	semidirect
23. C₂×D₄×D₁₉	C₂²	semidirect
24. C₂×D₄×D₁₉	C₂²	semidirect
25. C₂×D₄×D₁₉	C₂²	semidirect
26. C₂×#64541	C₂²	semidirect
27. C₂²×D₇₆	C₂²	semidirect
28. C₂²×D₇₆	C₂²	semidirect
29. C₂²×D₇₆	C₂²	semidirect
30. C₁₉×#126	C₂²	semidirect
31. C₁₉×#124	C₂²	semidirect
32. C₁₉×#123	C₂²	semidirect
33. C₁₉×#123	C₂²	semidirect
34. C₁₉×C₂²⋊Q₈	C₂²	semidirect
36. C₄×D₄×C₁₉	C₂²	semidirect
37. C₁₉×#117	C₂²	semidirect
38. C₂×C₂²⋊C₄×C₁₉	C₂²	semidirect
39. #10597399	C₂²	semidirect
40. #10597393	C₂²	semidirect
41. #10597393	C₂²	semidirect
42. #10597386	C₂²	semidirect
43. #10597385	C₂²	semidirect
44. #10597383	C₂²	semidirect
45. #10597383	C₂²	semidirect
46. #10597383	C₂²	semidirect
47. #10597376	C₂²	semidirect
48. #10597376	C₂²	semidirect
49. #10597375	C₂²	semidirect
50. #10597375	C₂²	semidirect
51. C₄×C₂²⋊D₁₉	C₂²	semidirect
52. C₂×(C₂×D₁₉)⋊C₄	C₂²	semidirect
53. C₂×(C₂×D₁₉)⋊C₄	C₂²	semidirect
54. #10597344	C₂²	semidirect
55. #10597344	C₂²	semidirect
56. #10597342	C₂²	semidirect
57. #10597341	C₂²	semidirect
58. #10597341	C₂²	semidirect
59. #10597341	C₂²	semidirect
60. #10597341	C₂²	semidirect
61. #10597341	C₂²	semidirect
62. #10597341	C₂²	semidirect
63. #10597341	C₂²	semidirect
64. #10597340	C₂²	semidirect
65. #10597340	C₂²	semidirect
66. #10597340	C₂²	semidirect
67. #10597340	C₂²	semidirect
68. #10597340	C₂²	semidirect
69. #10597339	C₂²	semidirect
70. #10597331	C₂²	semidirect
71. #10597331	C₂²	semidirect
72. #10597330	C₂²	semidirect
73. #10597330	C₂²	semidirect
74. #10597330	C₂²	semidirect
75. #10597330	C₂²	semidirect
76. #10597330	C₂²	semidirect
77. #10597329	C₂²	semidirect
79. #10597328	C₂²	semidirect
80. #10597328	C₂²	semidirect
81. #10597328	C₂²	semidirect
82. #10597328	C₂²	semidirect
83. #10597328	C₂²	semidirect
84. #10597328	C₂²	semidirect
85. #10597328	C₂²	semidirect
86. #10597328	C₂²	semidirect
87. #10597328	C₂²	semidirect
88. #10597328	C₂²	semidirect
89. #10597328	C₂²	semidirect
90. #10597328	C₂²	semidirect
91. #10597328	C₂²	semidirect
92. #10597328	C₂²	semidirect
93. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
94. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
95. C₂²⋊C₄×D₁₉	C₂²	semidirect
96. C₂²⋊C₄×D₁₉	C₂²	semidirect
97. C₂²⋊C₄×D₁₉	C₂²	semidirect
98. C₂²⋊C₄×D₁₉	C₂²	semidirect
99. #10597324	C₂²	semidirect
100. #10597322	C₂²	semidirect
101. #10597321	C₂²	semidirect
102. #10597321	C₂²	semidirect
103. #10597320	C₂²	semidirect
104. #10597320	C₂²	semidirect
105. C₄×D₇₆	C₂²	semidirect
106. #10597318	C₂²	semidirect
116. C₂³×D₁₉	C₂³	semidirect
117. C₂×Q₈×C₁₉	C₂³	semidirect
122. C₂²×C₄×C₁₉	C₂³	semidirect
132. C₂×C₂²⋊D₁₉	C₂³	semidirect
152. C₂×D₇₆	C₂³	semidirect
153. C₂×D₇₆	C₂³	semidirect
154. C₂×D₇₆	C₂³	semidirect
155. C₂×D₇₆	C₂³	semidirect
158. C₂×C₄×D₁₉	C₂³	semidirect
159. C₂×C₄×D₁₉	C₂³	semidirect
160. C₂×C₄×D₁₉	C₂³	semidirect
161. C₂×C₄×D₁₉	C₂³	semidirect
162. C₂×Dic₃₈	C₂³	semidirect
163. C₄⋊C₄×C₁₉	C₂³	semidirect
164. C₄⋊C₄×C₁₉	C₂³	semidirect
165. C₄⋊C₄×C₁₉	C₂³	semidirect
166. C₄⋊C₄×C₁₉	C₂³	semidirect
173. C₂²⋊C₄×C₁₉	C₂³	semidirect
174. C₂²⋊C₄×C₁₉	C₂³	semidirect
175. C₄²×C₁₉	C₂³	semidirect
176. C₄²×C₁₉	C₂³	semidirect
179. C₂²⋊Dic₁₉	C₂³	semidirect
191. (C₂×D₁₉)⋊C₄	C₂³	semidirect
192. (C₂×D₁₉)⋊C₄	C₂³	semidirect
193. (C₂×D₁₉)⋊C₄	C₂³	semidirect
194. (C₂×D₁₉)⋊C₄	C₂³	semidirect
195. (C₂×D₁₉)⋊C₄	C₂³	semidirect
196. (C₂×D₁₉)⋊C₄	C₂³	semidirect
197. (C₂×D₁₉)⋊C₄	C₂³	semidirect
198. C₄⋊Dic₁₉	C₂³	semidirect
199. Dic₁₉⋊C₄	C₂³	semidirect
200. Dic₁₉⋊C₄	C₂³	semidirect
201. Dic₁₉⋊C₄	C₂³	semidirect
202. Dic₁₉⋊C₄	C₂³	semidirect
203. C₄×Dic₁₉	C₂³	semidirect
204. C₄×Dic₁₉	C₂³	semidirect
327. #551	D₁₉	semidirect
369. #126	C₂×D₁₉	semidirect
376. #124	C₂×D₁₉	semidirect
385. #123	C₂×D₁₉	semidirect
386. #123	C₂×D₁₉	semidirect
389. C₂²⋊Q₈	C₂×D₁₉	semidirect
430. C₄×D₄	C₂×D₁₉	semidirect
432. #117	C₂×D₁₉	semidirect
439. C₂×C₂²⋊C₄	C₂×D₁₉	semidirect
440. C₁₉	#3532	semidirect
454. C₂×Q₈	C₂²×D₁₉	semidirect
496. C₂²×C₄	C₂²×D₁₉	semidirect
502. C₄⋊C₄	C₂²×D₁₉	semidirect
503. C₄⋊C₄	C₂²×D₁₉	semidirect
504. C₄⋊C₄	C₂²×D₁₉	semidirect
505. C₄⋊C₄	C₂²×D₁₉	semidirect
533. C₂²⋊C₄	C₂²×D₁₉	semidirect
534. C₂²⋊C₄	C₂²×D₁₉	semidirect
537. C₄²	C₂²×D₁₉	semidirect
538. C₄²	C₂²×D₁₉	semidirect

Maximal subgroups

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

subgroup	index
#11927286	2
#11927285	2
#11927284	2
#11927218	2
#11927186	2
#11927185	2
#11927184	2
D₄×D₇₆	2
#11927176	2
#11927134	2
#11927133	2
#11927127	2
#11927113	2
#11927112	2
#11927105	2
C₂×#10597328	2
#120×D₁₉	2
C₁₉×#551	2
#3532	19