Subgroups — #14577829

Order 2432.

1166 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927291	C₂	1	2	yes	maximal, complemented
2	#11927284	C₂	1	2	yes	maximal, complemented
3	#11927242	C₂	1	2	yes	maximal, complemented
4	#11927217	C₂	1	2	yes	maximal, complemented
5	#11927186	C₂	1	2	yes	maximal, complemented
6	#11927184	C₂	1	2	yes	maximal, complemented
7	#11927184	C₂	1	2	yes	maximal, complemented
8	D₄×C₂²⋊D₁₉	C₂	1	2	yes	maximal, complemented
9	#11927146	C₂	1	2	yes	maximal, complemented
10	#11927141	C₂	1	1	yes	maximal, characteristic, complemented
11	#11927138	C₂	1	2	yes	maximal, complemented
12	#11927132	C₂	1	1	yes	maximal, characteristic, complemented
13	#11927130	C₂	1	2	yes	maximal, complemented
14	#11927125	C₂	1	1	yes	maximal, characteristic, complemented
15	#11927106	C₂	1	1	yes	maximal, characteristic, complemented
16	#11927105	C₂	1	2	yes	maximal, complemented
17	#11927055	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#10597376	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₁₉×#123	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂²×D₄×C₁₉	C₂²	1	1	yes	characteristic
21	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
22	C₂²×C₂²⋊D₁₉	C₂²	1	2	yes	complemented
23	C₂²×C₂²⋊D₁₉	C₂²	1	2	yes	complemented
24	C₂×D₄×D₁₉	C₂²	1	2	yes	complemented
25	C₂×#64541	C₂²	1	1	yes	characteristic, complemented
26	C₂×#64541	C₂²	1	2	yes	complemented
27	C₂²×D₇₆	C₂²	1	1	yes	characteristic, complemented
28	C₁₉×#123	C₂²	1	2	yes	complemented
29	C₁₉×#123	C₂²	1	2	yes	complemented
30	C₁₉×#123	C₂²	1	2	yes	complemented
31	C₁₉×#123	C₂²	1	2	yes	complemented
32	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
37	#10597399	C₂²	1	2	yes	complemented
38	#10597399	C₂²	1	2	yes	complemented
39	#10597386	C₂²	1	2	yes	complemented
40	#10597385	C₂²	1	2	yes	—
41	#10597385	C₂²	1	2	yes	complemented
42	#10597384	C₂²	1	2	yes	complemented
43	#10597383	C₂²	1	2	yes	—
44	#10597383	C₂²	1	2	yes	complemented
45	D₄×Dic₁₉	C₂²	1	2	yes	complemented
46	#10597376	C₂²	1	1	yes	characteristic
47	#10597376	C₂²	1	1	yes	characteristic, complemented
48	#10597376	C₂²	1	1	yes	characteristic, complemented
49	#10597376	C₂²	1	2	yes	complemented
50	#10597376	C₂²	1	1	yes	characteristic, complemented
51	#10597376	C₂²	1	2	yes	complemented
52	#10597376	C₂²	1	1	yes	characteristic, complemented
53	#10597376	C₂²	1	1	yes	characteristic, complemented
54	#10597376	C₂²	1	2	yes	complemented
55	#10597376	C₂²	1	2	yes	complemented
56	#10597375	C₂²	1	2	yes	complemented
57	#10597375	C₂²	1	2	yes	complemented
58	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	complemented
59	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	complemented
60	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	complemented
61	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	complemented
62	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	2	yes	complemented
63	#10597372	C₂²	1	1	yes	characteristic, complemented
64	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic, complemented
65	#10597370	C₂²	1	1	yes	characteristic, complemented
66	#10597370	C₂²	1	1	yes	characteristic, complemented
67	#10597344	C₂²	1	2	yes	complemented
68	#10597344	C₂²	1	2	yes	complemented
69	#10597344	C₂²	1	2	yes	complemented
70	#10597343	C₂²	1	2	yes	complemented
71	#10597343	C₂²	1	2	yes	complemented
72	#10597342	C₂²	1	2	yes	complemented
73	#10597341	C₂²	1	2	yes	complemented
74	#10597341	C₂²	1	2	yes	complemented
75	#10597341	C₂²	1	2	yes	complemented
76	#10597340	C₂²	1	2	yes	complemented
77	#10597340	C₂²	1	2	yes	complemented
78	#10597340	C₂²	1	2	yes	complemented
79	#10597339	C₂²	1	2	yes	complemented
80	#10597338	C₂²	1	2	yes	complemented
81	#10597336	C₂²	1	2	yes	complemented
82	#10597335	C₂²	1	2	yes	complemented
83	#10597332	C₂²	1	2	yes	complemented
84	#10597332	C₂²	1	2	yes	complemented
85	#10597331	C₂²	1	2	yes	complemented
86	#10597331	C₂²	1	2	yes	complemented
87	#10597331	C₂²	1	2	yes	complemented
88	#10597330	C₂²	1	2	yes	complemented
89	#10597330	C₂²	1	2	yes	complemented
90	#10597330	C₂²	1	2	yes	complemented
91	#10597330	C₂²	1	2	yes	complemented
92	#10597330	C₂²	1	2	yes	complemented
93	#10597329	C₂²	1	2	yes	complemented
94	#10597329	C₂²	1	2	yes	complemented
95	#10597329	C₂²	1	2	yes	complemented
96	#10597328	C₂²	1	2	yes	complemented
97	#10597328	C₂²	1	2	yes	complemented
98	#10597328	C₂²	1	2	yes	complemented
99	#10597328	C₂²	1	2	yes	complemented
100	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	complemented
101	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	complemented
102	C₂²⋊C₄×D₁₉	C₂²	1	2	yes	complemented
103	C₂²⋊C₄×D₁₉	C₂²	1	2	yes	complemented
104	#10597325	C₂²	1	2	yes	complemented
105	#10597324	C₂²	1	2	yes	complemented
106	#10597324	C₂²	1	2	yes	complemented
107	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
108	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
109	C₂³×D₁₉	C₂³	1	2	yes	—
110	C₂³×D₁₉	C₂³	1	2	yes	—
111	C₂×D₄×C₁₉	—	4	2	no	—
112	C₂×D₄×C₁₉	C₂³	1	2	yes	—
113	C₂×D₄×C₁₉	C₂³	1	2	yes	—
114	C₂²×C₄×C₁₉	—	4	2	no	—
115	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
116	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
117	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
118	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
119	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
120	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
121	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
122	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
123	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
124	C₂×C₂²⋊D₁₉	—	4	4	no	—
125	C₂×C₂²⋊D₁₉	—	4	4	no	—
126	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
127	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
128	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
129	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
130	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
131	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
137	C₂²×Dic₁₉	C₂³	1	2	yes	—
138	C₂²×Dic₁₉	C₂³	1	2	yes	—
139	D₄×D₁₉	—	4	4	no	—
140	#64541	—	4	2	no	—
141	#64541	—	4	4	no	—
142	C₂×D₇₆	—	4	2	no	—
143	C₂×D₇₆	C₂³	1	1	yes	characteristic
144	C₂×D₇₆	C₂³	1	2	yes	—
145	C₂×D₇₆	C₂³	1	1	yes	characteristic
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×C₄×D₁₉	C₂³	1	2	yes	—
151	C₂×C₄×D₁₉	C₂³	1	2	yes	—
152	C₂×C₄×D₁₉	C₂³	1	2	yes	—
153	C₂×C₄×D₁₉	C₂³	1	2	yes	—
154	C₂×C₄×D₁₉	C₂³	1	2	yes	—
155	C₂×Dic₃₈	C₂³	1	2	yes	—
156	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
157	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
158	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
159	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
160	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
161	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
162	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
163	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
164	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
165	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
166	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
167	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
168	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
169	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
170	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
171	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
172	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
173	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
174	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
175	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
176	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
177	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
178	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
179	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
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	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
187	C₄⋊Dic₁₉	C₂³	1	2	yes	—
188	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
189	C₄⋊Dic₁₉	C₂³	1	2	yes	—
190	C₄⋊Dic₁₉	C₂³	1	2	yes	—
191	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
192	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
193	Dic₁₉⋊C₄	C₂³	1	2	yes	—
194	Dic₁₉⋊C₄	C₂³	1	2	yes	—
195	Dic₁₉⋊C₄	C₂³	1	2	yes	—
196	Dic₁₉⋊C₄	C₂³	1	2	yes	—
197	Dic₁₉⋊C₄	C₂³	1	2	yes	—
198	Dic₁₉⋊C₄	C₂³	1	2	yes	—
199	C₄×Dic₁₉	C₂³	1	2	yes	—
200	C₄×Dic₁₉	C₂³	1	2	yes	—
201	C₄×Dic₁₉	C₂³	1	2	yes	—
202	C₂³×C₁₉	—	2	2	no	—
203	C₂³×C₁₉	—	2	2	no	—
204	C₂³×C₁₉	—	2	2	no	—
205	C₂³×C₁₉	—	4	1	no	—
206	C₂³×C₁₉	—	4	1	no	—
207	C₂³×C₁₉	—	4	1	no	—
208	C₂³×C₁₉	C₂⁴	1	2	yes	—
209	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
210	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
211	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
212	C₂²×D₁₉	—	2	4	no	—
213	C₂²×D₁₉	—	4	2	no	—
214	C₂²×D₁₉	—	4	2	no	—
215	C₂²×D₁₉	—	4	2	no	—
216	C₂²×D₁₉	—	4	2	no	—
217	C₂²×D₁₉	—	4	2	no	—
218	C₂²×D₁₉	C₂⁴	1	2	yes	—
219	C₂²×D₁₉	C₂⁴	1	2	yes	—
220	C₂²×D₁₉	C₂⁴	1	2	yes	—
221	D₄×C₁₉	—	2	4	no	—
222	D₄×C₁₉	—	4	2	no	—
223	C₂×C₄×C₁₉	—	2	2	no	—
224	C₂×C₄×C₁₉	—	2	2	no	—
225	C₂×C₄×C₁₉	—	2	2	no	—
226	C₂×C₄×C₁₉	—	4	1	no	—
227	C₂×C₄×C₁₉	—	4	1	no	—
228	C₂×C₄×C₁₉	—	4	1	no	—
229	C₂×C₄×C₁₉	—	4	1	no	—
230	C₂×C₄×C₁₉	—	4	1	no	—
231	C₂×C₄×C₁₉	—	4	1	no	—
232	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
233	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
234	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
235	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
236	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
237	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
238	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
239	C₂²⋊D₁₉	—	2	4	no	—
240	C₂²⋊D₁₉	—	2	4	no	—
241	C₂²⋊D₁₉	—	2	4	no	—
242	C₂²⋊D₁₉	—	2	4	no	—
243	C₂²⋊D₁₉	—	4	2	no	—
244	C₂²⋊D₁₉	—	4	2	no	—
245	C₂²⋊D₁₉	—	4	2	no	—
246	C₂²⋊D₁₉	—	4	2	no	—
247	C₂²⋊D₁₉	—	4	2	no	—
248	C₂²⋊D₁₉	—	4	2	no	—
249	C₂²⋊D₁₉	—	4	2	no	—
250	C₂×Dic₁₉	—	4	2	no	—
251	C₂×Dic₁₉	—	4	2	no	—
252	C₂×Dic₁₉	C₂⁴	1	2	yes	—
253	C₂×Dic₁₉	C₂⁴	1	2	yes	—
254	C₂×Dic₁₉	C₂⁴	1	2	yes	—
255	C₂×Dic₁₉	C₂⁴	1	2	yes	—
256	C₂×Dic₁₉	C₂⁴	1	2	yes	—
257	D₇₆	—	4	1	no	—
258	D₇₆	—	4	2	no	—
259	D₇₆	—	4	1	no	—
260	D₇₆	—	4	2	no	—
261	D₇₆	—	4	2	no	—
262	D₇₆	—	4	1	no	—
263	D₇₆	—	4	2	no	—
264	C₄×D₁₉	—	4	2	no	—
265	C₄×D₁₉	—	4	2	no	—
266	C₄×D₁₉	—	4	2	no	—
267	C₄×D₁₉	—	4	2	no	—
268	C₄×D₁₉	—	4	2	no	—
269	Dic₃₈	—	4	1	no	—
270	Dic₃₈	—	4	2	no	—
271	#3534	—	19	1	no	maximal, Sylow
272	C₂²×C₁₉	—	2	1	no	—
273	C₂²×C₁₉	—	2	1	no	—
274	C₂²×C₁₉	—	2	1	no	—
275	C₂²×C₁₉	—	2	1	no	—
276	C₂²×C₁₉	—	2	2	no	—
277	C₂²×C₁₉	—	2	1	no	—
278	C₂²×C₁₉	—	2	2	no	—
279	C₂²×C₁₉	—	2	1	no	—
280	C₂²×C₁₉	—	2	1	no	—
281	C₂²×C₁₉	—	2	2	no	—
282	C₂²×C₁₉	—	4	4	no	—
283	C₂²×C₁₉	—	8	2	no	—
284	C₂²×C₁₉	H(5,𝔽₂)	1	2	yes	—
285	C₂²×C₁₉	H(5,𝔽₂)	1	2	yes	—
286	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
287	C₂×D₁₉	—	2	2	no	—
288	C₂×D₁₉	—	2	2	no	—
289	C₂×D₁₉	—	2	2	no	—
290	C₂×D₁₉	—	2	2	no	—
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	—	8	4	no	—
297	C₂×D₁₉	—	8	4	no	—
298	C₄×C₁₉	—	2	2	no	—
299	C₄×C₁₉	—	2	1	no	—
300	C₄×C₁₉	—	2	1	no	—
301	C₄×C₁₉	—	2	2	no	—
302	C₄×C₁₉	—	2	1	no	—
303	C₄×C₁₉	—	2	1	no	—
304	C₄×C₁₉	—	2	2	no	—
305	Dic₁₉	—	2	2	no	—
306	Dic₁₉	—	2	2	no	—
307	Dic₁₉	—	2	2	no	—
308	Dic₁₉	—	2	2	no	—
309	Dic₁₉	—	2	2	no	—
310	#562	—	19	2	no	—
311	#560	—	19	2	no	—
312	#553	—	19	2	no	—
313	#551	—	19	2	no	—
314	#546	—	19	2	no	—
315	#546	—	19	2	no	—
316	#546	—	19	2	no	—
317	D₄²	—	19	2	no	—
318	#540	—	19	2	no	—
319	#539	—	19	2	no	—
320	#539	—	19	1	no	—
321	#538	—	19	2	no	—
322	#538	—	19	1	no	—
323	#537	—	19	1	no	—
324	#534	—	19	2	no	—
325	#534	—	19	1	no	—
326	#525	—	19	1	no	—
327	C₂×#123	D₁₉	1	1	yes	characteristic, complemented
328	C₂×#121	—	19	1	no	—
329	C₂×C₁₉	—	2	2	no	—
330	C₂×C₁₉	—	2	2	no	—
331	C₂×C₁₉	—	4	2	no	—
332	C₂×C₁₉	—	4	1	no	—
333	C₂×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
334	C₂×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
335	C₂×C₁₉	#585	1	1	yes	characteristic
336	D₁₉	—	4	2	no	—
337	D₁₉	—	4	2	no	—
338	D₁₉	—	4	2	no	—
339	C₂×#41	—	19	1	no	—
340	C₂×#41	—	19	2	no	—
341	C₂²×D₄	—	19	2	no	—
342	C₂²×D₄	—	19	2	no	—
343	C₂²×D₄	—	19	2	no	—
344	C₂²×D₄	—	19	1	no	—
345	C₂²×D₄	C₂×D₁₉	1	1	yes	characteristic
346	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic, complemented
347	#127	—	19	2	no	—
348	#126	—	19	2	no	—
349	#126	—	19	2	no	—
350	#126	—	19	2	no	—
351	#126	—	19	2	no	—
352	#125	—	19	2	no	—
353	#125	—	19	2	no	—
354	#124	—	19	2	no	—
355	#124	—	19	2	no	—
356	#124	—	19	2	no	—
357	#123	—	19	2	no	—
358	#123	—	19	2	no	—
359	#123	—	19	2	no	—
360	#123	—	19	2	no	—
361	#123	—	19	2	no	—
362	#123	—	19	2	no	—
363	#123	—	19	2	no	—
364	#123	—	19	2	no	—
365	#123	—	19	2	no	—
366	#123	—	19	2	no	—
367	#123	C₂×D₁₉	1	2	yes	complemented
368	#123	C₂×D₁₉	1	2	yes	complemented
369	#123	C₂×D₁₉	1	2	yes	complemented
370	#123	C₂×D₁₉	1	2	yes	complemented
371	C₂²⋊Q₈	—	19	1	no	—
372	C₂²⋊Q₈	—	19	1	no	—
373	C₂²⋊Q₈	—	19	2	no	—
374	C₂²⋊Q₈	—	19	2	no	—
375	C₂²⋊Q₈	—	19	2	no	—
376	C₂²⋊Q₈	—	19	2	no	—
377	C₂²⋊Q₈	—	19	2	no	—
378	#121	—	19	2	no	—
379	#121	—	19	2	no	—
380	#121	—	19	2	no	—
381	#121	—	19	1	no	—
382	#121	—	19	1	no	—
383	#121	—	19	1	no	—
384	#121	—	19	1	no	—
385	#121	—	19	2	no	—
386	#121	—	19	2	no	—
387	#121	—	19	1	no	—
388	#121	—	19	1	no	—
389	#121	—	19	2	no	—
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	#120	—	19	2	no	—
400	#120	—	19	2	no	—
401	#120	—	19	2	no	—
402	#120	—	19	2	no	—
403	#120	—	19	2	no	—
404	#120	—	19	2	no	—
405	#120	—	19	2	no	—
406	#120	—	19	2	no	—
407	C₄×D₄	—	19	2	no	—
408	C₄×D₄	—	19	2	no	—
409	C₄×D₄	—	19	2	no	—
410	C₄×D₄	—	19	2	no	—
411	C₄×D₄	—	19	2	no	—
412	C₄×D₄	—	19	2	no	—
413	C₄×D₄	—	19	2	no	—
414	C₄×D₄	—	19	2	no	—
415	#117	—	19	1	no	—
416	#117	—	19	2	no	—
417	C₂×C₄⋊C₄	—	19	1	no	—
418	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic, complemented
419	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic, complemented
420	C₂×C₂²⋊C₄	—	19	2	no	—
421	C₂×C₂²⋊C₄	—	19	2	no	—
422	C₂×C₂²⋊C₄	—	19	2	no	—
423	C₂×C₂²⋊C₄	C₂×D₁₉	1	1	yes	characteristic, complemented
424	C₂×C₂²⋊C₄	C₂×D₁₉	1	1	yes	characteristic, complemented
425	C₂×C₂²⋊C₄	C₂×D₁₉	1	1	yes	characteristic, complemented
426	C₁₉	#3534	1	1	yes	characteristic, complemented, Sylow
427	C₂⁴	—	19	2	no	—
428	C₂⁴	—	19	2	no	—
429	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
430	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
431	#41	—	76	2	no	—
432	#41	—	76	4	no	—
433	C₂×Q₈	—	19	1	no	—
434	C₂×Q₈	—	19	2	no	—
435	C₂×D₄	—	4	2	no	—
436	C₂×D₄	—	19	2	no	—
437	C₂×D₄	—	19	2	no	—
438	C₂×D₄	—	19	2	no	—
439	C₂×D₄	—	19	2	no	—
440	C₂×D₄	—	19	2	no	—
441	C₂×D₄	—	19	2	no	—
442	C₂×D₄	—	19	2	no	—
443	C₂×D₄	—	19	2	no	—
444	C₂×D₄	—	19	2	no	—
445	C₂×D₄	—	19	2	no	—
446	C₂×D₄	—	19	2	no	—
447	C₂×D₄	—	19	2	no	—
448	C₂×D₄	—	19	1	no	—
449	C₂×D₄	—	19	2	no	—
450	C₂×D₄	—	19	1	no	—
451	C₂×D₄	—	19	2	no	—
452	C₂×D₄	—	19	1	no	—
453	C₂×D₄	—	19	2	no	—
454	C₂×D₄	—	76	2	no	—
455	C₂×D₄	—	76	4	no	—
456	C₂×D₄	—	76	4	no	—
457	C₂×D₄	—	76	4	no	—
458	C₂×D₄	C₂²×D₁₉	1	2	yes	—
459	C₂×D₄	C₂²×D₁₉	1	2	yes	—
460	C₂²×C₄	—	4	2	no	—
461	C₂²×C₄	—	19	2	no	—
462	C₂²×C₄	—	19	2	no	—
463	C₂²×C₄	—	19	2	no	—
464	C₂²×C₄	—	19	2	no	—
465	C₂²×C₄	—	19	2	no	—
466	C₂²×C₄	—	19	2	no	—
467	C₂²×C₄	—	19	2	no	—
468	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
469	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
470	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
471	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
472	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
473	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
474	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
475	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
476	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
477	C₄⋊C₄	—	19	2	no	—
478	C₄⋊C₄	—	19	2	no	—
479	C₄⋊C₄	—	19	2	no	—
480	C₄⋊C₄	—	19	2	no	—
481	C₄⋊C₄	—	19	2	no	—
482	C₄⋊C₄	—	19	2	no	—
483	C₄⋊C₄	—	19	1	no	—
484	C₄⋊C₄	—	19	2	no	—
485	C₄⋊C₄	—	19	1	no	—
486	C₄⋊C₄	—	19	1	no	—
487	C₄⋊C₄	—	19	2	no	—
488	C₄⋊C₄	—	19	1	no	—
489	C₄⋊C₄	—	19	2	no	—
490	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
491	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
492	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
493	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
494	C₂²⋊C₄	—	19	2	no	—
495	C₂²⋊C₄	—	19	2	no	—
496	C₂²⋊C₄	—	19	2	no	—
497	C₂²⋊C₄	—	19	2	no	—
498	C₂²⋊C₄	—	19	2	no	—
499	C₂²⋊C₄	—	19	2	no	—
500	C₂²⋊C₄	—	19	2	no	—
501	C₂²⋊C₄	—	19	2	no	—
502	C₂²⋊C₄	—	19	2	no	—
503	C₂²⋊C₄	—	19	2	no	—
504	C₂²⋊C₄	—	19	2	no	—
505	C₂²⋊C₄	—	19	2	no	—
506	C₂²⋊C₄	—	19	2	no	—
507	C₂²⋊C₄	—	19	2	no	—
508	C₂²⋊C₄	—	19	2	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	C₂²×D₁₉	1	2	yes	—
514	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
515	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
516	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
517	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
518	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
519	C₄²	—	19	2	no	—
520	C₄²	—	19	2	no	—
521	C₄²	—	19	2	no	—
522	C₂³	—	2	2	no	—
523	C₂³	—	2	2	no	—
524	C₂³	—	2	2	no	—
525	C₂³	—	4	1	no	—
526	C₂³	—	4	1	no	—
527	C₂³	—	4	1	no	—
528	C₂³	—	19	2	no	—
529	C₂³	—	19	2	no	—
530	C₂³	—	19	2	no	—
531	C₂³	—	38	4	no	—
532	C₂³	—	76	2	no	—
533	C₂³	—	76	2	no	—
534	C₂³	—	76	2	no	—
535	C₂³	—	76	2	no	—
536	C₂³	—	76	2	no	—
537	C₂³	C₂³×D₁₉	1	2	yes	—
538	C₂³	C₂³×D₁₉	1	1	yes	characteristic
539	C₂³	C₂³×D₁₉	1	1	yes	characteristic
540	C₂³	C₂³×D₁₉	1	1	yes	characteristic
541	Q₈	—	76	1	no	—
542	Q₈	—	76	2	no	—
543	D₄	—	2	4	no	—
544	D₄	—	4	2	no	—
545	D₄	—	38	4	no	—
546	D₄	—	38	4	no	—
547	D₄	—	38	4	no	—
548	D₄	—	38	4	no	—
549	D₄	—	76	1	no	—
550	D₄	—	76	2	no	—
551	D₄	—	76	1	no	—
552	D₄	—	76	2	no	—
553	D₄	—	76	1	no	—
554	D₄	—	76	2	no	—
555	D₄	—	76	2	no	—
556	D₄	—	76	2	no	—
557	D₄	—	76	2	no	—
558	D₄	—	76	2	no	—
559	D₄	—	76	2	no	—
560	D₄	—	76	2	no	—
561	D₄	—	76	2	no	—
562	D₄	—	76	2	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	—	4	1	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	19	2	no	—
573	C₂×C₄	—	19	2	no	—
574	C₂×C₄	—	19	2	no	—
575	C₂×C₄	—	19	2	no	—
576	C₂×C₄	—	19	2	no	—
577	C₂×C₄	—	76	2	no	—
578	C₂×C₄	—	76	2	no	—
579	C₂×C₄	—	76	2	no	—
580	C₂×C₄	—	76	2	no	—
581	C₂×C₄	—	76	2	no	—
582	C₂×C₄	—	76	2	no	—
583	C₂×C₄	—	76	2	no	—
584	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
585	C₂×C₄	C₂³×D₁₉	1	2	yes	—
586	C₂×C₄	C₂³×D₁₉	1	2	yes	—
587	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
588	C₂×C₄	C₂³×D₁₉	1	2	yes	—
589	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
590	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
591	C₂²	—	2	1	no	—
592	C₂²	—	2	1	no	—
593	C₂²	—	2	1	no	—
594	C₂²	—	2	1	no	—
595	C₂²	—	2	1	no	—
596	C₂²	—	2	2	no	—
597	C₂²	—	2	2	no	—
598	C₂²	—	2	1	no	—
599	C₂²	—	2	1	no	—
600	C₂²	—	2	2	no	—
601	C₂²	—	4	4	no	—
602	C₂²	—	8	2	no	—
603	C₂²	—	38	2	no	—
604	C₂²	—	38	2	no	—
605	C₂²	—	38	2	no	—
606	C₂²	—	38	2	no	—
607	C₂²	—	38	2	no	—
608	C₂²	—	38	2	no	—
609	C₂²	—	38	2	no	—
610	C₂²	—	38	2	no	—
611	C₂²	—	38	2	no	—
612	C₂²	—	152	4	no	—
613	C₂²	—	152	4	no	—
614	C₂²	#10597430	1	2	yes	—
615	C₂²	#10597435	1	2	yes	—
616	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
617	C₄	—	2	1	no	—
618	C₄	—	2	1	no	—
619	C₄	—	2	1	no	—
620	C₄	—	2	1	no	—
621	C₄	—	2	2	no	—
622	C₄	—	2	2	no	—
623	C₄	—	2	2	no	—
624	C₄	—	38	2	no	—
625	C₄	—	38	2	no	—
626	C₄	—	38	2	no	—
627	C₄	—	38	2	no	—
628	C₄	—	38	2	no	—
629	C₂	—	2	2	no	—
630	C₂	—	2	2	no	—
631	C₂	—	4	1	no	—
632	C₂	—	4	2	no	—
633	C₂	—	76	2	no	—
634	C₂	—	76	2	no	—
635	C₂	—	76	2	no	—
636	C₂	C₂×#10597430	1	1	yes	characteristic
637	C₂	C₂×#10597435	1	1	yes	characteristic
638	C₂	#11927380	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Fitting	C₂×C₁₉×#123	C₂
hypercenter	C₂×#123	D₁₉
hypocenter	C₁₉	#3534
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×#123

Complements

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

N	H ≅ G/N	type
1. #11927291	C₂	semidirect
2. #11927284	C₂	semidirect
3. #11927242	C₂	semidirect
4. #11927217	C₂	semidirect
5. #11927186	C₂	semidirect
6. #11927184	C₂	semidirect
7. #11927184	C₂	semidirect
8. D₄×C₂²⋊D₁₉	C₂	semidirect
9. #11927146	C₂	semidirect
10. #11927141	C₂	semidirect
11. #11927138	C₂	semidirect
12. #11927132	C₂	semidirect
13. #11927130	C₂	semidirect
14. #11927125	C₂	semidirect
15. #11927106	C₂	semidirect
16. #11927105	C₂	semidirect
17. #11927055	C₂	semidirect
18. C₂×#10597376	C₂	semidirect
19. C₂×C₁₉×#123	C₂	semidirect
21. C₂³×C₄×C₁₉	C₂²	semidirect
22. C₂²×C₂²⋊D₁₉	C₂²	semidirect
23. C₂²×C₂²⋊D₁₉	C₂²	semidirect
24. C₂×D₄×D₁₉	C₂²	semidirect
25. C₂×#64541	C₂²	semidirect
26. C₂×#64541	C₂²	semidirect
27. C₂²×D₇₆	C₂²	semidirect
28. C₁₉×#123	C₂²	semidirect
29. C₁₉×#123	C₂²	semidirect
30. C₁₉×#123	C₂²	semidirect
31. C₁₉×#123	C₂²	semidirect
32. C₂×C₄⋊C₄×C₁₉	C₂²	semidirect
33. C₂×C₄⋊C₄×C₁₉	C₂²	semidirect
34. C₂×C₂²⋊C₄×C₁₉	C₂²	semidirect
35. C₂×C₂²⋊C₄×C₁₉	C₂²	semidirect
36. C₂×C₂²⋊C₄×C₁₉	C₂²	semidirect
37. #10597399	C₂²	semidirect
38. #10597399	C₂²	semidirect
39. #10597386	C₂²	semidirect
41. #10597385	C₂²	semidirect
42. #10597384	C₂²	semidirect
44. #10597383	C₂²	semidirect
45. D₄×Dic₁₉	C₂²	semidirect
47. #10597376	C₂²	semidirect
48. #10597376	C₂²	semidirect
49. #10597376	C₂²	semidirect
50. #10597376	C₂²	semidirect
51. #10597376	C₂²	semidirect
52. #10597376	C₂²	semidirect
53. #10597376	C₂²	semidirect
54. #10597376	C₂²	semidirect
55. #10597376	C₂²	semidirect
56. #10597375	C₂²	semidirect
57. #10597375	C₂²	semidirect
58. C₄×C₂²⋊D₁₉	C₂²	semidirect
59. C₄×C₂²⋊D₁₉	C₂²	semidirect
60. C₄×C₂²⋊D₁₉	C₂²	semidirect
61. C₄×C₂²⋊D₁₉	C₂²	semidirect
62. C₂×(C₂×D₁₉)⋊C₄	C₂²	semidirect
63. #10597372	C₂²	semidirect
64. C₂×C₄⋊Dic₁₉	C₂²	semidirect
65. #10597370	C₂²	semidirect
66. #10597370	C₂²	semidirect
67. #10597344	C₂²	semidirect
68. #10597344	C₂²	semidirect
69. #10597344	C₂²	semidirect
70. #10597343	C₂²	semidirect
71. #10597343	C₂²	semidirect
72. #10597342	C₂²	semidirect
73. #10597341	C₂²	semidirect
74. #10597341	C₂²	semidirect
75. #10597341	C₂²	semidirect
76. #10597340	C₂²	semidirect
77. #10597340	C₂²	semidirect
78. #10597340	C₂²	semidirect
79. #10597339	C₂²	semidirect
80. #10597338	C₂²	semidirect
81. #10597336	C₂²	semidirect
82. #10597335	C₂²	semidirect
83. #10597332	C₂²	semidirect
84. #10597332	C₂²	semidirect
85. #10597331	C₂²	semidirect
86. #10597331	C₂²	semidirect
87. #10597331	C₂²	semidirect
88. #10597330	C₂²	semidirect
89. #10597330	C₂²	semidirect
90. #10597330	C₂²	semidirect
91. #10597330	C₂²	semidirect
92. #10597330	C₂²	semidirect
93. #10597329	C₂²	semidirect
94. #10597329	C₂²	semidirect
95. #10597329	C₂²	semidirect
96. #10597328	C₂²	semidirect
97. #10597328	C₂²	semidirect
98. #10597328	C₂²	semidirect
99. #10597328	C₂²	semidirect
100. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
101. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
102. C₂²⋊C₄×D₁₉	C₂²	semidirect
103. C₂²⋊C₄×D₁₉	C₂²	semidirect
104. #10597325	C₂²	semidirect
105. #10597324	C₂²	semidirect
106. #10597324	C₂²	semidirect
327. C₂×#123	D₁₉	semidirect
346. C₂³×C₄	C₂×D₁₉	semidirect
367. #123	C₂×D₁₉	semidirect
368. #123	C₂×D₁₉	semidirect
369. #123	C₂×D₁₉	semidirect
370. #123	C₂×D₁₉	semidirect
418. C₂×C₄⋊C₄	C₂×D₁₉	semidirect
419. C₂×C₄⋊C₄	C₂×D₁₉	semidirect
423. C₂×C₂²⋊C₄	C₂×D₁₉	semidirect
424. C₂×C₂²⋊C₄	C₂×D₁₉	semidirect
425. C₂×C₂²⋊C₄	C₂×D₁₉	semidirect
426. C₁₉	#3534	semidirect

Maximal subgroups

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

subgroup	index
#11927291	2
#11927284	2
#11927242	2
#11927217	2
#11927186	2
#11927184	2
D₄×C₂²⋊D₁₉	2
#11927146	2
#11927141	2
#11927138	2
#11927132	2
#11927130	2
#11927125	2
#11927106	2
#11927105	2
#11927055	2
C₂×#10597376	2
C₂×C₁₉×#123	2
#3534	19