Subgroups — #14577474

Order 2432.

1152 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927243	C₂	1	4	yes	maximal, complemented
2	#11927240	C₂	1	2	yes	maximal, complemented
3	#11927234	C₂	1	2	yes	maximal, complemented
4	#11927223	C₂	1	4	yes	maximal, complemented
5	#11927203	C₂	1	2	yes	maximal, complemented
6	#11927190	C₂	1	2	yes	maximal, complemented
7	#11927141	C₂	1	2	yes	maximal, complemented
8	#11927132	C₂	1	2	yes	maximal, complemented
9	#11927103	C₂	1	2	yes	maximal, complemented
10	#11927078	C₂	1	2	yes	maximal, complemented
11	#11927055	C₂	1	2	yes	maximal, complemented
12	C₂×#10597370	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#10597376	C₂	1	1	yes	maximal, characteristic, complemented
14	#11927017	C₂	1	2	yes	maximal, complemented
15	C₂×C₄×D₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×D₄×C₁₉	C₂²	1	1	yes	characteristic
17	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
18	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
19	C₂²×C₂²⋊D₁₉	C₂²	1	2	yes	—
20	C₂×#64541	C₂²	1	2	yes	complemented
21	C₂²×D₇₆	C₂²	1	1	yes	characteristic, complemented
22	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic, complemented
23	C₄×D₄×C₁₉	C₂²	1	2	yes	—
24	C₄×D₄×C₁₉	C₂²	1	2	yes	—
25	C₄×D₄×C₁₉	C₂²	1	2	yes	complemented
26	C₄×D₄×C₁₉	C₂²	1	2	yes	complemented
27	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic, complemented
31	#10597399	C₂²	1	4	yes	complemented
32	C₂×C₂²⋊Dic₁₉	C₂²	1	2	yes	—
33	#10597385	C₂²	1	4	yes	complemented
34	#10597385	C₂²	1	4	yes	complemented
35	#10597383	C₂²	1	4	yes	—
36	#10597381	C₂²	1	4	yes	—
37	#10597376	C₂²	1	2	yes	—
38	#10597376	C₂²	1	2	yes	—
39	#10597376	C₂²	1	2	yes	complemented
40	#10597376	C₂²	1	2	yes	complemented
41	#10597376	C₂²	1	2	yes	complemented
42	#10597375	C₂²	1	4	yes	complemented
43	#10597375	C₂²	1	4	yes	complemented
44	C₄×C₂²⋊D₁₉	C₂²	1	4	yes	complemented
45	C₄×C₂²⋊D₁₉	C₂²	1	4	yes	complemented
46	C₄×C₂²⋊D₁₉	C₂²	1	4	yes	complemented
47	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	2	yes	complemented
48	#10597372	C₂²	1	2	yes	complemented
49	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic, complemented
50	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic, complemented
51	#10597370	C₂²	1	2	yes	complemented
52	#10597370	C₂²	1	2	yes	complemented
53	#10597370	C₂²	1	2	yes	complemented
54	#10597370	C₂²	1	2	yes	complemented
55	#10597370	C₂²	1	2	yes	complemented
56	C₂×Dic₁₉⋊C₄	C₂²	1	2	yes	complemented
57	#10597344	C₂²	1	4	yes	complemented
58	#10597342	C₂²	1	4	yes	complemented
59	#10597340	C₂²	1	4	yes	complemented
60	#10597335	C₂²	1	4	yes	complemented
61	#10597331	C₂²	1	4	yes	complemented
62	#10597330	C₂²	1	4	yes	complemented
63	#10597329	C₂²	1	4	yes	complemented
64	(C₂²⋊D₁₉)⋊C₄	C₂²	1	4	yes	complemented
65	(C₂²⋊D₁₉)⋊C₄	C₂²	1	4	yes	complemented
66	C₂²⋊C₄×D₁₉	C₂²	1	4	yes	complemented
67	#10597325	C₂²	1	4	yes	complemented
68	#10597323	C₂²	1	4	yes	complemented
69	#10597322	C₂²	1	4	yes	complemented
70	#10597321	C₂²	1	2	yes	complemented
71	C₄×D₇₆	C₂²	1	2	yes	complemented
72	#10597318	C₂²	1	4	yes	complemented
73	#10597316	C₂²	1	2	yes	complemented
74	C₄×Dic₃₈	C₂²	1	2	yes	complemented
75	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
76	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
77	C₂³×D₁₉	C₂³	1	2	yes	—
78	C₂×D₄×C₁₉	—	2	4	no	—
79	C₂×D₄×C₁₉	C₂³	1	2	yes	—
80	C₂×D₄×C₁₉	C₂³	1	2	yes	—
81	C₂²×C₄×C₁₉	—	4	2	no	—
82	C₂²×C₄×C₁₉	—	4	2	no	—
83	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
84	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
85	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
86	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
87	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
88	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
89	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
90	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
91	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
92	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
93	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
94	C₂×C₂²⋊D₁₉	—	2	8	no	—
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	C₂²×Dic₁₉	C₂³	1	2	yes	—
100	C₂²×Dic₁₉	C₂³	1	2	yes	—
101	C₂²×Dic₁₉	C₂³	1	2	yes	—
102	#64541	—	4	4	no	—
103	C₂×D₇₆	—	4	2	no	—
104	C₂×D₇₆	C₂³	1	2	yes	—
105	C₂×D₇₆	C₂³	1	2	yes	—
106	C₂×C₄×D₁₉	C₂³	1	4	yes	—
107	C₂×C₄×D₁₉	C₂³	1	4	yes	—
108	C₂×Dic₃₈	—	4	2	no	—
109	C₂×Dic₃₈	C₂³	1	2	yes	—
110	C₂×Dic₃₈	C₂³	1	2	yes	—
111	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
112	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
113	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
114	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
115	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
116	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
117	C₄²×C₁₉	C₂³	1	2	yes	—
118	C₄²×C₁₉	C₂³	1	2	yes	—
119	C₂²⋊Dic₁₉	C₂³	1	4	yes	—
120	C₂²⋊Dic₁₉	C₂³	1	4	yes	—
121	C₂²⋊Dic₁₉	C₂³	1	4	yes	—
122	C₂²⋊Dic₁₉	C₂³	1	4	yes	—
123	(C₂×D₁₉)⋊C₄	C₂³	1	4	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	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
129	C₄⋊Dic₁₉	C₂³	1	2	yes	—
130	C₄⋊Dic₁₉	C₂³	1	2	yes	—
131	C₄⋊Dic₁₉	C₂³	1	2	yes	—
132	C₄⋊Dic₁₉	C₂³	1	2	yes	—
133	Dic₁₉⋊C₄	C₂³	1	4	yes	—
134	Dic₁₉⋊C₄	C₂³	1	4	yes	—
135	Dic₁₉⋊C₄	C₂³	1	4	yes	—
136	Dic₁₉⋊C₄	C₂³	1	4	yes	—
137	Dic₁₉⋊C₄	C₂³	1	4	yes	—
138	Dic₁₉⋊C₄	C₂³	1	4	yes	—
139	C₄×Dic₁₉	C₂³	1	4	yes	—
140	C₄×Dic₁₉	C₂³	1	4	yes	—
141	C₂³×C₁₉	—	2	2	no	—
142	C₂³×C₁₉	—	4	1	no	—
143	C₂³×C₁₉	—	4	1	no	—
144	C₂³×C₁₉	—	4	1	no	—
145	C₂³×C₁₉	—	4	1	no	—
146	C₂³×C₁₉	#41	1	4	yes	complemented
147	C₂³×C₁₉	C₂⁴	1	2	yes	—
148	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
149	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
150	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
151	C₂²×D₁₉	—	2	4	no	—
152	C₂²×D₁₉	—	4	2	no	—
153	C₂²×D₁₉	—	4	2	no	—
154	C₂²×D₁₉	C₂⁴	1	4	yes	—
155	D₄×C₁₉	—	2	4	no	—
156	D₄×C₁₉	—	2	4	no	—
157	C₂×C₄×C₁₉	—	2	2	no	—
158	C₂×C₄×C₁₉	—	2	2	no	—
159	C₂×C₄×C₁₉	—	2	2	no	—
160	C₂×C₄×C₁₉	—	2	4	no	—
161	C₂×C₄×C₁₉	—	2	2	no	—
162	C₂×C₄×C₁₉	—	4	1	no	—
163	C₂×C₄×C₁₉	—	4	1	no	—
164	C₂×C₄×C₁₉	—	4	1	no	—
165	C₂×C₄×C₁₉	—	4	2	no	—
166	C₂×C₄×C₁₉	—	4	1	no	—
167	C₂×C₄×C₁₉	—	4	1	no	—
168	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
169	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
170	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
171	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
172	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
173	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
174	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
175	C₂²⋊D₁₉	—	2	8	no	—
176	C₂²⋊D₁₉	—	2	8	no	—
177	C₂²⋊D₁₉	—	4	4	no	—
178	C₂²⋊D₁₉	—	4	4	no	—
179	C₂×Dic₁₉	—	2	4	no	—
180	C₂×Dic₁₉	—	4	2	no	—
181	C₂×Dic₁₉	—	4	2	no	—
182	C₂×Dic₁₉	C₂⁴	1	4	yes	—
183	C₂×Dic₁₉	C₂⁴	1	4	yes	—
184	C₂×Dic₁₉	C₂⁴	1	4	yes	—
185	D₇₆	—	2	4	no	—
186	D₇₆	—	4	2	no	—
187	C₄×D₁₉	—	4	4	no	—
188	C₄×D₁₉	—	4	4	no	—
189	Dic₃₈	—	2	4	no	—
190	Dic₃₈	—	4	2	no	—
191	#3505	—	19	1	no	maximal, Sylow
192	C₂²×C₁₉	—	2	1	no	—
193	C₂²×C₁₉	—	2	1	no	—
194	C₂²×C₁₉	—	2	1	no	—
195	C₂²×C₁₉	—	2	1	no	—
196	C₂²×C₁₉	—	2	1	no	—
197	C₂²×C₁₉	—	2	1	no	—
198	C₂²×C₁₉	—	2	2	no	—
199	C₂²×C₁₉	—	2	2	no	—
200	C₂²×C₁₉	—	2	2	no	—
201	C₂²×C₁₉	—	4	4	no	—
202	C₂²×C₁₉	—	4	4	no	—
203	C₂²×C₁₉	C₂×#41	1	2	yes	—
204	C₂²×C₁₉	C₂×#41	1	2	yes	—
205	C₂²×C₁₉	C₂×#41	1	2	yes	—
206	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
207	C₂×D₁₉	—	2	4	no	—
208	C₂×D₁₉	—	2	4	no	—
209	C₂×D₁₉	—	2	4	no	—
210	C₂×D₁₉	—	8	4	no	—
211	C₄×C₁₉	—	2	2	no	—
212	C₄×C₁₉	—	2	1	no	—
213	C₄×C₁₉	—	2	2	no	—
214	C₄×C₁₉	—	2	1	no	—
215	C₄×C₁₉	—	2	1	no	—
216	C₄×C₁₉	—	2	2	no	—
217	C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
218	Dic₁₉	—	2	4	no	—
219	Dic₁₉	—	2	4	no	—
220	Dic₁₉	—	2	4	no	—
221	#553	—	19	2	no	—
222	#553	—	19	4	no	—
223	#552	—	19	2	no	—
224	#551	—	19	4	no	—
225	#548	—	19	2	no	—
226	#546	—	19	2	no	—
227	#539	—	19	2	no	—
228	#538	—	19	2	no	—
229	#534	—	19	2	no	—
230	#529	—	19	2	no	—
231	#525	—	19	2	no	—
232	C₂×C₂²⋊Q₈	—	19	1	no	—
233	C₂×#121	—	19	1	no	—
234	#518	—	19	2	no	—
235	C₂×C₄×D₄	D₁₉	1	1	yes	characteristic, complemented
236	C₂×C₁₉	—	2	2	no	—
237	C₂×C₁₉	—	2	2	no	—
238	C₂×C₁₉	—	2	2	no	—
239	C₂×C₁₉	—	4	2	no	—
240	C₂×C₁₉	C₂²×#41	1	1	yes	characteristic
241	C₂×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
242	C₂×C₁₉	#585	1	1	yes	characteristic
243	D₁₉	—	4	4	no	—
244	C₂×#41	—	19	2	no	—
245	C₂²×Q₈	—	19	1	no	—
246	C₂²×D₄	—	19	2	no	—
247	C₂²×D₄	—	19	1	no	—
248	C₂²×D₄	C₂×D₁₉	1	1	yes	characteristic
249	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic
250	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic, complemented
251	#126	—	19	4	no	—
252	#126	—	19	4	no	—
253	#126	—	19	4	no	—
254	#125	—	19	4	no	—
255	#125	—	19	2	no	—
256	#124	—	19	4	no	—
257	#124	—	19	2	no	—
258	#123	—	19	4	no	—
259	#123	—	19	4	no	—
260	#123	—	19	4	no	—
261	#123	—	19	4	no	—
262	#123	—	19	4	no	—
263	C₂²⋊Q₈	—	19	2	no	—
264	C₂²⋊Q₈	—	19	2	no	—
265	C₂²⋊Q₈	—	19	2	no	—
266	C₂²⋊Q₈	—	19	2	no	—
267	C₂²⋊Q₈	—	19	2	no	—
268	C₂²⋊Q₈	—	19	4	no	—
269	#121	—	19	4	no	—
270	#121	—	19	4	no	—
271	#121	—	19	2	no	—
272	#121	—	19	2	no	—
273	#121	—	19	2	no	—
274	#121	—	19	2	no	—
275	#121	—	19	2	no	—
276	#121	—	19	4	no	—
277	#120	—	19	4	no	—
278	#120	—	19	4	no	—
279	C₄×Q₈	—	19	2	no	—
280	C₄×D₄	—	19	4	no	—
281	C₄×D₄	—	19	4	no	—
282	C₄×D₄	—	19	4	no	—
283	C₄×D₄	—	19	4	no	—
284	C₄×D₄	—	19	4	no	—
285	C₄×D₄	—	19	2	no	—
286	C₄×D₄	C₂×D₁₉	1	2	yes	—
287	C₄×D₄	C₂×D₁₉	1	2	yes	—
288	C₄×D₄	C₂×D₁₉	1	2	yes	complemented
289	C₄×D₄	C₂×D₁₉	1	2	yes	complemented
290	#117	—	19	2	no	—
291	#117	—	19	4	no	—
292	#117	—	19	4	no	—
293	C₂×C₄⋊C₄	—	19	1	no	—
294	C₂×C₄⋊C₄	—	19	2	no	—
295	C₂×C₄⋊C₄	—	19	1	no	—
296	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic, complemented
297	C₂×C₂²⋊C₄	—	19	2	no	—
298	C₂×C₂²⋊C₄	—	19	2	no	—
299	C₂×C₂²⋊C₄	—	19	4	no	—
300	C₂×C₂²⋊C₄	C₂×D₁₉	1	1	yes	characteristic
301	C₂×C₂²⋊C₄	C₂×D₁₉	1	1	yes	characteristic, complemented
302	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic, complemented
303	C₁₉	#3505	1	1	yes	characteristic, complemented, Sylow
304	C₂⁴	—	19	2	no	—
305	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
306	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
307	#41	—	76	4	no	—
308	C₂×Q₈	—	19	2	no	—
309	C₂×Q₈	—	19	2	no	—
310	C₂×Q₈	—	76	2	no	—
311	C₂×D₄	—	2	4	no	—
312	C₂×D₄	—	19	4	no	—
313	C₂×D₄	—	19	4	no	—
314	C₂×D₄	—	19	4	no	—
315	C₂×D₄	—	19	4	no	—
316	C₂×D₄	—	19	2	no	—
317	C₂×D₄	—	19	2	no	—
318	C₂×D₄	—	38	8	no	—
319	C₂×D₄	—	76	2	no	—
320	C₂×D₄	C₂²×D₁₉	1	2	yes	—
321	C₂×D₄	C₂²×D₁₉	1	2	yes	—
322	C₂²×C₄	—	4	2	no	—
323	C₂²×C₄	—	4	2	no	—
324	C₂²×C₄	—	19	2	no	—
325	C₂²×C₄	—	19	2	no	—
326	C₂²×C₄	—	19	2	no	—
327	C₂²×C₄	—	19	4	no	—
328	C₂²×C₄	—	19	4	no	—
329	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
330	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
331	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
332	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
333	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
334	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
335	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
336	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
337	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
338	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
339	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
340	C₄⋊C₄	—	19	4	no	—
341	C₄⋊C₄	—	19	4	no	—
342	C₄⋊C₄	—	19	4	no	—
343	C₄⋊C₄	—	19	4	no	—
344	C₄⋊C₄	—	19	4	no	—
345	C₄⋊C₄	—	19	4	no	—
346	C₄⋊C₄	—	19	2	no	—
347	C₄⋊C₄	—	19	2	no	—
348	C₄⋊C₄	—	19	2	no	—
349	C₄⋊C₄	—	19	2	no	—
350	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
351	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
352	C₂²⋊C₄	—	19	4	no	—
353	C₂²⋊C₄	—	19	4	no	—
354	C₂²⋊C₄	—	19	4	no	—
355	C₂²⋊C₄	—	19	4	no	—
356	C₂²⋊C₄	—	19	4	no	—
357	C₂²⋊C₄	—	19	4	no	—
358	C₂²⋊C₄	—	19	4	no	—
359	C₂²⋊C₄	—	19	4	no	—
360	C₂²⋊C₄	—	19	4	no	—
361	C₂²⋊C₄	—	19	4	no	—
362	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
363	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
364	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
365	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
366	C₄²	—	19	4	no	—
367	C₄²	—	19	4	no	—
368	C₄²	C₂²×D₁₉	1	2	yes	—
369	C₄²	C₂²×D₁₉	1	2	yes	—
370	C₂³	—	2	2	no	—
371	C₂³	—	4	1	no	—
372	C₂³	—	4	1	no	—
373	C₂³	—	4	1	no	—
374	C₂³	—	4	1	no	—
375	C₂³	—	19	4	no	—
376	C₂³	—	38	4	no	—
377	C₂³	—	76	2	no	—
378	C₂³	—	76	2	no	—
379	C₂³	#64541	1	4	yes	complemented
380	C₂³	C₂³×D₁₉	1	2	yes	—
381	C₂³	C₂³×D₁₉	1	1	yes	characteristic
382	C₂³	C₂³×D₁₉	1	1	yes	characteristic
383	C₂³	C₂³×D₁₉	1	1	yes	characteristic
384	Q₈	—	38	4	no	—
385	Q₈	—	76	2	no	—
386	D₄	—	2	4	no	—
387	D₄	—	2	4	no	—
388	D₄	—	38	8	no	—
389	D₄	—	38	8	no	—
390	D₄	—	38	4	no	—
391	D₄	—	76	2	no	—
392	D₄	—	76	4	no	—
393	D₄	—	76	4	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	19	4	no	—
406	C₂×C₄	—	19	4	no	—
407	C₂×C₄	—	19	4	no	—
408	C₂×C₄	—	38	4	no	—
409	C₂×C₄	—	76	4	no	—
410	C₂×C₄	—	76	4	no	—
411	C₂×C₄	—	76	2	no	—
412	C₂×C₄	—	76	2	no	—
413	C₂×C₄	C₂³×D₁₉	1	2	yes	—
414	C₂×C₄	C₂³×D₁₉	1	2	yes	—
415	C₂×C₄	C₂³×D₁₉	1	2	yes	—
416	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
417	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
418	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
419	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
420	C₂²	—	2	1	no	—
421	C₂²	—	2	1	no	—
422	C₂²	—	2	1	no	—
423	C₂²	—	2	1	no	—
424	C₂²	—	2	1	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	2	2	no	—
427	C₂²	—	2	2	no	—
428	C₂²	—	2	2	no	—
429	C₂²	—	4	4	no	—
430	C₂²	—	4	4	no	—
431	C₂²	—	38	4	no	—
432	C₂²	—	38	4	no	—
433	C₂²	—	38	4	no	—
434	C₂²	—	152	4	no	—
435	C₂²	C₂×#64541	1	2	yes	—
436	C₂²	C₂×#64541	1	2	yes	—
437	C₂²	C₂×#64541	1	2	yes	—
438	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
439	C₄	—	2	2	no	—
440	C₄	—	2	1	no	—
441	C₄	—	2	2	no	—
442	C₄	—	2	1	no	—
443	C₄	—	2	1	no	—
444	C₄	—	2	2	no	—
445	C₄	—	38	4	no	—
446	C₄	—	38	4	no	—
447	C₄	—	38	4	no	—
448	C₄	#10597430	1	2	yes	—
449	C₂	—	2	2	no	—
450	C₂	—	2	2	no	—
451	C₂	—	2	2	no	—
452	C₂	—	4	2	no	—
453	C₂	—	76	4	no	—
454	C₂	C₂²×#64541	1	1	yes	characteristic
455	C₂	C₂×#10597430	1	1	yes	characteristic
456	C₂	#11927380	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Fitting	C₂×C₄×D₄×C₁₉	C₂
hypercenter	C₂×C₄×D₄	D₁₉
hypocenter	C₁₉	#3505
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. #11927243	C₂	semidirect
2. #11927240	C₂	semidirect
3. #11927234	C₂	semidirect
4. #11927223	C₂	semidirect
5. #11927203	C₂	semidirect
6. #11927190	C₂	semidirect
7. #11927141	C₂	semidirect
8. #11927132	C₂	semidirect
9. #11927103	C₂	semidirect
10. #11927078	C₂	semidirect
11. #11927055	C₂	semidirect
12. C₂×#10597370	C₂	semidirect
13. C₂×#10597376	C₂	semidirect
14. #11927017	C₂	semidirect
15. C₂×C₄×D₄×C₁₉	C₂	semidirect
18. C₂³×C₄×C₁₉	C₂²	semidirect
20. C₂×#64541	C₂²	semidirect
21. C₂²×D₇₆	C₂²	semidirect
22. C₂²×Dic₃₈	C₂²	semidirect
25. C₄×D₄×C₁₉	C₂²	semidirect
26. C₄×D₄×C₁₉	C₂²	semidirect
27. C₂×C₄⋊C₄×C₁₉	C₂²	semidirect
29. C₂×C₂²⋊C₄×C₁₉	C₂²	semidirect
30. C₂×C₄²×C₁₉	C₂²	semidirect
31. #10597399	C₂²	semidirect
33. #10597385	C₂²	semidirect
34. #10597385	C₂²	semidirect
39. #10597376	C₂²	semidirect
40. #10597376	C₂²	semidirect
41. #10597376	C₂²	semidirect
42. #10597375	C₂²	semidirect
43. #10597375	C₂²	semidirect
44. C₄×C₂²⋊D₁₉	C₂²	semidirect
45. C₄×C₂²⋊D₁₉	C₂²	semidirect
46. C₄×C₂²⋊D₁₉	C₂²	semidirect
47. C₂×(C₂×D₁₉)⋊C₄	C₂²	semidirect
48. #10597372	C₂²	semidirect
49. C₂×C₄⋊Dic₁₉	C₂²	semidirect
50. C₂×C₄⋊Dic₁₉	C₂²	semidirect
51. #10597370	C₂²	semidirect
52. #10597370	C₂²	semidirect
53. #10597370	C₂²	semidirect
54. #10597370	C₂²	semidirect
55. #10597370	C₂²	semidirect
56. C₂×Dic₁₉⋊C₄	C₂²	semidirect
57. #10597344	C₂²	semidirect
58. #10597342	C₂²	semidirect
59. #10597340	C₂²	semidirect
60. #10597335	C₂²	semidirect
61. #10597331	C₂²	semidirect
62. #10597330	C₂²	semidirect
63. #10597329	C₂²	semidirect
64. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
65. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
66. C₂²⋊C₄×D₁₉	C₂²	semidirect
67. #10597325	C₂²	semidirect
68. #10597323	C₂²	semidirect
69. #10597322	C₂²	semidirect
70. #10597321	C₂²	semidirect
71. C₄×D₇₆	C₂²	semidirect
72. #10597318	C₂²	semidirect
73. #10597316	C₂²	semidirect
74. C₄×Dic₃₈	C₂²	semidirect
146. C₂³×C₁₉	#41	semidirect
235. C₂×C₄×D₄	D₁₉	semidirect
250. C₂³×C₄	C₂×D₁₉	semidirect
288. C₄×D₄	C₂×D₁₉	semidirect
289. C₄×D₄	C₂×D₁₉	semidirect
296. C₂×C₄⋊C₄	C₂×D₁₉	semidirect
301. C₂×C₂²⋊C₄	C₂×D₁₉	semidirect
302. C₂×C₄²	C₂×D₁₉	semidirect
303. C₁₉	#3505	semidirect
379. C₂³	#64541	semidirect

Maximal subgroups

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

subgroup	index
#11927243	2
#11927240	2
#11927234	2
#11927223	2
#11927203	2
#11927190	2
#11927141	2
#11927132	2
#11927103	2
#11927078	2
#11927055	2
C₂×#10597370	2
C₂×#10597376	2
#11927017	2
C₂×C₄×D₄×C₁₉	2
#3505	19