Subgroups — #14577597

Order 2432.

1142 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927279	C₂	1	1	yes	maximal, characteristic, complemented
2	#11927268	C₂	1	1	yes	maximal, characteristic, complemented
3	#11927260	C₂	1	2	yes	maximal, complemented
4	#11927221	C₂	1	4	yes	maximal, complemented
5	#11927205	C₂	1	2	yes	maximal, complemented
6	#11927189	C₂	1	2	yes	maximal, complemented
7	#11927185	C₂	1	2	yes	maximal, complemented
8	D₄×D₇₆	C₂	1	1	yes	maximal, characteristic, complemented
9	#11927168	C₂	1	2	yes	maximal, complemented
10	#11927134	C₂	1	4	yes	maximal, complemented
11	#11927095	C₂	1	1	yes	maximal, characteristic, complemented
12	#11927081	C₂	1	1	yes	maximal, characteristic, complemented
13	#11927080	C₂	1	2	yes	maximal, complemented
14	C₂×#10597393	C₂	1	2	yes	maximal, complemented
15	#11927016	C₂	1	2	yes	maximal, complemented
16	C₄×#64543	C₂	1	1	yes	maximal, characteristic, complemented
17	D₄×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×Q₈×C₁₉	C₂²	1	2	yes	complemented
19	C₂×#64545	C₂²	1	2	yes	complemented
20	C₂×#64543	C₂²	1	1	yes	characteristic
21	C₂×D₄×D₁₉	C₂²	1	2	yes	—
22	C₂²×D₇₆	C₂²	1	2	yes	—
23	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
24	C₁₉×C₄⋊Q₈	C₂²	1	2	yes	complemented
25	C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	complemented
26	C₁₉×C₂²⋊Q₈	C₂²	1	4	yes	complemented
27	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
28	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
29	C₄×D₄×C₁₉	C₂²	1	2	yes	—
30	#10597393	C₂²	1	1	yes	characteristic
31	#10597393	C₂²	1	2	yes	—
32	#10597393	C₂²	1	2	yes	complemented
33	#10597393	C₂²	1	4	yes	complemented
34	#10597393	C₂²	1	2	yes	complemented
35	#10597393	C₂²	1	4	yes	complemented
36	#10597393	C₂²	1	4	yes	complemented
37	#10597392	C₂²	1	1	yes	characteristic, complemented
38	#10597392	C₂²	1	4	yes	complemented
39	Q₈×Dic₁₉	C₂²	1	2	yes	complemented
40	D₄×Dic₁₉	C₂²	1	1	yes	characteristic
41	#10597376	C₂²	1	2	yes	—
42	#10597376	C₂²	1	4	yes	complemented
43	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	complemented
44	C₄×C₂²⋊D₁₉	C₂²	1	4	yes	complemented
45	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	4	yes	complemented
46	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	4	yes	complemented
47	C₂×C₄×Dic₁₉	C₂²	1	2	yes	complemented
48	#10597344	C₂²	1	4	yes	complemented
49	#10597344	C₂²	1	2	yes	complemented
50	#10597344	C₂²	1	4	yes	complemented
51	#10597343	C₂²	1	2	yes	complemented
52	#10597341	C₂²	1	1	yes	characteristic
53	#10597341	C₂²	1	2	yes	—
54	#10597341	C₂²	1	2	yes	complemented
55	#10597341	C₂²	1	2	yes	complemented
56	#10597341	C₂²	1	4	yes	complemented
57	#10597340	C₂²	1	2	yes	complemented
58	#10597340	C₂²	1	4	yes	complemented
59	#10597340	C₂²	1	4	yes	complemented
60	#10597339	C₂²	1	2	yes	complemented
61	#10597339	C₂²	1	2	yes	complemented
62	#10597339	C₂²	1	2	yes	complemented
63	#10597338	C₂²	1	4	yes	complemented
64	#10597338	C₂²	1	1	yes	characteristic, complemented
65	#10597338	C₂²	1	2	yes	complemented
66	#10597336	C₂²	1	1	yes	characteristic, complemented
67	#10597333	C₂²	1	1	yes	characteristic, complemented
68	#10597332	C₂²	1	4	yes	complemented
69	#10597328	C₂²	1	4	yes	—
70	#10597328	C₂²	1	4	yes	complemented
71	(C₂²⋊D₁₉)⋊C₄	C₂²	1	4	yes	complemented
72	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	complemented
73	C₂²⋊C₄×D₁₉	C₂²	1	4	yes	complemented
74	#10597323	C₂²	1	2	yes	complemented
75	#10597321	C₂²	1	2	yes	complemented
76	#10597320	C₂²	1	1	yes	characteristic
77	C₄×D₇₆	C₂²	1	1	yes	characteristic
78	C₄×D₇₆	C₂²	1	2	yes	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	C₂×Q₈×C₁₉	—	4	4	no	—
85	C₂×Q₈×C₁₉	C₂³	1	2	yes	—
86	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
87	C₂×Q₈×C₁₉	C₂³	1	4	yes	—
88	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
89	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
90	C₂²×C₄×C₁₉	C₂³	1	4	yes	—
91	C₂×C₂²⋊D₁₉	C₂³	1	4	yes	—
92	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
93	C₂²×Dic₁₉	C₂³	1	2	yes	—
94	C₂²×Dic₁₉	C₂³	1	2	yes	—
95	#64545	—	4	4	no	—
96	#64543	—	2	4	no	—
97	D₄×D₁₉	—	2	8	no	—
98	C₂×D₇₆	—	4	4	no	—
99	C₂×D₇₆	C₂³	1	2	yes	—
100	C₂×D₇₆	C₂³	1	1	yes	characteristic
101	C₂×D₇₆	C₂³	1	2	yes	—
102	C₂×D₇₆	C₂³	1	4	yes	—
103	C₂×D₇₆	C₂³	1	4	yes	—
104	C₂×D₇₆	C₂³	1	2	yes	—
105	C₂×D₇₆	C₂³	1	2	yes	—
106	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
107	C₂×C₄×D₁₉	C₂³	1	2	yes	—
108	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
109	C₂×C₄×D₁₉	C₂³	1	4	yes	—
110	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
111	C₂×C₄×D₁₉	C₂³	1	4	yes	—
112	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
113	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
114	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
115	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
116	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
117	C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
118	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
119	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
120	C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
121	C₄²×C₁₉	C₂³	1	1	yes	characteristic
122	C₄²×C₁₉	C₂³	1	2	yes	—
123	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
124	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
125	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
126	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
127	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
128	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
129	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
130	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
131	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
132	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
133	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
134	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
135	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
136	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
137	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
138	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
139	C₄⋊Dic₁₉	C₂³	1	4	yes	—
140	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
141	C₄⋊Dic₁₉	C₂³	1	2	yes	—
142	Dic₁₉⋊C₄	C₂³	1	2	yes	—
143	Dic₁₉⋊C₄	C₂³	1	2	yes	—
144	Dic₁₉⋊C₄	C₂³	1	2	yes	—
145	Dic₁₉⋊C₄	C₂³	1	2	yes	—
146	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
147	C₄×Dic₁₉	C₂³	1	2	yes	—
148	C₄×Dic₁₉	C₂³	1	4	yes	—
149	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
150	C₄×Dic₁₉	C₂³	1	2	yes	—
151	C₄×Dic₁₉	C₂³	1	2	yes	—
152	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
153	C₂³×C₁₉	C₂⁴	1	2	yes	—
154	C₂²×D₁₉	—	2	8	no	—
155	C₂²×D₁₉	—	4	4	no	—
156	C₂²×D₁₉	—	4	4	no	—
157	C₂²×D₁₉	C₂⁴	1	2	yes	—
158	C₂²×D₁₉	C₂⁴	1	4	yes	—
159	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
160	Q₈×C₁₉	—	2	4	no	—
161	Q₈×C₁₉	—	2	2	no	—
162	Q₈×C₁₉	—	4	4	no	—
163	D₄×C₁₉	#41	1	4	yes	complemented
164	C₂×C₄×C₁₉	—	2	4	no	—
165	C₂×C₄×C₁₉	—	4	4	no	—
166	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
167	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
168	C₂×C₄×C₁₉	C₂⁴	1	4	yes	—
169	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
170	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
171	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
172	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
173	C₂²⋊D₁₉	—	2	8	no	—
174	C₂²⋊D₁₉	—	2	4	no	—
175	C₂×Dic₁₉	—	2	4	no	—
176	C₂×Dic₁₉	—	4	2	no	—
177	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
178	C₂×Dic₁₉	C₂⁴	1	2	yes	—
179	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
180	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
181	C₂×Dic₁₉	C₂⁴	1	2	yes	—
182	C₂×Dic₁₉	C₂⁴	1	2	yes	—
183	D₇₆	—	2	4	no	—
184	D₇₆	—	2	2	no	—
185	D₇₆	—	2	4	no	—
186	D₇₆	—	4	4	no	—
187	D₇₆	—	4	2	no	—
188	D₇₆	—	4	2	no	—
189	D₇₆	—	4	4	no	—
190	C₄×D₁₉	—	2	4	no	—
191	C₄×D₁₉	—	2	2	no	—
192	C₄×D₁₉	—	2	2	no	—
193	C₄×D₁₉	—	4	4	no	—
194	C₄×D₁₉	—	4	1	no	—
195	C₄×D₁₉	—	4	4	no	—
196	Dic₃₈	—	2	2	no	—
197	#3514	—	19	1	no	maximal, Sylow
198	C₂²×C₁₉	—	2	2	no	—
199	C₂²×C₁₉	—	2	2	no	—
200	C₂²×C₁₉	C₂×#41	1	4	yes	—
201	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
202	C₂×D₁₉	—	2	1	no	—
203	C₂×D₁₉	—	2	2	no	—
204	C₂×D₁₉	—	2	4	no	—
205	C₂×D₁₉	—	2	1	no	—
206	C₂×D₁₉	—	2	4	no	—
207	C₂×D₁₉	—	2	2	no	—
208	C₂×D₁₉	—	2	1	no	—
209	C₂×D₁₉	—	2	4	no	—
210	C₂×D₁₉	—	2	2	no	—
211	C₂×D₁₉	—	8	8	no	—
212	C₄×C₁₉	—	2	4	no	—
213	C₄×C₁₉	—	2	2	no	—
214	C₄×C₁₉	—	2	2	no	—
215	C₄×C₁₉	—	2	2	no	—
216	C₄×C₁₉	—	2	1	no	—
217	C₄×C₁₉	C₂×#41	1	2	yes	—
218	C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
219	Dic₁₉	—	2	2	no	—
220	Dic₁₉	—	2	1	no	—
221	Dic₁₉	—	2	2	no	—
222	Dic₁₉	—	2	1	no	—
223	Dic₁₉	—	2	2	no	—
224	Dic₁₉	—	2	1	no	—
225	#559	—	19	1	no	—
226	#556	—	19	1	no	—
227	#555	—	19	2	no	—
228	#551	—	19	4	no	—
229	D₄×Q₈	D₁₉	1	1	yes	characteristic, complemented
230	#548	—	19	2	no	—
231	#546	—	19	2	no	—
232	#546	—	19	2	no	—
233	D₄²	—	19	1	no	—
234	#542	—	19	2	no	—
235	#538	—	19	4	no	—
236	#532	—	19	1	no	—
237	#529	—	19	2	no	—
238	#529	—	19	1	no	—
239	C₂×#124	—	19	2	no	—
240	#518	—	19	2	no	—
241	C₄×#41	—	19	1	no	—
242	C₂×C₁₉	—	2	4	no	—
243	C₂×C₁₉	C₂²×#41	1	1	yes	characteristic
244	C₂×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
245	C₂×C₁₉	#585	1	1	yes	characteristic
246	D₁₉	—	4	1	no	—
247	D₁₉	—	4	4	no	—
248	D₁₉	—	4	2	no	—
249	C₂×#41	—	19	2	no	—
250	C₂×#41	—	19	1	no	—
251	C₂²×Q₈	C₂×D₁₉	1	2	yes	complemented
252	C₂²×D₄	—	19	2	no	—
253	C₂²×D₄	—	19	2	no	—
254	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
255	C₄⋊Q₈	C₂×D₁₉	1	2	yes	complemented
256	#127	—	19	1	no	—
257	#126	—	19	4	no	—
258	#126	—	19	2	no	—
259	#126	—	19	4	no	—
260	#125	—	19	1	no	—
261	#124	—	19	1	no	—
262	#124	—	19	2	no	—
263	#124	—	19	2	no	—
264	#124	—	19	4	no	—
265	#124	—	19	2	no	—
266	#124	—	19	4	no	—
267	#124	—	19	4	no	—
268	#124	—	19	2	no	—
269	#123	—	19	2	no	—
270	#123	—	19	4	no	—
271	#123	—	19	4	no	—
272	#123	—	19	4	no	—
273	C₂²⋊Q₈	—	19	1	no	—
274	C₂²⋊Q₈	—	19	4	no	—
275	C₂²⋊Q₈	—	19	2	no	—
276	C₂²⋊Q₈	C₂×D₁₉	1	2	yes	complemented
277	C₂²⋊Q₈	C₂×D₁₉	1	4	yes	complemented
278	#121	—	19	2	no	—
279	#121	—	19	4	no	—
280	#121	—	19	1	no	—
281	#121	—	19	2	no	—
282	#121	—	19	2	no	—
283	#121	—	19	4	no	—
284	#121	—	19	2	no	—
285	#120	—	19	4	no	—
286	#120	—	19	4	no	—
287	C₄×Q₈	—	19	2	no	—
288	C₄×Q₈	—	19	1	no	—
289	C₄×Q₈	—	19	1	no	—
290	C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
291	C₄×D₄	—	19	1	no	—
292	C₄×D₄	—	19	2	no	—
293	C₄×D₄	—	19	4	no	—
294	C₄×D₄	—	19	2	no	—
295	C₄×D₄	—	19	2	no	—
296	C₄×D₄	—	19	2	no	—
297	C₄×D₄	—	19	2	no	—
298	C₄×D₄	—	19	4	no	—
299	C₄×D₄	—	19	2	no	—
300	C₄×D₄	—	19	1	no	—
301	C₄×D₄	—	19	2	no	—
302	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
303	C₄×D₄	C₂×D₁₉	1	2	yes	—
304	#117	—	19	1	no	—
305	#117	—	19	2	no	—
306	#117	—	19	4	no	—
307	#117	—	19	2	no	—
308	#117	—	19	2	no	—
309	C₂×C₂²⋊C₄	—	19	4	no	—
310	C₂×C₂²⋊C₄	—	19	4	no	—
311	C₂×C₂²⋊C₄	—	19	4	no	—
312	C₂×C₄²	—	19	2	no	—
313	C₂×C₄²	—	19	1	no	—
314	C₁₉	#3514	1	1	yes	characteristic, complemented, Sylow
315	C₂⁴	—	19	4	no	—
316	#41	—	38	4	no	—
317	#41	—	76	4	no	—
318	C₂×Q₈	—	4	4	no	—
319	C₂×Q₈	—	19	1	no	—
320	C₂×Q₈	C₂²×D₁₉	1	2	yes	—
321	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
322	C₂×Q₈	C₂²×D₁₉	1	4	yes	—
323	C₂×D₄	—	19	2	no	—
324	C₂×D₄	—	19	4	no	—
325	C₂×D₄	—	19	2	no	—
326	C₂×D₄	—	19	1	no	—
327	C₂×D₄	—	19	2	no	—
328	C₂×D₄	—	19	2	no	—
329	C₂×D₄	—	19	2	no	—
330	C₂×D₄	—	19	4	no	—
331	C₂×D₄	—	19	4	no	—
332	C₂×D₄	—	38	8	no	—
333	C₂×D₄	—	76	4	no	—
334	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
335	C₂²×C₄	—	19	2	no	—
336	C₂²×C₄	—	19	2	no	—
337	C₂²×C₄	—	19	1	no	—
338	C₂²×C₄	—	19	1	no	—
339	C₂²×C₄	—	19	2	no	—
340	C₂²×C₄	—	19	1	no	—
341	C₂²×C₄	—	19	4	no	—
342	C₂²×C₄	—	19	4	no	—
343	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
344	C₂²×C₄	C₂²×D₁₉	1	4	yes	—
345	C₄⋊C₄	—	19	2	no	—
346	C₄⋊C₄	—	19	2	no	—
347	C₄⋊C₄	—	19	2	no	—
348	C₄⋊C₄	—	19	2	no	—
349	C₄⋊C₄	—	19	1	no	—
350	C₄⋊C₄	—	19	2	no	—
351	C₄⋊C₄	—	19	1	no	—
352	C₄⋊C₄	—	19	4	no	—
353	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
354	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
355	C₄⋊C₄	C₂²×D₁₉	1	4	yes	—
356	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
357	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
358	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
359	C₂²⋊C₄	—	19	2	no	—
360	C₂²⋊C₄	—	19	2	no	—
361	C₂²⋊C₄	—	19	4	no	—
362	C₂²⋊C₄	—	19	2	no	—
363	C₂²⋊C₄	—	19	2	no	—
364	C₂²⋊C₄	—	19	4	no	—
365	C₂²⋊C₄	—	19	4	no	—
366	C₂²⋊C₄	—	19	4	no	—
367	C₂²⋊C₄	—	19	4	no	—
368	C₂²⋊C₄	—	19	4	no	—
369	C₂²⋊C₄	—	19	2	no	—
370	C₂²⋊C₄	—	19	4	no	—
371	C₂²⋊C₄	—	19	2	no	—
372	C₂²⋊C₄	—	19	4	no	—
373	C₂²⋊C₄	—	19	2	no	—
374	C₂²⋊C₄	C₂²×D₁₉	1	4	yes	—
375	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
376	C₄²	—	19	1	no	—
377	C₄²	—	19	2	no	—
378	C₄²	—	19	1	no	—
379	C₄²	—	19	1	no	—
380	C₄²	—	19	2	no	—
381	C₄²	—	19	2	no	—
382	C₄²	—	19	4	no	—
383	C₄²	C₂²×D₁₉	1	1	yes	characteristic
384	C₄²	C₂²×D₁₉	1	2	yes	—
385	C₂³	—	19	2	no	—
386	C₂³	—	19	4	no	—
387	C₂³	—	19	1	no	—
388	C₂³	—	38	8	no	—
389	C₂³	—	76	4	no	—
390	C₂³	—	76	4	no	—
391	C₂³	C₂³×D₁₉	1	2	yes	—
392	Q₈	—	2	2	no	—
393	Q₈	—	2	4	no	—
394	Q₈	—	4	4	no	—
395	Q₈	—	38	2	no	—
396	D₄	—	38	8	no	—
397	D₄	—	38	4	no	—
398	D₄	—	38	2	no	—
399	D₄	—	38	4	no	—
400	D₄	—	38	4	no	—
401	D₄	—	76	4	no	—
402	D₄	—	76	4	no	—
403	D₄	—	76	2	no	—
404	D₄	—	76	2	no	—
405	D₄	#64545	1	4	yes	complemented
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	4	4	no	—
408	C₂×C₄	—	19	1	no	—
409	C₂×C₄	—	19	1	no	—
410	C₂×C₄	—	19	2	no	—
411	C₂×C₄	—	19	2	no	—
412	C₂×C₄	—	19	2	no	—
413	C₂×C₄	—	19	1	no	—
414	C₂×C₄	—	38	4	no	—
415	C₂×C₄	—	38	2	no	—
416	C₂×C₄	—	38	4	no	—
417	C₂×C₄	—	38	2	no	—
418	C₂×C₄	—	76	4	no	—
419	C₂×C₄	—	76	4	no	—
420	C₂×C₄	—	76	1	no	—
421	C₂×C₄	—	76	2	no	—
422	C₂×C₄	C₂³×D₁₉	1	2	yes	—
423	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
424	C₂×C₄	C₂³×D₁₉	1	4	yes	—
425	C₂×C₄	C₂³×D₁₉	1	2	yes	—
426	C₂×C₄	C₂³×D₁₉	1	2	yes	—
427	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
428	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
429	C₂²	—	2	2	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	38	1	no	—
432	C₂²	—	38	2	no	—
433	C₂²	—	38	4	no	—
434	C₂²	—	38	1	no	—
435	C₂²	—	38	4	no	—
436	C₂²	—	38	2	no	—
437	C₂²	—	38	1	no	—
438	C₂²	—	38	4	no	—
439	C₂²	—	38	2	no	—
440	C₂²	—	152	8	no	—
441	C₂²	C₂×#64545	1	4	yes	—
442	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
443	C₄	—	2	2	no	—
444	C₄	—	2	2	no	—
445	C₄	—	2	4	no	—
446	C₄	—	2	2	no	—
447	C₄	—	2	1	no	—
448	C₄	—	38	1	no	—
449	C₄	—	38	2	no	—
450	C₄	—	38	2	no	—
451	C₄	—	38	1	no	—
452	C₄	—	38	2	no	—
453	C₄	—	38	1	no	—
454	C₄	#10597430	1	2	yes	—
455	C₄	C₂×#64545	1	2	yes	—
456	C₂	—	2	4	no	—
457	C₂	—	76	2	no	—
458	C₂	—	76	4	no	—
459	C₂	—	76	1	no	—
460	C₂	C₂²×#64545	1	1	yes	characteristic
461	C₂	C₂×#10597430	1	1	yes	characteristic
462	C₂	#11927381	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Fitting	D₄×Q₈×C₁₉	C₂
hypercenter	D₄×Q₈	D₁₉
hypocenter	C₁₉	#3514
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ D₄×Q₈

Complements

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

N	H ≅ G/N	type
1. #11927279	C₂	semidirect
2. #11927268	C₂	semidirect
3. #11927260	C₂	semidirect
4. #11927221	C₂	semidirect
5. #11927205	C₂	semidirect
6. #11927189	C₂	semidirect
7. #11927185	C₂	semidirect
8. D₄×D₇₆	C₂	semidirect
9. #11927168	C₂	semidirect
10. #11927134	C₂	semidirect
11. #11927095	C₂	semidirect
12. #11927081	C₂	semidirect
13. #11927080	C₂	semidirect
14. C₂×#10597393	C₂	semidirect
15. #11927016	C₂	semidirect
16. C₄×#64543	C₂	semidirect
17. D₄×Q₈×C₁₉	C₂	semidirect
18. C₂²×Q₈×C₁₉	C₂²	semidirect
19. C₂×#64545	C₂²	semidirect
23. C₁₉×C₄⋊Q₈	C₂²	semidirect
24. C₁₉×C₄⋊Q₈	C₂²	semidirect
25. C₁₉×C₂²⋊Q₈	C₂²	semidirect
26. C₁₉×C₂²⋊Q₈	C₂²	semidirect
27. C₄×Q₈×C₁₉	C₂²	semidirect
32. #10597393	C₂²	semidirect
33. #10597393	C₂²	semidirect
34. #10597393	C₂²	semidirect
35. #10597393	C₂²	semidirect
36. #10597393	C₂²	semidirect
37. #10597392	C₂²	semidirect
38. #10597392	C₂²	semidirect
39. Q₈×Dic₁₉	C₂²	semidirect
42. #10597376	C₂²	semidirect
43. C₄×C₂²⋊D₁₉	C₂²	semidirect
44. C₄×C₂²⋊D₁₉	C₂²	semidirect
45. C₂×(C₂×D₁₉)⋊C₄	C₂²	semidirect
46. C₂×(C₂×D₁₉)⋊C₄	C₂²	semidirect
47. C₂×C₄×Dic₁₉	C₂²	semidirect
48. #10597344	C₂²	semidirect
49. #10597344	C₂²	semidirect
50. #10597344	C₂²	semidirect
51. #10597343	C₂²	semidirect
54. #10597341	C₂²	semidirect
55. #10597341	C₂²	semidirect
56. #10597341	C₂²	semidirect
57. #10597340	C₂²	semidirect
58. #10597340	C₂²	semidirect
59. #10597340	C₂²	semidirect
60. #10597339	C₂²	semidirect
61. #10597339	C₂²	semidirect
62. #10597339	C₂²	semidirect
63. #10597338	C₂²	semidirect
64. #10597338	C₂²	semidirect
65. #10597338	C₂²	semidirect
66. #10597336	C₂²	semidirect
67. #10597333	C₂²	semidirect
68. #10597332	C₂²	semidirect
70. #10597328	C₂²	semidirect
71. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
72. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
73. C₂²⋊C₄×D₁₉	C₂²	semidirect
74. #10597323	C₂²	semidirect
75. #10597321	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
163. D₄×C₁₉	#41	semidirect
229. D₄×Q₈	D₁₉	semidirect
251. C₂²×Q₈	C₂×D₁₉	semidirect
254. C₄⋊Q₈	C₂×D₁₉	semidirect
255. C₄⋊Q₈	C₂×D₁₉	semidirect
276. C₂²⋊Q₈	C₂×D₁₉	semidirect
277. C₂²⋊Q₈	C₂×D₁₉	semidirect
290. C₄×Q₈	C₂×D₁₉	semidirect
314. C₁₉	#3514	semidirect
405. D₄	#64545	semidirect

Maximal subgroups

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

subgroup	index
#11927279	2
#11927268	2
#11927260	2
#11927221	2
#11927205	2
#11927189	2
#11927185	2
D₄×D₇₆	2
#11927168	2
#11927134	2
#11927095	2
#11927081	2
#11927080	2
C₂×#10597393	2
#11927016	2
C₄×#64543	2
D₄×Q₈×C₁₉	2
#3514	19