Subgroups — #14577596

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	#11927267	C₂	1	1	yes	maximal, characteristic, complemented
3	#11927257	C₂	1	2	yes	maximal, complemented
4	#11927218	C₂	1	4	yes	maximal, complemented
5	D₄×Dic₃₈	C₂	1	1	yes	maximal, characteristic, complemented
6	#11927203	C₂	1	2	yes	maximal, complemented
7	#11927190	C₂	1	2	yes	maximal, complemented
8	#11927182	C₂	1	2	yes	maximal, complemented
9	D₄×D₇₆	C₂	1	1	yes	maximal, characteristic, complemented
10	#11927166	C₂	1	2	yes	maximal, complemented
11	#11927127	C₂	1	4	yes	maximal, complemented
12	#11927094	C₂	1	1	yes	maximal, characteristic, complemented
13	#11927078	C₂	1	1	yes	maximal, characteristic, complemented
14	#11927078	C₂	1	2	yes	maximal, complemented
15	C₂×#10597321	C₂	1	2	yes	maximal, complemented
16	#11927016	C₂	1	2	yes	maximal, complemented
17	C₄×#41×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#41×C₁₉	C₂²	1	1	yes	characteristic
19	C₂×D₄×D₁₉	C₂²	1	2	yes	—
20	C₂×#64541	C₂²	1	2	yes	complemented
21	C₂²×D₇₆	C₂²	1	2	yes	—
22	C₂²×Dic₃₈	C₂²	1	2	yes	complemented
23	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
24	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
25	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
26	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
27	C₄×D₄×C₁₉	C₂²	1	2	yes	complemented
28	C₄×D₄×C₁₉	C₂²	1	2	yes	complemented
29	C₁₉×#117	C₂²	1	2	yes	complemented
30	C₁₉×#117	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₄²×C₁₉	C₂²	1	2	yes	complemented
32	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic, complemented
33	#10597393	C₂²	1	2	yes	complemented
34	#10597392	C₂²	1	2	yes	complemented
35	#10597385	C₂²	1	4	yes	complemented
36	#10597383	C₂²	1	4	yes	complemented
37	D₄×Dic₁₉	C₂²	1	2	yes	—
38	#10597376	C₂²	1	2	yes	—
39	#10597376	C₂²	1	1	yes	characteristic
40	#10597376	C₂²	1	2	yes	complemented
41	#10597376	C₂²	1	2	yes	complemented
42	#10597375	C₂²	1	2	yes	complemented
43	#10597375	C₂²	1	4	yes	complemented
44	C₄×C₂²⋊D₁₉	C₂²	1	4	yes	complemented
45	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	complemented
46	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	4	yes	complemented
47	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	4	yes	complemented
48	#10597370	C₂²	1	2	yes	complemented
49	#10597370	C₂²	1	1	yes	characteristic, complemented
50	#10597344	C₂²	1	4	yes	complemented
51	#10597342	C₂²	1	4	yes	complemented
52	#10597341	C₂²	1	2	yes	—
53	#10597340	C₂²	1	4	yes	complemented
54	#10597340	C₂²	1	4	yes	complemented
55	#10597339	C₂²	1	2	yes	complemented
56	#10597338	C₂²	1	2	yes	complemented
57	#10597334	C₂²	1	2	yes	complemented
58	#10597331	C₂²	1	4	yes	complemented
59	#10597330	C₂²	1	4	yes	complemented
60	#10597328	C₂²	1	4	yes	—
61	(C₂²⋊D₁₉)⋊C₄	C₂²	1	4	yes	complemented
62	C₂²⋊C₄×D₁₉	C₂²	1	4	yes	complemented
63	#10597324	C₂²	1	4	yes	complemented
64	#10597322	C₂²	1	4	yes	complemented
65	#10597322	C₂²	1	2	yes	complemented
66	#10597321	C₂²	1	1	yes	characteristic
67	#10597321	C₂²	1	2	yes	—
68	#10597321	C₂²	1	2	yes	complemented
69	#10597321	C₂²	1	4	yes	complemented
70	#10597321	C₂²	1	2	yes	complemented
71	#10597321	C₂²	1	4	yes	complemented
72	#10597320	C₂²	1	1	yes	characteristic
73	C₄×D₇₆	C₂²	1	1	yes	characteristic
74	C₄×D₇₆	C₂²	1	2	yes	complemented
75	C₄×D₇₆	C₂²	1	2	yes	complemented
76	C₄×D₇₆	C₂²	1	2	yes	complemented
77	#10597318	C₂²	1	2	yes	complemented
78	#10597318	C₂²	1	4	yes	complemented
79	#10597316	C₂²	1	1	yes	characteristic, complemented
80	#10597315	C₂²	1	1	yes	characteristic, complemented
81	C₄×Dic₃₈	C₂²	1	2	yes	complemented
82	C₄×Dic₃₈	C₂²	1	1	yes	characteristic, complemented
83	C₂³×D₁₉	C₂³	1	4	yes	—
84	#41×C₁₉	—	2	4	no	—
85	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
86	C₂×D₄×C₁₉	C₂³	1	2	yes	—
87	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
88	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
89	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
90	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
91	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
92	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
93	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
94	C₂×C₂²⋊D₁₉	C₂³	1	4	yes	—
95	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
96	C₂×C₂²⋊D₁₉	C₂³	1	4	yes	—
97	C₂²×Dic₁₉	C₂³	1	4	yes	—
98	D₄×D₁₉	—	2	8	no	—
99	#64541	—	4	4	no	—
100	C₂×D₇₆	—	4	4	no	—
101	C₂×D₇₆	C₂³	1	1	yes	characteristic
102	C₂×D₇₆	C₂³	1	2	yes	—
103	C₂×D₇₆	C₂³	1	2	yes	—
104	C₂×D₇₆	C₂³	1	2	yes	—
105	C₂×D₇₆	C₂³	1	4	yes	—
106	C₂×C₄×D₁₉	C₂³	1	2	yes	—
107	C₂×C₄×D₁₉	C₂³	1	4	yes	—
108	C₂×C₄×D₁₉	C₂³	1	4	yes	—
109	C₂×Dic₃₈	—	4	4	no	—
110	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
111	C₂×Dic₃₈	C₂³	1	2	yes	—
112	C₂×Dic₃₈	C₂³	1	4	yes	—
113	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
114	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
115	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
116	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
117	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
118	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
119	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
120	C₄²×C₁₉	C₂³	1	1	yes	characteristic
121	C₄²×C₁₉	C₂³	1	2	yes	—
122	C₄²×C₁₉	C₂³	1	1	yes	characteristic
123	C₄²×C₁₉	C₂³	1	1	yes	characteristic
124	C₄²×C₁₉	C₂³	1	1	yes	characteristic
125	C₄²×C₁₉	C₂³	1	2	yes	—
126	C₄²×C₁₉	C₂³	1	2	yes	—
127	C₂²⋊Dic₁₉	C₂³	1	4	yes	—
128	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
129	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
130	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
131	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
132	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
133	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
134	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
135	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
136	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
137	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
138	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
139	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
140	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
141	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
142	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
143	C₄⋊Dic₁₉	C₂³	1	2	yes	—
144	C₄⋊Dic₁₉	C₂³	1	2	yes	—
145	Dic₁₉⋊C₄	C₂³	1	4	yes	—
146	Dic₁₉⋊C₄	C₂³	1	2	yes	—
147	Dic₁₉⋊C₄	C₂³	1	2	yes	—
148	Dic₁₉⋊C₄	C₂³	1	2	yes	—
149	Dic₁₉⋊C₄	C₂³	1	4	yes	—
150	Dic₁₉⋊C₄	C₂³	1	2	yes	—
151	C₄×Dic₁₉	C₂³	1	2	yes	—
152	C₄×Dic₁₉	C₂³	1	4	yes	—
153	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
154	C₂³×C₁₉	C₂⁴	1	2	yes	—
155	C₂²×D₁₉	—	2	8	no	—
156	C₂²×D₁₉	—	4	4	no	—
157	C₂²×D₁₉	—	4	4	no	—
158	C₂²×D₁₉	C₂⁴	1	2	yes	—
159	C₂²×D₁₉	C₂⁴	1	4	yes	—
160	Q₈×C₁₉	—	2	2	no	—
161	D₄×C₁₉	—	2	4	no	—
162	D₄×C₁₉	#41	1	4	yes	complemented
163	C₂×C₄×C₁₉	—	2	4	no	—
164	C₂×C₄×C₁₉	—	2	2	no	—
165	C₂×C₄×C₁₉	—	2	4	no	—
166	C₂×C₄×C₁₉	—	2	2	no	—
167	C₂×C₄×C₁₉	—	4	2	no	—
168	C₂×C₄×C₁₉	—	4	1	no	—
169	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
170	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
171	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
172	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
173	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
174	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
175	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
176	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
177	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
178	C₂²⋊D₁₉	—	2	8	no	—
179	C₂²⋊D₁₉	—	4	4	no	—
180	C₂²⋊D₁₉	—	4	2	no	—
181	C₂×Dic₁₉	—	4	4	no	—
182	C₂×Dic₁₉	C₂⁴	1	2	yes	—
183	C₂×Dic₁₉	C₂⁴	1	2	yes	—
184	C₂×Dic₁₉	C₂⁴	1	4	yes	—
185	C₂×Dic₁₉	C₂⁴	1	2	yes	—
186	D₇₆	—	2	4	no	—
187	D₇₆	—	2	2	no	—
188	D₇₆	—	2	4	no	—
189	D₇₆	—	4	4	no	—
190	D₇₆	—	4	2	no	—
191	C₄×D₁₉	—	2	4	no	—
192	C₄×D₁₉	—	4	4	no	—
193	C₄×D₁₉	—	4	4	no	—
194	Dic₃₈	—	2	2	no	—
195	Dic₃₈	—	2	4	no	—
196	Dic₃₈	—	4	4	no	—
197	#3514	—	19	1	no	maximal, Sylow
198	C₂²×C₁₉	—	2	2	no	—
199	C₂²×C₁₉	—	2	2	no	—
200	C₂²×C₁₉	—	2	1	no	—
201	C₂²×C₁₉	—	2	1	no	—
202	C₂²×C₁₉	—	2	1	no	—
203	C₂²×C₁₉	C₂×#41	1	4	yes	—
204	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
205	C₂×D₁₉	—	2	2	no	—
206	C₂×D₁₉	—	2	4	no	—
207	C₂×D₁₉	—	2	4	no	—
208	C₂×D₁₉	—	2	2	no	—
209	C₂×D₁₉	—	2	4	no	—
210	C₂×D₁₉	—	2	2	no	—
211	C₂×D₁₉	—	8	8	no	—
212	C₄×C₁₉	—	2	1	no	—
213	C₄×C₁₉	—	2	2	no	—
214	C₄×C₁₉	—	2	2	no	—
215	C₄×C₁₉	—	2	1	no	—
216	C₄×C₁₉	—	2	2	no	—
217	C₄×C₁₉	—	2	1	no	—
218	C₄×C₁₉	—	2	1	no	—
219	C₄×C₁₉	C₂×#41	1	2	yes	—
220	C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
221	Dic₁₉	—	2	2	no	—
222	Dic₁₉	—	2	2	no	—
223	Dic₁₉	—	2	4	no	—
224	Dic₁₉	—	2	2	no	—
225	#559	—	19	1	no	—
226	#556	—	19	1	no	—
227	#555	—	19	2	no	—
228	#551	—	19	4	no	—
229	D₄×Q₈	—	19	1	no	—
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	D₁₉	1	1	yes	characteristic, complemented
242	C₂×C₁₉	—	2	4	no	—
243	C₂×C₁₉	—	4	1	no	—
244	C₂×C₁₉	C₂²×#41	1	1	yes	characteristic
245	C₂×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
246	C₂×C₁₉	#585	1	1	yes	characteristic
247	D₁₉	—	4	4	no	—
248	D₁₉	—	4	2	no	—
249	C₂×#41	—	19	2	no	—
250	C₂×#41	C₂×D₁₉	1	1	yes	characteristic
251	C₂²×Q₈	—	19	2	no	—
252	C₂²×D₄	—	19	2	no	—
253	C₂²×D₄	—	19	2	no	—
254	C₄⋊Q₈	—	19	2	no	—
255	C₄⋊Q₈	—	19	1	no	—
256	#127	—	19	1	no	—
257	#126	—	19	4	no	—
258	#126	—	19	4	no	—
259	#126	—	19	2	no	—
260	#125	—	19	1	no	—
261	#124	—	19	2	no	—
262	#124	—	19	4	no	—
263	#124	—	19	1	no	—
264	#124	—	19	2	no	—
265	#124	—	19	4	no	—
266	#124	—	19	2	no	—
267	#124	—	19	2	no	—
268	#124	—	19	4	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	2	no	—
274	C₂²⋊Q₈	—	19	2	no	—
275	C₂²⋊Q₈	—	19	1	no	—
276	C₂²⋊Q₈	—	19	4	no	—
277	C₂²⋊Q₈	—	19	4	no	—
278	#121	—	19	4	no	—
279	#121	—	19	2	no	—
280	#121	—	19	1	no	—
281	#121	—	19	2	no	—
282	#121	—	19	2	no	—
283	#121	—	19	2	no	—
284	#121	—	19	4	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	C₂×D₁₉	1	1	yes	characteristic, complemented
290	C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
291	C₄×D₄	—	19	2	no	—
292	C₄×D₄	—	19	4	no	—
293	C₄×D₄	—	19	2	no	—
294	C₄×D₄	—	19	2	no	—
295	C₄×D₄	—	19	4	no	—
296	C₄×D₄	—	19	2	no	—
297	C₄×D₄	—	19	1	no	—
298	C₄×D₄	—	19	2	no	—
299	C₄×D₄	—	19	2	no	—
300	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
301	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
302	C₄×D₄	C₂×D₁₉	1	2	yes	complemented
303	C₄×D₄	C₂×D₁₉	1	2	yes	complemented
304	#117	—	19	2	no	—
305	#117	—	19	2	no	—
306	#117	—	19	4	no	—
307	#117	C₂×D₁₉	1	2	yes	complemented
308	#117	C₂×D₁₉	1	1	yes	characteristic, complemented
309	C₂×C₂²⋊C₄	—	19	4	no	—
310	C₂×C₂²⋊C₄	—	19	4	no	—
311	C₂×C₂²⋊C₄	—	19	4	no	—
312	C₂×C₄²	C₂×D₁₉	1	2	yes	complemented
313	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic, complemented
314	C₁₉	#3514	1	1	yes	characteristic, complemented, Sylow
315	C₂⁴	—	19	4	no	—
316	#41	—	2	4	no	—
317	#41	—	76	4	no	—
318	C₂×Q₈	—	19	1	no	—
319	C₂×Q₈	—	19	2	no	—
320	C₂×Q₈	—	19	4	no	—
321	C₂×Q₈	—	76	4	no	—
322	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
323	C₂×D₄	—	19	4	no	—
324	C₂×D₄	—	19	2	no	—
325	C₂×D₄	—	19	4	no	—
326	C₂×D₄	—	19	2	no	—
327	C₂×D₄	—	19	1	no	—
328	C₂×D₄	—	19	2	no	—
329	C₂×D₄	—	19	2	no	—
330	C₂×D₄	—	19	4	no	—
331	C₂×D₄	—	38	8	no	—
332	C₂×D₄	—	76	4	no	—
333	C₂×D₄	C₂²×D₁₉	1	2	yes	—
334	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
335	C₂²×C₄	—	19	4	no	—
336	C₂²×C₄	—	19	2	no	—
337	C₂²×C₄	—	19	4	no	—
338	C₂²×C₄	—	19	4	no	—
339	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
340	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
341	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
342	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
343	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
344	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
345	C₄⋊C₄	—	19	2	no	—
346	C₄⋊C₄	—	19	2	no	—
347	C₄⋊C₄	—	19	2	no	—
348	C₄⋊C₄	—	19	4	no	—
349	C₄⋊C₄	—	19	4	no	—
350	C₄⋊C₄	—	19	2	no	—
351	C₄⋊C₄	—	19	2	no	—
352	C₄⋊C₄	—	19	1	no	—
353	C₄⋊C₄	—	19	1	no	—
354	C₄⋊C₄	—	19	2	no	—
355	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
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	4	no	—
360	C₂²⋊C₄	—	19	2	no	—
361	C₂²⋊C₄	—	19	2	no	—
362	C₂²⋊C₄	—	19	4	no	—
363	C₂²⋊C₄	—	19	2	no	—
364	C₂²⋊C₄	—	19	2	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	4	no	—
370	C₂²⋊C₄	—	19	4	no	—
371	C₂²⋊C₄	—	19	2	no	—
372	C₂²⋊C₄	—	19	4	no	—
373	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
374	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
375	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
376	C₄²	—	19	4	no	—
377	C₄²	—	19	2	no	—
378	C₄²	C₂²×D₁₉	1	1	yes	characteristic
379	C₄²	C₂²×D₁₉	1	2	yes	—
380	C₄²	C₂²×D₁₉	1	1	yes	characteristic
381	C₄²	C₂²×D₁₉	1	1	yes	characteristic
382	C₄²	C₂²×D₁₉	1	1	yes	characteristic
383	C₄²	C₂²×D₁₉	1	2	yes	—
384	C₄²	C₂²×D₁₉	1	2	yes	—
385	C₂³	—	19	2	no	—
386	C₂³	—	19	4	no	—
387	C₂³	—	38	8	no	—
388	C₂³	—	76	4	no	—
389	C₂³	—	76	4	no	—
390	C₂³	C₂³×D₁₉	1	1	yes	characteristic
391	C₂³	C₂³×D₁₉	1	2	yes	—
392	Q₈	—	2	2	no	—
393	Q₈	—	38	2	no	—
394	Q₈	—	38	4	no	—
395	Q₈	—	76	4	no	—
396	D₄	—	2	4	no	—
397	D₄	—	38	8	no	—
398	D₄	—	38	4	no	—
399	D₄	—	38	2	no	—
400	D₄	—	38	4	no	—
401	D₄	—	76	4	no	—
402	D₄	—	76	2	no	—
403	D₄	—	76	4	no	—
404	D₄	—	76	2	no	—
405	D₄	#64541	1	4	yes	complemented
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	19	2	no	—
413	C₂×C₄	—	19	2	no	—
414	C₂×C₄	—	19	2	no	—
415	C₂×C₄	—	19	4	no	—
416	C₂×C₄	—	38	4	no	—
417	C₂×C₄	—	76	4	no	—
418	C₂×C₄	—	76	4	no	—
419	C₂×C₄	—	76	4	no	—
420	C₂×C₄	C₂³×D₁₉	1	2	yes	—
421	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
422	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
423	C₂×C₄	C₂³×D₁₉	1	2	yes	—
424	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
425	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
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	—	2	1	no	—
432	C₂²	—	2	1	no	—
433	C₂²	—	2	1	no	—
434	C₂²	—	38	2	no	—
435	C₂²	—	38	4	no	—
436	C₂²	—	38	4	no	—
437	C₂²	—	38	2	no	—
438	C₂²	—	38	4	no	—
439	C₂²	—	38	2	no	—
440	C₂²	—	152	8	no	—
441	C₂²	C₂×#64541	1	4	yes	—
442	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
443	C₄	—	2	1	no	—
444	C₄	—	2	2	no	—
445	C₄	—	2	1	no	—
446	C₄	—	2	2	no	—
447	C₄	—	2	1	no	—
448	C₄	—	2	2	no	—
449	C₄	—	2	1	no	—
450	C₄	—	38	2	no	—
451	C₄	—	38	4	no	—
452	C₄	—	38	2	no	—
453	C₄	—	38	2	no	—
454	C₄	C₂×#64541	1	2	yes	—
455	C₄	#10597435	1	2	yes	—
456	C₂	—	2	4	no	—
457	C₂	—	4	1	no	—
458	C₂	—	76	2	no	—
459	C₂	—	76	4	no	—
460	C₂	C₂²×#64541	1	1	yes	characteristic
461	C₂	C₂×#10597435	1	1	yes	characteristic
462	C₂	#11927380	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Fitting	C₄×#41×C₁₉	C₂
hypercenter	C₄×#41	D₁₉
hypocenter	C₁₉	#3514
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄×#41

Complements

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

N	H ≅ G/N	type
1. #11927279	C₂	semidirect
2. #11927267	C₂	semidirect
3. #11927257	C₂	semidirect
4. #11927218	C₂	semidirect
5. D₄×Dic₃₈	C₂	semidirect
6. #11927203	C₂	semidirect
7. #11927190	C₂	semidirect
8. #11927182	C₂	semidirect
9. D₄×D₇₆	C₂	semidirect
10. #11927166	C₂	semidirect
11. #11927127	C₂	semidirect
12. #11927094	C₂	semidirect
13. #11927078	C₂	semidirect
14. #11927078	C₂	semidirect
15. C₂×#10597321	C₂	semidirect
16. #11927016	C₂	semidirect
17. C₄×#41×C₁₉	C₂	semidirect
20. C₂×#64541	C₂²	semidirect
22. C₂²×Dic₃₈	C₂²	semidirect
23. C₄×Q₈×C₁₉	C₂²	semidirect
24. C₄×Q₈×C₁₉	C₂²	semidirect
27. C₄×D₄×C₁₉	C₂²	semidirect
28. C₄×D₄×C₁₉	C₂²	semidirect
29. C₁₉×#117	C₂²	semidirect
30. C₁₉×#117	C₂²	semidirect
31. C₂×C₄²×C₁₉	C₂²	semidirect
32. C₂×C₄²×C₁₉	C₂²	semidirect
33. #10597393	C₂²	semidirect
34. #10597392	C₂²	semidirect
35. #10597385	C₂²	semidirect
36. #10597383	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. C₂×(C₂×D₁₉)⋊C₄	C₂²	semidirect
47. C₂×(C₂×D₁₉)⋊C₄	C₂²	semidirect
48. #10597370	C₂²	semidirect
49. #10597370	C₂²	semidirect
50. #10597344	C₂²	semidirect
51. #10597342	C₂²	semidirect
53. #10597340	C₂²	semidirect
54. #10597340	C₂²	semidirect
55. #10597339	C₂²	semidirect
56. #10597338	C₂²	semidirect
57. #10597334	C₂²	semidirect
58. #10597331	C₂²	semidirect
59. #10597330	C₂²	semidirect
61. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
62. C₂²⋊C₄×D₁₉	C₂²	semidirect
63. #10597324	C₂²	semidirect
64. #10597322	C₂²	semidirect
65. #10597322	C₂²	semidirect
68. #10597321	C₂²	semidirect
69. #10597321	C₂²	semidirect
70. #10597321	C₂²	semidirect
71. #10597321	C₂²	semidirect
74. C₄×D₇₆	C₂²	semidirect
75. C₄×D₇₆	C₂²	semidirect
76. C₄×D₇₆	C₂²	semidirect
77. #10597318	C₂²	semidirect
78. #10597318	C₂²	semidirect
79. #10597316	C₂²	semidirect
80. #10597315	C₂²	semidirect
81. C₄×Dic₃₈	C₂²	semidirect
82. C₄×Dic₃₈	C₂²	semidirect
162. D₄×C₁₉	#41	semidirect
241. C₄×#41	D₁₉	semidirect
289. C₄×Q₈	C₂×D₁₉	semidirect
290. C₄×Q₈	C₂×D₁₉	semidirect
302. C₄×D₄	C₂×D₁₉	semidirect
303. C₄×D₄	C₂×D₁₉	semidirect
307. #117	C₂×D₁₉	semidirect
308. #117	C₂×D₁₉	semidirect
312. C₂×C₄²	C₂×D₁₉	semidirect
313. C₂×C₄²	C₂×D₁₉	semidirect
314. C₁₉	#3514	semidirect
405. D₄	#64541	semidirect

Maximal subgroups

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

subgroup	index
#11927279	2
#11927267	2
#11927257	2
#11927218	2
D₄×Dic₃₈	2
#11927203	2
#11927190	2
#11927182	2
D₄×D₇₆	2
#11927166	2
#11927127	2
#11927094	2
#11927078	2
C₂×#10597321	2
#11927016	2
C₄×#41×C₁₉	2
#3514	19