Subgroups — #16792678

Order 3328.

836 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13131514	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#6118	C₂	1	1	yes	maximal, characteristic
3	#13130054	C₂	1	4	yes	maximal, complemented
4	#13130047	C₂	1	2	yes	maximal, complemented
5	#13130046	C₂	1	2	yes	maximal, complemented
6	#13130037	C₂	1	2	yes	maximal, complemented
7	C₈×#6118	C₂	1	2	yes	maximal, complemented
8	D₁₃×#431	C₂	1	1	yes	maximal, characteristic
9	C₂²×#6118	C₄	1	2	yes	—
10	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
11	#11719129	C₄	1	2	yes	—
12	#11719126	C₄	1	2	yes	—
13	C₄×#6122	C₂²	1	2	yes	—
14	C₂×#88110	C₄	1	2	yes	—
15	C₂×C₄×#1057	C₂²	1	2	yes	—
16	#11719055	C₄	1	2	yes	—
17	#11719054	C₄	1	2	yes	—
18	#11719051	C₂²	1	2	yes	—
19	#11719049	C₂²	1	2	yes	—
20	C₄×#6118	C₄	1	2	yes	—
21	C₄×#6118	C₄	1	2	yes	—
22	C₄×#6118	C₂²	1	1	yes	characteristic
23	C₄×#6118	C₂²	1	1	yes	characteristic
24	C₄×#6118	C₂²	1	2	yes	—
25	C₁₃×#431	C₄	1	1	yes	characteristic
26	#11718586	C₄	1	1	yes	characteristic
27	#11718494	C₂²	1	2	yes	—
28	D₁₃×C₄⋊C₈	C₄	1	2	yes	—
29	D₁₃×C₂²⋊C₈	C₄	1	1	yes	characteristic
30	D₁₃×C₂²⋊C₈	C₄	1	1	yes	characteristic
31	#11718379	C₂²	1	1	yes	characteristic
32	#11718379	C₂²	1	1	yes	characteristic
33	#11718346	C₄	1	2	yes	—
34	C₄×C₈×D₁₃	C₂²	1	2	yes	—
35	#1057⋊C₈	C₂²	1	4	yes	complemented
36	#1057⋊C₈	C₂²	1	4	yes	complemented
37	#11718251	C₂²	1	4	yes	complemented
38	C₈×#1057	C₂²	1	4	yes	complemented
39	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
42	C₂×#6122	C₂×C₄	1	4	yes	—
43	C₂²×#1057	C₂×C₄	1	4	yes	—
44	C₂×#6118	—	2	8	no	—
45	C₂×#6118	C₂×C₄	1	2	yes	—
46	C₂×#6118	C₂×C₄	1	4	yes	—
47	C₂×#6118	C₂×C₄	1	2	yes	—
48	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
52	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
53	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
54	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
55	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
56	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
57	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
58	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
59	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
60	C₄²×D₁₃	C₂³	1	1	yes	characteristic
61	C₄²×D₁₃	C₂³	1	1	yes	characteristic
62	#88112	C₂×C₄	1	4	yes	—
63	#88111	C₂×C₄	1	4	yes	—
64	#88111	C₂×C₄	1	4	yes	—
65	#88110	C₂×C₄	1	2	yes	—
66	#88110	C₂×C₄	1	4	yes	—
67	#88110	C₂×C₄	1	2	yes	—
68	#88110	C₂×C₄	1	4	yes	—
69	C₄⋊#1057	C₂×C₄	1	4	yes	—
70	C₄×#1057	C₂×C₄	1	4	yes	—
71	C₄×#1057	C₂³	1	2	yes	—
72	C₄×#1057	C₂³	1	4	yes	—
73	C₄×#1057	C₂³	1	2	yes	—
74	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
75	C₁₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
76	C₁₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
77	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
78	C₂²⋊#1055	C₂×C₄	1	1	yes	characteristic
79	C₂²⋊#1055	C₂×C₄	1	1	yes	characteristic
80	#88060	C₂×C₄	1	2	yes	—
81	#88060	C₂×C₄	1	2	yes	—
82	#88054	C₂×C₄	1	2	yes	—
83	#88054	C₂×C₄	1	2	yes	—
84	C₈×Dic₁₃	C₂³	1	2	yes	—
85	C₈×Dic₁₃	C₂³	1	2	yes	—
86	C₄⋊#1055	C₂×C₄	1	2	yes	—
87	C₄×#1055	C₂×C₄	1	2	yes	—
88	#17327	—	13	1	no	maximal, Sylow
89	C₂³×D₁₃	C₄²	1	1	yes	characteristic
90	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
91	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
92	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
93	C₂²×Dic₁₃	C₄²	1	1	yes	characteristic
94	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
95	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
96	C₂×C₄×D₁₃	—	2	4	no	—
97	C₂×C₄×D₁₃	—	2	4	no	—
98	C₂×C₄×D₁₃	—	4	2	no	—
99	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
100	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
101	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
102	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
103	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
104	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
105	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
111	#6122	—	2	8	no	—
112	C₂×#1057	—	2	8	no	—
113	C₂×#1057	C₂²×C₄	1	4	yes	—
114	C₂×#1057	C₂²×C₄	1	8	yes	—
115	C₂×#1057	C₂²×C₄	1	4	yes	—
116	#6118	—	2	4	no	—
117	#6118	—	2	8	no	—
118	#6118	M₁₆	1	8	yes	complemented
119	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
120	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
121	C₄²×C₁₃	C₄²	1	1	yes	characteristic
122	C₄²×C₁₃	C₄²	1	1	yes	characteristic
123	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
124	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
125	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
126	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
127	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
128	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
129	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
130	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
131	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
132	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
133	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
134	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
135	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
136	C₄×Dic₁₃	C₂⁴	1	1	yes	characteristic
137	C₂×#1055	C₂²×C₄	1	2	yes	—
138	C₂×#1055	C₂²×C₄	1	2	yes	—
139	C₈×D₁₃	—	4	2	no	—
140	C₈×D₁₃	—	4	2	no	—
141	#2920	—	13	1	no	—
142	C₂×#431	—	13	1	no	—
143	C₂×C₄×M₁₆	—	13	1	no	—
144	#1453	—	13	4	no	—
145	#1451	—	13	2	no	—
146	#1451	—	13	2	no	—
147	C₈×M₁₆	—	13	2	no	—
148	C₈×M₁₆	—	13	2	no	—
149	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
150	C₂²×D₁₃	—	2	2	no	—
151	C₂²×D₁₃	—	2	2	no	—
152	C₂²×D₁₃	—	4	1	no	—
153	C₂²×D₁₃	C₂×C₄²	1	1	yes	characteristic
154	C₂²×D₁₃	C₂×C₄²	1	1	yes	characteristic
155	C₂×C₄×C₁₃	—	2	2	no	—
156	C₂×C₄×C₁₃	—	2	2	no	—
157	C₂×C₄×C₁₃	—	2	2	no	—
158	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
159	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
160	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
161	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
162	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
163	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
164	C₂×Dic₁₃	—	2	2	no	—
165	C₂×Dic₁₃	—	4	1	no	—
166	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
167	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
168	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
169	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
170	C₂×Dic₁₃	#131	1	4	yes	—
171	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
172	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
173	C₄×D₁₃	—	2	2	no	—
174	C₄×D₁₃	—	2	2	no	—
175	C₄×D₁₃	—	2	2	no	—
176	C₄×D₁₃	—	2	2	no	—
177	C₄×D₁₃	—	2	2	no	—
178	C₄×D₁₃	—	2	2	no	—
179	C₄×D₁₃	—	2	2	no	—
180	C₄×D₁₃	—	2	2	no	—
181	C₄×D₁₃	—	2	2	no	—
182	C₄×D₁₃	—	4	1	no	—
183	C₄×D₁₃	—	4	1	no	—
184	C₄×D₁₃	C₂×M₁₆	1	4	yes	—
185	#1057	—	2	4	no	—
186	#1057	—	2	8	no	—
187	#1057	C₂×M₁₆	1	8	yes	—
188	C₈×C₁₃	—	2	2	no	—
189	C₈×C₁₃	—	2	2	no	—
190	#1055	—	2	2	no	—
191	#1055	—	2	2	no	—
192	C₂²×M₁₆	—	13	2	no	—
193	C₂²×C₄²	—	13	1	no	—
194	#432	—	13	2	no	—
195	#432	—	13	2	no	—
196	#431	—	13	2	no	—
197	#431	—	13	2	no	—
198	#431	—	13	1	no	—
199	#431	—	13	2	no	—
200	#431	—	13	1	no	—
201	#431	—	13	1	no	—
202	#431	—	13	2	no	—
203	#431	#261	1	1	yes	characteristic
204	#423	—	13	2	no	—
205	C₂×C₄⋊C₈	—	13	2	no	—
206	#407	—	13	2	no	—
207	C₂×C₂²⋊C₈	—	13	1	no	—
208	C₂×C₂²⋊C₈	—	13	1	no	—
209	C₄×M₁₆	—	13	2	no	—
210	C₄×M₁₆	—	13	2	no	—
211	C₄×M₁₆	—	13	1	no	—
212	C₄×M₁₆	—	13	1	no	—
213	C₄×M₁₆	—	13	2	no	—
214	C₄×M₁₆	—	13	2	no	—
215	C₂×#97	—	13	2	no	—
216	C₂×C₄×C₈	—	13	2	no	—
217	C₂×C₄×C₈	—	13	2	no	—
218	#322	—	13	4	no	—
219	#322	—	13	4	no	—
220	#322	—	13	4	no	—
221	C₈²	—	13	4	no	—
222	C₂²×C₁₃	—	2	1	no	—
223	C₂²×C₁₃	—	2	1	no	—
224	C₂²×C₁₃	#405	1	2	yes	—
225	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
226	C₂×D₁₃	—	2	1	no	—
227	C₂×D₁₃	—	2	1	no	—
228	C₂×D₁₃	—	2	1	no	—
229	C₂×D₁₃	—	2	1	no	—
230	C₂×D₁₃	—	2	1	no	—
231	C₂×D₁₃	—	4	4	no	—
232	C₂×D₁₃	C₄×M₁₆	1	2	yes	—
233	C₄×C₁₃	—	2	1	no	—
234	C₄×C₁₃	—	2	1	no	—
235	C₄×C₁₃	—	2	1	no	—
236	C₄×C₁₃	—	2	1	no	—
237	C₄×C₁₃	C₄×M₁₆	1	2	yes	—
238	C₄×C₁₃	#568	1	2	yes	—
239	Dic₁₃	—	2	1	no	—
240	Dic₁₃	—	2	1	no	—
241	Dic₁₃	—	2	1	no	—
242	Dic₁₃	#405	1	2	yes	—
243	Dic₁₃	C₂²×M₁₆	1	2	yes	—
244	Dic₁₃	C₂×#131	1	2	yes	—
245	C₂³×C₄	—	13	1	no	—
246	C₂³×C₄	—	13	1	no	—
247	C₂³×C₄	—	13	1	no	—
248	C₂×M₁₆	—	13	2	no	—
249	C₂×M₁₆	—	13	4	no	—
250	C₂×M₁₆	—	13	2	no	—
251	C₂×M₁₆	—	13	4	no	—
252	C₂×M₁₆	—	26	8	no	—
253	C₂²×C₈	—	13	4	no	—
254	C₂²×C₈	—	13	2	no	—
255	C₂²×C₈	—	13	2	no	—
256	C₂×C₄²	—	13	1	no	—
257	C₂×C₄²	—	13	1	no	—
258	C₂×C₄²	—	13	1	no	—
259	C₂×C₄²	—	13	1	no	—
260	C₂×C₄²	—	13	1	no	—
261	C₂×C₄²	—	13	1	no	—
262	C₂×C₄²	—	13	1	no	—
263	C₂×C₄²	—	13	1	no	—
264	C₂×C₄²	—	13	1	no	—
265	C₂×C₄²	—	13	1	no	—
266	C₂×C₄²	—	13	1	no	—
267	C₂×C₄²	C₂×#261	1	1	yes	characteristic
268	C₄⋊C₈	—	13	4	no	—
269	C₄⋊C₈	—	13	4	no	—
270	C₄⋊C₈	—	13	2	no	—
271	C₄⋊C₈	—	13	2	no	—
272	C₄⋊C₈	—	13	2	no	—
273	C₄⋊C₈	C₂×#261	1	2	yes	—
274	C₂²⋊C₈	—	13	4	no	—
275	C₂²⋊C₈	—	13	4	no	—
276	C₂²⋊C₈	—	13	1	no	—
277	C₂²⋊C₈	—	13	1	no	—
278	C₂²⋊C₈	—	13	2	no	—
279	C₂²⋊C₈	—	13	2	no	—
280	C₂²⋊C₈	C₂×#261	1	1	yes	characteristic
281	C₂²⋊C₈	C₂×#261	1	1	yes	characteristic
282	#97	—	13	2	no	—
283	#97	—	13	4	no	—
284	#97	—	13	2	no	—
285	#97	—	13	4	no	—
286	C₄×C₈	—	13	4	no	—
287	C₄×C₈	—	13	2	no	—
288	C₄×C₈	—	13	4	no	—
289	C₄×C₈	—	13	2	no	—
290	C₄×C₈	—	13	2	no	—
291	C₄×C₈	—	13	2	no	—
292	C₄×C₈	—	13	2	no	—
293	C₄×C₈	C₂×#261	1	2	yes	—
294	C₂×C₁₃	—	2	2	no	—
295	C₂×C₁₃	C₂×C₄×M₁₆	1	1	yes	characteristic
296	C₂×C₁₃	C₂×#405	1	1	yes	characteristic
297	C₂×C₁₃	#2873	1	1	yes	characteristic
298	D₁₃	—	2	2	no	—
299	D₁₃	—	4	1	no	—
300	C₂⁴	—	13	1	no	—
301	C₂²×C₄	—	13	1	no	—
302	C₂²×C₄	—	13	1	no	—
303	C₂²×C₄	—	13	1	no	—
304	C₂²×C₄	—	13	1	no	—
305	C₂²×C₄	—	13	1	no	—
306	C₂²×C₄	—	13	1	no	—
307	C₂²×C₄	—	13	1	no	—
308	C₂²×C₄	—	13	1	no	—
309	C₂²×C₄	—	13	1	no	—
310	C₂²×C₄	—	13	1	no	—
311	C₂²×C₄	—	13	1	no	—
312	C₂²×C₄	—	13	1	no	—
313	C₂²×C₄	—	13	1	no	—
314	C₂²×C₄	—	13	1	no	—
315	C₂²×C₄	—	13	1	no	—
316	C₂²×C₄	—	26	4	no	—
317	C₂²×C₄	—	26	4	no	—
318	C₂²×C₄	—	52	2	no	—
319	C₂²×C₄	C₄×#261	1	1	yes	characteristic
320	C₂²×C₄	C₄×#261	1	1	yes	characteristic
321	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
322	M₁₆	—	13	8	no	—
323	M₁₆	—	26	8	no	—
324	M₁₆	—	26	4	no	—
325	M₁₆	—	26	8	no	—
326	C₂×C₈	—	13	4	no	—
327	C₂×C₈	—	13	4	no	—
328	C₂×C₈	—	13	8	no	—
329	C₂×C₈	—	13	2	no	—
330	C₂×C₈	—	13	2	no	—
331	C₂×C₈	—	26	8	no	—
332	C₂×C₈	—	52	2	no	—
333	C₂×C₈	—	52	2	no	—
334	C₂×C₈	C₂²×#261	1	2	yes	—
335	C₂×C₈	C₂²×#261	1	2	yes	—
336	C₄²	—	13	1	no	—
337	C₄²	—	13	1	no	—
338	C₄²	—	13	1	no	—
339	C₄²	—	13	1	no	—
340	C₄²	—	13	1	no	—
341	C₄²	—	13	1	no	—
342	C₄²	—	13	1	no	—
343	C₄²	—	13	1	no	—
344	C₄²	—	13	1	no	—
345	C₄²	—	13	1	no	—
346	C₄²	—	13	1	no	—
347	C₄²	—	13	1	no	—
348	C₄²	C₄×#261	1	1	yes	characteristic
349	C₄²	C₄×#261	1	1	yes	characteristic
350	C₄²	C₂²×#261	1	1	yes	characteristic
351	C₄²	C₂²×#261	1	1	yes	characteristic
352	C₁₃	#17327	1	1	yes	characteristic, complemented, Sylow
353	C₂³	—	13	1	no	—
354	C₂³	—	13	1	no	—
355	C₂³	—	26	2	no	—
356	C₂³	—	26	2	no	—
357	C₂³	—	52	1	no	—
358	C₂³	C₂×C₄×#261	1	1	yes	characteristic
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	13	4	no	—
363	C₂×C₄	—	13	1	no	—
364	C₂×C₄	—	13	1	no	—
365	C₂×C₄	—	13	1	no	—
366	C₂×C₄	—	13	4	no	—
367	C₂×C₄	—	13	1	no	—
368	C₂×C₄	—	13	1	no	—
369	C₂×C₄	—	13	1	no	—
370	C₂×C₄	—	26	2	no	—
371	C₂×C₄	—	26	2	no	—
372	C₂×C₄	—	26	2	no	—
373	C₂×C₄	—	26	2	no	—
374	C₂×C₄	—	26	2	no	—
375	C₂×C₄	—	26	2	no	—
376	C₂×C₄	—	26	2	no	—
377	C₂×C₄	—	26	2	no	—
378	C₂×C₄	—	26	2	no	—
379	C₂×C₄	—	26	2	no	—
380	C₂×C₄	—	52	1	no	—
381	C₂×C₄	—	52	1	no	—
382	C₂×C₄	—	52	1	no	—
383	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
384	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
385	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
386	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
387	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
388	C₂×C₄	C₂³×#261	1	1	yes	characteristic
389	C₈	—	2	2	no	—
390	C₈	—	2	2	no	—
391	C₈	—	13	8	no	—
392	C₈	—	26	4	no	—
393	C₈	—	26	8	no	—
394	C₈	—	26	2	no	—
395	C₈	—	26	2	no	—
396	C₂²	—	2	1	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	13	2	no	—
399	C₂²	—	26	1	no	—
400	C₂²	—	26	1	no	—
401	C₂²	—	26	1	no	—
402	C₂²	—	26	1	no	—
403	C₂²	—	26	1	no	—
404	C₂²	—	52	4	no	—
405	C₂²	#11719089	1	2	yes	—
406	C₂²	C₂²×C₄×#261	1	1	yes	characteristic
407	C₄	—	2	1	no	—
408	C₄	—	2	1	no	—
409	C₄	—	2	1	no	—
410	C₄	—	2	1	no	—
411	C₄	—	13	2	no	—
412	C₄	—	13	2	no	—
413	C₄	—	13	2	no	—
414	C₄	—	26	1	no	—
415	C₄	—	26	1	no	—
416	C₄	—	26	1	no	—
417	C₄	M₁₆×#261	1	2	yes	—
418	C₄	#11719629	1	2	yes	—
419	C₂	—	2	2	no	—
420	C₂	—	26	2	no	—
421	C₂	—	52	1	no	—
422	C₂	C₂×M₁₆×#261	1	1	yes	characteristic
423	C₂	C₂×#11719089	1	1	yes	characteristic
424	C₂	#13131401	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#261
commutator, socle	C₂²×C₁₃	C₂²×C₄²
Fitting	C₁₃×#431	C₄
prime radical	C₂³×D₁₃	C₄²
cosocle	C₄×Dic₁₃	C₂⁴
hypercenter	#431	#261
hypocenter	C₁₃	#17327
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ #431

Complements

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

N	H ≅ G/N	type
3. #13130054	C₂	semidirect
4. #13130047	C₂	semidirect
5. #13130046	C₂	semidirect
6. #13130037	C₂	semidirect
7. C₈×#6118	C₂	semidirect
35. #1057⋊C₈	C₂²	semidirect
36. #1057⋊C₈	C₂²	semidirect
37. #11718251	C₂²	semidirect
38. C₈×#1057	C₂²	semidirect
118. #6118	M₁₆	semidirect
352. C₁₃	#17327	semidirect

Maximal subgroups

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

subgroup	index
#13131514	2
C₂×C₄×#6118	2
#13130054	2
#13130047	2
#13130046	2
#13130037	2
C₈×#6118	2
D₁₃×#431	2
#17327	13