Subgroups — #16797259

Order 3328.

1002 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₃⋊#432	C₂	1	1	yes	maximal, characteristic
2	C₂×#11719057	C₂	1	1	yes	maximal, characteristic
3	#13130625	C₂	1	4	yes	maximal, complemented
4	#13130564	C₂	1	2	yes	maximal
5	C₂²⋊C₈×#261	C₂	1	2	yes	maximal
6	#13130554	C₂	1	2	yes	maximal, complemented
7	#13130492	C₂	1	2	yes	maximal, complemented
8	D₁₃×#431	C₂	1	1	yes	maximal, characteristic
9	C₂²×C₄×#261	C₂²	1	2	yes	—
10	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
11	C₂×(C₂×#261)⋊C₄	C₄	1	2	yes	—
12	C₂×(C₂×#261)⋊C₄	C₄	1	2	yes	—
13	#11719130	C₄	1	2	yes	complemented
14	#11719128	C₄	1	2	yes	complemented
15	D₁₃⋊(C₂²⋊C₈)	C₂²	1	2	yes	—
16	C₂×#88100	C₂²	1	4	yes	—
17	C₂×C₈×#261	C₂²	1	4	yes	—
18	#11719057	C₄	1	2	yes	—
19	#11719057	C₄	1	2	yes	—
20	#11719057	C₂²	1	1	yes	characteristic
21	#11719057	C₂²	1	2	yes	—
22	#11719057	C₂²	1	1	yes	characteristic
23	#11719055	C₄	1	2	yes	complemented
24	#11719054	C₄	1	2	yes	complemented
25	D₁₃⋊(C₄⋊C₈)	C₂²	1	2	yes	—
26	#11719047	C₂²	1	2	yes	—
27	C₁₃×#431	C₄	1	1	yes	characteristic, complemented
28	#11718586	C₄	1	1	yes	characteristic, complemented
29	#11718494	C₄	1	2	yes	complemented
30	D₁₃×C₄⋊C₈	C₂²	1	2	yes	—
31	D₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
32	D₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
33	#11718379	C₄	1	1	yes	characteristic, complemented
34	#11718379	C₄	1	1	yes	characteristic, complemented
35	#11718346	C₄	1	2	yes	complemented
36	C₄×C₈×D₁₃	C₂²	1	2	yes	—
37	(C₂×#261)⋊C₈	C₂²	1	4	yes	—
38	(C₂×#261)⋊C₈	C₂²	1	4	yes	—
39	C₂³×#261	C₂×C₄	1	4	yes	—
40	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
43	C₂×C₄×#261	—	2	8	no	—
44	C₂×C₄×#261	C₂×C₄	1	4	yes	—
45	C₂×C₄×#261	C₂³	1	2	yes	—
46	C₂×C₄×#261	C₂³	1	2	yes	—
47	C₂×D₁₃⋊C₈	C₂³	1	4	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	C₂×C₄	1	1	yes	characteristic
52	C₂×C₈×D₁₃	C₂³	1	2	yes	—
53	C₂×C₈×D₁₃	C₂³	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	C₂²⋊#1057	C₂×C₄	1	4	yes	—
63	(C₂×#261)⋊C₄	C₂×C₄	1	2	yes	—
64	(C₂×#261)⋊C₄	C₂×C₄	1	2	yes	—
65	(C₂×#261)⋊C₄	C₂×C₄	1	4	yes	—
66	(C₂×#261)⋊C₄	C₂×C₄	1	4	yes	—
67	(C₂×#261)⋊C₄	C₂×C₄	1	2	yes	—
68	(C₂×#261)⋊C₄	C₂×C₄	1	2	yes	—
69	#88112	C₂×C₄	1	4	yes	complemented
70	#88111	C₂×C₄	1	4	yes	—
71	#88110	C₂×C₄	1	4	yes	complemented
72	#88110	C₂×C₄	1	4	yes	complemented
73	C₄⋊#1057	C₂×C₄	1	4	yes	complemented
74	#88100	—	2	8	no	—
75	C₈×#261	—	2	8	no	—
76	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	complemented
77	C₁₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
78	C₁₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
79	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	complemented
80	C₂²⋊#1055	C₂×C₄	1	1	yes	characteristic
81	C₂²⋊#1055	C₂×C₄	1	1	yes	characteristic
82	#88060	C₂×C₄	1	2	yes	—
83	#88060	C₂×C₄	1	2	yes	—
84	#88054	C₂×C₄	1	2	yes	complemented
85	#88054	C₂×C₄	1	2	yes	complemented
86	C₈×Dic₁₃	C₂×C₄	1	2	yes	complemented
87	C₈×Dic₁₃	C₂×C₄	1	2	yes	complemented
88	C₄⋊#1055	C₂×C₄	1	2	yes	complemented
89	C₄×#1055	C₂×C₄	1	2	yes	complemented
90	#20469	—	13	1	no	maximal, Sylow
91	C₂³×D₁₃	C₂²×C₄	1	1	yes	characteristic
92	C₂²×#261	—	2	8	no	—
93	C₂²×#261	—	2	8	no	—
94	C₂²×#261	—	4	4	no	—
95	C₂²×#261	C₂²×C₄	1	4	yes	—
96	C₂²×#261	C₂²×C₄	1	4	yes	—
97	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
98	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
99	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
100	C₂²×Dic₁₃	C₄²	1	1	yes	characteristic
101	C₂²×Dic₁₃	C₄²	1	1	yes	characteristic
102	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₄×D₁₃	—	2	4	no	—
104	C₂×C₄×D₁₃	—	2	4	no	—
105	C₂×C₄×D₁₃	—	4	2	no	—
106	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
107	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
108	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
109	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
110	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
118	C₂×#1057	C₂²×C₄	1	8	yes	—
119	C₄×#261	—	2	8	no	—
120	C₄×#261	—	2	4	no	—
121	C₄×#261	#41	1	8	yes	—
122	D₁₃⋊C₈	—	2	4	no	—
123	D₁₃⋊C₈	—	2	4	no	—
124	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
125	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
126	C₄²×C₁₃	C₄²	1	1	yes	characteristic
127	C₄²×C₁₃	C₄²	1	1	yes	characteristic
128	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
129	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
130	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
131	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
132	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
133	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
134	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
135	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
136	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
137	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
138	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
139	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
140	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
141	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
142	C₂×#1055	C₂²×C₄	1	2	yes	—
143	C₂×#1055	C₂²×C₄	1	2	yes	—
144	C₈×D₁₃	—	2	4	no	—
145	C₈×D₁₃	—	2	4	no	—
146	C₂×#432	—	13	1	no	—
147	C₂×#431	—	13	1	no	—
148	C₂×#376	—	13	1	no	—
149	#1768	—	13	4	no	—
150	#1749	—	13	2	no	—
151	C₄×C₂²⋊C₈	—	13	2	no	—
152	#1746	—	13	2	no	—
153	#1726	—	13	2	no	—
154	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
155	C₂²×D₁₃	—	2	2	no	—
156	C₂²×D₁₃	—	2	2	no	—
157	C₂²×D₁₃	C₂×C₄²	1	1	yes	characteristic
158	C₂²×D₁₃	#131	1	4	yes	—
159	C₂²×D₁₃	C₂³×C₄	1	1	yes	characteristic
160	C₂×#261	—	2	4	no	—
161	C₂×#261	—	2	4	no	—
162	C₂×#261	—	2	4	no	—
163	C₂×#261	—	2	4	no	—
164	C₂×#261	—	2	4	no	—
165	C₂×#261	—	4	16	no	—
166	C₂×#261	#117	1	8	yes	—
167	C₂×C₄×C₁₃	—	2	2	no	—
168	C₂×C₄×C₁₃	—	2	2	no	—
169	C₂×C₄×C₁₃	—	4	1	no	—
170	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
171	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
172	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
173	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
174	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
175	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
176	C₂×Dic₁₃	—	2	2	no	—
177	C₂×Dic₁₃	—	2	2	no	—
178	C₂×Dic₁₃	—	4	1	no	—
179	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
180	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
181	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
182	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
183	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
184	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
185	C₄×D₁₃	—	2	2	no	—
186	C₄×D₁₃	—	2	2	no	—
187	C₄×D₁₃	—	2	2	no	—
188	C₄×D₁₃	—	2	2	no	—
189	C₄×D₁₃	—	2	2	no	—
190	C₄×D₁₃	—	2	2	no	—
191	C₄×D₁₃	—	2	2	no	—
192	C₄×D₁₃	—	2	2	no	—
193	C₄×D₁₃	—	2	2	no	—
194	C₄×D₁₃	—	4	1	no	—
195	C₄×D₁₃	—	4	1	no	—
196	C₄×D₁₃	C₂×#41	1	4	yes	—
197	#1057	—	2	8	no	—
198	C₈×C₁₃	—	2	2	no	—
199	C₈×C₁₃	—	2	2	no	—
200	#1055	—	2	2	no	—
201	#1055	—	2	2	no	—
202	C₂²×C₄²	—	13	1	no	—
203	C₂²×C₄²	—	13	2	no	—
204	#432	—	13	2	no	—
205	#432	—	13	2	no	—
206	#432	—	13	2	no	—
207	#432	—	13	2	no	—
208	#431	—	13	1	no	—
209	#431	—	13	2	no	—
210	#431	—	13	1	no	—
211	#431	—	13	1	no	—
212	#431	—	13	2	no	—
213	#431	#261	1	1	yes	characteristic, complemented
214	C₂×C₄⋊C₈	—	13	2	no	—
215	C₂×C₄⋊C₈	—	13	2	no	—
216	C₂×C₂²⋊C₈	—	13	2	no	—
217	C₂×C₂²⋊C₈	—	13	1	no	—
218	C₂×C₂²⋊C₈	—	13	1	no	—
219	C₂×#97	—	13	2	no	—
220	C₂×#97	—	13	4	no	—
221	C₂×C₄×C₈	—	13	2	no	—
222	C₂×C₄×C₈	—	13	4	no	—
223	#376	—	13	2	no	—
224	#376	—	13	2	no	—
225	#376	—	13	1	no	—
226	#376	—	13	1	no	—
227	#376	—	13	2	no	—
228	C₂×#95	—	13	2	no	—
229	C₂×#95	—	13	2	no	—
230	#336	—	13	4	no	—
231	#336	—	13	4	no	—
232	C₂²×C₁₃	—	2	1	no	—
233	C₂²×C₁₃	—	2	1	no	—
234	C₂²×C₁₃	#405	1	2	yes	—
235	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
236	C₂×D₁₃	—	2	1	no	—
237	C₂×D₁₃	—	2	1	no	—
238	C₂×D₁₃	—	2	8	no	—
239	C₂×D₁₃	#405	1	2	yes	—
240	C₂×D₁₃	C₂×#117	1	2	yes	—
241	C₂×D₁₃	C₂×#131	1	2	yes	—
242	C₂×D₁₃	#568	1	2	yes	—
243	#261	—	2	8	no	—
244	#261	—	4	4	no	—
245	C₄×C₁₃	—	2	1	no	—
246	C₄×C₁₃	—	2	1	no	—
247	C₄×C₁₃	—	2	1	no	—
248	C₄×C₁₃	—	2	1	no	—
249	C₄×C₁₃	—	2	1	no	—
250	C₄×C₁₃	C₄×#41	1	2	yes	—
251	Dic₁₃	—	2	1	no	—
252	Dic₁₃	—	2	1	no	—
253	Dic₁₃	—	2	1	no	—
254	Dic₁₃	—	2	1	no	—
255	Dic₁₃	—	2	1	no	—
256	Dic₁₃	C₄×#41	1	2	yes	—
257	C₂³×C₄	—	13	1	no	—
258	C₂³×C₄	—	13	1	no	—
259	C₂³×C₄	—	13	1	no	—
260	C₂³×C₄	—	13	4	no	—
261	C₂²×C₈	—	13	4	no	—
262	C₂²×C₈	—	13	2	no	—
263	C₂²×C₈	—	13	2	no	—
264	C₂×C₄²	—	13	2	no	—
265	C₂×C₄²	—	13	1	no	—
266	C₂×C₄²	—	13	1	no	—
267	C₂×C₄²	—	13	1	no	—
268	C₂×C₄²	—	13	1	no	—
269	C₂×C₄²	—	13	1	no	—
270	C₂×C₄²	—	13	1	no	—
271	C₂×C₄²	—	13	1	no	—
272	C₂×C₄²	—	13	1	no	—
273	C₂×C₄²	—	13	1	no	—
274	C₂×C₄²	—	13	1	no	—
275	C₂×C₄²	—	13	1	no	—
276	C₂×C₄²	—	13	2	no	—
277	C₂×C₄²	—	13	4	no	—
278	C₂×C₄²	—	26	8	no	—
279	C₂×C₄²	C₂×#261	1	1	yes	characteristic
280	C₄⋊C₈	—	13	4	no	—
281	C₄⋊C₈	—	13	4	no	—
282	C₄⋊C₈	—	13	2	no	—
283	C₄⋊C₈	—	13	2	no	—
284	C₄⋊C₈	—	13	2	no	—
285	C₄⋊C₈	C₂×#261	1	2	yes	complemented
286	C₂²⋊C₈	—	13	4	no	—
287	C₂²⋊C₈	—	13	4	no	—
288	C₂²⋊C₈	—	13	1	no	—
289	C₂²⋊C₈	—	13	1	no	—
290	C₂²⋊C₈	—	13	2	no	—
291	C₂²⋊C₈	—	13	2	no	—
292	C₂²⋊C₈	C₂×#261	1	1	yes	characteristic
293	C₂²⋊C₈	C₂×#261	1	1	yes	characteristic
294	#97	—	13	4	no	—
295	#97	—	13	4	no	—
296	#97	—	26	8	no	—
297	C₄×C₈	—	13	2	no	—
298	C₄×C₈	—	13	2	no	—
299	C₄×C₈	—	13	2	no	—
300	C₄×C₈	—	26	8	no	—
301	C₄×C₈	C₂×#261	1	2	yes	complemented
302	#95	—	13	2	no	—
303	#95	—	13	2	no	—
304	#95	—	13	4	no	—
305	#95	—	13	4	no	—
306	#95	—	13	2	no	—
307	#95	—	13	2	no	—
308	C₂×C₁₃	—	2	2	no	—
309	C₂×C₁₃	C₄×#117	1	1	yes	characteristic
310	C₂×C₁₃	C₂×#405	1	1	yes	characteristic
311	C₂×C₁₃	#2873	1	1	yes	characteristic
312	D₁₃	—	2	2	no	—
313	D₁₃	#2924	1	4	yes	—
314	C₂⁴	—	13	1	no	—
315	C₂²×C₄	—	13	1	no	—
316	C₂²×C₄	—	13	4	no	—
317	C₂²×C₄	—	13	1	no	—
318	C₂²×C₄	—	13	1	no	—
319	C₂²×C₄	—	13	1	no	—
320	C₂²×C₄	—	13	1	no	—
321	C₂²×C₄	—	13	1	no	—
322	C₂²×C₄	—	13	1	no	—
323	C₂²×C₄	—	13	1	no	—
324	C₂²×C₄	—	13	1	no	—
325	C₂²×C₄	—	13	1	no	—
326	C₂²×C₄	—	13	1	no	—
327	C₂²×C₄	—	13	1	no	—
328	C₂²×C₄	—	13	1	no	—
329	C₂²×C₄	—	13	1	no	—
330	C₂²×C₄	—	13	1	no	—
331	C₂²×C₄	—	13	4	no	—
332	C₂²×C₄	—	26	4	no	—
333	C₂²×C₄	—	26	4	no	—
334	C₂²×C₄	—	26	8	no	—
335	C₂²×C₄	—	26	8	no	—
336	C₂²×C₄	—	52	2	no	—
337	C₂²×C₄	—	52	4	no	—
338	C₂²×C₄	C₄×#261	1	1	yes	characteristic
339	C₂²×C₄	C₄×#261	1	1	yes	characteristic
340	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
341	C₂×C₈	—	13	8	no	—
342	C₂×C₈	—	13	2	no	—
343	C₂×C₈	—	13	2	no	—
344	C₂×C₈	—	26	4	no	—
345	C₂×C₈	—	26	4	no	—
346	C₂×C₈	—	26	4	no	—
347	C₂×C₈	—	26	4	no	—
348	C₂×C₈	C₂²×#261	1	2	yes	—
349	C₂×C₈	C₂²×#261	1	2	yes	—
350	C₄²	—	13	8	no	—
351	C₄²	—	13	1	no	—
352	C₄²	—	13	1	no	—
353	C₄²	—	13	1	no	—
354	C₄²	—	13	1	no	—
355	C₄²	—	13	1	no	—
356	C₄²	—	13	1	no	—
357	C₄²	—	13	1	no	—
358	C₄²	—	13	1	no	—
359	C₄²	—	13	1	no	—
360	C₄²	—	13	1	no	—
361	C₄²	—	13	1	no	—
362	C₄²	—	13	1	no	—
363	C₄²	—	26	4	no	—
364	C₄²	—	26	8	no	—
365	C₄²	C₄×#261	1	1	yes	characteristic
366	C₄²	C₄×#261	1	1	yes	characteristic
367	C₄²	C₂²×#261	1	1	yes	characteristic
368	C₄²	C₂²×#261	1	1	yes	characteristic
369	C₁₃	#20469	1	1	yes	characteristic, complemented, Sylow
370	C₂³	—	13	1	no	—
371	C₂³	—	13	4	no	—
372	C₂³	—	13	1	no	—
373	C₂³	—	26	2	no	—
374	C₂³	—	26	2	no	—
375	C₂³	C₂×C₄×#261	1	1	yes	characteristic
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	13	1	no	—
380	C₂×C₄	—	13	4	no	—
381	C₂×C₄	—	13	8	no	—
382	C₂×C₄	—	13	1	no	—
383	C₂×C₄	—	13	1	no	—
384	C₂×C₄	—	13	1	no	—
385	C₂×C₄	—	13	1	no	—
386	C₂×C₄	—	13	1	no	—
387	C₂×C₄	—	26	2	no	—
388	C₂×C₄	—	26	2	no	—
389	C₂×C₄	—	26	2	no	—
390	C₂×C₄	—	26	2	no	—
391	C₂×C₄	—	26	2	no	—
392	C₂×C₄	—	26	2	no	—
393	C₂×C₄	—	26	2	no	—
394	C₂×C₄	—	26	2	no	—
395	C₂×C₄	—	26	2	no	—
396	C₂×C₄	—	26	4	no	—
397	C₂×C₄	—	26	4	no	—
398	C₂×C₄	—	26	2	no	—
399	C₂×C₄	—	26	2	no	—
400	C₂×C₄	—	26	4	no	—
401	C₂×C₄	—	26	4	no	—
402	C₂×C₄	—	26	4	no	—
403	C₂×C₄	—	52	1	no	—
404	C₂×C₄	—	52	1	no	—
405	C₂×C₄	—	52	1	no	—
406	C₂×C₄	—	52	16	no	—
407	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
408	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
409	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
410	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
411	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
412	C₂×C₄	C₂³×#261	1	1	yes	characteristic
413	C₈	—	2	2	no	—
414	C₈	—	2	2	no	—
415	C₈	—	26	8	no	—
416	C₈	—	26	2	no	—
417	C₈	—	26	2	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	13	2	no	—
421	C₂²	—	13	2	no	—
422	C₂²	—	13	2	no	—
423	C₂²	—	13	2	no	—
424	C₂²	—	26	8	no	—
425	C₂²	—	26	1	no	—
426	C₂²	—	26	1	no	—
427	C₂²	#11719089	1	2	yes	—
428	C₂²	C₂²×C₄×#261	1	1	yes	characteristic
429	C₄	—	2	1	no	—
430	C₄	—	2	1	no	—
431	C₄	—	2	1	no	—
432	C₄	—	2	1	no	—
433	C₄	—	2	1	no	—
434	C₄	—	13	2	no	—
435	C₄	—	26	8	no	—
436	C₄	—	26	1	no	—
437	C₄	—	26	1	no	—
438	C₄	—	26	1	no	—
439	C₄	—	26	1	no	—
440	C₄	—	26	1	no	—
441	C₄	—	52	4	no	—
442	C₄	#41×#261	1	2	yes	—
443	C₂	—	2	2	no	—
444	C₂	—	13	4	no	—
445	C₂	—	26	2	no	—
446	C₂	#117×#261	1	1	yes	characteristic
447	C₂	C₂×#11719089	1	1	yes	characteristic
448	C₂	#13131399	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	C₂²×C₄
cosocle	C₂×C₄×D₁₃	C₂⁴
hypercenter	#431	#261
hypocenter	C₁₃	#20469
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. #13130625	C₂	semidirect
6. #13130554	C₂	semidirect
7. #13130492	C₂	semidirect
13. #11719130	C₄	semidirect
14. #11719128	C₄	semidirect
23. #11719055	C₄	semidirect
24. #11719054	C₄	semidirect
27. C₁₃×#431	C₄	semidirect
28. #11718586	C₄	semidirect
29. #11718494	C₄	semidirect
33. #11718379	C₄	semidirect
34. #11718379	C₄	semidirect
35. #11718346	C₄	semidirect
69. #88112	C₂×C₄	semidirect
71. #88110	C₂×C₄	semidirect
72. #88110	C₂×C₄	semidirect
73. C₄⋊#1057	C₂×C₄	semidirect
76. C₁₃×C₄⋊C₈	C₂×C₄	semidirect
79. C₄×C₈×C₁₃	C₂×C₄	semidirect
84. #88054	C₂×C₄	semidirect
85. #88054	C₂×C₄	semidirect
86. C₈×Dic₁₃	C₂×C₄	semidirect
87. C₈×Dic₁₃	C₂×C₄	semidirect
88. C₄⋊#1055	C₂×C₄	semidirect
89. C₄×#1055	C₂×C₄	semidirect
213. #431	#261	semidirect
285. C₄⋊C₈	C₂×#261	semidirect
301. C₄×C₈	C₂×#261	semidirect
369. C₁₃	#20469	semidirect

Maximal subgroups

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

subgroup	index
D₁₃⋊#432	2
C₂×#11719057	2
#13130625	2
#13130564	2
C₂²⋊C₈×#261	2
#13130554	2
#13130492	2
D₁₃×#431	2
#20469	13