Subgroups — #16797716

Order 3328.

898 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₃⋊#446	C₂	1	1	yes	maximal, characteristic
2	C₄×Q₈×#261	C₂	1	1	yes	maximal, characteristic
3	#13130637	C₂	1	2	yes	maximal
4	#13130634	C₂	1	2	yes	maximal
5	#13130629	C₂	1	1	yes	maximal, characteristic
6	C₈×C₄⋊#261	C₂	1	1	yes	maximal, characteristic
7	#13130623	C₂	1	1	yes	maximal, characteristic
8	C₄⋊C₈×#261	C₂	1	2	yes	maximal
9	#13130552	C₂	1	2	yes	maximal
10	#13130549	C₂	1	1	yes	maximal, characteristic
11	D₁₃×#446	C₂	1	1	yes	maximal, characteristic
12	C₂×Q₈×#261	C₄	1	2	yes	—
13	C₄×Q₈×D₁₃	C₂²	1	1	yes	characteristic
14	#11719158	C₄	1	2	yes	complemented
15	C₂×#88100	C₂²	1	2	yes	—
16	C₂×C₈×#261	C₂²	1	2	yes	—
17	C₂×C₈×#261	C₂²	1	2	yes	—
18	C₄⋊C₄×#261	C₄	1	4	yes	—
19	C₄⋊C₄×#261	C₄	1	2	yes	—
20	#11719080	C₄	1	2	yes	complemented
21	#11719078	C₄	1	4	yes	complemented
22	C₄×C₄⋊#261	C₂²	1	1	yes	characteristic
23	C₄×C₄⋊#261	C₂²	1	2	yes	—
24	C₄²×#261	C₂²	1	1	yes	characteristic
25	C₄²×#261	C₂²	1	2	yes	—
26	D₁₃⋊(C₄⋊C₈)	C₂²	1	2	yes	—
27	D₁₃⋊(C₄⋊C₈)	C₂²	1	1	yes	characteristic
28	#11719047	C₂²	1	2	yes	—
29	C₄×D₁₃⋊C₈	C₂²	1	1	yes	characteristic
30	C₁₃×#446	C₄	1	1	yes	characteristic, complemented
31	#11718685	C₄	1	1	yes	characteristic, complemented
32	D₁₃×C₄⋊C₈	C₂²	1	2	yes	—
33	D₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
34	#11718492	C₄	1	1	yes	characteristic, complemented
35	#11718489	C₄	1	2	yes	complemented
36	D₁₃×#97	C₂²	1	2	yes	—
37	#11718362	C₄	1	2	yes	complemented
38	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
39	#11718340	C₄	1	1	yes	characteristic, complemented
40	(C₂×#261)⋊C₈	C₂²	1	1	yes	characteristic
41	(C₂×#261)⋊C₈	C₂²	1	1	yes	characteristic
42	(C₂×#261)⋊C₈	C₂²	1	1	yes	characteristic
43	(C₂×#261)⋊C₈	C₂²	1	1	yes	characteristic
44	(C₂×#261)⋊C₈	C₂²	1	2	yes	—
45	(C₂×#261)⋊C₈	C₂²	1	2	yes	—
46	(C₂×#261)⋊C₈	C₂²	1	2	yes	—
47	C₂×Q₈×D₁₃	C₂×C₄	1	1	yes	characteristic
48	Q₈×#261	—	2	8	no	—
49	C₂×C₄⋊#261	C₂×C₄	1	4	yes	—
50	C₂×C₄⋊#261	C₂×C₄	1	2	yes	—
51	C₂×C₄×#261	C₂×C₄	1	2	yes	—
52	C₂×C₄×#261	C₂×C₄	1	4	yes	—
53	C₂×C₄×#261	C₂×C₄	1	4	yes	—
54	C₂×C₄×#261	C₂×C₄	1	2	yes	—
55	C₂×C₄×#261	C₂³	1	1	yes	characteristic
56	C₂×C₄×#261	C₂³	1	2	yes	—
57	C₂×C₄×#261	C₂³	1	1	yes	characteristic
58	C₂×D₁₃⋊C₈	C₂³	1	1	yes	characteristic
59	C₂×D₁₃⋊C₈	C₂³	1	1	yes	characteristic
60	C₂×D₁₃⋊C₈	C₂³	1	2	yes	—
61	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
62	Q₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
63	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
64	C₂×C₈×D₁₃	C₂³	1	2	yes	—
65	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
66	C₄⋊C₄×D₁₃	C₂×C₄	1	2	yes	—
67	C₄⋊C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
68	#88141	C₂×C₄	1	2	yes	—
69	#88141	C₂×C₄	1	1	yes	characteristic
70	C₄²×D₁₃	C₂³	1	1	yes	characteristic
71	C₄²×D₁₃	C₂³	1	2	yes	—
72	C₄×Dic₂₆	C₂×C₄	1	2	yes	—
73	C₄×Dic₂₆	C₂×C₄	1	1	yes	characteristic
74	(C₂×#261)⋊C₄	C₂×C₄	1	4	yes	—
75	(C₂×#261)⋊C₄	C₂×C₄	1	2	yes	—
76	#88112	C₂×C₄	1	2	yes	—
77	#88112	C₂×C₄	1	4	yes	—
78	#88110	C₂×C₄	1	4	yes	—
79	#88110	C₂×C₄	1	4	yes	—
80	C₄⋊#1057	C₂×C₄	1	4	yes	—
81	C₄⋊#1057	C₂×C₄	1	2	yes	—
82	C₄×#1057	C₂×C₄	1	2	yes	—
83	C₄×#1057	C₂×C₄	1	2	yes	—
84	#88100	—	4	2	no	—
85	C₈×#261	—	4	2	no	—
86	C₈×#261	—	4	2	no	—
87	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
88	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
89	C₁₃×#97	C₂×C₄	1	2	yes	—
90	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
91	#88055	C₂×C₄	1	2	yes	—
92	#88055	C₂×C₄	1	2	yes	—
93	#88054	C₂×C₄	1	2	yes	—
94	#88054	C₂×C₄	1	2	yes	—
95	#88054	C₂×C₄	1	2	yes	—
96	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
97	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
98	C₄⋊#1055	C₂×C₄	1	1	yes	characteristic
99	C₄⋊#1055	C₂×C₄	1	2	yes	—
100	#88043	C₂×C₄	1	2	yes	—
101	C₄×#1055	C₂×C₄	1	1	yes	characteristic
102	#20573	—	13	1	no	maximal, Sylow
103	C₂²×#261	C₂²×C₄	1	2	yes	—
104	C₂²×#261	C₂²×C₄	1	4	yes	—
105	C₂²×#261	C₂²×C₄	1	2	yes	—
106	C₂×Q₈×C₁₃	C₄²	1	1	yes	characteristic
107	Q₈×D₁₃	—	2	4	no	—
108	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
110	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
111	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
113	C₂×Dic₂₆	C₄²	1	1	yes	characteristic
114	C₂×Dic₂₆	C₄²	1	2	yes	—
115	C₂×#1057	C₂²×C₄	1	2	yes	—
116	C₂×#1057	C₂²×C₄	1	2	yes	—
117	C₂×#1057	C₂²×C₄	1	4	yes	—
118	C₄⋊#261	—	2	8	no	—
119	C₄⋊#261	M₁₆	1	8	yes	—
120	C₄×#261	—	2	8	no	—
121	C₄×#261	—	2	8	no	—
122	C₄×#261	—	2	4	no	—
123	C₄×#261	—	2	4	no	—
124	C₄×#261	—	2	2	no	—
125	C₄×#261	—	2	1	no	—
126	C₄×#261	—	2	2	no	—
127	C₄×#261	—	2	1	no	—
128	C₄×#261	—	2	1	no	—
129	C₄×#261	—	2	1	no	—
130	D₁₃⋊C₈	—	2	1	no	—
131	D₁₃⋊C₈	—	2	2	no	—
132	D₁₃⋊C₈	—	2	1	no	—
133	D₁₃⋊C₈	—	2	1	no	—
134	D₁₃⋊C₈	—	2	1	no	—
135	D₁₃⋊C₈	—	2	2	no	—
136	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
139	C₁₃×C₄⋊C₄	C₄²	1	2	yes	—
140	C₁₃×C₄⋊C₄	C₄²	1	1	yes	characteristic
141	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
142	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
143	C₄⋊Dic₁₃	C₄²	1	2	yes	—
144	C₄⋊Dic₁₃	C₄²	1	1	yes	characteristic
145	#6101	C₄²	1	2	yes	—
146	#6101	C₄²	1	2	yes	—
147	#6101	C₄²	1	2	yes	—
148	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
149	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
150	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
151	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
152	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
153	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
154	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
155	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
156	C₂×#1055	C₂²×C₄	1	2	yes	—
157	C₈×D₁₃	—	2	1	no	—
158	C₈×D₁₃	—	2	2	no	—
159	C₈×D₁₃	—	2	1	no	—
160	C₈×D₁₃	—	2	1	no	—
161	C₈×D₁₃	—	2	1	no	—
162	C₈×D₁₃	—	2	2	no	—
163	C₂×#446	—	13	1	no	—
164	C₂×#446	—	13	1	no	—
165	C₄²×Q₈	—	13	1	no	—
166	#1771	—	13	2	no	—
167	#1771	—	13	2	no	—
168	C₈×C₄⋊C₄	—	13	1	no	—
169	C₈×C₄⋊C₄	—	13	1	no	—
170	#1767	—	13	1	no	—
171	C₄×C₄⋊C₈	—	13	2	no	—
172	#1745	—	13	2	no	—
173	#1744	—	13	1	no	—
174	C₂²×D₁₃	C₂³×C₄	1	1	yes	characteristic
175	C₂×#261	—	2	2	no	—
176	C₂×#261	—	2	4	no	—
177	C₂×#261	—	2	2	no	—
178	C₂×#261	—	2	4	no	—
179	C₂×#261	—	2	2	no	—
180	C₂×#261	—	2	2	no	—
181	C₂×#261	—	2	2	no	—
182	C₂×#261	C₂×M₁₆	1	8	yes	—
183	C₂×#261	#131	1	4	yes	—
184	Q₈×C₁₃	—	2	2	no	—
185	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
186	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
187	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
188	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
189	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
190	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
191	C₂×Dic₁₃	C₂×C₄²	1	2	yes	—
192	C₂×Dic₁₃	C₂×C₄²	1	2	yes	—
193	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
194	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
195	C₄×D₁₃	—	2	4	no	—
196	C₄×D₁₃	—	2	4	no	—
197	C₄×D₁₃	—	2	2	no	—
198	C₄×D₁₃	C₂×M₁₆	1	4	yes	—
199	C₄×D₁₃	H(5,𝔽₂)	1	1	yes	characteristic
200	C₄×D₁₃	2₋¹⁺⁴	1	1	yes	characteristic
201	C₄×D₁₃	2₋¹⁺⁴	1	1	yes	characteristic
202	C₄×D₁₃	2₋¹⁺⁴	1	1	yes	characteristic
203	Dic₂₆	—	2	2	no	—
204	Dic₂₆	—	2	4	no	—
205	#1057	—	2	2	no	—
206	#1057	—	2	2	no	—
207	#1057	—	2	4	no	—
208	C₈×C₁₃	—	2	1	no	—
209	C₈×C₁₃	—	2	1	no	—
210	C₈×C₁₃	—	2	2	no	—
211	#1055	—	2	1	no	—
212	#1055	—	2	1	no	—
213	#1055	—	2	2	no	—
214	C₂×C₄×Q₈	—	13	1	no	—
215	C₂×C₄×Q₈	—	13	2	no	—
216	#446	—	13	4	no	—
217	#446	—	13	2	no	—
218	#446	—	13	2	no	—
219	#446	—	13	1	no	—
220	#446	—	13	2	no	—
221	#446	—	13	1	no	—
222	#446	—	13	2	no	—
223	#446	—	13	1	no	—
224	#446	#261	1	1	yes	characteristic, complemented
225	C₂×C₄⋊C₈	—	13	2	no	—
226	C₂×C₄⋊C₈	—	13	1	no	—
227	C₂×C₄⋊C₈	—	13	2	no	—
228	C₂×C₄⋊C₈	—	13	1	no	—
229	C₂×#97	—	13	2	no	—
230	C₂×#97	—	13	2	no	—
231	C₂×#97	—	13	2	no	—
232	C₂×C₄×C₈	—	13	1	no	—
233	C₂×C₄×C₈	—	13	1	no	—
234	C₂×C₄×C₈	—	13	2	no	—
235	C₂×C₄×C₈	—	13	2	no	—
236	C₄×C₄⋊C₄	—	13	1	no	—
237	C₄×C₄⋊C₄	—	13	2	no	—
238	C₄×C₄⋊C₄	—	13	2	no	—
239	C₄×C₄⋊C₄	—	13	4	no	—
240	C₄³	—	13	1	no	—
241	C₄³	—	13	2	no	—
242	#336	—	13	1	no	—
243	#336	—	13	1	no	—
244	#336	—	13	1	no	—
245	#336	—	13	1	no	—
246	#336	—	13	2	no	—
247	#336	—	13	2	no	—
248	#336	—	13	2	no	—
249	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
250	C₂×D₁₃	#519	1	1	yes	characteristic
251	C₂×D₁₃	#520	1	1	yes	characteristic
252	C₂×D₁₃	C₂²×M₁₆	1	2	yes	—
253	C₂×D₁₃	C₂×#131	1	2	yes	—
254	#261	—	2	4	no	—
255	#261	—	2	8	no	—
256	#261	—	4	2	no	—
257	C₄×C₁₃	—	2	2	no	—
258	C₄×C₁₃	—	2	1	no	—
259	C₄×C₁₃	—	2	2	no	—
260	C₄×C₁₃	C₄×M₁₆	1	2	yes	—
261	C₄×C₁₃	#519	1	1	yes	characteristic
262	C₄×C₁₃	#520	1	1	yes	characteristic
263	Dic₁₃	—	2	2	no	—
264	Dic₁₃	—	2	1	no	—
265	Dic₁₃	—	2	2	no	—
266	Dic₁₃	C₄×M₁₆	1	2	yes	—
267	Dic₁₃	#519	1	1	yes	characteristic
268	Dic₁₃	#520	1	1	yes	characteristic
269	C₂²×Q₈	—	13	1	no	—
270	C₂²×C₈	—	13	1	no	—
271	C₂²×C₈	—	13	1	no	—
272	C₂²×C₈	—	13	2	no	—
273	C₂²×C₈	—	13	1	no	—
274	C₂²×C₈	—	13	1	no	—
275	C₂²×C₈	—	13	2	no	—
276	C₄×Q₈	—	13	1	no	—
277	C₄×Q₈	—	13	2	no	—
278	C₄×Q₈	—	13	1	no	—
279	C₄×Q₈	—	13	2	no	—
280	C₄×Q₈	—	13	1	no	—
281	C₄×Q₈	—	26	8	no	—
282	C₄×Q₈	C₂×#261	1	1	yes	characteristic
283	C₂×C₄⋊C₄	—	13	2	no	—
284	C₂×C₄⋊C₄	—	13	1	no	—
285	C₂×C₄⋊C₄	—	13	2	no	—
286	C₂×C₄⋊C₄	—	13	4	no	—
287	C₂×C₄²	—	13	1	no	—
288	C₂×C₄²	—	13	2	no	—
289	C₂×C₄²	—	13	2	no	—
290	C₂×C₄²	—	13	4	no	—
291	C₂×C₄²	—	13	1	no	—
292	C₂×C₄²	—	13	2	no	—
293	C₂×C₄²	—	13	1	no	—
294	C₂×C₄²	—	13	4	no	—
295	C₂×C₄²	—	13	2	no	—
296	C₄⋊C₈	—	13	2	no	—
297	C₄⋊C₈	—	13	4	no	—
298	C₄⋊C₈	—	13	2	no	—
299	C₄⋊C₈	—	13	4	no	—
300	C₄⋊C₈	—	13	2	no	—
301	C₄⋊C₈	—	13	2	no	—
302	C₄⋊C₈	—	13	2	no	—
303	C₄⋊C₈	—	13	1	no	—
304	C₄⋊C₈	—	13	2	no	—
305	C₄⋊C₈	C₂×#261	1	1	yes	characteristic
306	C₄⋊C₈	C₂×#261	1	2	yes	—
307	#97	—	13	4	no	—
308	#97	—	13	4	no	—
309	#97	—	13	2	no	—
310	#97	—	13	2	no	—
311	#97	—	13	2	no	—
312	#97	—	52	2	no	—
313	#97	C₂×#261	1	2	yes	—
314	C₄×C₈	—	13	2	no	—
315	C₄×C₈	—	13	2	no	—
316	C₄×C₈	—	13	1	no	—
317	C₄×C₈	—	13	1	no	—
318	C₄×C₈	—	13	1	no	—
319	C₄×C₈	—	52	2	no	—
320	C₄×C₈	—	52	2	no	—
321	C₄×C₈	C₂×#261	1	1	yes	characteristic
322	#95	—	13	2	no	—
323	#95	—	13	4	no	—
324	C₂×C₁₃	#2276	1	1	yes	characteristic
325	C₂×C₁₃	C₂×C₄×M₁₆	1	1	yes	characteristic
326	C₂×C₁₃	C₄×#131	1	1	yes	characteristic
327	D₁₃	#2984	1	2	yes	—
328	D₁₃	#2990	1	2	yes	—
329	C₂×Q₈	—	13	2	no	—
330	C₂×Q₈	—	13	1	no	—
331	C₂×Q₈	—	26	4	no	—
332	C₂×Q₈	C₄×#261	1	1	yes	characteristic
333	C₂²×C₄	—	13	1	no	—
334	C₂²×C₄	—	13	1	no	—
335	C₂²×C₄	—	13	4	no	—
336	C₂²×C₄	—	13	2	no	—
337	C₂²×C₄	—	13	1	no	—
338	C₂²×C₄	—	13	2	no	—
339	C₂²×C₄	—	13	2	no	—
340	C₂²×C₄	—	13	2	no	—
341	C₂×C₈	—	13	2	no	—
342	C₂×C₈	—	13	2	no	—
343	C₂×C₈	—	13	4	no	—
344	C₂×C₈	—	13	1	no	—
345	C₂×C₈	—	13	1	no	—
346	C₂×C₈	—	13	2	no	—
347	C₂×C₈	—	26	1	no	—
348	C₂×C₈	—	26	2	no	—
349	C₂×C₈	—	26	1	no	—
350	C₂×C₈	—	26	1	no	—
351	C₂×C₈	—	26	1	no	—
352	C₂×C₈	—	26	2	no	—
353	C₂×C₈	—	26	1	no	—
354	C₂×C₈	—	26	2	no	—
355	C₂×C₈	—	26	1	no	—
356	C₂×C₈	—	26	1	no	—
357	C₂×C₈	—	26	2	no	—
358	C₂×C₈	—	26	1	no	—
359	C₂×C₈	C₂²×#261	1	1	yes	characteristic
360	C₂×C₈	C₂²×#261	1	1	yes	characteristic
361	C₂×C₈	C₂²×#261	1	2	yes	—
362	C₄⋊C₄	—	13	8	no	—
363	C₄⋊C₄	—	13	2	no	—
364	C₄⋊C₄	—	13	2	no	—
365	C₄⋊C₄	—	13	2	no	—
366	C₄⋊C₄	—	13	2	no	—
367	C₄⋊C₄	—	13	1	no	—
368	C₄⋊C₄	—	26	8	no	—
369	C₄⋊C₄	C₄×#261	1	2	yes	—
370	C₄⋊C₄	C₄×#261	1	1	yes	characteristic
371	C₄²	—	13	1	no	—
372	C₄²	—	13	1	no	—
373	C₄²	—	13	2	no	—
374	C₄²	—	13	2	no	—
375	C₄²	—	13	1	no	—
376	C₄²	—	13	2	no	—
377	C₄²	—	26	2	no	—
378	C₄²	—	26	1	no	—
379	C₄²	—	26	4	no	—
380	C₄²	—	26	8	no	—
381	C₄²	—	26	2	no	—
382	C₄²	—	26	1	no	—
383	C₄²	—	26	1	no	—
384	C₄²	—	26	1	no	—
385	C₄²	—	26	8	no	—
386	C₄²	—	26	4	no	—
387	C₄²	C₂²×#261	1	1	yes	characteristic
388	C₄²	C₂²×#261	1	2	yes	—
389	C₁₃	#20573	1	1	yes	characteristic, complemented, Sylow
390	C₂³	—	13	1	no	—
391	Q₈	—	2	2	no	—
392	Q₈	—	26	4	no	—
393	Q₈	—	26	2	no	—
394	C₂×C₄	—	13	1	no	—
395	C₂×C₄	—	13	1	no	—
396	C₂×C₄	—	13	4	no	—
397	C₂×C₄	—	13	1	no	—
398	C₂×C₄	—	13	1	no	—
399	C₂×C₄	—	13	1	no	—
400	C₂×C₄	—	13	1	no	—
401	C₂×C₄	—	13	4	no	—
402	C₂×C₄	—	13	8	no	—
403	C₂×C₄	—	13	1	no	—
404	C₂×C₄	—	13	2	no	—
405	C₂×C₄	—	13	2	no	—
406	C₂×C₄	—	26	4	no	—
407	C₂×C₄	—	26	4	no	—
408	C₂×C₄	—	26	2	no	—
409	C₂×C₄	—	26	2	no	—
410	C₂×C₄	—	26	2	no	—
411	C₂×C₄	—	26	4	no	—
412	C₂×C₄	—	26	4	no	—
413	C₂×C₄	—	26	2	no	—
414	C₂×C₄	—	26	2	no	—
415	C₂×C₄	—	26	2	no	—
416	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
417	C₂×C₄	C₂×C₄×#261	1	2	yes	—
418	C₂×C₄	C₂×C₄×#261	1	2	yes	—
419	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
420	C₂×C₄	C₂³×#261	1	1	yes	characteristic
421	C₈	—	2	1	no	—
422	C₈	—	2	1	no	—
423	C₈	—	2	2	no	—
424	C₈	—	26	2	no	—
425	C₈	—	26	2	no	—
426	C₈	—	26	4	no	—
427	C₈	—	26	1	no	—
428	C₈	—	26	1	no	—
429	C₈	—	26	2	no	—
430	C₂²	—	13	1	no	—
431	C₂²	—	13	1	no	—
432	C₂²	—	13	2	no	—
433	C₂²	—	13	2	no	—
434	C₂²	C₂²×C₄×#261	1	1	yes	characteristic
435	C₄	—	2	2	no	—
436	C₄	—	2	1	no	—
437	C₄	—	2	2	no	—
438	C₄	—	13	1	no	—
439	C₄	—	13	1	no	—
440	C₄	—	13	2	no	—
441	C₄	—	26	8	no	—
442	C₄	—	26	4	no	—
443	C₄	—	26	2	no	—
444	C₄	—	26	1	no	—
445	C₄	—	26	2	no	—
446	C₄	—	52	2	no	—
447	C₄	M₁₆×#261	1	2	yes	—
448	C₄	#11719627	1	1	yes	characteristic
449	C₄	#11719631	1	1	yes	characteristic
450	C₂	—	13	2	no	—
451	C₂	—	13	2	no	—
452	C₂	#13131276	1	1	yes	characteristic
453	C₂	C₂×M₁₆×#261	1	1	yes	characteristic
454	C₂	#131×#261	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#261
commutator, socle	C₂²×C₁₃	C₂²×C₄²
Fitting	C₁₃×#446	C₄
prime radical	C₂²×D₁₃	C₂³×C₄
cosocle	C₂×C₄×D₁₃	C₂⁴
hypercenter	#446	#261
hypocenter	C₁₃	#20573
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ #446

Complements

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

N	H ≅ G/N	type
14. #11719158	C₄	semidirect
20. #11719080	C₄	semidirect
21. #11719078	C₄	semidirect
30. C₁₃×#446	C₄	semidirect
31. #11718685	C₄	semidirect
34. #11718492	C₄	semidirect
35. #11718489	C₄	semidirect
37. #11718362	C₄	semidirect
39. #11718340	C₄	semidirect
224. #446	#261	semidirect
389. C₁₃	#20573	semidirect

Maximal subgroups

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

subgroup	index
D₁₃⋊#446	2
C₄×Q₈×#261	2
#13130637	2
#13130634	2
#13130629	2
C₈×C₄⋊#261	2
#13130623	2
C₄⋊C₈×#261	2
#13130552	2
#13130549	2
D₁₃×#446	2
#20573	13