Subgroups — #16797467

Order 3328.

938 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	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	#13130623	C₂	1	2	yes	maximal
9	C₄×#88100	C₂	1	1	yes	maximal, characteristic
10	#97×#261	C₂	1	2	yes	maximal
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×#88100	C₂²	1	1	yes	characteristic
17	C₂×#88100	C₂²	1	1	yes	characteristic
18	C₂×#88100	C₂²	1	1	yes	characteristic
19	C₂×#88100	C₂²	1	1	yes	characteristic
20	C₂×C₈×#261	C₂²	1	2	yes	—
21	C₂×C₈×#261	C₂²	1	2	yes	—
22	C₄⋊C₄×#261	C₄	1	4	yes	—
23	C₄⋊C₄×#261	C₄	1	2	yes	—
24	#11719080	C₄	1	2	yes	complemented
25	#11719078	C₄	1	4	yes	complemented
26	C₄×C₄⋊#261	C₂²	1	1	yes	characteristic
27	C₄×C₄⋊#261	C₂²	1	2	yes	—
28	C₄²×#261	C₂²	1	2	yes	—
29	C₄²×#261	C₂²	1	1	yes	characteristic
30	D₁₃⋊(C₄⋊C₈)	C₂²	1	1	yes	characteristic
31	D₁₃⋊(C₄⋊C₈)	C₂²	1	2	yes	—
32	#11719047	C₂²	1	2	yes	—
33	C₄×D₁₃⋊C₈	C₂²	1	1	yes	characteristic
34	C₁₃×#446	C₄	1	1	yes	characteristic, complemented
35	#11718685	C₄	1	1	yes	characteristic, complemented
36	D₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
37	D₁₃×C₄⋊C₈	C₂²	1	2	yes	—
38	#11718492	C₄	1	1	yes	characteristic, complemented
39	#11718489	C₄	1	2	yes	complemented
40	D₁₃×#97	C₂²	1	2	yes	—
41	#11718362	C₄	1	2	yes	complemented
42	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
43	#11718340	C₄	1	1	yes	characteristic, complemented
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	4	yes	—
52	C₂×C₄×#261	C₂×C₄	1	2	yes	—
53	C₂×C₄×#261	C₂×C₄	1	2	yes	—
54	C₂×C₄×#261	C₂×C₄	1	4	yes	—
55	C₂×C₄×#261	C₂³	1	2	yes	—
56	C₂×C₄×#261	C₂³	1	1	yes	characteristic
57	C₂×C₄×#261	C₂³	1	1	yes	characteristic
58	C₂×D₁₃⋊C₈	C₂³	1	1	yes	characteristic
59	C₂×D₁₃⋊C₈	C₂³	1	2	yes	—
60	C₂×D₁₃⋊C₈	C₂³	1	1	yes	characteristic
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	2	yes	—
64	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
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	—	2	4	no	—
85	#88100	—	2	2	no	—
86	#88100	—	2	2	no	—
87	#88100	—	2	2	no	—
88	#88100	Q₈	1	4	yes	complemented
89	C₈×#261	—	2	4	no	—
90	C₈×#261	—	2	4	no	—
91	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
92	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
93	C₁₃×#97	C₂×C₄	1	2	yes	—
94	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
95	#88055	C₂×C₄	1	2	yes	—
96	#88055	C₂×C₄	1	2	yes	—
97	#88054	C₂×C₄	1	2	yes	—
98	#88054	C₂×C₄	1	2	yes	—
99	#88054	C₂×C₄	1	2	yes	—
100	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
101	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
102	C₄⋊#1055	C₂×C₄	1	1	yes	characteristic
103	C₄⋊#1055	C₂×C₄	1	2	yes	—
104	#88043	C₂×C₄	1	2	yes	—
105	C₄×#1055	C₂×C₄	1	1	yes	characteristic
106	#20520	—	13	1	no	maximal, Sylow
107	C₂²×#261	C₂²×C₄	1	2	yes	—
108	C₂²×#261	C₂²×C₄	1	2	yes	—
109	C₂²×#261	C₂²×C₄	1	4	yes	—
110	C₂×Q₈×C₁₃	C₄²	1	1	yes	characteristic
111	Q₈×D₁₃	—	2	4	no	—
112	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
114	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
115	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
117	C₂×Dic₂₆	C₄²	1	1	yes	characteristic
118	C₂×Dic₂₆	C₄²	1	2	yes	—
119	C₂×#1057	C₂²×C₄	1	2	yes	—
120	C₂×#1057	C₂²×C₄	1	4	yes	—
121	C₂×#1057	C₂²×C₄	1	2	yes	—
122	C₄⋊#261	—	2	8	no	—
123	C₄⋊#261	M₁₆	1	8	yes	—
124	C₄×#261	—	2	8	no	—
125	C₄×#261	—	2	4	no	—
126	C₄×#261	—	2	2	no	—
127	C₄×#261	—	2	2	no	—
128	C₄×#261	—	2	1	no	—
129	C₄×#261	—	2	1	no	—
130	C₄×#261	—	4	4	no	—
131	C₄×#261	—	4	2	no	—
132	C₄×#261	C₂×Q₈	1	2	yes	—
133	C₄×#261	#41	1	2	yes	—
134	D₁₃⋊C₈	—	2	2	no	—
135	D₁₃⋊C₈	—	2	1	no	—
136	D₁₃⋊C₈	—	2	1	no	—
137	D₁₃⋊C₈	—	2	2	no	—
138	D₁₃⋊C₈	C₂×Q₈	1	2	yes	—
139	D₁₃⋊C₈	#41	1	2	yes	—
140	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
142	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
143	C₁₃×C₄⋊C₄	C₄²	1	2	yes	—
144	C₁₃×C₄⋊C₄	C₄²	1	1	yes	characteristic
145	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
146	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
147	C₄⋊Dic₁₃	C₄²	1	2	yes	—
148	C₄⋊Dic₁₃	C₄²	1	1	yes	characteristic
149	#6101	C₄²	1	2	yes	—
150	#6101	C₄²	1	2	yes	—
151	#6101	C₄²	1	2	yes	—
152	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
153	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
154	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
155	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
156	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
157	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
158	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
159	C₂×#1055	C₂²×C₄	1	2	yes	—
160	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
161	C₈×D₁₃	—	2	2	no	—
162	C₈×D₁₃	—	2	1	no	—
163	C₈×D₁₃	—	2	2	no	—
164	C₈×D₁₃	—	2	1	no	—
165	C₈×D₁₃	C₂×Q₈	1	2	yes	—
166	C₈×D₁₃	#41	1	2	yes	—
167	C₂×#446	—	13	1	no	—
168	C₂×#446	—	13	1	no	—
169	C₄²×Q₈	—	13	1	no	—
170	#1771	—	13	2	no	—
171	#1771	—	13	2	no	—
172	C₈×C₄⋊C₄	—	13	1	no	—
173	C₈×C₄⋊C₄	—	13	1	no	—
174	#1767	—	13	2	no	—
175	#1767	—	13	1	no	—
176	C₄×#97	—	13	2	no	—
177	C₄×#97	—	13	1	no	—
178	C₂²×D₁₃	C₂³×C₄	1	1	yes	characteristic
179	C₂×#261	—	2	4	no	—
180	C₂×#261	—	2	2	no	—
181	C₂×#261	—	2	2	no	—
182	C₂×#261	—	2	4	no	—
183	C₂×#261	—	2	2	no	—
184	C₂×#261	—	2	2	no	—
185	C₂×#261	—	2	2	no	—
186	C₂×#261	C₄×Q₈	1	4	yes	—
187	C₂×#261	C₂×M₁₆	1	8	yes	—
188	Q₈×C₁₃	—	2	2	no	—
189	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
190	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
191	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
192	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
193	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
194	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
195	C₂×Dic₁₃	C₂×C₄²	1	2	yes	—
196	C₂×Dic₁₃	C₂×C₄²	1	2	yes	—
197	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
198	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
199	C₄×D₁₃	—	2	4	no	—
200	C₄×D₁₃	—	2	4	no	—
201	C₄×D₁₃	—	2	2	no	—
202	C₄×D₁₃	C₂×M₁₆	1	4	yes	—
203	C₄×D₁₃	C₂²×Q₈	1	1	yes	characteristic
204	C₄×D₁₃	C₂×#41	1	1	yes	characteristic
205	C₄×D₁₃	C₂×#41	1	1	yes	characteristic
206	C₄×D₁₃	C₂×#41	1	1	yes	characteristic
207	Dic₂₆	—	2	2	no	—
208	Dic₂₆	—	2	4	no	—
209	#1057	—	2	4	no	—
210	#1057	—	2	2	no	—
211	#1057	C₄×Q₈	1	4	yes	complemented
212	C₈×C₁₃	—	2	2	no	—
213	C₈×C₁₃	—	2	1	no	—
214	C₈×C₁₃	C₄×Q₈	1	2	yes	complemented
215	#1055	—	2	2	no	—
216	#1055	—	2	1	no	—
217	#1055	C₄×Q₈	1	2	yes	complemented
218	C₂×C₄×Q₈	—	13	1	no	—
219	C₂×C₄×Q₈	—	13	2	no	—
220	#446	—	13	4	no	—
221	#446	—	13	2	no	—
222	#446	—	13	2	no	—
223	#446	—	13	1	no	—
224	#446	—	13	2	no	—
225	#446	—	13	1	no	—
226	#446	—	13	2	no	—
227	#446	—	13	1	no	—
228	#446	#261	1	1	yes	characteristic, complemented
229	C₂×C₄⋊C₈	—	13	1	no	—
230	C₂×C₄⋊C₈	—	13	2	no	—
231	C₂×C₄⋊C₈	—	13	1	no	—
232	C₂×C₄⋊C₈	—	13	2	no	—
233	C₂×#97	—	13	2	no	—
234	C₂×#97	—	13	1	no	—
235	C₂×#97	—	13	2	no	—
236	C₂×#97	—	13	2	no	—
237	C₂×#97	—	13	1	no	—
238	C₂×#97	—	13	1	no	—
239	C₂×#97	—	13	1	no	—
240	C₂×C₄×C₈	—	13	1	no	—
241	C₂×C₄×C₈	—	13	1	no	—
242	C₂×C₄×C₈	—	13	2	no	—
243	C₂×C₄×C₈	—	13	2	no	—
244	C₄×C₄⋊C₄	—	13	1	no	—
245	C₄×C₄⋊C₄	—	13	2	no	—
246	C₄×C₄⋊C₄	—	13	2	no	—
247	C₄×C₄⋊C₄	—	13	4	no	—
248	C₄³	—	13	1	no	—
249	C₄³	—	13	2	no	—
250	#336	—	13	2	no	—
251	#336	—	13	2	no	—
252	#336	—	13	2	no	—
253	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
254	C₂×D₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
255	C₂×D₁₃	C₄×#41	1	1	yes	characteristic
256	C₂×D₁₃	C₂²×M₁₆	1	2	yes	—
257	C₂×D₁₃	#568	1	2	yes	—
258	#261	—	2	4	no	—
259	#261	—	2	8	no	—
260	#261	—	4	2	no	—
261	C₄×C₁₃	—	2	2	no	—
262	C₄×C₁₃	—	2	1	no	—
263	C₄×C₁₃	—	2	2	no	—
264	C₄×C₁₃	C₄×M₁₆	1	2	yes	—
265	C₄×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
266	C₄×C₁₃	C₄×#41	1	1	yes	characteristic
267	Dic₁₃	—	2	2	no	—
268	Dic₁₃	—	2	1	no	—
269	Dic₁₃	—	2	2	no	—
270	Dic₁₃	C₄×M₁₆	1	2	yes	—
271	Dic₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
272	Dic₁₃	C₄×#41	1	1	yes	characteristic
273	C₂²×Q₈	—	13	1	no	—
274	C₂²×C₈	—	13	1	no	—
275	C₂²×C₈	—	13	1	no	—
276	C₂²×C₈	—	13	1	no	—
277	C₂²×C₈	—	13	2	no	—
278	C₂²×C₈	—	13	1	no	—
279	C₂²×C₈	—	13	2	no	—
280	C₄×Q₈	—	13	1	no	—
281	C₄×Q₈	—	13	2	no	—
282	C₄×Q₈	—	13	1	no	—
283	C₄×Q₈	—	13	2	no	—
284	C₄×Q₈	—	13	1	no	—
285	C₄×Q₈	—	26	8	no	—
286	C₄×Q₈	C₂×#261	1	1	yes	characteristic
287	C₂×C₄⋊C₄	—	13	2	no	—
288	C₂×C₄⋊C₄	—	13	1	no	—
289	C₂×C₄⋊C₄	—	13	2	no	—
290	C₂×C₄⋊C₄	—	13	4	no	—
291	C₂×C₄²	—	13	1	no	—
292	C₂×C₄²	—	13	1	no	—
293	C₂×C₄²	—	13	2	no	—
294	C₂×C₄²	—	13	2	no	—
295	C₂×C₄²	—	13	4	no	—
296	C₂×C₄²	—	13	2	no	—
297	C₂×C₄²	—	13	1	no	—
298	C₂×C₄²	—	13	4	no	—
299	C₂×C₄²	—	13	2	no	—
300	C₄⋊C₈	—	13	2	no	—
301	C₄⋊C₈	—	13	4	no	—
302	C₄⋊C₈	—	13	2	no	—
303	C₄⋊C₈	—	13	4	no	—
304	C₄⋊C₈	—	13	2	no	—
305	C₄⋊C₈	—	13	2	no	—
306	C₄⋊C₈	—	13	2	no	—
307	C₄⋊C₈	—	13	1	no	—
308	C₄⋊C₈	—	13	2	no	—
309	C₄⋊C₈	C₂×#261	1	1	yes	characteristic
310	C₄⋊C₈	C₂×#261	1	2	yes	—
311	#97	—	13	4	no	—
312	#97	—	13	4	no	—
313	#97	—	13	4	no	—
314	#97	—	13	2	no	—
315	#97	—	13	2	no	—
316	#97	—	13	2	no	—
317	#97	—	26	4	no	—
318	#97	—	26	2	no	—
319	#97	—	26	2	no	—
320	#97	—	26	2	no	—
321	#97	C₂×#261	1	2	yes	—
322	C₄×C₈	—	13	2	no	—
323	C₄×C₈	—	13	2	no	—
324	C₄×C₈	—	13	1	no	—
325	C₄×C₈	—	13	1	no	—
326	C₄×C₈	—	13	1	no	—
327	C₄×C₈	—	26	4	no	—
328	C₄×C₈	—	26	4	no	—
329	C₄×C₈	C₂×#261	1	1	yes	characteristic
330	#95	—	13	2	no	—
331	#95	—	13	4	no	—
332	C₂×C₁₃	C₄²×Q₈	1	1	yes	characteristic
333	C₂×C₁₃	C₂×C₄×M₁₆	1	1	yes	characteristic
334	C₂×C₁₃	#2875	1	1	yes	characteristic
335	D₁₃	Q₈×M₁₆	1	2	yes	—
336	D₁₃	#2970	1	2	yes	—
337	C₂×Q₈	—	13	2	no	—
338	C₂×Q₈	—	13	1	no	—
339	C₂×Q₈	—	26	4	no	—
340	C₂×Q₈	C₄×#261	1	1	yes	characteristic
341	C₂²×C₄	—	13	1	no	—
342	C₂²×C₄	—	13	1	no	—
343	C₂²×C₄	—	13	4	no	—
344	C₂²×C₄	—	13	2	no	—
345	C₂²×C₄	—	13	1	no	—
346	C₂²×C₄	—	13	2	no	—
347	C₂²×C₄	—	13	2	no	—
348	C₂²×C₄	—	13	2	no	—
349	C₂×C₈	—	13	2	no	—
350	C₂×C₈	—	13	2	no	—
351	C₂×C₈	—	13	2	no	—
352	C₂×C₈	—	13	1	no	—
353	C₂×C₈	—	13	2	no	—
354	C₂×C₈	—	13	2	no	—
355	C₂×C₈	—	13	2	no	—
356	C₂×C₈	—	13	4	no	—
357	C₂×C₈	—	13	1	no	—
358	C₂×C₈	—	13	2	no	—
359	C₂×C₈	—	26	2	no	—
360	C₂×C₈	—	26	2	no	—
361	C₂×C₈	—	26	1	no	—
362	C₂×C₈	—	26	1	no	—
363	C₂×C₈	—	26	2	no	—
364	C₂×C₈	—	26	1	no	—
365	C₂×C₈	—	26	1	no	—
366	C₂×C₈	—	26	2	no	—
367	C₂×C₈	C₂²×#261	1	1	yes	characteristic
368	C₂×C₈	C₂²×#261	1	2	yes	—
369	C₂×C₈	C₂²×#261	1	1	yes	characteristic
370	C₄⋊C₄	—	13	8	no	—
371	C₄⋊C₄	—	13	2	no	—
372	C₄⋊C₄	—	13	2	no	—
373	C₄⋊C₄	—	13	2	no	—
374	C₄⋊C₄	—	13	2	no	—
375	C₄⋊C₄	—	13	1	no	—
376	C₄⋊C₄	—	26	8	no	—
377	C₄⋊C₄	C₄×#261	1	2	yes	—
378	C₄⋊C₄	C₄×#261	1	1	yes	characteristic
379	C₄²	—	13	2	no	—
380	C₄²	—	13	2	no	—
381	C₄²	—	13	1	no	—
382	C₄²	—	13	1	no	—
383	C₄²	—	13	2	no	—
384	C₄²	—	13	2	no	—
385	C₄²	—	13	1	no	—
386	C₄²	—	13	2	no	—
387	C₄²	—	26	2	no	—
388	C₄²	—	26	2	no	—
389	C₄²	—	26	1	no	—
390	C₄²	—	26	1	no	—
391	C₄²	—	26	4	no	—
392	C₄²	—	26	8	no	—
393	C₄²	—	52	4	no	—
394	C₄²	—	52	2	no	—
395	C₄²	C₂²×#261	1	1	yes	characteristic
396	C₄²	C₂²×#261	1	2	yes	—
397	C₁₃	#20520	1	1	yes	characteristic, complemented, Sylow
398	C₂³	—	13	1	no	—
399	Q₈	—	2	2	no	—
400	Q₈	—	26	4	no	—
401	Q₈	—	26	2	no	—
402	C₂×C₄	—	13	1	no	—
403	C₂×C₄	—	13	1	no	—
404	C₂×C₄	—	13	4	no	—
405	C₂×C₄	—	13	1	no	—
406	C₂×C₄	—	13	1	no	—
407	C₂×C₄	—	13	1	no	—
408	C₂×C₄	—	13	1	no	—
409	C₂×C₄	—	13	4	no	—
410	C₂×C₄	—	13	8	no	—
411	C₂×C₄	—	13	1	no	—
412	C₂×C₄	—	13	2	no	—
413	C₂×C₄	—	13	2	no	—
414	C₂×C₄	—	26	4	no	—
415	C₂×C₄	—	26	4	no	—
416	C₂×C₄	—	26	2	no	—
417	C₂×C₄	—	26	2	no	—
418	C₂×C₄	—	26	4	no	—
419	C₂×C₄	—	26	2	no	—
420	C₂×C₄	—	26	4	no	—
421	C₂×C₄	—	26	2	no	—
422	C₂×C₄	—	26	2	no	—
423	C₂×C₄	—	26	2	no	—
424	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
425	C₂×C₄	C₂×C₄×#261	1	2	yes	—
426	C₂×C₄	C₂×C₄×#261	1	2	yes	—
427	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
428	C₂×C₄	C₂³×#261	1	1	yes	characteristic
429	C₈	—	2	2	no	—
430	C₈	—	2	1	no	—
431	C₈	—	13	4	no	—
432	C₈	—	13	2	no	—
433	C₈	—	26	2	no	—
434	C₈	—	26	4	no	—
435	C₈	—	26	1	no	—
436	C₈	—	26	2	no	—
437	C₈	Q₈×#261	1	2	yes	complemented
438	C₂²	—	13	1	no	—
439	C₂²	—	13	1	no	—
440	C₂²	—	13	2	no	—
441	C₂²	—	13	2	no	—
442	C₂²	C₂²×C₄×#261	1	1	yes	characteristic
443	C₄	—	2	2	no	—
444	C₄	—	2	1	no	—
445	C₄	—	2	2	no	—
446	C₄	—	13	1	no	—
447	C₄	—	13	1	no	—
448	C₄	—	13	2	no	—
449	C₄	—	26	8	no	—
450	C₄	—	26	4	no	—
451	C₄	—	26	2	no	—
452	C₄	—	26	1	no	—
453	C₄	—	26	2	no	—
454	C₄	—	52	2	no	—
455	C₄	M₁₆×#261	1	2	yes	—
456	C₄	C₂×Q₈×#261	1	1	yes	characteristic
457	C₄	#41×#261	1	1	yes	characteristic
458	C₂	—	13	2	no	—
459	C₂	—	13	2	no	—
460	C₂	C₄×Q₈×#261	1	1	yes	characteristic
461	C₂	C₂×M₁₆×#261	1	1	yes	characteristic
462	C₂	#13131406	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	#20520
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
24. #11719080	C₄	semidirect
25. #11719078	C₄	semidirect
34. C₁₃×#446	C₄	semidirect
35. #11718685	C₄	semidirect
38. #11718492	C₄	semidirect
39. #11718489	C₄	semidirect
41. #11718362	C₄	semidirect
43. #11718340	C₄	semidirect
88. #88100	Q₈	semidirect
211. #1057	C₄×Q₈	semidirect
214. C₈×C₁₃	C₄×Q₈	semidirect
217. #1055	C₄×Q₈	semidirect
228. #446	#261	semidirect
397. C₁₃	#20520	semidirect
437. C₈	Q₈×#261	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×#88100	2
#97×#261	2
D₁₃×#446	2
#20520	13