Subgroups — #15755611

Order 3328.

688 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#88147	C₂	1	1	yes	maximal, characteristic
2	#13114952	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#88054	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11718051	C₂	1	1	yes	maximal, characteristic
5	C₂×#11718075	C₂	1	1	yes	maximal, characteristic
6	#13112677	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1279	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#88147	C₄	1	1	yes	characteristic
9	C₂×#88147	C₄	1	1	yes	characteristic
10	C₂×C₄×D₅₂	C₂²	1	1	yes	characteristic
11	C₂×C₄²×D₁₃	—	2	1	no	—
12	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₂×#88054	—	2	1	no	—
16	C₄⋊C₄×Dic₁₃	C₄	1	1	yes	characteristic
17	C₄⋊C₄×Dic₁₃	C₄	1	1	yes	characteristic
18	C₄×#6103	—	2	1	no	—
19	C₄²×Dic₁₃	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
21	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
22	#11718327	—	2	1	no	—
23	#11718327	—	2	1	no	—
24	#11718142	—	2	1	no	—
25	#11718142	—	2	1	no	—
26	#11718142	—	2	1	no	—
27	#11718075	—	2	2	no	—
28	#11718051	—	2	2	no	—
29	C₂²×D₅₂	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₄×D₁₃	—	2	1	no	—
31	C₂²×C₄×D₁₃	—	2	1	no	—
32	C₂²×C₄×D₁₃	—	2	1	no	—
33	C₂²×C₈×C₁₃	—	2	1	no	—
34	C₂²×C₈×C₁₃	—	2	1	no	—
35	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
36	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄²×C₁₃	—	2	1	no	—
38	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
39	C₂×#6103	—	2	1	no	—
40	C₂×#6103	—	2	1	no	—
41	C₂×#6103	—	2	1	no	—
42	C₂×C₄⋊Dic₁₃	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄×Dic₁₃	—	2	1	no	—
44	C₂×C₄×Dic₁₃	—	2	1	no	—
45	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
48	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
49	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
50	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
51	C₂²×#1055	—	2	1	no	—
52	C₂²×#1055	—	2	1	no	—
53	#88147	—	2	2	no	—
54	#88147	—	2	2	no	—
55	#88147	—	2	2	no	—
56	#88147	C₈	1	4	yes	complemented
57	C₄×D₅₂	—	2	1	no	—
58	C₄×D₅₂	—	2	1	no	—
59	C₄×D₅₂	D₄	1	2	yes	—
60	C₄×D₅₂	Q₈	1	2	yes	—
61	C₄²×D₁₃	—	4	2	no	—
62	C₄²×D₁₃	—	4	2	no	—
63	C₁₃×C₄⋊C₈	—	2	1	no	—
64	C₁₃×C₄⋊C₈	—	2	1	no	—
65	C₄×C₈×C₁₃	—	2	1	no	—
66	C₄×C₈×C₁₃	—	2	1	no	—
67	C₁₃×#95	—	2	1	no	—
68	#88071	—	2	1	no	—
69	#88071	—	2	1	no	—
70	#88054	—	2	4	no	—
71	C₄⋊#1055	—	2	1	no	—
72	C₄⋊#1055	—	2	1	no	—
73	C₄×#1055	—	2	1	no	—
74	C₄×#1055	—	2	1	no	—
75	#8565	—	13	1	no	maximal, Sylow
76	C₂³×D₁₃	—	2	1	no	—
77	C₂²×C₄×C₁₃	—	2	1	no	—
78	C₂²×C₄×C₁₃	—	2	1	no	—
79	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
82	C₂²×Dic₁₃	—	2	1	no	—
83	C₂²×Dic₁₃	C₂²⋊C₄	1	1	yes	characteristic
84	C₂²×Dic₁₃	C₂²⋊C₄	1	1	yes	characteristic
85	C₂²×Dic₁₃	C₂²⋊C₄	1	1	yes	characteristic
86	C₂²×Dic₁₃	C₂²⋊C₄	1	1	yes	characteristic
87	C₂×D₅₂	—	2	1	no	—
88	C₂×D₅₂	—	2	1	no	—
89	C₂×D₅₂	—	2	1	no	—
90	C₂×D₅₂	C₄⋊C₄	1	2	yes	—
91	C₂×D₅₂	C₂×C₈	1	2	yes	—
92	C₂×D₅₂	M₁₆	1	2	yes	—
93	C₂×C₄×D₁₃	—	2	4	no	—
94	C₂×C₄×D₁₃	—	2	2	no	—
95	C₂×C₄×D₁₃	—	2	2	no	—
96	C₂×C₄×D₁₃	—	2	4	no	—
97	C₂×C₄×D₁₃	—	4	2	no	—
98	C₂×C₄×D₁₃	—	4	2	no	—
99	C₂×C₄×D₁₃	—	4	2	no	—
100	C₂×C₄×D₁₃	—	4	1	no	—
101	C₂×C₄×D₁₃	—	4	1	no	—
102	C₂×C₄×D₁₃	—	4	1	no	—
103	C₂×C₄×D₁₃	—	4	1	no	—
104	C₂×C₄×D₁₃	—	4	2	no	—
105	C₂×C₈×C₁₃	—	2	2	no	—
106	C₂×C₈×C₁₃	—	4	1	no	—
107	C₂×C₈×C₁₃	—	4	1	no	—
108	C₂×C₈×C₁₃	—	4	1	no	—
109	C₂×C₈×C₁₃	—	4	1	no	—
110	C₂×C₈×C₁₃	—	4	1	no	—
111	C₁₃×C₄⋊C₄	—	2	1	no	—
112	C₁₃×C₄⋊C₄	—	2	1	no	—
113	C₁₃×C₄⋊C₄	C₂×C₈	1	2	yes	—
114	C₁₃×C₄⋊C₄	M₁₆	1	2	yes	—
115	C₄²×C₁₃	—	4	1	no	—
116	C₄²×C₁₃	—	4	1	no	—
117	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
118	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
119	C₄²×C₁₃	#41	1	1	yes	characteristic
120	C₄²×C₁₃	#41	1	1	yes	characteristic
121	#6103	—	2	4	no	—
122	#6103	—	2	2	no	—
123	#6103	—	2	2	no	—
124	#6103	—	2	4	no	—
125	C₄⋊Dic₁₃	—	2	1	no	—
126	C₄⋊Dic₁₃	C₄⋊C₄	1	2	yes	—
127	C₄×Dic₁₃	—	2	1	no	—
128	C₄×Dic₁₃	—	2	1	no	—
129	C₄×Dic₁₃	—	2	1	no	—
130	C₄×Dic₁₃	—	2	1	no	—
131	C₄×Dic₁₃	—	2	1	no	—
132	C₄×Dic₁₃	—	2	1	no	—
133	C₄×Dic₁₃	—	2	2	no	—
134	C₄×Dic₁₃	—	4	1	no	—
135	C₄×Dic₁₃	—	4	2	no	—
136	C₄×Dic₁₃	—	4	2	no	—
137	C₄×Dic₁₃	C₂×C₈	1	2	yes	—
138	C₄×Dic₁₃	M₁₆	1	2	yes	—
139	C₂×#1055	—	2	2	no	—
140	C₂×#1055	—	4	1	no	—
141	C₂×#1055	—	4	1	no	—
142	C₂×#1055	—	4	1	no	—
143	C₂×#1055	—	4	1	no	—
144	C₂×#1055	—	4	1	no	—
145	C₄²×D₄	—	13	1	no	—
146	#1831	—	13	1	no	—
147	C₄×C₄⋊C₈	—	13	1	no	—
148	C₂×D₄⋊C₈	—	13	1	no	—
149	C₂×D₄⋊C₈	—	13	1	no	—
150	#1279	—	13	1	no	—
151	#1279	D₁₃	1	1	yes	characteristic, complemented
152	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
153	C₂²×D₁₃	—	2	2	no	—
154	C₂²×D₁₃	—	2	2	no	—
155	C₂²×D₁₃	—	2	2	no	—
156	C₂²×D₁₃	—	4	1	no	—
157	C₂²×D₁₃	—	4	1	no	—
158	C₂²×D₁₃	—	4	1	no	—
159	C₂²×D₁₃	—	4	1	no	—
160	C₂×C₄×C₁₃	—	2	1	no	—
161	C₂×C₄×C₁₃	—	2	1	no	—
162	C₂×C₄×C₁₃	—	2	2	no	—
163	C₂×C₄×C₁₃	—	2	2	no	—
164	C₂×C₄×C₁₃	—	4	1	no	—
165	C₂×C₄×C₁₃	—	4	1	no	—
166	C₂×C₄×C₁₃	—	4	1	no	—
167	C₂×C₄×C₁₃	—	4	1	no	—
168	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
169	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
170	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
171	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
172	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
173	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
174	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
175	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
176	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
177	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
178	C₂×C₄×C₁₃	#135	1	1	yes	characteristic
179	C₂×C₄×C₁₃	#135	1	1	yes	characteristic
180	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
181	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
182	C₂×Dic₁₃	—	2	1	no	—
183	C₂×Dic₁₃	—	2	1	no	—
184	C₂×Dic₁₃	—	2	1	no	—
185	C₂×Dic₁₃	—	2	1	no	—
186	C₂×Dic₁₃	—	2	1	no	—
187	C₂×Dic₁₃	—	2	1	no	—
188	C₂×Dic₁₃	—	2	2	no	—
189	C₂×Dic₁₃	—	2	1	no	—
190	C₂×Dic₁₃	—	2	1	no	—
191	C₂×Dic₁₃	—	2	1	no	—
192	C₂×Dic₁₃	—	4	1	no	—
193	C₂×Dic₁₃	—	4	1	no	—
194	C₂×Dic₁₃	C₂²⋊C₈	1	2	yes	—
195	C₂×Dic₁₃	C₂²⋊C₈	1	2	yes	—
196	C₂×Dic₁₃	#104	1	2	yes	—
197	D₅₂	—	2	2	no	—
198	D₅₂	—	2	2	no	—
199	D₅₂	—	2	2	no	—
200	D₅₂	C₄⋊C₈	1	4	yes	complemented
201	C₄×D₁₃	—	4	8	no	—
202	C₄×D₁₃	—	4	8	no	—
203	C₄×D₁₃	—	4	2	no	—
204	C₄×D₁₃	—	4	2	no	—
205	C₄×D₁₃	—	4	2	no	—
206	C₄×D₁₃	—	4	2	no	—
207	C₈×C₁₃	—	4	2	no	—
208	C₈×C₁₃	—	8	1	no	—
209	#1055	—	4	2	no	—
210	#1055	—	8	1	no	—
211	C₂×C₄×D₄	—	13	1	no	—
212	C₂×C₄×D₄	—	13	1	no	—
213	C₂×C₄×D₄	—	13	1	no	—
214	C₂²×C₄²	—	26	1	no	—
215	C₂×C₄⋊C₈	—	13	1	no	—
216	C₂×C₄⋊C₈	—	26	1	no	—
217	C₂×C₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic
218	C₂×C₄×C₈	—	13	1	no	—
219	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
220	C₄×C₄⋊C₄	—	13	1	no	—
221	C₄×C₄⋊C₄	—	13	1	no	—
222	C₄×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
223	C₄×C₂²⋊C₄	—	26	1	no	—
224	C₄×C₂²⋊C₄	—	26	1	no	—
225	C₄×C₂²⋊C₄	—	26	1	no	—
226	C₄³	—	13	1	no	—
227	#336	—	26	1	no	—
228	#336	—	26	1	no	—
229	#336	—	26	1	no	—
230	D₄⋊C₈	—	26	2	no	—
231	D₄⋊C₈	—	26	2	no	—
232	C₂²×C₁₃	#380	1	1	yes	characteristic
233	C₂²×C₁₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
234	C₂²×C₁₃	#407	1	1	yes	characteristic
235	C₂²×C₁₃	#416	1	1	yes	characteristic
236	C₂²×C₁₃	#418	1	1	yes	characteristic
237	C₂²×C₁₃	C₂×#104	1	1	yes	characteristic
238	C₂²×C₁₃	#421	1	1	yes	characteristic
239	C₂×D₁₃	—	2	4	no	—
240	C₂×D₁₃	—	4	2	no	—
241	C₂×D₁₃	—	4	2	no	—
242	C₂×D₁₃	—	4	2	no	—
243	C₂×D₁₃	—	4	2	no	—
244	C₂×D₁₃	—	4	2	no	—
245	C₂×D₁₃	—	4	2	no	—
246	C₄×C₁₃	—	2	1	no	—
247	C₄×C₁₃	—	2	1	no	—
248	C₄×C₁₃	—	4	2	no	—
249	C₄×C₁₃	—	4	2	no	—
250	C₄×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
251	C₄×C₁₃	#423	1	1	yes	characteristic
252	C₄×C₁₃	#431	1	1	yes	characteristic
253	C₄×C₁₃	#432	1	1	yes	characteristic
254	C₄×C₁₃	#463	1	1	yes	characteristic
255	C₄×C₁₃	#463	1	1	yes	characteristic
256	C₄×C₁₃	#478	1	1	yes	characteristic
257	C₄×C₁₃	#478	1	1	yes	characteristic
258	Dic₁₃	—	2	2	no	—
259	Dic₁₃	—	2	2	no	—
260	Dic₁₃	—	2	2	no	—
261	Dic₁₃	—	4	2	no	—
262	Dic₁₃	—	4	1	no	—
263	C₂²×D₄	—	13	1	no	—
264	C₂³×C₄	—	26	1	no	—
265	C₂³×C₄	—	26	1	no	—
266	C₂³×C₄	—	26	1	no	—
267	C₂²×C₈	—	2	1	no	—
268	C₂²×C₈	—	2	1	no	—
269	C₂²×C₈	—	26	1	no	—
270	C₂²×C₈	—	26	1	no	—
271	C₄×D₄	—	13	4	no	—
272	C₄×D₄	—	13	2	no	—
273	C₄×D₄	—	13	2	no	—
274	C₄×D₄	—	26	2	no	—
275	C₄×D₄	—	26	2	no	—
276	C₄×D₄	—	26	2	no	—
277	C₄×D₄	—	26	1	no	—
278	C₄×D₄	—	26	1	no	—
279	C₂×C₄⋊C₄	—	13	1	no	—
280	C₂×C₄⋊C₄	C₄×D₁₃	1	1	yes	characteristic
281	C₂×C₄⋊C₄	C₄×D₁₃	1	1	yes	characteristic
282	C₂×C₂²⋊C₄	—	26	1	no	—
283	C₂×C₂²⋊C₄	—	26	1	no	—
284	C₂×C₂²⋊C₄	—	26	1	no	—
285	C₂×C₄²	—	2	1	no	—
286	C₂×C₄²	—	13	1	no	—
287	C₂×C₄²	—	13	1	no	—
288	C₂×C₄²	—	13	1	no	—
289	C₂×C₄²	—	13	1	no	—
290	C₂×C₄²	—	13	1	no	—
291	C₂×C₄²	—	13	1	no	—
292	C₂×C₄²	—	26	1	no	—
293	C₂×C₄²	—	26	1	no	—
294	C₂×C₄²	—	52	2	no	—
295	C₂×C₄²	—	52	2	no	—
296	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
297	C₄⋊C₈	—	2	1	no	—
298	C₄⋊C₈	—	2	1	no	—
299	C₄⋊C₈	—	26	4	no	—
300	C₄⋊C₈	—	26	1	no	—
301	C₄⋊C₈	—	26	1	no	—
302	C₄×C₈	—	2	1	no	—
303	C₄×C₈	—	2	1	no	—
304	C₄×C₈	—	26	1	no	—
305	C₄×C₈	—	26	1	no	—
306	#95	—	2	1	no	—
307	#95	—	26	1	no	—
308	#95	—	26	1	no	—
309	C₂×C₁₃	#1476	1	1	yes	characteristic
310	C₂×C₁₃	#1478	1	1	yes	characteristic
311	C₂×C₁₃	#1488	1	1	yes	characteristic
312	C₂×C₁₃	#1490	1	1	yes	characteristic
313	C₂×C₁₃	#1797	1	1	yes	characteristic
314	C₂×C₁₃	#1804	1	1	yes	characteristic
315	C₂×C₁₃	#1806	1	1	yes	characteristic
316	D₁₃	—	4	4	no	—
317	C₂⁴	—	26	1	no	—
318	C₂×D₄	—	13	2	no	—
319	C₂×D₄	—	13	2	no	—
320	C₂×D₄	—	13	2	no	—
321	C₂×D₄	—	26	1	no	—
322	C₂×D₄	—	26	1	no	—
323	C₂×D₄	—	26	1	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	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	—	26	4	no	—
331	C₂²×C₄	—	26	4	no	—
332	C₂²×C₄	—	26	1	no	—
333	C₂²×C₄	—	26	2	no	—
334	C₂²×C₄	—	26	2	no	—
335	C₂²×C₄	—	52	2	no	—
336	C₂²×C₄	—	52	2	no	—
337	C₂²×C₄	—	52	2	no	—
338	C₂²×C₄	—	52	2	no	—
339	C₂²×C₄	—	52	1	no	—
340	C₂²×C₄	—	52	1	no	—
341	C₂²×C₄	—	52	1	no	—
342	C₂²×C₄	—	52	1	no	—
343	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
344	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
345	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	4	1	no	—
348	C₂×C₈	—	4	1	no	—
349	C₂×C₈	—	4	1	no	—
350	C₂×C₈	—	4	1	no	—
351	C₂×C₈	—	4	1	no	—
352	C₂×C₈	—	26	2	no	—
353	C₂×C₈	—	52	1	no	—
354	C₂×C₈	—	52	1	no	—
355	C₂×C₈	—	52	1	no	—
356	C₂×C₈	—	52	1	no	—
357	C₂×C₈	—	52	1	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	13	2	no	—
361	C₄⋊C₄	—	26	1	no	—
362	C₄⋊C₄	C₈×D₁₃	1	2	yes	—
363	C₄⋊C₄	#6094	1	2	yes	—
364	C₂²⋊C₄	—	26	4	no	—
365	C₂²⋊C₄	—	26	4	no	—
366	C₂²⋊C₄	—	26	2	no	—
367	C₂²⋊C₄	—	26	2	no	—
368	C₄²	—	4	1	no	—
369	C₄²	—	4	1	no	—
370	C₄²	—	13	2	no	—
371	C₄²	—	13	2	no	—
372	C₄²	—	26	2	no	—
373	C₄²	—	26	1	no	—
374	C₄²	—	26	1	no	—
375	C₄²	—	26	1	no	—
376	C₄²	—	26	1	no	—
377	C₄²	—	26	1	no	—
378	C₄²	—	26	1	no	—
379	C₄²	—	52	1	no	—
380	C₄²	—	52	2	no	—
381	C₄²	—	52	2	no	—
382	C₄²	#6127	1	1	yes	characteristic
383	C₄²	#6127	1	1	yes	characteristic
384	C₄²	D₄×D₁₃	1	1	yes	characteristic
385	C₄²	Q₈×D₁₃	1	1	yes	characteristic
386	C₁₃	#8565	1	1	yes	characteristic, complemented, Sylow
387	C₂³	—	26	2	no	—
388	C₂³	—	26	2	no	—
389	C₂³	—	26	2	no	—
390	C₂³	—	52	1	no	—
391	C₂³	—	52	1	no	—
392	C₂³	—	52	1	no	—
393	C₂³	—	52	1	no	—
394	C₂³	C₂²⋊C₄×D₁₃	1	1	yes	characteristic
395	D₄	—	13	4	no	—
396	D₄	—	26	2	no	—
397	D₄	—	26	2	no	—
398	D₄	—	26	2	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	13	2	no	—
408	C₂×C₄	—	13	2	no	—
409	C₂×C₄	—	13	2	no	—
410	C₂×C₄	—	26	1	no	—
411	C₂×C₄	—	26	1	no	—
412	C₂×C₄	—	26	1	no	—
413	C₂×C₄	—	26	1	no	—
414	C₂×C₄	—	26	1	no	—
415	C₂×C₄	—	26	1	no	—
416	C₂×C₄	—	26	1	no	—
417	C₂×C₄	—	26	1	no	—
418	C₂×C₄	—	26	2	no	—
419	C₂×C₄	—	26	1	no	—
420	C₂×C₄	—	52	8	no	—
421	C₂×C₄	—	52	8	no	—
422	C₂×C₄	—	52	1	no	—
423	C₂×C₄	—	52	1	no	—
424	C₂×C₄	—	52	2	no	—
425	C₂×C₄	—	52	2	no	—
426	C₂×C₄	—	52	2	no	—
427	C₂×C₄	—	52	2	no	—
428	C₂×C₄	#88126	1	1	yes	characteristic
429	C₂×C₄	#88138	1	1	yes	characteristic
430	C₂×C₄	#88138	1	1	yes	characteristic
431	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
432	C₂×C₄	#88150	1	1	yes	characteristic
433	C₂×C₄	#88150	1	1	yes	characteristic
434	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
435	C₂×C₄	C₂×#6094	1	1	yes	characteristic
436	C₂×C₄	M₁₆×D₁₃	1	1	yes	characteristic
437	C₂×C₄	M₁₆×D₁₃	1	1	yes	characteristic
438	C₂×C₄	#88165	1	1	yes	characteristic
439	C₂×C₄	#88168	1	1	yes	characteristic
440	C₂×C₄	#88170	1	1	yes	characteristic
441	C₂×C₄	#88173	1	1	yes	characteristic
442	C₈	—	4	2	no	—
443	C₈	—	8	1	no	—
444	C₈	—	52	2	no	—
445	C₈	—	104	1	no	—
446	C₂²	—	26	4	no	—
447	C₂²	—	52	2	no	—
448	C₂²	—	52	2	no	—
449	C₂²	—	52	2	no	—
450	C₂²	—	52	2	no	—
451	C₂²	—	52	2	no	—
452	C₂²	—	52	2	no	—
453	C₂²	#11718328	1	1	yes	characteristic
454	C₂²	D₁₃×C₂²⋊C₈	1	1	yes	characteristic
455	C₂²	#11718387	1	1	yes	characteristic
456	C₂²	#11718431	1	1	yes	characteristic
457	C₂²	#11718465	1	1	yes	characteristic
458	C₂²	D₁₃×#104	1	1	yes	characteristic
459	C₂²	#11718482	1	1	yes	characteristic
460	C₄	—	2	1	no	—
461	C₄	—	2	1	no	—
462	C₄	—	4	2	no	—
463	C₄	—	4	2	no	—
464	C₄	—	26	2	no	—
465	C₄	—	26	2	no	—
466	C₄	—	26	2	no	—
467	C₄	—	52	1	no	—
468	C₄	—	52	2	no	—
469	C₄	#11718346	1	1	yes	characteristic
470	C₄	#11718366	1	1	yes	characteristic
471	C₄	#11718448	1	1	yes	characteristic
472	C₄	#11718480	1	1	yes	characteristic
473	C₄	D₁₃×C₄⋊C₈	1	1	yes	characteristic
474	C₄	#11718498	1	1	yes	characteristic
475	C₄	#11718532	1	1	yes	characteristic
476	C₄	#11718552	1	1	yes	characteristic
477	C₂	—	52	4	no	—
478	C₂	#13113217	1	1	yes	characteristic
479	C₂	#13113225	1	1	yes	characteristic
480	C₂	#13113269	1	1	yes	characteristic
481	C₂	#13113277	1	1	yes	characteristic
482	C₂	#13114815	1	1	yes	characteristic
483	C₂	#13114845	1	1	yes	characteristic
484	C₂	#13114855	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₁₃
commutator	C₂×C₄×C₁₃	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₁₃×#1279	C₂
socle	C₂³×C₁₃	C₂×C₂²⋊C₄
prime radical	C₂²×D₅₂	C₂×C₄
cosocle	C₂×C₄²×C₁₃	C₂³
hypercenter	#1279	D₁₃
hypocenter	C₁₃	#8565
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ #1279

Complements

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

N	H ≅ G/N	type
2. #13114952	C₂	semidirect
3. C₄×#88054	C₂	semidirect
6. #13112677	C₂	semidirect
7. C₁₃×#1279	C₂	semidirect
56. #88147	C₈	semidirect
151. #1279	D₁₃	semidirect
200. D₅₂	C₄⋊C₈	semidirect
386. C₁₃	#8565	semidirect

Maximal subgroups

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

subgroup	index
C₄×#88147	2
#13114952	2
C₄×#88054	2
C₂×#11718051	2
C₂×#11718075	2
#13112677	2
C₁₃×#1279	2
#8565	13