Subgroups — #15753884

Order 3328.

696 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13117398	C₂	1	1	yes	maximal, characteristic
2	#13114691	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄⋊C₈×Dic₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11718077	C₂	1	1	yes	maximal, characteristic
5	C₂×#11718077	C₂	1	1	yes	maximal, characteristic
6	#13112719	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1296	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#88147	—	2	1	no	—
9	C₂×#88147	—	2	1	no	—
10	C₂×#88147	C₄	1	2	yes	—
11	C₂×#88128	C₂²	1	1	yes	characteristic
12	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
14	C₁₃×#384	C₂²	1	1	yes	characteristic
15	C₂×#88055	—	2	1	no	—
16	C₂×C₈×Dic₁₃	—	2	1	no	—
17	#11718649	—	2	1	no	—
18	#11718649	—	2	1	no	—
19	#11718649	C₄	1	2	yes	—
20	C₄²×Dic₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
23	#11718142	—	2	1	no	—
24	#11718142	—	2	1	no	—
25	#11718077	C₄	1	4	yes	complemented
26	#11718077	C₄	1	4	yes	complemented
27	C₂²×D₅₂	—	2	1	no	—
28	C₂²×D₅₂	—	2	1	no	—
29	C₂²×D₅₂	C₂×C₄	1	2	yes	—
30	C₂²×C₄×D₁₃	—	2	2	no	—
31	C₂²×C₈×C₁₃	—	2	1	no	—
32	C₂²×C₈×C₁₃	—	2	1	no	—
33	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
34	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
35	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
36	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
37	C₂×#6103	—	2	2	no	—
38	C₂×#6103	—	2	2	no	—
39	C₂×#6103	—	2	2	no	—
40	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
43	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
44	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
45	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
46	C₂²×#1055	—	2	1	no	—
47	C₂²×#1055	—	2	1	no	—
48	#88147	—	4	2	no	—
49	#88147	—	4	2	no	—
50	#88147	—	4	4	no	—
51	#88147	—	4	2	no	—
52	#88147	—	4	2	no	—
53	#88128	—	2	1	no	—
54	#88128	—	2	1	no	—
55	#88128	C₂×C₄	1	2	yes	—
56	#88128	C₂×C₄	1	2	yes	—
57	C₁₃×C₄⋊C₈	—	2	1	no	—
58	C₁₃×C₄⋊C₈	—	2	1	no	—
59	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	complemented
60	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	complemented
61	#88055	—	4	2	no	—
62	C₈×Dic₁₃	—	4	2	no	—
63	C₄⋊#1055	—	2	1	no	—
64	C₄⋊#1055	—	2	1	no	—
65	C₄⋊#1055	C₂×C₄	1	2	yes	complemented
66	C₄⋊#1055	C₂×C₄	1	2	yes	complemented
67	#8234	—	13	1	no	maximal, Sylow
68	C₂³×D₁₃	—	2	2	no	—
69	C₂²×C₄×C₁₃	—	2	2	no	—
70	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
71	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
73	C₂²×Dic₁₃	C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×Dic₁₃	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×Dic₁₃	C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×Dic₁₃	C₂²⋊C₄	1	1	yes	characteristic
77	C₂×D₅₂	—	2	2	no	—
78	C₂×D₅₂	—	2	2	no	—
79	C₂×D₅₂	—	2	2	no	—
80	C₂×D₅₂	—	2	2	no	—
81	C₂×D₅₂	—	2	2	no	—
82	C₂×D₅₂	—	4	2	no	—
83	C₂×D₅₂	—	4	2	no	—
84	C₂×D₅₂	—	4	1	no	—
85	C₂×D₅₂	—	4	1	no	—
86	C₂×D₅₂	—	4	1	no	—
87	C₂×D₅₂	—	4	1	no	—
88	C₂×D₅₂	—	4	1	no	—
89	C₂×D₅₂	—	4	1	no	—
90	C₂×D₅₂	—	4	1	no	—
91	C₂×D₅₂	—	4	1	no	—
92	C₂×D₅₂	C₄²	1	4	yes	—
93	C₂×C₄×D₁₃	—	4	4	no	—
94	C₂×C₄×D₁₃	—	4	4	no	—
95	C₂×C₄×D₁₃	—	4	4	no	—
96	C₂×C₈×C₁₃	—	2	2	no	—
97	C₂×C₈×C₁₃	—	2	2	no	—
98	C₂×C₈×C₁₃	—	4	1	no	—
99	C₂×C₈×C₁₃	—	4	1	no	—
100	C₂×C₈×C₁₃	—	4	1	no	—
101	C₂×C₈×C₁₃	—	4	1	no	—
102	C₁₃×C₄⋊C₄	—	4	2	no	—
103	C₁₃×C₄⋊C₄	—	4	1	no	—
104	C₁₃×C₄⋊C₄	—	4	1	no	—
105	C₁₃×C₄⋊C₄	—	4	1	no	—
106	C₁₃×C₄⋊C₄	—	4	1	no	—
107	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
108	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
109	C₄²×C₁₃	#41	1	1	yes	characteristic
110	C₄²×C₁₃	#41	1	1	yes	characteristic
111	#6103	—	4	4	no	—
112	#6103	—	4	4	no	—
113	#6103	—	4	4	no	—
114	C₄×Dic₁₃	—	2	1	no	—
115	C₄×Dic₁₃	—	2	1	no	—
116	C₄×Dic₁₃	—	2	1	no	—
117	C₄×Dic₁₃	—	2	1	no	—
118	C₄×Dic₁₃	—	2	1	no	—
119	C₄×Dic₁₃	—	2	1	no	—
120	C₄×Dic₁₃	—	2	2	no	—
121	C₄×Dic₁₃	—	4	1	no	—
122	C₄×Dic₁₃	D₈	1	2	yes	—
123	C₄×Dic₁₃	SD₁₆	1	2	yes	—
124	C₂×#1055	—	2	2	no	—
125	C₂×#1055	—	2	2	no	—
126	C₂×#1055	—	4	1	no	—
127	C₂×#1055	—	4	1	no	—
128	C₂×#1055	—	4	1	no	—
129	C₂×#1055	—	4	1	no	—
130	C₄×#127	—	13	1	no	—
131	#1767	—	13	1	no	—
132	C₄×C₄⋊C₈	—	13	1	no	—
133	C₂×#331	—	13	1	no	—
134	C₂×#331	—	13	1	no	—
135	#1296	—	13	1	no	—
136	#1296	D₁₃	1	1	yes	characteristic, complemented
137	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
138	C₂²×D₁₃	—	2	4	no	—
139	C₂²×D₁₃	—	4	2	no	—
140	C₂²×D₁₃	—	4	2	no	—
141	C₂²×D₁₃	—	4	2	no	—
142	C₂²×D₁₃	—	4	2	no	—
143	C₂²×D₁₃	—	4	2	no	—
144	C₂²×D₁₃	—	4	2	no	—
145	C₂×C₄×C₁₃	—	2	1	no	—
146	C₂×C₄×C₁₃	—	2	1	no	—
147	C₂×C₄×C₁₃	—	4	2	no	—
148	C₂×C₄×C₁₃	—	4	2	no	—
149	C₂×C₄×C₁₃	—	4	2	no	—
150	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
151	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
152	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
153	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
154	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
155	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
156	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
157	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
158	C₂×C₄×C₁₃	#135	1	1	yes	characteristic
159	C₂×C₄×C₁₃	#135	1	1	yes	characteristic
160	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
161	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
162	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
163	C₂×C₄×C₁₃	#137	1	1	yes	characteristic
164	C₂×Dic₁₃	—	2	1	no	—
165	C₂×Dic₁₃	—	2	1	no	—
166	C₂×Dic₁₃	—	2	1	no	—
167	C₂×Dic₁₃	—	2	1	no	—
168	C₂×Dic₁₃	—	2	1	no	—
169	C₂×Dic₁₃	—	2	1	no	—
170	C₂×Dic₁₃	—	2	1	no	—
171	C₂×Dic₁₃	—	2	1	no	—
172	C₂×Dic₁₃	—	2	1	no	—
173	C₂×Dic₁₃	#100	1	2	yes	—
174	C₂×Dic₁₃	#102	1	2	yes	—
175	C₂×Dic₁₃	#102	1	2	yes	—
176	D₅₂	—	4	4	no	—
177	D₅₂	—	4	4	no	—
178	D₅₂	—	4	2	no	—
179	D₅₂	—	4	2	no	—
180	D₅₂	—	4	2	no	—
181	D₅₂	—	4	2	no	—
182	D₅₂	—	4	2	no	—
183	D₅₂	—	4	2	no	—
184	D₅₂	—	4	2	no	—
185	D₅₂	—	4	2	no	—
186	C₄×D₁₃	—	8	8	no	—
187	C₈×C₁₃	—	4	2	no	—
188	C₈×C₁₃	—	4	2	no	—
189	#1055	—	4	2	no	—
190	#1055	—	4	2	no	—
191	C₂×#127	—	13	1	no	—
192	C₂×C₄×D₄	—	13	2	no	—
193	C₂×C₄×D₄	—	26	1	no	—
194	C₂×C₄×D₄	—	26	1	no	—
195	C₂×C₄⋊C₈	—	13	1	no	—
196	C₂×C₄⋊C₈	—	13	1	no	—
197	C₂×C₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic
198	C₂×C₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic
199	C₂×#97	—	26	1	no	—
200	C₂×C₄×C₈	—	26	1	no	—
201	#390	—	13	2	no	—
202	#390	—	26	1	no	—
203	#390	—	26	1	no	—
204	#384	C₂×D₁₃	1	1	yes	characteristic
205	C₄³	—	13	1	no	—
206	#336	—	26	1	no	—
207	#336	—	26	1	no	—
208	#331	—	13	4	no	—
209	#331	—	13	4	no	—
210	C₂²×C₁₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
211	C₂²×C₁₃	C₂×#100	1	1	yes	characteristic
212	C₂²×C₁₃	#413	1	1	yes	characteristic
213	C₂²×C₁₃	C₂×#102	1	1	yes	characteristic
214	C₂²×C₁₃	#416	1	1	yes	characteristic
215	C₂²×C₁₃	#417	1	1	yes	characteristic
216	C₂²×C₁₃	#418	1	1	yes	characteristic
217	C₂×D₁₃	—	4	4	no	—
218	C₂×D₁₃	—	4	4	no	—
219	C₂×D₁₃	—	4	4	no	—
220	C₂×D₁₃	—	8	2	no	—
221	C₂×D₁₃	—	8	2	no	—
222	C₂×D₁₃	—	8	2	no	—
223	C₂×D₁₃	—	8	2	no	—
224	C₄×C₁₃	—	2	1	no	—
225	C₄×C₁₃	—	2	1	no	—
226	C₄×C₁₃	—	8	2	no	—
227	C₄×C₁₃	C₄×D₈	1	1	yes	characteristic
228	C₄×C₁₃	C₄×D₈	1	1	yes	characteristic
229	C₄×C₁₃	C₄×SD₁₆	1	1	yes	characteristic
230	C₄×C₁₃	C₄×SD₁₆	1	1	yes	characteristic
231	C₄×C₁₃	#440	1	1	yes	characteristic
232	C₄×C₁₃	#440	1	1	yes	characteristic
233	C₄×C₁₃	#442	1	1	yes	characteristic
234	C₄×C₁₃	#442	1	1	yes	characteristic
235	Dic₁₃	—	2	2	no	—
236	Dic₁₃	—	2	2	no	—
237	Dic₁₃	—	2	2	no	—
238	Dic₁₃	—	4	1	no	—
239	C₂²×D₄	—	13	2	no	—
240	C₂²×D₄	—	26	1	no	—
241	C₂²×D₄	—	26	1	no	—
242	C₂³×C₄	—	26	2	no	—
243	C₂²×C₈	—	2	1	no	—
244	C₂²×C₈	—	2	1	no	—
245	C₂²×C₈	—	26	1	no	—
246	C₂²×C₈	—	26	1	no	—
247	#127	—	13	2	no	—
248	#127	—	13	2	no	—
249	#127	—	26	1	no	—
250	#127	—	26	1	no	—
251	C₄×D₄	—	52	2	no	—
252	C₄×D₄	—	52	2	no	—
253	C₄×D₄	—	52	2	no	—
254	C₄×D₄	—	52	2	no	—
255	C₄×D₄	—	52	4	no	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄⋊C₄	—	2	1	no	—
258	C₂×C₄⋊C₄	C₄×D₁₃	1	2	yes	—
259	C₂×C₂²⋊C₄	—	26	2	no	—
260	C₂×C₂²⋊C₄	—	26	2	no	—
261	C₂×C₂²⋊C₄	—	26	2	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	—	13	1	no	—
268	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
269	C₄⋊C₈	—	2	1	no	—
270	C₄⋊C₈	—	2	1	no	—
271	C₄⋊C₈	—	13	2	no	—
272	C₄⋊C₈	—	13	2	no	—
273	C₄⋊C₈	—	26	1	no	—
274	C₄⋊C₈	—	26	1	no	—
275	C₄⋊C₈	C₄×D₁₃	1	2	yes	complemented
276	C₄⋊C₈	C₄×D₁₃	1	2	yes	complemented
277	#97	—	52	2	no	—
278	C₄×C₈	—	52	2	no	—
279	C₂×C₁₃	#1545	1	1	yes	characteristic
280	C₂×C₁₃	#1547	1	1	yes	characteristic
281	C₂×C₁₃	#1551	1	1	yes	characteristic
282	C₂×C₁₃	#1553	1	1	yes	characteristic
283	C₂×C₁₃	C₄×#100	1	1	yes	characteristic
284	C₂×C₁₃	C₄×#102	1	1	yes	characteristic
285	C₂×C₁₃	#1762	1	1	yes	characteristic
286	D₁₃	—	8	4	no	—
287	C₂⁴	—	26	2	no	—
288	C₂×D₄	—	13	4	no	—
289	C₂×D₄	—	26	2	no	—
290	C₂×D₄	—	26	2	no	—
291	C₂×D₄	—	26	2	no	—
292	C₂×D₄	—	26	2	no	—
293	C₂×D₄	—	26	2	no	—
294	C₂×D₄	—	52	2	no	—
295	C₂×D₄	—	52	2	no	—
296	C₂×D₄	—	52	1	no	—
297	C₂×D₄	—	52	1	no	—
298	C₂×D₄	—	52	1	no	—
299	C₂×D₄	—	52	1	no	—
300	C₂×D₄	—	52	1	no	—
301	C₂×D₄	—	52	1	no	—
302	C₂×D₄	—	52	1	no	—
303	C₂×D₄	—	52	1	no	—
304	C₂²×C₄	—	2	2	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	—	52	4	no	—
310	C₂²×C₄	—	52	4	no	—
311	C₂²×C₄	—	52	4	no	—
312	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
313	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
314	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	4	1	no	—
318	C₂×C₈	—	4	1	no	—
319	C₂×C₈	—	4	1	no	—
320	C₂×C₈	—	4	1	no	—
321	C₂×C₈	—	26	2	no	—
322	C₂×C₈	—	26	2	no	—
323	C₂×C₈	—	52	1	no	—
324	C₂×C₈	—	52	1	no	—
325	C₂×C₈	—	52	1	no	—
326	C₂×C₈	—	52	1	no	—
327	C₄⋊C₄	—	4	2	no	—
328	C₄⋊C₄	—	4	1	no	—
329	C₄⋊C₄	—	4	1	no	—
330	C₄⋊C₄	—	4	1	no	—
331	C₄⋊C₄	—	4	1	no	—
332	C₂²⋊C₄	—	52	4	no	—
333	C₂²⋊C₄	—	52	4	no	—
334	C₂²⋊C₄	—	52	4	no	—
335	C₄²	—	13	2	no	—
336	C₄²	—	13	2	no	—
337	C₄²	—	26	2	no	—
338	C₄²	—	26	1	no	—
339	C₄²	—	26	1	no	—
340	C₄²	—	26	1	no	—
341	C₄²	—	26	1	no	—
342	C₄²	—	26	1	no	—
343	C₄²	—	26	1	no	—
344	C₄²	—	52	1	no	—
345	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
346	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
347	C₄²	#6129	1	1	yes	characteristic
348	C₄²	#6131	1	1	yes	characteristic
349	C₁₃	#8234	1	1	yes	characteristic, complemented, Sylow
350	C₂³	—	26	4	no	—
351	C₂³	—	52	2	no	—
352	C₂³	—	52	2	no	—
353	C₂³	—	52	2	no	—
354	C₂³	—	52	2	no	—
355	C₂³	—	52	2	no	—
356	C₂³	—	52	2	no	—
357	C₂³	C₂²⋊C₄×D₁₃	1	1	yes	characteristic
358	D₄	—	52	4	no	—
359	D₄	—	52	4	no	—
360	D₄	—	52	2	no	—
361	D₄	—	52	2	no	—
362	D₄	—	52	2	no	—
363	D₄	—	52	2	no	—
364	D₄	—	52	2	no	—
365	D₄	—	52	2	no	—
366	D₄	—	52	2	no	—
367	D₄	—	52	2	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	13	2	no	—
374	C₂×C₄	—	13	2	no	—
375	C₂×C₄	—	13	2	no	—
376	C₂×C₄	—	26	1	no	—
377	C₂×C₄	—	26	1	no	—
378	C₂×C₄	—	26	1	no	—
379	C₂×C₄	—	26	1	no	—
380	C₂×C₄	—	26	1	no	—
381	C₂×C₄	—	26	1	no	—
382	C₂×C₄	—	26	1	no	—
383	C₂×C₄	—	26	1	no	—
384	C₂×C₄	—	26	1	no	—
385	C₂×C₄	—	104	8	no	—
386	C₂×C₄	C₄²×D₁₃	1	1	yes	characteristic
387	C₂×C₄	#88135	1	1	yes	characteristic
388	C₂×C₄	#88135	1	1	yes	characteristic
389	C₂×C₄	#88146	1	1	yes	characteristic
390	C₂×C₄	#88147	1	1	yes	characteristic
391	C₂×C₄	#88147	1	1	yes	characteristic
392	C₂×C₄	D₈×D₁₃	1	1	yes	characteristic
393	C₂×C₄	#88165	1	1	yes	characteristic
394	C₂×C₄	SD₁₆×D₁₃	1	1	yes	characteristic
395	C₂×C₄	#88168	1	1	yes	characteristic
396	C₂×C₄	#88168	1	1	yes	characteristic
397	C₂×C₄	#88170	1	1	yes	characteristic
398	C₂×C₄	#88172	1	1	yes	characteristic
399	C₂×C₄	#88173	1	1	yes	characteristic
400	C₈	—	4	2	no	—
401	C₈	—	4	2	no	—
402	C₈	—	52	2	no	—
403	C₈	—	52	2	no	—
404	C₂²	—	52	4	no	—
405	C₂²	—	52	4	no	—
406	C₂²	—	52	4	no	—
407	C₂²	—	104	2	no	—
408	C₂²	—	104	2	no	—
409	C₂²	—	104	2	no	—
410	C₂²	—	104	2	no	—
411	C₂²	#11718327	1	1	yes	characteristic
412	C₂²	D₁₃×#100	1	1	yes	characteristic
413	C₂²	#11718412	1	1	yes	characteristic
414	C₂²	D₁₃×#102	1	1	yes	characteristic
415	C₂²	#11718431	1	1	yes	characteristic
416	C₂²	#11718464	1	1	yes	characteristic
417	C₂²	#11718465	1	1	yes	characteristic
418	C₄	—	2	1	no	—
419	C₄	—	2	1	no	—
420	C₄	—	8	2	no	—
421	C₄	—	26	2	no	—
422	C₄	—	26	2	no	—
423	C₄	—	26	2	no	—
424	C₄	—	52	1	no	—
425	C₄	#11718417	1	1	yes	characteristic
426	C₄	#11718446	1	1	yes	characteristic
427	C₄	#11718449	1	1	yes	characteristic
428	C₄	#11718478	1	1	yes	characteristic
429	C₄	#11718513	1	1	yes	characteristic
430	C₄	#11718530	1	1	yes	characteristic
431	C₄	#11718533	1	1	yes	characteristic
432	C₄	#11718550	1	1	yes	characteristic
433	C₂	—	104	4	no	—
434	C₂	#13113502	1	1	yes	characteristic
435	C₂	#13113512	1	1	yes	characteristic
436	C₂	#13113530	1	1	yes	characteristic
437	C₂	#13113540	1	1	yes	characteristic
438	C₂	#13114627	1	1	yes	characteristic
439	C₂	#13114650	1	1	yes	characteristic
440	C₂	#13114660	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²⋊C₄×D₁₃
commutator	C₂×C₄×C₁₃	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₁₃×#1296	C₂
socle	C₂³×C₁₃	C₂×C₂²⋊C₄
prime radical	C₂×#88128	C₂²
cosocle	C₂×C₄²×C₁₃	C₂³
hypercenter	#1296	D₁₃
hypocenter	C₁₃	#8234
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1296

Complements

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

N	H ≅ G/N	type
2. #13114691	C₂	semidirect
3. C₄⋊C₈×Dic₁₃	C₂	semidirect
6. #13112719	C₂	semidirect
7. C₁₃×#1296	C₂	semidirect
25. #11718077	C₄	semidirect
26. #11718077	C₄	semidirect
59. C₁₃×C₄⋊C₈	C₂×C₄	semidirect
60. C₁₃×C₄⋊C₈	C₂×C₄	semidirect
65. C₄⋊#1055	C₂×C₄	semidirect
66. C₄⋊#1055	C₂×C₄	semidirect
136. #1296	D₁₃	semidirect
275. C₄⋊C₈	C₄×D₁₃	semidirect
276. C₄⋊C₈	C₄×D₁₃	semidirect
349. C₁₃	#8234	semidirect

Maximal subgroups

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

subgroup	index
#13117398	2
#13114691	2
C₄⋊C₈×Dic₁₃	2
C₂×#11718077	2
#13112719	2
C₁₃×#1296	2
#8234	13