Subgroups — #15832014

Order 3328.

702 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13123467	C₂	1	1	yes	maximal, characteristic
2	#13123464	C₂	1	1	yes	maximal, characteristic
3	C₂×D₁₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
4	#13113620	C₂	1	2	yes	maximal, complemented
5	#13113618	C₂	1	2	yes	maximal, complemented
6	#13113609	C₂	1	2	yes	maximal, complemented
7	#13113605	C₂	1	2	yes	maximal, complemented
8	#13113589	C₂	1	1	yes	maximal, characteristic, complemented
9	#13113588	C₂	1	1	yes	maximal, characteristic, complemented
10	#13113586	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1565	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₈×D₁₃	—	2	1	no	—
13	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
14	C₁₃×#431	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
16	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
17	#11718787	C₄	1	1	yes	characteristic
18	#11718787	C₄	1	1	yes	characteristic
19	#11718779	C₄	1	1	yes	characteristic
20	#11718779	C₄	1	1	yes	characteristic
21	C₂×#88054	—	2	1	no	—
22	#11718586	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
24	C₄×#6099	C₂²	1	1	yes	characteristic
25	#11718498	C₂²	1	1	yes	characteristic
26	#11718498	C₂²	1	1	yes	characteristic
27	#11718496	C₂²	1	1	yes	characteristic
28	#11718496	C₂²	1	1	yes	characteristic
29	D₁₃×C₄⋊C₈	—	2	1	no	—
30	D₁₃×C₄⋊C₈	—	2	1	no	—
31	D₁₃×C₄⋊C₈	C₂²	1	2	yes	—
32	D₁₃×C₄⋊C₈	C₂²	1	2	yes	—
33	#11718387	—	2	1	no	—
34	#11718380	—	2	1	no	—
35	#11718366	C₄	1	2	yes	—
36	#11718366	C₄	1	2	yes	—
37	C₄×#6094	—	2	1	no	—
38	#11718346	—	2	1	no	—
39	#11718346	C₂²	1	2	yes	—
40	#11718346	C₂²	1	2	yes	—
41	C₁₃×#335	C₂²	1	2	yes	complemented
42	C₁₃×#334	C₂²	1	2	yes	complemented
43	#11718072	C₂²	1	2	yes	complemented
44	#11718072	C₂²	1	2	yes	complemented
45	#11718071	C₂²	1	2	yes	complemented
46	#11718071	C₂²	1	2	yes	complemented
47	#11718050	C₂²	1	2	yes	complemented
48	#11718049	C₂²	1	2	yes	complemented
49	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
50	C₂²×C₄×D₁₃	D₄	1	1	yes	characteristic
51	C₂²×C₄×D₁₃	Q₈	1	1	yes	characteristic
52	C₂×C₁₃×M₁₆	C₂×C₄	1	1	yes	characteristic
53	C₂×C₁₃×M₁₆	C₂×C₄	1	1	yes	characteristic
54	C₂²×C₈×C₁₃	—	2	1	no	—
55	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
56	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
58	C₂×C₄×Dic₁₃	Q₈	1	1	yes	characteristic
59	C₂×#6099	C₂×C₄	1	1	yes	characteristic
60	C₂×#6099	C₂×C₄	1	1	yes	characteristic
61	C₂²×#1055	—	2	1	no	—
62	C₂×#6094	—	2	1	no	—
63	C₂×#6094	—	2	1	no	—
64	C₂×C₈×D₁₃	—	2	2	no	—
65	C₂×C₈×D₁₃	—	2	2	no	—
66	C₂×C₈×D₁₃	—	4	4	no	—
67	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
68	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
69	C₄²×D₁₃	D₄	1	1	yes	characteristic
70	C₄²×D₁₃	D₄	1	1	yes	characteristic
71	C₄²×D₁₃	Q₈	1	1	yes	characteristic
72	C₄²×D₁₃	Q₈	1	1	yes	characteristic
73	C₄²×D₁₃	C₂³	1	1	yes	characteristic
74	C₄²×D₁₃	C₂³	1	1	yes	characteristic
75	C₁₃×C₄⋊C₈	—	2	1	no	—
76	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
77	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
78	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
79	C₁₃×C₂²⋊C₈	—	2	1	no	—
80	C₁₃×#97	C₂×C₄	1	2	yes	—
81	C₄×C₈×C₁₃	—	2	1	no	—
82	C₄×C₈×C₁₃	C₂³	1	2	yes	—
83	C₂²⋊#1055	—	2	1	no	—
84	#88060	—	2	1	no	—
85	#88060	—	2	1	no	—
86	#88060	C₂×C₄	1	2	yes	—
87	#88060	C₂×C₄	1	2	yes	—
88	#88060	C₂×C₄	1	2	yes	—
89	#88060	C₂×C₄	1	2	yes	—
90	#88055	—	2	1	no	—
91	#88055	—	2	1	no	—
92	#88054	—	2	2	no	—
93	#88054	—	2	2	no	—
94	#88054	—	2	1	no	—
95	#88054	—	2	1	no	—
96	#88054	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	C₄⋊#1055	—	2	1	no	—
101	C₄⋊#1055	C₂³	1	2	yes	—
102	C₄⋊#1055	C₂³	1	1	yes	characteristic
103	C₄⋊#1055	C₂³	1	1	yes	characteristic
104	#88043	C₂×C₄	1	2	yes	—
105	C₄×#1055	—	2	1	no	—
106	C₄×#1055	C₂³	1	2	yes	—
107	#17807	—	13	1	no	maximal, Sylow
108	C₂³×D₁₃	C₄⋊C₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
112	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
113	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
114	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
115	C₂×C₄×D₁₃	—	2	2	no	—
116	C₂×C₄×D₁₃	—	2	2	no	—
117	C₂×C₄×D₁₃	—	2	2	no	—
118	C₂×C₄×D₁₃	—	2	2	no	—
119	C₂×C₄×D₁₃	—	4	2	no	—
120	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
121	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
122	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
123	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
124	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
125	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
126	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
129	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
130	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
131	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
132	C₁₃×M₁₆	—	2	2	no	—
133	C₁₃×M₁₆	—	2	2	no	—
134	C₂×C₈×C₁₃	—	2	1	no	—
135	C₂×C₈×C₁₃	—	2	1	no	—
136	C₂×C₈×C₁₃	—	2	2	no	—
137	C₂×C₈×C₁₃	—	4	2	no	—
138	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
139	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
140	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
141	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
142	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
143	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
144	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
145	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
146	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
147	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
148	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
149	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
150	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
151	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
152	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
153	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
154	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
155	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
156	#6099	—	2	2	no	—
157	#6099	—	2	2	no	—
158	C₂×#1055	—	2	1	no	—
159	C₂×#1055	—	2	1	no	—
160	C₂×#1055	—	2	2	no	—
161	C₂×#1055	—	4	2	no	—
162	C₂×#1055	C₂²×C₄	1	2	yes	—
163	C₂×#1055	C₂²×C₄	1	2	yes	—
164	#6094	—	4	2	no	—
165	#6094	—	4	2	no	—
166	C₈×D₁₃	—	4	4	no	—
167	C₈×D₁₃	—	4	4	no	—
168	#2920	—	13	1	no	—
169	#2920	—	13	1	no	—
170	C₂²×C₄⋊C₈	—	13	1	no	—
171	#1573	—	13	2	no	—
172	#1573	—	13	2	no	—
173	#1571	—	13	2	no	—
174	#1570	—	13	2	no	—
175	#1565	—	13	1	no	—
176	#1565	—	13	1	no	—
177	#1565	—	13	1	no	—
178	#1565	D₁₃	1	1	yes	characteristic, complemented
179	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
180	C₂²×D₁₃	—	2	2	no	—
181	C₂²×D₁₃	—	2	2	no	—
182	C₂²×D₁₃	—	2	2	no	—
183	C₂²×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
184	C₂²×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
185	C₂×C₄×C₁₃	—	2	1	no	—
186	C₂×C₄×C₁₃	—	2	1	no	—
187	C₂×C₄×C₁₃	—	4	1	no	—
188	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
189	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
190	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
191	C₂×C₄×C₁₃	#131	1	2	yes	—
192	C₂×C₄×C₁₃	#131	1	2	yes	—
193	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
194	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
196	C₂×Dic₁₃	—	2	2	no	—
197	C₂×Dic₁₃	—	2	2	no	—
198	C₂×Dic₁₃	—	4	1	no	—
199	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
200	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
201	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
202	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
203	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
204	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
205	C₄×D₁₃	—	2	2	no	—
206	C₄×D₁₃	—	2	2	no	—
207	C₄×D₁₃	—	2	2	no	—
208	C₄×D₁₃	—	2	1	no	—
209	C₄×D₁₃	—	2	1	no	—
210	C₄×D₁₃	—	2	1	no	—
211	C₄×D₁₃	—	2	1	no	—
212	C₄×D₁₃	—	2	1	no	—
213	C₄×D₁₃	—	2	1	no	—
214	C₄×D₁₃	—	2	2	no	—
215	C₄×D₁₃	—	2	2	no	—
216	C₄×D₁₃	—	2	2	no	—
217	C₄×D₁₃	—	4	1	no	—
218	C₄×D₁₃	—	4	1	no	—
219	C₄×D₁₃	AGL(1,ℤ/8)	1	2	yes	—
220	C₄×D₁₃	#137	1	2	yes	—
221	C₈×C₁₃	—	2	2	no	—
222	C₈×C₁₃	—	2	2	no	—
223	C₈×C₁₃	—	4	2	no	—
224	C₈×C₁₃	—	4	1	no	—
225	C₈×C₁₃	—	4	1	no	—
226	#1055	—	2	2	no	—
227	#1055	—	2	2	no	—
228	#1055	—	4	2	no	—
229	#1055	—	4	1	no	—
230	#1055	—	4	1	no	—
231	C₂³×C₈	—	26	1	no	—
232	C₂²×C₄²	—	13	1	no	—
233	#432	—	13	2	no	—
234	#432	—	13	2	no	—
235	#432	—	13	1	no	—
236	#432	—	13	1	no	—
237	#432	—	26	1	no	—
238	#431	—	13	2	no	—
239	#431	—	13	2	no	—
240	#431	—	13	1	no	—
241	#431	—	26	1	no	—
242	#431	C₂×D₁₃	1	1	yes	characteristic
243	#423	—	13	1	no	—
244	#423	—	13	1	no	—
245	#423	—	13	1	no	—
246	#423	—	13	1	no	—
247	C₂×C₄⋊C₈	—	13	1	no	—
248	C₂×C₄⋊C₈	—	13	2	no	—
249	C₂×C₄⋊C₈	—	13	2	no	—
250	C₂×C₄⋊C₈	—	26	1	no	—
251	C₂×C₄⋊C₈	—	26	1	no	—
252	C₂×C₄⋊C₈	—	26	1	no	—
253	C₂×C₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic
254	#407	—	13	1	no	—
255	#407	—	13	1	no	—
256	#407	—	26	1	no	—
257	C₄×M₁₆	—	13	1	no	—
258	C₄×M₁₆	—	26	1	no	—
259	C₄×M₁₆	C₂×D₁₃	1	1	yes	characteristic
260	#335	—	13	2	no	—
261	#335	—	13	2	no	—
262	#335	—	13	2	no	—
263	#335	C₂×D₁₃	1	2	yes	complemented
264	#334	—	13	2	no	—
265	#334	—	13	2	no	—
266	#334	—	13	2	no	—
267	#334	C₂×D₁₃	1	2	yes	complemented
268	C₂²×C₁₃	—	2	1	no	—
269	C₂²×C₁₃	—	2	1	no	—
270	C₂²×C₁₃	#424	1	2	yes	—
271	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
272	C₂×D₁₃	—	2	8	no	—
273	C₂×D₁₃	—	2	1	no	—
274	C₂×D₁₃	—	2	1	no	—
275	C₂×D₁₃	—	2	1	no	—
276	C₂×D₁₃	—	2	1	no	—
277	C₂×D₁₃	#428	1	2	yes	—
278	C₂×D₁₃	#430	1	2	yes	—
279	C₄×C₁₃	—	2	1	no	—
280	C₄×C₁₃	—	2	1	no	—
281	C₄×C₁₃	—	2	1	no	—
282	C₄×C₁₃	#424	1	2	yes	—
283	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
284	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
285	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
286	C₄×C₁₃	C₂×#137	1	1	yes	characteristic
287	Dic₁₃	—	2	1	no	—
288	Dic₁₃	—	2	1	no	—
289	Dic₁₃	—	2	1	no	—
290	Dic₁₃	—	2	1	no	—
291	Dic₁₃	—	2	1	no	—
292	Dic₁₃	#428	1	2	yes	—
293	C₂³×C₄	—	13	1	no	—
294	C₂³×C₄	—	13	1	no	—
295	C₂³×C₄	—	13	1	no	—
296	C₂×M₁₆	—	13	1	no	—
297	C₂×M₁₆	—	13	1	no	—
298	C₂×M₁₆	—	26	1	no	—
299	C₂×M₁₆	—	26	1	no	—
300	C₂×M₁₆	C₄×D₁₃	1	1	yes	characteristic
301	C₂×M₁₆	C₄×D₁₃	1	1	yes	characteristic
302	C₂²×C₈	—	2	1	no	—
303	C₂²×C₈	—	26	2	no	—
304	C₂²×C₈	—	26	2	no	—
305	C₂²×C₈	—	26	1	no	—
306	C₂²×C₈	—	52	4	no	—
307	C₂×C₄²	—	13	1	no	—
308	C₂×C₄²	—	13	1	no	—
309	C₂×C₄²	—	13	1	no	—
310	C₂×C₄²	—	13	1	no	—
311	C₂×C₄²	—	13	1	no	—
312	C₂×C₄²	—	13	1	no	—
313	C₂×C₄²	—	13	1	no	—
314	C₂×C₄²	—	13	1	no	—
315	C₂×C₄²	—	13	1	no	—
316	C₂×C₄²	—	13	1	no	—
317	C₂×C₄²	—	13	1	no	—
318	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
319	C₄⋊C₈	—	2	1	no	—
320	C₄⋊C₈	—	13	2	no	—
321	C₄⋊C₈	—	13	2	no	—
322	C₄⋊C₈	—	13	2	no	—
323	C₄⋊C₈	—	13	2	no	—
324	C₄⋊C₈	—	13	1	no	—
325	C₄⋊C₈	—	13	2	no	—
326	C₄⋊C₈	—	13	1	no	—
327	C₄⋊C₈	—	26	2	no	—
328	C₄⋊C₈	—	26	2	no	—
329	C₄⋊C₈	—	26	1	no	—
330	C₄⋊C₈	—	26	1	no	—
331	C₄⋊C₈	—	26	1	no	—
332	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
333	C₄⋊C₈	C₂²×D₁₃	1	2	yes	—
334	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
335	C₂²⋊C₈	—	2	1	no	—
336	C₂²⋊C₈	—	13	2	no	—
337	C₂²⋊C₈	—	13	2	no	—
338	C₂²⋊C₈	—	13	2	no	—
339	C₂²⋊C₈	—	13	2	no	—
340	C₂²⋊C₈	—	26	1	no	—
341	C₂²⋊C₈	—	26	1	no	—
342	C₂²⋊C₈	—	26	1	no	—
343	#97	—	13	2	no	—
344	#97	—	26	1	no	—
345	#97	—	26	1	no	—
346	#97	C₄×D₁₃	1	2	yes	—
347	C₄×C₈	—	2	1	no	—
348	C₄×C₈	—	13	2	no	—
349	C₄×C₈	—	26	1	no	—
350	C₄×C₈	C₂²×D₁₃	1	2	yes	—
351	C₂×C₁₃	—	2	2	no	—
352	C₂×C₁₃	C₂×#424	1	1	yes	characteristic
353	C₂×C₁₃	C₂×#428	1	1	yes	characteristic
354	C₂×C₁₃	C₂×#430	1	1	yes	characteristic
355	D₁₃	—	2	2	no	—
356	D₁₃	—	2	2	no	—
357	C₂⁴	—	13	1	no	—
358	C₂²×C₄	—	13	1	no	—
359	C₂²×C₄	—	13	1	no	—
360	C₂²×C₄	—	13	1	no	—
361	C₂²×C₄	—	13	1	no	—
362	C₂²×C₄	—	13	1	no	—
363	C₂²×C₄	—	13	1	no	—
364	C₂²×C₄	—	13	1	no	—
365	C₂²×C₄	—	13	1	no	—
366	C₂²×C₄	—	13	1	no	—
367	C₂²×C₄	—	13	1	no	—
368	C₂²×C₄	—	13	1	no	—
369	C₂²×C₄	—	13	1	no	—
370	C₂²×C₄	—	13	1	no	—
371	C₂²×C₄	—	13	1	no	—
372	C₂²×C₄	—	13	1	no	—
373	C₂²×C₄	—	26	2	no	—
374	C₂²×C₄	—	26	2	no	—
375	C₂²×C₄	—	26	2	no	—
376	C₂²×C₄	—	26	2	no	—
377	C₂²×C₄	—	52	2	no	—
378	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
379	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
380	C₂²×C₄	Q₈×D₁₃	1	1	yes	characteristic
381	M₁₆	—	2	2	no	—
382	M₁₆	—	2	2	no	—
383	M₁₆	—	26	2	no	—
384	M₁₆	—	26	2	no	—
385	M₁₆	—	52	2	no	—
386	M₁₆	—	52	2	no	—
387	C₂×C₈	—	2	1	no	—
388	C₂×C₈	—	2	1	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	4	2	no	—
391	C₂×C₈	—	13	2	no	—
392	C₂×C₈	—	13	2	no	—
393	C₂×C₈	—	26	1	no	—
394	C₂×C₈	—	26	1	no	—
395	C₂×C₈	—	26	2	no	—
396	C₂×C₈	—	52	4	no	—
397	C₂×C₈	—	52	4	no	—
398	C₂×C₈	—	52	2	no	—
399	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
400	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
401	C₄²	—	13	1	no	—
402	C₄²	—	13	1	no	—
403	C₄²	—	13	1	no	—
404	C₄²	—	13	1	no	—
405	C₄²	—	13	1	no	—
406	C₄²	—	13	1	no	—
407	C₄²	—	13	1	no	—
408	C₄²	—	13	1	no	—
409	C₄²	—	13	1	no	—
410	C₄²	—	13	1	no	—
411	C₄²	—	13	1	no	—
412	C₄²	—	13	1	no	—
413	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
414	C₄²	D₄×D₁₃	1	1	yes	characteristic
415	C₄²	Q₈×D₁₃	1	1	yes	characteristic
416	C₄²	C₂³×D₁₃	1	1	yes	characteristic
417	C₁₃	#17807	1	1	yes	characteristic, complemented, Sylow
418	C₂³	—	13	1	no	—
419	C₂³	—	13	1	no	—
420	C₂³	—	26	2	no	—
421	C₂³	—	26	2	no	—
422	C₂³	—	26	2	no	—
423	C₂³	C₄⋊C₄×D₁₃	1	1	yes	characteristic
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	13	1	no	—
428	C₂×C₄	—	13	2	no	—
429	C₂×C₄	—	13	2	no	—
430	C₂×C₄	—	13	1	no	—
431	C₂×C₄	—	13	1	no	—
432	C₂×C₄	—	13	1	no	—
433	C₂×C₄	—	13	1	no	—
434	C₂×C₄	—	13	1	no	—
435	C₂×C₄	—	26	2	no	—
436	C₂×C₄	—	26	2	no	—
437	C₂×C₄	—	26	2	no	—
438	C₂×C₄	—	26	2	no	—
439	C₂×C₄	—	26	2	no	—
440	C₂×C₄	—	26	2	no	—
441	C₂×C₄	—	26	1	no	—
442	C₂×C₄	—	26	1	no	—
443	C₂×C₄	—	26	1	no	—
444	C₂×C₄	—	26	1	no	—
445	C₂×C₄	—	26	1	no	—
446	C₂×C₄	—	26	1	no	—
447	C₂×C₄	—	26	2	no	—
448	C₂×C₄	—	26	2	no	—
449	C₂×C₄	—	52	1	no	—
450	C₂×C₄	—	52	1	no	—
451	C₂×C₄	—	52	1	no	—
452	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
453	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
454	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
455	C₂×C₄	#88155	1	2	yes	—
456	C₂×C₄	#88161	1	2	yes	—
457	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
458	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
459	C₂×C₄	C₂×Q₈×D₁₃	1	1	yes	characteristic
460	C₈	—	2	2	no	—
461	C₈	—	2	2	no	—
462	C₈	—	4	2	no	—
463	C₈	—	4	1	no	—
464	C₈	—	4	1	no	—
465	C₈	—	26	2	no	—
466	C₈	—	26	2	no	—
467	C₈	—	52	2	no	—
468	C₈	—	52	1	no	—
469	C₈	—	52	1	no	—
470	C₂²	—	2	1	no	—
471	C₂²	—	2	1	no	—
472	C₂²	—	13	2	no	—
473	C₂²	—	13	2	no	—
474	C₂²	—	26	8	no	—
475	C₂²	—	26	1	no	—
476	C₂²	—	26	1	no	—
477	C₂²	—	26	1	no	—
478	C₂²	—	26	1	no	—
479	C₂²	#11718500	1	2	yes	—
480	C₂²	C₂×C₄⋊C₄×D₁₃	1	1	yes	characteristic
481	C₄	—	2	1	no	—
482	C₄	—	2	1	no	—
483	C₄	—	2	1	no	—
484	C₄	—	13	2	no	—
485	C₄	—	26	1	no	—
486	C₄	—	26	1	no	—
487	C₄	—	26	1	no	—
488	C₄	—	26	1	no	—
489	C₄	—	26	1	no	—
490	C₄	#11718500	1	2	yes	—
491	C₄	C₂×#88155	1	1	yes	characteristic
492	C₄	C₂×#88161	1	1	yes	characteristic
493	C₄	D₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
494	C₄	D₁₃×#137	1	1	yes	characteristic
495	C₂	—	2	2	no	—
496	C₂	—	26	2	no	—
497	C₂	—	26	2	no	—
498	C₂	C₂×#11718500	1	1	yes	characteristic
499	C₂	D₁₃×#428	1	1	yes	characteristic
500	C₂	D₁₃×#430	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₄²	C₂³×D₁₃
Fitting	C₁₃×#1565	C₂
socle	C₂²×C₁₃	C₂²×C₄⋊C₄
prime radical	C₂³×D₁₃	C₄⋊C₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#1565	D₁₃
hypocenter	C₁₃	#17807
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1565

Complements

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

N	H ≅ G/N	type
4. #13113620	C₂	semidirect
5. #13113618	C₂	semidirect
6. #13113609	C₂	semidirect
7. #13113605	C₂	semidirect
8. #13113589	C₂	semidirect
9. #13113588	C₂	semidirect
10. #13113586	C₂	semidirect
11. C₁₃×#1565	C₂	semidirect
41. C₁₃×#335	C₂²	semidirect
42. C₁₃×#334	C₂²	semidirect
43. #11718072	C₂²	semidirect
44. #11718072	C₂²	semidirect
45. #11718071	C₂²	semidirect
46. #11718071	C₂²	semidirect
47. #11718050	C₂²	semidirect
48. #11718049	C₂²	semidirect
178. #1565	D₁₃	semidirect
263. #335	C₂×D₁₃	semidirect
267. #334	C₂×D₁₃	semidirect
417. C₁₃	#17807	semidirect

Maximal subgroups

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

subgroup	index
#13123467	2
#13123464	2
C₂×D₁₃×C₄⋊C₈	2
#13113620	2
#13113618	2
#13113609	2
#13113605	2
#13113589	2
#13113588	2
#13113586	2
C₁₃×#1565	2
#17807	13