Subgroups — #15830417

Order 3328.

1042 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13128132	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718598	C₂	1	1	yes	maximal, characteristic, complemented
3	#13113414	C₂	1	4	yes	maximal, complemented
4	#13113388	C₂	1	2	yes	maximal, complemented
5	#13113384	C₂	1	2	yes	maximal, complemented
6	#13113341	C₂	1	4	yes	maximal, complemented
7	C₁₃×#2920	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
9	#11719496	—	2	1	no	—
10	#11719496	—	2	1	no	—
11	#11719496	C₂²	1	2	yes	—
12	#11719184	—	2	1	no	—
13	#11719184	—	2	1	no	—
14	#11719184	—	2	1	no	—
15	#11719184	—	2	1	no	—
16	#11719184	C₄	1	2	yes	complemented
17	#11719184	C₂²	1	2	yes	—
18	#11719182	C₄	1	1	yes	characteristic, complemented
19	#11719182	C₄	1	1	yes	characteristic, complemented
20	#11719182	C₂²	1	1	yes	characteristic
21	C₄×#6127	—	2	1	no	—
22	C₄×#6127	—	2	1	no	—
23	C₄×#6127	C₄	1	2	yes	complemented
24	#11719175	C₄	1	1	yes	characteristic, complemented
25	#11719175	C₄	1	1	yes	characteristic, complemented
26	#11719175	C₂²	1	1	yes	characteristic
27	C₁₃×#432	—	2	1	no	—
28	C₁₃×#432	C₂²	1	2	yes	—
29	C₁₃×#431	—	2	1	no	—
30	C₁₃×#431	C₂²	1	2	yes	—
31	C₁₃×#423	—	2	1	no	—
32	C₁₃×#407	C₂²	1	2	yes	—
33	C₄×C₁₃×M₁₆	—	2	1	no	—
34	C₂×#88071	—	2	1	no	—
35	C₂×#88071	—	2	1	no	—
36	C₂×#88071	C₂²	1	2	yes	—
37	#11718598	—	2	1	no	—
38	#11718598	—	2	1	no	—
39	#11718598	C₂²	1	2	yes	—
40	#11718598	C₂²	1	2	yes	—
41	#11718062	C₂²	1	8	yes	—
42	#11718059	C₂²	1	8	yes	—
43	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
46	C₂³×Dic₁₃	—	2	2	no	—
47	C₂×#6127	—	2	1	no	—
48	C₂×#6127	—	2	1	no	—
49	C₂×#6127	C₂×C₄	1	2	yes	—
50	C₂×C₁₃×M₁₆	—	2	2	no	—
51	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
56	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
57	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
58	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
59	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
60	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
61	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
63	#88207	—	2	2	no	—
64	#88184	—	2	1	no	—
65	#88184	—	2	1	no	—
66	#88184	—	2	1	no	—
67	#88184	—	2	1	no	—
68	#88184	C₂×C₄	1	2	yes	—
69	#88184	C₂³	1	2	yes	—
70	#88183	—	2	2	no	—
71	#88183	—	2	2	no	—
72	#88183	—	2	2	no	—
73	C₄×C₂²⋊D₁₃	—	2	2	no	—
74	C₄×C₂²⋊D₁₃	—	2	2	no	—
75	C₄×C₂²⋊D₁₃	—	2	2	no	—
76	C₄×C₂²⋊D₁₃	—	2	2	no	—
77	C₄×C₂²⋊D₁₃	—	2	2	no	—
78	C₄×C₂²⋊D₁₃	—	2	2	no	—
79	#88180	—	2	1	no	—
80	#88180	—	2	1	no	—
81	#88180	C₂×C₄	1	2	yes	—
82	#88178	—	2	1	no	—
83	#88178	—	2	1	no	—
84	#88178	—	2	1	no	—
85	#88178	—	2	1	no	—
86	#88178	C₂×C₄	1	2	yes	—
87	#88178	C₂³	1	2	yes	—
88	#88130	—	2	2	no	—
89	#88130	—	2	2	no	—
90	#88129	—	2	1	no	—
91	#88129	—	2	1	no	—
92	#88129	C₂×C₄	1	2	yes	complemented
93	#88128	C₂×C₄	1	1	yes	characteristic, complemented
94	C₄×D₅₂	—	2	1	no	—
95	C₄×D₅₂	—	2	1	no	—
96	C₄×D₅₂	—	2	1	no	—
97	C₄×D₅₂	—	2	1	no	—
98	C₄×D₅₂	C₂×C₄	1	2	yes	complemented
99	C₄×D₅₂	C₂×C₄	1	2	yes	complemented
100	#88126	—	2	2	no	—
101	#88126	—	2	2	no	—
102	#88126	—	2	2	no	—
103	C₄²×D₁₃	—	2	2	no	—
104	#88124	—	2	1	no	—
105	#88124	—	2	1	no	—
106	#88124	C₂×C₄	1	2	yes	complemented
107	#88123	C₂×C₄	1	1	yes	characteristic, complemented
108	#88123	C₂×C₄	1	1	yes	characteristic, complemented
109	#88123	C₂×C₄	1	1	yes	characteristic, complemented
110	C₄×Dic₂₆	—	2	1	no	—
111	C₄×Dic₂₆	—	2	1	no	—
112	C₄×Dic₂₆	—	2	1	no	—
113	C₄×Dic₂₆	—	2	1	no	—
114	C₄×Dic₂₆	C₂×C₄	1	2	yes	complemented
115	C₄×Dic₂₆	C₂×C₄	1	2	yes	complemented
116	C₁₃×C₄⋊C₈	—	2	2	no	—
117	C₁₃×C₄⋊C₈	—	2	2	no	—
118	C₁₃×C₂²⋊C₈	—	2	2	no	—
119	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
120	C₁₃×#97	—	2	2	no	—
121	C₄×C₈×C₁₃	—	2	2	no	—
122	#88071	—	2	2	no	—
123	#88071	—	2	2	no	—
124	#88071	—	2	2	no	—
125	#88071	—	2	2	no	—
126	#88071	—	2	2	no	—
127	#88071	C₂³	1	4	yes	—
128	#17593	—	13	1	no	maximal, Sylow
129	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₃	—	4	2	no	—
131	C₂²×C₄×C₁₃	—	4	2	no	—
132	C₂²×C₄×C₁₃	—	4	2	no	—
133	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
141	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
143	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
151	C₂×C₂²⋊D₁₃	—	2	2	no	—
152	C₂×C₂²⋊D₁₃	—	2	2	no	—
153	C₂×C₂²⋊D₁₃	—	2	2	no	—
154	C₂²×Dic₁₃	—	2	4	no	—
155	C₂²×Dic₁₃	—	4	4	no	—
156	C₂²×Dic₁₃	—	4	4	no	—
157	C₂²×Dic₁₃	—	4	4	no	—
158	#6127	—	4	4	no	—
159	#6127	—	4	4	no	—
160	#6127	—	4	4	no	—
161	C₂×D₅₂	—	2	1	no	—
162	C₂×D₅₂	—	2	1	no	—
163	C₂×D₅₂	C₂²×C₄	1	2	yes	—
164	C₂×C₄×D₁₃	—	2	2	no	—
165	C₂×C₄×D₁₃	—	2	2	no	—
166	C₂×C₄×D₁₃	—	2	2	no	—
167	C₂×Dic₂₆	—	2	1	no	—
168	C₂×Dic₂₆	—	2	1	no	—
169	C₂×Dic₂₆	C₂²×C₄	1	2	yes	—
170	C₁₃×M₁₆	—	4	4	no	—
171	C₂×C₈×C₁₃	—	2	4	no	—
172	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
173	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
174	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
175	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
176	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
177	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
178	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
179	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
180	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
181	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
182	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
183	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
184	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
185	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
186	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
187	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
188	C₂²⋊Dic₁₃	—	2	2	no	—
189	C₂²⋊Dic₁₃	—	2	2	no	—
190	C₂²⋊Dic₁₃	—	2	2	no	—
191	#6103	—	2	2	no	—
192	#6103	—	2	2	no	—
193	#6103	—	2	2	no	—
194	#6103	—	2	2	no	—
195	#6103	—	2	2	no	—
196	#6103	—	2	2	no	—
197	C₄⋊Dic₁₃	—	2	1	no	—
198	C₄⋊Dic₁₃	—	2	1	no	—
199	C₄⋊Dic₁₃	—	2	1	no	—
200	C₄⋊Dic₁₃	—	2	1	no	—
201	C₄⋊Dic₁₃	C₂²×C₄	1	2	yes	—
202	C₄⋊Dic₁₃	C₂²×C₄	1	2	yes	—
203	#6101	—	2	2	no	—
204	#6101	—	2	2	no	—
205	#6101	—	2	2	no	—
206	#6101	—	2	2	no	—
207	#6101	—	2	2	no	—
208	#6101	—	2	2	no	—
209	C₄×Dic₁₃	—	2	2	no	—
210	C₄×Dic₁₃	—	2	2	no	—
211	C₄×Dic₁₃	—	2	2	no	—
212	#3444	—	13	1	no	—
213	#2920	D₁₃	1	1	yes	characteristic, complemented
214	C₂×#383	—	13	1	no	—
215	#1521	—	13	4	no	—
216	#1515	—	13	2	no	—
217	#1514	—	13	2	no	—
218	#1504	—	13	4	no	—
219	C₂³×C₁₃	—	2	2	no	—
220	C₂³×C₁₃	—	2	2	no	—
221	C₂³×C₁₃	—	2	2	no	—
222	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
223	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
224	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
225	C₂²×D₁₃	—	2	2	no	—
226	C₂×C₄×C₁₃	—	2	2	no	—
227	C₂×C₄×C₁₃	—	2	2	no	—
228	C₂×C₄×C₁₃	—	2	2	no	—
229	C₂×C₄×C₁₃	—	2	2	no	—
230	C₂×C₄×C₁₃	—	2	2	no	—
231	C₂×C₄×C₁₃	—	2	2	no	—
232	C₂×C₄×C₁₃	—	4	1	no	—
233	C₂×C₄×C₁₃	—	4	1	no	—
234	C₂×C₄×C₁₃	—	4	1	no	—
235	C₂×C₄×C₁₃	—	4	1	no	—
236	C₂×C₄×C₁₃	—	4	1	no	—
237	C₂×C₄×C₁₃	—	4	1	no	—
238	C₂×C₄×C₁₃	—	4	1	no	—
239	C₂×C₄×C₁₃	—	4	1	no	—
240	C₂×C₄×C₁₃	—	4	1	no	—
241	C₂×C₄×C₁₃	—	4	1	no	—
242	C₂×C₄×C₁₃	—	4	1	no	—
243	C₂×C₄×C₁₃	—	4	1	no	—
244	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
245	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
246	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
247	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
248	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
249	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
250	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
251	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
252	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
253	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
254	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
255	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
256	C₂²⋊D₁₃	—	4	4	no	—
257	C₂²⋊D₁₃	—	4	4	no	—
258	C₂²⋊D₁₃	—	4	4	no	—
259	C₂×Dic₁₃	—	2	2	no	—
260	C₂×Dic₁₃	—	2	2	no	—
261	C₂×Dic₁₃	—	2	2	no	—
262	C₂×Dic₁₃	—	4	4	no	—
263	C₂×Dic₁₃	—	4	4	no	—
264	C₂×Dic₁₃	—	4	4	no	—
265	C₂×Dic₁₃	—	8	8	no	—
266	D₅₂	—	4	2	no	—
267	D₅₂	—	4	2	no	—
268	D₅₂	—	4	2	no	—
269	C₄×D₁₃	—	4	4	no	—
270	C₄×D₁₃	—	4	4	no	—
271	C₄×D₁₃	—	4	4	no	—
272	Dic₂₆	—	4	2	no	—
273	Dic₂₆	—	4	2	no	—
274	Dic₂₆	—	4	2	no	—
275	C₈×C₁₃	—	4	4	no	—
276	#533	—	13	1	no	—
277	#533	—	13	1	no	—
278	#533	—	13	1	no	—
279	#532	—	13	1	no	—
280	#532	—	13	1	no	—
281	#532	—	13	1	no	—
282	#529	—	13	2	no	—
283	#529	—	13	2	no	—
284	#529	—	26	1	no	—
285	#529	—	26	1	no	—
286	#529	—	26	1	no	—
287	#529	—	26	1	no	—
288	#525	—	13	2	no	—
289	#525	—	26	1	no	—
290	#525	—	26	1	no	—
291	C₄×#41	—	13	2	no	—
292	C₄×#41	—	26	1	no	—
293	C₄×#41	—	26	1	no	—
294	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
295	#432	—	2	1	no	—
296	#432	C₂×D₁₃	1	2	yes	—
297	#431	—	2	1	no	—
298	#431	C₂×D₁₃	1	2	yes	—
299	#423	—	2	1	no	—
300	#407	C₂×D₁₃	1	2	yes	—
301	C₄×M₁₆	—	2	1	no	—
302	#383	—	13	2	no	—
303	#383	—	13	2	no	—
304	#383	—	26	1	no	—
305	#383	—	26	1	no	—
306	C₂×#95	—	13	2	no	—
307	C₂×#95	—	26	1	no	—
308	C₂×#95	—	26	1	no	—
309	#328	—	13	8	no	—
310	#327	—	13	8	no	—
311	C₂²×C₁₃	—	2	8	no	—
312	C₂²×C₁₃	—	2	1	no	—
313	C₂²×C₁₃	—	2	1	no	—
314	C₂²×C₁₃	—	2	1	no	—
315	C₂²×C₁₃	—	2	1	no	—
316	C₂²×C₁₃	—	2	1	no	—
317	C₂²×C₁₃	—	2	1	no	—
318	C₂²×C₁₃	#410	1	2	yes	—
319	C₂²×C₁₃	#421	1	2	yes	—
320	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
321	C₂²×C₁₃	#575	1	2	yes	—
322	C₂×D₁₃	—	4	2	no	—
323	C₂×D₁₃	—	4	2	no	—
324	C₂×D₁₃	—	4	2	no	—
325	C₄×C₁₃	—	2	1	no	—
326	C₄×C₁₃	—	2	1	no	—
327	C₄×C₁₃	—	2	1	no	—
328	C₄×C₁₃	—	2	1	no	—
329	C₄×C₁₃	—	2	1	no	—
330	C₄×C₁₃	—	2	1	no	—
331	C₄×C₁₃	—	2	1	no	—
332	C₄×C₁₃	—	2	1	no	—
333	C₄×C₁₃	—	2	1	no	—
334	C₄×C₁₃	—	2	1	no	—
335	C₄×C₁₃	—	2	1	no	—
336	C₄×C₁₃	—	2	1	no	—
337	Dic₁₃	—	4	2	no	—
338	Dic₁₃	—	4	2	no	—
339	Dic₁₃	—	4	2	no	—
340	Dic₁₃	—	8	4	no	—
341	C₂×#41	—	13	2	no	—
342	C₂×#41	—	26	1	no	—
343	C₂×#41	—	26	1	no	—
344	C₂³×C₄	—	26	2	no	—
345	C₂³×C₄	D₅₂	1	1	yes	characteristic
346	C₂³×C₄	D₅₂	1	1	yes	characteristic
347	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
348	C₂×M₁₆	—	2	2	no	—
349	C₄⋊Q₈	—	13	1	no	—
350	C₄⋊Q₈	—	13	1	no	—
351	C₄⋊Q₈	—	13	1	no	—
352	#127	—	13	1	no	—
353	#126	—	26	2	no	—
354	#126	—	26	2	no	—
355	#125	—	13	2	no	—
356	#125	—	26	1	no	—
357	#125	—	26	1	no	—
358	#124	—	13	2	no	—
359	#124	—	26	1	no	—
360	#124	—	26	1	no	—
361	#123	—	26	2	no	—
362	#123	—	26	2	no	—
363	#123	—	26	2	no	—
364	C₂²⋊Q₈	—	13	2	no	—
365	C₂²⋊Q₈	—	13	2	no	—
366	C₂²⋊Q₈	—	26	1	no	—
367	C₂²⋊Q₈	—	26	1	no	—
368	C₂²⋊Q₈	—	26	1	no	—
369	C₂²⋊Q₈	—	26	1	no	—
370	#121	—	13	2	no	—
371	#121	—	13	2	no	—
372	#121	—	26	1	no	—
373	#121	—	26	1	no	—
374	#121	—	26	1	no	—
375	#121	—	26	1	no	—
376	#120	—	26	2	no	—
377	C₄×Q₈	—	13	2	no	—
378	C₄×Q₈	—	13	2	no	—
379	C₄×Q₈	—	26	1	no	—
380	C₄×Q₈	—	26	1	no	—
381	C₄×Q₈	—	26	1	no	—
382	C₄×Q₈	—	26	1	no	—
383	C₄×D₄	—	13	2	no	—
384	C₄×D₄	—	13	2	no	—
385	C₄×D₄	—	26	2	no	—
386	C₄×D₄	—	26	2	no	—
387	C₄×D₄	—	26	2	no	—
388	C₄×D₄	—	26	2	no	—
389	C₄×D₄	—	26	2	no	—
390	C₄×D₄	—	26	2	no	—
391	C₄×D₄	—	26	1	no	—
392	C₄×D₄	—	26	1	no	—
393	C₄×D₄	—	26	1	no	—
394	C₄×D₄	—	26	1	no	—
395	#117	—	13	2	no	—
396	#117	—	26	1	no	—
397	#117	—	26	1	no	—
398	#117	—	26	2	no	—
399	#117	—	26	2	no	—
400	#117	—	26	2	no	—
401	C₂×C₄²	—	26	2	no	—
402	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
403	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
404	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
405	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
406	C₂×C₄²	D₅₂	1	1	yes	characteristic
407	C₂×C₄²	D₅₂	1	1	yes	characteristic
408	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
409	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
410	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
411	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
412	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
413	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
414	C₄⋊C₈	—	2	2	no	—
415	C₄⋊C₈	—	2	2	no	—
416	C₂²⋊C₈	—	2	2	no	—
417	C₂²⋊C₈	C₂²×D₁₃	1	4	yes	—
418	#97	—	2	2	no	—
419	C₄×C₈	—	2	2	no	—
420	#95	—	13	4	no	—
421	#95	—	26	2	no	—
422	#95	—	26	2	no	—
423	#95	—	26	2	no	—
424	#95	—	26	2	no	—
425	#95	—	26	2	no	—
426	C₂×C₁₃	—	2	2	no	—
427	C₂×C₁₃	—	2	2	no	—
428	C₂×C₁₃	—	2	2	no	—
429	C₂×C₁₃	C₂×#410	1	1	yes	characteristic
430	C₂×C₁₃	#2896	1	1	yes	characteristic
431	C₂×C₁₃	C₂×#421	1	1	yes	characteristic
432	D₁₃	—	8	2	no	—
433	C₂⁴	C₂×D₅₂	1	1	yes	characteristic
434	#41	—	52	4	no	—
435	#41	—	52	4	no	—
436	#41	—	52	4	no	—
437	C₂×Q₈	—	13	2	no	—
438	C₂×Q₈	—	26	1	no	—
439	C₂×Q₈	—	26	1	no	—
440	C₂×D₄	—	13	2	no	—
441	C₂×D₄	—	26	2	no	—
442	C₂×D₄	—	26	2	no	—
443	C₂×D₄	—	26	2	no	—
444	C₂×D₄	—	26	1	no	—
445	C₂×D₄	—	26	1	no	—
446	C₂²×C₄	—	4	2	no	—
447	C₂²×C₄	—	4	2	no	—
448	C₂²×C₄	—	4	2	no	—
449	C₂²×C₄	—	26	2	no	—
450	C₂²×C₄	—	26	2	no	—
451	C₂²×C₄	—	26	2	no	—
452	C₂²×C₄	—	26	4	no	—
453	C₂²×C₄	—	52	4	no	—
454	C₂²×C₄	—	52	4	no	—
455	C₂²×C₄	—	52	4	no	—
456	C₂²×C₄	#6103	1	1	yes	characteristic
457	C₂²×C₄	#6103	1	1	yes	characteristic
458	C₂²×C₄	#6103	1	1	yes	characteristic
459	C₂²×C₄	#6103	1	1	yes	characteristic
460	C₂²×C₄	#6103	1	1	yes	characteristic
461	C₂²×C₄	#6103	1	1	yes	characteristic
462	C₂²×C₄	#6103	1	1	yes	characteristic
463	C₂²×C₄	#6103	1	1	yes	characteristic
464	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
465	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
466	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
467	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
468	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
469	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
470	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
471	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
472	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
473	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
474	M₁₆	—	4	4	no	—
475	C₂×C₈	—	2	4	no	—
476	C₄⋊C₄	—	13	2	no	—
477	C₄⋊C₄	—	13	2	no	—
478	C₄⋊C₄	—	26	2	no	—
479	C₄⋊C₄	—	26	2	no	—
480	C₄⋊C₄	—	26	1	no	—
481	C₄⋊C₄	—	26	1	no	—
482	C₄⋊C₄	—	26	1	no	—
483	C₄⋊C₄	—	26	1	no	—
484	C₄⋊C₄	—	26	2	no	—
485	C₄⋊C₄	—	26	2	no	—
486	C₄⋊C₄	—	26	2	no	—
487	C₄⋊C₄	—	26	2	no	—
488	C₂²⋊C₄	—	26	2	no	—
489	C₂²⋊C₄	—	26	2	no	—
490	C₂²⋊C₄	—	26	2	no	—
491	C₂²⋊C₄	—	26	2	no	—
492	C₂²⋊C₄	—	26	2	no	—
493	C₂²⋊C₄	—	26	2	no	—
494	C₂²⋊C₄	—	26	2	no	—
495	C₂²⋊C₄	—	26	2	no	—
496	C₂²⋊C₄	—	26	2	no	—
497	C₄²	—	26	2	no	—
498	C₄²	—	26	2	no	—
499	C₄²	—	26	2	no	—
500	C₄²	#6103	1	1	yes	characteristic
501	C₄²	#6103	1	1	yes	characteristic
502	C₄²	#6103	1	1	yes	characteristic
503	C₄²	#6103	1	1	yes	characteristic
504	C₄²	#6103	1	1	yes	characteristic
505	C₄²	#6103	1	1	yes	characteristic
506	C₄²	#6103	1	1	yes	characteristic
507	C₄²	#6103	1	1	yes	characteristic
508	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
509	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
510	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
511	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
512	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
513	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
514	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
515	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
516	C₁₃	#17593	1	1	yes	characteristic, complemented, Sylow
517	C₂³	—	2	2	no	—
518	C₂³	—	2	2	no	—
519	C₂³	—	2	2	no	—
520	C₂³	—	26	2	no	—
521	C₂³	C₂×#6103	1	1	yes	characteristic
522	C₂³	C₂×#6103	1	1	yes	characteristic
523	C₂³	C₂²×D₅₂	1	1	yes	characteristic
524	Q₈	—	52	2	no	—
525	Q₈	—	52	2	no	—
526	Q₈	—	52	2	no	—
527	D₄	—	52	2	no	—
528	D₄	—	52	2	no	—
529	D₄	—	52	2	no	—
530	D₄	—	52	4	no	—
531	D₄	—	52	4	no	—
532	D₄	—	52	4	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	26	2	no	—
552	C₂×C₄	—	26	2	no	—
553	C₂×C₄	—	26	2	no	—
554	C₂×C₄	—	52	4	no	—
555	C₂×C₄	—	52	4	no	—
556	C₂×C₄	—	52	4	no	—
557	C₂×C₄	—	52	4	no	—
558	C₂×C₄	—	52	4	no	—
559	C₂×C₄	—	52	4	no	—
560	C₂×C₄	—	104	8	no	—
561	C₂×C₄	C₂×#6103	1	1	yes	characteristic
562	C₂×C₄	C₂×#6103	1	1	yes	characteristic
563	C₂×C₄	C₂×#6103	1	1	yes	characteristic
564	C₂×C₄	C₂×#6103	1	1	yes	characteristic
565	C₂×C₄	C₂×#6103	1	1	yes	characteristic
566	C₂×C₄	C₂×#6103	1	1	yes	characteristic
567	C₂×C₄	C₂×#6103	1	1	yes	characteristic
568	C₂×C₄	C₂×#6103	1	1	yes	characteristic
569	C₂×C₄	C₂×#6103	1	1	yes	characteristic
570	C₂×C₄	C₂×#6103	1	1	yes	characteristic
571	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
572	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
573	C₈	—	4	4	no	—
574	C₂²	—	2	8	no	—
575	C₂²	—	2	1	no	—
576	C₂²	—	2	1	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	2	1	no	—
579	C₂²	—	2	1	no	—
580	C₂²	—	2	1	no	—
581	C₂²	—	52	2	no	—
582	C₂²	—	52	2	no	—
583	C₂²	—	52	2	no	—
584	C₂²	#11718667	1	2	yes	—
585	C₂²	#11718800	1	2	yes	—
586	C₂²	#11719453	1	2	yes	—
587	C₂²	C₂²×#6103	1	1	yes	characteristic
588	C₄	—	2	1	no	—
589	C₄	—	2	1	no	—
590	C₄	—	2	1	no	—
591	C₄	—	2	1	no	—
592	C₄	—	2	1	no	—
593	C₄	—	2	1	no	—
594	C₄	—	2	1	no	—
595	C₄	—	2	1	no	—
596	C₄	—	2	1	no	—
597	C₄	—	2	1	no	—
598	C₄	—	2	1	no	—
599	C₄	—	2	1	no	—
600	C₄	—	52	2	no	—
601	C₄	—	52	2	no	—
602	C₄	—	52	2	no	—
603	C₄	—	104	4	no	—
604	C₂	—	2	2	no	—
605	C₂	—	2	2	no	—
606	C₂	—	2	2	no	—
607	C₂	—	104	2	no	—
608	C₂	C₂×#11718667	1	1	yes	characteristic
609	C₂	#13123356	1	1	yes	characteristic
610	C₂	C₂×#11718800	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×#6103
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₁₃×#2920	C₂
socle	C₂²×C₁₃	C₂²×C₂²⋊C₄
prime radical	#13128132	C₂
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	#2920	D₁₃
hypocenter	C₁₃	#17593
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄² ◁ #2920

Complements

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

N	H ≅ G/N	type
2. C₂×#11718598	C₂	semidirect
3. #13113414	C₂	semidirect
4. #13113388	C₂	semidirect
5. #13113384	C₂	semidirect
6. #13113341	C₂	semidirect
7. C₁₃×#2920	C₂	semidirect
16. #11719184	C₄	semidirect
18. #11719182	C₄	semidirect
19. #11719182	C₄	semidirect
23. C₄×#6127	C₄	semidirect
24. #11719175	C₄	semidirect
25. #11719175	C₄	semidirect
92. #88129	C₂×C₄	semidirect
93. #88128	C₂×C₄	semidirect
98. C₄×D₅₂	C₂×C₄	semidirect
99. C₄×D₅₂	C₂×C₄	semidirect
106. #88124	C₂×C₄	semidirect
107. #88123	C₂×C₄	semidirect
108. #88123	C₂×C₄	semidirect
109. #88123	C₂×C₄	semidirect
114. C₄×Dic₂₆	C₂×C₄	semidirect
115. C₄×Dic₂₆	C₂×C₄	semidirect
213. #2920	D₁₃	semidirect
516. C₁₃	#17593	semidirect

Maximal subgroups

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

subgroup	index
#13128132	2
C₂×#11718598	2
#13113414	2
#13113388	2
#13113384	2
#13113341	2
C₁₃×#2920	2
#17593	13