Subgroups — #15833623

Order 3328.

726 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13125412	C₂	1	1	yes	maximal, characteristic
2	#13123545	C₂	1	1	yes	maximal, characteristic, complemented
3	#13123543	C₂	1	1	yes	maximal, characteristic, complemented
4	#13113668	C₂	1	1	yes	maximal, characteristic, complemented
5	#13113667	C₂	1	1	yes	maximal, characteristic, complemented
6	#13113666	C₂	1	1	yes	maximal, characteristic, complemented
7	#13113665	C₂	1	1	yes	maximal, characteristic, complemented
8	#13113664	C₂	1	1	yes	maximal, characteristic, complemented
9	#13113663	C₂	1	1	yes	maximal, characteristic, complemented
10	#13113662	C₂	1	1	yes	maximal, characteristic, complemented
11	#13113593	C₂	1	1	yes	maximal, characteristic, complemented
12	#13113285	C₂	1	1	yes	maximal, characteristic, complemented
13	#13113285	C₂	1	1	yes	maximal, characteristic, complemented
14	D₁₃×#322	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1581	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#88161	—	2	1	no	—
17	C₂×#88155	—	2	1	no	—
18	#11719253	C₂²	1	1	yes	characteristic
19	#11719253	C₂²	1	1	yes	characteristic
20	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
21	C₁₃×#436	C₂²	1	1	yes	characteristic
22	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
23	#11718818	C₄	1	1	yes	characteristic
24	#11718812	C₄	1	1	yes	characteristic
25	#11718789	—	2	1	no	—
26	C₈×C₂²⋊D₁₃	—	2	1	no	—
27	C₄×#6104	C₂²	1	1	yes	characteristic
28	C₄×#6104	C₂²	1	1	yes	characteristic
29	#11718673	C₂²	1	1	yes	characteristic
30	D₄×#1055	C₂²	1	1	yes	characteristic
31	#11718544	C₄	1	1	yes	characteristic
32	#11718535	C₄	1	1	yes	characteristic
33	#11718499	C₂²	1	1	yes	characteristic
34	#11718498	C₂²	1	1	yes	characteristic
35	#11718498	C₂²	1	1	yes	characteristic
36	#11718495	C₂²	1	1	yes	characteristic
37	#11718436	C₄	1	1	yes	characteristic
38	#11718436	C₄	1	1	yes	characteristic
39	#11718421	C₄	1	1	yes	characteristic
40	#11718421	C₄	1	1	yes	characteristic
41	#11718390	—	2	1	no	—
42	#11718388	—	2	1	no	—
43	#11718388	—	2	1	no	—
44	#11718386	—	2	1	no	—
45	C₄×D₁₀₄	C₂²	1	1	yes	characteristic
46	#11718349	C₂²	1	1	yes	characteristic
47	C₈×D₅₂	C₂²	1	1	yes	characteristic
48	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
49	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
50	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
51	C₁₃×#335	C₂²	1	1	yes	characteristic
52	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
53	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
54	C₁₃×#322	C₂²	1	1	yes	characteristic
55	D₄⋊#1055	C₂²	1	1	yes	characteristic
56	D₄⋊#1055	C₂²	1	1	yes	characteristic
57	#11718075	C₂²	1	1	yes	characteristic
58	#11718075	C₂²	1	1	yes	characteristic
59	#11718071	C₂²	1	1	yes	characteristic
60	#11718071	C₂²	1	1	yes	characteristic
61	#11718051	C₂²	1	1	yes	characteristic
62	#11718051	C₂²	1	1	yes	characteristic
63	#11718050	C₂²	1	1	yes	characteristic
64	#11718047	C₂²	1	1	yes	characteristic
65	#11718046	C₂²	1	1	yes	characteristic
66	#11718046	C₂²	1	1	yes	characteristic
67	C₂×#6127	—	2	1	no	—
68	C₂×#6127	—	2	1	no	—
69	C₂×C₁₃×D₈	C₂×C₄	1	1	yes	characteristic
70	C₂×C₁₃×M₁₆	—	2	1	no	—
71	C₂²×C₈×C₁₃	—	2	1	no	—
72	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
73	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
74	#88194	C₂×C₄	1	1	yes	characteristic
75	#88194	C₂×C₄	1	1	yes	characteristic
76	#88192	C₂×C₄	1	1	yes	characteristic
77	#88192	C₂×C₄	1	1	yes	characteristic
78	C₂×#6104	C₂×C₄	1	1	yes	characteristic
79	C₂×#6104	C₂×C₄	1	1	yes	characteristic
80	C₄×C₂²⋊D₁₃	—	2	1	no	—
81	C₄×C₂²⋊D₁₃	—	2	1	no	—
82	C₂×#6099	—	2	1	no	—
83	C₂²×#1055	—	2	1	no	—
84	#88161	—	4	4	no	—
85	C₂×D₁₀₄	C₂×C₄	1	1	yes	characteristic
86	#88155	—	4	4	no	—
87	C₂×#6094	—	2	1	no	—
88	C₂×#6094	—	2	1	no	—
89	C₂×#6094	—	2	1	no	—
90	C₂×#6094	—	2	1	no	—
91	C₂×C₈×D₁₃	—	2	1	no	—
92	C₂×C₈×D₁₃	—	2	1	no	—
93	C₂×C₈×D₁₃	—	2	1	no	—
94	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
95	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
96	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
97	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
98	#88149	C₂×C₄	1	1	yes	characteristic
99	#88149	C₂×C₄	1	1	yes	characteristic
100	#88142	C₂×C₄	1	1	yes	characteristic
101	#88142	C₂×C₄	1	1	yes	characteristic
102	#88139	—	2	1	no	—
103	#88139	—	2	1	no	—
104	#88138	—	2	1	no	—
105	#88138	—	2	1	no	—
106	C₄×D₅₂	C₂³	1	1	yes	characteristic
107	C₄×D₅₂	C₂³	1	1	yes	characteristic
108	C₄²×D₁₃	C₂³	1	1	yes	characteristic
109	C₁₃×#107	C₂×C₄	1	1	yes	characteristic
110	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
111	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
112	C₁₃×#102	C₂×C₄	1	1	yes	characteristic
113	C₁₃×#102	C₂×C₄	1	1	yes	characteristic
114	C₁₃×C₂²⋊C₈	—	2	1	no	—
115	C₁₃×C₂²⋊C₈	—	2	1	no	—
116	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
117	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
118	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
119	#88072	C₂×C₄	1	1	yes	characteristic
120	#88072	C₂×C₄	1	1	yes	characteristic
121	C₂²⋊#1055	—	2	1	no	—
122	C₂²⋊#1055	—	2	1	no	—
123	#88061	C₂×C₄	1	1	yes	characteristic
124	#88061	C₂×C₄	1	1	yes	characteristic
125	#88060	—	2	1	no	—
126	#88060	—	2	1	no	—
127	#88060	—	2	1	no	—
128	#88060	—	2	1	no	—
129	#88058	C₂×C₄	1	1	yes	characteristic
130	#88054	—	2	1	no	—
131	#88054	—	2	1	no	—
132	C₈×Dic₁₃	—	2	1	no	—
133	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
134	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
135	C₈×Dic₁₃	D₄	1	1	yes	characteristic
136	C₈×Dic₁₃	D₄	1	1	yes	characteristic
137	#88049	C₂×C₄	1	1	yes	characteristic
138	#88049	C₂×C₄	1	1	yes	characteristic
139	#88047	C₂×C₄	1	1	yes	characteristic
140	#88047	C₂×C₄	1	1	yes	characteristic
141	C₄⋊#1055	C₂³	1	1	yes	characteristic
142	C₄⋊#1055	C₂³	1	1	yes	characteristic
143	C₄×#1055	C₂³	1	1	yes	characteristic
144	C₄×#1055	C₂³	1	1	yes	characteristic
145	C₄×#1055	C₂³	1	1	yes	characteristic
146	#17975	—	13	1	no	maximal, Sylow
147	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
148	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₃	—	2	1	no	—
150	C₂²×C₄×C₁₃	—	2	1	no	—
151	C₂×C₂²⋊D₁₃	—	2	1	no	—
152	C₂×C₂²⋊D₁₃	—	2	1	no	—
153	C₂×C₂²⋊D₁₃	—	2	1	no	—
154	C₂×C₂²⋊D₁₃	—	2	1	no	—
155	C₂×C₂²⋊D₁₃	—	2	1	no	—
156	C₂×C₂²⋊D₁₃	—	2	1	no	—
157	#6127	—	4	2	no	—
158	#6127	—	4	2	no	—
159	#6127	—	4	2	no	—
160	#6127	—	4	2	no	—
161	C₂×D₅₂	—	2	1	no	—
162	C₂×D₅₂	—	2	1	no	—
163	C₂×D₅₂	C₂²×C₄	1	1	yes	characteristic
164	C₂×D₅₂	C₂²×C₄	1	1	yes	characteristic
165	C₂×C₄×D₁₃	—	2	1	no	—
166	C₂×C₄×D₁₃	—	2	1	no	—
167	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
168	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
169	C₂×C₄×D₁₃	#41	1	1	yes	characteristic
170	C₂×Dic₂₆	—	2	1	no	—
171	C₂×Dic₂₆	—	2	1	no	—
172	C₁₃×D₈	—	4	1	no	—
173	C₁₃×M₁₆	—	4	2	no	—
174	C₂×C₈×C₁₃	—	2	1	no	—
175	C₂×C₈×C₁₃	—	2	1	no	—
176	C₂×C₈×C₁₃	—	2	1	no	—
177	C₂×C₈×C₁₃	—	4	2	no	—
178	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
179	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
180	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
181	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
182	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
183	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
184	C₁₃×C₂²⋊C₄	—	2	1	no	—
185	C₁₃×C₂²⋊C₄	—	2	1	no	—
186	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
187	C₂²⋊Dic₁₃	—	2	1	no	—
188	C₂²⋊Dic₁₃	—	2	1	no	—
189	#6104	—	4	1	no	—
190	#6104	—	4	1	no	—
191	#6103	—	2	1	no	—
192	#6103	—	2	1	no	—
193	#6103	—	2	1	no	—
194	#6103	—	2	1	no	—
195	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
196	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
197	#6101	—	2	1	no	—
198	#6101	—	2	1	no	—
199	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
200	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
201	C₄×Dic₁₃	#41	1	1	yes	characteristic
202	#6099	—	4	2	no	—
203	C₂×#1055	—	2	1	no	—
204	C₂×#1055	—	2	1	no	—
205	C₂×#1055	—	2	1	no	—
206	C₂×#1055	—	4	2	no	—
207	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
208	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
209	C₂×#1055	C₂×D₄	1	1	yes	characteristic
210	C₂×#1055	C₂×D₄	1	1	yes	characteristic
211	D₁₀₄	—	4	1	no	—
212	#6094	—	4	2	no	—
213	#6094	—	4	2	no	—
214	#6094	—	4	2	no	—
215	#6094	—	4	2	no	—
216	C₈×D₁₃	—	2	2	no	—
217	C₈×D₁₃	—	4	1	no	—
218	C₈×D₁₃	—	4	1	no	—
219	C₈×D₁₃	—	4	2	no	—
220	C₈×D₁₃	—	4	2	no	—
221	C₈×D₁₃	—	4	2	no	—
222	C₈×D₁₃	D₈	1	4	yes	complemented
223	#3169	—	13	1	no	—
224	#2931	—	13	1	no	—
225	#2931	—	13	1	no	—
226	#1581	—	13	1	no	—
227	#1581	—	13	1	no	—
228	#1581	—	13	1	no	—
229	#1581	—	13	1	no	—
230	#1581	—	13	1	no	—
231	#1581	—	13	1	no	—
232	#1581	—	13	1	no	—
233	#1581	D₁₃	1	1	yes	characteristic, complemented
234	#1567	—	13	1	no	—
235	#1492	—	13	1	no	—
236	#1492	—	13	1	no	—
237	C₂×#322	—	13	1	no	—
238	C₂³×C₁₃	—	2	1	no	—
239	C₂³×C₁₃	—	2	1	no	—
240	C₂²×D₁₃	—	2	1	no	—
241	C₂²×D₁₃	—	2	1	no	—
242	C₂²×D₁₃	C₄×D₄	1	1	yes	characteristic
243	D₄×C₁₃	—	2	1	no	—
244	D₄×C₁₃	—	2	1	no	—
245	D₄×C₁₃	—	2	1	no	—
246	D₄×C₁₃	—	2	1	no	—
247	C₂×C₄×C₁₃	—	2	1	no	—
248	C₂×C₄×C₁₃	—	2	1	no	—
249	C₂×C₄×C₁₃	—	4	1	no	—
250	C₂×C₄×C₁₃	—	4	1	no	—
251	C₂×C₄×C₁₃	—	4	1	no	—
252	C₂×C₄×C₁₃	—	4	1	no	—
253	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
254	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
255	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
256	C₂²⋊D₁₃	—	4	2	no	—
257	C₂²⋊D₁₃	—	4	2	no	—
258	C₂²⋊D₁₃	—	4	2	no	—
259	C₂²⋊D₁₃	—	4	2	no	—
260	C₂²⋊D₁₃	—	4	2	no	—
261	C₂²⋊D₁₃	—	4	2	no	—
262	C₂×Dic₁₃	—	2	1	no	—
263	C₂×Dic₁₃	—	2	1	no	—
264	C₂×Dic₁₃	C₄×D₄	1	1	yes	characteristic
265	C₂×Dic₁₃	C₄×D₄	1	1	yes	characteristic
266	C₂×Dic₁₃	C₄×D₄	1	1	yes	characteristic
267	D₅₂	—	2	1	no	—
268	D₅₂	—	2	1	no	—
269	D₅₂	—	2	1	no	—
270	D₅₂	—	2	1	no	—
271	D₅₂	—	4	2	no	—
272	D₅₂	—	4	2	no	—
273	C₄×D₁₃	—	2	1	no	—
274	C₄×D₁₃	—	2	1	no	—
275	C₄×D₁₃	—	2	2	no	—
276	C₄×D₁₃	—	4	1	no	—
277	C₄×D₁₃	—	4	1	no	—
278	C₄×D₁₃	—	4	1	no	—
279	C₄×D₁₃	—	4	1	no	—
280	C₄×D₁₃	C₂×D₈	1	2	yes	—
281	C₄×D₁₃	#135	1	2	yes	—
282	Dic₂₆	—	4	2	no	—
283	Dic₂₆	—	4	2	no	—
284	C₈×C₁₃	—	2	1	no	—
285	C₈×C₁₃	—	2	1	no	—
286	C₈×C₁₃	—	2	1	no	—
287	C₈×C₁₃	—	4	1	no	—
288	C₈×C₁₃	—	4	1	no	—
289	C₈×C₁₃	—	4	1	no	—
290	C₈×C₁₃	C₂×D₈	1	2	yes	—
291	#1055	—	2	1	no	—
292	#1055	—	2	1	no	—
293	#1055	—	2	1	no	—
294	#1055	—	4	1	no	—
295	#1055	—	4	1	no	—
296	#1055	—	4	1	no	—
297	#1055	C₂×D₈	1	2	yes	—
298	C₂×#131	—	26	1	no	—
299	C₂×#131	—	26	1	no	—
300	#532	—	13	1	no	—
301	#532	—	13	1	no	—
302	#500	—	13	1	no	—
303	#493	—	13	1	no	—
304	#486	—	13	1	no	—
305	#486	—	13	1	no	—
306	#466	—	13	1	no	—
307	#466	—	13	1	no	—
308	#466	—	13	1	no	—
309	#466	—	13	1	no	—
310	C₄×D₈	—	13	1	no	—
311	C₄×D₈	—	13	1	no	—
312	C₄×D₈	—	13	1	no	—
313	C₄×D₈	C₂×D₁₃	1	1	yes	characteristic
314	#436	—	13	1	no	—
315	#436	—	13	1	no	—
316	#436	—	13	1	no	—
317	#436	—	26	1	no	—
318	#436	—	26	1	no	—
319	#436	C₂×D₁₃	1	1	yes	characteristic
320	C₈×D₄	—	13	1	no	—
321	C₈×D₄	—	13	1	no	—
322	C₈×D₄	—	13	1	no	—
323	C₈×D₄	—	26	1	no	—
324	C₈×D₄	—	26	1	no	—
325	C₈×D₄	C₂×D₁₃	1	1	yes	characteristic
326	#423	—	13	1	no	—
327	#423	—	13	1	no	—
328	#408	—	26	1	no	—
329	#408	—	26	1	no	—
330	C₂×C₄×C₈	—	13	1	no	—
331	C₂×C₄×C₈	—	13	1	no	—
332	C₂×C₄×C₈	—	13	1	no	—
333	#335	—	13	1	no	—
334	#335	—	13	1	no	—
335	#335	—	13	1	no	—
336	#335	C₂×D₁₃	1	1	yes	characteristic
337	D₄⋊C₈	—	13	1	no	—
338	D₄⋊C₈	—	13	1	no	—
339	D₄⋊C₈	—	13	1	no	—
340	D₄⋊C₈	—	13	1	no	—
341	D₄⋊C₈	—	13	1	no	—
342	D₄⋊C₈	—	13	1	no	—
343	D₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic
344	D₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic
345	#322	—	13	1	no	—
346	#322	—	13	1	no	—
347	#322	—	13	1	no	—
348	#322	C₂×D₁₃	1	1	yes	characteristic
349	C₂²×C₁₃	—	4	1	no	—
350	C₂²×C₁₃	—	4	1	no	—
351	C₂²×C₁₃	—	4	1	no	—
352	C₂²×C₁₃	—	4	1	no	—
353	C₂²×C₁₃	—	4	1	no	—
354	C₂²×C₁₃	—	4	1	no	—
355	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
356	C₂×D₁₃	—	2	1	no	—
357	C₂×D₁₃	—	2	1	no	—
358	C₂×D₁₃	—	4	1	no	—
359	C₂×D₁₃	—	4	1	no	—
360	C₂×D₁₃	—	4	1	no	—
361	C₂×D₁₃	—	4	1	no	—
362	C₂×D₁₃	—	4	1	no	—
363	C₂×D₁₃	—	4	1	no	—
364	C₂×D₁₃	C₄×D₈	1	2	yes	—
365	C₄×C₁₃	—	2	1	no	—
366	C₄×C₁₃	—	4	1	no	—
367	C₄×C₁₃	—	4	1	no	—
368	C₄×C₁₃	#568	1	1	yes	characteristic
369	C₄×C₁₃	#568	1	1	yes	characteristic
370	C₄×C₁₃	C₂²×D₈	1	1	yes	characteristic
371	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
372	Dic₁₃	—	2	1	no	—
373	Dic₁₃	—	4	1	no	—
374	Dic₁₃	—	4	1	no	—
375	Dic₁₃	C₄×D₈	1	2	yes	—
376	Dic₁₃	#444	1	2	yes	—
377	C₂×#41	—	26	1	no	—
378	C₂×#41	—	26	1	no	—
379	C₂×D₈	—	13	1	no	—
380	C₂×D₈	—	13	1	no	—
381	C₂×D₈	—	13	1	no	—
382	C₂×D₈	C₄×D₁₃	1	1	yes	characteristic
383	#131	—	52	4	no	—
384	#131	—	52	4	no	—
385	C₂×M₁₆	—	2	1	no	—
386	C₂×M₁₆	—	26	1	no	—
387	C₂×M₁₆	—	26	1	no	—
388	C₂×M₁₆	—	26	1	no	—
389	C₂×M₁₆	—	26	1	no	—
390	C₂×M₁₆	—	26	1	no	—
391	C₂²×C₈	—	2	1	no	—
392	C₂²×C₈	—	13	1	no	—
393	C₂²×C₈	—	13	1	no	—
394	C₂²×C₈	—	13	1	no	—
395	C₂²×C₈	—	13	1	no	—
396	C₂²×C₈	—	26	1	no	—
397	C₂²×C₈	—	26	1	no	—
398	C₂²×C₈	—	26	1	no	—
399	C₂²×C₈	—	26	1	no	—
400	C₄⋊Q₈	—	13	1	no	—
401	C₄⋊Q₈	—	13	1	no	—
402	#127	—	13	1	no	—
403	#127	—	13	1	no	—
404	#124	—	26	1	no	—
405	#124	—	26	1	no	—
406	#121	—	13	1	no	—
407	#121	—	13	1	no	—
408	#121	—	13	1	no	—
409	#121	—	13	1	no	—
410	#121	—	26	1	no	—
411	#121	—	26	1	no	—
412	C₄×D₄	—	13	1	no	—
413	C₄×D₄	—	13	1	no	—
414	C₄×D₄	—	26	1	no	—
415	C₄×D₄	—	26	1	no	—
416	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
417	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
418	C₂×C₄²	—	13	1	no	—
419	#107	—	13	1	no	—
420	#107	—	13	1	no	—
421	#107	—	13	1	no	—
422	#107	C₄×D₁₃	1	1	yes	characteristic
423	C₄⋊C₈	—	13	1	no	—
424	C₄⋊C₈	—	13	1	no	—
425	C₄⋊C₈	—	26	1	no	—
426	C₄⋊C₈	—	26	1	no	—
427	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
428	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
429	#102	—	13	1	no	—
430	#102	—	13	1	no	—
431	#102	—	13	1	no	—
432	#102	—	13	1	no	—
433	#102	—	13	1	no	—
434	#102	—	13	1	no	—
435	#102	C₄×D₁₃	1	1	yes	characteristic
436	#102	C₄×D₁₃	1	1	yes	characteristic
437	C₂²⋊C₈	—	2	1	no	—
438	C₂²⋊C₈	—	2	1	no	—
439	C₂²⋊C₈	—	26	1	no	—
440	C₂²⋊C₈	—	26	1	no	—
441	C₂²⋊C₈	—	26	1	no	—
442	C₂²⋊C₈	—	26	1	no	—
443	C₂²⋊C₈	—	26	1	no	—
444	C₂²⋊C₈	—	26	1	no	—
445	C₄×C₈	—	13	1	no	—
446	C₄×C₈	—	13	1	no	—
447	C₄×C₈	—	13	1	no	—
448	C₄×C₈	—	13	1	no	—
449	C₄×C₈	—	13	1	no	—
450	C₄×C₈	—	13	1	no	—
451	C₄×C₈	—	13	1	no	—
452	C₄×C₈	—	26	1	no	—
453	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
454	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
455	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
456	C₂×C₁₃	—	8	1	no	—
457	C₂×C₁₃	—	8	1	no	—
458	C₂×C₁₃	#2932	1	1	yes	characteristic
459	C₂×C₁₃	C₂×C₄×D₈	1	1	yes	characteristic
460	C₂×C₁₃	C₂×#444	1	1	yes	characteristic
461	D₁₃	—	2	2	no	—
462	D₁₃	—	8	1	no	—
463	D₁₃	—	8	1	no	—
464	#41	—	52	2	no	—
465	#41	—	52	2	no	—
466	#41	—	52	2	no	—
467	#41	—	52	2	no	—
468	C₂×Q₈	—	26	1	no	—
469	C₂×Q₈	—	26	1	no	—
470	C₂×D₄	—	13	1	no	—
471	C₂×D₄	—	13	1	no	—
472	C₂×D₄	—	26	1	no	—
473	C₂×D₄	—	26	1	no	—
474	C₂×D₄	—	26	1	no	—
475	C₂×D₄	—	26	1	no	—
476	C₂×D₄	—	26	1	no	—
477	C₂×D₄	—	26	1	no	—
478	C₂×D₄	—	26	1	no	—
479	C₂×D₄	—	26	1	no	—
480	C₂×D₄	C₂×C₄×D₁₃	1	1	yes	characteristic
481	C₂×D₄	C₂×C₄×D₁₃	1	1	yes	characteristic
482	C₂²×C₄	—	2	1	no	—
483	C₂²×C₄	—	2	1	no	—
484	C₂²×C₄	—	13	1	no	—
485	C₂²×C₄	—	13	1	no	—
486	C₂²×C₄	—	13	1	no	—
487	C₂²×C₄	—	26	1	no	—
488	C₂²×C₄	—	26	1	no	—
489	D₈	—	4	1	no	—
490	D₈	—	52	1	no	—
491	D₈	—	52	1	no	—
492	D₈	—	52	1	no	—
493	M₁₆	—	4	2	no	—
494	M₁₆	—	52	2	no	—
495	M₁₆	—	52	2	no	—
496	M₁₆	—	52	2	no	—
497	M₁₆	—	52	2	no	—
498	M₁₆	—	52	2	no	—
499	C₂×C₈	—	2	1	no	—
500	C₂×C₈	—	2	1	no	—
501	C₂×C₈	—	2	1	no	—
502	C₂×C₈	—	4	2	no	—
503	C₂×C₈	—	13	1	no	—
504	C₂×C₈	—	13	4	no	—
505	C₂×C₈	—	13	1	no	—
506	C₂×C₈	—	13	1	no	—
507	C₂×C₈	—	13	1	no	—
508	C₂×C₈	—	26	2	no	—
509	C₂×C₈	—	26	1	no	—
510	C₂×C₈	—	26	1	no	—
511	C₂×C₈	—	26	1	no	—
512	C₂×C₈	—	52	1	no	—
513	C₂×C₈	—	52	1	no	—
514	C₂×C₈	—	52	2	no	—
515	C₂×C₈	—	52	2	no	—
516	C₂×C₈	—	52	2	no	—
517	C₂×C₈	—	52	2	no	—
518	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
519	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
520	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
521	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
522	C₄⋊C₄	—	13	1	no	—
523	C₄⋊C₄	—	13	1	no	—
524	C₄⋊C₄	—	26	1	no	—
525	C₄⋊C₄	—	26	1	no	—
526	C₄⋊C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
527	C₄⋊C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
528	C₂²⋊C₄	—	2	1	no	—
529	C₂²⋊C₄	—	2	1	no	—
530	C₂²⋊C₄	—	26	1	no	—
531	C₂²⋊C₄	—	26	1	no	—
532	C₂²⋊C₄	—	26	1	no	—
533	C₂²⋊C₄	—	26	1	no	—
534	C₂²⋊C₄	—	26	1	no	—
535	C₂²⋊C₄	—	26	1	no	—
536	C₄²	—	13	1	no	—
537	C₄²	—	13	1	no	—
538	C₄²	—	13	1	no	—
539	C₄²	C₂³×D₁₃	1	1	yes	characteristic
540	C₁₃	#17975	1	1	yes	characteristic, complemented, Sylow
541	C₂³	—	2	1	no	—
542	C₂³	—	2	1	no	—
543	C₂³	—	13	1	no	—
544	C₂³	—	26	1	no	—
545	C₂³	—	26	1	no	—
546	Q₈	—	52	2	no	—
547	Q₈	—	52	2	no	—
548	D₄	—	2	1	no	—
549	D₄	—	2	1	no	—
550	D₄	—	2	1	no	—
551	D₄	—	2	1	no	—
552	D₄	—	26	1	no	—
553	D₄	—	26	1	no	—
554	D₄	—	26	1	no	—
555	D₄	—	26	1	no	—
556	D₄	—	52	2	no	—
557	D₄	—	52	2	no	—
558	D₄	—	52	2	no	—
559	D₄	—	52	2	no	—
560	D₄	—	52	2	no	—
561	D₄	—	52	2	no	—
562	D₄	—	52	2	no	—
563	D₄	—	52	2	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	—	13	1	no	—
571	C₂×C₄	—	13	1	no	—
572	C₂×C₄	—	13	2	no	—
573	C₂×C₄	—	13	2	no	—
574	C₂×C₄	—	13	1	no	—
575	C₂×C₄	—	26	2	no	—
576	C₂×C₄	—	26	1	no	—
577	C₂×C₄	—	26	1	no	—
578	C₂×C₄	—	26	1	no	—
579	C₂×C₄	—	26	1	no	—
580	C₂×C₄	—	52	1	no	—
581	C₂×C₄	—	52	1	no	—
582	C₂×C₄	—	52	1	no	—
583	C₂×C₄	—	52	1	no	—
584	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
585	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
586	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
587	C₈	—	2	1	no	—
588	C₈	—	2	1	no	—
589	C₈	—	2	1	no	—
590	C₈	—	4	1	no	—
591	C₈	—	4	1	no	—
592	C₈	—	4	1	no	—
593	C₈	—	13	2	no	—
594	C₈	—	26	1	no	—
595	C₈	—	26	1	no	—
596	C₈	—	26	1	no	—
597	C₈	—	52	1	no	—
598	C₈	—	52	1	no	—
599	C₈	—	52	1	no	—
600	C₈	D₈×D₁₃	1	2	yes	—
601	C₂²	—	4	1	no	—
602	C₂²	—	4	1	no	—
603	C₂²	—	4	1	no	—
604	C₂²	—	4	1	no	—
605	C₂²	—	4	1	no	—
606	C₂²	—	4	1	no	—
607	C₂²	—	13	2	no	—
608	C₂²	—	26	1	no	—
609	C₂²	—	26	1	no	—
610	C₂²	—	52	1	no	—
611	C₂²	—	52	1	no	—
612	C₂²	—	52	1	no	—
613	C₂²	—	52	1	no	—
614	C₂²	—	52	1	no	—
615	C₂²	—	52	1	no	—
616	C₂²	C₄×D₄×D₁₃	1	1	yes	characteristic
617	C₄	—	2	1	no	—
618	C₄	—	4	1	no	—
619	C₄	—	4	1	no	—
620	C₄	—	13	2	no	—
621	C₄	—	13	2	no	—
622	C₄	—	26	1	no	—
623	C₄	—	52	1	no	—
624	C₄	—	52	1	no	—
625	C₄	#11719450	1	1	yes	characteristic
626	C₄	#11719455	1	1	yes	characteristic
627	C₄	C₂×D₈×D₁₃	1	1	yes	characteristic
628	C₄	D₁₃×#135	1	1	yes	characteristic
629	C₂	—	8	1	no	—
630	C₂	—	8	1	no	—
631	C₂	—	26	2	no	—
632	C₂	—	104	1	no	—
633	C₂	—	104	1	no	—
634	C₂	#13123550	1	1	yes	characteristic
635	C₂	C₄×D₈×D₁₃	1	1	yes	characteristic
636	C₂	D₁₃×#444	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×#1581	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	#13125412	C₂
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#1581	D₁₃
hypocenter	C₁₃	#17975
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1581

Complements

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

N	H ≅ G/N	type
2. #13123545	C₂	semidirect
3. #13123543	C₂	semidirect
4. #13113668	C₂	semidirect
5. #13113667	C₂	semidirect
6. #13113666	C₂	semidirect
7. #13113665	C₂	semidirect
8. #13113664	C₂	semidirect
9. #13113663	C₂	semidirect
10. #13113662	C₂	semidirect
11. #13113593	C₂	semidirect
12. #13113285	C₂	semidirect
13. #13113285	C₂	semidirect
14. D₁₃×#322	C₂	semidirect
15. C₁₃×#1581	C₂	semidirect
222. C₈×D₁₃	D₈	semidirect
233. #1581	D₁₃	semidirect
540. C₁₃	#17975	semidirect

Maximal subgroups

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

subgroup	index
#13125412	2
#13123545	2
#13123543	2
#13113668	2
#13113667	2
#13113666	2
#13113665	2
#13113664	2
#13113663	2
#13113662	2
#13113593	2
#13113285	2
D₁₃×#322	2
C₁₃×#1581	2
#17975	13