Subgroups — #15832161

Order 3328.

610 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13123792	C₂	1	1	yes	maximal, characteristic
2	#13123503	C₂	1	1	yes	maximal, characteristic
3	#13123497	C₂	1	1	yes	maximal, characteristic
4	#13113616	C₂	1	1	yes	maximal, characteristic, complemented
5	#13113615	C₂	1	1	yes	maximal, characteristic, complemented
6	#13113615	C₂	1	1	yes	maximal, characteristic, complemented
7	#13113605	C₂	1	1	yes	maximal, characteristic, complemented
8	#13113605	C₂	1	1	yes	maximal, characteristic, complemented
9	#13113597	C₂	1	1	yes	maximal, characteristic, complemented
10	#13113596	C₂	1	1	yes	maximal, characteristic, complemented
11	#13113593	C₂	1	1	yes	maximal, characteristic, complemented
12	#13113582	C₂	1	1	yes	maximal, characteristic, complemented
13	#13113581	C₂	1	1	yes	maximal, characteristic, complemented
14	D₁₃×#335	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1572	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#6127	C₂²	1	1	yes	characteristic
17	C₁₃×#432	C₂²	1	1	yes	characteristic
18	C₁₃×#431	C₂²	1	1	yes	characteristic
19	C₁₃×#431	C₂²	1	1	yes	characteristic
20	#11718587	C₂²	1	1	yes	characteristic
21	#11718586	C₂²	1	1	yes	characteristic
22	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
23	#11718498	C₂²	1	1	yes	characteristic
24	#11718498	C₂²	1	1	yes	characteristic
25	#11718496	C₂²	1	1	yes	characteristic
26	#11718496	C₂²	1	1	yes	characteristic
27	#11718495	C₄	1	1	yes	characteristic
28	#11718495	C₄	1	1	yes	characteristic
29	#11718494	C₂²	1	1	yes	characteristic
30	#11718494	C₂²	1	1	yes	characteristic
31	D₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
32	D₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	#11718491	C₄	1	1	yes	characteristic
34	#11718491	C₄	1	1	yes	characteristic
35	#11718388	—	2	1	no	—
36	#11718388	—	2	1	no	—
37	#11718386	C₄	1	1	yes	characteristic
38	#11718386	C₄	1	1	yes	characteristic
39	#11718386	C₄	1	1	yes	characteristic
40	#11718386	C₄	1	1	yes	characteristic
41	#11718381	—	2	1	no	—
42	#11718381	—	2	1	no	—
43	#11718370	—	2	1	no	—
44	#11718369	—	2	1	no	—
45	#11718351	—	2	1	no	—
46	#11718350	—	2	1	no	—
47	#11718346	C₂²	1	1	yes	characteristic
48	#11718346	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×#335	C₂²	1	1	yes	characteristic
53	C₁₃×#334	C₂²	1	1	yes	characteristic
54	C₁₃×#334	C₂²	1	1	yes	characteristic
55	#11718072	C₂²	1	1	yes	characteristic
56	#11718072	C₂²	1	1	yes	characteristic
57	#11718072	C₂²	1	1	yes	characteristic
58	#11718072	C₂²	1	1	yes	characteristic
59	#11718071	C₂²	1	1	yes	characteristic
60	#11718071	C₂²	1	1	yes	characteristic
61	#11718071	C₂²	1	1	yes	characteristic
62	#11718071	C₂²	1	1	yes	characteristic
63	#11718050	C₂²	1	1	yes	characteristic
64	#11718050	C₂²	1	1	yes	characteristic
65	#11718049	C₂²	1	1	yes	characteristic
66	#11718049	C₂²	1	1	yes	characteristic
67	C₂×#6127	D₄	1	1	yes	characteristic
68	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
69	C₄×C₂²⋊D₁₃	C₂×C₄	1	1	yes	characteristic
70	C₄×C₂²⋊D₁₃	C₂×C₄	1	1	yes	characteristic
71	C₄×C₂²⋊D₁₃	Q₈	1	1	yes	characteristic
72	C₄×C₂²⋊D₁₃	Q₈	1	1	yes	characteristic
73	#88180	D₄	1	1	yes	characteristic
74	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
75	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
76	C₂×#6094	—	2	1	no	—
77	C₂×#6094	—	2	1	no	—
78	C₂×C₈×D₁₃	—	2	1	no	—
79	C₂×C₈×D₁₃	—	2	1	no	—
80	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
81	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
82	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
83	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
84	C₄×D₅₂	C₂×C₄	1	1	yes	characteristic
85	C₄×D₅₂	Q₈	1	1	yes	characteristic
86	#88126	D₄	1	1	yes	characteristic
87	#88126	D₄	1	1	yes	characteristic
88	C₄²×D₁₃	C₂³	1	1	yes	characteristic
89	C₄²×D₁₃	C₂³	1	1	yes	characteristic
90	C₄×Dic₂₆	C₂×C₄	1	1	yes	characteristic
91	C₄×Dic₂₆	Q₈	1	1	yes	characteristic
92	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
93	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
94	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
95	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
96	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
97	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
98	C₁₃×C₂²⋊C₈	—	2	1	no	—
99	C₁₃×C₂²⋊C₈	—	2	1	no	—
100	C₁₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
101	C₁₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
102	C₁₃×#97	—	2	1	no	—
103	C₄×C₈×C₁₃	—	2	1	no	—
104	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
105	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
106	C₂²⋊#1055	—	2	1	no	—
107	C₂²⋊#1055	—	2	1	no	—
108	#88060	—	2	1	no	—
109	#88060	—	2	1	no	—
110	#88060	—	2	1	no	—
111	#88060	—	2	1	no	—
112	#88060	C₂×C₄	1	1	yes	characteristic
113	#88060	C₂×C₄	1	1	yes	characteristic
114	#88060	C₂×C₄	1	1	yes	characteristic
115	#88060	C₂×C₄	1	1	yes	characteristic
116	#88055	—	2	1	no	—
117	#88055	—	2	1	no	—
118	#88054	—	2	1	no	—
119	#88054	—	2	1	no	—
120	#88054	—	2	1	no	—
121	#88054	—	2	1	no	—
122	#88054	C₂×C₄	1	1	yes	characteristic
123	#88054	C₂×C₄	1	1	yes	characteristic
124	#88054	C₂×C₄	1	1	yes	characteristic
125	#88054	C₂×C₄	1	1	yes	characteristic
126	C₈×Dic₁₃	—	2	1	no	—
127	C₈×Dic₁₃	—	2	1	no	—
128	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
129	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
130	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
131	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
132	C₄⋊#1055	C₂³	1	1	yes	characteristic
133	C₄⋊#1055	C₂³	1	1	yes	characteristic
134	C₄⋊#1055	C₂³	1	1	yes	characteristic
135	C₄⋊#1055	C₂³	1	1	yes	characteristic
136	#88043	—	2	1	no	—
137	C₄×#1055	—	2	1	no	—
138	C₄×#1055	C₂×C₄	1	1	yes	characteristic
139	C₄×#1055	C₂×C₄	1	1	yes	characteristic
140	C₄×#1055	C₂³	1	1	yes	characteristic
141	C₄×#1055	C₂³	1	1	yes	characteristic
142	#17829	—	13	1	no	maximal, Sylow
143	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
146	C₂×C₂²⋊D₁₃	C₄⋊C₄	1	1	yes	characteristic
147	C₂×C₂²⋊D₁₃	C₄⋊C₄	1	1	yes	characteristic
148	#6127	—	2	2	no	—
149	#6127	—	2	2	no	—
150	C₂×D₅₂	C₄⋊C₄	1	1	yes	characteristic
151	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
153	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
154	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
155	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
156	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
157	C₂×Dic₂₆	C₄⋊C₄	1	1	yes	characteristic
158	C₂×C₈×C₁₃	—	2	1	no	—
159	C₂×C₈×C₁₃	—	2	1	no	—
160	C₂×C₈×C₁₃	—	2	1	no	—
161	C₂×C₈×C₁₃	—	2	1	no	—
162	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
163	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
164	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
165	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
166	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
167	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
168	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
169	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
170	C₂²⋊Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
171	C₂²⋊Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
172	#6103	C₄⋊C₄	1	1	yes	characteristic
173	#6103	C₄⋊C₄	1	1	yes	characteristic
174	#6103	C₄⋊C₄	1	1	yes	characteristic
175	#6103	C₄⋊C₄	1	1	yes	characteristic
176	C₄⋊Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
177	C₄⋊Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
178	#6101	C₄⋊C₄	1	1	yes	characteristic
179	#6101	C₄⋊C₄	1	1	yes	characteristic
180	#6101	C₄⋊C₄	1	1	yes	characteristic
181	#6101	C₄⋊C₄	1	1	yes	characteristic
182	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
183	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
184	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
185	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
186	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
187	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
188	C₂×#1055	—	2	2	no	—
189	C₂×#1055	—	2	1	no	—
190	C₂×#1055	—	2	1	no	—
191	C₂×#1055	—	2	1	no	—
192	C₂×#1055	—	2	1	no	—
193	C₂×#1055	—	4	1	no	—
194	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
195	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
196	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
197	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
198	#6094	—	4	2	no	—
199	#6094	—	4	2	no	—
200	C₈×D₁₃	—	2	2	no	—
201	C₈×D₁₃	—	2	2	no	—
202	C₈×D₁₃	—	4	1	no	—
203	C₈×D₁₃	—	4	1	no	—
204	C₈×D₁₃	—	4	2	no	—
205	C₈×D₁₃	—	4	2	no	—
206	C₈×#41	—	13	1	no	—
207	#2925	—	13	1	no	—
208	#2925	—	13	1	no	—
209	#1572	—	13	1	no	—
210	#1572	—	13	1	no	—
211	#1572	—	13	1	no	—
212	#1572	D₁₃	1	1	yes	characteristic, complemented
213	#1570	—	13	1	no	—
214	#1570	—	13	1	no	—
215	#1568	—	13	1	no	—
216	#1568	—	13	1	no	—
217	#1567	—	13	1	no	—
218	#1564	—	13	1	no	—
219	#1564	—	13	1	no	—
220	C₂×#335	—	13	1	no	—
221	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
222	C₂²×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
223	C₂²×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
224	C₂×C₄×C₁₃	—	2	1	no	—
225	C₂×C₄×C₁₃	—	2	1	no	—
226	C₂×C₄×C₁₃	—	2	1	no	—
227	C₂×C₄×C₁₃	—	2	1	no	—
228	C₂×C₄×C₁₃	—	4	1	no	—
229	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
230	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
231	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
232	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
233	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
234	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
235	C₂²⋊D₁₃	—	2	2	no	—
236	C₂²⋊D₁₃	—	2	2	no	—
237	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
238	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
239	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
240	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
241	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
242	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
243	D₅₂	—	2	2	no	—
244	C₄×D₁₃	—	2	1	no	—
245	C₄×D₁₃	—	2	1	no	—
246	C₄×D₁₃	—	2	1	no	—
247	C₄×D₁₃	—	2	1	no	—
248	C₄×D₁₃	—	2	1	no	—
249	C₄×D₁₃	—	2	1	no	—
250	C₄×D₁₃	—	4	1	no	—
251	C₄×D₁₃	—	4	1	no	—
252	C₄×D₁₃	#135	1	2	yes	—
253	C₄×D₁₃	#135	1	2	yes	—
254	Dic₂₆	—	2	2	no	—
255	C₈×C₁₃	—	2	1	no	—
256	C₈×C₁₃	—	2	1	no	—
257	C₈×C₁₃	—	2	1	no	—
258	C₈×C₁₃	—	2	1	no	—
259	C₈×C₁₃	—	4	1	no	—
260	C₈×C₁₃	—	4	1	no	—
261	C₈×C₁₃	—	4	1	no	—
262	C₈×C₁₃	—	4	1	no	—
263	#1055	—	2	1	no	—
264	#1055	—	2	1	no	—
265	#1055	—	2	1	no	—
266	#1055	—	4	1	no	—
267	#1055	—	4	1	no	—
268	#1055	—	4	1	no	—
269	#1055	—	4	1	no	—
270	#1055	#131	1	2	yes	—
271	C₄×#41	—	13	1	no	—
272	C₈×Q₈	—	13	1	no	—
273	C₈×Q₈	—	13	1	no	—
274	C₈×D₄	—	13	1	no	—
275	C₈×D₄	—	13	1	no	—
276	C₈×D₄	—	13	1	no	—
277	C₈×D₄	—	13	1	no	—
278	C₈×D₄	—	13	1	no	—
279	C₈×D₄	—	13	1	no	—
280	#433	—	26	1	no	—
281	#433	—	26	1	no	—
282	#433	—	26	1	no	—
283	#433	—	26	1	no	—
284	#432	—	13	1	no	—
285	#432	—	13	1	no	—
286	#432	—	13	1	no	—
287	#432	C₂×D₁₃	1	1	yes	characteristic
288	#431	—	13	1	no	—
289	#431	—	13	1	no	—
290	#431	—	13	1	no	—
291	#431	—	13	1	no	—
292	#431	—	13	1	no	—
293	#431	C₂×D₁₃	1	1	yes	characteristic
294	#431	C₂×D₁₃	1	1	yes	characteristic
295	#423	—	13	1	no	—
296	#423	—	13	1	no	—
297	C₂×C₄⋊C₈	—	13	1	no	—
298	C₂×C₄⋊C₈	—	13	1	no	—
299	#408	—	26	1	no	—
300	#408	—	26	1	no	—
301	#405	—	26	1	no	—
302	#405	—	26	1	no	—
303	C₂×C₄×C₈	—	13	1	no	—
304	C₂×C₄×C₈	—	13	1	no	—
305	C₂×C₄×C₈	—	13	1	no	—
306	#335	—	13	1	no	—
307	#335	—	13	1	no	—
308	#335	—	13	1	no	—
309	#335	—	13	1	no	—
310	#335	—	13	1	no	—
311	#335	—	13	1	no	—
312	#335	C₂×D₁₃	1	1	yes	characteristic
313	#335	C₂×D₁₃	1	1	yes	characteristic
314	#334	—	13	1	no	—
315	#334	—	13	1	no	—
316	#334	—	13	1	no	—
317	#334	—	13	1	no	—
318	#334	—	13	1	no	—
319	#334	—	13	1	no	—
320	#334	C₂×D₁₃	1	1	yes	characteristic
321	#334	C₂×D₁₃	1	1	yes	characteristic
322	C₂²×C₁₃	—	2	1	no	—
323	C₂²×C₁₃	—	2	1	no	—
324	C₂²×C₁₃	—	2	1	no	—
325	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
326	C₂×D₁₃	—	2	1	no	—
327	C₂×D₁₃	—	2	1	no	—
328	C₂×D₁₃	—	2	1	no	—
329	C₂×D₁₃	—	2	1	no	—
330	C₂×D₁₃	—	2	1	no	—
331	C₂×D₁₃	#427	1	2	yes	—
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	C₂×#131	1	1	yes	characteristic
337	C₄×C₁₃	#568	1	1	yes	characteristic
338	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
339	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
340	Dic₁₃	—	2	1	no	—
341	Dic₁₃	—	2	1	no	—
342	Dic₁₃	—	2	1	no	—
343	Dic₁₃	—	2	1	no	—
344	Dic₁₃	—	2	1	no	—
345	Dic₁₃	#427	1	2	yes	—
346	C₂×#41	—	13	1	no	—
347	C₂×M₁₆	—	26	1	no	—
348	C₂×M₁₆	—	26	1	no	—
349	C₂²×C₈	—	13	1	no	—
350	C₂²×C₈	—	13	1	no	—
351	C₂²×C₈	—	13	1	no	—
352	C₂²×C₈	—	13	1	no	—
353	C₂²×C₈	—	13	1	no	—
354	C₂²×C₈	—	13	1	no	—
355	C₂²×C₈	—	26	1	no	—
356	C₂²×C₈	—	26	1	no	—
357	C₄×Q₈	—	13	1	no	—
358	C₄×Q₈	—	13	1	no	—
359	C₄×D₄	—	13	1	no	—
360	C₄×D₄	—	13	1	no	—
361	C₄×D₄	—	13	1	no	—
362	C₄×D₄	—	13	1	no	—
363	C₄×D₄	—	13	1	no	—
364	C₄×D₄	—	13	1	no	—
365	#117	—	13	1	no	—
366	#117	—	13	1	no	—
367	#117	—	13	1	no	—
368	C₂×C₄²	—	13	1	no	—
369	C₂×C₄²	—	13	1	no	—
370	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
371	C₄⋊C₈	—	13	1	no	—
372	C₄⋊C₈	—	13	1	no	—
373	C₄⋊C₈	—	13	1	no	—
374	C₄⋊C₈	—	13	1	no	—
375	C₄⋊C₈	—	13	1	no	—
376	C₄⋊C₈	—	13	1	no	—
377	C₄⋊C₈	—	13	1	no	—
378	C₄⋊C₈	—	13	1	no	—
379	C₄⋊C₈	—	26	1	no	—
380	C₄⋊C₈	—	26	1	no	—
381	C₄⋊C₈	—	26	1	no	—
382	C₄⋊C₈	—	26	1	no	—
383	C₄⋊C₈	C₄×D₁₃	1	1	yes	characteristic
384	C₄⋊C₈	C₄×D₁₃	1	1	yes	characteristic
385	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
386	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
387	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
388	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
389	C₂²⋊C₈	—	2	1	no	—
390	C₂²⋊C₈	—	2	1	no	—
391	C₂²⋊C₈	—	13	1	no	—
392	C₂²⋊C₈	—	13	1	no	—
393	C₂²⋊C₈	—	13	1	no	—
394	C₂²⋊C₈	—	13	1	no	—
395	C₂²⋊C₈	—	26	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	C₂²⋊C₈	—	26	1	no	—
401	C₂²⋊C₈	C₄×D₁₃	1	1	yes	characteristic
402	C₂²⋊C₈	C₄×D₁₃	1	1	yes	characteristic
403	#97	—	2	1	no	—
404	#97	—	26	1	no	—
405	#97	—	26	1	no	—
406	#97	—	26	1	no	—
407	C₄×C₈	—	2	1	no	—
408	C₄×C₈	—	13	1	no	—
409	C₄×C₈	—	13	1	no	—
410	C₄×C₈	—	13	1	no	—
411	C₄×C₈	—	13	1	no	—
412	C₄×C₈	—	13	1	no	—
413	C₄×C₈	—	13	1	no	—
414	C₄×C₈	—	13	1	no	—
415	C₄×C₈	—	13	1	no	—
416	C₄×C₈	—	26	1	no	—
417	C₄×C₈	—	26	1	no	—
418	C₄×C₈	—	26	1	no	—
419	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
420	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
421	C₂×C₁₃	—	4	1	no	—
422	C₂×C₁₃	#2906	1	1	yes	characteristic
423	C₂×C₁₃	C₂×#427	1	1	yes	characteristic
424	C₂×C₁₃	#2916	1	1	yes	characteristic
425	D₁₃	—	2	2	no	—
426	D₁₃	—	4	1	no	—
427	#41	—	26	2	no	—
428	#41	—	26	2	no	—
429	C₂×Q₈	—	13	1	no	—
430	C₂×D₄	—	13	1	no	—
431	C₂×D₄	—	13	1	no	—
432	C₂×D₄	—	13	1	no	—
433	C₂²×C₄	—	13	1	no	—
434	C₂²×C₄	—	13	1	no	—
435	C₂²×C₄	—	13	1	no	—
436	C₂²×C₄	—	13	1	no	—
437	C₂²×C₄	—	13	1	no	—
438	C₂²×C₄	—	13	1	no	—
439	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
440	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
441	C₂²×C₄	Q₈×D₁₃	1	1	yes	characteristic
442	M₁₆	—	52	2	no	—
443	M₁₆	—	52	2	no	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	2	1	no	—
447	C₂×C₈	—	2	1	no	—
448	C₂×C₈	—	13	1	no	—
449	C₂×C₈	—	13	1	no	—
450	C₂×C₈	—	13	1	no	—
451	C₂×C₈	—	13	1	no	—
452	C₂×C₈	—	26	2	no	—
453	C₂×C₈	—	26	2	no	—
454	C₂×C₈	—	26	2	no	—
455	C₂×C₈	—	26	1	no	—
456	C₂×C₈	—	26	1	no	—
457	C₂×C₈	—	26	1	no	—
458	C₂×C₈	—	26	1	no	—
459	C₂×C₈	—	52	1	no	—
460	C₂×C₈	—	52	1	no	—
461	C₂×C₈	—	52	2	no	—
462	C₂×C₈	—	52	2	no	—
463	C₂×C₈	—	52	1	no	—
464	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
465	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
466	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
467	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
468	C₄⋊C₄	—	13	1	no	—
469	C₄⋊C₄	—	13	1	no	—
470	C₄⋊C₄	—	13	1	no	—
471	C₄⋊C₄	—	13	1	no	—
472	C₄⋊C₄	—	13	1	no	—
473	C₄⋊C₄	—	13	1	no	—
474	C₂²⋊C₄	—	13	1	no	—
475	C₂²⋊C₄	—	13	1	no	—
476	C₂²⋊C₄	—	13	1	no	—
477	C₂²⋊C₄	—	13	1	no	—
478	C₂²⋊C₄	—	13	1	no	—
479	C₂²⋊C₄	—	13	1	no	—
480	C₄²	—	13	1	no	—
481	C₄²	—	13	1	no	—
482	C₄²	—	13	1	no	—
483	C₄²	—	13	1	no	—
484	C₄²	—	13	1	no	—
485	C₄²	—	13	1	no	—
486	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
487	C₄²	D₄×D₁₃	1	1	yes	characteristic
488	C₄²	Q₈×D₁₃	1	1	yes	characteristic
489	C₄²	C₂³×D₁₃	1	1	yes	characteristic
490	C₁₃	#17829	1	1	yes	characteristic, complemented, Sylow
491	C₂³	—	13	1	no	—
492	C₂³	—	13	1	no	—
493	C₂³	C₄⋊C₄×D₁₃	1	1	yes	characteristic
494	Q₈	—	26	2	no	—
495	D₄	—	26	2	no	—
496	D₄	—	26	2	no	—
497	D₄	—	26	2	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	—	13	1	no	—
504	C₂×C₄	—	13	2	no	—
505	C₂×C₄	—	13	2	no	—
506	C₂×C₄	—	13	1	no	—
507	C₂×C₄	—	13	1	no	—
508	C₂×C₄	—	13	1	no	—
509	C₂×C₄	—	13	1	no	—
510	C₂×C₄	—	13	1	no	—
511	C₂×C₄	—	26	1	no	—
512	C₂×C₄	—	26	1	no	—
513	C₂×C₄	—	26	1	no	—
514	C₂×C₄	—	26	1	no	—
515	C₂×C₄	—	26	1	no	—
516	C₂×C₄	—	26	1	no	—
517	C₂×C₄	—	52	1	no	—
518	C₂×C₄	—	52	1	no	—
519	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
520	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
521	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
522	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
523	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
524	C₂×C₄	C₂×Q₈×D₁₃	1	1	yes	characteristic
525	C₈	—	2	1	no	—
526	C₈	—	2	1	no	—
527	C₈	—	2	1	no	—
528	C₈	—	2	1	no	—
529	C₈	—	4	1	no	—
530	C₈	—	4	1	no	—
531	C₈	—	4	1	no	—
532	C₈	—	4	1	no	—
533	C₈	—	13	2	no	—
534	C₈	—	26	1	no	—
535	C₈	—	26	1	no	—
536	C₈	—	26	1	no	—
537	C₈	—	52	1	no	—
538	C₈	—	52	1	no	—
539	C₈	—	52	1	no	—
540	C₈	—	52	1	no	—
541	C₂²	—	2	1	no	—
542	C₂²	—	2	1	no	—
543	C₂²	—	2	1	no	—
544	C₂²	—	13	2	no	—
545	C₂²	—	26	1	no	—
546	C₂²	—	26	1	no	—
547	C₂²	—	26	1	no	—
548	C₂²	—	26	1	no	—
549	C₂²	—	26	1	no	—
550	C₂²	C₂×C₄⋊C₄×D₁₃	1	1	yes	characteristic
551	C₄	—	2	1	no	—
552	C₄	—	2	1	no	—
553	C₄	—	2	1	no	—
554	C₄	—	2	1	no	—
555	C₄	—	13	2	no	—
556	C₄	—	26	1	no	—
557	C₄	—	26	1	no	—
558	C₄	—	26	1	no	—
559	C₄	—	26	1	no	—
560	C₄	—	26	1	no	—
561	C₄	D₁₃×#131	1	1	yes	characteristic
562	C₄	#11719455	1	1	yes	characteristic
563	C₄	D₁₃×#135	1	1	yes	characteristic
564	C₄	D₁₃×#135	1	1	yes	characteristic
565	C₂	—	4	1	no	—
566	C₂	—	26	2	no	—
567	C₂	—	52	1	no	—
568	C₂	#13123403	1	1	yes	characteristic
569	C₂	D₁₃×#427	1	1	yes	characteristic
570	C₂	#13123446	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×#1572	C₂
socle	C₂²×C₁₃	C₂²×C₄⋊C₄
prime radical	C₂×#6127	D₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#1572	D₁₃
hypocenter	C₁₃	#17829
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1572

Complements

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

N	H ≅ G/N	type
4. #13113616	C₂	semidirect
5. #13113615	C₂	semidirect
6. #13113615	C₂	semidirect
7. #13113605	C₂	semidirect
8. #13113605	C₂	semidirect
9. #13113597	C₂	semidirect
10. #13113596	C₂	semidirect
11. #13113593	C₂	semidirect
12. #13113582	C₂	semidirect
13. #13113581	C₂	semidirect
14. D₁₃×#335	C₂	semidirect
15. C₁₃×#1572	C₂	semidirect
212. #1572	D₁₃	semidirect
490. C₁₃	#17829	semidirect

Maximal subgroups

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

subgroup	index
#13123792	2
#13123503	2
#13123497	2
#13113616	2
#13113615	2
#13113605	2
#13113597	2
#13113596	2
#13113593	2
#13113582	2
#13113581	2
D₁₃×#335	2
C₁₃×#1572	2
#17829	13