Subgroups — #15832008

Order 3328.

668 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13123464	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718346	C₂	1	1	yes	maximal, characteristic
3	D₁₃×#431	C₂	1	1	yes	maximal, characteristic
4	#13113626	C₂	1	2	yes	maximal, complemented
5	#13113623	C₂	1	2	yes	maximal, complemented
6	#13113620	C₂	1	2	yes	maximal, complemented
7	#13113618	C₂	1	2	yes	maximal, complemented
8	#13113584	C₂	1	1	yes	maximal, characteristic, complemented
9	#13113582	C₂	1	1	yes	maximal, characteristic, complemented
10	#13113582	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1564	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
13	C₁₃×#431	C₂²	1	1	yes	characteristic
14	C₁₃×#431	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
16	C₂×#88060	C₄	1	1	yes	characteristic
17	C₂×#88060	C₄	1	1	yes	characteristic
18	C₂×#88054	C₄	1	1	yes	characteristic
19	C₂×#88054	C₄	1	1	yes	characteristic
20	#11718586	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	2	yes	—
24	#11718496	C₂²	1	2	yes	—
25	#11718494	C₂²	1	2	yes	—
26	D₁₃×C₄⋊C₈	C₂²	1	2	yes	—
27	#11718387	—	2	1	no	—
28	D₁₃×C₂²⋊C₈	—	2	1	no	—
29	#11718380	—	2	1	no	—
30	#11718379	—	2	1	no	—
31	C₄×#6094	—	2	1	no	—
32	#11718346	—	2	1	no	—
33	#11718346	—	2	1	no	—
34	#11718346	C₄	1	1	yes	characteristic
35	#11718346	C₄	1	1	yes	characteristic
36	#11718346	C₄	1	1	yes	characteristic
37	#11718346	C₄	1	1	yes	characteristic
38	#11718346	C₂²	1	1	yes	characteristic
39	#11718346	C₂²	1	1	yes	characteristic
40	#11718346	C₂²	1	1	yes	characteristic
41	#11718346	C₂²	1	1	yes	characteristic
42	C₄×C₈×D₁₃	—	2	1	no	—
43	C₁₃×#335	C₂²	1	2	yes	complemented
44	C₁₃×#334	C₂²	1	2	yes	complemented
45	#11718072	C₂²	1	2	yes	complemented
46	#11718072	C₂²	1	2	yes	complemented
47	#11718071	C₂²	1	2	yes	complemented
48	#11718071	C₂²	1	2	yes	complemented
49	#11718050	C₂²	1	2	yes	complemented
50	#11718049	C₂²	1	2	yes	complemented
51	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₄×D₁₃	D₄	1	1	yes	characteristic
53	C₂²×C₄×D₁₃	Q₈	1	1	yes	characteristic
54	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
55	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
57	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
59	C₂×C₄×Dic₁₃	Q₈	1	1	yes	characteristic
60	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
61	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
62	C₂×#6094	—	2	2	no	—
63	C₂×C₈×D₁₃	—	2	2	no	—
64	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
65	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
66	C₄²×D₁₃	D₄	1	1	yes	characteristic
67	C₄²×D₁₃	D₄	1	1	yes	characteristic
68	C₄²×D₁₃	Q₈	1	1	yes	characteristic
69	C₄²×D₁₃	Q₈	1	1	yes	characteristic
70	C₄²×D₁₃	C₂³	1	1	yes	characteristic
71	C₄²×D₁₃	C₂³	1	1	yes	characteristic
72	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
73	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
74	C₁₃×C₂²⋊C₈	—	2	1	no	—
75	C₁₃×C₂²⋊C₈	—	2	1	no	—
76	C₄×C₈×C₁₃	—	2	1	no	—
77	C₄×C₈×C₁₃	—	2	1	no	—
78	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
79	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
80	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
81	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
82	C₂²⋊#1055	—	2	1	no	—
83	C₂²⋊#1055	—	2	1	no	—
84	#88060	—	2	2	no	—
85	#88060	—	2	2	no	—
86	#88060	C₂×C₄	1	1	yes	characteristic
87	#88060	C₂×C₄	1	1	yes	characteristic
88	#88060	C₂×C₄	1	1	yes	characteristic
89	#88060	C₂×C₄	1	1	yes	characteristic
90	#88060	C₂×C₄	1	1	yes	characteristic
91	#88060	C₂×C₄	1	1	yes	characteristic
92	#88060	C₂×C₄	1	1	yes	characteristic
93	#88060	C₂×C₄	1	1	yes	characteristic
94	#88055	—	2	2	no	—
95	#88054	—	2	2	no	—
96	#88054	—	2	2	no	—
97	#88054	C₂×C₄	1	1	yes	characteristic
98	#88054	C₂×C₄	1	1	yes	characteristic
99	#88054	C₂×C₄	1	1	yes	characteristic
100	#88054	C₂×C₄	1	1	yes	characteristic
101	#88054	C₂×C₄	1	1	yes	characteristic
102	#88054	C₂×C₄	1	1	yes	characteristic
103	#88054	C₂×C₄	1	1	yes	characteristic
104	#88054	C₂×C₄	1	1	yes	characteristic
105	C₈×Dic₁₃	—	2	2	no	—
106	C₄⋊#1055	C₂³	1	2	yes	—
107	C₄⋊#1055	C₂³	1	2	yes	—
108	C₄×#1055	—	2	1	no	—
109	C₄×#1055	—	2	1	no	—
110	C₄×#1055	C₂×C₄	1	1	yes	characteristic
111	C₄×#1055	C₂×C₄	1	1	yes	characteristic
112	C₄×#1055	C₂³	1	1	yes	characteristic
113	C₄×#1055	C₂³	1	1	yes	characteristic
114	#17806	—	13	1	no	maximal, Sylow
115	C₂³×D₁₃	C₄⋊C₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
119	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
120	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
121	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
122	C₂×C₄×D₁₃	—	2	2	no	—
123	C₂×C₄×D₁₃	—	2	2	no	—
124	C₂×C₄×D₁₃	—	2	4	no	—
125	C₂×C₄×D₁₃	—	4	2	no	—
126	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
127	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
128	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
129	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
130	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
131	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
132	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
135	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
136	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
137	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
138	C₂×C₈×C₁₃	—	2	2	no	—
139	C₂×C₈×C₁₃	—	2	2	no	—
140	C₂×C₈×C₁₃	—	2	2	no	—
141	C₂×C₈×C₁₃	—	2	2	no	—
142	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
143	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
144	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
145	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
146	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
147	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
148	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
149	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
150	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
151	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
152	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
153	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
154	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
155	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
156	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
157	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
158	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
159	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
160	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
161	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
162	C₂×#1055	—	2	2	no	—
163	C₂×#1055	—	2	2	no	—
164	C₂×#1055	—	2	2	no	—
165	C₂×#1055	—	2	2	no	—
166	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
167	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
168	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
169	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
170	#6094	—	4	4	no	—
171	C₈×D₁₃	—	4	4	no	—
172	#2920	—	13	1	no	—
173	C₂×#431	—	13	1	no	—
174	C₂×#431	—	13	1	no	—
175	#1574	—	13	2	no	—
176	#1574	—	13	2	no	—
177	#1573	—	13	2	no	—
178	#1573	—	13	2	no	—
179	#1564	—	13	1	no	—
180	#1564	—	13	1	no	—
181	#1564	—	13	1	no	—
182	#1564	D₁₃	1	1	yes	characteristic, complemented
183	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
184	C₂²×D₁₃	—	2	2	no	—
185	C₂²×D₁₃	—	2	2	no	—
186	C₂²×D₁₃	—	4	1	no	—
187	C₂²×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
188	C₂²×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
189	C₂×C₄×C₁₃	—	2	2	no	—
190	C₂×C₄×C₁₃	—	2	2	no	—
191	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
192	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
193	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
194	C₂×C₄×C₁₃	#131	1	2	yes	—
195	C₂×C₄×C₁₃	#131	1	2	yes	—
196	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
197	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
198	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
199	C₂×Dic₁₃	—	2	2	no	—
200	C₂×Dic₁₃	—	2	2	no	—
201	C₂×Dic₁₃	—	4	1	no	—
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	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
206	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
207	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
208	C₄×D₁₃	—	2	2	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	2	no	—
214	C₄×D₁₃	—	2	2	no	—
215	C₄×D₁₃	—	2	2	no	—
216	C₄×D₁₃	—	2	2	no	—
217	C₄×D₁₃	—	2	2	no	—
218	C₄×D₁₃	—	2	2	no	—
219	C₄×D₁₃	—	4	1	no	—
220	C₄×D₁₃	—	4	1	no	—
221	C₄×D₁₃	#108	1	4	yes	—
222	C₈×C₁₃	—	2	1	no	—
223	C₈×C₁₃	—	2	1	no	—
224	C₈×C₁₃	—	2	1	no	—
225	C₈×C₁₃	—	2	1	no	—
226	C₈×C₁₃	—	4	2	no	—
227	C₈×C₁₃	—	4	2	no	—
228	#1055	—	2	1	no	—
229	#1055	—	2	1	no	—
230	#1055	—	2	1	no	—
231	#1055	—	2	1	no	—
232	#1055	—	4	2	no	—
233	#1055	—	4	2	no	—
234	C₂²×C₄²	—	13	1	no	—
235	#432	—	13	2	no	—
236	#432	—	26	1	no	—
237	#431	—	13	1	no	—
238	#431	—	13	1	no	—
239	#431	—	13	1	no	—
240	#431	—	13	1	no	—
241	#431	—	13	1	no	—
242	#431	—	13	1	no	—
243	#431	—	13	1	no	—
244	#431	—	13	1	no	—
245	#431	—	13	1	no	—
246	#431	—	13	1	no	—
247	#431	—	13	2	no	—
248	#431	—	26	1	no	—
249	#431	—	26	1	no	—
250	#431	—	26	1	no	—
251	#431	C₂×D₁₃	1	1	yes	characteristic
252	#431	C₂×D₁₃	1	1	yes	characteristic
253	#423	—	13	2	no	—
254	C₂×C₄⋊C₈	—	13	1	no	—
255	C₂×C₄⋊C₈	—	13	1	no	—
256	C₂×C₄⋊C₈	—	13	2	no	—
257	#407	—	26	1	no	—
258	C₂×C₂²⋊C₈	—	13	1	no	—
259	C₂×C₂²⋊C₈	—	13	1	no	—
260	C₂×C₂²⋊C₈	—	26	1	no	—
261	C₄×M₁₆	—	26	1	no	—
262	C₂×C₄×C₈	—	13	1	no	—
263	C₂×C₄×C₈	—	26	1	no	—
264	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
265	#335	—	13	2	no	—
266	#335	—	13	2	no	—
267	#335	—	13	2	no	—
268	#335	C₂×D₁₃	1	2	yes	complemented
269	#334	—	13	2	no	—
270	#334	—	13	2	no	—
271	#334	—	13	2	no	—
272	#334	C₂×D₁₃	1	2	yes	complemented
273	C₂²×C₁₃	—	2	1	no	—
274	C₂²×C₁₃	—	2	1	no	—
275	C₂²×C₁₃	#424	1	2	yes	—
276	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
277	C₂×D₁₃	—	2	1	no	—
278	C₂×D₁₃	—	2	1	no	—
279	C₂×D₁₃	—	2	1	no	—
280	C₂×D₁₃	—	2	1	no	—
281	C₂×D₁₃	—	2	1	no	—
282	C₂×D₁₃	—	4	4	no	—
283	C₂×D₁₃	C₂×#108	1	2	yes	—
284	C₄×C₁₃	—	2	1	no	—
285	C₄×C₁₃	—	2	1	no	—
286	C₄×C₁₃	#424	1	2	yes	—
287	C₄×C₁₃	C₂×#108	1	2	yes	—
288	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
289	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
290	C₄×C₁₃	#575	1	2	yes	—
291	Dic₁₃	—	2	1	no	—
292	Dic₁₃	—	2	1	no	—
293	Dic₁₃	—	2	1	no	—
294	Dic₁₃	—	2	1	no	—
295	Dic₁₃	—	2	1	no	—
296	Dic₁₃	C₂×#108	1	2	yes	—
297	C₂³×C₄	—	13	1	no	—
298	C₂³×C₄	—	13	1	no	—
299	C₂³×C₄	—	13	1	no	—
300	C₂×M₁₆	—	26	2	no	—
301	C₂²×C₈	—	13	1	no	—
302	C₂²×C₈	—	13	1	no	—
303	C₂²×C₈	—	26	2	no	—
304	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
305	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
306	C₂×C₄²	—	13	1	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	C₂²×D₁₃	1	1	yes	characteristic
318	C₄⋊C₈	—	13	1	no	—
319	C₄⋊C₈	—	13	1	no	—
320	C₄⋊C₈	—	13	1	no	—
321	C₄⋊C₈	—	13	1	no	—
322	C₄⋊C₈	—	13	1	no	—
323	C₄⋊C₈	—	13	1	no	—
324	C₄⋊C₈	—	13	1	no	—
325	C₄⋊C₈	—	13	1	no	—
326	C₄⋊C₈	—	13	2	no	—
327	C₄⋊C₈	—	13	2	no	—
328	C₄⋊C₈	—	26	2	no	—
329	C₄⋊C₈	—	26	2	no	—
330	C₄⋊C₈	C₂²×D₁₃	1	2	yes	—
331	C₄⋊C₈	C₂²×D₁₃	1	2	yes	—
332	C₂²⋊C₈	—	2	1	no	—
333	C₂²⋊C₈	—	2	1	no	—
334	C₂²⋊C₈	—	13	1	no	—
335	C₂²⋊C₈	—	13	1	no	—
336	C₂²⋊C₈	—	13	1	no	—
337	C₂²⋊C₈	—	13	1	no	—
338	C₂²⋊C₈	—	13	1	no	—
339	C₂²⋊C₈	—	13	1	no	—
340	C₂²⋊C₈	—	13	1	no	—
341	C₂²⋊C₈	—	13	1	no	—
342	C₂²⋊C₈	—	26	2	no	—
343	C₂²⋊C₈	—	26	2	no	—
344	C₂²⋊C₈	—	26	1	no	—
345	C₂²⋊C₈	—	26	1	no	—
346	#97	—	26	2	no	—
347	C₄×C₈	—	2	1	no	—
348	C₄×C₈	—	2	1	no	—
349	C₄×C₈	—	13	1	no	—
350	C₄×C₈	—	13	1	no	—
351	C₄×C₈	—	13	1	no	—
352	C₄×C₈	—	13	1	no	—
353	C₄×C₈	—	26	2	no	—
354	C₄×C₈	—	26	1	no	—
355	C₄×C₈	—	26	1	no	—
356	C₄×C₈	C₄×D₁₃	1	1	yes	characteristic
357	C₄×C₈	C₄×D₁₃	1	1	yes	characteristic
358	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
359	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
360	C₂×C₁₃	—	2	2	no	—
361	C₂×C₁₃	C₂×#424	1	1	yes	characteristic
362	C₂×C₁₃	#2911	1	1	yes	characteristic
363	C₂×C₁₃	C₂²×#108	1	1	yes	characteristic
364	D₁₃	—	2	2	no	—
365	D₁₃	—	4	1	no	—
366	C₂⁴	—	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	—	13	1	no	—
374	C₂²×C₄	—	13	1	no	—
375	C₂²×C₄	—	13	1	no	—
376	C₂²×C₄	—	13	1	no	—
377	C₂²×C₄	—	13	1	no	—
378	C₂²×C₄	—	13	1	no	—
379	C₂²×C₄	—	13	1	no	—
380	C₂²×C₄	—	13	1	no	—
381	C₂²×C₄	—	13	1	no	—
382	C₂²×C₄	—	26	4	no	—
383	C₂²×C₄	—	26	2	no	—
384	C₂²×C₄	—	26	2	no	—
385	C₂²×C₄	—	52	2	no	—
386	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
387	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
388	C₂²×C₄	Q₈×D₁₃	1	1	yes	characteristic
389	M₁₆	—	52	4	no	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	2	2	no	—
394	C₂×C₈	—	13	1	no	—
395	C₂×C₈	—	13	1	no	—
396	C₂×C₈	—	13	1	no	—
397	C₂×C₈	—	13	1	no	—
398	C₂×C₈	—	26	2	no	—
399	C₂×C₈	—	26	2	no	—
400	C₂×C₈	—	26	2	no	—
401	C₂×C₈	—	26	2	no	—
402	C₂×C₈	—	52	4	no	—
403	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
404	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
405	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
406	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
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	—	13	1	no	—
414	C₄²	—	13	1	no	—
415	C₄²	—	13	1	no	—
416	C₄²	—	13	1	no	—
417	C₄²	—	13	1	no	—
418	C₄²	—	13	1	no	—
419	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
420	C₄²	D₄×D₁₃	1	1	yes	characteristic
421	C₄²	Q₈×D₁₃	1	1	yes	characteristic
422	C₄²	C₂³×D₁₃	1	1	yes	characteristic
423	C₁₃	#17806	1	1	yes	characteristic, complemented, Sylow
424	C₂³	—	13	1	no	—
425	C₂³	—	13	1	no	—
426	C₂³	—	26	2	no	—
427	C₂³	—	26	2	no	—
428	C₂³	—	52	1	no	—
429	C₂³	C₄⋊C₄×D₁₃	1	1	yes	characteristic
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	13	1	no	—
433	C₂×C₄	—	13	4	no	—
434	C₂×C₄	—	13	1	no	—
435	C₂×C₄	—	13	1	no	—
436	C₂×C₄	—	13	1	no	—
437	C₂×C₄	—	13	1	no	—
438	C₂×C₄	—	13	1	no	—
439	C₂×C₄	—	26	2	no	—
440	C₂×C₄	—	26	2	no	—
441	C₂×C₄	—	26	2	no	—
442	C₂×C₄	—	26	2	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	—	26	2	no	—
450	C₂×C₄	—	26	2	no	—
451	C₂×C₄	—	26	2	no	—
452	C₂×C₄	—	52	1	no	—
453	C₂×C₄	—	52	1	no	—
454	C₂×C₄	—	52	1	no	—
455	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
456	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
457	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
458	C₂×C₄	#88155	1	2	yes	—
459	C₂×C₄	#88161	1	2	yes	—
460	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
461	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
462	C₂×C₄	C₂×Q₈×D₁₃	1	1	yes	characteristic
463	C₈	—	2	1	no	—
464	C₈	—	2	1	no	—
465	C₈	—	2	1	no	—
466	C₈	—	2	1	no	—
467	C₈	—	4	2	no	—
468	C₈	—	4	2	no	—
469	C₈	—	26	1	no	—
470	C₈	—	26	1	no	—
471	C₈	—	26	1	no	—
472	C₈	—	26	1	no	—
473	C₈	—	52	2	no	—
474	C₈	—	52	2	no	—
475	C₂²	—	2	1	no	—
476	C₂²	—	2	1	no	—
477	C₂²	—	13	2	no	—
478	C₂²	—	26	1	no	—
479	C₂²	—	26	1	no	—
480	C₂²	—	26	1	no	—
481	C₂²	—	26	1	no	—
482	C₂²	—	26	1	no	—
483	C₂²	—	52	4	no	—
484	C₂²	#11718500	1	2	yes	—
485	C₂²	C₂×C₄⋊C₄×D₁₃	1	1	yes	characteristic
486	C₄	—	2	1	no	—
487	C₄	—	2	1	no	—
488	C₄	—	13	2	no	—
489	C₄	—	26	1	no	—
490	C₄	—	26	1	no	—
491	C₄	—	26	1	no	—
492	C₄	—	26	1	no	—
493	C₄	—	26	1	no	—
494	C₄	#11718500	1	2	yes	—
495	C₄	D₁₃×#108	1	2	yes	—
496	C₄	C₂×#88155	1	1	yes	characteristic
497	C₄	C₂×#88161	1	1	yes	characteristic
498	C₄	#11719473	1	2	yes	—
499	C₂	—	2	2	no	—
500	C₂	—	26	2	no	—
501	C₂	—	52	1	no	—
502	C₂	C₂×#11718500	1	1	yes	characteristic
503	C₂	#13123424	1	1	yes	characteristic
504	C₂	C₂×D₁₃×#108	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	D₄×D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₄²	C₂³×D₁₃
Fitting	C₁₃×#1564	C₂
socle	C₂²×C₁₃	C₂²×C₄⋊C₄
prime radical	C₂³×D₁₃	C₄⋊C₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#1564	D₁₃
hypocenter	C₁₃	#17806
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄² ◁ C₂×C₄² ◁ #1564

Complements

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

N	H ≅ G/N	type
4. #13113626	C₂	semidirect
5. #13113623	C₂	semidirect
6. #13113620	C₂	semidirect
7. #13113618	C₂	semidirect
8. #13113584	C₂	semidirect
9. #13113582	C₂	semidirect
10. #13113582	C₂	semidirect
11. C₁₃×#1564	C₂	semidirect
43. C₁₃×#335	C₂²	semidirect
44. C₁₃×#334	C₂²	semidirect
45. #11718072	C₂²	semidirect
46. #11718072	C₂²	semidirect
47. #11718071	C₂²	semidirect
48. #11718071	C₂²	semidirect
49. #11718050	C₂²	semidirect
50. #11718049	C₂²	semidirect
182. #1564	D₁₃	semidirect
268. #335	C₂×D₁₃	semidirect
272. #334	C₂×D₁₃	semidirect
423. C₁₃	#17806	semidirect

Maximal subgroups

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

subgroup	index
#13123464	2
C₂×#11718346	2
D₁₃×#431	2
#13113626	2
#13113623	2
#13113620	2
#13113618	2
#13113584	2
#13113582	2
C₁₃×#1564	2
#17806	13