Subgroups — #15873541

Order 3328.

724 conjugacy classes of subgroups.

The subgroup lattice has 518 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	C₂×#11718494	C₂	1	1	yes	maximal, characteristic
3	D₁₃×#423	C₂	1	1	yes	maximal, characteristic
4	#13115612	C₂	1	1	yes	maximal, characteristic, complemented
5	#13115611	C₂	1	1	yes	maximal, characteristic, complemented
6	#13115609	C₂	1	1	yes	maximal, characteristic, complemented
7	#13115042	C₂	1	2	yes	maximal
8	#13115039	C₂	1	2	yes	maximal
9	#13115006	C₂	1	2	yes	maximal, complemented
10	#13114972	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1950	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×M₁₆×D₁₃	C₂²	1	2	yes	—
13	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#108	C₂²	1	2	yes	—
15	C₁₃×#423	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
17	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
18	#11718787	C₂²	1	1	yes	characteristic
19	#11718787	C₂²	1	1	yes	characteristic
20	C₂×#88062	C₂²	1	2	yes	—
21	C₂×#88062	C₂²	1	2	yes	—
22	#11718779	C₂²	1	2	yes	—
23	#11718779	C₂²	1	1	yes	characteristic
24	#11718779	C₂²	1	1	yes	characteristic
25	C₂×#88060	C₂²	1	2	yes	—
26	C₂×#88059	C₂²	1	2	yes	—
27	C₂×C₈×Dic₁₃	C₂²	1	2	yes	—
28	#11718585	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
30	C₄×#6099	C₂²	1	1	yes	characteristic
31	#11718498	—	2	1	no	—
32	#11718498	—	2	1	no	—
33	#11718494	C₄	1	2	yes	—
34	#11718494	C₄	1	2	yes	—
35	#11718494	C₄	1	2	yes	—
36	#11718494	C₄	1	2	yes	—
37	D₁₃×C₄⋊C₈	—	2	1	no	—
38	D₁₃×C₄⋊C₈	—	2	1	no	—
39	#11718366	—	2	1	no	—
40	#11718366	—	2	1	no	—
41	#11718346	—	2	1	no	—
42	#11718346	—	2	1	no	—
43	C₁₃×#341	C₂²	1	2	yes	—
44	#11718150	C₂²	1	2	yes	—
45	#11718150	C₂²	1	2	yes	—
46	#11718144	C₂²	1	2	yes	—
47	C₂²×C₄×D₁₃	Q₈	1	1	yes	characteristic
48	C₂²×C₄×D₁₃	Q₈	1	1	yes	characteristic
49	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
50	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
51	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
52	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
54	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
55	C₂×C₄×Dic₁₃	Q₈	1	1	yes	characteristic
56	C₂×C₄×Dic₁₃	Q₈	1	1	yes	characteristic
57	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
58	C₂×#6099	C₂³	1	1	yes	characteristic
59	C₂×#6099	C₂³	1	2	yes	—
60	C₂×#6099	C₂³	1	1	yes	characteristic
61	C₂²×#1055	C₂³	1	2	yes	—
62	M₁₆×D₁₃	—	4	2	no	—
63	M₁₆×D₁₃	—	4	2	no	—
64	C₂×#6094	—	2	2	no	—
65	C₂×C₈×D₁₃	—	2	2	no	—
66	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
67	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
68	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
69	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
70	C₄²×D₁₃	D₄	1	1	yes	characteristic
71	C₄²×D₁₃	D₄	1	1	yes	characteristic
72	C₄²×D₁₃	D₄	1	1	yes	characteristic
73	C₄²×D₁₃	D₄	1	1	yes	characteristic
74	C₁₃×#108	—	4	2	no	—
75	C₁₃×C₄⋊C₈	—	2	1	no	—
76	C₁₃×C₄⋊C₈	—	2	1	no	—
77	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
78	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
79	C₁₃×#97	—	2	1	no	—
80	C₄×C₈×C₁₃	—	2	1	no	—
81	#88062	—	4	2	no	—
82	#88062	—	4	2	no	—
83	#88060	—	2	1	no	—
84	#88060	—	2	1	no	—
85	#88060	—	2	1	no	—
86	#88060	—	2	1	no	—
87	#88060	C₂×C₄	1	4	yes	—
88	#88060	C₂×C₄	1	4	yes	—
89	#88059	—	4	2	no	—
90	#88054	—	2	2	no	—
91	#88054	—	2	2	no	—
92	#88054	—	2	1	no	—
93	#88054	—	2	1	no	—
94	#88054	—	2	1	no	—
95	#88054	—	2	1	no	—
96	C₈×Dic₁₃	C₂×C₄	1	4	yes	—
97	C₈×Dic₁₃	C₂×C₄	1	4	yes	—
98	C₄⋊#1055	—	2	1	no	—
99	C₄⋊#1055	—	2	1	no	—
100	C₄⋊#1055	C₂×C₄	1	2	yes	—
101	C₄⋊#1055	C₂×C₄	1	2	yes	—
102	#88043	—	2	1	no	—
103	C₄×#1055	—	2	1	no	—
104	#21993	—	13	1	no	maximal, Sylow
105	C₂³×D₁₃	C₂×Q₈	1	1	yes	characteristic
106	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
107	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
108	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
109	C₂²×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
110	C₂²×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
111	C₂²×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
112	C₂×C₄×D₁₃	—	2	1	no	—
113	C₂×C₄×D₁₃	—	2	1	no	—
114	C₂×C₄×D₁₃	—	2	1	no	—
115	C₂×C₄×D₁₃	—	2	1	no	—
116	C₂×C₄×D₁₃	—	2	4	no	—
117	C₂×C₄×D₁₃	—	4	2	no	—
118	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
119	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
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	C₁₃×M₁₆	—	2	1	no	—
131	C₁₃×M₁₆	—	2	2	no	—
132	C₁₃×M₁₆	—	2	2	no	—
133	C₁₃×M₁₆	—	2	1	no	—
134	C₁₃×M₁₆	—	2	1	no	—
135	C₁₃×M₁₆	—	2	1	no	—
136	C₂×C₈×C₁₃	—	2	2	no	—
137	C₂×C₈×C₁₃	—	2	2	no	—
138	C₂×C₈×C₁₃	—	2	1	no	—
139	C₂×C₈×C₁₃	—	2	1	no	—
140	C₂×C₈×C₁₃	—	2	2	no	—
141	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
142	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
143	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
144	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
145	C₄²×C₁₃	C₂×D₄	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	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	C₂²×C₄	1	1	yes	characteristic
155	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
156	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
157	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
158	#6099	—	2	2	no	—
159	#6099	—	2	2	no	—
160	#6099	—	2	1	no	—
161	#6099	—	2	1	no	—
162	#6099	—	2	1	no	—
163	#6099	—	2	1	no	—
164	C₂×#1055	—	2	2	no	—
165	C₂×#1055	—	2	2	no	—
166	C₂×#1055	—	2	2	no	—
167	C₂×#1055	—	2	1	no	—
168	C₂×#1055	—	2	1	no	—
169	C₂×#1055	C₂²×C₄	1	4	yes	—
170	#6094	—	4	4	no	—
171	C₈×D₁₃	—	4	4	no	—
172	#2920	—	13	1	no	—
173	C₂×#431	—	13	1	no	—
174	C₂×#423	—	13	1	no	—
175	#1950	—	13	1	no	—
176	#1950	—	13	1	no	—
177	#1950	—	13	1	no	—
178	#1950	D₁₃	1	1	yes	characteristic, complemented
179	#1855	—	13	2	no	—
180	#1855	—	13	2	no	—
181	#1848	—	13	2	no	—
182	#1837	—	13	2	no	—
183	C₂³×C₁₃	C₂²×Q₈	1	1	yes	characteristic
184	C₂²×D₁₃	—	2	1	no	—
185	C₂²×D₁₃	—	2	1	no	—
186	C₂²×D₁₃	—	2	2	no	—
187	C₂²×D₁₃	—	4	1	no	—
188	C₂²×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
189	C₂²×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
190	C₂×C₄×C₁₃	—	2	2	no	—
191	C₂×C₄×C₁₃	—	4	1	no	—
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	C₂×C₄⋊C₄	1	1	yes	characteristic
195	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
196	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
197	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
198	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
199	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
200	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
201	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
202	C₂×Dic₁₃	—	2	1	no	—
203	C₂×Dic₁₃	—	2	1	no	—
204	C₂×Dic₁₃	—	2	2	no	—
205	C₂×Dic₁₃	—	2	2	no	—
206	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
207	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
208	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
209	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
210	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
211	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
212	C₄×D₁₃	—	2	2	no	—
213	C₄×D₁₃	—	2	1	no	—
214	C₄×D₁₃	—	2	1	no	—
215	C₄×D₁₃	—	2	1	no	—
216	C₄×D₁₃	—	2	1	no	—
217	C₄×D₁₃	—	2	1	no	—
218	C₄×D₁₃	—	2	1	no	—
219	C₄×D₁₃	—	2	1	no	—
220	C₄×D₁₃	—	2	1	no	—
221	C₄×D₁₃	—	2	2	no	—
222	C₄×D₁₃	—	2	2	no	—
223	C₄×D₁₃	—	2	2	no	—
224	C₄×D₁₃	—	2	2	no	—
225	C₄×D₁₃	—	4	1	no	—
226	C₄×D₁₃	—	4	1	no	—
227	C₄×D₁₃	#108	1	4	yes	complemented
228	C₈×C₁₃	—	2	4	no	—
229	C₈×C₁₃	—	4	2	no	—
230	C₈×C₁₃	—	4	1	no	—
231	C₈×C₁₃	—	4	1	no	—
232	#1055	—	2	4	no	—
233	#1055	—	4	2	no	—
234	#1055	—	4	1	no	—
235	#1055	—	4	1	no	—
236	C₂²×M₁₆	—	13	2	no	—
237	C₂²×C₄²	—	13	1	no	—
238	#432	—	26	1	no	—
239	#432	—	26	1	no	—
240	#431	—	13	2	no	—
241	#431	—	13	2	no	—
242	#431	—	13	2	no	—
243	#431	—	13	2	no	—
244	#431	—	26	1	no	—
245	#431	—	26	1	no	—
246	C₂×#108	—	13	2	no	—
247	C₂×#108	—	13	2	no	—
248	C₂×#108	—	13	2	no	—
249	C₂×#108	C₂×D₁₃	1	2	yes	—
250	#423	—	13	1	no	—
251	#423	—	13	2	no	—
252	#423	—	13	1	no	—
253	#423	—	13	1	no	—
254	#423	—	26	1	no	—
255	#423	—	26	1	no	—
256	#423	C₂×D₁₃	1	1	yes	characteristic
257	C₂×C₄⋊C₈	—	13	1	no	—
258	C₂×C₄⋊C₈	—	26	1	no	—
259	C₂×C₄⋊C₈	—	26	1	no	—
260	C₂×C₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic
261	#407	—	13	1	no	—
262	#407	—	13	1	no	—
263	C₂×C₂²⋊C₈	—	13	2	no	—
264	C₄×M₁₆	—	13	1	no	—
265	C₄×M₁₆	C₂×D₁₃	1	1	yes	characteristic
266	C₂×C₄×C₈	—	13	2	no	—
267	#341	—	13	2	no	—
268	#341	—	13	2	no	—
269	#341	—	13	2	no	—
270	#341	C₂×D₁₃	1	2	yes	—
271	C₂²×C₁₃	—	2	1	no	—
272	C₂²×C₁₃	—	2	1	no	—
273	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
274	C₂²×C₁₃	#544	1	1	yes	characteristic
275	C₂²×C₁₃	#544	1	1	yes	characteristic
276	C₂×D₁₃	—	2	1	no	—
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	—	4	2	no	—
282	C₂×D₁₃	—	4	2	no	—
283	C₂×D₁₃	C₂×#108	1	2	yes	—
284	C₄×C₁₃	—	2	1	no	—
285	C₄×C₁₃	—	2	1	no	—
286	C₄×C₁₃	—	2	1	no	—
287	C₄×C₁₃	C₂×#108	1	2	yes	—
288	C₄×C₁₃	#520	1	1	yes	characteristic
289	C₄×C₁₃	#520	1	1	yes	characteristic
290	C₄×C₁₃	#535	1	1	yes	characteristic
291	C₄×C₁₃	#536	1	1	yes	characteristic
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	Dic₁₃	#430	1	2	yes	—
298	C₂³×C₄	—	13	1	no	—
299	C₂³×C₄	—	13	1	no	—
300	C₂³×C₄	—	13	1	no	—
301	C₂×M₁₆	—	13	2	no	—
302	C₂×M₁₆	—	13	1	no	—
303	C₂×M₁₆	—	13	1	no	—
304	C₂×M₁₆	—	26	2	no	—
305	C₂×M₁₆	—	52	2	no	—
306	C₂×M₁₆	—	52	2	no	—
307	C₂×M₁₆	C₂²×D₁₃	1	2	yes	—
308	C₂×M₁₆	C₂²×D₁₃	1	1	yes	characteristic
309	C₂×M₁₆	C₂²×D₁₃	1	1	yes	characteristic
310	C₂²×C₈	—	13	2	no	—
311	C₂²×C₈	—	26	2	no	—
312	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
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	—	13	1	no	—
319	C₂×C₄²	—	13	1	no	—
320	C₂×C₄²	—	13	1	no	—
321	C₂×C₄²	—	13	1	no	—
322	C₂×C₄²	—	13	1	no	—
323	C₂×C₄²	—	13	1	no	—
324	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
325	#108	—	4	2	no	—
326	#108	—	52	2	no	—
327	#108	—	52	2	no	—
328	#108	—	52	2	no	—
329	C₄⋊C₈	—	2	1	no	—
330	C₄⋊C₈	—	2	1	no	—
331	C₄⋊C₈	—	13	2	no	—
332	C₄⋊C₈	—	13	2	no	—
333	C₄⋊C₈	—	26	2	no	—
334	C₄⋊C₈	—	26	2	no	—
335	C₄⋊C₈	—	26	1	no	—
336	C₄⋊C₈	—	26	1	no	—
337	C₄⋊C₈	—	26	1	no	—
338	C₄⋊C₈	—	26	1	no	—
339	C₄⋊C₈	—	26	1	no	—
340	C₄⋊C₈	—	26	1	no	—
341	C₄⋊C₈	C₄×D₁₃	1	2	yes	—
342	C₄⋊C₈	C₄×D₁₃	1	2	yes	—
343	C₂²⋊C₈	—	13	4	no	—
344	C₂²⋊C₈	—	13	4	no	—
345	C₂²⋊C₈	—	26	1	no	—
346	C₂²⋊C₈	—	26	1	no	—
347	C₂²⋊C₈	—	26	1	no	—
348	C₂²⋊C₈	—	26	1	no	—
349	#97	—	2	1	no	—
350	#97	—	26	1	no	—
351	C₄×C₈	—	2	1	no	—
352	C₄×C₈	—	13	4	no	—
353	C₄×C₈	—	13	4	no	—
354	C₄×C₈	—	26	1	no	—
355	C₂×C₁₃	—	2	1	no	—
356	C₂×C₁₃	—	2	1	no	—
357	C₂×C₁₃	#2317	1	1	yes	characteristic
358	C₂×C₁₃	C₂²×#108	1	1	yes	characteristic
359	C₂×C₁₃	C₂×#430	1	1	yes	characteristic
360	D₁₃	—	2	2	no	—
361	D₁₃	—	4	1	no	—
362	C₂⁴	—	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	—	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	—	26	4	no	—
379	C₂²×C₄	—	26	1	no	—
380	C₂²×C₄	—	26	1	no	—
381	C₂²×C₄	—	26	1	no	—
382	C₂²×C₄	—	26	1	no	—
383	C₂²×C₄	—	52	2	no	—
384	C₂²×C₄	Q₈×D₁₃	1	1	yes	characteristic
385	C₂²×C₄	Q₈×D₁₃	1	1	yes	characteristic
386	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
387	M₁₆	—	2	1	no	—
388	M₁₆	—	2	2	no	—
389	M₁₆	—	2	1	no	—
390	M₁₆	—	2	1	no	—
391	M₁₆	—	2	2	no	—
392	M₁₆	—	2	1	no	—
393	M₁₆	—	26	1	no	—
394	M₁₆	—	26	2	no	—
395	M₁₆	—	26	1	no	—
396	M₁₆	—	26	1	no	—
397	M₁₆	—	26	2	no	—
398	M₁₆	—	26	1	no	—
399	M₁₆	—	52	4	no	—
400	C₂×C₈	—	2	2	no	—
401	C₂×C₈	—	2	2	no	—
402	C₂×C₈	—	2	1	no	—
403	C₂×C₈	—	2	1	no	—
404	C₂×C₈	—	2	2	no	—
405	C₂×C₈	—	13	4	no	—
406	C₂×C₈	—	26	2	no	—
407	C₂×C₈	—	26	2	no	—
408	C₂×C₈	—	26	1	no	—
409	C₂×C₈	—	26	1	no	—
410	C₂×C₈	—	26	2	no	—
411	C₂×C₈	—	52	4	no	—
412	C₂×C₈	C₂×C₄×D₁₃	1	4	yes	—
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	—	13	1	no	—
420	C₄²	—	13	1	no	—
421	C₄²	—	13	1	no	—
422	C₄²	—	13	1	no	—
423	C₄²	—	13	1	no	—
424	C₄²	—	13	1	no	—
425	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
426	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
427	C₄²	D₄×D₁₃	1	1	yes	characteristic
428	C₄²	D₄×D₁₃	1	1	yes	characteristic
429	C₁₃	#21993	1	1	yes	characteristic, complemented, Sylow
430	C₂³	—	13	1	no	—
431	C₂³	—	13	1	no	—
432	C₂³	—	26	2	no	—
433	C₂³	—	26	1	no	—
434	C₂³	—	26	1	no	—
435	C₂³	—	52	1	no	—
436	C₂³	C₂×Q₈×D₁₃	1	1	yes	characteristic
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	13	1	no	—
440	C₂×C₄	—	13	1	no	—
441	C₂×C₄	—	13	4	no	—
442	C₂×C₄	—	13	1	no	—
443	C₂×C₄	—	13	1	no	—
444	C₂×C₄	—	13	1	no	—
445	C₂×C₄	—	13	1	no	—
446	C₂×C₄	—	26	2	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	—	26	1	no	—
453	C₂×C₄	—	26	1	no	—
454	C₂×C₄	—	26	1	no	—
455	C₂×C₄	—	26	1	no	—
456	C₂×C₄	—	26	1	no	—
457	C₂×C₄	—	26	1	no	—
458	C₂×C₄	—	26	1	no	—
459	C₂×C₄	—	26	1	no	—
460	C₂×C₄	—	26	2	no	—
461	C₂×C₄	—	26	1	no	—
462	C₂×C₄	—	26	1	no	—
463	C₂×C₄	—	52	1	no	—
464	C₂×C₄	—	52	1	no	—
465	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
466	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
467	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
468	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
469	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
470	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
471	C₂×C₄	#88251	1	1	yes	characteristic
472	C₂×C₄	#88254	1	1	yes	characteristic
473	C₂×C₄	#88256	1	1	yes	characteristic
474	C₂×C₄	#88257	1	1	yes	characteristic
475	C₈	—	2	4	no	—
476	C₈	—	4	2	no	—
477	C₈	—	4	1	no	—
478	C₈	—	4	1	no	—
479	C₈	—	26	4	no	—
480	C₈	—	52	2	no	—
481	C₈	—	52	1	no	—
482	C₈	—	52	1	no	—
483	C₂²	—	2	1	no	—
484	C₂²	—	2	1	no	—
485	C₂²	—	13	2	no	—
486	C₂²	—	26	1	no	—
487	C₂²	—	26	1	no	—
488	C₂²	—	26	1	no	—
489	C₂²	—	26	1	no	—
490	C₂²	—	26	1	no	—
491	C₂²	—	52	2	no	—
492	C₂²	—	52	2	no	—
493	C₂²	C₂×C₄⋊C₄×D₁₃	1	1	yes	characteristic
494	C₂²	#11719394	1	1	yes	characteristic
495	C₂²	#11719434	1	1	yes	characteristic
496	C₄	—	2	1	no	—
497	C₄	—	2	1	no	—
498	C₄	—	2	1	no	—
499	C₄	—	13	2	no	—
500	C₄	—	13	2	no	—
501	C₄	—	26	1	no	—
502	C₄	—	26	1	no	—
503	C₄	—	26	1	no	—
504	C₄	—	26	1	no	—
505	C₄	D₁₃×#108	1	2	yes	—
506	C₄	#11719251	1	1	yes	characteristic
507	C₄	#11719279	1	1	yes	characteristic
508	C₄	#11719312	1	1	yes	characteristic
509	C₄	#11719333	1	1	yes	characteristic
510	C₂	—	2	1	no	—
511	C₂	—	2	1	no	—
512	C₂	—	26	2	no	—
513	C₂	—	52	1	no	—
514	C₂	#13117458	1	1	yes	characteristic
515	C₂	C₂×D₁₃×#108	1	1	yes	characteristic
516	C₂	D₁₃×#430	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₁₃×#1950	C₂
socle	C₂²×C₁₃	C₂²×C₄⋊C₄
prime radical	C₂³×D₁₃	C₂×Q₈
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	#1950	D₁₃
hypocenter	C₁₃	#21993
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1950

Complements

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

N	H ≅ G/N	type
4. #13115612	C₂	semidirect
5. #13115611	C₂	semidirect
6. #13115609	C₂	semidirect
9. #13115006	C₂	semidirect
10. #13114972	C₂	semidirect
11. C₁₃×#1950	C₂	semidirect
178. #1950	D₁₃	semidirect
227. C₄×D₁₃	#108	semidirect
429. C₁₃	#21993	semidirect

Maximal subgroups

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

subgroup	index
#13123467	2
C₂×#11718494	2
D₁₃×#423	2
#13115612	2
#13115611	2
#13115609	2
#13115042	2
#13115039	2
#13115006	2
#13114972	2
C₁₃×#1950	2
#21993	13