Subgroups — D₁₃×#1950 #15866435

Order 3328.

938 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₃×#108	C₂	1	2	yes	maximal
2	D₁₃×#423	C₂	1	1	yes	maximal, characteristic
3	C₂×D₁₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₄×M₁₆×D₁₃	C₂	1	1	yes	maximal, characteristic
5	#13115612	C₂	1	1	yes	maximal, characteristic, complemented
6	#13115611	C₂	1	1	yes	maximal, characteristic, complemented
7	#13115610	C₂	1	2	yes	maximal, complemented
8	#13115609	C₂	1	1	yes	maximal, characteristic, complemented
9	#13115608	C₂	1	2	yes	maximal, complemented
10	D₁₃×#341	C₂	1	2	yes	maximal
11	C₁₃×#1950	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×M₁₆×D₁₃	C₂²	1	2	yes	—
13	C₂×M₁₆×D₁₃	C₂²	1	1	yes	characteristic
14	C₂×M₁₆×D₁₃	C₂²	1	1	yes	characteristic
15	C₂²×C₈×D₁₃	C₂²	1	2	yes	—
16	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#108	C₂²	1	2	yes	—
18	C₁₃×#423	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
21	C₂×#88062	C₂²	1	2	yes	—
22	C₂×#88062	C₂²	1	2	yes	—
23	#11718779	C₂²	1	2	yes	—
24	M₁₆×Dic₁₃	C₂²	1	1	yes	characteristic
25	M₁₆×Dic₁₃	C₂²	1	1	yes	characteristic
26	C₂×#88059	C₂²	1	2	yes	—
27	C₂×#88054	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	D₁₃×#108	—	2	8	no	—
32	#11718498	—	2	1	no	—
33	#11718498	—	2	1	no	—
34	D₁₃×C₄⋊C₈	—	2	1	no	—
35	D₁₃×C₄⋊C₈	—	2	1	no	—
36	D₁₃×C₄⋊C₈	C₄	1	2	yes	—
37	D₁₃×C₄⋊C₈	C₄	1	2	yes	—
38	D₁₃×C₄⋊C₈	C₄	1	2	yes	—
39	D₁₃×C₄⋊C₈	C₄	1	2	yes	—
40	#11718368	—	2	1	no	—
41	D₁₃×#97	—	2	1	no	—
42	C₄×#6094	—	2	1	no	—
43	C₄×C₈×D₁₃	—	2	1	no	—
44	C₁₃×#341	C₂²	1	2	yes	—
45	#11718150	C₂²	1	2	yes	—
46	#11718150	C₂²	1	2	yes	—
47	#11718144	C₂²	1	2	yes	—
48	C₂²×C₄×D₁₃	Q₈	1	1	yes	characteristic
49	C₂²×C₄×D₁₃	Q₈	1	1	yes	characteristic
50	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
51	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
52	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
53	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
55	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
56	C₂×C₄×Dic₁₃	Q₈	1	1	yes	characteristic
57	C₂×C₄×Dic₁₃	Q₈	1	1	yes	characteristic
58	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
59	C₂×#6099	C₂³	1	2	yes	—
60	C₂×#6099	C₂³	1	1	yes	characteristic
61	C₂×#6099	C₂³	1	1	yes	characteristic
62	C₂²×#1055	C₂³	1	2	yes	—
63	M₁₆×D₁₃	—	2	2	no	—
64	M₁₆×D₁₃	—	2	2	no	—
65	M₁₆×D₁₃	—	2	4	no	—
66	M₁₆×D₁₃	—	2	4	no	—
67	M₁₆×D₁₃	D₄	1	4	yes	—
68	M₁₆×D₁₃	Q₈	1	4	yes	—
69	C₂×#6094	—	2	1	no	—
70	C₂×#6094	—	2	1	no	—
71	C₂×#6094	—	2	2	no	—
72	C₂×C₈×D₁₃	—	2	4	no	—
73	C₂×C₈×D₁₃	—	2	1	no	—
74	C₂×C₈×D₁₃	—	2	1	no	—
75	C₂×C₈×D₁₃	—	2	4	no	—
76	C₂×C₈×D₁₃	—	2	2	no	—
77	C₂×C₈×D₁₃	C₂×C₄	1	4	yes	—
78	C₂×C₈×D₁₃	C₂×C₄	1	4	yes	—
79	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
80	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
81	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
82	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
83	C₄²×D₁₃	D₄	1	1	yes	characteristic
84	C₄²×D₁₃	D₄	1	1	yes	characteristic
85	C₄²×D₁₃	D₄	1	1	yes	characteristic
86	C₄²×D₁₃	D₄	1	1	yes	characteristic
87	C₁₃×#108	—	2	4	no	—
88	C₁₃×C₄⋊C₈	—	2	1	no	—
89	C₁₃×C₄⋊C₈	—	2	1	no	—
90	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
91	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
92	C₁₃×#97	—	2	1	no	—
93	C₄×C₈×C₁₃	—	2	1	no	—
94	#88062	—	2	4	no	—
95	#88062	—	2	4	no	—
96	#88059	—	2	4	no	—
97	#88055	—	2	1	no	—
98	#88055	—	2	1	no	—
99	#88054	—	2	2	no	—
100	#88054	—	2	2	no	—
101	#88054	C₂×C₄	1	4	yes	—
102	#88054	C₂×C₄	1	4	yes	—
103	C₈×Dic₁₃	—	2	1	no	—
104	C₈×Dic₁₃	—	2	1	no	—
105	C₄⋊#1055	—	2	1	no	—
106	C₄⋊#1055	—	2	1	no	—
107	C₄⋊#1055	C₂×C₄	1	2	yes	—
108	C₄⋊#1055	C₂×C₄	1	2	yes	—
109	#88043	—	2	1	no	—
110	C₄×#1055	—	2	1	no	—
111	C₂×#1950	—	13	1	no	maximal, Sylow
112	C₂³×D₁₃	C₂×Q₈	1	1	yes	characteristic
113	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
114	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
115	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
116	C₂²×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
117	C₂²×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
118	C₂²×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
119	C₂×C₄×D₁₃	—	2	4	no	—
120	C₂×C₄×D₁₃	—	4	2	no	—
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	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	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₄×D₁₃	C₂×D₄	1	2	yes	—
132	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
133	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
134	C₂×C₄×D₁₃	C₂×Q₈	1	2	yes	—
135	C₂×C₄×D₁₃	#41	1	2	yes	—
136	C₂×C₄×D₁₃	#41	1	2	yes	—
137	C₁₃×M₁₆	—	2	1	no	—
138	C₁₃×M₁₆	—	2	1	no	—
139	C₁₃×M₁₆	—	2	2	no	—
140	C₁₃×M₁₆	—	2	2	no	—
141	C₁₃×M₁₆	C₂×D₄	1	2	yes	—
142	C₁₃×M₁₆	C₂×Q₈	1	2	yes	—
143	C₂×C₈×C₁₃	—	2	1	no	—
144	C₂×C₈×C₁₃	—	2	1	no	—
145	C₂×C₈×C₁₃	—	2	2	no	—
146	C₂×C₈×C₁₃	—	2	2	no	—
147	C₂×C₈×C₁₃	—	2	2	no	—
148	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
149	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
150	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
151	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
152	C₄²×C₁₃	C₂×D₄	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	C₄⋊C₄	1	1	yes	characteristic
157	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
158	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
159	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
160	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
161	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
162	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
163	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
164	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
165	#6099	—	2	1	no	—
166	#6099	—	2	1	no	—
167	#6099	—	2	2	no	—
168	#6099	—	2	2	no	—
169	#6099	C₂×D₄	1	2	yes	—
170	#6099	C₂×Q₈	1	2	yes	—
171	C₂×#1055	—	2	2	no	—
172	C₂×#1055	—	2	1	no	—
173	C₂×#1055	—	2	1	no	—
174	C₂×#1055	—	2	2	no	—
175	C₂×#1055	—	2	2	no	—
176	C₂×#1055	C₂²×C₄	1	4	yes	—
177	#6094	—	2	4	no	—
178	#6094	—	2	4	no	—
179	#6094	—	4	4	no	—
180	C₈×D₁₃	—	2	8	no	—
181	C₈×D₁₃	—	2	8	no	—
182	C₈×D₁₃	—	2	4	no	—
183	C₈×D₁₃	—	2	4	no	—
184	C₈×D₁₃	—	4	4	no	—
185	C₂²×#108	—	13	2	no	—
186	C₂×#423	—	13	1	no	—
187	C₂²×C₄⋊C₈	—	13	1	no	—
188	C₂×C₄×M₁₆	—	13	1	no	—
189	#1950	—	13	2	no	—
190	#1950	—	13	1	no	—
191	#1950	—	13	1	no	—
192	#1950	—	13	1	no	—
193	#1950	—	13	2	no	—
194	#1950	D₁₃	1	1	yes	characteristic, direct product factor
195	C₂×#341	—	13	2	no	—
196	C₂³×C₁₃	C₂²×Q₈	1	1	yes	characteristic
197	C₂²×D₁₃	—	2	2	no	—
198	C₂²×D₁₃	—	2	2	no	—
199	C₂²×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
200	C₂²×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
201	C₂²×D₁₃	#125	1	2	yes	—
202	C₂²×D₁₃	C₄⋊Q₈	1	2	yes	—
203	C₂×C₄×C₁₃	—	2	2	no	—
204	C₂×C₄×C₁₃	—	4	1	no	—
205	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
206	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
207	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
208	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
209	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
210	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
213	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
214	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
215	C₂×Dic₁₃	—	2	2	no	—
216	C₂×Dic₁₃	—	4	1	no	—
217	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
218	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
219	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
220	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
221	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
222	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
223	C₂×Dic₁₃	#125	1	2	yes	—
224	C₂×Dic₁₃	C₄⋊Q₈	1	2	yes	—
225	C₄×D₁₃	—	2	2	no	—
226	C₄×D₁₃	—	2	2	no	—
227	C₄×D₁₃	—	2	2	no	—
228	C₄×D₁₃	—	2	2	no	—
229	C₄×D₁₃	—	2	2	no	—
230	C₄×D₁₃	—	4	1	no	—
231	C₄×D₁₃	—	4	1	no	—
232	C₄×D₁₃	#108	1	4	yes	complemented
233	C₄×D₁₃	C₄×D₄	1	2	yes	—
234	C₄×D₁₃	C₄×D₄	1	2	yes	—
235	C₄×D₁₃	C₄×Q₈	1	2	yes	—
236	C₄×D₁₃	C₄×Q₈	1	2	yes	—
237	C₄×D₁₃	#121	1	2	yes	—
238	C₄×D₁₃	#121	1	2	yes	—
239	C₄×D₁₃	C₂²⋊Q₈	1	2	yes	—
240	C₄×D₁₃	C₂²⋊Q₈	1	2	yes	—
241	C₈×C₁₃	—	2	4	no	—
242	C₈×C₁₃	—	2	2	no	—
243	C₈×C₁₃	—	2	2	no	—
244	C₈×C₁₃	—	4	2	no	—
245	#1055	—	2	4	no	—
246	#1055	—	2	2	no	—
247	#1055	—	2	2	no	—
248	#1055	—	4	2	no	—
249	C₂²×M₁₆	—	13	1	no	—
250	C₂²×M₁₆	—	13	1	no	—
251	C₂²×M₁₆	—	13	2	no	—
252	C₂³×C₈	—	13	2	no	—
253	C₂²×C₄²	—	13	1	no	—
254	C₂×#108	—	13	2	no	—
255	C₂×#108	—	13	2	no	—
256	C₂×#108	—	13	2	no	—
257	C₂×#108	—	26	8	no	—
258	C₂×#108	C₂×D₁₃	1	2	yes	—
259	#423	—	13	2	no	—
260	#423	—	13	1	no	—
261	#423	—	26	1	no	—
262	#423	—	26	1	no	—
263	#423	C₂×D₁₃	1	1	yes	characteristic
264	C₂×C₄⋊C₈	—	13	2	no	—
265	C₂×C₄⋊C₈	—	13	1	no	—
266	C₂×C₄⋊C₈	—	13	2	no	—
267	C₂×C₄⋊C₈	—	13	2	no	—
268	C₂×C₄⋊C₈	—	13	2	no	—
269	C₂×C₄⋊C₈	—	13	2	no	—
270	C₂×C₄⋊C₈	—	26	1	no	—
271	C₂×C₄⋊C₈	—	26	1	no	—
272	C₂×C₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic
273	C₄×M₁₆	—	13	1	no	—
274	C₄×M₁₆	—	13	1	no	—
275	C₄×M₁₆	—	13	1	no	—
276	C₄×M₁₆	—	26	1	no	—
277	C₄×M₁₆	—	26	1	no	—
278	C₄×M₁₆	C₂×D₁₃	1	1	yes	characteristic
279	C₂×#97	—	26	1	no	—
280	C₂×C₄×C₈	—	26	1	no	—
281	#341	—	13	2	no	—
282	#341	—	13	2	no	—
283	#341	—	13	2	no	—
284	#341	C₂×D₁₃	1	2	yes	—
285	C₂²×C₁₃	—	2	1	no	—
286	C₂²×C₁₃	—	2	1	no	—
287	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
288	C₂²×C₁₃	C₂×#125	1	1	yes	characteristic
289	C₂²×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
290	C₂×D₁₃	—	2	1	no	—
291	C₂×D₁₃	—	2	1	no	—
292	C₂×D₁₃	—	2	4	no	—
293	C₂×D₁₃	—	2	4	no	—
294	C₂×D₁₃	#389	1	2	yes	—
295	C₂×D₁₃	#389	1	2	yes	—
296	C₂×D₁₃	C₂×#108	1	2	yes	—
297	C₂×D₁₃	#430	1	2	yes	—
298	C₄×C₁₃	—	2	1	no	—
299	C₄×C₁₃	—	2	1	no	—
300	C₄×C₁₃	—	2	1	no	—
301	C₄×C₁₃	C₂×#108	1	2	yes	complemented
302	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
303	C₄×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
304	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
305	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
306	Dic₁₃	—	2	1	no	—
307	Dic₁₃	—	2	1	no	—
308	Dic₁₃	—	2	1	no	—
309	Dic₁₃	#389	1	2	yes	—
310	Dic₁₃	#389	1	2	yes	—
311	Dic₁₃	C₂×#108	1	2	yes	complemented
312	C₂³×C₄	—	13	1	no	—
313	C₂³×C₄	—	13	1	no	—
314	C₂³×C₄	—	13	1	no	—
315	C₂×M₁₆	—	13	1	no	—
316	C₂×M₁₆	—	13	1	no	—
317	C₂×M₁₆	—	13	4	no	—
318	C₂×M₁₆	—	13	4	no	—
319	C₂×M₁₆	—	13	2	no	—
320	C₂×M₁₆	—	26	1	no	—
321	C₂×M₁₆	—	26	1	no	—
322	C₂×M₁₆	—	26	2	no	—
323	C₂×M₁₆	—	26	2	no	—
324	C₂×M₁₆	—	26	2	no	—
325	C₂×M₁₆	—	26	4	no	—
326	C₂×M₁₆	—	26	4	no	—
327	C₂×M₁₆	C₂²×D₁₃	1	2	yes	—
328	C₂×M₁₆	C₂²×D₁₃	1	1	yes	characteristic
329	C₂×M₁₆	C₂²×D₁₃	1	1	yes	characteristic
330	C₂²×C₈	—	13	2	no	—
331	C₂²×C₈	—	13	4	no	—
332	C₂²×C₈	—	13	4	no	—
333	C₂²×C₈	—	26	4	no	—
334	C₂²×C₈	—	26	4	no	—
335	C₂²×C₈	—	26	1	no	—
336	C₂²×C₈	—	26	1	no	—
337	C₂²×C₈	—	26	2	no	—
338	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
339	C₂×C₄²	—	13	1	no	—
340	C₂×C₄²	—	13	1	no	—
341	C₂×C₄²	—	13	1	no	—
342	C₂×C₄²	—	13	1	no	—
343	C₂×C₄²	—	13	1	no	—
344	C₂×C₄²	—	13	1	no	—
345	C₂×C₄²	—	13	1	no	—
346	C₂×C₄²	—	13	1	no	—
347	C₂×C₄²	—	13	1	no	—
348	C₂×C₄²	—	13	1	no	—
349	C₂×C₄²	—	13	1	no	—
350	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
351	#108	—	2	4	no	—
352	#108	—	26	4	no	—
353	#108	—	26	4	no	—
354	#108	—	26	4	no	—
355	C₄⋊C₈	—	2	1	no	—
356	C₄⋊C₈	—	2	1	no	—
357	C₄⋊C₈	—	13	4	no	—
358	C₄⋊C₈	—	13	4	no	—
359	C₄⋊C₈	—	13	2	no	—
360	C₄⋊C₈	—	13	2	no	—
361	C₄⋊C₈	—	26	2	no	—
362	C₄⋊C₈	—	26	2	no	—
363	C₄⋊C₈	—	26	1	no	—
364	C₄⋊C₈	—	26	1	no	—
365	C₄⋊C₈	C₄×D₁₃	1	2	yes	—
366	C₄⋊C₈	C₄×D₁₃	1	2	yes	—
367	#97	—	2	1	no	—
368	#97	—	26	1	no	—
369	#97	—	26	1	no	—
370	#97	—	26	1	no	—
371	C₄×C₈	—	2	1	no	—
372	C₄×C₈	—	26	1	no	—
373	C₄×C₈	—	26	1	no	—
374	C₄×C₈	—	26	1	no	—
375	C₂×C₁₃	—	2	1	no	—
376	C₂×C₁₃	—	2	1	no	—
377	C₂×C₁₃	C₂×#389	1	1	yes	characteristic
378	C₂×C₁₃	C₂²×#108	1	1	yes	characteristic
379	C₂×C₁₃	C₂×#430	1	1	yes	characteristic
380	D₁₃	—	2	2	no	—
381	D₁₃	#1950	1	4	yes	direct product factor
382	C₂⁴	—	13	1	no	—
383	C₂²×C₄	—	13	1	no	—
384	C₂²×C₄	—	13	1	no	—
385	C₂²×C₄	—	13	1	no	—
386	C₂²×C₄	—	13	1	no	—
387	C₂²×C₄	—	13	2	no	—
388	C₂²×C₄	—	13	1	no	—
389	C₂²×C₄	—	13	1	no	—
390	C₂²×C₄	—	13	2	no	—
391	C₂²×C₄	—	13	2	no	—
392	C₂²×C₄	—	13	2	no	—
393	C₂²×C₄	—	13	1	no	—
394	C₂²×C₄	—	13	1	no	—
395	C₂²×C₄	—	13	1	no	—
396	C₂²×C₄	—	13	1	no	—
397	C₂²×C₄	—	13	1	no	—
398	C₂²×C₄	—	13	1	no	—
399	C₂²×C₄	—	13	1	no	—
400	C₂²×C₄	—	13	1	no	—
401	C₂²×C₄	—	13	1	no	—
402	C₂²×C₄	—	26	4	no	—
403	C₂²×C₄	—	52	2	no	—
404	C₂²×C₄	Q₈×D₁₃	1	1	yes	characteristic
405	C₂²×C₄	Q₈×D₁₃	1	1	yes	characteristic
406	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
407	M₁₆	—	2	1	no	—
408	M₁₆	—	2	1	no	—
409	M₁₆	—	2	2	no	—
410	M₁₆	—	2	2	no	—
411	M₁₆	—	13	2	no	—
412	M₁₆	—	13	2	no	—
413	M₁₆	—	26	4	no	—
414	M₁₆	—	26	4	no	—
415	M₁₆	—	26	1	no	—
416	M₁₆	—	26	1	no	—
417	M₁₆	—	26	2	no	—
418	M₁₆	—	26	2	no	—
419	M₁₆	—	52	4	no	—
420	M₁₆	D₄×D₁₃	1	2	yes	—
421	M₁₆	Q₈×D₁₃	1	2	yes	—
422	C₂×C₈	—	2	2	no	—
423	C₂×C₈	—	2	1	no	—
424	C₂×C₈	—	2	1	no	—
425	C₂×C₈	—	2	2	no	—
426	C₂×C₈	—	2	2	no	—
427	C₂×C₈	—	13	4	no	—
428	C₂×C₈	—	26	8	no	—
429	C₂×C₈	—	26	8	no	—
430	C₂×C₈	—	26	4	no	—
431	C₂×C₈	—	26	4	no	—
432	C₂×C₈	—	26	2	no	—
433	C₂×C₈	—	26	1	no	—
434	C₂×C₈	—	26	1	no	—
435	C₂×C₈	—	26	2	no	—
436	C₂×C₈	—	26	2	no	—
437	C₂×C₈	—	52	4	no	—
438	C₂×C₈	C₂×C₄×D₁₃	1	4	yes	—
439	C₄²	—	13	1	no	—
440	C₄²	—	13	1	no	—
441	C₄²	—	13	1	no	—
442	C₄²	—	13	1	no	—
443	C₄²	—	13	1	no	—
444	C₄²	—	13	1	no	—
445	C₄²	—	13	1	no	—
446	C₄²	—	13	1	no	—
447	C₄²	—	13	1	no	—
448	C₄²	—	13	1	no	—
449	C₄²	—	13	1	no	—
450	C₄²	—	13	1	no	—
451	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
452	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
453	C₄²	D₄×D₁₃	1	1	yes	characteristic
454	C₄²	D₄×D₁₃	1	1	yes	characteristic
455	C₁₃	C₂×#1950	1	1	yes	characteristic, complemented, Sylow
456	C₂³	—	13	1	no	—
457	C₂³	—	13	2	no	—
458	C₂³	—	13	1	no	—
459	C₂³	—	13	2	no	—
460	C₂³	—	26	2	no	—
461	C₂³	—	26	2	no	—
462	C₂³	C₂×Q₈×D₁₃	1	1	yes	characteristic
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	4	1	no	—
465	C₂×C₄	—	13	2	no	—
466	C₂×C₄	—	13	1	no	—
467	C₂×C₄	—	13	1	no	—
468	C₂×C₄	—	13	1	no	—
469	C₂×C₄	—	13	2	no	—
470	C₂×C₄	—	13	2	no	—
471	C₂×C₄	—	13	2	no	—
472	C₂×C₄	—	13	2	no	—
473	C₂×C₄	—	13	2	no	—
474	C₂×C₄	—	13	2	no	—
475	C₂×C₄	—	13	2	no	—
476	C₂×C₄	—	13	4	no	—
477	C₂×C₄	—	13	2	no	—
478	C₂×C₄	—	13	2	no	—
479	C₂×C₄	—	13	1	no	—
480	C₂×C₄	—	13	1	no	—
481	C₂×C₄	—	13	1	no	—
482	C₂×C₄	—	26	2	no	—
483	C₂×C₄	—	26	2	no	—
484	C₂×C₄	—	26	2	no	—
485	C₂×C₄	—	26	2	no	—
486	C₂×C₄	—	26	2	no	—
487	C₂×C₄	—	26	2	no	—
488	C₂×C₄	—	52	1	no	—
489	C₂×C₄	—	52	1	no	—
490	C₂×C₄	—	52	1	no	—
491	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
492	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
493	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
494	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
495	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
496	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
497	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
498	C₂×C₄	C₂×Q₈×D₁₃	1	1	yes	characteristic
499	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
500	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
501	C₈	—	2	4	no	—
502	C₈	—	2	2	no	—
503	C₈	—	2	2	no	—
504	C₈	—	4	2	no	—
505	C₈	—	26	4	no	—
506	C₈	—	26	2	no	—
507	C₈	—	26	2	no	—
508	C₈	—	52	2	no	—
509	C₂²	—	2	1	no	—
510	C₂²	—	2	1	no	—
511	C₂²	—	13	2	no	—
512	C₂²	—	13	2	no	—
513	C₂²	—	13	2	no	—
514	C₂²	—	13	2	no	—
515	C₂²	—	26	4	no	—
516	C₂²	—	26	4	no	—
517	C₂²	—	26	1	no	—
518	C₂²	—	26	1	no	—
519	C₂²	C₂×C₄⋊C₄×D₁₃	1	1	yes	characteristic
520	C₂²	D₁₃×#125	1	1	yes	characteristic
521	C₂²	D₁₃×C₄⋊Q₈	1	1	yes	characteristic
522	C₄	—	2	1	no	—
523	C₄	—	2	1	no	—
524	C₄	—	2	1	no	—
525	C₄	—	13	2	no	—
526	C₄	—	13	2	no	—
527	C₄	—	13	2	no	—
528	C₄	—	26	1	no	—
529	C₄	—	26	1	no	—
530	C₄	—	26	1	no	—
531	C₄	D₁₃×#108	1	2	yes	complemented
532	C₄	C₄×D₄×D₁₃	1	1	yes	characteristic
533	C₄	C₄×Q₈×D₁₃	1	1	yes	characteristic
534	C₄	D₁₃×#121	1	1	yes	characteristic
535	C₄	D₁₃×C₂²⋊Q₈	1	1	yes	characteristic
536	C₂	—	2	1	no	—
537	C₂	—	2	1	no	—
538	C₂	—	13	4	no	—
539	C₂	—	26	2	no	—
540	C₂	D₁₃×#389	1	1	yes	characteristic
541	C₂	C₂×D₁₃×#108	1	1	yes	characteristic
542	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	C₂×#1950
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
5. #13115612	C₂	semidirect
6. #13115611	C₂	semidirect
7. #13115610	C₂	semidirect
8. #13115609	C₂	semidirect
9. #13115608	C₂	semidirect
11. C₁₃×#1950	C₂	semidirect
194. #1950	D₁₃	direct (N × H)
232. C₄×D₁₃	#108	semidirect
301. C₄×C₁₃	C₂×#108	semidirect
311. Dic₁₃	C₂×#108	semidirect
381. D₁₃	#1950	direct (N × H)
455. C₁₃	C₂×#1950	semidirect
531. C₄	D₁₃×#108	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₁₃×#108	2
D₁₃×#423	2
C₂×D₁₃×C₄⋊C₈	2
C₄×M₁₆×D₁₃	2
#13115612	2
#13115611	2
#13115610	2
#13115609	2
#13115608	2
D₁₃×#341	2
C₁₃×#1950	2
C₂×#1950	13

Subgroups — D13×#1950 #15866435

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃×#1950 #15866435