Subgroups — C₁₃×#61288 #15747627

Order 3328.

1846 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3511	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3356	C₂	1	4	yes	maximal, complemented
3	C₁₃×#3354	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3340	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3335	C₂	1	4	yes	maximal, complemented
6	C₂×C₁₃×#498	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3099	C₂	1	4	yes	maximal, complemented
8	C₁₃×#3079	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3060	C₂	1	2	yes	maximal, complemented
10	C₄×C₁₃×#135	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2931	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#2912	C₂	1	2	yes	maximal, complemented
13	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#131	C₂²	1	2	yes	—
15	C₁₃×#556	C₂²	1	4	yes	—
16	C₁₃×#555	C₂²	1	4	yes	—
17	C₁₃×#554	C₂²	1	4	yes	—
18	C₁₃×#553	—	2	4	no	—
19	C₁₃×#548	—	2	4	no	—
20	C₁₃×#547	C₂²	1	4	yes	—
21	C₁₃×#542	—	2	4	no	—
22	C₁₃×#537	C₂²	1	4	yes	—
23	C₁₃×#533	—	2	2	no	—
24	C₁₃×#532	—	2	2	no	—
25	C₁₃×#532	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
27	C₁₃×#520	C₂²	1	4	yes	—
28	C₄×C₁₃×#41	C₂²	1	2	yes	—
29	C₁₃×#498	C₂²	1	4	yes	—
30	C₁₃×#498	C₂²	1	4	yes	—
31	C₁₃×#485	C₂²	1	8	yes	—
32	C₁₃×#483	C₂²	1	8	yes	—
33	C₁₃×#482	C₂²	1	8	yes	—
34	C₁₃×#481	C₂²	1	8	yes	—
35	C₁₃×#477	C₂²	1	4	yes	—
36	C₁₃×#476	C₂²	1	4	yes	—
37	C₁₃×#475	C₂²	1	4	yes	—
38	C₁₃×#474	C₂²	1	4	yes	—
39	C₁₃×#470	C₂²	1	4	yes	—
40	C₁₃×#469	C₂²	1	4	yes	—
41	C₁₃×#465	C₂²	1	8	yes	—
42	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
43	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
44	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
45	C₄×C₁₃×D₈	C₂²	1	2	yes	—
46	C₁₃×#436	C₂²	1	4	yes	—
47	C₈×D₄×C₁₃	C₂²	1	4	yes	—
48	C₁₃×#428	C₂²	1	4	yes	—
49	C₁₃×#428	C₂²	1	8	yes	—
50	C₁₃×#427	C₂²	1	4	yes	—
51	C₁₃×#427	C₂²	1	1	yes	characteristic
52	C₂×C₁₃×#106	C₂²	1	2	yes	—
53	C₂×C₁₃×#106	C₂²	1	4	yes	—
54	C₂×C₁₃×#106	C₂²	1	2	yes	—
55	C₁₃×#423	C₂²	1	1	yes	characteristic
56	C₁₃×#417	C₂²	1	4	yes	—
57	C₁₃×#416	C₂²	1	2	yes	—
58	C₁₃×#408	C₂²	1	2	yes	—
59	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
60	C₂×C₁₃×#41	—	2	4	no	—
61	C₂×C₁₃×#41	C₂³	1	2	yes	—
62	C₂×C₁₃×#41	C₂³	1	2	yes	—
63	C₂²×Q₈×C₁₃	—	2	2	no	—
64	C₁₃×#135	—	2	4	no	—
65	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
66	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
67	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
68	C₁₃×#131	—	2	8	no	—
69	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
70	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
71	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
73	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
74	C₁₃×C₄⋊Q₈	—	2	2	no	—
75	C₁₃×C₄⋊Q₈	—	2	2	no	—
76	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
77	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
78	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
79	C₁₃×#127	D₄	1	1	yes	characteristic
80	C₁₃×#126	—	2	8	no	—
81	C₁₃×#125	—	2	4	no	—
82	C₁₃×#124	—	2	4	no	—
83	C₁₃×#124	—	2	8	no	—
84	C₁₃×#124	D₄	1	2	yes	—
85	C₁₃×#123	—	2	8	no	—
86	C₁₃×C₂²⋊Q₈	—	2	4	no	—
87	C₁₃×C₂²⋊Q₈	—	2	4	no	—
88	C₁₃×C₂²⋊Q₈	—	2	8	no	—
89	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
90	C₁₃×#121	—	2	4	no	—
91	C₁₃×#121	—	2	4	no	—
92	C₁₃×#121	—	2	8	no	—
93	C₁₃×#121	D₄	1	4	yes	—
94	C₁₃×#121	C₂³	1	8	yes	—
95	C₄×Q₈×C₁₃	—	2	4	no	—
96	C₄×Q₈×C₁₃	—	2	4	no	—
97	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
98	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
99	C₄×D₄×C₁₃	—	2	4	no	—
100	C₄×D₄×C₁₃	—	2	8	no	—
101	C₄×D₄×C₁₃	—	2	4	no	—
102	C₄×D₄×C₁₃	—	2	2	no	—
103	C₄×D₄×C₁₃	—	2	2	no	—
104	C₄×D₄×C₁₃	C₂³	1	2	yes	—
105	C₄×D₄×C₁₃	C₂³	1	2	yes	—
106	C₄×D₄×C₁₃	C₂³	1	4	yes	—
107	C₁₃×#117	—	2	4	no	—
108	C₁₃×#117	—	2	2	no	—
109	C₁₃×#117	C₂³	1	2	yes	—
110	C₁₃×#117	C₂³	1	8	yes	—
111	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
112	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
113	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
114	C₂×C₄²×C₁₃	—	2	2	no	—
115	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
116	C₁₃×#107	C₂³	1	2	yes	—
117	C₁₃×#107	C₂³	1	8	yes	—
118	C₁₃×#106	C₂³	1	1	yes	characteristic
119	C₁₃×#106	C₂³	1	4	yes	—
120	C₁₃×#106	C₂³	1	4	yes	—
121	C₁₃×#106	C₂³	1	8	yes	—
122	C₁₃×#106	C₂³	1	8	yes	—
123	C₁₃×#106	C₂³	1	1	yes	characteristic
124	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
125	C₁₃×#103	C₂³	1	2	yes	—
126	C₁₃×#103	C₂³	1	2	yes	—
127	C₁₃×#103	C₂³	1	8	yes	—
128	C₁₃×#102	C₂³	1	2	yes	—
129	C₁₃×#102	C₂³	1	2	yes	—
130	C₁₃×#102	C₂³	1	8	yes	—
131	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
132	C₄×C₈×C₁₃	C₂³	1	2	yes	—
133	C₄×C₈×C₁₃	C₂³	1	2	yes	—
134	#61288	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
135	C₁₃×#41	—	2	4	no	—
136	C₁₃×#41	—	2	4	no	—
137	C₁₃×#41	—	2	4	no	—
138	C₁₃×#41	—	2	4	no	—
139	C₁₃×#41	—	8	8	no	—
140	C₂×Q₈×C₁₃	—	2	4	no	—
141	C₂×Q₈×C₁₃	—	2	4	no	—
142	C₂×Q₈×C₁₃	—	8	4	no	—
143	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
144	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
145	C₂×D₄×C₁₃	—	2	2	no	—
146	C₂×D₄×C₁₃	—	2	8	no	—
147	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
148	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
149	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
150	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
151	C₂²×C₄×C₁₃	—	2	4	no	—
152	C₂²×C₄×C₁₃	—	2	8	no	—
153	C₂²×C₄×C₁₃	—	2	2	no	—
154	C₂²×C₄×C₁₃	—	2	2	no	—
155	C₂²×C₄×C₁₃	—	2	2	no	—
156	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
157	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
158	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
159	C₁₃×Q₁₆	—	2	2	no	—
160	C₁₃×SD₁₆	—	2	4	no	—
161	C₁₃×D₈	—	2	2	no	—
162	C₁₃×M₁₆	—	2	4	no	—
163	C₁₃×M₁₆	—	2	8	no	—
164	C₂×C₈×C₁₃	—	2	2	no	—
165	C₂×C₈×C₁₃	—	2	8	no	—
166	C₂×C₈×C₁₃	#41	1	4	yes	complemented
167	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
168	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
169	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
170	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
171	C₁₃×C₄⋊C₄	—	2	4	no	—
172	C₁₃×C₄⋊C₄	—	2	4	no	—
173	C₁₃×C₄⋊C₄	—	2	4	no	—
174	C₁₃×C₄⋊C₄	—	2	8	no	—
175	C₁₃×C₄⋊C₄	—	2	2	no	—
176	C₁₃×C₄⋊C₄	—	2	2	no	—
177	C₁₃×C₄⋊C₄	—	2	8	no	—
178	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
179	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
180	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
181	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
182	C₁₃×C₂²⋊C₄	—	2	2	no	—
183	C₁₃×C₂²⋊C₄	—	2	8	no	—
184	C₁₃×C₂²⋊C₄	—	2	8	no	—
185	C₁₃×C₂²⋊C₄	—	2	2	no	—
186	C₁₃×C₂²⋊C₄	—	2	2	no	—
187	C₁₃×C₂²⋊C₄	—	2	8	no	—
188	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
189	C₄²×C₁₃	—	2	2	no	—
190	C₄²×C₁₃	—	2	2	no	—
191	C₄²×C₁₃	—	2	2	no	—
192	C₄²×C₁₃	—	2	8	no	—
193	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
194	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
195	C₄²×C₁₃	C₂⁴	1	2	yes	—
196	#3511	C₂×C₁₃	1	2	yes	complemented
197	#3356	C₂×C₁₃	1	4	yes	complemented
198	#3354	C₂×C₁₃	1	4	yes	complemented
199	#3340	C₂×C₁₃	1	4	yes	complemented
200	#3335	C₂×C₁₃	1	4	yes	complemented
201	C₂×#498	C₂×C₁₃	1	1	yes	characteristic, complemented
202	#3099	C₂×C₁₃	1	4	yes	complemented
203	#3079	C₂×C₁₃	1	2	yes	complemented
204	#3060	C₂×C₁₃	1	2	yes	complemented
205	C₄×#135	C₂×C₁₃	1	1	yes	characteristic, complemented
206	#2931	C₂×C₁₃	1	1	yes	characteristic, complemented
207	#2912	C₂×C₁₃	1	2	yes	complemented
208	C₂³×C₁₃	—	2	2	no	—
209	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
210	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
211	Q₈×C₁₃	—	2	4	no	—
212	Q₈×C₁₃	—	2	2	no	—
213	Q₈×C₁₃	—	2	2	no	—
214	Q₈×C₁₃	—	4	8	no	—
215	Q₈×C₁₃	—	8	4	no	—
216	D₄×C₁₃	—	2	8	no	—
217	D₄×C₁₃	—	2	4	no	—
218	D₄×C₁₃	—	2	8	no	—
219	D₄×C₁₃	—	2	2	no	—
220	D₄×C₁₃	—	2	2	no	—
221	D₄×C₁₃	—	4	4	no	—
222	D₄×C₁₃	—	8	8	no	—
223	C₂×C₄×C₁₃	—	2	4	no	—
224	C₂×C₄×C₁₃	—	2	4	no	—
225	C₂×C₄×C₁₃	—	2	4	no	—
226	C₂×C₄×C₁₃	—	2	2	no	—
227	C₂×C₄×C₁₃	—	2	2	no	—
228	C₂×C₄×C₁₃	—	2	2	no	—
229	C₂×C₄×C₁₃	—	2	8	no	—
230	C₂×C₄×C₁₃	—	4	4	no	—
231	C₂×C₄×C₁₃	—	4	4	no	—
232	C₂×C₄×C₁₃	—	4	4	no	—
233	C₂×C₄×C₁₃	—	8	4	no	—
234	C₂×C₄×C₁₃	—	8	8	no	—
235	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
236	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
237	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
238	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
239	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
240	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
241	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
242	C₈×C₁₃	—	2	4	no	—
243	C₈×C₁₃	—	2	2	no	—
244	C₈×C₁₃	C₂×#41	1	2	yes	—
245	C₈×C₁₃	C₂×#41	1	2	yes	—
246	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
247	C₂×#131	C₂²×C₁₃	1	2	yes	—
248	#556	C₂²×C₁₃	1	4	yes	—
249	#555	C₂²×C₁₃	1	4	yes	—
250	#554	C₂²×C₁₃	1	4	yes	—
251	#553	—	2	4	no	—
252	#548	—	2	4	no	—
253	#547	C₂²×C₁₃	1	4	yes	—
254	#542	—	2	4	no	—
255	#537	C₂²×C₁₃	1	4	yes	—
256	#533	—	2	2	no	—
257	#532	—	2	2	no	—
258	#532	C₂²×C₁₃	1	1	yes	characteristic
259	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
260	#520	C₂²×C₁₃	1	4	yes	—
261	C₄×#41	C₂²×C₁₃	1	2	yes	—
262	#498	C₂²×C₁₃	1	4	yes	—
263	#498	C₂²×C₁₃	1	4	yes	—
264	#485	C₂²×C₁₃	1	8	yes	—
265	#483	C₂²×C₁₃	1	8	yes	—
266	#482	C₂²×C₁₃	1	8	yes	—
267	#481	C₂²×C₁₃	1	8	yes	—
268	#477	C₂²×C₁₃	1	4	yes	—
269	#476	C₂²×C₁₃	1	4	yes	—
270	#475	C₂²×C₁₃	1	4	yes	—
271	#474	C₂²×C₁₃	1	4	yes	—
272	#470	C₂²×C₁₃	1	4	yes	—
273	#469	C₂²×C₁₃	1	4	yes	—
274	#465	C₂²×C₁₃	1	8	yes	—
275	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
276	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
277	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
278	C₄×D₈	C₂²×C₁₃	1	2	yes	—
279	#436	C₂²×C₁₃	1	4	yes	—
280	C₈×D₄	C₂²×C₁₃	1	4	yes	—
281	#428	C₂²×C₁₃	1	4	yes	—
282	#428	C₂²×C₁₃	1	8	yes	—
283	#427	C₂²×C₁₃	1	4	yes	—
284	#427	C₂²×C₁₃	1	1	yes	characteristic
285	C₂×#106	C₂²×C₁₃	1	4	yes	—
286	C₂×#106	C₂²×C₁₃	1	2	yes	—
287	C₂×#106	C₂²×C₁₃	1	2	yes	—
288	#423	C₂²×C₁₃	1	1	yes	characteristic
289	#417	C₂²×C₁₃	1	4	yes	—
290	#416	C₂²×C₁₃	1	2	yes	—
291	#408	C₂²×C₁₃	1	2	yes	—
292	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
293	C₂²×C₁₃	—	2	2	no	—
294	C₂²×C₁₃	—	2	4	no	—
295	C₂²×C₁₃	—	2	8	no	—
296	C₂²×C₁₃	—	4	2	no	—
297	C₂²×C₁₃	—	4	2	no	—
298	C₂²×C₁₃	—	4	2	no	—
299	C₂²×C₁₃	#547	1	2	yes	—
300	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
301	C₄×C₁₃	—	2	4	no	—
302	C₄×C₁₃	—	2	2	no	—
303	C₄×C₁₃	—	4	2	no	—
304	C₄×C₁₃	—	4	2	no	—
305	C₄×C₁₃	—	4	2	no	—
306	C₄×C₁₃	—	4	8	no	—
307	C₄×C₁₃	#547	1	2	yes	—
308	C₄×C₁₃	#577	1	4	yes	—
309	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
310	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
311	C₂×#41	—	2	4	no	—
312	C₂×#41	C₂³×C₁₃	1	2	yes	—
313	C₂×#41	C₂³×C₁₃	1	2	yes	—
314	C₂²×Q₈	—	2	2	no	—
315	#135	—	2	4	no	—
316	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
317	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
318	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
319	#131	—	2	8	no	—
320	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
321	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
322	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
323	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
324	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
325	C₄⋊Q₈	—	2	2	no	—
326	C₄⋊Q₈	—	2	2	no	—
327	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
328	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
329	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
330	#127	D₄×C₁₃	1	1	yes	characteristic
331	#126	—	2	8	no	—
332	#125	—	2	4	no	—
333	#124	—	2	4	no	—
334	#124	—	2	8	no	—
335	#124	D₄×C₁₃	1	2	yes	—
336	#123	—	2	8	no	—
337	C₂²⋊Q₈	—	2	4	no	—
338	C₂²⋊Q₈	—	2	4	no	—
339	C₂²⋊Q₈	—	2	8	no	—
340	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
341	#121	—	2	4	no	—
342	#121	—	2	4	no	—
343	#121	—	2	8	no	—
344	#121	D₄×C₁₃	1	4	yes	—
345	#121	C₂³×C₁₃	1	8	yes	—
346	C₄×Q₈	—	2	4	no	—
347	C₄×Q₈	—	2	4	no	—
348	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
349	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
350	C₄×D₄	—	2	4	no	—
351	C₄×D₄	—	2	8	no	—
352	C₄×D₄	—	2	4	no	—
353	C₄×D₄	—	2	2	no	—
354	C₄×D₄	—	2	2	no	—
355	C₄×D₄	C₂³×C₁₃	1	2	yes	—
356	C₄×D₄	C₂³×C₁₃	1	2	yes	—
357	C₄×D₄	C₂³×C₁₃	1	4	yes	—
358	#117	—	2	4	no	—
359	#117	—	2	2	no	—
360	#117	C₂³×C₁₃	1	2	yes	—
361	#117	C₂³×C₁₃	1	8	yes	—
362	C₂×C₄⋊C₄	—	2	2	no	—
363	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
364	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
365	C₂×C₄²	—	2	2	no	—
366	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
367	#107	C₂³×C₁₃	1	2	yes	—
368	#107	C₂³×C₁₃	1	8	yes	—
369	#106	C₂³×C₁₃	1	1	yes	characteristic
370	#106	C₂³×C₁₃	1	4	yes	—
371	#106	C₂³×C₁₃	1	4	yes	—
372	#106	C₂³×C₁₃	1	8	yes	—
373	#106	C₂³×C₁₃	1	8	yes	—
374	#106	C₂³×C₁₃	1	1	yes	characteristic
375	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
376	#103	C₂³×C₁₃	1	2	yes	—
377	#103	C₂³×C₁₃	1	2	yes	—
378	#103	C₂³×C₁₃	1	8	yes	—
379	#102	C₂³×C₁₃	1	2	yes	—
380	#102	C₂³×C₁₃	1	2	yes	—
381	#102	C₂³×C₁₃	1	8	yes	—
382	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
383	C₄×C₈	C₂³×C₁₃	1	2	yes	—
384	C₄×C₈	C₂³×C₁₃	1	2	yes	—
385	C₂×C₁₃	—	2	2	no	—
386	C₂×C₁₃	—	4	4	no	—
387	C₂×C₁₃	—	8	2	no	—
388	C₂×C₁₃	C₂×#547	1	1	yes	characteristic
389	C₂×C₁₃	C₂×#577	1	2	yes	—
390	#41	—	2	4	no	—
391	#41	—	2	4	no	—
392	#41	—	2	4	no	—
393	#41	—	2	4	no	—
394	#41	—	8	8	no	—
395	C₂×Q₈	—	2	4	no	—
396	C₂×Q₈	—	2	4	no	—
397	C₂×Q₈	—	8	4	no	—
398	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
399	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
400	C₂×D₄	—	2	2	no	—
401	C₂×D₄	—	2	8	no	—
402	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
403	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
404	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
405	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
406	C₂²×C₄	—	2	4	no	—
407	C₂²×C₄	—	2	8	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	2	2	no	—
411	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
412	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
413	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
414	Q₁₆	—	2	2	no	—
415	SD₁₆	—	2	4	no	—
416	D₈	—	2	2	no	—
417	M₁₆	—	2	4	no	—
418	M₁₆	—	2	8	no	—
419	C₂×C₈	—	2	2	no	—
420	C₂×C₈	—	2	8	no	—
421	C₂×C₈	C₁₃×#41	1	4	yes	complemented
422	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
423	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
424	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
425	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
426	C₄⋊C₄	—	2	4	no	—
427	C₄⋊C₄	—	2	4	no	—
428	C₄⋊C₄	—	2	4	no	—
429	C₄⋊C₄	—	2	8	no	—
430	C₄⋊C₄	—	2	2	no	—
431	C₄⋊C₄	—	2	2	no	—
432	C₄⋊C₄	—	2	8	no	—
433	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
434	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
435	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
436	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
437	C₂²⋊C₄	—	2	2	no	—
438	C₂²⋊C₄	—	2	8	no	—
439	C₂²⋊C₄	—	2	8	no	—
440	C₂²⋊C₄	—	2	2	no	—
441	C₂²⋊C₄	—	2	2	no	—
442	C₂²⋊C₄	—	2	8	no	—
443	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
444	C₄²	—	2	2	no	—
445	C₄²	—	2	2	no	—
446	C₄²	—	2	2	no	—
447	C₄²	—	2	8	no	—
448	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
449	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
450	C₄²	C₂⁴×C₁₃	1	2	yes	—
451	C₁₃	#61288	1	1	yes	characteristic, direct product factor, Sylow
452	C₂³	—	2	2	no	—
453	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
454	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
455	Q₈	—	2	4	no	—
456	Q₈	—	2	2	no	—
457	Q₈	—	2	2	no	—
458	Q₈	—	4	8	no	—
459	Q₈	—	8	4	no	—
460	D₄	—	2	8	no	—
461	D₄	—	2	4	no	—
462	D₄	—	2	8	no	—
463	D₄	—	2	2	no	—
464	D₄	—	2	2	no	—
465	D₄	—	4	4	no	—
466	D₄	—	8	8	no	—
467	C₂×C₄	—	2	4	no	—
468	C₂×C₄	—	2	4	no	—
469	C₂×C₄	—	2	4	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	8	no	—
474	C₂×C₄	—	4	4	no	—
475	C₂×C₄	—	4	4	no	—
476	C₂×C₄	—	4	4	no	—
477	C₂×C₄	—	8	4	no	—
478	C₂×C₄	—	8	8	no	—
479	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
480	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
481	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
482	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
483	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
484	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
485	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
486	C₈	—	2	4	no	—
487	C₈	—	2	2	no	—
488	C₈	C₂×C₁₃×#41	1	2	yes	—
489	C₈	C₂×C₁₃×#41	1	2	yes	—
490	C₂²	—	2	2	no	—
491	C₂²	—	2	8	no	—
492	C₂²	—	2	4	no	—
493	C₂²	—	4	2	no	—
494	C₂²	—	4	2	no	—
495	C₂²	—	4	2	no	—
496	C₂²	C₁₃×#547	1	2	yes	—
497	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
498	C₄	—	2	2	no	—
499	C₄	—	2	4	no	—
500	C₄	—	4	2	no	—
501	C₄	—	4	2	no	—
502	C₄	—	4	8	no	—
503	C₄	—	4	2	no	—
504	C₄	C₁₃×#547	1	2	yes	—
505	C₄	C₁₃×#577	1	4	yes	—
506	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
507	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
508	C₂	—	2	2	no	—
509	C₂	—	4	4	no	—
510	C₂	—	8	2	no	—
511	C₂	C₂×C₁₃×#547	1	1	yes	characteristic
512	C₂	C₂×C₁₃×#577	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3511	C₂	semidirect
2. C₁₃×#3356	C₂	semidirect
3. C₁₃×#3354	C₂	semidirect
4. C₁₃×#3340	C₂	semidirect
5. C₁₃×#3335	C₂	semidirect
6. C₂×C₁₃×#498	C₂	semidirect
7. C₁₃×#3099	C₂	semidirect
8. C₁₃×#3079	C₂	semidirect
9. C₁₃×#3060	C₂	semidirect
10. C₄×C₁₃×#135	C₂	semidirect
11. C₁₃×#2931	C₂	semidirect
12. C₁₃×#2912	C₂	semidirect
134. #61288	C₁₃	direct (N × H)
166. C₂×C₈×C₁₃	#41	semidirect
196. #3511	C₂×C₁₃	semidirect
197. #3356	C₂×C₁₃	semidirect
198. #3354	C₂×C₁₃	semidirect
199. #3340	C₂×C₁₃	semidirect
200. #3335	C₂×C₁₃	semidirect
201. C₂×#498	C₂×C₁₃	semidirect
202. #3099	C₂×C₁₃	semidirect
203. #3079	C₂×C₁₃	semidirect
204. #3060	C₂×C₁₃	semidirect
205. C₄×#135	C₂×C₁₃	semidirect
206. #2931	C₂×C₁₃	semidirect
207. #2912	C₂×C₁₃	semidirect
421. C₂×C₈	C₁₃×#41	semidirect
451. C₁₃	#61288	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#3511	2
C₁₃×#3356	2
C₁₃×#3354	2
C₁₃×#3340	2
C₁₃×#3335	2
C₂×C₁₃×#498	2
C₁₃×#3099	2
C₁₃×#3079	2
C₁₃×#3060	2
C₄×C₁₃×#135	2
C₁₃×#2931	2
C₁₃×#2912	2
#61288	13

Subgroups — C13×#61288 #15747627

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61288 #15747627