Subgroups — C₁₃×#61287 #15747626

Order 3328.

1846 conjugacy classes of subgroups.

The subgroup lattice has 576 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×#3357	C₂	1	4	yes	maximal, complemented
3	C₁₃×#3353	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3342	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3341	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3338	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3334	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#500	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3098	C₂	1	4	yes	maximal, complemented
10	C₁₃×#3079	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3061	C₂	1	2	yes	maximal, complemented
12	C₄×C₁₃×#135	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#2931	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#2913	C₂	1	2	yes	maximal, complemented
15	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#131	C₂²	1	2	yes	—
17	C₁₃×#556	C₂²	1	4	yes	—
18	C₁₃×#555	C₂²	1	4	yes	—
19	C₁₃×#554	C₂²	1	4	yes	—
20	C₁₃×#553	—	2	4	no	—
21	C₁₃×#548	—	2	4	no	—
22	C₁₃×#547	C₂²	1	4	yes	—
23	C₁₃×#542	—	2	4	no	—
24	C₁₃×#537	C₂²	1	4	yes	—
25	C₁₃×#533	—	2	2	no	—
26	C₁₃×#532	—	2	2	no	—
27	C₁₃×#532	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
29	C₁₃×#520	C₂²	1	4	yes	—
30	C₄×C₁₃×#41	C₂²	1	2	yes	—
31	C₁₃×#500	C₂²	1	2	yes	—
32	C₁₃×#500	C₂²	1	2	yes	—
33	C₁₃×#500	C₂²	1	2	yes	—
34	C₁₃×#500	C₂²	1	2	yes	—
35	C₁₃×#485	C₂²	1	8	yes	—
36	C₁₃×#484	C₂²	1	8	yes	—
37	C₁₃×#482	C₂²	1	8	yes	—
38	C₁₃×#480	C₂²	1	8	yes	—
39	C₁₃×#477	C₂²	1	4	yes	—
40	C₁₃×#476	C₂²	1	4	yes	—
41	C₁₃×#475	C₂²	1	4	yes	—
42	C₁₃×#474	C₂²	1	4	yes	—
43	C₁₃×#468	C₂²	1	8	yes	—
44	C₁₃×#467	C₂²	1	4	yes	—
45	C₁₃×#466	C₂²	1	4	yes	—
46	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
47	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
48	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
49	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
50	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
51	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
52	C₁₃×#436	C₂²	1	2	yes	—
53	C₁₃×#436	C₂²	1	2	yes	—
54	C₈×D₄×C₁₃	C₂²	1	2	yes	—
55	C₈×D₄×C₁₃	C₂²	1	2	yes	—
56	C₁₃×#428	C₂²	1	4	yes	—
57	C₁₃×#428	C₂²	1	8	yes	—
58	C₁₃×#427	C₂²	1	4	yes	—
59	C₁₃×#427	C₂²	1	1	yes	characteristic
60	C₂×C₁₃×#107	C₂²	1	2	yes	—
61	C₂×C₁₃×#107	C₂²	1	4	yes	—
62	C₂×C₁₃×#107	C₂²	1	2	yes	—
63	C₁₃×#423	C₂²	1	1	yes	characteristic
64	C₁₃×#417	C₂²	1	4	yes	—
65	C₁₃×#416	C₂²	1	2	yes	—
66	C₁₃×#408	C₂²	1	2	yes	—
67	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
68	C₂×C₁₃×#41	—	2	4	no	—
69	C₂×C₁₃×#41	C₂³	1	2	yes	—
70	C₂×C₁₃×#41	C₂³	1	2	yes	—
71	C₂²×Q₈×C₁₃	—	2	2	no	—
72	C₁₃×#135	—	2	4	no	—
73	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
74	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
75	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
76	C₁₃×#131	—	2	8	no	—
77	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
78	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
79	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
81	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
82	C₁₃×C₄⋊Q₈	—	2	2	no	—
83	C₁₃×C₄⋊Q₈	—	2	2	no	—
84	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
85	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
86	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
87	C₁₃×#127	D₄	1	1	yes	characteristic
88	C₁₃×#126	—	2	8	no	—
89	C₁₃×#125	—	2	4	no	—
90	C₁₃×#124	—	2	4	no	—
91	C₁₃×#124	—	2	8	no	—
92	C₁₃×#124	D₄	1	2	yes	—
93	C₁₃×#123	—	2	8	no	—
94	C₁₃×C₂²⋊Q₈	—	2	4	no	—
95	C₁₃×C₂²⋊Q₈	—	2	4	no	—
96	C₁₃×C₂²⋊Q₈	—	2	8	no	—
97	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
98	C₁₃×#121	—	2	4	no	—
99	C₁₃×#121	—	2	4	no	—
100	C₁₃×#121	—	2	8	no	—
101	C₁₃×#121	D₄	1	2	yes	—
102	C₁₃×#121	D₄	1	2	yes	—
103	C₁₃×#121	C₂³	1	8	yes	—
104	C₄×Q₈×C₁₃	—	2	4	no	—
105	C₄×Q₈×C₁₃	—	2	4	no	—
106	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
107	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
108	C₄×D₄×C₁₃	—	2	4	no	—
109	C₄×D₄×C₁₃	—	2	8	no	—
110	C₄×D₄×C₁₃	—	2	4	no	—
111	C₄×D₄×C₁₃	—	2	2	no	—
112	C₄×D₄×C₁₃	—	2	2	no	—
113	C₄×D₄×C₁₃	C₂³	1	2	yes	—
114	C₄×D₄×C₁₃	C₂³	1	2	yes	—
115	C₄×D₄×C₁₃	C₂³	1	2	yes	—
116	C₄×D₄×C₁₃	C₂³	1	2	yes	—
117	C₁₃×#117	—	2	4	no	—
118	C₁₃×#117	—	2	2	no	—
119	C₁₃×#117	C₂³	1	2	yes	—
120	C₁₃×#117	C₂³	1	8	yes	—
121	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
122	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
123	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
124	C₂×C₄²×C₁₃	—	2	2	no	—
125	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
126	C₁₃×#107	C₂³	1	1	yes	characteristic
127	C₁₃×#107	C₂³	1	4	yes	—
128	C₁₃×#107	C₂³	1	4	yes	—
129	C₁₃×#107	C₂³	1	8	yes	—
130	C₁₃×#107	C₂³	1	4	yes	—
131	C₁₃×#107	C₂³	1	4	yes	—
132	C₁₃×#107	C₂³	1	1	yes	characteristic
133	C₁₃×#106	C₂³	1	2	yes	—
134	C₁₃×#106	C₂³	1	8	yes	—
135	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
136	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
137	C₁₃×#103	C₂³	1	2	yes	—
138	C₁₃×#103	C₂³	1	2	yes	—
139	C₁₃×#103	C₂³	1	8	yes	—
140	C₁₃×#102	C₂³	1	2	yes	—
141	C₁₃×#102	C₂³	1	2	yes	—
142	C₁₃×#102	C₂³	1	8	yes	—
143	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
144	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
145	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
146	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
147	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
148	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
149	#61287	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
150	C₁₃×#41	—	2	4	no	—
151	C₁₃×#41	—	2	4	no	—
152	C₁₃×#41	—	2	4	no	—
153	C₁₃×#41	—	2	4	no	—
154	C₁₃×#41	—	8	8	no	—
155	C₂×Q₈×C₁₃	—	2	4	no	—
156	C₂×Q₈×C₁₃	—	2	4	no	—
157	C₂×Q₈×C₁₃	—	8	4	no	—
158	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
159	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
160	C₂×D₄×C₁₃	—	2	2	no	—
161	C₂×D₄×C₁₃	—	2	8	no	—
162	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
163	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
164	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
165	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
166	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
167	C₂²×C₄×C₁₃	—	2	4	no	—
168	C₂²×C₄×C₁₃	—	2	8	no	—
169	C₂²×C₄×C₁₃	—	2	2	no	—
170	C₂²×C₄×C₁₃	—	2	2	no	—
171	C₂²×C₄×C₁₃	—	2	2	no	—
172	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
175	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
176	C₁₃×Q₁₆	—	2	2	no	—
177	C₁₃×SD₁₆	—	2	4	no	—
178	C₁₃×D₈	—	2	2	no	—
179	C₁₃×M₁₆	—	2	4	no	—
180	C₁₃×M₁₆	—	2	8	no	—
181	C₂×C₈×C₁₃	—	2	2	no	—
182	C₂×C₈×C₁₃	—	2	8	no	—
183	C₂×C₈×C₁₃	#41	1	4	yes	complemented
184	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
185	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
186	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
187	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
188	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
189	C₁₃×C₄⋊C₄	—	2	4	no	—
190	C₁₃×C₄⋊C₄	—	2	4	no	—
191	C₁₃×C₄⋊C₄	—	2	4	no	—
192	C₁₃×C₄⋊C₄	—	2	8	no	—
193	C₁₃×C₄⋊C₄	—	2	2	no	—
194	C₁₃×C₄⋊C₄	—	2	2	no	—
195	C₁₃×C₄⋊C₄	—	2	8	no	—
196	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
197	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
198	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
199	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
200	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
201	C₁₃×C₂²⋊C₄	—	2	2	no	—
202	C₁₃×C₂²⋊C₄	—	2	8	no	—
203	C₁₃×C₂²⋊C₄	—	2	8	no	—
204	C₁₃×C₂²⋊C₄	—	2	2	no	—
205	C₁₃×C₂²⋊C₄	—	2	2	no	—
206	C₁₃×C₂²⋊C₄	—	2	8	no	—
207	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
208	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
209	C₄²×C₁₃	—	2	2	no	—
210	C₄²×C₁₃	—	2	2	no	—
211	C₄²×C₁₃	—	2	2	no	—
212	C₄²×C₁₃	—	2	8	no	—
213	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
214	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
215	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
216	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
217	#3511	C₂×C₁₃	1	2	yes	complemented
218	#3357	C₂×C₁₃	1	4	yes	complemented
219	#3353	C₂×C₁₃	1	4	yes	complemented
220	#3342	C₂×C₁₃	1	2	yes	complemented
221	#3341	C₂×C₁₃	1	2	yes	complemented
222	#3338	C₂×C₁₃	1	2	yes	complemented
223	#3334	C₂×C₁₃	1	2	yes	complemented
224	C₂×#500	C₂×C₁₃	1	1	yes	characteristic, complemented
225	#3098	C₂×C₁₃	1	4	yes	complemented
226	#3079	C₂×C₁₃	1	2	yes	complemented
227	#3061	C₂×C₁₃	1	2	yes	complemented
228	C₄×#135	C₂×C₁₃	1	1	yes	characteristic, complemented
229	#2931	C₂×C₁₃	1	1	yes	characteristic, complemented
230	#2913	C₂×C₁₃	1	2	yes	complemented
231	C₂³×C₁₃	—	2	2	no	—
232	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
233	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
234	Q₈×C₁₃	—	2	4	no	—
235	Q₈×C₁₃	—	2	2	no	—
236	Q₈×C₁₃	—	2	2	no	—
237	Q₈×C₁₃	—	4	8	no	—
238	Q₈×C₁₃	—	8	4	no	—
239	D₄×C₁₃	—	2	8	no	—
240	D₄×C₁₃	—	2	4	no	—
241	D₄×C₁₃	—	2	4	no	—
242	D₄×C₁₃	—	2	4	no	—
243	D₄×C₁₃	—	2	2	no	—
244	D₄×C₁₃	—	2	2	no	—
245	D₄×C₁₃	—	4	4	no	—
246	D₄×C₁₃	—	8	8	no	—
247	C₂×C₄×C₁₃	—	2	2	no	—
248	C₂×C₄×C₁₃	—	2	2	no	—
249	C₂×C₄×C₁₃	—	2	4	no	—
250	C₂×C₄×C₁₃	—	2	4	no	—
251	C₂×C₄×C₁₃	—	2	2	no	—
252	C₂×C₄×C₁₃	—	2	2	no	—
253	C₂×C₄×C₁₃	—	2	2	no	—
254	C₂×C₄×C₁₃	—	2	8	no	—
255	C₂×C₄×C₁₃	—	4	4	no	—
256	C₂×C₄×C₁₃	—	4	4	no	—
257	C₂×C₄×C₁₃	—	4	4	no	—
258	C₂×C₄×C₁₃	—	8	4	no	—
259	C₂×C₄×C₁₃	—	8	8	no	—
260	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
261	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
262	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
263	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
264	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
265	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
266	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
267	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
268	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
269	C₈×C₁₃	—	2	4	no	—
270	C₈×C₁₃	—	2	1	no	—
271	C₈×C₁₃	—	2	1	no	—
272	C₈×C₁₃	C₂×#41	1	2	yes	—
273	C₈×C₁₃	C₂×#41	1	2	yes	—
274	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
275	C₂×#131	C₂²×C₁₃	1	2	yes	—
276	#556	C₂²×C₁₃	1	4	yes	—
277	#555	C₂²×C₁₃	1	4	yes	—
278	#554	C₂²×C₁₃	1	4	yes	—
279	#553	—	2	4	no	—
280	#548	—	2	4	no	—
281	#547	C₂²×C₁₃	1	4	yes	—
282	#542	—	2	4	no	—
283	#537	C₂²×C₁₃	1	4	yes	—
284	#533	—	2	2	no	—
285	#532	—	2	2	no	—
286	#532	C₂²×C₁₃	1	1	yes	characteristic
287	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
288	#520	C₂²×C₁₃	1	4	yes	—
289	C₄×#41	C₂²×C₁₃	1	2	yes	—
290	#500	C₂²×C₁₃	1	2	yes	—
291	#500	C₂²×C₁₃	1	2	yes	—
292	#500	C₂²×C₁₃	1	2	yes	—
293	#500	C₂²×C₁₃	1	2	yes	—
294	#485	C₂²×C₁₃	1	8	yes	—
295	#484	C₂²×C₁₃	1	8	yes	—
296	#482	C₂²×C₁₃	1	8	yes	—
297	#480	C₂²×C₁₃	1	8	yes	—
298	#477	C₂²×C₁₃	1	4	yes	—
299	#476	C₂²×C₁₃	1	4	yes	—
300	#475	C₂²×C₁₃	1	4	yes	—
301	#474	C₂²×C₁₃	1	4	yes	—
302	#468	C₂²×C₁₃	1	8	yes	—
303	#467	C₂²×C₁₃	1	4	yes	—
304	#466	C₂²×C₁₃	1	4	yes	—
305	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
306	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
307	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
308	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
309	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
310	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
311	#436	C₂²×C₁₃	1	2	yes	—
312	#436	C₂²×C₁₃	1	2	yes	—
313	C₈×D₄	C₂²×C₁₃	1	2	yes	—
314	C₈×D₄	C₂²×C₁₃	1	2	yes	—
315	#428	C₂²×C₁₃	1	4	yes	—
316	#428	C₂²×C₁₃	1	8	yes	—
317	#427	C₂²×C₁₃	1	4	yes	—
318	#427	C₂²×C₁₃	1	1	yes	characteristic
319	C₂×#107	C₂²×C₁₃	1	4	yes	—
320	C₂×#107	C₂²×C₁₃	1	2	yes	—
321	C₂×#107	C₂²×C₁₃	1	2	yes	—
322	#423	C₂²×C₁₃	1	1	yes	characteristic
323	#417	C₂²×C₁₃	1	4	yes	—
324	#416	C₂²×C₁₃	1	2	yes	—
325	#408	C₂²×C₁₃	1	2	yes	—
326	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
327	C₂²×C₁₃	—	2	1	no	—
328	C₂²×C₁₃	—	2	1	no	—
329	C₂²×C₁₃	—	2	4	no	—
330	C₂²×C₁₃	—	2	4	no	—
331	C₂²×C₁₃	—	2	4	no	—
332	C₂²×C₁₃	—	4	2	no	—
333	C₂²×C₁₃	—	4	2	no	—
334	C₂²×C₁₃	—	4	2	no	—
335	C₂²×C₁₃	#547	1	2	yes	—
336	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
337	C₄×C₁₃	—	2	4	no	—
338	C₄×C₁₃	—	2	1	no	—
339	C₄×C₁₃	—	2	1	no	—
340	C₄×C₁₃	—	4	2	no	—
341	C₄×C₁₃	—	4	2	no	—
342	C₄×C₁₃	—	4	8	no	—
343	C₄×C₁₃	—	4	2	no	—
344	C₄×C₁₃	#547	1	2	yes	—
345	C₄×C₁₃	#576	1	2	yes	—
346	C₄×C₁₃	#578	1	2	yes	—
347	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
348	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
349	C₂×#41	—	2	4	no	—
350	C₂×#41	C₂³×C₁₃	1	2	yes	—
351	C₂×#41	C₂³×C₁₃	1	2	yes	—
352	C₂²×Q₈	—	2	2	no	—
353	#135	—	2	4	no	—
354	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
355	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
356	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
357	#131	—	2	8	no	—
358	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
359	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
360	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
361	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
362	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
363	C₄⋊Q₈	—	2	2	no	—
364	C₄⋊Q₈	—	2	2	no	—
365	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
366	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
367	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
368	#127	D₄×C₁₃	1	1	yes	characteristic
369	#126	—	2	8	no	—
370	#125	—	2	4	no	—
371	#124	—	2	4	no	—
372	#124	—	2	8	no	—
373	#124	D₄×C₁₃	1	2	yes	—
374	#123	—	2	8	no	—
375	C₂²⋊Q₈	—	2	4	no	—
376	C₂²⋊Q₈	—	2	4	no	—
377	C₂²⋊Q₈	—	2	8	no	—
378	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
379	#121	—	2	4	no	—
380	#121	—	2	4	no	—
381	#121	—	2	8	no	—
382	#121	D₄×C₁₃	1	2	yes	—
383	#121	D₄×C₁₃	1	2	yes	—
384	#121	C₂³×C₁₃	1	8	yes	—
385	C₄×Q₈	—	2	4	no	—
386	C₄×Q₈	—	2	4	no	—
387	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
388	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
389	C₄×D₄	—	2	4	no	—
390	C₄×D₄	—	2	8	no	—
391	C₄×D₄	—	2	4	no	—
392	C₄×D₄	—	2	2	no	—
393	C₄×D₄	—	2	2	no	—
394	C₄×D₄	C₂³×C₁₃	1	2	yes	—
395	C₄×D₄	C₂³×C₁₃	1	2	yes	—
396	C₄×D₄	C₂³×C₁₃	1	2	yes	—
397	C₄×D₄	C₂³×C₁₃	1	2	yes	—
398	#117	—	2	4	no	—
399	#117	—	2	2	no	—
400	#117	C₂³×C₁₃	1	2	yes	—
401	#117	C₂³×C₁₃	1	8	yes	—
402	C₂×C₄⋊C₄	—	2	2	no	—
403	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
404	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
405	C₂×C₄²	—	2	2	no	—
406	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
407	#107	C₂³×C₁₃	1	1	yes	characteristic
408	#107	C₂³×C₁₃	1	4	yes	—
409	#107	C₂³×C₁₃	1	4	yes	—
410	#107	C₂³×C₁₃	1	8	yes	—
411	#107	C₂³×C₁₃	1	4	yes	—
412	#107	C₂³×C₁₃	1	4	yes	—
413	#107	C₂³×C₁₃	1	1	yes	characteristic
414	#106	C₂³×C₁₃	1	2	yes	—
415	#106	C₂³×C₁₃	1	8	yes	—
416	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
417	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
418	#103	C₂³×C₁₃	1	2	yes	—
419	#103	C₂³×C₁₃	1	2	yes	—
420	#103	C₂³×C₁₃	1	8	yes	—
421	#102	C₂³×C₁₃	1	2	yes	—
422	#102	C₂³×C₁₃	1	2	yes	—
423	#102	C₂³×C₁₃	1	8	yes	—
424	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
425	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
426	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
427	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
428	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
429	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
430	C₂×C₁₃	—	2	2	no	—
431	C₂×C₁₃	—	4	4	no	—
432	C₂×C₁₃	—	8	2	no	—
433	C₂×C₁₃	C₂×#547	1	1	yes	characteristic
434	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
435	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
436	#41	—	2	4	no	—
437	#41	—	2	4	no	—
438	#41	—	2	4	no	—
439	#41	—	2	4	no	—
440	#41	—	8	8	no	—
441	C₂×Q₈	—	2	4	no	—
442	C₂×Q₈	—	2	4	no	—
443	C₂×Q₈	—	8	4	no	—
444	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
445	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
446	C₂×D₄	—	2	2	no	—
447	C₂×D₄	—	2	8	no	—
448	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
449	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
450	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
451	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
452	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
453	C₂²×C₄	—	2	4	no	—
454	C₂²×C₄	—	2	8	no	—
455	C₂²×C₄	—	2	2	no	—
456	C₂²×C₄	—	2	2	no	—
457	C₂²×C₄	—	2	2	no	—
458	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
459	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
460	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
461	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
462	Q₁₆	—	2	2	no	—
463	SD₁₆	—	2	4	no	—
464	D₈	—	2	2	no	—
465	M₁₆	—	2	4	no	—
466	M₁₆	—	2	8	no	—
467	C₂×C₈	—	2	2	no	—
468	C₂×C₈	—	2	8	no	—
469	C₂×C₈	C₁₃×#41	1	4	yes	complemented
470	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
471	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
472	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
473	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
474	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
475	C₄⋊C₄	—	2	4	no	—
476	C₄⋊C₄	—	2	4	no	—
477	C₄⋊C₄	—	2	4	no	—
478	C₄⋊C₄	—	2	8	no	—
479	C₄⋊C₄	—	2	2	no	—
480	C₄⋊C₄	—	2	2	no	—
481	C₄⋊C₄	—	2	8	no	—
482	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
483	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
484	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
485	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
486	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
487	C₂²⋊C₄	—	2	2	no	—
488	C₂²⋊C₄	—	2	8	no	—
489	C₂²⋊C₄	—	2	8	no	—
490	C₂²⋊C₄	—	2	2	no	—
491	C₂²⋊C₄	—	2	2	no	—
492	C₂²⋊C₄	—	2	8	no	—
493	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
494	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
495	C₄²	—	2	2	no	—
496	C₄²	—	2	2	no	—
497	C₄²	—	2	2	no	—
498	C₄²	—	2	8	no	—
499	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
500	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
501	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
502	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
503	C₁₃	#61287	1	1	yes	characteristic, direct product factor, Sylow
504	C₂³	—	2	2	no	—
505	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
506	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
507	Q₈	—	2	4	no	—
508	Q₈	—	2	2	no	—
509	Q₈	—	2	2	no	—
510	Q₈	—	4	8	no	—
511	Q₈	—	8	4	no	—
512	D₄	—	2	8	no	—
513	D₄	—	2	4	no	—
514	D₄	—	2	4	no	—
515	D₄	—	2	4	no	—
516	D₄	—	2	2	no	—
517	D₄	—	2	2	no	—
518	D₄	—	4	4	no	—
519	D₄	—	8	8	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	4	no	—
523	C₂×C₄	—	2	4	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	8	no	—
528	C₂×C₄	—	4	4	no	—
529	C₂×C₄	—	4	4	no	—
530	C₂×C₄	—	4	4	no	—
531	C₂×C₄	—	8	4	no	—
532	C₂×C₄	—	8	8	no	—
533	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
534	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
535	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
536	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
537	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
538	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
539	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
540	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
541	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
542	C₈	—	2	4	no	—
543	C₈	—	2	1	no	—
544	C₈	—	2	1	no	—
545	C₈	C₂×C₁₃×#41	1	2	yes	—
546	C₈	C₂×C₁₃×#41	1	2	yes	—
547	C₂²	—	2	1	no	—
548	C₂²	—	2	1	no	—
549	C₂²	—	2	4	no	—
550	C₂²	—	2	4	no	—
551	C₂²	—	2	4	no	—
552	C₂²	—	4	2	no	—
553	C₂²	—	4	2	no	—
554	C₂²	—	4	2	no	—
555	C₂²	C₁₃×#547	1	2	yes	—
556	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
557	C₄	—	2	1	no	—
558	C₄	—	2	1	no	—
559	C₄	—	2	4	no	—
560	C₄	—	4	2	no	—
561	C₄	—	4	8	no	—
562	C₄	—	4	2	no	—
563	C₄	—	4	2	no	—
564	C₄	C₁₃×#547	1	2	yes	—
565	C₄	C₁₃×#576	1	2	yes	—
566	C₄	C₁₃×#578	1	2	yes	—
567	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
568	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
569	C₂	—	2	2	no	—
570	C₂	—	4	4	no	—
571	C₂	—	8	2	no	—
572	C₂	C₂×C₁₃×#547	1	1	yes	characteristic
573	C₂	C₂×C₁₃×#576	1	1	yes	characteristic
574	C₂	C₂×C₁₃×#578	1	1	yes	characteristic

	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×#3357	C₂	semidirect
3. C₁₃×#3353	C₂	semidirect
4. C₁₃×#3342	C₂	semidirect
5. C₁₃×#3341	C₂	semidirect
6. C₁₃×#3338	C₂	semidirect
7. C₁₃×#3334	C₂	semidirect
8. C₂×C₁₃×#500	C₂	semidirect
9. C₁₃×#3098	C₂	semidirect
10. C₁₃×#3079	C₂	semidirect
11. C₁₃×#3061	C₂	semidirect
12. C₄×C₁₃×#135	C₂	semidirect
13. C₁₃×#2931	C₂	semidirect
14. C₁₃×#2913	C₂	semidirect
149. #61287	C₁₃	direct (N × H)
183. C₂×C₈×C₁₃	#41	semidirect
217. #3511	C₂×C₁₃	semidirect
218. #3357	C₂×C₁₃	semidirect
219. #3353	C₂×C₁₃	semidirect
220. #3342	C₂×C₁₃	semidirect
221. #3341	C₂×C₁₃	semidirect
222. #3338	C₂×C₁₃	semidirect
223. #3334	C₂×C₁₃	semidirect
224. C₂×#500	C₂×C₁₃	semidirect
225. #3098	C₂×C₁₃	semidirect
226. #3079	C₂×C₁₃	semidirect
227. #3061	C₂×C₁₃	semidirect
228. C₄×#135	C₂×C₁₃	semidirect
229. #2931	C₂×C₁₃	semidirect
230. #2913	C₂×C₁₃	semidirect
469. C₂×C₈	C₁₃×#41	semidirect
503. C₁₃	#61287	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×#3357	2
C₁₃×#3353	2
C₁₃×#3342	2
C₁₃×#3341	2
C₁₃×#3338	2
C₁₃×#3334	2
C₂×C₁₃×#500	2
C₁₃×#3098	2
C₁₃×#3079	2
C₁₃×#3061	2
C₄×C₁₃×#135	2
C₁₃×#2931	2
C₁₃×#2913	2
#61287	13

Subgroups — C13×#61287 #15747626

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61287 #15747626