Subgroups — C₁₃×#61565 #15747904

Order 3328.

2142 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3506	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#547	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3303	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3302	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3284	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3283	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3209	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3206	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3190	C₂	1	4	yes	maximal, complemented
10	C₁₃×#3101	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3100	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3002	C₂	1	4	yes	maximal, complemented
13	C₁₃×#2972	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×C₁₃×#41	C₂²	1	2	yes	—
15	C₂×C₁₃×#135	C₂²	1	8	yes	complemented
16	C₁₃×#559	—	2	2	no	—
17	C₁₃×#556	C₂²	1	2	yes	complemented
18	C₁₃×#555	C₂²	1	2	yes	complemented
19	C₁₃×#553	—	2	2	no	—
20	C₁₃×#550	C₂²	1	2	yes	complemented
21	C₁₃×#547	—	2	2	no	—
22	C₁₃×#547	—	2	2	no	—
23	C₁₃×#547	C₂²	1	4	yes	—
24	C₁₃×#547	C₂²	1	4	yes	—
25	C₁₃×#547	C₂²	1	2	yes	complemented
26	C₁₃×#538	—	2	2	no	—
27	C₁₃×#535	—	2	1	no	—
28	C₁₃×#533	C₂²	1	1	yes	characteristic
29	C₁₃×#532	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
31	C₁₃×#525	C₂²	1	4	yes	—
32	C₂×C₁₃×#123	—	2	2	no	—
33	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
34	C₂×C₁₃×#121	—	2	1	no	—
35	C₁₃×#520	—	2	1	no	—
36	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
38	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
39	C₁₃×#494	C₂²	1	2	yes	complemented
40	C₁₃×#492	C₂²	1	2	yes	complemented
41	C₁₃×#487	C₂²	1	2	yes	complemented
42	C₁₃×#487	C₂²	1	2	yes	complemented
43	C₁₃×#485	C₂²	1	8	yes	complemented
44	C₁₃×#483	C₂²	1	2	yes	—
45	C₁₃×#480	C₂²	1	2	yes	—
46	C₁₃×#476	C₂²	1	2	yes	complemented
47	C₁₃×#474	C₂²	1	2	yes	complemented
48	C₁₃×#467	C₂²	1	8	yes	complemented
49	C₁₃×#465	C₂²	1	8	yes	complemented
50	C₁₃×#462	C₂²	1	4	yes	complemented
51	C₁₃×#461	C₂²	1	2	yes	complemented
52	C₁₃×#461	C₂²	1	4	yes	complemented
53	C₁₃×#459	C₂²	1	2	yes	complemented
54	C₁₃×#452	C₂²	1	8	yes	complemented
55	C₁₃×#452	C₂²	1	8	yes	complemented
56	C₁₃×#451	C₂²	1	4	yes	—
57	C₁₃×#450	C₂²	1	2	yes	—
58	C₁₃×#449	C₂²	1	8	yes	complemented
59	C₁₃×#448	C₂²	1	4	yes	—
60	C₁₃×#447	C₂²	1	2	yes	—
61	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
62	C₄×C₁₃×D₈	C₂²	1	4	yes	complemented
63	C₈×D₄×C₁₃	C₂²	1	4	yes	complemented
64	C₈×D₄×C₁₃	C₂²	1	4	yes	complemented
65	C₁₃×#431	C₂²	1	1	yes	characteristic
66	C₁₃×#431	C₂²	1	1	yes	characteristic
67	C₁₃×#416	C₂²	1	8	yes	complemented
68	C₂×C₁₃×C₂²⋊C₈	C₂²	1	4	yes	—
69	C₂×C₁₃×#41	—	2	1	no	—
70	C₂×C₁₃×#41	—	2	4	no	—
71	C₂×C₁₃×#41	—	4	8	no	—
72	C₂×C₁₃×#41	C₂³	1	8	yes	—
73	C₂×C₁₃×#41	C₂³	1	4	yes	—
74	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
75	C₂²×D₄×C₁₃	—	2	2	no	—
76	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
77	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
78	C₂³×C₄×C₁₃	—	2	1	no	—
79	C₂³×C₄×C₁₃	—	2	2	no	—
80	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
81	C₁₃×#135	—	4	16	no	—
82	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	—
83	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
84	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
85	C₂×C₁₃×D₈	C₂³	1	4	yes	—
86	C₂²×C₈×C₁₃	C₂³	1	8	yes	—
87	C₁₃×C₄⋊Q₈	—	2	1	no	—
88	C₁₃×C₄⋊Q₈	—	2	1	no	—
89	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
90	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
91	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
92	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
93	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
94	C₁₃×#127	—	2	2	no	—
95	C₁₃×#127	C₂³	1	1	yes	characteristic
96	C₁₃×#126	—	2	4	no	—
97	C₁₃×#125	—	2	1	no	—
98	C₁₃×#124	—	2	2	no	—
99	C₁₃×#124	—	2	4	no	—
100	C₁₃×#124	—	2	1	no	—
101	C₁₃×#123	—	2	4	no	—
102	C₁₃×#123	—	2	8	no	—
103	C₁₃×#123	—	2	8	no	—
104	C₁₃×#123	—	2	4	no	—
105	C₁₃×C₂²⋊Q₈	—	2	4	no	—
106	C₁₃×C₂²⋊Q₈	—	2	1	no	—
107	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
108	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
109	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
110	C₁₃×#121	—	2	4	no	—
111	C₁₃×#121	—	2	4	no	—
112	C₁₃×#121	—	2	2	no	—
113	C₁₃×#121	—	2	2	no	—
114	C₁₃×#121	—	2	1	no	—
115	C₁₃×#121	—	2	4	no	—
116	C₁₃×#121	C₂³	1	2	yes	—
117	C₁₃×#121	C₂³	1	4	yes	—
118	C₁₃×#120	—	2	4	no	—
119	C₄×Q₈×C₁₃	—	2	2	no	—
120	C₄×Q₈×C₁₃	—	2	1	no	—
121	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
122	C₄×D₄×C₁₃	—	2	4	no	—
123	C₄×D₄×C₁₃	—	2	4	no	—
124	C₄×D₄×C₁₃	—	2	2	no	—
125	C₄×D₄×C₁₃	—	2	1	no	—
126	C₄×D₄×C₁₃	—	2	1	no	—
127	C₄×D₄×C₁₃	—	2	1	no	—
128	C₄×D₄×C₁₃	D₄	1	2	yes	—
129	C₄×D₄×C₁₃	D₄	1	2	yes	—
130	C₄×D₄×C₁₃	C₂³	1	2	yes	—
131	C₄×D₄×C₁₃	C₂³	1	2	yes	—
132	C₄×D₄×C₁₃	C₂³	1	2	yes	—
133	C₄×D₄×C₁₃	C₂³	1	2	yes	—
134	C₄×D₄×C₁₃	C₂³	1	2	yes	—
135	C₁₃×#117	—	2	1	no	—
136	C₁₃×#117	—	2	2	no	—
137	C₁₃×#117	C₂³	1	4	yes	—
138	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
139	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
140	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
141	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
142	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
143	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
144	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
145	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
146	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
147	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
148	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
149	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
150	C₁₃×#107	C₂³	1	4	yes	—
151	C₁₃×#106	C₂³	1	4	yes	—
152	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
153	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
154	C₁₃×#103	C₂³	1	8	yes	—
155	C₁₃×#103	C₂³	1	8	yes	—
156	C₁₃×#103	C₂³	1	4	yes	—
157	C₁₃×#102	C₂³	1	4	yes	—
158	C₁₃×#102	C₂³	1	4	yes	—
159	C₁₃×#102	C₂³	1	4	yes	—
160	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
161	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
162	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
163	C₄×C₈×C₁₃	C₂³	1	2	yes	—
164	C₄×C₈×C₁₃	C₂³	1	2	yes	—
165	#61565	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
166	C₂⁴×C₁₃	—	2	1	no	—
167	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
168	C₁₃×#41	—	2	16	no	—
169	C₁₃×#41	—	4	8	no	—
170	C₁₃×#41	—	4	8	no	—
171	C₁₃×#41	—	4	16	no	—
172	C₁₃×#41	—	4	4	no	—
173	C₂×Q₈×C₁₃	—	2	1	no	—
174	C₂×Q₈×C₁₃	—	2	2	no	—
175	C₂×Q₈×C₁₃	—	2	1	no	—
176	C₂×Q₈×C₁₃	—	4	4	no	—
177	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
178	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
179	C₂×D₄×C₁₃	—	2	4	no	—
180	C₂×D₄×C₁₃	—	2	2	no	—
181	C₂×D₄×C₁₃	—	2	8	no	—
182	C₂×D₄×C₁₃	—	2	4	no	—
183	C₂×D₄×C₁₃	—	2	4	no	—
184	C₂×D₄×C₁₃	—	2	4	no	—
185	C₂×D₄×C₁₃	—	2	1	no	—
186	C₂×D₄×C₁₃	—	2	1	no	—
187	C₂×D₄×C₁₃	—	2	1	no	—
188	C₂×D₄×C₁₃	—	4	8	no	—
189	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
190	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
191	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
192	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
193	C₂²×C₄×C₁₃	—	2	1	no	—
194	C₂²×C₄×C₁₃	—	2	2	no	—
195	C₂²×C₄×C₁₃	—	2	2	no	—
196	C₂²×C₄×C₁₃	—	2	2	no	—
197	C₂²×C₄×C₁₃	—	2	8	no	—
198	C₂²×C₄×C₁₃	—	2	2	no	—
199	C₂²×C₄×C₁₃	—	2	4	no	—
200	C₂²×C₄×C₁₃	—	4	4	no	—
201	C₂²×C₄×C₁₃	—	4	8	no	—
202	C₂²×C₄×C₁₃	—	4	4	no	—
203	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
204	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
205	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
206	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
207	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
208	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
209	C₁₃×Q₁₆	—	4	8	no	—
210	C₁₃×SD₁₆	—	2	8	no	—
211	C₁₃×SD₁₆	—	4	8	no	—
212	C₁₃×D₈	—	2	8	no	—
213	C₂×C₈×C₁₃	—	4	8	no	—
214	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
215	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
216	C₁₃×C₄⋊C₄	—	2	2	no	—
217	C₁₃×C₄⋊C₄	—	2	2	no	—
218	C₁₃×C₄⋊C₄	—	2	8	no	—
219	C₁₃×C₄⋊C₄	—	2	1	no	—
220	C₁₃×C₄⋊C₄	—	2	4	no	—
221	C₁₃×C₄⋊C₄	—	2	2	no	—
222	C₁₃×C₄⋊C₄	—	2	2	no	—
223	C₁₃×C₄⋊C₄	—	2	1	no	—
224	C₁₃×C₄⋊C₄	—	2	1	no	—
225	C₁₃×C₄⋊C₄	—	2	2	no	—
226	C₁₃×C₄⋊C₄	—	2	1	no	—
227	C₁₃×C₄⋊C₄	—	2	1	no	—
228	C₁₃×C₄⋊C₄	—	2	2	no	—
229	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
230	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
231	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
232	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
233	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
234	C₁₃×C₂²⋊C₄	—	2	8	no	—
235	C₁₃×C₂²⋊C₄	—	2	2	no	—
236	C₁₃×C₂²⋊C₄	—	2	4	no	—
237	C₁₃×C₂²⋊C₄	—	2	4	no	—
238	C₁₃×C₂²⋊C₄	—	2	2	no	—
239	C₁₃×C₂²⋊C₄	—	2	2	no	—
240	C₁₃×C₂²⋊C₄	—	2	4	no	—
241	C₁₃×C₂²⋊C₄	—	2	2	no	—
242	C₁₃×C₂²⋊C₄	—	2	2	no	—
243	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
244	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
245	C₄²×C₁₃	—	2	4	no	—
246	C₄²×C₁₃	—	2	2	no	—
247	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
248	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
249	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
250	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
251	#3506	C₂×C₁₃	1	1	yes	characteristic, complemented
252	C₂×#547	C₂×C₁₃	1	1	yes	characteristic, complemented
253	#3303	C₂×C₁₃	1	4	yes	complemented
254	#3302	C₂×C₁₃	1	4	yes	complemented
255	#3284	C₂×C₁₃	1	4	yes	complemented
256	#3283	C₂×C₁₃	1	4	yes	complemented
257	#3209	C₂×C₁₃	1	1	yes	characteristic, complemented
258	#3206	C₂×C₁₃	1	1	yes	characteristic, complemented
259	#3190	C₂×C₁₃	1	4	yes	complemented
260	#3101	C₂×C₁₃	1	1	yes	characteristic, complemented
261	#3100	C₂×C₁₃	1	1	yes	characteristic, complemented
262	#3002	C₂×C₁₃	1	4	yes	complemented
263	#2972	C₂×C₁₃	1	1	yes	characteristic, complemented
264	C₂³×C₁₃	—	2	4	no	—
265	C₂³×C₁₃	—	2	2	no	—
266	C₂³×C₁₃	—	2	4	no	—
267	C₂³×C₁₃	—	2	2	no	—
268	C₂³×C₁₃	—	4	2	no	—
269	C₂³×C₁₃	—	4	2	no	—
270	C₂³×C₁₃	—	4	2	no	—
271	C₂³×C₁₃	—	4	2	no	—
272	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
273	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
274	Q₈×C₁₃	—	2	4	no	—
275	Q₈×C₁₃	—	2	8	no	—
276	Q₈×C₁₃	—	4	4	no	—
277	Q₈×C₁₃	—	4	2	no	—
278	Q₈×C₁₃	—	8	1	no	—
279	D₄×C₁₃	—	2	4	no	—
280	D₄×C₁₃	—	2	4	no	—
281	D₄×C₁₃	—	2	4	no	—
282	D₄×C₁₃	—	2	2	no	—
283	D₄×C₁₃	—	2	4	no	—
284	D₄×C₁₃	—	4	16	no	—
285	D₄×C₁₃	—	4	4	no	—
286	D₄×C₁₃	—	4	2	no	—
287	D₄×C₁₃	—	8	1	no	—
288	D₄×C₁₃	—	8	4	no	—
289	D₄×C₁₃	—	8	4	no	—
290	D₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
291	C₂×C₄×C₁₃	—	2	8	no	—
292	C₂×C₄×C₁₃	—	2	2	no	—
293	C₂×C₄×C₁₃	—	2	2	no	—
294	C₂×C₄×C₁₃	—	2	2	no	—
295	C₂×C₄×C₁₃	—	2	2	no	—
296	C₂×C₄×C₁₃	—	2	2	no	—
297	C₂×C₄×C₁₃	—	2	4	no	—
298	C₂×C₄×C₁₃	—	4	2	no	—
299	C₂×C₄×C₁₃	—	4	4	no	—
300	C₂×C₄×C₁₃	—	4	1	no	—
301	C₂×C₄×C₁₃	—	4	16	no	—
302	C₂×C₄×C₁₃	—	4	4	no	—
303	C₂×C₄×C₁₃	—	4	2	no	—
304	C₂×C₄×C₁₃	—	4	4	no	—
305	C₂×C₄×C₁₃	—	4	4	no	—
306	C₂×C₄×C₁₃	—	4	4	no	—
307	C₂×C₄×C₁₃	—	8	4	no	—
308	C₂×C₄×C₁₃	#135	1	4	yes	complemented
309	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
310	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
311	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
312	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
313	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
314	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
315	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
316	C₈×C₁₃	—	2	4	no	—
317	C₈×C₁₃	—	2	4	no	—
318	C₂²×#41	C₂²×C₁₃	1	2	yes	—
319	C₂×#135	C₂²×C₁₃	1	8	yes	complemented
320	#559	—	2	2	no	—
321	#556	C₂²×C₁₃	1	2	yes	complemented
322	#555	C₂²×C₁₃	1	2	yes	complemented
323	#553	—	2	2	no	—
324	#550	C₂²×C₁₃	1	2	yes	complemented
325	#547	—	2	2	no	—
326	#547	—	2	2	no	—
327	#547	C₂²×C₁₃	1	4	yes	—
328	#547	C₂²×C₁₃	1	4	yes	—
329	#547	C₂²×C₁₃	1	2	yes	complemented
330	#538	—	2	2	no	—
331	#535	—	2	1	no	—
332	#533	C₂²×C₁₃	1	1	yes	characteristic
333	#532	C₂²×C₁₃	1	1	yes	characteristic
334	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
335	#525	C₂²×C₁₃	1	4	yes	—
336	C₂×#123	—	2	2	no	—
337	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
338	C₂×#121	—	2	1	no	—
339	#520	—	2	1	no	—
340	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
341	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
342	C₂²×C₄⋊C₄	—	2	1	no	—
343	#494	C₂²×C₁₃	1	2	yes	complemented
344	#492	C₂²×C₁₃	1	2	yes	complemented
345	#487	C₂²×C₁₃	1	2	yes	complemented
346	#487	C₂²×C₁₃	1	2	yes	complemented
347	#485	C₂²×C₁₃	1	8	yes	complemented
348	#483	C₂²×C₁₃	1	2	yes	—
349	#480	C₂²×C₁₃	1	2	yes	—
350	#476	C₂²×C₁₃	1	2	yes	complemented
351	#474	C₂²×C₁₃	1	2	yes	complemented
352	#467	C₂²×C₁₃	1	8	yes	complemented
353	#465	C₂²×C₁₃	1	8	yes	complemented
354	#462	C₂²×C₁₃	1	4	yes	complemented
355	#461	C₂²×C₁₃	1	2	yes	complemented
356	#461	C₂²×C₁₃	1	4	yes	complemented
357	#459	C₂²×C₁₃	1	2	yes	complemented
358	#452	C₂²×C₁₃	1	8	yes	complemented
359	#452	C₂²×C₁₃	1	8	yes	complemented
360	#451	C₂²×C₁₃	1	4	yes	—
361	#450	C₂²×C₁₃	1	2	yes	—
362	#449	C₂²×C₁₃	1	8	yes	complemented
363	#448	C₂²×C₁₃	1	4	yes	—
364	#447	C₂²×C₁₃	1	2	yes	—
365	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
366	C₄×D₈	C₂²×C₁₃	1	4	yes	complemented
367	C₈×D₄	C₂²×C₁₃	1	4	yes	complemented
368	C₈×D₄	C₂²×C₁₃	1	4	yes	complemented
369	#431	C₂²×C₁₃	1	1	yes	characteristic
370	#431	C₂²×C₁₃	1	1	yes	characteristic
371	#416	C₂²×C₁₃	1	8	yes	complemented
372	C₂×C₂²⋊C₈	C₂²×C₁₃	1	4	yes	—
373	C₂²×C₁₃	—	2	1	no	—
374	C₂²×C₁₃	—	2	1	no	—
375	C₂²×C₁₃	—	2	4	no	—
376	C₂²×C₁₃	—	2	4	no	—
377	C₂²×C₁₃	—	2	4	no	—
378	C₂²×C₁₃	—	2	4	no	—
379	C₂²×C₁₃	—	4	8	no	—
380	C₂²×C₁₃	—	4	2	no	—
381	C₂²×C₁₃	—	4	2	no	—
382	C₂²×C₁₃	—	4	2	no	—
383	C₂²×C₁₃	—	4	2	no	—
384	C₂²×C₁₃	—	4	2	no	—
385	C₂²×C₁₃	—	8	4	no	—
386	C₂²×C₁₃	C₂×#135	1	2	yes	—
387	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
388	C₄×C₁₃	—	2	1	no	—
389	C₄×C₁₃	—	2	1	no	—
390	C₄×C₁₃	—	2	4	no	—
391	C₄×C₁₃	—	2	1	no	—
392	C₄×C₁₃	—	4	2	no	—
393	C₄×C₁₃	—	4	4	no	—
394	C₄×C₁₃	—	4	2	no	—
395	C₄×C₁₃	—	4	2	no	—
396	C₄×C₁₃	—	4	2	no	—
397	C₄×C₁₃	C₂×#135	1	2	yes	—
398	C₄×C₁₃	C₂×#135	1	2	yes	—
399	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
400	C₂×#41	—	2	1	no	—
401	C₂×#41	—	2	4	no	—
402	C₂×#41	—	4	8	no	—
403	C₂×#41	C₂³×C₁₃	1	8	yes	—
404	C₂×#41	C₂³×C₁₃	1	4	yes	—
405	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
406	C₂²×D₄	—	2	2	no	—
407	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
408	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
409	C₂³×C₄	—	2	1	no	—
410	C₂³×C₄	—	2	2	no	—
411	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
412	#135	—	4	16	no	—
413	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	—
414	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
415	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
416	C₂×D₈	C₂³×C₁₃	1	4	yes	—
417	C₂²×C₈	C₂³×C₁₃	1	8	yes	—
418	C₄⋊Q₈	—	2	1	no	—
419	C₄⋊Q₈	—	2	1	no	—
420	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
421	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
422	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
423	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
424	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
425	#127	—	2	2	no	—
426	#127	C₂³×C₁₃	1	1	yes	characteristic
427	#126	—	2	4	no	—
428	#125	—	2	1	no	—
429	#124	—	2	2	no	—
430	#124	—	2	4	no	—
431	#124	—	2	1	no	—
432	#123	—	2	4	no	—
433	#123	—	2	8	no	—
434	#123	—	2	8	no	—
435	#123	—	2	4	no	—
436	C₂²⋊Q₈	—	2	4	no	—
437	C₂²⋊Q₈	—	2	1	no	—
438	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
439	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
440	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
441	#121	—	2	4	no	—
442	#121	—	2	4	no	—
443	#121	—	2	2	no	—
444	#121	—	2	2	no	—
445	#121	—	2	1	no	—
446	#121	—	2	4	no	—
447	#121	C₂³×C₁₃	1	2	yes	—
448	#121	C₂³×C₁₃	1	4	yes	—
449	#120	—	2	4	no	—
450	C₄×Q₈	—	2	2	no	—
451	C₄×Q₈	—	2	1	no	—
452	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
453	C₄×D₄	—	2	4	no	—
454	C₄×D₄	—	2	4	no	—
455	C₄×D₄	—	2	2	no	—
456	C₄×D₄	—	2	1	no	—
457	C₄×D₄	—	2	1	no	—
458	C₄×D₄	—	2	1	no	—
459	C₄×D₄	D₄×C₁₃	1	2	yes	—
460	C₄×D₄	D₄×C₁₃	1	2	yes	—
461	C₄×D₄	C₂³×C₁₃	1	2	yes	—
462	C₄×D₄	C₂³×C₁₃	1	2	yes	—
463	C₄×D₄	C₂³×C₁₃	1	2	yes	—
464	C₄×D₄	C₂³×C₁₃	1	2	yes	—
465	C₄×D₄	C₂³×C₁₃	1	2	yes	—
466	#117	—	2	1	no	—
467	#117	—	2	2	no	—
468	#117	C₂³×C₁₃	1	4	yes	—
469	C₂×C₄⋊C₄	—	2	1	no	—
470	C₂×C₄⋊C₄	—	2	2	no	—
471	C₂×C₄⋊C₄	—	2	1	no	—
472	C₂×C₄⋊C₄	—	2	4	no	—
473	C₂×C₄⋊C₄	—	2	4	no	—
474	C₂×C₄⋊C₄	—	2	2	no	—
475	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
476	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
477	C₂×C₂²⋊C₄	—	2	2	no	—
478	C₂×C₂²⋊C₄	—	2	1	no	—
479	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
480	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
481	#107	C₂³×C₁₃	1	4	yes	—
482	#106	C₂³×C₁₃	1	4	yes	—
483	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
484	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
485	#103	C₂³×C₁₃	1	8	yes	—
486	#103	C₂³×C₁₃	1	8	yes	—
487	#103	C₂³×C₁₃	1	4	yes	—
488	#102	C₂³×C₁₃	1	4	yes	—
489	#102	C₂³×C₁₃	1	4	yes	—
490	#102	C₂³×C₁₃	1	4	yes	—
491	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
492	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
493	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
494	C₄×C₈	C₂³×C₁₃	1	2	yes	—
495	C₄×C₈	C₂³×C₁₃	1	2	yes	—
496	C₂×C₁₃	—	2	2	no	—
497	C₂×C₁₃	—	4	4	no	—
498	C₂×C₁₃	—	4	4	no	—
499	C₂×C₁₃	—	8	2	no	—
500	C₂×C₁₃	#3484	1	1	yes	characteristic
501	C₂×C₁₃	C₂²×#135	1	1	yes	characteristic
502	C₂×C₁₃	#3586	1	1	yes	characteristic
503	C₂⁴	—	2	1	no	—
504	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
505	#41	—	2	16	no	—
506	#41	—	4	8	no	—
507	#41	—	4	8	no	—
508	#41	—	4	16	no	—
509	#41	—	4	4	no	—
510	C₂×Q₈	—	2	1	no	—
511	C₂×Q₈	—	2	2	no	—
512	C₂×Q₈	—	2	1	no	—
513	C₂×Q₈	—	4	4	no	—
514	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
515	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
516	C₂×D₄	—	2	4	no	—
517	C₂×D₄	—	2	2	no	—
518	C₂×D₄	—	2	8	no	—
519	C₂×D₄	—	2	4	no	—
520	C₂×D₄	—	2	4	no	—
521	C₂×D₄	—	2	4	no	—
522	C₂×D₄	—	2	1	no	—
523	C₂×D₄	—	2	1	no	—
524	C₂×D₄	—	2	1	no	—
525	C₂×D₄	—	4	8	no	—
526	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
527	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
528	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
529	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
530	C₂²×C₄	—	2	1	no	—
531	C₂²×C₄	—	2	2	no	—
532	C₂²×C₄	—	2	2	no	—
533	C₂²×C₄	—	2	2	no	—
534	C₂²×C₄	—	2	8	no	—
535	C₂²×C₄	—	2	2	no	—
536	C₂²×C₄	—	2	4	no	—
537	C₂²×C₄	—	4	4	no	—
538	C₂²×C₄	—	4	8	no	—
539	C₂²×C₄	—	4	4	no	—
540	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
541	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
542	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
543	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
544	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
545	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
546	Q₁₆	—	4	8	no	—
547	SD₁₆	—	2	8	no	—
548	SD₁₆	—	4	8	no	—
549	D₈	—	2	8	no	—
550	C₂×C₈	—	4	8	no	—
551	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
552	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
553	C₄⋊C₄	—	2	2	no	—
554	C₄⋊C₄	—	2	2	no	—
555	C₄⋊C₄	—	2	8	no	—
556	C₄⋊C₄	—	2	1	no	—
557	C₄⋊C₄	—	2	4	no	—
558	C₄⋊C₄	—	2	2	no	—
559	C₄⋊C₄	—	2	2	no	—
560	C₄⋊C₄	—	2	1	no	—
561	C₄⋊C₄	—	2	1	no	—
562	C₄⋊C₄	—	2	2	no	—
563	C₄⋊C₄	—	2	1	no	—
564	C₄⋊C₄	—	2	1	no	—
565	C₄⋊C₄	—	2	2	no	—
566	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
567	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
568	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
569	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
570	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
571	C₂²⋊C₄	—	2	8	no	—
572	C₂²⋊C₄	—	2	2	no	—
573	C₂²⋊C₄	—	2	4	no	—
574	C₂²⋊C₄	—	2	4	no	—
575	C₂²⋊C₄	—	2	2	no	—
576	C₂²⋊C₄	—	2	2	no	—
577	C₂²⋊C₄	—	2	4	no	—
578	C₂²⋊C₄	—	2	2	no	—
579	C₂²⋊C₄	—	2	2	no	—
580	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
581	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
582	C₄²	—	2	4	no	—
583	C₄²	—	2	2	no	—
584	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
585	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
586	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
587	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
588	C₁₃	#61565	1	1	yes	characteristic, direct product factor, Sylow
589	C₂³	—	2	4	no	—
590	C₂³	—	2	2	no	—
591	C₂³	—	2	4	no	—
592	C₂³	—	2	2	no	—
593	C₂³	—	4	2	no	—
594	C₂³	—	4	2	no	—
595	C₂³	—	4	2	no	—
596	C₂³	—	4	2	no	—
597	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
598	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
599	Q₈	—	2	4	no	—
600	Q₈	—	2	8	no	—
601	Q₈	—	4	4	no	—
602	Q₈	—	4	2	no	—
603	Q₈	—	8	1	no	—
604	D₄	—	2	4	no	—
605	D₄	—	2	4	no	—
606	D₄	—	2	4	no	—
607	D₄	—	2	2	no	—
608	D₄	—	2	4	no	—
609	D₄	—	4	16	no	—
610	D₄	—	4	4	no	—
611	D₄	—	4	2	no	—
612	D₄	—	8	1	no	—
613	D₄	—	8	4	no	—
614	D₄	—	8	4	no	—
615	D₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
616	C₂×C₄	—	2	8	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	4	no	—
623	C₂×C₄	—	4	2	no	—
624	C₂×C₄	—	4	4	no	—
625	C₂×C₄	—	4	1	no	—
626	C₂×C₄	—	4	16	no	—
627	C₂×C₄	—	4	4	no	—
628	C₂×C₄	—	4	2	no	—
629	C₂×C₄	—	4	4	no	—
630	C₂×C₄	—	4	4	no	—
631	C₂×C₄	—	4	4	no	—
632	C₂×C₄	—	8	4	no	—
633	C₂×C₄	C₁₃×#135	1	4	yes	complemented
634	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
635	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
636	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
637	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
638	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
639	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
640	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
641	C₈	—	2	4	no	—
642	C₈	—	2	4	no	—
643	C₂²	—	2	1	no	—
644	C₂²	—	2	1	no	—
645	C₂²	—	2	4	no	—
646	C₂²	—	2	4	no	—
647	C₂²	—	2	4	no	—
648	C₂²	—	2	4	no	—
649	C₂²	—	4	8	no	—
650	C₂²	—	4	2	no	—
651	C₂²	—	4	2	no	—
652	C₂²	—	4	2	no	—
653	C₂²	—	4	2	no	—
654	C₂²	—	4	2	no	—
655	C₂²	—	8	4	no	—
656	C₂²	C₂×C₁₃×#135	1	2	yes	—
657	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
658	C₄	—	2	1	no	—
659	C₄	—	2	1	no	—
660	C₄	—	2	4	no	—
661	C₄	—	2	1	no	—
662	C₄	—	4	2	no	—
663	C₄	—	4	2	no	—
664	C₄	—	4	2	no	—
665	C₄	—	4	4	no	—
666	C₄	—	4	2	no	—
667	C₄	C₂×C₁₃×#135	1	2	yes	—
668	C₄	C₂×C₁₃×#135	1	2	yes	—
669	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
670	C₂	—	2	2	no	—
671	C₂	—	4	4	no	—
672	C₂	—	4	4	no	—
673	C₂	—	8	2	no	—
674	C₂	C₁₃×#3484	1	1	yes	characteristic
675	C₂	C₂²×C₁₃×#135	1	1	yes	characteristic
676	C₂	C₁₃×#3586	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 ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3506	C₂	semidirect
2. C₂×C₁₃×#547	C₂	semidirect
3. C₁₃×#3303	C₂	semidirect
4. C₁₃×#3302	C₂	semidirect
5. C₁₃×#3284	C₂	semidirect
6. C₁₃×#3283	C₂	semidirect
7. C₁₃×#3209	C₂	semidirect
8. C₁₃×#3206	C₂	semidirect
9. C₁₃×#3190	C₂	semidirect
10. C₁₃×#3101	C₂	semidirect
11. C₁₃×#3100	C₂	semidirect
12. C₁₃×#3002	C₂	semidirect
13. C₁₃×#2972	C₂	semidirect
15. C₂×C₁₃×#135	C₂²	semidirect
17. C₁₃×#556	C₂²	semidirect
18. C₁₃×#555	C₂²	semidirect
20. C₁₃×#550	C₂²	semidirect
25. C₁₃×#547	C₂²	semidirect
39. C₁₃×#494	C₂²	semidirect
40. C₁₃×#492	C₂²	semidirect
41. C₁₃×#487	C₂²	semidirect
42. C₁₃×#487	C₂²	semidirect
43. C₁₃×#485	C₂²	semidirect
46. C₁₃×#476	C₂²	semidirect
47. C₁₃×#474	C₂²	semidirect
48. C₁₃×#467	C₂²	semidirect
49. C₁₃×#465	C₂²	semidirect
50. C₁₃×#462	C₂²	semidirect
51. C₁₃×#461	C₂²	semidirect
52. C₁₃×#461	C₂²	semidirect
53. C₁₃×#459	C₂²	semidirect
54. C₁₃×#452	C₂²	semidirect
55. C₁₃×#452	C₂²	semidirect
58. C₁₃×#449	C₂²	semidirect
61. C₄×C₁₃×SD₁₆	C₂²	semidirect
62. C₄×C₁₃×D₈	C₂²	semidirect
63. C₈×D₄×C₁₃	C₂²	semidirect
64. C₈×D₄×C₁₃	C₂²	semidirect
67. C₁₃×#416	C₂²	semidirect
165. #61565	C₁₃	direct (N × H)
251. #3506	C₂×C₁₃	semidirect
252. C₂×#547	C₂×C₁₃	semidirect
253. #3303	C₂×C₁₃	semidirect
254. #3302	C₂×C₁₃	semidirect
255. #3284	C₂×C₁₃	semidirect
256. #3283	C₂×C₁₃	semidirect
257. #3209	C₂×C₁₃	semidirect
258. #3206	C₂×C₁₃	semidirect
259. #3190	C₂×C₁₃	semidirect
260. #3101	C₂×C₁₃	semidirect
261. #3100	C₂×C₁₃	semidirect
262. #3002	C₂×C₁₃	semidirect
263. #2972	C₂×C₁₃	semidirect
308. C₂×C₄×C₁₃	#135	semidirect
319. C₂×#135	C₂²×C₁₃	semidirect
321. #556	C₂²×C₁₃	semidirect
322. #555	C₂²×C₁₃	semidirect
324. #550	C₂²×C₁₃	semidirect
329. #547	C₂²×C₁₃	semidirect
343. #494	C₂²×C₁₃	semidirect
344. #492	C₂²×C₁₃	semidirect
345. #487	C₂²×C₁₃	semidirect
346. #487	C₂²×C₁₃	semidirect
347. #485	C₂²×C₁₃	semidirect
350. #476	C₂²×C₁₃	semidirect
351. #474	C₂²×C₁₃	semidirect
352. #467	C₂²×C₁₃	semidirect
353. #465	C₂²×C₁₃	semidirect
354. #462	C₂²×C₁₃	semidirect
355. #461	C₂²×C₁₃	semidirect
356. #461	C₂²×C₁₃	semidirect
357. #459	C₂²×C₁₃	semidirect
358. #452	C₂²×C₁₃	semidirect
359. #452	C₂²×C₁₃	semidirect
362. #449	C₂²×C₁₃	semidirect
365. C₄×SD₁₆	C₂²×C₁₃	semidirect
366. C₄×D₈	C₂²×C₁₃	semidirect
367. C₈×D₄	C₂²×C₁₃	semidirect
368. C₈×D₄	C₂²×C₁₃	semidirect
371. #416	C₂²×C₁₃	semidirect
588. C₁₃	#61565	direct (N × H)
633. C₂×C₄	C₁₃×#135	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#3506	2
C₂×C₁₃×#547	2
C₁₃×#3303	2
C₁₃×#3302	2
C₁₃×#3284	2
C₁₃×#3283	2
C₁₃×#3209	2
C₁₃×#3206	2
C₁₃×#3190	2
C₁₃×#3101	2
C₁₃×#3100	2
C₁₃×#3002	2
C₁₃×#2972	2
#61565	13

Subgroups — C13×#61565 #15747904

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61565 #15747904