Subgroups — C₁₃×#36699 #15723038

Order 3328.

1958 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#529	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2822	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2821	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2821	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2820	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2817	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2816	C₂	1	2	yes	maximal
9	C₁₃×#2814	C₂	1	4	yes	maximal, complemented
10	C₁₃×#2399	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2398	C₂	1	2	yes	maximal, complemented
12	C₁₃×#2396	C₂	1	4	yes	maximal, complemented
13	C₁₃×#2395	C₂	1	4	yes	maximal, complemented
14	C₁₃×#2283	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#533	—	2	8	no	—
16	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₁₃×#529	—	2	8	no	—
19	C₂×C₁₃×#126	C₂²	1	2	yes	—
20	C₂×C₁₃×#125	C₂²	1	2	yes	—
21	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#123	C₂²	1	2	yes	—
24	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
25	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
26	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
29	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
30	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#117	C₂²	1	2	yes	—
34	C₂×C₁₃×#117	C₂²	1	2	yes	—
35	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
36	C₁₃×#400	C₂²	1	4	yes	—
37	C₁₃×#400	C₂²	1	4	yes	—
38	C₁₃×#400	C₂²	1	4	yes	—
39	C₁₃×#399	C₂²	1	4	yes	—
40	C₁₃×#399	C₂²	1	4	yes	—
41	C₁₃×#398	C₂²	1	4	yes	—
42	C₁₃×#398	C₂²	1	8	yes	—
43	C₁₃×#398	C₂²	1	4	yes	—
44	C₁₃×#398	C₂²	1	4	yes	—
45	C₁₃×#397	C₂²	1	8	yes	—
46	C₁₃×#397	C₂²	1	4	yes	—
47	C₁₃×#397	C₂²	1	4	yes	—
48	C₁₃×#396	C₂²	1	8	yes	—
49	C₁₃×#395	C₂²	1	4	yes	—
50	C₁₃×#395	C₂²	1	4	yes	—
51	C₁₃×#395	C₂²	1	4	yes	—
52	C₁₃×#394	C₂²	1	8	yes	—
53	C₁₃×#394	C₂²	1	4	yes	—
54	C₁₃×#393	C₂²	1	4	yes	—
55	C₁₃×#393	C₂²	1	4	yes	—
56	C₁₃×#383	C₂²	1	2	yes	—
57	C₁₃×#382	C₂²	1	2	yes	—
58	C₁₃×#381	C₂²	1	2	yes	—
59	C₁₃×#380	C₂²	1	2	yes	—
60	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
61	C₄×C₁₃×C₄⋊C₄	C₂²	1	8	yes	—
62	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
63	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	—
64	C₁₃×#376	C₂²	1	2	yes	—
65	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
66	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
67	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
68	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
69	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
71	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
74	C₁₃×C₄⋊Q₈	—	2	4	no	—
75	C₁₃×C₄⋊Q₈	—	2	4	no	—
76	C₁₃×#126	—	2	8	no	—
77	C₁₃×#125	—	2	4	no	—
78	C₁₃×#125	—	2	8	no	—
79	C₁₃×#124	—	2	4	no	—
80	C₁₃×#123	—	2	8	no	—
81	C₁₃×C₂²⋊Q₈	—	2	4	no	—
82	C₁₃×C₂²⋊Q₈	—	2	8	no	—
83	C₁₃×C₂²⋊Q₈	—	2	8	no	—
84	C₁₃×#121	—	2	4	no	—
85	C₄×Q₈×C₁₃	—	2	4	no	—
86	C₄×Q₈×C₁₃	—	2	8	no	—
87	C₄×Q₈×C₁₃	—	2	8	no	—
88	C₄×D₄×C₁₃	—	2	8	no	—
89	C₄×D₄×C₁₃	—	2	4	no	—
90	C₁₃×#117	—	2	8	no	—
91	C₁₃×#117	—	2	8	no	—
92	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
93	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
94	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
95	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
96	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
97	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
98	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
99	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
100	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
101	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
102	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
103	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
104	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
105	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
106	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
107	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
108	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
109	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
110	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
111	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
112	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
113	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
114	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
115	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
116	C₂×C₄²×C₁₃	D₄	1	8	yes	—
117	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
118	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
119	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
120	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
121	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
122	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
123	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
124	C₁₃×#95	C₂³	1	4	yes	—
125	C₁₃×#95	C₂³	1	8	yes	—
126	C₁₃×#95	C₂³	1	8	yes	—
127	C₁₃×#95	C₂³	1	4	yes	—
128	C₁₃×#95	C₂³	1	8	yes	—
129	C₁₃×#95	C₂³	1	8	yes	—
130	C₁₃×#95	C₂³	1	4	yes	—
131	C₁₃×#95	C₂³	1	4	yes	—
132	#36699	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
133	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
134	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
135	C₂×Q₈×C₁₃	—	2	2	no	—
136	C₂×Q₈×C₁₃	—	2	4	no	—
137	C₂×Q₈×C₁₃	—	2	4	no	—
138	C₂×Q₈×C₁₃	—	4	2	no	—
139	C₂×Q₈×C₁₃	—	4	4	no	—
140	C₂×Q₈×C₁₃	—	4	4	no	—
141	C₂×D₄×C₁₃	—	2	4	no	—
142	C₂×D₄×C₁₃	—	2	2	no	—
143	C₂×D₄×C₁₃	—	4	2	no	—
144	C₂×D₄×C₁₃	—	4	4	no	—
145	C₂²×C₄×C₁₃	—	2	4	no	—
146	C₂²×C₄×C₁₃	—	2	4	no	—
147	C₂²×C₄×C₁₃	—	2	8	no	—
148	C₂²×C₄×C₁₃	—	4	2	no	—
149	C₂²×C₄×C₁₃	—	4	2	no	—
150	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
151	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
152	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
153	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
154	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
155	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
156	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
157	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
158	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
159	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
160	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
161	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
162	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
163	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
164	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
165	C₁₃×C₄⋊C₄	—	2	4	no	—
166	C₁₃×C₄⋊C₄	—	2	4	no	—
167	C₁₃×C₄⋊C₄	—	2	4	no	—
168	C₁₃×C₄⋊C₄	—	2	4	no	—
169	C₁₃×C₄⋊C₄	—	2	2	no	—
170	C₁₃×C₄⋊C₄	—	2	4	no	—
171	C₁₃×C₄⋊C₄	—	2	2	no	—
172	C₁₃×C₄⋊C₄	—	2	8	no	—
173	C₁₃×C₄⋊C₄	—	2	8	no	—
174	C₁₃×C₄⋊C₄	—	2	4	no	—
175	C₁₃×C₄⋊C₄	—	2	4	no	—
176	C₁₃×C₄⋊C₄	—	2	4	no	—
177	C₁₃×C₄⋊C₄	—	4	4	no	—
178	C₁₃×C₄⋊C₄	—	4	8	no	—
179	C₁₃×C₄⋊C₄	—	4	8	no	—
180	C₁₃×C₂²⋊C₄	—	2	8	no	—
181	C₁₃×C₂²⋊C₄	—	2	4	no	—
182	C₁₃×C₂²⋊C₄	—	2	4	no	—
183	C₁₃×C₂²⋊C₄	—	2	4	no	—
184	C₁₃×C₂²⋊C₄	—	2	4	no	—
185	C₁₃×C₂²⋊C₄	—	2	4	no	—
186	C₁₃×C₂²⋊C₄	—	4	4	no	—
187	C₁₃×C₂²⋊C₄	—	4	8	no	—
188	C₁₃×C₂²⋊C₄	—	4	8	no	—
189	C₄²×C₁₃	—	2	4	no	—
190	C₄²×C₁₃	—	2	8	no	—
191	C₄²×C₁₃	—	2	8	no	—
192	C₄²×C₁₃	C₂×D₄	1	4	yes	—
193	C₄²×C₁₃	C₂×D₄	1	4	yes	—
194	C₄²×C₁₃	C₂×D₄	1	4	yes	—
195	C₄²×C₁₃	C₂×D₄	1	4	yes	—
196	C₂×#533	C₂×C₁₃	1	1	yes	characteristic, complemented
197	C₂×#529	C₂×C₁₃	1	1	yes	characteristic
198	#2822	C₂×C₁₃	1	2	yes	complemented
199	#2821	C₂×C₁₃	1	2	yes	complemented
200	#2821	C₂×C₁₃	1	2	yes	complemented
201	#2820	C₂×C₁₃	1	2	yes	complemented
202	#2817	C₂×C₁₃	1	2	yes	complemented
203	#2816	C₂×C₁₃	1	2	yes	—
204	#2814	C₂×C₁₃	1	4	yes	complemented
205	#2399	C₂×C₁₃	1	2	yes	complemented
206	#2398	C₂×C₁₃	1	2	yes	complemented
207	#2396	C₂×C₁₃	1	4	yes	complemented
208	#2395	C₂×C₁₃	1	4	yes	complemented
209	#2283	C₂×C₁₃	1	1	yes	characteristic, complemented
210	C₂³×C₁₃	—	2	2	no	—
211	C₂³×C₁₃	—	2	2	no	—
212	C₂³×C₁₃	—	2	2	no	—
213	C₂³×C₁₃	—	2	2	no	—
214	C₂³×C₁₃	—	2	4	no	—
215	C₂³×C₁₃	—	2	4	no	—
216	C₂³×C₁₃	—	2	4	no	—
217	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
218	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
219	Q₈×C₁₃	—	4	4	no	—
220	Q₈×C₁₃	—	4	8	no	—
221	Q₈×C₁₃	—	4	8	no	—
222	D₄×C₁₃	—	4	4	no	—
223	D₄×C₁₃	—	4	8	no	—
224	C₂×C₄×C₁₃	—	2	2	no	—
225	C₂×C₄×C₁₃	—	2	2	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	—	2	2	no	—
231	C₂×C₄×C₁₃	—	2	2	no	—
232	C₂×C₄×C₁₃	—	2	4	no	—
233	C₂×C₄×C₁₃	—	2	4	no	—
234	C₂×C₄×C₁₃	—	2	2	no	—
235	C₂×C₄×C₁₃	—	2	8	no	—
236	C₂×C₄×C₁₃	—	2	4	no	—
237	C₂×C₄×C₁₃	—	2	8	no	—
238	C₂×C₄×C₁₃	—	2	4	no	—
239	C₂×C₄×C₁₃	—	2	8	no	—
240	C₂×C₄×C₁₃	—	2	8	no	—
241	C₂×C₄×C₁₃	—	2	4	no	—
242	C₂×C₄×C₁₃	—	2	4	no	—
243	C₂×C₄×C₁₃	—	2	4	no	—
244	C₂×C₄×C₁₃	—	4	4	no	—
245	C₂×C₄×C₁₃	—	4	4	no	—
246	C₂×C₄×C₁₃	—	4	8	no	—
247	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
248	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
249	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
250	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
251	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
252	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
253	C₂×C₄×C₁₃	2₋¹⁺⁴	1	4	yes	—
254	#533	—	2	8	no	—
255	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
256	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
257	#529	—	2	8	no	—
258	C₂×#126	C₂²×C₁₃	1	2	yes	—
259	C₂×#125	C₂²×C₁₃	1	2	yes	—
260	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
261	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
262	C₂×#123	C₂²×C₁₃	1	2	yes	—
263	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
264	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
265	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
266	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
267	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
268	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
269	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
270	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
271	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
272	C₂×#117	C₂²×C₁₃	1	2	yes	—
273	C₂×#117	C₂²×C₁₃	1	2	yes	—
274	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
275	#400	C₂²×C₁₃	1	4	yes	—
276	#400	C₂²×C₁₃	1	4	yes	—
277	#400	C₂²×C₁₃	1	4	yes	—
278	#399	C₂²×C₁₃	1	4	yes	—
279	#399	C₂²×C₁₃	1	4	yes	—
280	#398	C₂²×C₁₃	1	4	yes	—
281	#398	C₂²×C₁₃	1	4	yes	—
282	#398	C₂²×C₁₃	1	4	yes	—
283	#398	C₂²×C₁₃	1	8	yes	—
284	#397	C₂²×C₁₃	1	8	yes	—
285	#397	C₂²×C₁₃	1	4	yes	—
286	#397	C₂²×C₁₃	1	4	yes	—
287	#396	C₂²×C₁₃	1	8	yes	—
288	#395	C₂²×C₁₃	1	4	yes	—
289	#395	C₂²×C₁₃	1	4	yes	—
290	#395	C₂²×C₁₃	1	4	yes	—
291	#394	C₂²×C₁₃	1	4	yes	—
292	#394	C₂²×C₁₃	1	8	yes	—
293	#393	C₂²×C₁₃	1	4	yes	—
294	#393	C₂²×C₁₃	1	4	yes	—
295	#383	C₂²×C₁₃	1	2	yes	—
296	#382	C₂²×C₁₃	1	2	yes	—
297	#381	C₂²×C₁₃	1	2	yes	—
298	#380	C₂²×C₁₃	1	2	yes	—
299	C₄×C₄⋊C₄	C₂²×C₁₃	1	8	yes	—
300	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
301	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
302	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	—
303	#376	C₂²×C₁₃	1	2	yes	—
304	C₂²×C₁₃	—	2	2	no	—
305	C₂²×C₁₃	—	2	2	no	—
306	C₂²×C₁₃	—	2	2	no	—
307	C₂²×C₁₃	—	4	4	no	—
308	C₂²×C₁₃	—	4	2	no	—
309	C₂²×C₁₃	—	4	2	no	—
310	C₂²×C₁₃	—	4	2	no	—
311	C₂²×C₁₃	—	4	8	no	—
312	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
313	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
314	C₂²×C₁₃	#585	1	2	yes	—
315	C₂²×C₁₃	#585	1	2	yes	—
316	C₄×C₁₃	—	2	2	no	—
317	C₄×C₁₃	—	2	2	no	—
318	C₄×C₁₃	—	2	2	no	—
319	C₄×C₁₃	—	2	2	no	—
320	C₄×C₁₃	—	2	2	no	—
321	C₄×C₁₃	—	4	2	no	—
322	C₄×C₁₃	—	4	2	no	—
323	C₄×C₁₃	—	4	2	no	—
324	C₄×C₁₃	—	4	4	no	—
325	C₄×C₁₃	—	4	4	no	—
326	C₄×C₁₃	—	4	8	no	—
327	C₄×C₁₃	#536	1	4	yes	—
328	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
329	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
330	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
331	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
332	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
333	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
334	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
335	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
336	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
337	C₄⋊Q₈	—	2	4	no	—
338	C₄⋊Q₈	—	2	4	no	—
339	#126	—	2	8	no	—
340	#125	—	2	4	no	—
341	#125	—	2	8	no	—
342	#124	—	2	4	no	—
343	#123	—	2	8	no	—
344	C₂²⋊Q₈	—	2	4	no	—
345	C₂²⋊Q₈	—	2	8	no	—
346	C₂²⋊Q₈	—	2	8	no	—
347	#121	—	2	4	no	—
348	C₄×Q₈	—	2	4	no	—
349	C₄×Q₈	—	2	8	no	—
350	C₄×Q₈	—	2	8	no	—
351	C₄×D₄	—	2	8	no	—
352	C₄×D₄	—	2	4	no	—
353	#117	—	2	8	no	—
354	#117	—	2	8	no	—
355	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
356	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
357	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
358	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
359	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
360	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
361	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
362	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
363	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
364	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
365	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
366	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
367	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
368	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
369	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
370	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
371	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
372	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
373	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
374	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
375	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
376	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
377	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
378	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
379	C₂×C₄²	D₄×C₁₃	1	8	yes	—
380	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
381	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
382	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
383	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
384	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
385	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
386	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
387	#95	C₂³×C₁₃	1	4	yes	—
388	#95	C₂³×C₁₃	1	4	yes	—
389	#95	C₂³×C₁₃	1	4	yes	—
390	#95	C₂³×C₁₃	1	8	yes	—
391	#95	C₂³×C₁₃	1	8	yes	—
392	#95	C₂³×C₁₃	1	4	yes	—
393	#95	C₂³×C₁₃	1	8	yes	—
394	#95	C₂³×C₁₃	1	8	yes	—
395	C₂×C₁₃	—	4	2	no	—
396	C₂×C₁₃	—	8	2	no	—
397	C₂×C₁₃	C₂×#536	1	1	yes	characteristic
398	C₂×C₁₃	#3449	1	1	yes	characteristic
399	C₂×C₁₃	#3449	1	1	yes	characteristic
400	C₂×C₁₃	#3531	1	4	yes	—
401	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
402	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
403	C₂×Q₈	—	2	2	no	—
404	C₂×Q₈	—	2	4	no	—
405	C₂×Q₈	—	2	4	no	—
406	C₂×Q₈	—	4	2	no	—
407	C₂×Q₈	—	4	4	no	—
408	C₂×Q₈	—	4	4	no	—
409	C₂×D₄	—	2	4	no	—
410	C₂×D₄	—	2	2	no	—
411	C₂×D₄	—	4	2	no	—
412	C₂×D₄	—	4	4	no	—
413	C₂²×C₄	—	2	4	no	—
414	C₂²×C₄	—	2	4	no	—
415	C₂²×C₄	—	2	8	no	—
416	C₂²×C₄	—	4	2	no	—
417	C₂²×C₄	—	4	2	no	—
418	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
419	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
420	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
421	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
422	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
423	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
424	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
425	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
426	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
427	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
428	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
429	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
430	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
431	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
432	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
433	C₄⋊C₄	—	2	4	no	—
434	C₄⋊C₄	—	2	4	no	—
435	C₄⋊C₄	—	2	4	no	—
436	C₄⋊C₄	—	2	4	no	—
437	C₄⋊C₄	—	2	2	no	—
438	C₄⋊C₄	—	2	4	no	—
439	C₄⋊C₄	—	2	2	no	—
440	C₄⋊C₄	—	2	8	no	—
441	C₄⋊C₄	—	2	8	no	—
442	C₄⋊C₄	—	2	4	no	—
443	C₄⋊C₄	—	2	4	no	—
444	C₄⋊C₄	—	2	4	no	—
445	C₄⋊C₄	—	4	4	no	—
446	C₄⋊C₄	—	4	8	no	—
447	C₄⋊C₄	—	4	8	no	—
448	C₂²⋊C₄	—	2	8	no	—
449	C₂²⋊C₄	—	2	4	no	—
450	C₂²⋊C₄	—	2	4	no	—
451	C₂²⋊C₄	—	2	4	no	—
452	C₂²⋊C₄	—	2	4	no	—
453	C₂²⋊C₄	—	2	4	no	—
454	C₂²⋊C₄	—	4	4	no	—
455	C₂²⋊C₄	—	4	8	no	—
456	C₂²⋊C₄	—	4	8	no	—
457	C₄²	—	2	4	no	—
458	C₄²	—	2	8	no	—
459	C₄²	—	2	8	no	—
460	C₄²	C₂×D₄×C₁₃	1	4	yes	—
461	C₄²	C₂×D₄×C₁₃	1	4	yes	—
462	C₄²	C₂×D₄×C₁₃	1	4	yes	—
463	C₄²	C₂×D₄×C₁₃	1	4	yes	—
464	C₁₃	#36699	1	1	yes	characteristic, direct product factor, Sylow
465	C₂³	—	2	2	no	—
466	C₂³	—	2	2	no	—
467	C₂³	—	2	2	no	—
468	C₂³	—	2	2	no	—
469	C₂³	—	2	4	no	—
470	C₂³	—	2	4	no	—
471	C₂³	—	2	4	no	—
472	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
473	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
474	Q₈	—	4	4	no	—
475	Q₈	—	4	8	no	—
476	Q₈	—	4	8	no	—
477	D₄	—	4	4	no	—
478	D₄	—	4	8	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	8	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	4	no	—
488	C₂×C₄	—	2	4	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	8	no	—
491	C₂×C₄	—	2	4	no	—
492	C₂×C₄	—	2	8	no	—
493	C₂×C₄	—	2	4	no	—
494	C₂×C₄	—	2	8	no	—
495	C₂×C₄	—	2	8	no	—
496	C₂×C₄	—	2	4	no	—
497	C₂×C₄	—	2	4	no	—
498	C₂×C₄	—	2	4	no	—
499	C₂×C₄	—	4	4	no	—
500	C₂×C₄	—	4	4	no	—
501	C₂×C₄	—	4	8	no	—
502	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
503	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
504	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
505	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
506	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
507	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
508	C₂×C₄	C₁₃×2₋¹⁺⁴	1	4	yes	—
509	C₂²	—	2	2	no	—
510	C₂²	—	2	2	no	—
511	C₂²	—	2	2	no	—
512	C₂²	—	4	4	no	—
513	C₂²	—	4	8	no	—
514	C₂²	—	4	2	no	—
515	C₂²	—	4	2	no	—
516	C₂²	—	4	2	no	—
517	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
518	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
519	C₂²	C₁₃×#585	1	2	yes	—
520	C₂²	C₁₃×#585	1	2	yes	—
521	C₄	—	2	2	no	—
522	C₄	—	2	2	no	—
523	C₄	—	2	2	no	—
524	C₄	—	2	2	no	—
525	C₄	—	2	2	no	—
526	C₄	—	4	8	no	—
527	C₄	—	4	2	no	—
528	C₄	—	4	2	no	—
529	C₄	—	4	2	no	—
530	C₄	—	4	4	no	—
531	C₄	—	4	4	no	—
532	C₄	C₁₃×#536	1	4	yes	—
533	C₂	—	4	2	no	—
534	C₂	—	8	2	no	—
535	C₂	C₂×C₁₃×#536	1	1	yes	characteristic
536	C₂	C₁₃×#3449	1	1	yes	characteristic
537	C₂	C₁₃×#3449	1	1	yes	characteristic
538	C₂	C₁₃×#3531	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
socle	C₂³×C₁₃	C₂⁵
prime radical	C₂×C₁₃×#121	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#533	C₂	semidirect
3. C₁₃×#2822	C₂	semidirect
4. C₁₃×#2821	C₂	semidirect
5. C₁₃×#2821	C₂	semidirect
6. C₁₃×#2820	C₂	semidirect
7. C₁₃×#2817	C₂	semidirect
9. C₁₃×#2814	C₂	semidirect
10. C₁₃×#2399	C₂	semidirect
11. C₁₃×#2398	C₂	semidirect
12. C₁₃×#2396	C₂	semidirect
13. C₁₃×#2395	C₂	semidirect
14. C₁₃×#2283	C₂	semidirect
132. #36699	C₁₃	direct (N × H)
196. C₂×#533	C₂×C₁₃	semidirect
198. #2822	C₂×C₁₃	semidirect
199. #2821	C₂×C₁₃	semidirect
200. #2821	C₂×C₁₃	semidirect
201. #2820	C₂×C₁₃	semidirect
202. #2817	C₂×C₁₃	semidirect
204. #2814	C₂×C₁₃	semidirect
205. #2399	C₂×C₁₃	semidirect
206. #2398	C₂×C₁₃	semidirect
207. #2396	C₂×C₁₃	semidirect
208. #2395	C₂×C₁₃	semidirect
209. #2283	C₂×C₁₃	semidirect
464. C₁₃	#36699	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#533	2
C₂×C₁₃×#529	2
C₁₃×#2822	2
C₁₃×#2821	2
C₁₃×#2820	2
C₁₃×#2817	2
C₁₃×#2816	2
C₁₃×#2814	2
C₁₃×#2399	2
C₁₃×#2398	2
C₁₃×#2396	2
C₁₃×#2395	2
C₁₃×#2283	2
#36699	13

Subgroups — C13×#36699 #15723038

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#36699 #15723038