Subgroups — C₁₃×#34602 #15720941

Order 3328.

2294 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#529	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2637	C₂	1	4	yes	maximal, complemented
4	C₁₃×#2634	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2632	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2627	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2623	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2618	C₂	1	2	yes	maximal
9	C₁₃×#2614	C₂	1	2	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	C₄×C₁₃×#123	C₂	1	4	yes	maximal, complemented
14	C₁₃×#2283	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
16	C₁₃×#529	—	2	8	no	—
17	C₂×C₁₃×#126	C₂²	1	2	yes	—
18	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#123	C₂²	1	4	yes	—
21	C₂×C₁₃×#123	C₂²	1	2	yes	—
22	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₁₃	—	2	8	no	—
25	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
26	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
27	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
28	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
29	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#117	C₂²	1	2	yes	—
33	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
34	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
36	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
37	C₁₃×#400	C₂²	1	4	yes	—
38	C₁₃×#400	C₂²	1	4	yes	—
39	C₁₃×#399	C₂²	1	4	yes	—
40	C₁₃×#398	C₂²	1	4	yes	—
41	C₁₃×#398	C₂²	1	4	yes	—
42	C₁₃×#398	C₂²	1	8	yes	—
43	C₁₃×#397	C₂²	1	4	yes	—
44	C₁₃×#396	C₂²	1	8	yes	—
45	C₁₃×#395	C₂²	1	4	yes	—
46	C₁₃×#395	C₂²	1	4	yes	—
47	C₁₃×#395	C₂²	1	4	yes	—
48	C₁₃×#394	C₂²	1	4	yes	—
49	C₁₃×#393	C₂²	1	4	yes	—
50	C₁₃×#393	C₂²	1	4	yes	—
51	C₁₃×#388	C₂²	1	8	yes	—
52	C₁₃×#387	C₂²	1	8	yes	—
53	C₁₃×#386	C₂²	1	4	yes	—
54	C₁₃×#385	C₂²	1	4	yes	—
55	C₁₃×#383	C₂²	1	2	yes	—
56	C₁₃×#382	C₂²	1	2	yes	—
57	C₁₃×#381	C₂²	1	2	yes	—
58	C₁₃×#381	C₂²	1	4	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	—	2	4	no	—
66	C₂²×Q₈×C₁₃	—	2	8	no	—
67	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
68	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
69	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
70	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
71	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
73	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
76	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
77	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
78	C₁₃×#126	—	2	8	no	—
79	C₁₃×#125	—	2	4	no	—
80	C₁₃×#124	—	2	4	no	—
81	C₁₃×#123	—	2	8	no	—
82	C₁₃×#123	—	2	16	no	—
83	C₁₃×C₂²⋊Q₈	—	2	4	no	—
84	C₁₃×#121	—	2	4	no	—
85	C₄×Q₈×C₁₃	—	2	8	no	—
86	C₄×Q₈×C₁₃	—	2	8	no	—
87	C₄×Q₈×C₁₃	—	2	8	no	—
88	C₄×Q₈×C₁₃	—	2	8	no	—
89	C₄×Q₈×C₁₃	—	2	4	no	—
90	C₄×D₄×C₁₃	—	2	8	no	—
91	C₄×D₄×C₁₃	—	2	4	no	—
92	C₁₃×#117	—	2	8	no	—
93	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
94	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
95	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
96	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
97	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
98	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
99	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
100	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	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	2	yes	—
105	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
106	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
107	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
108	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
109	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	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	2	yes	—
114	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
115	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
116	C₂×C₄²×C₁₃	—	2	8	no	—
117	C₂×C₄²×C₁₃	D₄	1	8	yes	—
118	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
119	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
120	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
121	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
122	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
123	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
124	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
125	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
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	4	yes	—
130	C₁₃×#95	C₂³	1	8	yes	—
131	C₁₃×#95	C₂³	1	8	yes	—
132	C₁₃×#95	C₂³	1	4	yes	—
133	C₁₃×#95	C₂³	1	4	yes	—
134	#34602	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
135	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
136	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
137	C₂×Q₈×C₁₃	—	2	32	no	—
138	C₂×Q₈×C₁₃	—	2	4	no	—
139	C₂×Q₈×C₁₃	—	2	4	no	—
140	C₂×Q₈×C₁₃	—	2	2	no	—
141	C₂×Q₈×C₁₃	—	2	8	no	—
142	C₂×Q₈×C₁₃	—	2	8	no	—
143	C₂×Q₈×C₁₃	—	4	2	no	—
144	C₂×D₄×C₁₃	—	2	4	no	—
145	C₂×D₄×C₁₃	—	2	8	no	—
146	C₂×D₄×C₁₃	—	2	2	no	—
147	C₂×D₄×C₁₃	—	4	2	no	—
148	C₂²×C₄×C₁₃	—	2	4	no	—
149	C₂²×C₄×C₁₃	—	2	4	no	—
150	C₂²×C₄×C₁₃	—	2	4	no	—
151	C₂²×C₄×C₁₃	—	2	4	no	—
152	C₂²×C₄×C₁₃	—	2	4	no	—
153	C₂²×C₄×C₁₃	—	2	4	no	—
154	C₂²×C₄×C₁₃	—	2	8	no	—
155	C₂²×C₄×C₁₃	—	4	2	no	—
156	C₂²×C₄×C₁₃	—	4	4	no	—
157	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
158	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
159	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
160	C₂²×C₄×C₁₃	#41	1	8	yes	—
161	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
162	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
163	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
164	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
165	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
166	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
167	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
168	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
169	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
170	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
171	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
172	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
173	C₁₃×C₄⋊C₄	—	2	8	no	—
174	C₁₃×C₄⋊C₄	—	2	8	no	—
175	C₁₃×C₄⋊C₄	—	2	4	no	—
176	C₁₃×C₄⋊C₄	—	2	4	no	—
177	C₁₃×C₄⋊C₄	—	2	4	no	—
178	C₁₃×C₄⋊C₄	—	2	4	no	—
179	C₁₃×C₄⋊C₄	—	2	2	no	—
180	C₁₃×C₄⋊C₄	—	2	4	no	—
181	C₁₃×C₄⋊C₄	—	2	2	no	—
182	C₁₃×C₄⋊C₄	—	2	4	no	—
183	C₁₃×C₄⋊C₄	—	2	16	no	—
184	C₁₃×C₄⋊C₄	—	4	4	no	—
185	C₁₃×C₄⋊C₄	—	4	8	no	—
186	C₁₃×C₂²⋊C₄	—	2	4	no	—
187	C₁₃×C₂²⋊C₄	—	2	8	no	—
188	C₁₃×C₂²⋊C₄	—	2	4	no	—
189	C₁₃×C₂²⋊C₄	—	2	4	no	—
190	C₁₃×C₂²⋊C₄	—	2	4	no	—
191	C₁₃×C₂²⋊C₄	—	2	4	no	—
192	C₁₃×C₂²⋊C₄	—	2	16	no	—
193	C₁₃×C₂²⋊C₄	—	4	8	no	—
194	C₄²×C₁₃	—	2	8	no	—
195	C₄²×C₁₃	—	2	8	no	—
196	C₄²×C₁₃	—	2	4	no	—
197	C₄²×C₁₃	—	2	8	no	—
198	C₄²×C₁₃	C₂×D₄	1	4	yes	—
199	C₄²×C₁₃	C₂×D₄	1	4	yes	—
200	C₄²×C₁₃	C₂×D₄	1	4	yes	—
201	C₄²×C₁₃	C₂×D₄	1	4	yes	—
202	C₂×#529	C₂×C₁₃	1	1	yes	characteristic
203	C₂²×C₄×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
204	#2637	C₂×C₁₃	1	4	yes	complemented
205	#2634	C₂×C₁₃	1	2	yes	complemented
206	#2632	C₂×C₁₃	1	2	yes	complemented
207	#2627	C₂×C₁₃	1	2	yes	complemented
208	#2623	C₂×C₁₃	1	2	yes	complemented
209	#2618	C₂×C₁₃	1	2	yes	—
210	#2614	C₂×C₁₃	1	2	yes	complemented
211	#2399	C₂×C₁₃	1	2	yes	complemented
212	#2398	C₂×C₁₃	1	2	yes	complemented
213	#2396	C₂×C₁₃	1	4	yes	complemented
214	C₄×#123	C₂×C₁₃	1	4	yes	complemented
215	#2283	C₂×C₁₃	1	1	yes	characteristic, complemented
216	C₂³×C₁₃	—	2	2	no	—
217	C₂³×C₁₃	—	2	2	no	—
218	C₂³×C₁₃	—	2	2	no	—
219	C₂³×C₁₃	—	2	4	no	—
220	C₂³×C₁₃	—	2	4	no	—
221	C₂³×C₁₃	—	2	4	no	—
222	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
223	C₂³×C₁₃	C₂×#41	1	4	yes	—
224	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
225	Q₈×C₁₃	—	2	16	no	—
226	Q₈×C₁₃	—	2	16	no	—
227	Q₈×C₁₃	—	4	4	no	—
228	D₄×C₁₃	—	4	4	no	—
229	D₄×C₁₃	—	4	8	no	—
230	C₂×C₄×C₁₃	—	2	8	no	—
231	C₂×C₄×C₁₃	—	2	16	no	—
232	C₂×C₄×C₁₃	—	2	4	no	—
233	C₂×C₄×C₁₃	—	2	2	no	—
234	C₂×C₄×C₁₃	—	2	2	no	—
235	C₂×C₄×C₁₃	—	2	4	no	—
236	C₂×C₄×C₁₃	—	2	2	no	—
237	C₂×C₄×C₁₃	—	2	2	no	—
238	C₂×C₄×C₁₃	—	2	2	no	—
239	C₂×C₄×C₁₃	—	2	8	no	—
240	C₂×C₄×C₁₃	—	2	4	no	—
241	C₂×C₄×C₁₃	—	2	2	no	—
242	C₂×C₄×C₁₃	—	2	2	no	—
243	C₂×C₄×C₁₃	—	2	2	no	—
244	C₂×C₄×C₁₃	—	2	8	no	—
245	C₂×C₄×C₁₃	—	2	4	no	—
246	C₂×C₄×C₁₃	—	2	8	no	—
247	C₂×C₄×C₁₃	—	2	4	no	—
248	C₂×C₄×C₁₃	—	2	8	no	—
249	C₂×C₄×C₁₃	—	2	8	no	—
250	C₂×C₄×C₁₃	—	2	4	no	—
251	C₂×C₄×C₁₃	—	4	4	no	—
252	C₂×C₄×C₁₃	—	4	8	no	—
253	C₂×C₄×C₁₃	—	4	8	no	—
254	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
255	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
256	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
257	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
258	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
259	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
260	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
261	C₂×C₄×C₁₃	2₋¹⁺⁴	1	4	yes	—
262	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
263	#529	—	2	8	no	—
264	C₂×#126	C₂²×C₁₃	1	2	yes	—
265	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
266	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
267	C₂×#123	C₂²×C₁₃	1	4	yes	—
268	C₂×#123	C₂²×C₁₃	1	2	yes	—
269	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
270	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
271	C₂×C₄×Q₈	—	2	8	no	—
272	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
273	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
274	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
275	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
276	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
277	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
278	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
279	C₂×#117	C₂²×C₁₃	1	2	yes	—
280	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
281	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
282	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
283	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
284	#400	C₂²×C₁₃	1	4	yes	—
285	#400	C₂²×C₁₃	1	4	yes	—
286	#399	C₂²×C₁₃	1	4	yes	—
287	#398	C₂²×C₁₃	1	4	yes	—
288	#398	C₂²×C₁₃	1	4	yes	—
289	#398	C₂²×C₁₃	1	8	yes	—
290	#397	C₂²×C₁₃	1	4	yes	—
291	#396	C₂²×C₁₃	1	8	yes	—
292	#395	C₂²×C₁₃	1	4	yes	—
293	#395	C₂²×C₁₃	1	4	yes	—
294	#395	C₂²×C₁₃	1	4	yes	—
295	#394	C₂²×C₁₃	1	4	yes	—
296	#393	C₂²×C₁₃	1	4	yes	—
297	#393	C₂²×C₁₃	1	4	yes	—
298	#388	C₂²×C₁₃	1	8	yes	—
299	#387	C₂²×C₁₃	1	8	yes	—
300	#386	C₂²×C₁₃	1	4	yes	—
301	#385	C₂²×C₁₃	1	4	yes	—
302	#383	C₂²×C₁₃	1	2	yes	—
303	#382	C₂²×C₁₃	1	2	yes	—
304	#381	C₂²×C₁₃	1	2	yes	—
305	#381	C₂²×C₁₃	1	4	yes	—
306	#380	C₂²×C₁₃	1	2	yes	—
307	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
308	C₄×C₄⋊C₄	C₂²×C₁₃	1	8	yes	—
309	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	—
310	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
311	#376	C₂²×C₁₃	1	2	yes	—
312	C₂²×C₁₃	—	2	2	no	—
313	C₂²×C₁₃	—	2	2	no	—
314	C₂²×C₁₃	—	2	8	no	—
315	C₂²×C₁₃	—	4	2	no	—
316	C₂²×C₁₃	—	4	2	no	—
317	C₂²×C₁₃	—	4	2	no	—
318	C₂²×C₁₃	—	4	8	no	—
319	C₂²×C₁₃	#525	1	4	yes	—
320	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
321	C₂²×C₁₃	C₂²×#41	1	2	yes	—
322	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
323	C₂²×C₁₃	#585	1	2	yes	—
324	C₄×C₁₃	—	2	2	no	—
325	C₄×C₁₃	—	2	2	no	—
326	C₄×C₁₃	—	2	8	no	—
327	C₄×C₁₃	—	2	2	no	—
328	C₄×C₁₃	—	2	2	no	—
329	C₄×C₁₃	—	2	2	no	—
330	C₄×C₁₃	—	4	2	no	—
331	C₄×C₁₃	—	4	2	no	—
332	C₄×C₁₃	—	4	4	no	—
333	C₄×C₁₃	—	4	2	no	—
334	C₄×C₁₃	—	4	8	no	—
335	C₄×C₁₃	#536	1	4	yes	—
336	C₂²×Q₈	—	2	4	no	—
337	C₂²×Q₈	—	2	8	no	—
338	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
339	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
340	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
341	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
342	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
343	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
344	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
345	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
346	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
347	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
348	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
349	#126	—	2	8	no	—
350	#125	—	2	4	no	—
351	#124	—	2	4	no	—
352	#123	—	2	8	no	—
353	#123	—	2	16	no	—
354	C₂²⋊Q₈	—	2	4	no	—
355	#121	—	2	4	no	—
356	C₄×Q₈	—	2	8	no	—
357	C₄×Q₈	—	2	8	no	—
358	C₄×Q₈	—	2	8	no	—
359	C₄×Q₈	—	2	8	no	—
360	C₄×Q₈	—	2	4	no	—
361	C₄×D₄	—	2	8	no	—
362	C₄×D₄	—	2	4	no	—
363	#117	—	2	8	no	—
364	C₂×C₄⋊C₄	—	2	8	no	—
365	C₂×C₄⋊C₄	—	2	4	no	—
366	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
367	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
368	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
369	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
370	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
371	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
372	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
373	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
374	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
375	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
376	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
377	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
378	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
379	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
380	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
381	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
382	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
383	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
384	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
385	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
386	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
387	C₂×C₄²	—	2	8	no	—
388	C₂×C₄²	D₄×C₁₃	1	8	yes	—
389	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
390	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
391	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
392	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
393	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
394	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
395	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
396	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
397	#95	C₂³×C₁₃	1	4	yes	—
398	#95	C₂³×C₁₃	1	4	yes	—
399	#95	C₂³×C₁₃	1	8	yes	—
400	#95	C₂³×C₁₃	1	4	yes	—
401	#95	C₂³×C₁₃	1	8	yes	—
402	#95	C₂³×C₁₃	1	4	yes	—
403	#95	C₂³×C₁₃	1	8	yes	—
404	#95	C₂³×C₁₃	1	8	yes	—
405	C₂×C₁₃	—	2	4	no	—
406	C₂×C₁₃	—	8	2	no	—
407	C₂×C₁₃	C₂×#525	1	1	yes	characteristic
408	C₂×C₁₃	C₂×#536	1	1	yes	characteristic
409	C₂×C₁₃	#3449	1	1	yes	characteristic
410	C₂×C₁₃	#3461	1	4	yes	—
411	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
412	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
413	C₂×Q₈	—	2	32	no	—
414	C₂×Q₈	—	2	4	no	—
415	C₂×Q₈	—	2	4	no	—
416	C₂×Q₈	—	2	2	no	—
417	C₂×Q₈	—	2	8	no	—
418	C₂×Q₈	—	2	8	no	—
419	C₂×Q₈	—	4	2	no	—
420	C₂×D₄	—	2	4	no	—
421	C₂×D₄	—	2	8	no	—
422	C₂×D₄	—	2	2	no	—
423	C₂×D₄	—	4	2	no	—
424	C₂²×C₄	—	2	4	no	—
425	C₂²×C₄	—	2	4	no	—
426	C₂²×C₄	—	2	4	no	—
427	C₂²×C₄	—	2	4	no	—
428	C₂²×C₄	—	2	4	no	—
429	C₂²×C₄	—	2	4	no	—
430	C₂²×C₄	—	2	8	no	—
431	C₂²×C₄	—	4	2	no	—
432	C₂²×C₄	—	4	4	no	—
433	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
434	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
435	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
436	C₂²×C₄	C₁₃×#41	1	8	yes	—
437	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
438	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
439	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
440	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
441	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
442	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
443	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
444	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
445	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
446	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
447	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
448	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
449	C₄⋊C₄	—	2	8	no	—
450	C₄⋊C₄	—	2	8	no	—
451	C₄⋊C₄	—	2	4	no	—
452	C₄⋊C₄	—	2	4	no	—
453	C₄⋊C₄	—	2	4	no	—
454	C₄⋊C₄	—	2	4	no	—
455	C₄⋊C₄	—	2	2	no	—
456	C₄⋊C₄	—	2	4	no	—
457	C₄⋊C₄	—	2	2	no	—
458	C₄⋊C₄	—	2	4	no	—
459	C₄⋊C₄	—	2	16	no	—
460	C₄⋊C₄	—	4	4	no	—
461	C₄⋊C₄	—	4	8	no	—
462	C₂²⋊C₄	—	2	4	no	—
463	C₂²⋊C₄	—	2	8	no	—
464	C₂²⋊C₄	—	2	4	no	—
465	C₂²⋊C₄	—	2	4	no	—
466	C₂²⋊C₄	—	2	4	no	—
467	C₂²⋊C₄	—	2	4	no	—
468	C₂²⋊C₄	—	2	16	no	—
469	C₂²⋊C₄	—	4	8	no	—
470	C₄²	—	2	8	no	—
471	C₄²	—	2	8	no	—
472	C₄²	—	2	4	no	—
473	C₄²	—	2	8	no	—
474	C₄²	C₂×D₄×C₁₃	1	4	yes	—
475	C₄²	C₂×D₄×C₁₃	1	4	yes	—
476	C₄²	C₂×D₄×C₁₃	1	4	yes	—
477	C₄²	C₂×D₄×C₁₃	1	4	yes	—
478	C₁₃	#34602	1	1	yes	characteristic, direct product factor, Sylow
479	C₂³	—	2	2	no	—
480	C₂³	—	2	2	no	—
481	C₂³	—	2	2	no	—
482	C₂³	—	2	4	no	—
483	C₂³	—	2	4	no	—
484	C₂³	—	2	4	no	—
485	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
486	C₂³	C₂×C₁₃×#41	1	4	yes	—
487	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
488	Q₈	—	2	16	no	—
489	Q₈	—	2	16	no	—
490	Q₈	—	4	4	no	—
491	D₄	—	4	4	no	—
492	D₄	—	4	8	no	—
493	C₂×C₄	—	2	8	no	—
494	C₂×C₄	—	2	16	no	—
495	C₂×C₄	—	2	4	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	4	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	8	no	—
503	C₂×C₄	—	2	4	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	8	no	—
508	C₂×C₄	—	2	4	no	—
509	C₂×C₄	—	2	8	no	—
510	C₂×C₄	—	2	4	no	—
511	C₂×C₄	—	2	8	no	—
512	C₂×C₄	—	2	8	no	—
513	C₂×C₄	—	2	4	no	—
514	C₂×C₄	—	4	4	no	—
515	C₂×C₄	—	4	8	no	—
516	C₂×C₄	—	4	8	no	—
517	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
518	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
519	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
520	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
521	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
522	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
523	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
524	C₂×C₄	C₁₃×2₋¹⁺⁴	1	4	yes	—
525	C₂²	—	2	2	no	—
526	C₂²	—	2	2	no	—
527	C₂²	—	2	8	no	—
528	C₂²	—	4	2	no	—
529	C₂²	—	4	2	no	—
530	C₂²	—	4	2	no	—
531	C₂²	—	4	8	no	—
532	C₂²	C₁₃×#525	1	4	yes	—
533	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
534	C₂²	C₂²×C₁₃×#41	1	2	yes	—
535	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
536	C₂²	C₁₃×#585	1	2	yes	—
537	C₄	—	2	2	no	—
538	C₄	—	2	2	no	—
539	C₄	—	2	8	no	—
540	C₄	—	2	2	no	—
541	C₄	—	2	2	no	—
542	C₄	—	2	2	no	—
543	C₄	—	4	2	no	—
544	C₄	—	4	2	no	—
545	C₄	—	4	4	no	—
546	C₄	—	4	2	no	—
547	C₄	—	4	8	no	—
548	C₄	C₁₃×#536	1	4	yes	—
549	C₂	—	2	4	no	—
550	C₂	—	8	2	no	—
551	C₂	C₂×C₁₃×#525	1	1	yes	characteristic
552	C₂	C₂×C₁₃×#536	1	1	yes	characteristic
553	C₂	C₁₃×#3449	1	1	yes	characteristic
554	C₂	C₁₃×#3461	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
2. C₂²×C₄×Q₈×C₁₃	C₂	semidirect
3. C₁₃×#2637	C₂	semidirect
4. C₁₃×#2634	C₂	semidirect
5. C₁₃×#2632	C₂	semidirect
6. C₁₃×#2627	C₂	semidirect
7. C₁₃×#2623	C₂	semidirect
9. C₁₃×#2614	C₂	semidirect
10. C₁₃×#2399	C₂	semidirect
11. C₁₃×#2398	C₂	semidirect
12. C₁₃×#2396	C₂	semidirect
13. C₄×C₁₃×#123	C₂	semidirect
14. C₁₃×#2283	C₂	semidirect
134. #34602	C₁₃	direct (N × H)
203. C₂²×C₄×Q₈	C₂×C₁₃	semidirect
204. #2637	C₂×C₁₃	semidirect
205. #2634	C₂×C₁₃	semidirect
206. #2632	C₂×C₁₃	semidirect
207. #2627	C₂×C₁₃	semidirect
208. #2623	C₂×C₁₃	semidirect
210. #2614	C₂×C₁₃	semidirect
211. #2399	C₂×C₁₃	semidirect
212. #2398	C₂×C₁₃	semidirect
213. #2396	C₂×C₁₃	semidirect
214. C₄×#123	C₂×C₁₃	semidirect
215. #2283	C₂×C₁₃	semidirect
478. C₁₃	#34602	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×#529	2
C₂²×C₄×Q₈×C₁₃	2
C₁₃×#2637	2
C₁₃×#2634	2
C₁₃×#2632	2
C₁₃×#2627	2
C₁₃×#2623	2
C₁₃×#2618	2
C₁₃×#2614	2
C₁₃×#2399	2
C₁₃×#2398	2
C₁₃×#2396	2
C₄×C₁₃×#123	2
C₁₃×#2283	2
#34602	13

Subgroups — C13×#34602 #15720941

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34602 #15720941