Subgroups — C₁₃×#34627 #15720966

Order 3328.

2294 conjugacy classes of subgroups.

The subgroup lattice has 564 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×C₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2638	C₂	1	4	yes	maximal, complemented
4	C₁₃×#2634	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2633	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2628	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2625	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2621	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2616	C₂	1	2	yes	maximal
10	C₁₃×#2399	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2398	C₂	1	2	yes	maximal, complemented
12	C₁₃×#2395	C₂	1	4	yes	maximal, complemented
13	C₄×C₁₃×C₂²⋊Q₈	C₂	1	4	yes	maximal, complemented
14	C₁₃×#2283	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
16	C₁₃×#533	—	2	8	no	—
17	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#125	C₂²	1	2	yes	—
20	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
21	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
22	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
23	C₄×C₁₃×#41	—	2	8	no	—
24	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
25	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
26	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
27	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
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	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×#117	C₂²	1	2	yes	—
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	4	yes	—
43	C₁₃×#397	C₂²	1	4	yes	—
44	C₁₃×#397	C₂²	1	4	yes	—
45	C₁₃×#397	C₂²	1	8	yes	—
46	C₁₃×#395	C₂²	1	4	yes	—
47	C₁₃×#395	C₂²	1	4	yes	—
48	C₁₃×#394	C₂²	1	4	yes	—
49	C₁₃×#394	C₂²	1	8	yes	—
50	C₁₃×#393	C₂²	1	4	yes	—
51	C₁₃×#391	C₂²	1	4	yes	—
52	C₁₃×#389	C₂²	1	4	yes	—
53	C₁₃×#387	C₂²	1	8	yes	—
54	C₁₃×#385	C₂²	1	8	yes	—
55	C₁₃×#383	C₂²	1	2	yes	—
56	C₁₃×#382	C₂²	1	2	yes	—
57	C₁₃×#381	C₂²	1	2	yes	—
58	C₁₃×#380	C₂²	1	2	yes	—
59	C₁₃×#380	C₂²	1	4	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	C₂×C₁₃×#41	—	2	4	no	—
66	C₂×C₁₃×#41	—	2	8	no	—
67	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
68	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
69	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
70	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
71	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
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×C₄⋊Q₈	—	2	4	no	—
79	C₁₃×C₄⋊Q₈	—	2	4	no	—
80	C₁₃×#125	—	2	8	no	—
81	C₁₃×C₂²⋊Q₈	—	2	8	no	—
82	C₁₃×C₂²⋊Q₈	—	2	8	no	—
83	C₁₃×C₂²⋊Q₈	—	2	16	no	—
84	C₄×Q₈×C₁₃	—	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	8	no	—
90	C₄×D₄×C₁₃	—	2	4	no	—
91	C₄×D₄×C₁₃	—	2	4	no	—
92	C₁₃×#117	—	2	4	no	—
93	C₁₃×#117	—	2	8	no	—
94	C₁₃×#117	—	2	8	no	—
95	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
96	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
97	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
98	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
99	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
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	2	yes	—
105	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
106	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
107	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
108	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
109	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
110	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	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×C₄²×C₁₃	—	2	8	no	—
116	C₂×C₄²×C₁₃	D₄	1	8	yes	—
117	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
118	C₂×C₄²×C₁₃	C₂³	1	2	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	4	yes	—
127	C₁₃×#95	C₂³	1	8	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	8	yes	—
132	C₁₃×#95	C₂³	1	4	yes	—
133	C₁₃×#95	C₂³	1	4	yes	—
134	#34627	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
135	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
136	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
137	C₁₃×#41	—	2	32	no	—
138	C₂×Q₈×C₁₃	—	2	2	no	—
139	C₂×Q₈×C₁₃	—	2	4	no	—
140	C₂×Q₈×C₁₃	—	2	4	no	—
141	C₂×Q₈×C₁₃	—	2	4	no	—
142	C₂×Q₈×C₁₃	—	2	8	no	—
143	C₂×Q₈×C₁₃	—	4	4	no	—
144	C₂×D₄×C₁₃	—	2	4	no	—
145	C₂×D₄×C₁₃	—	2	4	no	—
146	C₂×D₄×C₁₃	—	2	4	no	—
147	C₂×D₄×C₁₃	—	2	2	no	—
148	C₂×D₄×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	4	no	—
155	C₂²×C₄×C₁₃	—	2	8	no	—
156	C₂²×C₄×C₁₃	—	4	2	no	—
157	C₂²×C₄×C₁₃	—	4	4	no	—
158	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
159	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
160	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
161	C₂²×C₄×C₁₃	#41	1	8	yes	—
162	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
163	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
164	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
165	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
166	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
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	2	yes	—
172	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
173	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
174	C₁₃×C₄⋊C₄	—	2	4	no	—
175	C₁₃×C₄⋊C₄	—	2	4	no	—
176	C₁₃×C₄⋊C₄	—	2	2	no	—
177	C₁₃×C₄⋊C₄	—	2	2	no	—
178	C₁₃×C₄⋊C₄	—	2	4	no	—
179	C₁₃×C₄⋊C₄	—	2	4	no	—
180	C₁₃×C₄⋊C₄	—	2	8	no	—
181	C₁₃×C₄⋊C₄	—	2	8	no	—
182	C₁₃×C₄⋊C₄	—	2	4	no	—
183	C₁₃×C₄⋊C₄	—	2	4	no	—
184	C₁₃×C₄⋊C₄	—	2	8	no	—
185	C₁₃×C₄⋊C₄	—	2	16	no	—
186	C₁₃×C₄⋊C₄	—	4	8	no	—
187	C₁₃×C₂²⋊C₄	—	2	4	no	—
188	C₁₃×C₂²⋊C₄	—	2	8	no	—
189	C₁₃×C₂²⋊C₄	—	2	16	no	—
190	C₁₃×C₂²⋊C₄	—	2	4	no	—
191	C₁₃×C₂²⋊C₄	—	2	4	no	—
192	C₁₃×C₂²⋊C₄	—	4	4	no	—
193	C₁₃×C₂²⋊C₄	—	4	8	no	—
194	C₄²×C₁₃	—	2	4	no	—
195	C₄²×C₁₃	—	2	4	no	—
196	C₄²×C₁₃	—	2	4	no	—
197	C₄²×C₁₃	—	2	8	no	—
198	C₄²×C₁₃	—	2	8	no	—
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	C₄²×C₁₃	C₂×D₄	1	4	yes	—
203	C₂×#533	C₂×C₁₃	1	1	yes	characteristic, complemented
204	C₂×C₄×#41	C₂×C₁₃	1	1	yes	characteristic
205	#2638	C₂×C₁₃	1	4	yes	complemented
206	#2634	C₂×C₁₃	1	2	yes	complemented
207	#2633	C₂×C₁₃	1	2	yes	complemented
208	#2628	C₂×C₁₃	1	2	yes	complemented
209	#2625	C₂×C₁₃	1	2	yes	complemented
210	#2621	C₂×C₁₃	1	2	yes	complemented
211	#2616	C₂×C₁₃	1	2	yes	—
212	#2399	C₂×C₁₃	1	2	yes	complemented
213	#2398	C₂×C₁₃	1	2	yes	complemented
214	#2395	C₂×C₁₃	1	4	yes	complemented
215	C₄×C₂²⋊Q₈	C₂×C₁₃	1	4	yes	complemented
216	#2283	C₂×C₁₃	1	1	yes	characteristic, complemented
217	C₂³×C₁₃	—	2	2	no	—
218	C₂³×C₁₃	—	2	2	no	—
219	C₂³×C₁₃	—	2	2	no	—
220	C₂³×C₁₃	—	2	2	no	—
221	C₂³×C₁₃	—	2	4	no	—
222	C₂³×C₁₃	—	2	2	no	—
223	C₂³×C₁₃	—	2	4	no	—
224	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
225	C₂³×C₁₃	C₂×#41	1	4	yes	—
226	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
227	Q₈×C₁₃	—	2	8	no	—
228	Q₈×C₁₃	—	4	8	no	—
229	Q₈×C₁₃	—	4	8	no	—
230	D₄×C₁₃	—	2	8	no	—
231	D₄×C₁₃	—	2	16	no	—
232	C₂×C₄×C₁₃	—	2	2	no	—
233	C₂×C₄×C₁₃	—	2	2	no	—
234	C₂×C₄×C₁₃	—	2	2	no	—
235	C₂×C₄×C₁₃	—	2	2	no	—
236	C₂×C₄×C₁₃	—	2	2	no	—
237	C₂×C₄×C₁₃	—	2	2	no	—
238	C₂×C₄×C₁₃	—	2	8	no	—
239	C₂×C₄×C₁₃	—	2	16	no	—
240	C₂×C₄×C₁₃	—	2	8	no	—
241	C₂×C₄×C₁₃	—	2	2	no	—
242	C₂×C₄×C₁₃	—	2	2	no	—
243	C₂×C₄×C₁₃	—	2	4	no	—
244	C₂×C₄×C₁₃	—	2	4	no	—
245	C₂×C₄×C₁₃	—	2	8	no	—
246	C₂×C₄×C₁₃	—	2	8	no	—
247	C₂×C₄×C₁₃	—	2	8	no	—
248	C₂×C₄×C₁₃	—	2	4	no	—
249	C₂×C₄×C₁₃	—	2	8	no	—
250	C₂×C₄×C₁₃	—	2	4	no	—
251	C₂×C₄×C₁₃	—	2	4	no	—
252	C₂×C₄×C₁₃	—	2	4	no	—
253	C₂×C₄×C₁₃	—	4	4	no	—
254	C₂×C₄×C₁₃	—	4	8	no	—
255	C₂×C₄×C₁₃	—	4	8	no	—
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	C₂²×D₄	1	2	yes	—
261	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
262	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
263	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
264	C₂×C₄×C₁₃	2₋¹⁺⁴	1	4	yes	—
265	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
266	#533	—	2	8	no	—
267	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
268	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
269	C₂×#125	C₂²×C₁₃	1	2	yes	—
270	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
271	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
272	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
273	C₄×#41	—	2	8	no	—
274	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
275	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
276	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
277	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
278	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
279	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
280	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
281	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
282	C₂×#117	C₂²×C₁₃	1	2	yes	—
283	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
284	C₂×#117	C₂²×C₁₃	1	2	yes	—
285	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
286	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
287	#400	C₂²×C₁₃	1	4	yes	—
288	#400	C₂²×C₁₃	1	4	yes	—
289	#399	C₂²×C₁₃	1	4	yes	—
290	#398	C₂²×C₁₃	1	4	yes	—
291	#398	C₂²×C₁₃	1	4	yes	—
292	#398	C₂²×C₁₃	1	4	yes	—
293	#397	C₂²×C₁₃	1	4	yes	—
294	#397	C₂²×C₁₃	1	4	yes	—
295	#397	C₂²×C₁₃	1	8	yes	—
296	#395	C₂²×C₁₃	1	4	yes	—
297	#395	C₂²×C₁₃	1	4	yes	—
298	#394	C₂²×C₁₃	1	4	yes	—
299	#394	C₂²×C₁₃	1	8	yes	—
300	#393	C₂²×C₁₃	1	4	yes	—
301	#391	C₂²×C₁₃	1	4	yes	—
302	#389	C₂²×C₁₃	1	4	yes	—
303	#387	C₂²×C₁₃	1	8	yes	—
304	#385	C₂²×C₁₃	1	8	yes	—
305	#383	C₂²×C₁₃	1	2	yes	—
306	#382	C₂²×C₁₃	1	2	yes	—
307	#381	C₂²×C₁₃	1	2	yes	—
308	#380	C₂²×C₁₃	1	2	yes	—
309	#380	C₂²×C₁₃	1	4	yes	—
310	C₄×C₄⋊C₄	C₂²×C₁₃	1	8	yes	—
311	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
312	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
313	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	—
314	#376	C₂²×C₁₃	1	2	yes	—
315	C₂²×C₁₃	—	2	2	no	—
316	C₂²×C₁₃	—	2	4	no	—
317	C₂²×C₁₃	—	2	2	no	—
318	C₂²×C₁₃	—	2	2	no	—
319	C₂²×C₁₃	—	2	8	no	—
320	C₂²×C₁₃	—	4	2	no	—
321	C₂²×C₁₃	—	4	2	no	—
322	C₂²×C₁₃	—	4	4	no	—
323	C₂²×C₁₃	—	4	4	no	—
324	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
325	C₂²×C₁₃	C₂²×#41	1	2	yes	—
326	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
327	C₂²×C₁₃	#585	1	2	yes	—
328	C₄×C₁₃	—	2	2	no	—
329	C₄×C₁₃	—	2	4	no	—
330	C₄×C₁₃	—	2	2	no	—
331	C₄×C₁₃	—	2	2	no	—
332	C₄×C₁₃	—	2	2	no	—
333	C₄×C₁₃	—	4	4	no	—
334	C₄×C₁₃	—	4	2	no	—
335	C₄×C₁₃	—	4	2	no	—
336	C₄×C₁₃	—	4	4	no	—
337	C₄×C₁₃	—	4	8	no	—
338	C₄×C₁₃	#525	1	4	yes	—
339	C₄×C₁₃	#536	1	4	yes	—
340	C₂×#41	—	2	4	no	—
341	C₂×#41	—	2	8	no	—
342	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
343	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
344	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
345	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
346	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
347	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
348	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
349	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
350	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
351	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
352	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
353	C₄⋊Q₈	—	2	4	no	—
354	C₄⋊Q₈	—	2	4	no	—
355	#125	—	2	8	no	—
356	C₂²⋊Q₈	—	2	8	no	—
357	C₂²⋊Q₈	—	2	8	no	—
358	C₂²⋊Q₈	—	2	16	no	—
359	C₄×Q₈	—	2	4	no	—
360	C₄×Q₈	—	2	4	no	—
361	C₄×Q₈	—	2	8	no	—
362	C₄×Q₈	—	2	8	no	—
363	C₄×D₄	—	2	8	no	—
364	C₄×D₄	—	2	8	no	—
365	C₄×D₄	—	2	4	no	—
366	C₄×D₄	—	2	4	no	—
367	#117	—	2	4	no	—
368	#117	—	2	8	no	—
369	#117	—	2	8	no	—
370	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
371	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
372	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
373	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
374	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
375	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
376	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
377	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
378	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
379	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
380	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
381	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
382	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
383	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
384	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
385	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
386	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
387	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
388	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
389	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
390	C₂×C₄²	—	2	8	no	—
391	C₂×C₄²	D₄×C₁₃	1	8	yes	—
392	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
393	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
394	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
395	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
396	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
397	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
398	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
399	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
400	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
401	#95	C₂³×C₁₃	1	4	yes	—
402	#95	C₂³×C₁₃	1	4	yes	—
403	#95	C₂³×C₁₃	1	4	yes	—
404	#95	C₂³×C₁₃	1	8	yes	—
405	#95	C₂³×C₁₃	1	8	yes	—
406	#95	C₂³×C₁₃	1	8	yes	—
407	#95	C₂³×C₁₃	1	4	yes	—
408	#95	C₂³×C₁₃	1	8	yes	—
409	C₂×C₁₃	—	4	2	no	—
410	C₂×C₁₃	—	4	4	no	—
411	C₂×C₁₃	C₂×#525	1	1	yes	characteristic
412	C₂×C₁₃	C₂×#536	1	1	yes	characteristic
413	C₂×C₁₃	#3449	1	1	yes	characteristic
414	C₂×C₁₃	#3461	1	4	yes	—
415	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
416	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
417	#41	—	2	32	no	—
418	C₂×Q₈	—	2	2	no	—
419	C₂×Q₈	—	2	4	no	—
420	C₂×Q₈	—	2	4	no	—
421	C₂×Q₈	—	2	4	no	—
422	C₂×Q₈	—	2	8	no	—
423	C₂×Q₈	—	4	4	no	—
424	C₂×D₄	—	2	4	no	—
425	C₂×D₄	—	2	4	no	—
426	C₂×D₄	—	2	4	no	—
427	C₂×D₄	—	2	2	no	—
428	C₂×D₄	—	2	4	no	—
429	C₂²×C₄	—	2	4	no	—
430	C₂²×C₄	—	2	4	no	—
431	C₂²×C₄	—	2	4	no	—
432	C₂²×C₄	—	2	4	no	—
433	C₂²×C₄	—	2	4	no	—
434	C₂²×C₄	—	2	4	no	—
435	C₂²×C₄	—	2	8	no	—
436	C₂²×C₄	—	4	2	no	—
437	C₂²×C₄	—	4	4	no	—
438	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
439	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
440	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
441	C₂²×C₄	C₁₃×#41	1	8	yes	—
442	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
443	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
444	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
445	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
446	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
447	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
448	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
449	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
450	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
451	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
452	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
453	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
454	C₄⋊C₄	—	2	4	no	—
455	C₄⋊C₄	—	2	4	no	—
456	C₄⋊C₄	—	2	2	no	—
457	C₄⋊C₄	—	2	2	no	—
458	C₄⋊C₄	—	2	4	no	—
459	C₄⋊C₄	—	2	4	no	—
460	C₄⋊C₄	—	2	8	no	—
461	C₄⋊C₄	—	2	8	no	—
462	C₄⋊C₄	—	2	4	no	—
463	C₄⋊C₄	—	2	4	no	—
464	C₄⋊C₄	—	2	8	no	—
465	C₄⋊C₄	—	2	16	no	—
466	C₄⋊C₄	—	4	8	no	—
467	C₂²⋊C₄	—	2	4	no	—
468	C₂²⋊C₄	—	2	8	no	—
469	C₂²⋊C₄	—	2	16	no	—
470	C₂²⋊C₄	—	2	4	no	—
471	C₂²⋊C₄	—	2	4	no	—
472	C₂²⋊C₄	—	4	4	no	—
473	C₂²⋊C₄	—	4	8	no	—
474	C₄²	—	2	4	no	—
475	C₄²	—	2	4	no	—
476	C₄²	—	2	4	no	—
477	C₄²	—	2	8	no	—
478	C₄²	—	2	8	no	—
479	C₄²	C₂×D₄×C₁₃	1	4	yes	—
480	C₄²	C₂×D₄×C₁₃	1	4	yes	—
481	C₄²	C₂×D₄×C₁₃	1	4	yes	—
482	C₄²	C₂×D₄×C₁₃	1	4	yes	—
483	C₁₃	#34627	1	1	yes	characteristic, direct product factor, Sylow
484	C₂³	—	2	2	no	—
485	C₂³	—	2	2	no	—
486	C₂³	—	2	2	no	—
487	C₂³	—	2	2	no	—
488	C₂³	—	2	4	no	—
489	C₂³	—	2	2	no	—
490	C₂³	—	2	4	no	—
491	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
492	C₂³	C₂×C₁₃×#41	1	4	yes	—
493	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
494	Q₈	—	2	8	no	—
495	Q₈	—	4	8	no	—
496	Q₈	—	4	8	no	—
497	D₄	—	2	8	no	—
498	D₄	—	2	16	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	8	no	—
506	C₂×C₄	—	2	16	no	—
507	C₂×C₄	—	2	8	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	4	no	—
511	C₂×C₄	—	2	4	no	—
512	C₂×C₄	—	2	8	no	—
513	C₂×C₄	—	2	8	no	—
514	C₂×C₄	—	2	8	no	—
515	C₂×C₄	—	2	4	no	—
516	C₂×C₄	—	2	8	no	—
517	C₂×C₄	—	2	4	no	—
518	C₂×C₄	—	2	4	no	—
519	C₂×C₄	—	2	4	no	—
520	C₂×C₄	—	4	4	no	—
521	C₂×C₄	—	4	8	no	—
522	C₂×C₄	—	4	8	no	—
523	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
524	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
525	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
526	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
527	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
528	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
529	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
530	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
531	C₂×C₄	C₁₃×2₋¹⁺⁴	1	4	yes	—
532	C₂²	—	2	2	no	—
533	C₂²	—	2	4	no	—
534	C₂²	—	2	2	no	—
535	C₂²	—	2	2	no	—
536	C₂²	—	2	8	no	—
537	C₂²	—	4	2	no	—
538	C₂²	—	4	2	no	—
539	C₂²	—	4	4	no	—
540	C₂²	—	4	4	no	—
541	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
542	C₂²	C₂²×C₁₃×#41	1	2	yes	—
543	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
544	C₂²	C₁₃×#585	1	2	yes	—
545	C₄	—	2	2	no	—
546	C₄	—	2	4	no	—
547	C₄	—	2	2	no	—
548	C₄	—	2	2	no	—
549	C₄	—	2	2	no	—
550	C₄	—	4	4	no	—
551	C₄	—	4	2	no	—
552	C₄	—	4	2	no	—
553	C₄	—	4	4	no	—
554	C₄	—	4	8	no	—
555	C₄	C₁₃×#525	1	4	yes	—
556	C₄	C₁₃×#536	1	4	yes	—
557	C₂	—	4	2	no	—
558	C₂	—	4	4	no	—
559	C₂	C₂×C₁₃×#525	1	1	yes	characteristic
560	C₂	C₂×C₁₃×#536	1	1	yes	characteristic
561	C₂	C₁₃×#3449	1	1	yes	characteristic
562	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	C₂²×C₁₃×#41	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×#2638	C₂	semidirect
4. C₁₃×#2634	C₂	semidirect
5. C₁₃×#2633	C₂	semidirect
6. C₁₃×#2628	C₂	semidirect
7. C₁₃×#2625	C₂	semidirect
8. C₁₃×#2621	C₂	semidirect
10. C₁₃×#2399	C₂	semidirect
11. C₁₃×#2398	C₂	semidirect
12. C₁₃×#2395	C₂	semidirect
13. C₄×C₁₃×C₂²⋊Q₈	C₂	semidirect
14. C₁₃×#2283	C₂	semidirect
134. #34627	C₁₃	direct (N × H)
203. C₂×#533	C₂×C₁₃	semidirect
205. #2638	C₂×C₁₃	semidirect
206. #2634	C₂×C₁₃	semidirect
207. #2633	C₂×C₁₃	semidirect
208. #2628	C₂×C₁₃	semidirect
209. #2625	C₂×C₁₃	semidirect
210. #2621	C₂×C₁₃	semidirect
212. #2399	C₂×C₁₃	semidirect
213. #2398	C₂×C₁₃	semidirect
214. #2395	C₂×C₁₃	semidirect
215. C₄×C₂²⋊Q₈	C₂×C₁₃	semidirect
216. #2283	C₂×C₁₃	semidirect
483. C₁₃	#34627	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×C₄×C₁₃×#41	2
C₁₃×#2638	2
C₁₃×#2634	2
C₁₃×#2633	2
C₁₃×#2628	2
C₁₃×#2625	2
C₁₃×#2621	2
C₁₃×#2616	2
C₁₃×#2399	2
C₁₃×#2398	2
C₁₃×#2395	2
C₄×C₁₃×C₂²⋊Q₈	2
C₁₃×#2283	2
#34627	13

Subgroups — C13×#34627 #15720966

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34627 #15720966