Subgroups — C₁₃×#34624 #15720963

Order 3328.

2626 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2662	C₂	1	4	yes	maximal, complemented
4	C₁₃×#2661	C₂	1	4	yes	maximal, complemented
5	C₁₃×#2660	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2657	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2641	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2640	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2620	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2619	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2392	C₂	1	4	yes	maximal, complemented
12	C₁₃×#2388	C₂	1	4	yes	maximal, complemented
13	C₄×C₁₃×#127	C₂	1	2	yes	maximal, complemented
14	C₄×C₁₃×#124	C₂	1	2	yes	maximal, complemented
15	C₄×C₁₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×#41	C₂²	1	2	yes	—
17	C₁₃×#532	—	2	8	no	—
18	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#127	C₂²	1	2	yes	—
20	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
21	C₁₃×#529	—	2	8	no	—
22	C₂×C₁₃×#126	C₂²	1	2	yes	—
23	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#124	C₂²	1	2	yes	—
25	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#124	C₂²	1	2	yes	—
27	C₂×C₁₃×#123	C₂²	1	2	yes	—
28	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#121	C₂²	1	2	yes	—
31	C₂×C₁₃×#121	C₂²	1	2	yes	—
32	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
37	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	—
38	C₂×C₁₃×#117	C₂²	1	2	yes	—
39	C₂×C₁₃×#117	C₂²	1	2	yes	—
40	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
41	C₁₃×#398	C₂²	1	4	yes	—
42	C₁₃×#397	C₂²	1	4	yes	—
43	C₁₃×#396	C₂²	1	8	yes	—
44	C₁₃×#395	C₂²	1	4	yes	—
45	C₁₃×#394	C₂²	1	8	yes	—
46	C₁₃×#394	C₂²	1	8	yes	—
47	C₁₃×#394	C₂²	1	4	yes	—
48	C₁₃×#394	C₂²	1	4	yes	—
49	C₁₃×#393	C₂²	1	4	yes	—
50	C₁₃×#392	C₂²	1	8	yes	—
51	C₁₃×#392	C₂²	1	4	yes	—
52	C₁₃×#392	C₂²	1	4	yes	—
53	C₁₃×#391	C₂²	1	2	yes	—
54	C₁₃×#390	C₂²	1	2	yes	—
55	C₁₃×#390	C₂²	1	2	yes	—
56	C₁₃×#390	C₂²	1	2	yes	—
57	C₁₃×#390	C₂²	1	8	yes	—
58	C₁₃×#388	C₂²	1	8	yes	—
59	C₁₃×#384	C₂²	1	2	yes	—
60	C₁₃×#382	C₂²	1	2	yes	—
61	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
62	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
63	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
64	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
65	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	—
66	C₁₃×#376	C₂²	1	1	yes	characteristic
67	C₁₃×#376	C₂²	1	1	yes	characteristic
68	C₄³×C₁₃	C₂²	1	2	yes	—
69	C₂×C₁₃×#41	—	2	8	no	—
70	C₂×C₁₃×#41	—	4	8	no	—
71	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
72	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
73	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
74	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
75	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
76	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
77	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
78	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
79	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
80	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
81	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
82	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
85	C₁₃×C₄⋊Q₈	—	2	4	no	—
86	C₁₃×#127	—	2	4	no	—
87	C₁₃×#127	—	2	8	no	—
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	—	2	8	no	—
93	C₁₃×#123	—	2	8	no	—
94	C₁₃×C₂²⋊Q₈	—	2	4	no	—
95	C₁₃×#121	—	2	4	no	—
96	C₁₃×#121	—	2	8	no	—
97	C₁₃×#121	—	2	8	no	—
98	C₄×Q₈×C₁₃	—	2	4	no	—
99	C₄×D₄×C₁₃	—	2	8	no	—
100	C₄×D₄×C₁₃	—	2	4	no	—
101	C₄×D₄×C₁₃	—	2	8	no	—
102	C₄×D₄×C₁₃	—	2	8	no	—
103	C₄×D₄×C₁₃	—	4	16	no	—
104	C₁₃×#117	—	2	8	no	—
105	C₁₃×#117	—	2	8	no	—
106	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
107	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
108	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
109	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
110	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
111	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
112	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
113	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
114	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
115	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
116	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
117	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
118	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
119	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
120	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
121	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
122	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
123	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
124	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
125	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
126	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
127	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
128	C₂×C₄²×C₁₃	D₄	1	8	yes	complemented
129	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
130	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
131	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
132	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
133	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
134	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
135	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
136	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
137	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
138	C₁₃×#95	C₂³	1	2	yes	—
139	C₁₃×#95	C₂³	1	2	yes	—
140	C₁₃×#95	C₂³	1	2	yes	—
141	C₁₃×#95	C₂³	1	2	yes	—
142	C₁₃×#95	C₂³	1	8	yes	—
143	C₁₃×#95	C₂³	1	8	yes	—
144	#34624	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
145	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
146	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
147	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
148	C₁₃×#41	—	4	32	no	—
149	C₂×Q₈×C₁₃	—	2	2	no	—
150	C₂×Q₈×C₁₃	—	2	4	no	—
151	C₂×Q₈×C₁₃	—	2	4	no	—
152	C₂×Q₈×C₁₃	—	4	4	no	—
153	C₂×D₄×C₁₃	—	2	4	no	—
154	C₂×D₄×C₁₃	—	2	8	no	—
155	C₂×D₄×C₁₃	—	2	2	no	—
156	C₂×D₄×C₁₃	—	2	4	no	—
157	C₂×D₄×C₁₃	—	2	4	no	—
158	C₂×D₄×C₁₃	—	2	4	no	—
159	C₂×D₄×C₁₃	—	2	4	no	—
160	C₂×D₄×C₁₃	—	2	16	no	—
161	C₂×D₄×C₁₃	—	2	4	no	—
162	C₂×D₄×C₁₃	—	2	4	no	—
163	C₂×D₄×C₁₃	—	4	8	no	—
164	C₂×D₄×C₁₃	—	4	8	no	—
165	C₂×D₄×C₁₃	—	4	4	no	—
166	C₂×D₄×C₁₃	—	4	4	no	—
167	C₂×D₄×C₁₃	—	4	4	no	—
168	C₂×D₄×C₁₃	—	4	8	no	—
169	C₂²×C₄×C₁₃	—	2	4	no	—
170	C₂²×C₄×C₁₃	—	2	4	no	—
171	C₂²×C₄×C₁₃	—	2	4	no	—
172	C₂²×C₄×C₁₃	—	2	8	no	—
173	C₂²×C₄×C₁₃	—	2	8	no	—
174	C₂²×C₄×C₁₃	—	2	16	no	—
175	C₂²×C₄×C₁₃	—	4	2	no	—
176	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
177	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
178	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
179	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
180	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
181	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
182	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
183	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
184	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
185	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
186	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
187	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
188	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
189	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
190	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
191	C₁₃×C₄⋊C₄	—	2	4	no	—
192	C₁₃×C₄⋊C₄	—	2	4	no	—
193	C₁₃×C₄⋊C₄	—	2	4	no	—
194	C₁₃×C₄⋊C₄	—	2	4	no	—
195	C₁₃×C₄⋊C₄	—	2	2	no	—
196	C₁₃×C₄⋊C₄	—	2	4	no	—
197	C₁₃×C₄⋊C₄	—	2	2	no	—
198	C₁₃×C₄⋊C₄	—	2	4	no	—
199	C₁₃×C₄⋊C₄	—	2	8	no	—
200	C₁₃×C₄⋊C₄	—	4	8	no	—
201	C₁₃×C₂²⋊C₄	—	2	4	no	—
202	C₁₃×C₂²⋊C₄	—	2	4	no	—
203	C₁₃×C₂²⋊C₄	—	2	4	no	—
204	C₁₃×C₂²⋊C₄	—	2	8	no	—
205	C₁₃×C₂²⋊C₄	—	2	8	no	—
206	C₁₃×C₂²⋊C₄	—	2	4	no	—
207	C₁₃×C₂²⋊C₄	—	2	4	no	—
208	C₁₃×C₂²⋊C₄	—	2	8	no	—
209	C₁₃×C₂²⋊C₄	—	2	16	no	—
210	C₁₃×C₂²⋊C₄	—	4	8	no	—
211	C₁₃×C₂²⋊C₄	—	4	8	no	—
212	C₁₃×C₂²⋊C₄	—	4	8	no	—
213	C₄²×C₁₃	—	2	4	no	—
214	C₄²×C₁₃	—	2	4	no	—
215	C₄²×C₁₃	—	2	8	no	—
216	C₄²×C₁₃	—	4	4	no	—
217	C₄²×C₁₃	C₂×D₄	1	4	yes	—
218	C₄²×C₁₃	C₂×D₄	1	4	yes	—
219	C₄²×C₁₃	C₂×D₄	1	4	yes	—
220	C₄²×C₁₃	C₂×D₄	1	4	yes	—
221	C₄²×C₁₃	#41	1	8	yes	complemented
222	C₂×#532	C₂×C₁₃	1	1	yes	characteristic, complemented
223	C₂×#529	C₂×C₁₃	1	1	yes	characteristic, complemented
224	#2662	C₂×C₁₃	1	4	yes	complemented
225	#2661	C₂×C₁₃	1	4	yes	complemented
226	#2660	C₂×C₁₃	1	1	yes	characteristic, complemented
227	#2657	C₂×C₁₃	1	1	yes	characteristic, complemented
228	#2641	C₂×C₁₃	1	1	yes	characteristic, complemented
229	#2640	C₂×C₁₃	1	1	yes	characteristic, complemented
230	#2620	C₂×C₁₃	1	2	yes	complemented
231	#2619	C₂×C₁₃	1	2	yes	complemented
232	#2392	C₂×C₁₃	1	4	yes	complemented
233	#2388	C₂×C₁₃	1	4	yes	complemented
234	C₄×#127	C₂×C₁₃	1	2	yes	complemented
235	C₄×#124	C₂×C₁₃	1	2	yes	complemented
236	C₄×#117	C₂×C₁₃	1	1	yes	characteristic, complemented
237	C₂³×C₁₃	—	2	2	no	—
238	C₂³×C₁₃	—	2	2	no	—
239	C₂³×C₁₃	—	2	2	no	—
240	C₂³×C₁₃	—	2	2	no	—
241	C₂³×C₁₃	—	2	4	no	—
242	C₂³×C₁₃	—	2	4	no	—
243	C₂³×C₁₃	—	2	4	no	—
244	C₂³×C₁₃	—	2	4	no	—
245	C₂³×C₁₃	—	2	4	no	—
246	C₂³×C₁₃	—	2	8	no	—
247	C₂³×C₁₃	—	2	8	no	—
248	C₂³×C₁₃	—	2	4	no	—
249	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
250	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
251	Q₈×C₁₃	—	4	8	no	—
252	Q₈×C₁₃	—	4	4	no	—
253	D₄×C₁₃	—	4	8	no	—
254	D₄×C₁₃	—	4	32	no	—
255	D₄×C₁₃	—	4	8	no	—
256	D₄×C₁₃	—	4	8	no	—
257	D₄×C₁₃	—	4	16	no	—
258	D₄×C₁₃	—	4	4	no	—
259	D₄×C₁₃	—	4	8	no	—
260	C₂×C₄×C₁₃	—	2	2	no	—
261	C₂×C₄×C₁₃	—	2	4	no	—
262	C₂×C₄×C₁₃	—	2	2	no	—
263	C₂×C₄×C₁₃	—	2	2	no	—
264	C₂×C₄×C₁₃	—	2	4	no	—
265	C₂×C₄×C₁₃	—	2	2	no	—
266	C₂×C₄×C₁₃	—	2	8	no	—
267	C₂×C₄×C₁₃	—	2	8	no	—
268	C₂×C₄×C₁₃	—	2	2	no	—
269	C₂×C₄×C₁₃	—	2	2	no	—
270	C₂×C₄×C₁₃	—	2	2	no	—
271	C₂×C₄×C₁₃	—	2	4	no	—
272	C₂×C₄×C₁₃	—	2	4	no	—
273	C₂×C₄×C₁₃	—	2	4	no	—
274	C₂×C₄×C₁₃	—	2	4	no	—
275	C₂×C₄×C₁₃	—	2	4	no	—
276	C₂×C₄×C₁₃	—	2	8	no	—
277	C₂×C₄×C₁₃	—	2	4	no	—
278	C₂×C₄×C₁₃	—	2	4	no	—
279	C₂×C₄×C₁₃	—	4	4	no	—
280	C₂×C₄×C₁₃	—	4	8	no	—
281	C₂×C₄×C₁₃	—	4	16	no	—
282	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
283	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
284	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
285	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
286	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
287	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
288	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
289	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
290	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
291	C₂²×#41	C₂²×C₁₃	1	2	yes	—
292	#532	—	2	8	no	—
293	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
294	C₂×#127	C₂²×C₁₃	1	2	yes	—
295	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
296	#529	—	2	8	no	—
297	C₂×#126	C₂²×C₁₃	1	2	yes	—
298	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
299	C₂×#124	C₂²×C₁₃	1	2	yes	—
300	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
301	C₂×#124	C₂²×C₁₃	1	2	yes	—
302	C₂×#123	C₂²×C₁₃	1	2	yes	—
303	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
304	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
305	C₂×#121	C₂²×C₁₃	1	2	yes	—
306	C₂×#121	C₂²×C₁₃	1	2	yes	—
307	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
308	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
309	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
310	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
311	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
312	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	—
313	C₂×#117	C₂²×C₁₃	1	2	yes	—
314	C₂×#117	C₂²×C₁₃	1	2	yes	—
315	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
316	#398	C₂²×C₁₃	1	4	yes	—
317	#397	C₂²×C₁₃	1	4	yes	—
318	#396	C₂²×C₁₃	1	8	yes	—
319	#395	C₂²×C₁₃	1	4	yes	—
320	#394	C₂²×C₁₃	1	8	yes	—
321	#394	C₂²×C₁₃	1	8	yes	—
322	#394	C₂²×C₁₃	1	4	yes	—
323	#394	C₂²×C₁₃	1	4	yes	—
324	#393	C₂²×C₁₃	1	4	yes	—
325	#392	C₂²×C₁₃	1	8	yes	—
326	#392	C₂²×C₁₃	1	4	yes	—
327	#392	C₂²×C₁₃	1	4	yes	—
328	#391	C₂²×C₁₃	1	2	yes	—
329	#390	C₂²×C₁₃	1	2	yes	—
330	#390	C₂²×C₁₃	1	2	yes	—
331	#390	C₂²×C₁₃	1	8	yes	—
332	#390	C₂²×C₁₃	1	2	yes	—
333	#388	C₂²×C₁₃	1	8	yes	—
334	#384	C₂²×C₁₃	1	2	yes	—
335	#382	C₂²×C₁₃	1	2	yes	—
336	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
337	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
338	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
339	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	—
340	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
341	#376	C₂²×C₁₃	1	1	yes	characteristic
342	#376	C₂²×C₁₃	1	1	yes	characteristic
343	C₄³	C₂²×C₁₃	1	2	yes	—
344	C₂²×C₁₃	—	2	2	no	—
345	C₂²×C₁₃	—	2	2	no	—
346	C₂²×C₁₃	—	2	2	no	—
347	C₂²×C₁₃	—	4	4	no	—
348	C₂²×C₁₃	—	4	2	no	—
349	C₂²×C₁₃	—	4	4	no	—
350	C₂²×C₁₃	—	4	4	no	—
351	C₂²×C₁₃	—	4	2	no	—
352	C₂²×C₁₃	—	4	4	no	—
353	C₂²×C₁₃	—	4	2	no	—
354	C₂²×C₁₃	—	4	8	no	—
355	C₂²×C₁₃	—	4	8	no	—
356	C₂²×C₁₃	—	4	8	no	—
357	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
358	C₂²×C₁₃	C₂²×#41	1	2	yes	—
359	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
360	C₂²×C₁₃	#585	1	2	yes	—
361	C₄×C₁₃	—	2	2	no	—
362	C₄×C₁₃	—	2	2	no	—
363	C₄×C₁₃	—	2	2	no	—
364	C₄×C₁₃	—	2	2	no	—
365	C₄×C₁₃	—	2	8	no	—
366	C₄×C₁₃	—	4	2	no	—
367	C₄×C₁₃	—	4	2	no	—
368	C₄×C₁₃	—	4	4	no	—
369	C₄×C₁₃	—	4	2	no	—
370	C₄×C₁₃	—	4	4	no	—
371	C₄×C₁₃	#532	1	4	yes	—
372	C₄×C₁₃	#535	1	4	yes	—
373	C₂×#41	—	2	8	no	—
374	C₂×#41	—	4	8	no	—
375	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
376	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
377	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
378	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
379	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
380	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
381	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
382	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
383	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
384	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
385	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
386	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
387	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
388	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
389	C₄⋊Q₈	—	2	4	no	—
390	#127	—	2	4	no	—
391	#127	—	2	8	no	—
392	#126	—	2	8	no	—
393	#125	—	2	4	no	—
394	#124	—	2	4	no	—
395	#124	—	2	8	no	—
396	#124	—	2	8	no	—
397	#123	—	2	8	no	—
398	C₂²⋊Q₈	—	2	4	no	—
399	#121	—	2	4	no	—
400	#121	—	2	8	no	—
401	#121	—	2	8	no	—
402	C₄×Q₈	—	2	4	no	—
403	C₄×D₄	—	2	8	no	—
404	C₄×D₄	—	2	4	no	—
405	C₄×D₄	—	2	8	no	—
406	C₄×D₄	—	2	8	no	—
407	C₄×D₄	—	4	16	no	—
408	#117	—	2	8	no	—
409	#117	—	2	8	no	—
410	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
411	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
412	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
413	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
414	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
415	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
416	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
417	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
418	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
419	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
420	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
421	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
422	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
423	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
424	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
425	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
426	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
427	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
428	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
429	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
430	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
431	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
432	C₂×C₄²	D₄×C₁₃	1	8	yes	complemented
433	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
434	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
435	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
436	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
437	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
438	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
439	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
440	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
441	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
442	#95	C₂³×C₁₃	1	2	yes	—
443	#95	C₂³×C₁₃	1	2	yes	—
444	#95	C₂³×C₁₃	1	2	yes	—
445	#95	C₂³×C₁₃	1	2	yes	—
446	#95	C₂³×C₁₃	1	8	yes	—
447	#95	C₂³×C₁₃	1	8	yes	—
448	C₂×C₁₃	—	4	2	no	—
449	C₂×C₁₃	—	8	4	no	—
450	C₂×C₁₃	—	8	2	no	—
451	C₂×C₁₃	C₂×#532	1	1	yes	characteristic
452	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
453	C₂×C₁₃	#3449	1	1	yes	characteristic
454	C₂×C₁₃	#3460	1	4	yes	—
455	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
456	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
457	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
458	#41	—	4	32	no	—
459	C₂×Q₈	—	2	2	no	—
460	C₂×Q₈	—	2	4	no	—
461	C₂×Q₈	—	2	4	no	—
462	C₂×Q₈	—	4	4	no	—
463	C₂×D₄	—	2	4	no	—
464	C₂×D₄	—	2	8	no	—
465	C₂×D₄	—	2	2	no	—
466	C₂×D₄	—	2	4	no	—
467	C₂×D₄	—	2	4	no	—
468	C₂×D₄	—	2	4	no	—
469	C₂×D₄	—	2	4	no	—
470	C₂×D₄	—	2	16	no	—
471	C₂×D₄	—	2	4	no	—
472	C₂×D₄	—	2	4	no	—
473	C₂×D₄	—	4	8	no	—
474	C₂×D₄	—	4	4	no	—
475	C₂×D₄	—	4	8	no	—
476	C₂×D₄	—	4	8	no	—
477	C₂×D₄	—	4	4	no	—
478	C₂×D₄	—	4	4	no	—
479	C₂²×C₄	—	2	4	no	—
480	C₂²×C₄	—	2	4	no	—
481	C₂²×C₄	—	2	4	no	—
482	C₂²×C₄	—	2	8	no	—
483	C₂²×C₄	—	2	8	no	—
484	C₂²×C₄	—	2	16	no	—
485	C₂²×C₄	—	4	2	no	—
486	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
487	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
488	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
489	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
490	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
491	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
492	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
493	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
494	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
495	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
496	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
497	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
498	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
499	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
500	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
501	C₄⋊C₄	—	2	4	no	—
502	C₄⋊C₄	—	2	4	no	—
503	C₄⋊C₄	—	2	4	no	—
504	C₄⋊C₄	—	2	4	no	—
505	C₄⋊C₄	—	2	2	no	—
506	C₄⋊C₄	—	2	4	no	—
507	C₄⋊C₄	—	2	2	no	—
508	C₄⋊C₄	—	2	4	no	—
509	C₄⋊C₄	—	2	8	no	—
510	C₄⋊C₄	—	4	8	no	—
511	C₂²⋊C₄	—	2	4	no	—
512	C₂²⋊C₄	—	2	4	no	—
513	C₂²⋊C₄	—	2	4	no	—
514	C₂²⋊C₄	—	2	8	no	—
515	C₂²⋊C₄	—	2	8	no	—
516	C₂²⋊C₄	—	2	4	no	—
517	C₂²⋊C₄	—	2	4	no	—
518	C₂²⋊C₄	—	2	8	no	—
519	C₂²⋊C₄	—	2	16	no	—
520	C₂²⋊C₄	—	4	8	no	—
521	C₂²⋊C₄	—	4	8	no	—
522	C₂²⋊C₄	—	4	8	no	—
523	C₄²	—	2	4	no	—
524	C₄²	—	2	4	no	—
525	C₄²	—	2	8	no	—
526	C₄²	—	4	4	no	—
527	C₄²	C₂×D₄×C₁₃	1	4	yes	—
528	C₄²	C₂×D₄×C₁₃	1	4	yes	—
529	C₄²	C₂×D₄×C₁₃	1	4	yes	—
530	C₄²	C₂×D₄×C₁₃	1	4	yes	—
531	C₄²	C₁₃×#41	1	8	yes	complemented
532	C₁₃	#34624	1	1	yes	characteristic, direct product factor, Sylow
533	C₂³	—	2	2	no	—
534	C₂³	—	2	2	no	—
535	C₂³	—	2	2	no	—
536	C₂³	—	2	2	no	—
537	C₂³	—	2	4	no	—
538	C₂³	—	2	4	no	—
539	C₂³	—	2	4	no	—
540	C₂³	—	2	4	no	—
541	C₂³	—	2	4	no	—
542	C₂³	—	2	8	no	—
543	C₂³	—	2	8	no	—
544	C₂³	—	2	4	no	—
545	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
546	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
547	Q₈	—	4	8	no	—
548	Q₈	—	4	4	no	—
549	D₄	—	4	8	no	—
550	D₄	—	4	32	no	—
551	D₄	—	4	8	no	—
552	D₄	—	4	8	no	—
553	D₄	—	4	16	no	—
554	D₄	—	4	4	no	—
555	D₄	—	4	8	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	4	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	4	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	8	no	—
563	C₂×C₄	—	2	8	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	4	no	—
568	C₂×C₄	—	2	4	no	—
569	C₂×C₄	—	2	4	no	—
570	C₂×C₄	—	2	4	no	—
571	C₂×C₄	—	2	4	no	—
572	C₂×C₄	—	2	8	no	—
573	C₂×C₄	—	2	4	no	—
574	C₂×C₄	—	2	4	no	—
575	C₂×C₄	—	4	4	no	—
576	C₂×C₄	—	4	8	no	—
577	C₂×C₄	—	4	16	no	—
578	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
579	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
580	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
581	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
582	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
583	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
584	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
585	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
586	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
587	C₂²	—	2	2	no	—
588	C₂²	—	2	2	no	—
589	C₂²	—	2	2	no	—
590	C₂²	—	4	4	no	—
591	C₂²	—	4	2	no	—
592	C₂²	—	4	4	no	—
593	C₂²	—	4	4	no	—
594	C₂²	—	4	2	no	—
595	C₂²	—	4	4	no	—
596	C₂²	—	4	2	no	—
597	C₂²	—	4	8	no	—
598	C₂²	—	4	8	no	—
599	C₂²	—	4	8	no	—
600	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
601	C₂²	C₂²×C₁₃×#41	1	2	yes	—
602	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
603	C₂²	C₁₃×#585	1	2	yes	—
604	C₄	—	2	2	no	—
605	C₄	—	2	2	no	—
606	C₄	—	2	2	no	—
607	C₄	—	2	2	no	—
608	C₄	—	2	8	no	—
609	C₄	—	4	2	no	—
610	C₄	—	4	2	no	—
611	C₄	—	4	4	no	—
612	C₄	—	4	2	no	—
613	C₄	—	4	4	no	—
614	C₄	C₁₃×#532	1	4	yes	—
615	C₄	C₁₃×#535	1	4	yes	—
616	C₂	—	4	2	no	—
617	C₂	—	8	4	no	—
618	C₂	—	8	2	no	—
619	C₂	C₂×C₁₃×#532	1	1	yes	characteristic
620	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
621	C₂	C₁₃×#3449	1	1	yes	characteristic
622	C₂	C₁₃×#3460	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
socle	C₂³×C₁₃	C₂⁵
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×#532	C₂	semidirect
2. C₂×C₁₃×#529	C₂	semidirect
3. C₁₃×#2662	C₂	semidirect
4. C₁₃×#2661	C₂	semidirect
5. C₁₃×#2660	C₂	semidirect
6. C₁₃×#2657	C₂	semidirect
7. C₁₃×#2641	C₂	semidirect
8. C₁₃×#2640	C₂	semidirect
9. C₁₃×#2620	C₂	semidirect
10. C₁₃×#2619	C₂	semidirect
11. C₁₃×#2392	C₂	semidirect
12. C₁₃×#2388	C₂	semidirect
13. C₄×C₁₃×#127	C₂	semidirect
14. C₄×C₁₃×#124	C₂	semidirect
15. C₄×C₁₃×#117	C₂	semidirect
128. C₂×C₄²×C₁₃	D₄	semidirect
144. #34624	C₁₃	direct (N × H)
221. C₄²×C₁₃	#41	semidirect
222. C₂×#532	C₂×C₁₃	semidirect
223. C₂×#529	C₂×C₁₃	semidirect
224. #2662	C₂×C₁₃	semidirect
225. #2661	C₂×C₁₃	semidirect
226. #2660	C₂×C₁₃	semidirect
227. #2657	C₂×C₁₃	semidirect
228. #2641	C₂×C₁₃	semidirect
229. #2640	C₂×C₁₃	semidirect
230. #2620	C₂×C₁₃	semidirect
231. #2619	C₂×C₁₃	semidirect
232. #2392	C₂×C₁₃	semidirect
233. #2388	C₂×C₁₃	semidirect
234. C₄×#127	C₂×C₁₃	semidirect
235. C₄×#124	C₂×C₁₃	semidirect
236. C₄×#117	C₂×C₁₃	semidirect
432. C₂×C₄²	D₄×C₁₃	semidirect
531. C₄²	C₁₃×#41	semidirect
532. C₁₃	#34624	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×#532	2
C₂×C₁₃×#529	2
C₁₃×#2662	2
C₁₃×#2661	2
C₁₃×#2660	2
C₁₃×#2657	2
C₁₃×#2641	2
C₁₃×#2640	2
C₁₃×#2620	2
C₁₃×#2619	2
C₁₃×#2392	2
C₁₃×#2388	2
C₄×C₁₃×#127	2
C₄×C₁₃×#124	2
C₄×C₁₃×#117	2
#34624	13

Subgroups — C13×#34624 #15720963

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34624 #15720963