Subgroups — C₂×C₁₃×#3461 #15749021

Order 3328.

7130 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3461	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₁₃×#544	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#542	C₂	1	4	yes	maximal, complemented
4	C₂×C₁₃×#541	C₂	1	4	yes	maximal, complemented
5	C₂×C₁₃×#539	C₂	1	4	yes	maximal, complemented
6	C₂×C₁₃×#537	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₃×#536	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#533	C₂	1	4	yes	maximal, complemented
9	C₂×C₁₃×#529	C₂	1	4	yes	maximal, complemented
10	C₂×C₁₃×#529	C₂	1	4	yes	maximal, complemented
11	C₂×C₄×C₁₃×#41	C₂	1	2	yes	maximal, complemented
12	C₂²×C₄×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₁₃×#41	C₂²	1	2	yes	—
14	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₁₃×#544	C₂²	1	16	yes	complemented
16	C₁₃×#542	C₂²	1	64	yes	complemented
17	C₁₃×#541	C₂²	1	64	yes	complemented
18	C₁₃×#539	C₂²	1	64	yes	complemented
19	C₁₃×#537	C₂²	1	16	yes	—
20	C₁₃×#536	C₂²	1	32	yes	complemented
21	C₁₃×#533	C₂²	1	64	yes	complemented
22	C₂×C₁₃×C₄⋊Q₈	C₂²	1	4	yes	—
23	C₂×C₁₃×C₄⋊Q₈	C₂²	1	4	yes	—
24	C₁₃×#529	C₂²	1	64	yes	complemented
25	C₁₃×#529	C₂²	1	64	yes	complemented
26	C₂×C₁₃×#126	C₂²	1	8	yes	—
27	C₂×C₁₃×#126	C₂²	1	8	yes	—
28	C₂×C₁₃×#125	C₂²	1	4	yes	—
29	C₂×C₁₃×#125	C₂²	1	4	yes	—
30	C₂×C₁₃×#125	C₂²	1	8	yes	—
31	C₂×C₁₃×#124	C₂²	1	4	yes	—
32	C₂×C₁₃×#124	C₂²	1	4	yes	—
33	C₂×C₁₃×#123	C₂²	1	8	yes	—
34	C₂×C₁₃×#123	C₂²	1	8	yes	—
35	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
36	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
37	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
38	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
39	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	8	yes	—
40	C₂×C₁₃×#121	C₂²	1	4	yes	—
41	C₂×C₁₃×#121	C₂²	1	4	yes	—
42	C₄×C₁₃×#41	C₂²	1	32	yes	complemented
43	C₂×C₄×Q₈×C₁₃	C₂²	1	4	yes	—
44	C₂×C₄×Q₈×C₁₃	C₂²	1	4	yes	—
45	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
46	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
47	C₂×C₄×Q₈×C₁₃	C₂²	1	4	yes	—
48	C₂×C₄×Q₈×C₁₃	C₂²	1	16	yes	complemented
49	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
50	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
51	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
52	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
53	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
54	C₂×C₁₃×#117	C₂²	1	2	yes	—
55	C₂×C₁₃×#117	C₂²	1	4	yes	—
56	C₂×C₁₃×#117	C₂²	1	8	yes	—
57	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
58	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
59	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
60	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
61	C₂²×C₄²×C₁₃	C₂²	1	4	yes	—
62	C₂×C₁₃×#41	—	2	16	no	—
63	C₂×C₁₃×#41	C₂³	1	16	yes	—
64	C₂²×Q₈×C₁₃	—	2	8	no	—
65	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
66	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
67	C₂²×Q₈×C₁₃	C₂³	1	8	yes	—
68	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
69	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
70	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
71	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
72	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
73	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
74	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
76	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
78	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
79	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
80	C₁₃×C₄⋊Q₈	C₂³	1	32	yes	—
81	C₁₃×C₄⋊Q₈	C₂³	1	32	yes	—
82	C₁₃×#126	C₂³	1	64	yes	—
83	C₁₃×#126	C₂³	1	64	yes	—
84	C₁₃×#125	C₂³	1	32	yes	—
85	C₁₃×#125	C₂³	1	32	yes	—
86	C₁₃×#125	C₂³	1	64	yes	—
87	C₁₃×#124	C₂³	1	32	yes	—
88	C₁₃×#124	C₂³	1	32	yes	—
89	C₁₃×#123	C₂³	1	64	yes	—
90	C₁₃×#123	C₂³	1	64	yes	—
91	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	—
92	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	—
93	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	—
94	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	—
95	C₁₃×C₂²⋊Q₈	C₂³	1	64	yes	—
96	C₁₃×#121	C₂³	1	32	yes	—
97	C₁₃×#121	C₂³	1	32	yes	—
98	C₄×Q₈×C₁₃	C₂³	1	32	yes	—
99	C₄×Q₈×C₁₃	C₂³	1	32	yes	—
100	C₄×Q₈×C₁₃	C₂³	1	16	yes	—
101	C₄×Q₈×C₁₃	C₂³	1	16	yes	—
102	C₄×Q₈×C₁₃	C₂³	1	32	yes	—
103	C₄×D₄×C₁₃	C₂³	1	16	yes	—
104	C₄×D₄×C₁₃	C₂³	1	32	yes	—
105	C₄×D₄×C₁₃	C₂³	1	32	yes	—
106	C₄×D₄×C₁₃	C₂³	1	16	yes	—
107	C₄×D₄×C₁₃	C₂³	1	32	yes	—
108	C₁₃×#117	C₂³	1	16	yes	—
109	C₁₃×#117	C₂³	1	32	yes	—
110	C₁₃×#117	C₂³	1	64	yes	—
111	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
112	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
113	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
114	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	yes	—
115	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
116	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
117	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
118	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
119	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
120	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
121	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
122	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
123	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
124	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
125	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
126	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
127	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
128	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
129	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	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	4	yes	—
134	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
135	C₂×C₄²×C₁₃	C₂³	1	16	yes	—
136	C₂×C₄²×C₁₃	C₂³	1	32	yes	—
137	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
138	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
139	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
140	C₂×#3461	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
141	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
142	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
143	C₁₃×#41	—	2	64	no	—
144	C₂×Q₈×C₁₃	—	2	16	no	—
145	C₂×Q₈×C₁₃	—	2	32	no	—
146	C₂×Q₈×C₁₃	—	2	8	no	—
147	C₂×Q₈×C₁₃	—	4	8	no	—
148	C₂×Q₈×C₁₃	C₂⁴	1	16	yes	—
149	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
150	C₂×Q₈×C₁₃	C₂⁴	1	16	yes	—
151	C₂×D₄×C₁₃	—	2	16	no	—
152	C₂×D₄×C₁₃	—	2	8	no	—
153	C₂×D₄×C₁₃	—	4	8	no	—
154	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
155	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
156	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
157	C₂²×C₄×C₁₃	—	2	8	no	—
158	C₂²×C₄×C₁₃	—	2	16	no	—
159	C₂²×C₄×C₁₃	—	2	4	no	—
160	C₂²×C₄×C₁₃	—	2	16	no	—
161	C₂²×C₄×C₁₃	—	4	2	no	—
162	C₂²×C₄×C₁₃	—	4	8	no	—
163	C₂²×C₄×C₁₃	—	4	4	no	—
164	C₂²×C₄×C₁₃	#41	1	8	yes	—
165	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
166	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
167	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
168	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
169	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
170	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
171	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
172	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
173	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
174	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
175	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
176	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
177	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
178	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
179	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
180	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
181	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
182	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
183	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	—
184	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
185	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
186	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
187	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
188	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	—
189	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	—
190	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
191	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
192	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	—
193	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
194	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
195	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
196	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
197	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
198	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
199	C₄²×C₁₃	C₂⁴	1	8	yes	—
200	C₄²×C₁₃	C₂⁴	1	8	yes	—
201	C₄²×C₁₃	C₂⁴	1	16	yes	—
202	C₄²×C₁₃	C₂⁴	1	16	yes	—
203	C₄²×C₁₃	C₂⁴	1	16	yes	—
204	C₄²×C₁₃	C₂⁴	1	16	yes	—
205	C₄²×C₁₃	C₂⁴	1	16	yes	—
206	#3461	C₂×C₁₃	1	32	yes	direct product factor
207	C₂×#544	C₂×C₁₃	1	1	yes	characteristic, complemented
208	C₂×#542	C₂×C₁₃	1	4	yes	complemented
209	C₂×#541	C₂×C₁₃	1	4	yes	complemented
210	C₂×#539	C₂×C₁₃	1	4	yes	complemented
211	C₂×#537	C₂×C₁₃	1	1	yes	characteristic
212	C₂×#536	C₂×C₁₃	1	2	yes	complemented
213	C₂×#533	C₂×C₁₃	1	4	yes	complemented
214	C₂×#529	C₂×C₁₃	1	4	yes	complemented
215	C₂×#529	C₂×C₁₃	1	4	yes	complemented
216	C₂×C₄×#41	C₂×C₁₃	1	2	yes	complemented
217	C₂²×C₄×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
218	C₂³×C₁₃	—	2	2	no	—
219	C₂³×C₁₃	—	2	2	no	—
220	C₂³×C₁₃	—	2	8	no	—
221	C₂³×C₁₃	—	2	8	no	—
222	C₂³×C₁₃	—	2	8	no	—
223	C₂³×C₁₃	C₂×#41	1	4	yes	—
224	C₂³×C₁₃	C₂⁵	1	8	yes	—
225	C₂³×C₁₃	C₂⁵	1	2	yes	—
226	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
227	Q₈×C₁₃	—	2	32	no	—
228	Q₈×C₁₃	—	2	16	no	—
229	Q₈×C₁₃	—	4	16	no	—
230	D₄×C₁₃	—	2	32	no	—
231	D₄×C₁₃	—	2	16	no	—
232	D₄×C₁₃	—	4	16	no	—
233	C₂×C₄×C₁₃	—	2	8	no	—
234	C₂×C₄×C₁₃	—	2	16	no	—
235	C₂×C₄×C₁₃	—	2	8	no	—
236	C₂×C₄×C₁₃	—	2	2	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	32	no	—
242	C₂×C₄×C₁₃	—	2	8	no	—
243	C₂×C₄×C₁₃	—	2	32	no	—
244	C₂×C₄×C₁₃	—	4	4	no	—
245	C₂×C₄×C₁₃	—	4	16	no	—
246	C₂×C₄×C₁₃	—	4	8	no	—
247	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
248	C₂×C₄×C₁₃	C₂×#41	1	16	yes	—
249	C₂×C₄×C₁₃	2₋¹⁺⁴	1	4	yes	—
250	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
251	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
252	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
253	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
254	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
255	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
256	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
257	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
258	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
259	C₂²×#41	C₂²×C₁₃	1	2	yes	—
260	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
261	#544	C₂²×C₁₃	1	16	yes	complemented
262	#542	C₂²×C₁₃	1	64	yes	complemented
263	#541	C₂²×C₁₃	1	64	yes	complemented
264	#539	C₂²×C₁₃	1	64	yes	complemented
265	#537	C₂²×C₁₃	1	16	yes	—
266	#536	C₂²×C₁₃	1	32	yes	complemented
267	#533	C₂²×C₁₃	1	64	yes	complemented
268	C₂×C₄⋊Q₈	C₂²×C₁₃	1	4	yes	—
269	C₂×C₄⋊Q₈	C₂²×C₁₃	1	4	yes	—
270	#529	C₂²×C₁₃	1	64	yes	complemented
271	#529	C₂²×C₁₃	1	64	yes	complemented
272	C₂×#126	C₂²×C₁₃	1	8	yes	—
273	C₂×#126	C₂²×C₁₃	1	8	yes	—
274	C₂×#125	C₂²×C₁₃	1	4	yes	—
275	C₂×#125	C₂²×C₁₃	1	4	yes	—
276	C₂×#125	C₂²×C₁₃	1	8	yes	—
277	C₂×#124	C₂²×C₁₃	1	4	yes	—
278	C₂×#124	C₂²×C₁₃	1	4	yes	—
279	C₂×#123	C₂²×C₁₃	1	8	yes	—
280	C₂×#123	C₂²×C₁₃	1	8	yes	—
281	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
282	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
283	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
284	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
285	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	8	yes	—
286	C₂×#121	C₂²×C₁₃	1	4	yes	—
287	C₂×#121	C₂²×C₁₃	1	4	yes	—
288	C₄×#41	C₂²×C₁₃	1	32	yes	complemented
289	C₂×C₄×Q₈	C₂²×C₁₃	1	4	yes	—
290	C₂×C₄×Q₈	C₂²×C₁₃	1	4	yes	—
291	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
292	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
293	C₂×C₄×Q₈	C₂²×C₁₃	1	4	yes	—
294	C₂×C₄×Q₈	C₂²×C₁₃	1	16	yes	complemented
295	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
296	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
297	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
298	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
299	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
300	C₂×#117	C₂²×C₁₃	1	2	yes	—
301	C₂×#117	C₂²×C₁₃	1	4	yes	—
302	C₂×#117	C₂²×C₁₃	1	8	yes	—
303	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
304	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
305	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
306	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
307	C₂²×C₄²	C₂²×C₁₃	1	4	yes	—
308	C₂²×C₁₃	—	2	2	no	—
309	C₂²×C₁₃	—	2	2	no	—
310	C₂²×C₁₃	—	2	8	no	—
311	C₂²×C₁₃	—	2	8	no	—
312	C₂²×C₁₃	—	2	8	no	—
313	C₂²×C₁₃	—	2	8	no	—
314	C₂²×C₁₃	—	4	16	no	—
315	C₂²×C₁₃	C₂²×#41	1	4	yes	—
316	C₂²×C₁₃	C₂²×#41	1	2	yes	—
317	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
318	C₂²×C₁₃	#585	1	2	yes	—
319	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
320	C₄×C₁₃	—	2	8	no	—
321	C₄×C₁₃	—	2	8	no	—
322	C₄×C₁₃	—	2	2	no	—
323	C₄×C₁₃	—	2	8	no	—
324	C₄×C₁₃	—	2	4	no	—
325	C₄×C₁₃	—	2	8	no	—
326	C₄×C₁₃	—	2	8	no	—
327	C₄×C₁₃	C₂²×#41	1	8	yes	—
328	C₄×C₁₃	C₂×2₋¹⁺⁴	1	4	yes	—
329	C₂×#41	—	2	16	no	—
330	C₂×#41	C₂³×C₁₃	1	16	yes	—
331	C₂²×Q₈	—	2	8	no	—
332	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
333	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
334	C₂²×Q₈	C₂³×C₁₃	1	8	yes	—
335	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
336	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
337	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
338	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
339	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
340	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
341	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
342	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
343	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
344	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
345	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
346	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
347	C₄⋊Q₈	C₂³×C₁₃	1	32	yes	—
348	C₄⋊Q₈	C₂³×C₁₃	1	32	yes	—
349	#126	C₂³×C₁₃	1	64	yes	—
350	#126	C₂³×C₁₃	1	64	yes	—
351	#125	C₂³×C₁₃	1	32	yes	—
352	#125	C₂³×C₁₃	1	32	yes	—
353	#125	C₂³×C₁₃	1	64	yes	—
354	#124	C₂³×C₁₃	1	32	yes	—
355	#124	C₂³×C₁₃	1	32	yes	—
356	#123	C₂³×C₁₃	1	64	yes	—
357	#123	C₂³×C₁₃	1	64	yes	—
358	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	—
359	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	—
360	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	—
361	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	—
362	C₂²⋊Q₈	C₂³×C₁₃	1	64	yes	—
363	#121	C₂³×C₁₃	1	32	yes	—
364	#121	C₂³×C₁₃	1	32	yes	—
365	C₄×Q₈	C₂³×C₁₃	1	32	yes	—
366	C₄×Q₈	C₂³×C₁₃	1	32	yes	—
367	C₄×Q₈	C₂³×C₁₃	1	16	yes	—
368	C₄×Q₈	C₂³×C₁₃	1	16	yes	—
369	C₄×Q₈	C₂³×C₁₃	1	32	yes	—
370	C₄×D₄	C₂³×C₁₃	1	16	yes	—
371	C₄×D₄	C₂³×C₁₃	1	32	yes	—
372	C₄×D₄	C₂³×C₁₃	1	32	yes	—
373	C₄×D₄	C₂³×C₁₃	1	16	yes	—
374	C₄×D₄	C₂³×C₁₃	1	32	yes	—
375	#117	C₂³×C₁₃	1	16	yes	—
376	#117	C₂³×C₁₃	1	32	yes	—
377	#117	C₂³×C₁₃	1	64	yes	—
378	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
379	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
380	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
381	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	yes	—
382	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
383	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
384	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
385	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
386	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
387	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
388	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
389	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
390	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
391	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
392	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
393	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
394	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
395	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
396	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
397	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
398	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
399	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
400	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
401	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
402	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
403	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
404	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
405	C₂×C₄²	C₂³×C₁₃	1	16	yes	—
406	C₂×C₄²	C₂³×C₁₃	1	32	yes	—
407	C₂×C₁₃	—	2	4	no	—
408	C₂×C₁₃	—	4	8	no	—
409	C₂×C₁₃	#3461	1	4	yes	direct product factor
410	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
411	C₂×C₁₃	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
412	C₂×C₁₃	C₂×#585	1	1	yes	characteristic
413	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
414	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
415	#41	—	2	64	no	—
416	C₂×Q₈	—	2	16	no	—
417	C₂×Q₈	—	2	32	no	—
418	C₂×Q₈	—	2	8	no	—
419	C₂×Q₈	—	4	8	no	—
420	C₂×Q₈	C₂⁴×C₁₃	1	16	yes	—
421	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
422	C₂×Q₈	C₂⁴×C₁₃	1	16	yes	—
423	C₂×D₄	—	2	16	no	—
424	C₂×D₄	—	2	8	no	—
425	C₂×D₄	—	4	8	no	—
426	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
427	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
428	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
429	C₂²×C₄	—	2	8	no	—
430	C₂²×C₄	—	2	16	no	—
431	C₂²×C₄	—	2	4	no	—
432	C₂²×C₄	—	2	16	no	—
433	C₂²×C₄	—	4	2	no	—
434	C₂²×C₄	—	4	8	no	—
435	C₂²×C₄	—	4	4	no	—
436	C₂²×C₄	C₁₃×#41	1	8	yes	—
437	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
438	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
439	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
440	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
441	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
442	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
443	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
444	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
445	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
446	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
447	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
448	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
449	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
450	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
451	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
452	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
453	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
454	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
455	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	—
456	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
457	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
458	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
459	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
460	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	—
461	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	—
462	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
463	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
464	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	—
465	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
466	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
467	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
468	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
469	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
470	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
471	C₄²	C₂⁴×C₁₃	1	8	yes	—
472	C₄²	C₂⁴×C₁₃	1	8	yes	—
473	C₄²	C₂⁴×C₁₃	1	16	yes	—
474	C₄²	C₂⁴×C₁₃	1	16	yes	—
475	C₄²	C₂⁴×C₁₃	1	16	yes	—
476	C₄²	C₂⁴×C₁₃	1	16	yes	—
477	C₄²	C₂⁴×C₁₃	1	16	yes	—
478	C₁₃	C₂×#3461	1	1	yes	characteristic, direct product factor, Sylow
479	C₂³	—	2	2	no	—
480	C₂³	—	2	2	no	—
481	C₂³	—	2	8	no	—
482	C₂³	—	2	8	no	—
483	C₂³	—	2	8	no	—
484	C₂³	C₂×C₁₃×#41	1	4	yes	—
485	C₂³	C₂⁵×C₁₃	1	8	yes	—
486	C₂³	C₂⁵×C₁₃	1	2	yes	—
487	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
488	Q₈	—	2	32	no	—
489	Q₈	—	2	16	no	—
490	Q₈	—	4	16	no	—
491	D₄	—	2	32	no	—
492	D₄	—	2	16	no	—
493	D₄	—	4	16	no	—
494	C₂×C₄	—	2	8	no	—
495	C₂×C₄	—	2	16	no	—
496	C₂×C₄	—	2	8	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	8	no	—
499	C₂×C₄	—	2	4	no	—
500	C₂×C₄	—	2	8	no	—
501	C₂×C₄	—	2	8	no	—
502	C₂×C₄	—	2	32	no	—
503	C₂×C₄	—	2	8	no	—
504	C₂×C₄	—	2	32	no	—
505	C₂×C₄	—	4	4	no	—
506	C₂×C₄	—	4	16	no	—
507	C₂×C₄	—	4	8	no	—
508	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
509	C₂×C₄	C₂×C₁₃×#41	1	16	yes	—
510	C₂×C₄	C₁₃×2₋¹⁺⁴	1	4	yes	—
511	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
512	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
513	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
514	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
515	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
516	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
517	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
518	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
519	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
520	C₂²	—	2	2	no	—
521	C₂²	—	2	2	no	—
522	C₂²	—	2	8	no	—
523	C₂²	—	2	8	no	—
524	C₂²	—	2	8	no	—
525	C₂²	—	2	8	no	—
526	C₂²	—	4	16	no	—
527	C₂²	C₂²×C₁₃×#41	1	4	yes	—
528	C₂²	C₂²×C₁₃×#41	1	2	yes	—
529	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
530	C₂²	C₁₃×#585	1	2	yes	—
531	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
532	C₄	—	2	8	no	—
533	C₄	—	2	8	no	—
534	C₄	—	2	2	no	—
535	C₄	—	2	8	no	—
536	C₄	—	2	4	no	—
537	C₄	—	2	8	no	—
538	C₄	—	2	8	no	—
539	C₄	C₂²×C₁₃×#41	1	8	yes	—
540	C₄	C₂×C₁₃×2₋¹⁺⁴	1	4	yes	—
541	C₂	—	2	4	no	—
542	C₂	—	4	8	no	—
543	C₂	C₁₃×#3461	1	4	yes	direct product factor
544	C₂	C₂³×C₁₃×#41	1	1	yes	characteristic
545	C₂	C₂²×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
546	C₂	C₂×C₁₃×#585	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₃
socle	C₂³×C₁₃	C₂⁵
prime radical	C₂×C₁₃×#537	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3461	C₂	direct (N × H)
2. C₂×C₁₃×#544	C₂	semidirect
3. C₂×C₁₃×#542	C₂	semidirect
4. C₂×C₁₃×#541	C₂	semidirect
5. C₂×C₁₃×#539	C₂	semidirect
7. C₂×C₁₃×#536	C₂	semidirect
8. C₂×C₁₃×#533	C₂	semidirect
9. C₂×C₁₃×#529	C₂	semidirect
10. C₂×C₁₃×#529	C₂	semidirect
11. C₂×C₄×C₁₃×#41	C₂	semidirect
12. C₂²×C₄×Q₈×C₁₃	C₂	semidirect
15. C₁₃×#544	C₂²	semidirect
16. C₁₃×#542	C₂²	semidirect
17. C₁₃×#541	C₂²	semidirect
18. C₁₃×#539	C₂²	semidirect
20. C₁₃×#536	C₂²	semidirect
21. C₁₃×#533	C₂²	semidirect
24. C₁₃×#529	C₂²	semidirect
25. C₁₃×#529	C₂²	semidirect
42. C₄×C₁₃×#41	C₂²	semidirect
48. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
140. C₂×#3461	C₁₃	direct (N × H)
206. #3461	C₂×C₁₃	direct (N × H)
207. C₂×#544	C₂×C₁₃	semidirect
208. C₂×#542	C₂×C₁₃	semidirect
209. C₂×#541	C₂×C₁₃	semidirect
210. C₂×#539	C₂×C₁₃	semidirect
212. C₂×#536	C₂×C₁₃	semidirect
213. C₂×#533	C₂×C₁₃	semidirect
214. C₂×#529	C₂×C₁₃	semidirect
215. C₂×#529	C₂×C₁₃	semidirect
216. C₂×C₄×#41	C₂×C₁₃	semidirect
217. C₂²×C₄×Q₈	C₂×C₁₃	semidirect
261. #544	C₂²×C₁₃	semidirect
262. #542	C₂²×C₁₃	semidirect
263. #541	C₂²×C₁₃	semidirect
264. #539	C₂²×C₁₃	semidirect
266. #536	C₂²×C₁₃	semidirect
267. #533	C₂²×C₁₃	semidirect
270. #529	C₂²×C₁₃	semidirect
271. #529	C₂²×C₁₃	semidirect
288. C₄×#41	C₂²×C₁₃	semidirect
294. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
409. C₂×C₁₃	#3461	direct (N × H)
478. C₁₃	C₂×#3461	direct (N × H)
543. C₂	C₁₃×#3461	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#3461	2
C₂×C₁₃×#544	2
C₂×C₁₃×#542	2
C₂×C₁₃×#541	2
C₂×C₁₃×#539	2
C₂×C₁₃×#537	2
C₂×C₁₃×#536	2
C₂×C₁₃×#533	2
C₂×C₁₃×#529	2
C₂×C₄×C₁₃×#41	2
C₂²×C₄×Q₈×C₁₃	2
C₂×#3461	13

Subgroups — C2×C13×#3461 #15749021

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3461 #15749021