Subgroups — C₂×C₁₃×#2626 #15720894

Order 3328.

4142 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2626	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#399	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×#396	C₂	1	4	yes	maximal, complemented
6	C₂×C₁₃×#393	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#385	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#380	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#379	C₂	1	2	yes	maximal
10	C₂⁶×C₁₃	C₂²	1	1	yes	characteristic
11	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
12	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
13	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×C₂²⋊Q₈	—	2	8	no	—
15	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	8	yes	complemented
16	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
17	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
18	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
19	C₂²×C₁₃×C₄⋊C₄	C₂²	1	4	yes	complemented
20	C₂²×C₁₃×C₂²⋊C₄	—	2	8	no	—
21	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
22	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
23	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	—
24	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
25	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
26	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
27	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
28	C₁₃×#399	C₂²	1	16	yes	complemented
29	C₁₃×#396	C₂²	1	32	yes	complemented
30	C₁₃×#393	C₂²	1	16	yes	complemented
31	C₁₃×#385	C₂²	1	16	yes	complemented
32	C₁₃×#380	C₂²	1	8	yes	complemented
33	C₁₃×#379	C₂²	1	16	yes	—
34	C₂×C₁₃×#95	C₂²	1	2	yes	complemented
35	C₂×C₁₃×#95	C₂²	1	4	yes	complemented
36	C₂⁵×C₁₃	—	2	4	no	—
37	C₂⁵×C₁₃	—	2	4	no	—
38	C₂⁵×C₁₃	—	4	4	no	—
39	C₂⁵×C₁₃	—	4	4	no	—
40	C₂⁵×C₁₃	Q₈	1	8	yes	complemented
41	C₂⁵×C₁₃	C₂³	1	2	yes	—
42	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
43	C₂⁵×C₁₃	C₂³	1	4	yes	—
44	C₂²×Q₈×C₁₃	—	2	4	no	—
45	C₂²×Q₈×C₁₃	—	4	4	no	—
46	C₂²×Q₈×C₁₃	C₂³	1	4	yes	complemented
47	C₂³×C₄×C₁₃	—	2	4	no	—
48	C₂³×C₄×C₁₃	—	4	4	no	—
49	C₂³×C₄×C₁₃	—	4	4	no	—
50	C₂³×C₄×C₁₃	D₄	1	8	yes	—
51	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
52	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
53	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
54	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
55	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
56	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
58	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
59	C₁₃×C₂²⋊Q₈	—	2	32	no	—
60	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
61	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
62	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
63	C₂×C₁₃×C₄⋊C₄	—	4	8	no	—
64	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	complemented
65	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	complemented
66	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	complemented
67	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	yes	complemented
68	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
69	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
70	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
71	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
72	C₂×C₁₃×C₂²⋊C₄	—	2	32	no	—
73	C₂×C₁₃×C₂²⋊C₄	—	4	8	no	—
74	C₂×C₁₃×C₂²⋊C₄	—	4	8	no	—
75	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
76	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
77	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
78	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
79	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
80	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
81	C₁₃×#95	C₂³	1	8	yes	complemented
82	C₁₃×#95	C₂³	1	16	yes	complemented
83	C₂×#2626	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
84	C₂⁴×C₁₃	—	2	4	no	—
85	C₂⁴×C₁₃	—	2	4	no	—
86	C₂⁴×C₁₃	—	2	32	no	—
87	C₂⁴×C₁₃	—	2	4	no	—
88	C₂⁴×C₁₃	—	2	8	no	—
89	C₂⁴×C₁₃	—	2	4	no	—
90	C₂⁴×C₁₃	—	2	8	no	—
91	C₂⁴×C₁₃	—	2	8	no	—
92	C₂⁴×C₁₃	—	2	8	no	—
93	C₂⁴×C₁₃	—	4	32	no	—
94	C₂⁴×C₁₃	—	4	8	no	—
95	C₂⁴×C₁₃	—	4	8	no	—
96	C₂⁴×C₁₃	—	4	16	no	—
97	C₂⁴×C₁₃	—	4	16	no	—
98	C₂⁴×C₁₃	—	4	32	no	—
99	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
100	C₂⁴×C₁₃	C₂×Q₈	1	8	yes	—
101	C₂⁴×C₁₃	C₂×Q₈	1	4	yes	—
102	C₂⁴×C₁₃	C₂×Q₈	1	16	yes	complemented
103	C₂⁴×C₁₃	#41	1	4	yes	—
104	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
105	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
106	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
107	C₂×Q₈×C₁₃	—	2	8	no	—
108	C₂×Q₈×C₁₃	—	4	8	no	—
109	C₂×Q₈×C₁₃	—	4	16	no	—
110	C₂²×C₄×C₁₃	—	2	4	no	—
111	C₂²×C₄×C₁₃	—	2	4	no	—
112	C₂²×C₄×C₁₃	—	2	8	no	—
113	C₂²×C₄×C₁₃	—	2	4	no	—
114	C₂²×C₄×C₁₃	—	2	4	no	—
115	C₂²×C₄×C₁₃	—	2	4	no	—
116	C₂²×C₄×C₁₃	—	2	8	no	—
117	C₂²×C₄×C₁₃	—	2	8	no	—
118	C₂²×C₄×C₁₃	—	2	8	no	—
119	C₂²×C₄×C₁₃	—	2	8	no	—
120	C₂²×C₄×C₁₃	—	2	8	no	—
121	C₂²×C₄×C₁₃	—	2	8	no	—
122	C₂²×C₄×C₁₃	—	4	16	no	—
123	C₂²×C₄×C₁₃	—	4	8	no	—
124	C₂²×C₄×C₁₃	—	4	8	no	—
125	C₂²×C₄×C₁₃	—	4	16	no	—
126	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
127	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
128	C₂²×C₄×C₁₃	C₂×D₄	1	16	yes	—
129	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
130	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
131	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
132	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
133	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
134	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
135	C₁₃×C₄⋊C₄	—	2	8	no	—
136	C₁₃×C₄⋊C₄	—	2	16	no	—
137	C₁₃×C₄⋊C₄	—	4	8	no	—
138	C₁₃×C₄⋊C₄	—	4	16	no	—
139	C₁₃×C₂²⋊C₄	—	2	16	no	—
140	C₁₃×C₂²⋊C₄	—	2	16	no	—
141	C₁₃×C₂²⋊C₄	—	2	16	no	—
142	C₁₃×C₂²⋊C₄	—	2	16	no	—
143	C₁₃×C₂²⋊C₄	—	4	16	no	—
144	C₁₃×C₂²⋊C₄	—	4	16	no	—
145	C₂²×C₂²⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
146	C₂³×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic
147	#2626	C₂×C₁₃	1	16	yes	direct product factor
148	C₂×#399	C₂×C₁₃	1	2	yes	complemented
149	C₂×#396	C₂×C₁₃	1	4	yes	complemented
150	C₂×#393	C₂×C₁₃	1	2	yes	complemented
151	C₂×#385	C₂×C₁₃	1	2	yes	complemented
152	C₂×#380	C₂×C₁₃	1	1	yes	characteristic, complemented
153	C₂×#379	C₂×C₁₃	1	2	yes	—
154	C₂³×C₁₃	—	2	8	no	—
155	C₂³×C₁₃	—	2	8	no	—
156	C₂³×C₁₃	—	2	16	no	—
157	C₂³×C₁₃	—	2	16	no	—
158	C₂³×C₁₃	—	2	4	no	—
159	C₂³×C₁₃	—	2	4	no	—
160	C₂³×C₁₃	—	2	16	no	—
161	C₂³×C₁₃	—	2	32	no	—
162	C₂³×C₁₃	—	2	32	no	—
163	C₂³×C₁₃	—	2	4	no	—
164	C₂³×C₁₃	—	2	4	no	—
165	C₂³×C₁₃	—	2	8	no	—
166	C₂³×C₁₃	—	2	8	no	—
167	C₂³×C₁₃	—	4	32	no	—
168	C₂³×C₁₃	—	4	128	no	—
169	C₂³×C₁₃	—	4	16	no	—
170	C₂³×C₁₃	—	4	16	no	—
171	C₂³×C₁₃	—	4	32	no	—
172	C₂³×C₁₃	—	4	8	no	—
173	C₂³×C₁₃	—	4	8	no	—
174	C₂³×C₁₃	—	4	16	no	—
175	C₂³×C₁₃	C₂²⋊Q₈	1	16	yes	—
176	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
177	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
178	C₂³×C₁₃	C₂²×Q₈	1	8	yes	—
179	C₂³×C₁₃	C₂²×Q₈	1	4	yes	—
180	C₂³×C₁₃	C₂²×Q₈	1	2	yes	—
181	C₂³×C₁₃	C₂×#41	1	4	yes	—
182	C₂³×C₁₃	C₂×#41	1	2	yes	—
183	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
184	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
185	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
186	Q₈×C₁₃	—	4	16	no	—
187	C₂×C₄×C₁₃	—	2	8	no	—
188	C₂×C₄×C₁₃	—	2	8	no	—
189	C₂×C₄×C₁₃	—	2	4	no	—
190	C₂×C₄×C₁₃	—	2	4	no	—
191	C₂×C₄×C₁₃	—	2	4	no	—
192	C₂×C₄×C₁₃	—	2	4	no	—
193	C₂×C₄×C₁₃	—	2	4	no	—
194	C₂×C₄×C₁₃	—	2	8	no	—
195	C₂×C₄×C₁₃	—	2	8	no	—
196	C₂×C₄×C₁₃	—	2	8	no	—
197	C₂×C₄×C₁₃	—	2	8	no	—
198	C₂×C₄×C₁₃	—	2	8	no	—
199	C₂×C₄×C₁₃	—	2	8	no	—
200	C₂×C₄×C₁₃	—	4	16	no	—
201	C₂×C₄×C₁₃	—	4	16	no	—
202	C₂×C₄×C₁₃	—	4	8	no	—
203	C₂×C₄×C₁₃	—	4	8	no	—
204	C₂×C₄×C₁₃	—	4	8	no	—
205	C₂×C₄×C₁₃	—	4	16	no	—
206	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
207	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
208	C₂⁶	C₂²×C₁₃	1	1	yes	characteristic
209	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
210	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
211	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
212	C₂×C₂²⋊Q₈	—	2	8	no	—
213	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	8	yes	complemented
214	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
215	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
216	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
217	C₂²×C₄⋊C₄	C₂²×C₁₃	1	4	yes	complemented
218	C₂²×C₂²⋊C₄	—	2	8	no	—
219	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	—
220	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
221	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
222	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
223	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
224	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
225	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
226	#399	C₂²×C₁₃	1	16	yes	complemented
227	#396	C₂²×C₁₃	1	32	yes	complemented
228	#393	C₂²×C₁₃	1	16	yes	complemented
229	#385	C₂²×C₁₃	1	16	yes	complemented
230	#380	C₂²×C₁₃	1	8	yes	complemented
231	#379	C₂²×C₁₃	1	16	yes	—
232	C₂×#95	C₂²×C₁₃	1	4	yes	complemented
233	C₂×#95	C₂²×C₁₃	1	2	yes	complemented
234	C₂²×C₁₃	—	2	32	no	—
235	C₂²×C₁₃	—	2	4	no	—
236	C₂²×C₁₃	—	2	4	no	—
237	C₂²×C₁₃	—	2	8	no	—
238	C₂²×C₁₃	—	2	8	no	—
239	C₂²×C₁₃	—	2	8	no	—
240	C₂²×C₁₃	—	2	16	no	—
241	C₂²×C₁₃	—	4	64	no	—
242	C₂²×C₁₃	—	4	32	no	—
243	C₂²×C₁₃	—	4	4	no	—
244	C₂²×C₁₃	—	4	4	no	—
245	C₂²×C₁₃	—	4	8	no	—
246	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	8	yes	—
247	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	4	yes	—
248	C₂²×C₁₃	#534	1	4	yes	—
249	C₂²×C₁₃	#535	1	4	yes	—
250	C₂²×C₁₃	#538	1	8	yes	—
251	C₂²×C₁₃	#543	1	8	yes	—
252	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
253	C₂²×C₁₃	C₂³×Q₈	1	1	yes	characteristic
254	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
255	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
256	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
257	C₄×C₁₃	—	2	4	no	—
258	C₄×C₁₃	—	2	4	no	—
259	C₄×C₁₃	—	4	4	no	—
260	C₄×C₁₃	—	4	4	no	—
261	C₄×C₁₃	—	4	4	no	—
262	C₄×C₁₃	—	4	8	no	—
263	C₂⁵	—	2	4	no	—
264	C₂⁵	—	2	4	no	—
265	C₂⁵	—	4	4	no	—
266	C₂⁵	—	4	4	no	—
267	C₂⁵	Q₈×C₁₃	1	8	yes	complemented
268	C₂⁵	C₂³×C₁₃	1	2	yes	—
269	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
270	C₂⁵	C₂³×C₁₃	1	4	yes	—
271	C₂²×Q₈	—	2	4	no	—
272	C₂²×Q₈	—	4	4	no	—
273	C₂²×Q₈	C₂³×C₁₃	1	4	yes	complemented
274	C₂³×C₄	—	2	4	no	—
275	C₂³×C₄	—	4	4	no	—
276	C₂³×C₄	—	4	4	no	—
277	C₂³×C₄	D₄×C₁₃	1	8	yes	—
278	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
279	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
280	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
281	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
282	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
283	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
284	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
285	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
286	C₂²⋊Q₈	—	2	32	no	—
287	C₂×C₄⋊C₄	—	2	4	no	—
288	C₂×C₄⋊C₄	—	2	8	no	—
289	C₂×C₄⋊C₄	—	4	4	no	—
290	C₂×C₄⋊C₄	—	4	8	no	—
291	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	complemented
292	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	complemented
293	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	complemented
294	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	yes	complemented
295	C₂×C₂²⋊C₄	—	2	8	no	—
296	C₂×C₂²⋊C₄	—	2	8	no	—
297	C₂×C₂²⋊C₄	—	2	8	no	—
298	C₂×C₂²⋊C₄	—	2	8	no	—
299	C₂×C₂²⋊C₄	—	2	32	no	—
300	C₂×C₂²⋊C₄	—	4	8	no	—
301	C₂×C₂²⋊C₄	—	4	8	no	—
302	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
303	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
304	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
305	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
306	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
307	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
308	#95	C₂³×C₁₃	1	8	yes	complemented
309	#95	C₂³×C₁₃	1	16	yes	complemented
310	C₂×C₁₃	—	2	8	no	—
311	C₂×C₁₃	—	4	8	no	—
312	C₂×C₁₃	#2626	1	8	yes	direct product factor
313	C₂×C₁₃	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
314	C₂×C₁₃	C₂×#534	1	1	yes	characteristic
315	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
316	C₂×C₁₃	C₂×#538	1	2	yes	—
317	C₂×C₁₃	C₂×#543	1	2	yes	—
318	C₂⁴	—	2	4	no	—
319	C₂⁴	—	2	4	no	—
320	C₂⁴	—	2	32	no	—
321	C₂⁴	—	2	4	no	—
322	C₂⁴	—	2	8	no	—
323	C₂⁴	—	2	4	no	—
324	C₂⁴	—	2	8	no	—
325	C₂⁴	—	2	8	no	—
326	C₂⁴	—	2	8	no	—
327	C₂⁴	—	4	32	no	—
328	C₂⁴	—	4	8	no	—
329	C₂⁴	—	4	8	no	—
330	C₂⁴	—	4	16	no	—
331	C₂⁴	—	4	16	no	—
332	C₂⁴	—	4	32	no	—
333	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
334	C₂⁴	C₂×Q₈×C₁₃	1	8	yes	—
335	C₂⁴	C₂×Q₈×C₁₃	1	4	yes	—
336	C₂⁴	C₂×Q₈×C₁₃	1	16	yes	complemented
337	C₂⁴	C₁₃×#41	1	4	yes	—
338	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
339	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
340	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
341	C₂×Q₈	—	2	8	no	—
342	C₂×Q₈	—	4	8	no	—
343	C₂×Q₈	—	4	16	no	—
344	C₂²×C₄	—	2	4	no	—
345	C₂²×C₄	—	2	4	no	—
346	C₂²×C₄	—	2	8	no	—
347	C₂²×C₄	—	2	4	no	—
348	C₂²×C₄	—	2	4	no	—
349	C₂²×C₄	—	2	4	no	—
350	C₂²×C₄	—	2	8	no	—
351	C₂²×C₄	—	2	8	no	—
352	C₂²×C₄	—	2	8	no	—
353	C₂²×C₄	—	2	8	no	—
354	C₂²×C₄	—	2	8	no	—
355	C₂²×C₄	—	2	8	no	—
356	C₂²×C₄	—	4	16	no	—
357	C₂²×C₄	—	4	8	no	—
358	C₂²×C₄	—	4	8	no	—
359	C₂²×C₄	—	4	16	no	—
360	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
361	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
362	C₂²×C₄	C₂×D₄×C₁₃	1	16	yes	—
363	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
364	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
365	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
366	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
367	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
368	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
369	C₄⋊C₄	—	2	8	no	—
370	C₄⋊C₄	—	2	16	no	—
371	C₄⋊C₄	—	4	8	no	—
372	C₄⋊C₄	—	4	16	no	—
373	C₂²⋊C₄	—	2	16	no	—
374	C₂²⋊C₄	—	2	16	no	—
375	C₂²⋊C₄	—	2	16	no	—
376	C₂²⋊C₄	—	2	16	no	—
377	C₂²⋊C₄	—	4	16	no	—
378	C₂²⋊C₄	—	4	16	no	—
379	C₁₃	C₂×#2626	1	1	yes	characteristic, direct product factor, Sylow
380	C₂³	—	2	8	no	—
381	C₂³	—	2	8	no	—
382	C₂³	—	2	16	no	—
383	C₂³	—	2	16	no	—
384	C₂³	—	2	4	no	—
385	C₂³	—	2	4	no	—
386	C₂³	—	2	16	no	—
387	C₂³	—	2	32	no	—
388	C₂³	—	2	32	no	—
389	C₂³	—	2	4	no	—
390	C₂³	—	2	4	no	—
391	C₂³	—	2	8	no	—
392	C₂³	—	2	8	no	—
393	C₂³	—	4	32	no	—
394	C₂³	—	4	128	no	—
395	C₂³	—	4	16	no	—
396	C₂³	—	4	16	no	—
397	C₂³	—	4	32	no	—
398	C₂³	—	4	8	no	—
399	C₂³	—	4	8	no	—
400	C₂³	—	4	16	no	—
401	C₂³	C₁₃×C₂²⋊Q₈	1	16	yes	—
402	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
403	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
404	C₂³	C₂²×Q₈×C₁₃	1	8	yes	—
405	C₂³	C₂²×Q₈×C₁₃	1	4	yes	—
406	C₂³	C₂²×Q₈×C₁₃	1	2	yes	—
407	C₂³	C₂×C₁₃×#41	1	4	yes	—
408	C₂³	C₂×C₁₃×#41	1	2	yes	—
409	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
410	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
411	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
412	Q₈	—	4	16	no	—
413	C₂×C₄	—	2	8	no	—
414	C₂×C₄	—	2	8	no	—
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	2	8	no	—
421	C₂×C₄	—	2	8	no	—
422	C₂×C₄	—	2	8	no	—
423	C₂×C₄	—	2	8	no	—
424	C₂×C₄	—	2	8	no	—
425	C₂×C₄	—	2	8	no	—
426	C₂×C₄	—	4	16	no	—
427	C₂×C₄	—	4	16	no	—
428	C₂×C₄	—	4	8	no	—
429	C₂×C₄	—	4	8	no	—
430	C₂×C₄	—	4	8	no	—
431	C₂×C₄	—	4	16	no	—
432	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
433	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
434	C₂²	—	2	32	no	—
435	C₂²	—	2	4	no	—
436	C₂²	—	2	4	no	—
437	C₂²	—	2	8	no	—
438	C₂²	—	2	8	no	—
439	C₂²	—	2	8	no	—
440	C₂²	—	2	16	no	—
441	C₂²	—	4	64	no	—
442	C₂²	—	4	32	no	—
443	C₂²	—	4	4	no	—
444	C₂²	—	4	4	no	—
445	C₂²	—	4	8	no	—
446	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	8	yes	—
447	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	4	yes	—
448	C₂²	C₁₃×#534	1	4	yes	—
449	C₂²	C₁₃×#535	1	4	yes	—
450	C₂²	C₁₃×#538	1	8	yes	—
451	C₂²	C₁₃×#543	1	8	yes	—
452	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
453	C₂²	C₂³×Q₈×C₁₃	1	1	yes	characteristic
454	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
455	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
456	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
457	C₄	—	2	4	no	—
458	C₄	—	2	4	no	—
459	C₄	—	4	4	no	—
460	C₄	—	4	4	no	—
461	C₄	—	4	4	no	—
462	C₄	—	4	8	no	—
463	C₂	—	2	8	no	—
464	C₂	—	4	8	no	—
465	C₂	C₁₃×#2626	1	8	yes	direct product factor
466	C₂	C₂²×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
467	C₂	C₂×C₁₃×#534	1	1	yes	characteristic
468	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
469	C₂	C₂×C₁₃×#538	1	2	yes	—
470	C₂	C₂×C₁₃×#543	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₃×C₂²⋊Q₈	C₂	semidirect
3. C₁₃×#2626	C₂	direct (N × H)
4. C₂×C₁₃×#399	C₂	semidirect
5. C₂×C₁₃×#396	C₂	semidirect
6. C₂×C₁₃×#393	C₂	semidirect
7. C₂×C₁₃×#385	C₂	semidirect
8. C₂×C₁₃×#380	C₂	semidirect
11. C₂³×Q₈×C₁₃	C₂²	semidirect
15. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
16. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
17. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
18. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
19. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
28. C₁₃×#399	C₂²	semidirect
29. C₁₃×#396	C₂²	semidirect
30. C₁₃×#393	C₂²	semidirect
31. C₁₃×#385	C₂²	semidirect
32. C₁₃×#380	C₂²	semidirect
34. C₂×C₁₃×#95	C₂²	semidirect
35. C₂×C₁₃×#95	C₂²	semidirect
40. C₂⁵×C₁₃	Q₈	semidirect
46. C₂²×Q₈×C₁₃	C₂³	semidirect
64. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
65. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
66. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
67. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
81. C₁₃×#95	C₂³	semidirect
82. C₁₃×#95	C₂³	semidirect
83. C₂×#2626	C₁₃	direct (N × H)
102. C₂⁴×C₁₃	C₂×Q₈	semidirect
145. C₂²×C₂²⋊Q₈	C₂×C₁₃	semidirect
147. #2626	C₂×C₁₃	direct (N × H)
148. C₂×#399	C₂×C₁₃	semidirect
149. C₂×#396	C₂×C₁₃	semidirect
150. C₂×#393	C₂×C₁₃	semidirect
151. C₂×#385	C₂×C₁₃	semidirect
152. C₂×#380	C₂×C₁₃	semidirect
209. C₂³×Q₈	C₂²×C₁₃	semidirect
213. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
214. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
215. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
216. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
217. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
226. #399	C₂²×C₁₃	semidirect
227. #396	C₂²×C₁₃	semidirect
228. #393	C₂²×C₁₃	semidirect
229. #385	C₂²×C₁₃	semidirect
230. #380	C₂²×C₁₃	semidirect
232. C₂×#95	C₂²×C₁₃	semidirect
233. C₂×#95	C₂²×C₁₃	semidirect
267. C₂⁵	Q₈×C₁₃	semidirect
273. C₂²×Q₈	C₂³×C₁₃	semidirect
291. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
292. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
293. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
294. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
308. #95	C₂³×C₁₃	semidirect
309. #95	C₂³×C₁₃	semidirect
312. C₂×C₁₃	#2626	direct (N × H)
336. C₂⁴	C₂×Q₈×C₁₃	semidirect
379. C₁₃	C₂×#2626	direct (N × H)
465. C₂	C₁₃×#2626	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×C₂²⋊Q₈	2
C₂³×C₁₃×C₂²⋊C₄	2
C₁₃×#2626	2
C₂×C₁₃×#399	2
C₂×C₁₃×#396	2
C₂×C₁₃×#393	2
C₂×C₁₃×#385	2
C₂×C₁₃×#380	2
C₂×C₁₃×#379	2
C₂×#2626	13

Subgroups — C2×C13×#2626 #15720894

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2626 #15720894