Subgroups — C₂×C₁₃×#3260 #15747250

Order 3328.

1882 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#541	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#540	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3260	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#479	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×#478	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#468	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#465	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#460	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₃×#461	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₃×#424	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
12	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
13	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₁₃×#541	—	2	4	no	—
16	C₁₃×#541	C₂²	1	8	yes	complemented
17	C₁₃×#540	—	2	4	no	—
18	C₁₃×#540	C₂²	1	8	yes	—
19	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#126	—	2	2	no	—
22	C₂×C₁₃×#125	—	2	2	no	—
23	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#123	—	2	2	no	—
26	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
27	C₂×C₁₃×#121	—	2	2	no	—
28	C₂×C₁₃×#121	C₂²	1	2	yes	—
29	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
31	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
32	C₁₃×#479	C₂²	1	16	yes	complemented
33	C₁₃×#478	C₂²	1	16	yes	complemented
34	C₁₃×#468	C₂²	1	16	yes	complemented
35	C₁₃×#465	C₂²	1	16	yes	complemented
36	C₁₃×#461	C₂²	1	16	yes	complemented
37	C₁₃×#460	C₂²	1	16	yes	complemented
38	C₂×C₁₃×#107	C₂²	1	2	yes	—
39	C₂×C₁₃×#106	C₂²	1	2	yes	—
40	C₁₃×#424	C₂²	1	8	yes	complemented
41	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
42	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
43	C₂×C₁₃×#103	C₂²	1	2	yes	—
44	C₂×C₁₃×#103	C₂²	1	2	yes	—
45	C₂×C₁₃×#102	C₂²	1	2	yes	—
46	C₂×C₁₃×#102	C₂²	1	2	yes	—
47	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
48	C₂²×D₄×C₁₃	—	2	2	no	—
49	C₂²×D₄×C₁₃	—	2	2	no	—
50	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
51	C₂³×C₄×C₁₃	—	2	2	no	—
52	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
53	C₂×C₁₃×SD₁₆	—	4	4	no	—
54	C₂×C₁₃×SD₁₆	—	4	4	no	—
55	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
56	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
57	C₂×C₁₃×M₁₆	—	4	2	no	—
58	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
59	C₂²×C₈×C₁₃	—	4	2	no	—
60	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
61	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
62	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
63	C₁₃×C₄⋊Q₈	—	2	2	no	—
64	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
65	C₁₃×#127	—	2	2	no	—
66	C₁₃×#127	C₂³	1	4	yes	—
67	C₁₃×#126	—	2	16	no	—
68	C₁₃×#125	—	2	16	no	—
69	C₁₃×#125	—	2	2	no	—
70	C₁₃×#125	—	2	2	no	—
71	C₁₃×#125	C₂³	1	4	yes	—
72	C₁₃×#125	C₂³	1	4	yes	—
73	C₁₃×#123	—	2	16	no	—
74	C₁₃×C₂²⋊Q₈	—	2	4	no	—
75	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
76	C₁₃×#121	—	2	4	no	—
77	C₁₃×#121	—	2	16	no	—
78	C₁₃×#121	C₂³	1	8	yes	—
79	C₄×Q₈×C₁₃	—	2	4	no	—
80	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
81	C₄×D₄×C₁₃	—	2	4	no	—
82	C₄×D₄×C₁₃	C₂³	1	8	yes	—
83	C₁₃×#117	D₄	1	4	yes	—
84	C₁₃×#117	C₂³	1	4	yes	—
85	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
86	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
87	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
88	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
89	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
90	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
91	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
92	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
93	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
94	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
95	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
96	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
97	C₂×C₄²×C₁₃	—	2	2	no	—
98	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
100	C₁₃×#107	C₂³	1	8	yes	—
101	C₁₃×#106	C₂³	1	8	yes	—
102	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
103	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
104	C₁₃×#103	C₂³	1	8	yes	—
105	C₁₃×#103	C₂³	1	8	yes	—
106	C₁₃×#102	C₂³	1	8	yes	—
107	C₁₃×#102	C₂³	1	8	yes	—
108	C₂×#3260	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
109	C₂⁴×C₁₃	—	2	2	no	—
110	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
111	C₂×Q₈×C₁₃	—	2	2	no	—
112	C₂×Q₈×C₁₃	—	2	4	no	—
113	C₂×Q₈×C₁₃	—	2	4	no	—
114	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
115	C₂×D₄×C₁₃	—	2	8	no	—
116	C₂×D₄×C₁₃	—	2	2	no	—
117	C₂×D₄×C₁₃	—	2	8	no	—
118	C₂×D₄×C₁₃	—	2	4	no	—
119	C₂×D₄×C₁₃	—	2	4	no	—
120	C₂×D₄×C₁₃	—	8	4	no	—
121	C₂×D₄×C₁₃	—	8	4	no	—
122	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
123	C₂²×C₄×C₁₃	—	2	2	no	—
124	C₂²×C₄×C₁₃	—	2	2	no	—
125	C₂²×C₄×C₁₃	—	2	2	no	—
126	C₂²×C₄×C₁₃	—	2	2	no	—
127	C₂²×C₄×C₁₃	—	2	2	no	—
128	C₂²×C₄×C₁₃	—	2	8	no	—
129	C₂²×C₄×C₁₃	—	8	4	no	—
130	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
132	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
135	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
136	C₁₃×SD₁₆	—	4	8	no	—
137	C₁₃×SD₁₆	—	4	8	no	—
138	C₁₃×M₁₆	—	4	4	no	—
139	C₂×C₈×C₁₃	—	2	4	no	—
140	C₂×C₈×C₁₃	—	2	4	no	—
141	C₂×C₈×C₁₃	—	4	4	no	—
142	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
143	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
144	C₁₃×C₄⋊C₄	—	2	8	no	—
145	C₁₃×C₄⋊C₄	—	2	8	no	—
146	C₁₃×C₄⋊C₄	—	2	8	no	—
147	C₁₃×C₄⋊C₄	—	2	8	no	—
148	C₁₃×C₄⋊C₄	—	2	8	no	—
149	C₁₃×C₄⋊C₄	—	2	2	no	—
150	C₁₃×C₄⋊C₄	—	2	2	no	—
151	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
152	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
153	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
154	C₁₃×C₂²⋊C₄	—	2	8	no	—
155	C₁₃×C₂²⋊C₄	—	2	8	no	—
156	C₁₃×C₂²⋊C₄	—	2	8	no	—
157	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
158	C₄²×C₁₃	—	2	8	no	—
159	C₄²×C₁₃	C₂×D₄	1	2	yes	—
160	C₄²×C₁₃	C₂×D₄	1	2	yes	—
161	C₄²×C₁₃	C₂⁴	1	2	yes	—
162	C₄²×C₁₃	C₂⁴	1	2	yes	—
163	C₂×#541	C₂×C₁₃	1	1	yes	characteristic, complemented
164	C₂×#540	C₂×C₁₃	1	1	yes	characteristic
165	#3260	C₂×C₁₃	1	16	yes	direct product factor
166	C₂×#479	C₂×C₁₃	1	2	yes	complemented
167	C₂×#478	C₂×C₁₃	1	2	yes	complemented
168	C₂×#468	C₂×C₁₃	1	2	yes	complemented
169	C₂×#465	C₂×C₁₃	1	2	yes	complemented
170	C₂×#460	C₂×C₁₃	1	2	yes	complemented
171	C₂×#461	C₂×C₁₃	1	2	yes	complemented
172	C₂×#424	C₂×C₁₃	1	1	yes	characteristic, complemented
173	C₂³×C₁₃	—	2	2	no	—
174	C₂³×C₁₃	—	2	4	no	—
175	C₂³×C₁₃	—	2	4	no	—
176	C₂³×C₁₃	—	4	4	no	—
177	C₂³×C₁₃	—	4	4	no	—
178	C₂³×C₁₃	—	4	4	no	—
179	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
180	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
181	Q₈×C₁₃	—	2	4	no	—
182	Q₈×C₁₃	—	2	4	no	—
183	Q₈×C₁₃	—	4	4	no	—
184	D₄×C₁₃	—	2	4	no	—
185	D₄×C₁₃	—	2	4	no	—
186	D₄×C₁₃	—	4	4	no	—
187	D₄×C₁₃	—	8	8	no	—
188	D₄×C₁₃	—	8	8	no	—
189	C₂×C₄×C₁₃	—	2	2	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	2	no	—
194	C₂×C₄×C₁₃	—	2	2	no	—
195	C₂×C₄×C₁₃	—	2	4	no	—
196	C₂×C₄×C₁₃	—	2	4	no	—
197	C₂×C₄×C₁₃	—	2	4	no	—
198	C₂×C₄×C₁₃	—	4	4	no	—
199	C₂×C₄×C₁₃	—	4	4	no	—
200	C₂×C₄×C₁₃	—	4	4	no	—
201	C₂×C₄×C₁₃	—	8	8	no	—
202	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
203	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
204	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
205	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
206	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
207	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
208	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
209	C₈×C₁₃	—	2	4	no	—
210	C₈×C₁₃	—	2	4	no	—
211	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
212	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
213	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
214	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
215	#541	—	2	4	no	—
216	#541	C₂²×C₁₃	1	8	yes	complemented
217	#540	—	2	4	no	—
218	#540	C₂²×C₁₃	1	8	yes	—
219	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
220	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
221	C₂×#126	—	2	2	no	—
222	C₂×#125	—	2	2	no	—
223	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
224	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
225	C₂×#123	—	2	2	no	—
226	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
227	C₂×#121	—	2	2	no	—
228	C₂×#121	C₂²×C₁₃	1	2	yes	—
229	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
230	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
231	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
232	#479	C₂²×C₁₃	1	16	yes	complemented
233	#478	C₂²×C₁₃	1	16	yes	complemented
234	#468	C₂²×C₁₃	1	16	yes	complemented
235	#465	C₂²×C₁₃	1	16	yes	complemented
236	#461	C₂²×C₁₃	1	16	yes	complemented
237	#460	C₂²×C₁₃	1	16	yes	complemented
238	C₂×#107	C₂²×C₁₃	1	2	yes	—
239	C₂×#106	C₂²×C₁₃	1	2	yes	—
240	#424	C₂²×C₁₃	1	8	yes	complemented
241	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
242	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
243	C₂×#103	C₂²×C₁₃	1	2	yes	—
244	C₂×#103	C₂²×C₁₃	1	2	yes	—
245	C₂×#102	C₂²×C₁₃	1	2	yes	—
246	C₂×#102	C₂²×C₁₃	1	2	yes	—
247	C₂²×C₁₃	—	2	2	no	—
248	C₂²×C₁₃	—	2	4	no	—
249	C₂²×C₁₃	—	4	4	no	—
250	C₂²×C₁₃	—	4	4	no	—
251	C₂²×C₁₃	—	4	4	no	—
252	C₂²×C₁₃	—	4	4	no	—
253	C₂²×C₁₃	—	8	8	no	—
254	C₂²×C₁₃	#537	1	2	yes	—
255	C₂²×C₁₃	#577	1	4	yes	—
256	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
257	C₄×C₁₃	—	2	2	no	—
258	C₄×C₁₃	—	2	4	no	—
259	C₄×C₁₃	—	2	4	no	—
260	C₄×C₁₃	—	4	4	no	—
261	C₄×C₁₃	—	4	4	no	—
262	C₄×C₁₃	—	4	4	no	—
263	C₄×C₁₃	#537	1	2	yes	—
264	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
265	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
266	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
267	C₂²×D₄	—	2	2	no	—
268	C₂²×D₄	—	2	2	no	—
269	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
270	C₂³×C₄	—	2	2	no	—
271	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
272	C₂×SD₁₆	—	4	4	no	—
273	C₂×SD₁₆	—	4	4	no	—
274	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
275	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
276	C₂×M₁₆	—	4	2	no	—
277	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
278	C₂²×C₈	—	4	2	no	—
279	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
280	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
281	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
282	C₄⋊Q₈	—	2	2	no	—
283	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
284	#127	—	2	2	no	—
285	#127	C₂³×C₁₃	1	4	yes	—
286	#126	—	2	16	no	—
287	#125	—	2	16	no	—
288	#125	—	2	2	no	—
289	#125	—	2	2	no	—
290	#125	C₂³×C₁₃	1	4	yes	—
291	#125	C₂³×C₁₃	1	4	yes	—
292	#123	—	2	16	no	—
293	C₂²⋊Q₈	—	2	4	no	—
294	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
295	#121	—	2	4	no	—
296	#121	—	2	16	no	—
297	#121	C₂³×C₁₃	1	8	yes	—
298	C₄×Q₈	—	2	4	no	—
299	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
300	C₄×D₄	—	2	4	no	—
301	C₄×D₄	C₂³×C₁₃	1	8	yes	—
302	#117	D₄×C₁₃	1	4	yes	—
303	#117	C₂³×C₁₃	1	4	yes	—
304	C₂×C₄⋊C₄	—	2	2	no	—
305	C₂×C₄⋊C₄	—	2	2	no	—
306	C₂×C₄⋊C₄	—	2	2	no	—
307	C₂×C₄⋊C₄	—	2	2	no	—
308	C₂×C₄⋊C₄	—	2	2	no	—
309	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
310	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
311	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
312	C₂×C₂²⋊C₄	—	2	2	no	—
313	C₂×C₂²⋊C₄	—	2	2	no	—
314	C₂×C₂²⋊C₄	—	2	2	no	—
315	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
316	C₂×C₄²	—	2	2	no	—
317	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
318	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
319	#107	C₂³×C₁₃	1	8	yes	—
320	#106	C₂³×C₁₃	1	8	yes	—
321	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
322	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
323	#103	C₂³×C₁₃	1	8	yes	—
324	#103	C₂³×C₁₃	1	8	yes	—
325	#102	C₂³×C₁₃	1	8	yes	—
326	#102	C₂³×C₁₃	1	8	yes	—
327	C₂×C₁₃	—	4	2	no	—
328	C₂×C₁₃	—	8	4	no	—
329	C₂×C₁₃	#3260	1	4	yes	direct product factor
330	C₂×C₁₃	C₂×#537	1	1	yes	characteristic
331	C₂×C₁₃	C₂×#577	1	2	yes	—
332	C₂⁴	—	2	2	no	—
333	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
334	C₂×Q₈	—	2	2	no	—
335	C₂×Q₈	—	2	4	no	—
336	C₂×Q₈	—	2	4	no	—
337	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
338	C₂×D₄	—	2	8	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	2	8	no	—
341	C₂×D₄	—	2	4	no	—
342	C₂×D₄	—	2	4	no	—
343	C₂×D₄	—	8	4	no	—
344	C₂×D₄	—	8	4	no	—
345	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	8	no	—
352	C₂²×C₄	—	8	4	no	—
353	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
354	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
355	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
356	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
357	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
358	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
359	SD₁₆	—	4	8	no	—
360	SD₁₆	—	4	8	no	—
361	M₁₆	—	4	4	no	—
362	C₂×C₈	—	2	4	no	—
363	C₂×C₈	—	2	4	no	—
364	C₂×C₈	—	4	4	no	—
365	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
366	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
367	C₄⋊C₄	—	2	8	no	—
368	C₄⋊C₄	—	2	8	no	—
369	C₄⋊C₄	—	2	8	no	—
370	C₄⋊C₄	—	2	8	no	—
371	C₄⋊C₄	—	2	8	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
375	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
376	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
377	C₂²⋊C₄	—	2	8	no	—
378	C₂²⋊C₄	—	2	8	no	—
379	C₂²⋊C₄	—	2	8	no	—
380	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
381	C₄²	—	2	8	no	—
382	C₄²	C₂×D₄×C₁₃	1	2	yes	—
383	C₄²	C₂×D₄×C₁₃	1	2	yes	—
384	C₄²	C₂⁴×C₁₃	1	2	yes	—
385	C₄²	C₂⁴×C₁₃	1	2	yes	—
386	C₁₃	C₂×#3260	1	1	yes	characteristic, direct product factor, Sylow
387	C₂³	—	2	2	no	—
388	C₂³	—	2	4	no	—
389	C₂³	—	2	4	no	—
390	C₂³	—	4	4	no	—
391	C₂³	—	4	4	no	—
392	C₂³	—	4	4	no	—
393	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
394	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
395	Q₈	—	2	4	no	—
396	Q₈	—	2	4	no	—
397	Q₈	—	4	4	no	—
398	D₄	—	2	4	no	—
399	D₄	—	2	4	no	—
400	D₄	—	4	4	no	—
401	D₄	—	8	8	no	—
402	D₄	—	8	8	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	4	4	no	—
413	C₂×C₄	—	4	4	no	—
414	C₂×C₄	—	4	4	no	—
415	C₂×C₄	—	8	8	no	—
416	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
417	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
418	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
419	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
420	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
421	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
422	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
423	C₈	—	2	4	no	—
424	C₈	—	2	4	no	—
425	C₂²	—	2	4	no	—
426	C₂²	—	2	2	no	—
427	C₂²	—	4	4	no	—
428	C₂²	—	4	4	no	—
429	C₂²	—	4	4	no	—
430	C₂²	—	4	4	no	—
431	C₂²	—	8	8	no	—
432	C₂²	C₁₃×#537	1	2	yes	—
433	C₂²	C₁₃×#577	1	4	yes	—
434	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
435	C₄	—	2	4	no	—
436	C₄	—	2	4	no	—
437	C₄	—	2	2	no	—
438	C₄	—	4	4	no	—
439	C₄	—	4	4	no	—
440	C₄	—	4	4	no	—
441	C₄	C₁₃×#537	1	2	yes	—
442	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
443	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
444	C₂	—	4	2	no	—
445	C₂	—	8	4	no	—
446	C₂	C₁₃×#3260	1	4	yes	direct product factor
447	C₂	C₂×C₁₃×#537	1	1	yes	characteristic
448	C₂	C₂×C₁₃×#577	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#540	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₁₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#541	C₂	semidirect
3. C₁₃×#3260	C₂	direct (N × H)
4. C₂×C₁₃×#479	C₂	semidirect
5. C₂×C₁₃×#478	C₂	semidirect
6. C₂×C₁₃×#468	C₂	semidirect
7. C₂×C₁₃×#465	C₂	semidirect
8. C₂×C₁₃×#460	C₂	semidirect
9. C₂×C₁₃×#461	C₂	semidirect
10. C₂×C₁₃×#424	C₂	semidirect
16. C₁₃×#541	C₂²	semidirect
32. C₁₃×#479	C₂²	semidirect
33. C₁₃×#478	C₂²	semidirect
34. C₁₃×#468	C₂²	semidirect
35. C₁₃×#465	C₂²	semidirect
36. C₁₃×#461	C₂²	semidirect
37. C₁₃×#460	C₂²	semidirect
40. C₁₃×#424	C₂²	semidirect
108. C₂×#3260	C₁₃	direct (N × H)
163. C₂×#541	C₂×C₁₃	semidirect
165. #3260	C₂×C₁₃	direct (N × H)
166. C₂×#479	C₂×C₁₃	semidirect
167. C₂×#478	C₂×C₁₃	semidirect
168. C₂×#468	C₂×C₁₃	semidirect
169. C₂×#465	C₂×C₁₃	semidirect
170. C₂×#460	C₂×C₁₃	semidirect
171. C₂×#461	C₂×C₁₃	semidirect
172. C₂×#424	C₂×C₁₃	semidirect
216. #541	C₂²×C₁₃	semidirect
232. #479	C₂²×C₁₃	semidirect
233. #478	C₂²×C₁₃	semidirect
234. #468	C₂²×C₁₃	semidirect
235. #465	C₂²×C₁₃	semidirect
236. #461	C₂²×C₁₃	semidirect
237. #460	C₂²×C₁₃	semidirect
240. #424	C₂²×C₁₃	semidirect
329. C₂×C₁₃	#3260	direct (N × H)
386. C₁₃	C₂×#3260	direct (N × H)
446. C₂	C₁₃×#3260	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×#541	2
C₂×C₁₃×#540	2
C₁₃×#3260	2
C₂×C₁₃×#479	2
C₂×C₁₃×#478	2
C₂×C₁₃×#468	2
C₂×C₁₃×#465	2
C₂×C₁₃×#460	2
C₂×C₁₃×#461	2
C₂×C₁₃×#424	2
C₂×#3260	13

Subgroups — C2×C13×#3260 #15747250

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3260 #15747250