Subgroups — C₂×C₁₃×#3217 #15747124

Order 3328.

2834 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#127	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3217	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#496	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×#490	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#460	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#459	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#450	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₃×#447	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₃×#432	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂³×D₄×C₁₃	—	2	1	no	—
12	C₂³×D₄×C₁₃	—	2	1	no	—
13	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
14	C₂²×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
15	C₂²×C₁₃×D₈	C₂²	1	4	yes	complemented
16	C₂×C₁₃×#127	—	2	1	no	—
17	C₂×C₁₃×#127	—	2	1	no	—
18	C₂×C₁₃×#127	—	2	4	no	—
19	C₂×C₁₃×#127	C₂²	1	2	yes	—
20	C₂×C₁₃×#127	C₂²	1	2	yes	—
21	C₂×C₁₃×#127	C₂²	1	8	yes	complemented
22	C₁₃×#529	—	2	4	no	—
23	C₁₃×#529	C₂²	1	8	yes	complemented
24	C₂×C₁₃×#126	—	2	1	no	—
25	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₁₃×#123	—	2	1	no	—
28	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₄×D₄×C₁₃	—	2	1	no	—
32	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₁₃×#117	—	2	1	no	—
34	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
35	C₁₃×#496	C₂²	1	16	yes	complemented
36	C₁₃×#490	C₂²	1	16	yes	complemented
37	C₁₃×#460	C₂²	1	16	yes	complemented
38	C₁₃×#459	C₂²	1	16	yes	complemented
39	C₁₃×#450	C₂²	1	16	yes	complemented
40	C₁₃×#447	C₂²	1	16	yes	complemented
41	C₁₃×#432	C₂²	1	8	yes	complemented
42	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	complemented
43	C₂×C₁₃×#102	C₂²	1	4	yes	complemented
44	C₂×C₁₃×#102	C₂²	1	4	yes	complemented
45	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
46	C₂×C₁₃×#97	C₂²	1	2	yes	complemented
47	C₂⁵×C₁₃	—	2	2	no	—
48	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
49	C₂²×D₄×C₁₃	—	2	1	no	—
50	C₂²×D₄×C₁₃	—	2	4	no	—
51	C₂²×D₄×C₁₃	—	2	2	no	—
52	C₂²×D₄×C₁₃	—	2	2	no	—
53	C₂²×D₄×C₁₃	—	2	2	no	—
54	C₂²×D₄×C₁₃	—	2	2	no	—
55	C₂²×D₄×C₁₃	—	2	2	no	—
56	C₂²×D₄×C₁₃	—	2	8	no	—
57	C₂²×D₄×C₁₃	—	2	8	no	—
58	C₂²×D₄×C₁₃	—	4	8	no	—
59	C₂²×D₄×C₁₃	—	4	8	no	—
60	C₂²×D₄×C₁₃	—	4	8	no	—
61	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
62	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
63	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
64	C₂³×C₄×C₁₃	—	2	1	no	—
65	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
66	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
67	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
68	C₂×C₁₃×SD₁₆	—	4	8	no	—
69	C₂×C₁₃×SD₁₆	C₂³	1	16	yes	complemented
70	C₂×C₁₃×D₈	—	4	8	no	—
71	C₂×C₁₃×D₈	C₂³	1	16	yes	complemented
72	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
73	C₁₃×#127	—	2	4	no	—
74	C₁₃×#127	—	2	4	no	—
75	C₁₃×#127	—	2	8	no	—
76	C₁₃×#127	—	2	8	no	—
77	C₁₃×#127	C₂³	1	8	yes	—
78	C₁₃×#127	C₂³	1	8	yes	—
79	C₁₃×#126	—	2	8	no	—
80	C₁₃×#125	—	2	2	no	—
81	C₁₃×#125	C₂³	1	4	yes	complemented
82	C₁₃×#124	—	2	2	no	—
83	C₁₃×#124	C₂³	1	4	yes	complemented
84	C₁₃×#123	—	2	8	no	—
85	C₁₃×C₂²⋊Q₈	—	2	2	no	—
86	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
87	C₁₃×#121	—	2	2	no	—
88	C₁₃×#121	C₂³	1	4	yes	—
89	C₄×Q₈×C₁₃	—	2	2	no	—
90	C₄×Q₈×C₁₃	C₂³	1	4	yes	complemented
91	C₄×D₄×C₁₃	—	2	8	no	—
92	C₄×D₄×C₁₃	—	2	2	no	—
93	C₄×D₄×C₁₃	C₂³	1	4	yes	complemented
94	C₁₃×#117	—	2	8	no	—
95	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
96	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
97	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
98	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
99	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
100	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
101	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
102	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
103	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
104	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
105	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
106	C₂×C₄²×C₁₃	—	2	1	no	—
107	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
108	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
109	C₂×C₄²×C₁₃	D₄	1	4	yes	—
110	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
111	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
112	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
113	C₁₃×C₄⋊C₈	C₂³	1	8	yes	complemented
114	C₁₃×#102	C₂³	1	16	yes	complemented
115	C₁₃×#102	C₂³	1	16	yes	complemented
116	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
117	C₁₃×#97	C₂³	1	8	yes	complemented
118	C₂×#3217	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
119	C₂⁴×C₁₃	—	2	8	no	—
120	C₂⁴×C₁₃	—	2	1	no	—
121	C₂⁴×C₁₃	—	2	4	no	—
122	C₂⁴×C₁₃	—	4	8	no	—
123	C₂⁴×C₁₃	—	4	8	no	—
124	C₂⁴×C₁₃	—	4	8	no	—
125	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
126	C₂×Q₈×C₁₃	—	2	1	no	—
127	C₂×Q₈×C₁₃	—	2	4	no	—
128	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
129	C₂×D₄×C₁₃	—	2	4	no	—
130	C₂×D₄×C₁₃	—	2	1	no	—
131	C₂×D₄×C₁₃	—	2	8	no	—
132	C₂×D₄×C₁₃	—	2	4	no	—
133	C₂×D₄×C₁₃	—	2	8	no	—
134	C₂×D₄×C₁₃	—	2	8	no	—
135	C₂×D₄×C₁₃	—	2	8	no	—
136	C₂×D₄×C₁₃	—	2	8	no	—
137	C₂×D₄×C₁₃	—	2	4	no	—
138	C₂×D₄×C₁₃	—	2	8	no	—
139	C₂×D₄×C₁₃	—	2	8	no	—
140	C₂×D₄×C₁₃	—	4	16	no	—
141	C₂×D₄×C₁₃	—	4	8	no	—
142	C₂×D₄×C₁₃	—	4	8	no	—
143	C₂×D₄×C₁₃	—	4	8	no	—
144	C₂×D₄×C₁₃	—	4	8	no	—
145	C₂×D₄×C₁₃	—	4	32	no	—
146	C₂×D₄×C₁₃	—	4	16	no	—
147	C₂×D₄×C₁₃	—	4	32	no	—
148	C₂×D₄×C₁₃	—	4	4	no	—
149	C₂×D₄×C₁₃	—	4	8	no	—
150	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
151	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
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	1	no	—
156	C₂²×C₄×C₁₃	—	2	1	no	—
157	C₂²×C₄×C₁₃	—	2	1	no	—
158	C₂²×C₄×C₁₃	—	2	4	no	—
159	C₂²×C₄×C₁₃	—	4	4	no	—
160	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
161	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
162	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
163	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
169	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
170	C₁₃×SD₁₆	—	4	16	no	—
171	C₁₃×D₈	—	4	16	no	—
172	C₂×C₈×C₁₃	—	2	8	no	—
173	C₂×C₈×C₁₃	C₂⁴	1	8	yes	—
174	C₁₃×C₄⋊C₄	—	2	4	no	—
175	C₁₃×C₄⋊C₄	—	2	4	no	—
176	C₁₃×C₄⋊C₄	—	2	4	no	—
177	C₁₃×C₄⋊C₄	—	2	4	no	—
178	C₁₃×C₄⋊C₄	—	2	1	no	—
179	C₁₃×C₄⋊C₄	—	2	1	no	—
180	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
181	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
182	C₁₃×C₂²⋊C₄	—	2	4	no	—
183	C₁₃×C₂²⋊C₄	—	2	4	no	—
184	C₁₃×C₂²⋊C₄	—	2	4	no	—
185	C₁₃×C₂²⋊C₄	—	2	4	no	—
186	C₁₃×C₂²⋊C₄	—	2	4	no	—
187	C₄²×C₁₃	—	2	4	no	—
188	C₄²×C₁₃	C₂×D₄	1	4	yes	—
189	C₄²×C₁₃	C₂×D₄	1	2	yes	—
190	C₄²×C₁₃	C₂×D₄	1	2	yes	—
191	C₄²×C₁₃	C₂×D₄	1	4	yes	—
192	C₄²×C₁₃	C₂⁴	1	2	yes	—
193	C₄²×C₁₃	C₂⁴	1	2	yes	—
194	C₂²×#127	C₂×C₁₃	1	1	yes	characteristic, complemented
195	C₂×#529	C₂×C₁₃	1	1	yes	characteristic, complemented
196	#3217	C₂×C₁₃	1	16	yes	direct product factor
197	C₂×#496	C₂×C₁₃	1	2	yes	complemented
198	C₂×#490	C₂×C₁₃	1	2	yes	complemented
199	C₂×#460	C₂×C₁₃	1	2	yes	complemented
200	C₂×#459	C₂×C₁₃	1	2	yes	complemented
201	C₂×#450	C₂×C₁₃	1	2	yes	complemented
202	C₂×#447	C₂×C₁₃	1	2	yes	complemented
203	C₂×#432	C₂×C₁₃	1	1	yes	characteristic, complemented
204	C₂³×C₁₃	—	2	2	no	—
205	C₂³×C₁₃	—	2	2	no	—
206	C₂³×C₁₃	—	2	2	no	—
207	C₂³×C₁₃	—	2	8	no	—
208	C₂³×C₁₃	—	4	16	no	—
209	C₂³×C₁₃	—	4	16	no	—
210	C₂³×C₁₃	—	4	8	no	—
211	C₂³×C₁₃	—	4	2	no	—
212	C₂³×C₁₃	—	4	2	no	—
213	C₂³×C₁₃	—	4	16	no	—
214	C₂³×C₁₃	—	4	8	no	—
215	C₂³×C₁₃	—	4	8	no	—
216	C₂³×C₁₃	—	4	2	no	—
217	C₂³×C₁₃	—	8	32	no	—
218	C₂³×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
219	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
220	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
221	Q₈×C₁₃	—	2	4	no	—
222	Q₈×C₁₃	—	4	2	no	—
223	D₄×C₁₃	—	2	4	no	—
224	D₄×C₁₃	—	2	8	no	—
225	D₄×C₁₃	—	2	8	no	—
226	D₄×C₁₃	—	4	16	no	—
227	D₄×C₁₃	—	4	16	no	—
228	D₄×C₁₃	—	4	16	no	—
229	D₄×C₁₃	—	4	16	no	—
230	D₄×C₁₃	—	4	8	no	—
231	D₄×C₁₃	—	4	2	no	—
232	D₄×C₁₃	—	4	8	no	—
233	D₄×C₁₃	—	4	16	no	—
234	C₂×C₄×C₁₃	—	2	2	no	—
235	C₂×C₄×C₁₃	—	2	8	no	—
236	C₂×C₄×C₁₃	—	2	2	no	—
237	C₂×C₄×C₁₃	—	2	2	no	—
238	C₂×C₄×C₁₃	—	2	2	no	—
239	C₂×C₄×C₁₃	—	2	4	no	—
240	C₂×C₄×C₁₃	—	2	8	no	—
241	C₂×C₄×C₁₃	—	2	4	no	—
242	C₂×C₄×C₁₃	—	2	2	no	—
243	C₂×C₄×C₁₃	—	2	2	no	—
244	C₂×C₄×C₁₃	—	2	2	no	—
245	C₂×C₄×C₁₃	—	4	2	no	—
246	C₂×C₄×C₁₃	—	4	2	no	—
247	C₂×C₄×C₁₃	—	4	2	no	—
248	C₂×C₄×C₁₃	—	4	8	no	—
249	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
250	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
251	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
252	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
253	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
254	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
255	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
256	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
257	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
258	C₈×C₁₃	—	2	8	no	—
259	C₂³×D₄	—	2	1	no	—
260	C₂³×D₄	—	2	1	no	—
261	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
262	C₂²×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
263	C₂²×D₈	C₂²×C₁₃	1	4	yes	complemented
264	C₂×#127	—	2	1	no	—
265	C₂×#127	—	2	1	no	—
266	C₂×#127	—	2	4	no	—
267	C₂×#127	C₂²×C₁₃	1	2	yes	—
268	C₂×#127	C₂²×C₁₃	1	2	yes	—
269	C₂×#127	C₂²×C₁₃	1	8	yes	complemented
270	#529	—	2	4	no	—
271	#529	C₂²×C₁₃	1	8	yes	complemented
272	C₂×#126	—	2	1	no	—
273	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic, complemented
274	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic, complemented
275	C₂×#123	—	2	1	no	—
276	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
277	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
278	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
279	C₂×C₄×D₄	—	2	1	no	—
280	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
281	C₂×#117	—	2	1	no	—
282	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
283	#496	C₂²×C₁₃	1	16	yes	complemented
284	#490	C₂²×C₁₃	1	16	yes	complemented
285	#460	C₂²×C₁₃	1	16	yes	complemented
286	#459	C₂²×C₁₃	1	16	yes	complemented
287	#450	C₂²×C₁₃	1	16	yes	complemented
288	#447	C₂²×C₁₃	1	16	yes	complemented
289	#432	C₂²×C₁₃	1	8	yes	complemented
290	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	complemented
291	C₂×#102	C₂²×C₁₃	1	4	yes	complemented
292	C₂×#102	C₂²×C₁₃	1	4	yes	complemented
293	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
294	C₂×#97	C₂²×C₁₃	1	2	yes	complemented
295	C₂²×C₁₃	—	2	2	no	—
296	C₂²×C₁₃	—	2	8	no	—
297	C₂²×C₁₃	—	2	2	no	—
298	C₂²×C₁₃	—	4	8	no	—
299	C₂²×C₁₃	—	4	2	no	—
300	C₂²×C₁₃	—	4	2	no	—
301	C₂²×C₁₃	—	4	8	no	—
302	C₂²×C₁₃	—	4	8	no	—
303	C₂²×C₁₃	—	4	2	no	—
304	C₂²×C₁₃	—	8	32	no	—
305	C₂²×C₁₃	—	8	4	no	—
306	C₂²×C₁₃	—	8	16	no	—
307	C₂²×C₁₃	#535	1	2	yes	—
308	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
309	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
310	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
311	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
312	C₄×C₁₃	—	2	2	no	—
313	C₄×C₁₃	—	2	2	no	—
314	C₄×C₁₃	—	2	2	no	—
315	C₄×C₁₃	—	2	2	no	—
316	C₄×C₁₃	—	4	2	no	—
317	C₄×C₁₃	—	4	2	no	—
318	C₄×C₁₃	—	4	2	no	—
319	C₄×C₁₃	#535	1	2	yes	—
320	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
321	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
322	C₂⁵	—	2	2	no	—
323	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
324	C₂²×D₄	—	2	1	no	—
325	C₂²×D₄	—	2	2	no	—
326	C₂²×D₄	—	2	4	no	—
327	C₂²×D₄	—	2	2	no	—
328	C₂²×D₄	—	2	2	no	—
329	C₂²×D₄	—	2	2	no	—
330	C₂²×D₄	—	2	2	no	—
331	C₂²×D₄	—	2	8	no	—
332	C₂²×D₄	—	2	8	no	—
333	C₂²×D₄	—	4	8	no	—
334	C₂²×D₄	—	4	8	no	—
335	C₂²×D₄	—	4	8	no	—
336	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
337	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
338	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
339	C₂³×C₄	—	2	1	no	—
340	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
341	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
342	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
343	C₂×SD₁₆	—	4	8	no	—
344	C₂×SD₁₆	C₂³×C₁₃	1	16	yes	complemented
345	C₂×D₈	—	4	8	no	—
346	C₂×D₈	C₂³×C₁₃	1	16	yes	complemented
347	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
348	#127	—	2	4	no	—
349	#127	—	2	4	no	—
350	#127	—	2	8	no	—
351	#127	—	2	8	no	—
352	#127	C₂³×C₁₃	1	8	yes	—
353	#127	C₂³×C₁₃	1	8	yes	—
354	#126	—	2	8	no	—
355	#125	—	2	2	no	—
356	#125	C₂³×C₁₃	1	4	yes	complemented
357	#124	—	2	2	no	—
358	#124	C₂³×C₁₃	1	4	yes	complemented
359	#123	—	2	8	no	—
360	C₂²⋊Q₈	—	2	2	no	—
361	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
362	#121	—	2	2	no	—
363	#121	C₂³×C₁₃	1	4	yes	—
364	C₄×Q₈	—	2	2	no	—
365	C₄×Q₈	C₂³×C₁₃	1	4	yes	complemented
366	C₄×D₄	—	2	8	no	—
367	C₄×D₄	—	2	2	no	—
368	C₄×D₄	C₂³×C₁₃	1	4	yes	complemented
369	#117	—	2	8	no	—
370	C₂×C₄⋊C₄	—	2	1	no	—
371	C₂×C₄⋊C₄	—	2	1	no	—
372	C₂×C₄⋊C₄	—	2	1	no	—
373	C₂×C₄⋊C₄	—	2	1	no	—
374	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
375	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
376	C₂×C₂²⋊C₄	—	2	1	no	—
377	C₂×C₂²⋊C₄	—	2	1	no	—
378	C₂×C₂²⋊C₄	—	2	1	no	—
379	C₂×C₂²⋊C₄	—	2	1	no	—
380	C₂×C₂²⋊C₄	—	2	1	no	—
381	C₂×C₄²	—	2	1	no	—
382	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
383	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
384	C₂×C₄²	D₄×C₁₃	1	4	yes	—
385	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
386	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
387	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
388	C₄⋊C₈	C₂³×C₁₃	1	8	yes	complemented
389	#102	C₂³×C₁₃	1	16	yes	complemented
390	#102	C₂³×C₁₃	1	16	yes	complemented
391	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
392	#97	C₂³×C₁₃	1	8	yes	complemented
393	C₂×C₁₃	—	2	4	no	—
394	C₂×C₁₃	—	8	2	no	—
395	C₂×C₁₃	—	8	8	no	—
396	C₂×C₁₃	#3217	1	4	yes	direct product factor
397	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
398	C₂×C₁₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
399	C₂×C₁₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
400	C₂⁴	—	2	1	no	—
401	C₂⁴	—	2	8	no	—
402	C₂⁴	—	2	4	no	—
403	C₂⁴	—	4	8	no	—
404	C₂⁴	—	4	8	no	—
405	C₂⁴	—	4	8	no	—
406	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
407	C₂×Q₈	—	2	1	no	—
408	C₂×Q₈	—	2	4	no	—
409	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
410	C₂×D₄	—	2	4	no	—
411	C₂×D₄	—	2	1	no	—
412	C₂×D₄	—	2	8	no	—
413	C₂×D₄	—	2	4	no	—
414	C₂×D₄	—	2	8	no	—
415	C₂×D₄	—	2	8	no	—
416	C₂×D₄	—	2	8	no	—
417	C₂×D₄	—	2	8	no	—
418	C₂×D₄	—	2	4	no	—
419	C₂×D₄	—	2	8	no	—
420	C₂×D₄	—	2	8	no	—
421	C₂×D₄	—	4	16	no	—
422	C₂×D₄	—	4	8	no	—
423	C₂×D₄	—	4	8	no	—
424	C₂×D₄	—	4	8	no	—
425	C₂×D₄	—	4	8	no	—
426	C₂×D₄	—	4	32	no	—
427	C₂×D₄	—	4	16	no	—
428	C₂×D₄	—	4	32	no	—
429	C₂×D₄	—	4	4	no	—
430	C₂×D₄	—	4	8	no	—
431	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
432	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
433	C₂²×C₄	—	2	4	no	—
434	C₂²×C₄	—	2	4	no	—
435	C₂²×C₄	—	2	4	no	—
436	C₂²×C₄	—	2	1	no	—
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	2	4	no	—
440	C₂²×C₄	—	4	4	no	—
441	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
442	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
443	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
444	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
445	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
446	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
447	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
448	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
449	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
450	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
451	SD₁₆	—	4	16	no	—
452	D₈	—	4	16	no	—
453	C₂×C₈	—	2	8	no	—
454	C₂×C₈	C₂⁴×C₁₃	1	8	yes	—
455	C₄⋊C₄	—	2	4	no	—
456	C₄⋊C₄	—	2	4	no	—
457	C₄⋊C₄	—	2	4	no	—
458	C₄⋊C₄	—	2	4	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
462	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
463	C₂²⋊C₄	—	2	4	no	—
464	C₂²⋊C₄	—	2	4	no	—
465	C₂²⋊C₄	—	2	4	no	—
466	C₂²⋊C₄	—	2	4	no	—
467	C₂²⋊C₄	—	2	4	no	—
468	C₄²	—	2	4	no	—
469	C₄²	C₂×D₄×C₁₃	1	4	yes	—
470	C₄²	C₂×D₄×C₁₃	1	2	yes	—
471	C₄²	C₂×D₄×C₁₃	1	2	yes	—
472	C₄²	C₂×D₄×C₁₃	1	4	yes	—
473	C₄²	C₂⁴×C₁₃	1	2	yes	—
474	C₄²	C₂⁴×C₁₃	1	2	yes	—
475	C₁₃	C₂×#3217	1	1	yes	characteristic, direct product factor, Sylow
476	C₂³	—	2	2	no	—
477	C₂³	—	2	2	no	—
478	C₂³	—	2	2	no	—
479	C₂³	—	2	8	no	—
480	C₂³	—	4	16	no	—
481	C₂³	—	4	16	no	—
482	C₂³	—	4	8	no	—
483	C₂³	—	4	2	no	—
484	C₂³	—	4	2	no	—
485	C₂³	—	4	16	no	—
486	C₂³	—	4	8	no	—
487	C₂³	—	4	8	no	—
488	C₂³	—	4	2	no	—
489	C₂³	—	8	32	no	—
490	C₂³	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
491	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
492	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
493	Q₈	—	2	4	no	—
494	Q₈	—	4	2	no	—
495	D₄	—	2	4	no	—
496	D₄	—	2	8	no	—
497	D₄	—	2	8	no	—
498	D₄	—	4	16	no	—
499	D₄	—	4	16	no	—
500	D₄	—	4	16	no	—
501	D₄	—	4	16	no	—
502	D₄	—	4	8	no	—
503	D₄	—	4	8	no	—
504	D₄	—	4	2	no	—
505	D₄	—	4	16	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	8	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	4	no	—
512	C₂×C₄	—	2	8	no	—
513	C₂×C₄	—	2	4	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	4	2	no	—
518	C₂×C₄	—	4	2	no	—
519	C₂×C₄	—	4	2	no	—
520	C₂×C₄	—	4	8	no	—
521	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
522	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
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	1	yes	characteristic
527	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
528	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
529	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
530	C₈	—	2	8	no	—
531	C₂²	—	2	2	no	—
532	C₂²	—	2	2	no	—
533	C₂²	—	2	8	no	—
534	C₂²	—	4	2	no	—
535	C₂²	—	4	8	no	—
536	C₂²	—	4	8	no	—
537	C₂²	—	4	2	no	—
538	C₂²	—	4	8	no	—
539	C₂²	—	4	2	no	—
540	C₂²	—	8	32	no	—
541	C₂²	—	8	4	no	—
542	C₂²	—	8	16	no	—
543	C₂²	C₁₃×#535	1	2	yes	—
544	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	4	yes	—
545	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
546	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
547	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
548	C₄	—	2	2	no	—
549	C₄	—	2	2	no	—
550	C₄	—	2	2	no	—
551	C₄	—	2	2	no	—
552	C₄	—	4	2	no	—
553	C₄	—	4	2	no	—
554	C₄	—	4	2	no	—
555	C₄	C₁₃×#535	1	2	yes	—
556	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	4	yes	—
557	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
558	C₂	—	2	4	no	—
559	C₂	—	8	8	no	—
560	C₂	—	8	2	no	—
561	C₂	C₁₃×#3217	1	4	yes	direct product factor
562	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
563	C₂	C₂²×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
564	C₂	C₂²×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₃×#127	C₂	semidirect
2. C₂×C₁₃×#529	C₂	semidirect
3. C₁₃×#3217	C₂	direct (N × H)
4. C₂×C₁₃×#496	C₂	semidirect
5. C₂×C₁₃×#490	C₂	semidirect
6. C₂×C₁₃×#460	C₂	semidirect
7. C₂×C₁₃×#459	C₂	semidirect
8. C₂×C₁₃×#450	C₂	semidirect
9. C₂×C₁₃×#447	C₂	semidirect
10. C₂×C₁₃×#432	C₂	semidirect
14. C₂²×C₁₃×SD₁₆	C₂²	semidirect
15. C₂²×C₁₃×D₈	C₂²	semidirect
21. C₂×C₁₃×#127	C₂²	semidirect
23. C₁₃×#529	C₂²	semidirect
25. C₂×C₁₃×#125	C₂²	semidirect
26. C₂×C₁₃×#124	C₂²	semidirect
30. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
32. C₂×C₄×D₄×C₁₃	C₂²	semidirect
35. C₁₃×#496	C₂²	semidirect
36. C₁₃×#490	C₂²	semidirect
37. C₁₃×#460	C₂²	semidirect
38. C₁₃×#459	C₂²	semidirect
39. C₁₃×#450	C₂²	semidirect
40. C₁₃×#447	C₂²	semidirect
41. C₁₃×#432	C₂²	semidirect
42. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
43. C₂×C₁₃×#102	C₂²	semidirect
44. C₂×C₁₃×#102	C₂²	semidirect
46. C₂×C₁₃×#97	C₂²	semidirect
69. C₂×C₁₃×SD₁₆	C₂³	semidirect
71. C₂×C₁₃×D₈	C₂³	semidirect
81. C₁₃×#125	C₂³	semidirect
83. C₁₃×#124	C₂³	semidirect
90. C₄×Q₈×C₁₃	C₂³	semidirect
93. C₄×D₄×C₁₃	C₂³	semidirect
113. C₁₃×C₄⋊C₈	C₂³	semidirect
114. C₁₃×#102	C₂³	semidirect
115. C₁₃×#102	C₂³	semidirect
117. C₁₃×#97	C₂³	semidirect
118. C₂×#3217	C₁₃	direct (N × H)
194. C₂²×#127	C₂×C₁₃	semidirect
195. C₂×#529	C₂×C₁₃	semidirect
196. #3217	C₂×C₁₃	direct (N × H)
197. C₂×#496	C₂×C₁₃	semidirect
198. C₂×#490	C₂×C₁₃	semidirect
199. C₂×#460	C₂×C₁₃	semidirect
200. C₂×#459	C₂×C₁₃	semidirect
201. C₂×#450	C₂×C₁₃	semidirect
202. C₂×#447	C₂×C₁₃	semidirect
203. C₂×#432	C₂×C₁₃	semidirect
262. C₂²×SD₁₆	C₂²×C₁₃	semidirect
263. C₂²×D₈	C₂²×C₁₃	semidirect
269. C₂×#127	C₂²×C₁₃	semidirect
271. #529	C₂²×C₁₃	semidirect
273. C₂×#125	C₂²×C₁₃	semidirect
274. C₂×#124	C₂²×C₁₃	semidirect
278. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
280. C₂×C₄×D₄	C₂²×C₁₃	semidirect
283. #496	C₂²×C₁₃	semidirect
284. #490	C₂²×C₁₃	semidirect
285. #460	C₂²×C₁₃	semidirect
286. #459	C₂²×C₁₃	semidirect
287. #450	C₂²×C₁₃	semidirect
288. #447	C₂²×C₁₃	semidirect
289. #432	C₂²×C₁₃	semidirect
290. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
291. C₂×#102	C₂²×C₁₃	semidirect
292. C₂×#102	C₂²×C₁₃	semidirect
294. C₂×#97	C₂²×C₁₃	semidirect
344. C₂×SD₁₆	C₂³×C₁₃	semidirect
346. C₂×D₈	C₂³×C₁₃	semidirect
356. #125	C₂³×C₁₃	semidirect
358. #124	C₂³×C₁₃	semidirect
365. C₄×Q₈	C₂³×C₁₃	semidirect
368. C₄×D₄	C₂³×C₁₃	semidirect
388. C₄⋊C₈	C₂³×C₁₃	semidirect
389. #102	C₂³×C₁₃	semidirect
390. #102	C₂³×C₁₃	semidirect
392. #97	C₂³×C₁₃	semidirect
396. C₂×C₁₃	#3217	direct (N × H)
475. C₁₃	C₂×#3217	direct (N × H)
561. C₂	C₁₃×#3217	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×#127	2
C₂×C₁₃×#529	2
C₁₃×#3217	2
C₂×C₁₃×#496	2
C₂×C₁₃×#490	2
C₂×C₁₃×#460	2
C₂×C₁₃×#459	2
C₂×C₁₃×#450	2
C₂×C₁₃×#447	2
C₂×C₁₃×#432	2
C₂×#3217	13

Subgroups — C2×C13×#3217 #15747124

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3217 #15747124