Subgroups — C₂×C₁₃×#3277 #15747375

Order 3328.

2762 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#137	C₂	1	2	yes	maximal, complemented
2	C₂×C₁₃×#548	C₂	1	2	yes	maximal, complemented
3	C₁₃×#3277	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#495	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#468	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#464	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#449	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#451	C₂	1	2	yes	maximal, complemented
9	C₂×C₄×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#436	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×C₁₃×#41	C₂²	1	2	yes	—
12	C₂³×Q₈×C₁₃	C₂²	1	2	yes	—
13	C₂×C₁₃×#137	—	2	16	no	—
14	C₂×C₁₃×#137	C₂²	1	16	yes	complemented
15	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
16	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
19	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
20	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
21	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
22	C₁₃×#548	—	2	8	no	—
23	C₁₃×#548	C₂²	1	16	yes	complemented
24	C₂×C₁₃×#124	—	2	2	no	—
25	C₂×C₁₃×#124	C₂²	1	2	yes	—
26	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
27	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
28	C₂×C₁₃×#121	—	2	2	no	—
29	C₂×C₁₃×#121	C₂²	1	2	yes	—
30	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₁₃	—	2	2	no	—
32	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
33	C₁₃×#495	C₂²	1	8	yes	complemented
34	C₁₃×#468	C₂²	1	16	yes	complemented
35	C₁₃×#464	C₂²	1	16	yes	complemented
36	C₁₃×#451	C₂²	1	16	yes	complemented
37	C₁₃×#449	C₂²	1	16	yes	complemented
38	C₄×C₁₃×Q₁₆	C₂²	1	8	yes	complemented
39	C₁₃×#436	C₂²	1	8	yes	complemented
40	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×#103	C₂²	1	2	yes	—
43	C₂×C₁₃×#103	C₂²	1	2	yes	—
44	C₂×C₁₃×#102	C₂²	1	2	yes	—
45	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
46	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
47	C₂×C₁₃×#41	—	2	4	no	—
48	C₂×C₁₃×#41	—	2	8	no	—
49	C₂×C₁₃×#41	—	4	4	no	—
50	C₂×C₁₃×#41	C₂³	1	8	yes	—
51	C₂²×Q₈×C₁₃	—	2	2	no	—
52	C₂²×Q₈×C₁₃	—	2	4	no	—
53	C₂²×Q₈×C₁₃	—	2	8	no	—
54	C₂²×Q₈×C₁₃	—	4	4	no	—
55	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
56	C₂²×Q₈×C₁₃	C₂³	1	8	yes	—
57	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
58	C₂²×D₄×C₁₃	—	2	2	no	—
59	C₂²×D₄×C₁₃	—	2	2	no	—
60	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
61	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
62	C₂³×C₄×C₁₃	—	2	2	no	—
63	C₂³×C₄×C₁₃	—	2	2	no	—
64	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
65	C₁₃×#137	—	2	64	no	—
66	C₂×C₁₃×Q₁₆	—	2	8	no	—
67	C₂×C₁₃×Q₁₆	—	4	2	no	—
68	C₂×C₁₃×Q₁₆	D₄	1	8	yes	complemented
69	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	—
70	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
71	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
72	C₂×C₁₃×SD₁₆	—	2	8	no	—
73	C₂×C₁₃×SD₁₆	—	2	8	no	—
74	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
75	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
76	C₂×C₁₃×D₈	—	4	2	no	—
77	C₂×C₁₃×D₈	C₂³	1	4	yes	—
78	C₂×C₁₃×M₁₆	—	2	8	no	—
79	C₂×C₁₃×M₁₆	C₂³	1	8	yes	—
80	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
82	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
83	C₁₃×#124	—	2	16	no	—
84	C₁₃×#124	—	2	4	no	—
85	C₁₃×#124	C₂³	1	8	yes	—
86	C₁₃×C₂²⋊Q₈	—	2	4	no	—
87	C₁₃×C₂²⋊Q₈	—	2	16	no	—
88	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
89	C₁₃×#121	—	2	16	no	—
90	C₁₃×#121	—	2	4	no	—
91	C₁₃×#121	C₂³	1	8	yes	—
92	C₄×Q₈×C₁₃	—	2	4	no	—
93	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
94	C₄×D₄×C₁₃	—	2	16	no	—
95	C₄×D₄×C₁₃	D₄	1	4	yes	—
96	C₄×D₄×C₁₃	C₂³	1	4	yes	—
97	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
98	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
99	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
100	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
101	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
102	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
103	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
104	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
105	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
106	C₂×C₄²×C₁₃	—	2	2	no	—
107	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
108	C₁₃×#107	C₂³	1	4	yes	—
109	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
110	C₁₃×#103	C₂³	1	8	yes	—
111	C₁₃×#103	C₂³	1	8	yes	—
112	C₁₃×#102	C₂³	1	8	yes	—
113	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
114	C₄×C₈×C₁₃	C₂³	1	4	yes	—
115	C₂×#3277	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
116	C₂⁴×C₁₃	—	2	2	no	—
117	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
118	C₁₃×#41	—	2	16	no	—
119	C₁₃×#41	—	4	8	no	—
120	C₁₃×#41	—	4	16	no	—
121	C₂×Q₈×C₁₃	—	2	2	no	—
122	C₂×Q₈×C₁₃	—	2	8	no	—
123	C₂×Q₈×C₁₃	—	2	2	no	—
124	C₂×Q₈×C₁₃	—	2	4	no	—
125	C₂×Q₈×C₁₃	—	2	16	no	—
126	C₂×Q₈×C₁₃	—	2	4	no	—
127	C₂×Q₈×C₁₃	—	2	4	no	—
128	C₂×Q₈×C₁₃	—	4	8	no	—
129	C₂×Q₈×C₁₃	—	4	8	no	—
130	C₂×Q₈×C₁₃	—	4	16	no	—
131	C₂×Q₈×C₁₃	C₂×D₄	1	8	yes	—
132	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
133	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
134	C₂×D₄×C₁₃	—	2	8	no	—
135	C₂×D₄×C₁₃	—	2	8	no	—
136	C₂×D₄×C₁₃	—	2	4	no	—
137	C₂×D₄×C₁₃	—	2	2	no	—
138	C₂×D₄×C₁₃	—	2	4	no	—
139	C₂×D₄×C₁₃	—	4	2	no	—
140	C₂×D₄×C₁₃	—	4	8	no	—
141	C₂×D₄×C₁₃	—	4	8	no	—
142	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
143	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
144	C₂²×C₄×C₁₃	—	2	2	no	—
145	C₂²×C₄×C₁₃	—	2	4	no	—
146	C₂²×C₄×C₁₃	—	2	4	no	—
147	C₂²×C₄×C₁₃	—	2	8	no	—
148	C₂²×C₄×C₁₃	—	2	2	no	—
149	C₂²×C₄×C₁₃	—	2	2	no	—
150	C₂²×C₄×C₁₃	—	2	8	no	—
151	C₂²×C₄×C₁₃	—	4	8	no	—
152	C₂²×C₄×C₁₃	—	4	8	no	—
153	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
154	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
157	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
158	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
159	C₁₃×Q₁₆	—	2	16	no	—
160	C₁₃×Q₁₆	—	4	4	no	—
161	C₁₃×Q₁₆	C₂×D₄	1	16	yes	complemented
162	C₁₃×SD₁₆	—	2	16	no	—
163	C₁₃×SD₁₆	—	2	16	no	—
164	C₁₃×D₈	—	4	4	no	—
165	C₁₃×M₁₆	—	2	16	no	—
166	C₂×C₈×C₁₃	—	2	4	no	—
167	C₂×C₈×C₁₃	—	2	2	no	—
168	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
169	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
170	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
171	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
172	C₁₃×C₄⋊C₄	—	2	8	no	—
173	C₁₃×C₄⋊C₄	—	2	8	no	—
174	C₁₃×C₄⋊C₄	—	2	2	no	—
175	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
176	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
177	C₁₃×C₂²⋊C₄	—	2	8	no	—
178	C₁₃×C₂²⋊C₄	—	2	8	no	—
179	C₁₃×C₂²⋊C₄	—	2	8	no	—
180	C₁₃×C₂²⋊C₄	—	2	8	no	—
181	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
182	C₄²×C₁₃	—	2	8	no	—
183	C₄²×C₁₃	C₂×D₄	1	2	yes	—
184	C₄²×C₁₃	C₂⁴	1	2	yes	—
185	C₂²×#137	C₂×C₁₃	1	2	yes	complemented
186	C₂×#548	C₂×C₁₃	1	2	yes	complemented
187	#3277	C₂×C₁₃	1	16	yes	direct product factor
188	C₂×#495	C₂×C₁₃	1	1	yes	characteristic, complemented
189	C₂×#468	C₂×C₁₃	1	2	yes	complemented
190	C₂×#464	C₂×C₁₃	1	2	yes	complemented
191	C₂×#449	C₂×C₁₃	1	2	yes	complemented
192	C₂×#451	C₂×C₁₃	1	2	yes	complemented
193	C₂×C₄×Q₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
194	C₂×#436	C₂×C₁₃	1	1	yes	characteristic, complemented
195	C₂³×C₁₃	—	2	4	no	—
196	C₂³×C₁₃	—	2	4	no	—
197	C₂³×C₁₃	—	2	4	no	—
198	C₂³×C₁₃	—	2	4	no	—
199	C₂³×C₁₃	—	4	4	no	—
200	C₂³×C₁₃	—	4	4	no	—
201	C₂³×C₁₃	—	4	4	no	—
202	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
203	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
204	Q₈×C₁₃	—	2	8	no	—
205	Q₈×C₁₃	—	2	4	no	—
206	Q₈×C₁₃	—	2	4	no	—
207	Q₈×C₁₃	—	2	4	no	—
208	Q₈×C₁₃	—	4	16	no	—
209	Q₈×C₁₃	—	4	4	no	—
210	Q₈×C₁₃	C₂²×D₄	1	8	yes	—
211	D₄×C₁₃	—	2	4	no	—
212	D₄×C₁₃	—	2	4	no	—
213	D₄×C₁₃	—	4	4	no	—
214	D₄×C₁₃	—	4	16	no	—
215	D₄×C₁₃	—	4	16	no	—
216	D₄×C₁₃	—	4	4	no	—
217	C₂×C₄×C₁₃	—	2	4	no	—
218	C₂×C₄×C₁₃	—	2	8	no	—
219	C₂×C₄×C₁₃	—	2	2	no	—
220	C₂×C₄×C₁₃	—	2	2	no	—
221	C₂×C₄×C₁₃	—	2	4	no	—
222	C₂×C₄×C₁₃	—	2	8	no	—
223	C₂×C₄×C₁₃	—	2	4	no	—
224	C₂×C₄×C₁₃	—	2	4	no	—
225	C₂×C₄×C₁₃	—	2	4	no	—
226	C₂×C₄×C₁₃	—	2	4	no	—
227	C₂×C₄×C₁₃	—	4	16	no	—
228	C₂×C₄×C₁₃	—	4	16	no	—
229	C₂×C₄×C₁₃	—	4	4	no	—
230	C₂×C₄×C₁₃	—	4	4	no	—
231	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
232	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
233	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
234	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
235	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
236	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
237	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
238	C₈×C₁₃	—	2	4	no	—
239	C₈×C₁₃	—	2	2	no	—
240	C₈×C₁₃	C₂²×D₄	1	4	yes	—
241	C₂²×#41	C₂²×C₁₃	1	2	yes	—
242	C₂³×Q₈	C₂²×C₁₃	1	2	yes	—
243	C₂×#137	—	2	16	no	—
244	C₂×#137	C₂²×C₁₃	1	16	yes	complemented
245	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
246	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
247	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
248	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
249	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
250	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
251	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
252	#548	—	2	8	no	—
253	#548	C₂²×C₁₃	1	16	yes	complemented
254	C₂×#124	—	2	2	no	—
255	C₂×#124	C₂²×C₁₃	1	2	yes	—
256	C₂×C₂²⋊Q₈	—	2	2	no	—
257	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
258	C₂×#121	—	2	2	no	—
259	C₂×#121	C₂²×C₁₃	1	2	yes	—
260	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
261	C₂×C₄×D₄	—	2	2	no	—
262	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
263	#495	C₂²×C₁₃	1	8	yes	complemented
264	#468	C₂²×C₁₃	1	16	yes	complemented
265	#464	C₂²×C₁₃	1	16	yes	complemented
266	#451	C₂²×C₁₃	1	16	yes	complemented
267	#449	C₂²×C₁₃	1	16	yes	complemented
268	C₄×Q₁₆	C₂²×C₁₃	1	8	yes	complemented
269	#436	C₂²×C₁₃	1	8	yes	complemented
270	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
271	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
272	C₂×#103	C₂²×C₁₃	1	2	yes	—
273	C₂×#103	C₂²×C₁₃	1	2	yes	—
274	C₂×#102	C₂²×C₁₃	1	2	yes	—
275	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
276	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
277	C₂²×C₁₃	—	2	4	no	—
278	C₂²×C₁₃	—	2	4	no	—
279	C₂²×C₁₃	—	2	4	no	—
280	C₂²×C₁₃	—	4	8	no	—
281	C₂²×C₁₃	—	4	4	no	—
282	C₂²×C₁₃	—	4	4	no	—
283	C₂²×C₁₃	—	4	4	no	—
284	C₂²×C₁₃	—	8	8	no	—
285	C₂²×C₁₃	D₄²	1	2	yes	—
286	C₂²×C₁₃	#575	1	2	yes	—
287	C₂²×C₁₃	#578	1	2	yes	—
288	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
289	C₄×C₁₃	—	2	4	no	—
290	C₄×C₁₃	—	2	8	no	—
291	C₄×C₁₃	—	2	2	no	—
292	C₄×C₁₃	—	2	2	no	—
293	C₄×C₁₃	—	4	4	no	—
294	C₄×C₁₃	—	4	4	no	—
295	C₄×C₁₃	D₄²	1	2	yes	—
296	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
297	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
298	C₂×#41	—	2	4	no	—
299	C₂×#41	—	2	8	no	—
300	C₂×#41	—	4	4	no	—
301	C₂×#41	C₂³×C₁₃	1	8	yes	—
302	C₂²×Q₈	—	2	2	no	—
303	C₂²×Q₈	—	2	4	no	—
304	C₂²×Q₈	—	2	8	no	—
305	C₂²×Q₈	—	4	4	no	—
306	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
307	C₂²×Q₈	C₂³×C₁₃	1	8	yes	—
308	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
309	C₂²×D₄	—	2	2	no	—
310	C₂²×D₄	—	2	2	no	—
311	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
312	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
313	C₂³×C₄	—	2	2	no	—
314	C₂³×C₄	—	2	2	no	—
315	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
316	#137	—	2	64	no	—
317	C₂×Q₁₆	—	2	8	no	—
318	C₂×Q₁₆	—	4	2	no	—
319	C₂×Q₁₆	D₄×C₁₃	1	8	yes	complemented
320	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	—
321	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
322	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
323	C₂×SD₁₆	—	2	8	no	—
324	C₂×SD₁₆	—	2	8	no	—
325	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
326	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
327	C₂×D₈	—	4	2	no	—
328	C₂×D₈	C₂³×C₁₃	1	4	yes	—
329	C₂×M₁₆	—	2	8	no	—
330	C₂×M₁₆	C₂³×C₁₃	1	8	yes	—
331	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
332	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
333	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
334	#124	—	2	16	no	—
335	#124	—	2	4	no	—
336	#124	C₂³×C₁₃	1	8	yes	—
337	C₂²⋊Q₈	—	2	4	no	—
338	C₂²⋊Q₈	—	2	16	no	—
339	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
340	#121	—	2	16	no	—
341	#121	—	2	4	no	—
342	#121	C₂³×C₁₃	1	8	yes	—
343	C₄×Q₈	—	2	4	no	—
344	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
345	C₄×D₄	—	2	16	no	—
346	C₄×D₄	D₄×C₁₃	1	4	yes	—
347	C₄×D₄	C₂³×C₁₃	1	4	yes	—
348	C₂×C₄⋊C₄	—	2	2	no	—
349	C₂×C₄⋊C₄	—	2	2	no	—
350	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
351	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
352	C₂×C₂²⋊C₄	—	2	2	no	—
353	C₂×C₂²⋊C₄	—	2	2	no	—
354	C₂×C₂²⋊C₄	—	2	2	no	—
355	C₂×C₂²⋊C₄	—	2	2	no	—
356	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
357	C₂×C₄²	—	2	2	no	—
358	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
359	#107	C₂³×C₁₃	1	4	yes	—
360	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
361	#103	C₂³×C₁₃	1	8	yes	—
362	#103	C₂³×C₁₃	1	8	yes	—
363	#102	C₂³×C₁₃	1	8	yes	—
364	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
365	C₄×C₈	C₂³×C₁₃	1	4	yes	—
366	C₂×C₁₃	—	4	4	no	—
367	C₂×C₁₃	—	8	4	no	—
368	C₂×C₁₃	#3277	1	4	yes	direct product factor
369	C₂×C₁₃	C₂×D₄²	1	1	yes	characteristic
370	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
371	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
372	C₂⁴	—	2	2	no	—
373	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
374	#41	—	2	16	no	—
375	#41	—	4	8	no	—
376	#41	—	4	16	no	—
377	C₂×Q₈	—	2	2	no	—
378	C₂×Q₈	—	2	8	no	—
379	C₂×Q₈	—	2	2	no	—
380	C₂×Q₈	—	2	4	no	—
381	C₂×Q₈	—	2	16	no	—
382	C₂×Q₈	—	2	4	no	—
383	C₂×Q₈	—	2	4	no	—
384	C₂×Q₈	—	4	8	no	—
385	C₂×Q₈	—	4	8	no	—
386	C₂×Q₈	—	4	16	no	—
387	C₂×Q₈	C₂×D₄×C₁₃	1	8	yes	—
388	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
389	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
390	C₂×D₄	—	2	8	no	—
391	C₂×D₄	—	2	8	no	—
392	C₂×D₄	—	2	4	no	—
393	C₂×D₄	—	2	2	no	—
394	C₂×D₄	—	2	4	no	—
395	C₂×D₄	—	4	2	no	—
396	C₂×D₄	—	4	8	no	—
397	C₂×D₄	—	4	8	no	—
398	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
399	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	2	4	no	—
402	C₂²×C₄	—	2	4	no	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	2	8	no	—
406	C₂²×C₄	—	2	8	no	—
407	C₂²×C₄	—	4	8	no	—
408	C₂²×C₄	—	4	8	no	—
409	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
410	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
411	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
412	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
413	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
414	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
415	Q₁₆	—	2	16	no	—
416	Q₁₆	—	4	4	no	—
417	Q₁₆	C₂×D₄×C₁₃	1	16	yes	complemented
418	SD₁₆	—	2	16	no	—
419	SD₁₆	—	2	16	no	—
420	D₈	—	4	4	no	—
421	M₁₆	—	2	16	no	—
422	C₂×C₈	—	2	4	no	—
423	C₂×C₈	—	2	2	no	—
424	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
425	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
426	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
427	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
428	C₄⋊C₄	—	2	8	no	—
429	C₄⋊C₄	—	2	8	no	—
430	C₄⋊C₄	—	2	2	no	—
431	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
432	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
433	C₂²⋊C₄	—	2	8	no	—
434	C₂²⋊C₄	—	2	8	no	—
435	C₂²⋊C₄	—	2	8	no	—
436	C₂²⋊C₄	—	2	8	no	—
437	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
438	C₄²	—	2	8	no	—
439	C₄²	C₂×D₄×C₁₃	1	2	yes	—
440	C₄²	C₂⁴×C₁₃	1	2	yes	—
441	C₁₃	C₂×#3277	1	1	yes	characteristic, direct product factor, Sylow
442	C₂³	—	2	4	no	—
443	C₂³	—	2	4	no	—
444	C₂³	—	2	4	no	—
445	C₂³	—	2	4	no	—
446	C₂³	—	4	4	no	—
447	C₂³	—	4	4	no	—
448	C₂³	—	4	4	no	—
449	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
450	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
451	Q₈	—	2	8	no	—
452	Q₈	—	2	4	no	—
453	Q₈	—	2	4	no	—
454	Q₈	—	2	4	no	—
455	Q₈	—	4	16	no	—
456	Q₈	—	4	4	no	—
457	Q₈	C₂²×D₄×C₁₃	1	8	yes	—
458	D₄	—	2	4	no	—
459	D₄	—	2	4	no	—
460	D₄	—	4	4	no	—
461	D₄	—	4	16	no	—
462	D₄	—	4	16	no	—
463	D₄	—	4	4	no	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	2	8	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	4	no	—
469	C₂×C₄	—	2	8	no	—
470	C₂×C₄	—	2	4	no	—
471	C₂×C₄	—	2	4	no	—
472	C₂×C₄	—	2	4	no	—
473	C₂×C₄	—	2	4	no	—
474	C₂×C₄	—	4	16	no	—
475	C₂×C₄	—	4	16	no	—
476	C₂×C₄	—	4	4	no	—
477	C₂×C₄	—	4	4	no	—
478	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
479	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
480	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
481	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
482	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
483	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
484	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
485	C₈	—	2	4	no	—
486	C₈	—	2	2	no	—
487	C₈	C₂²×D₄×C₁₃	1	4	yes	—
488	C₂²	—	2	4	no	—
489	C₂²	—	2	4	no	—
490	C₂²	—	2	4	no	—
491	C₂²	—	4	8	no	—
492	C₂²	—	4	4	no	—
493	C₂²	—	4	4	no	—
494	C₂²	—	4	4	no	—
495	C₂²	—	8	8	no	—
496	C₂²	D₄²×C₁₃	1	2	yes	—
497	C₂²	C₁₃×#575	1	2	yes	—
498	C₂²	C₁₃×#578	1	2	yes	—
499	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
500	C₄	—	2	2	no	—
501	C₄	—	2	2	no	—
502	C₄	—	2	4	no	—
503	C₄	—	2	8	no	—
504	C₄	—	4	4	no	—
505	C₄	—	4	4	no	—
506	C₄	D₄²×C₁₃	1	2	yes	—
507	C₄	C₂³×D₄×C₁₃	1	1	yes	characteristic
508	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
509	C₂	—	4	4	no	—
510	C₂	—	8	4	no	—
511	C₂	C₁₃×#3277	1	4	yes	direct product factor
512	C₂	C₂×D₄²×C₁₃	1	1	yes	characteristic
513	C₂	C₂×C₁₃×#575	1	1	yes	characteristic
514	C₂	C₂×C₁₃×#578	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 ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₃×#137	C₂	semidirect
2. C₂×C₁₃×#548	C₂	semidirect
3. C₁₃×#3277	C₂	direct (N × H)
4. C₂×C₁₃×#495	C₂	semidirect
5. C₂×C₁₃×#468	C₂	semidirect
6. C₂×C₁₃×#464	C₂	semidirect
7. C₂×C₁₃×#449	C₂	semidirect
8. C₂×C₁₃×#451	C₂	semidirect
9. C₂×C₄×C₁₃×Q₁₆	C₂	semidirect
10. C₂×C₁₃×#436	C₂	semidirect
14. C₂×C₁₃×#137	C₂²	semidirect
23. C₁₃×#548	C₂²	semidirect
33. C₁₃×#495	C₂²	semidirect
34. C₁₃×#468	C₂²	semidirect
35. C₁₃×#464	C₂²	semidirect
36. C₁₃×#451	C₂²	semidirect
37. C₁₃×#449	C₂²	semidirect
38. C₄×C₁₃×Q₁₆	C₂²	semidirect
39. C₁₃×#436	C₂²	semidirect
68. C₂×C₁₃×Q₁₆	D₄	semidirect
115. C₂×#3277	C₁₃	direct (N × H)
161. C₁₃×Q₁₆	C₂×D₄	semidirect
185. C₂²×#137	C₂×C₁₃	semidirect
186. C₂×#548	C₂×C₁₃	semidirect
187. #3277	C₂×C₁₃	direct (N × H)
188. C₂×#495	C₂×C₁₃	semidirect
189. C₂×#468	C₂×C₁₃	semidirect
190. C₂×#464	C₂×C₁₃	semidirect
191. C₂×#449	C₂×C₁₃	semidirect
192. C₂×#451	C₂×C₁₃	semidirect
193. C₂×C₄×Q₁₆	C₂×C₁₃	semidirect
194. C₂×#436	C₂×C₁₃	semidirect
244. C₂×#137	C₂²×C₁₃	semidirect
253. #548	C₂²×C₁₃	semidirect
263. #495	C₂²×C₁₃	semidirect
264. #468	C₂²×C₁₃	semidirect
265. #464	C₂²×C₁₃	semidirect
266. #451	C₂²×C₁₃	semidirect
267. #449	C₂²×C₁₃	semidirect
268. C₄×Q₁₆	C₂²×C₁₃	semidirect
269. #436	C₂²×C₁₃	semidirect
319. C₂×Q₁₆	D₄×C₁₃	semidirect
368. C₂×C₁₃	#3277	direct (N × H)
417. Q₁₆	C₂×D₄×C₁₃	semidirect
441. C₁₃	C₂×#3277	direct (N × H)
511. C₂	C₁₃×#3277	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×#137	2
C₂×C₁₃×#548	2
C₁₃×#3277	2
C₂×C₁₃×#495	2
C₂×C₁₃×#468	2
C₂×C₁₃×#464	2
C₂×C₁₃×#449	2
C₂×C₁₃×#451	2
C₂×C₄×C₁₃×Q₁₆	2
C₂×C₁₃×#436	2
C₂×#3277	13

Subgroups — C2×C13×#3277 #15747375

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3277 #15747375