Subgroups — C₂×C₁₃×#3325 #15747484

Order 3328.

2630 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#555	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3325	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#486	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#482	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#476	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#469	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#459	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#447	C₂	1	2	yes	maximal, complemented
10	C₂×C₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#436	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#418	C₂	1	2	yes	maximal, complemented
13	C₂³×D₄×C₁₃	—	2	1	no	—
14	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
15	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
16	C₂²×C₁₃×D₈	C₂²	1	2	yes	complemented
17	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	complemented
18	C₁₃×#555	—	2	4	no	—
19	C₁₃×#555	C₂²	1	8	yes	complemented
20	D₄²×C₁₃	—	2	4	no	—
21	D₄²×C₁₃	C₂²	1	8	yes	complemented
22	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#124	—	2	2	no	—
25	C₂×C₁₃×#121	—	2	1	no	—
26	C₂×C₁₃×#121	—	2	1	no	—
27	C₂×C₁₃×#121	C₂²	1	2	yes	—
28	C₂×C₁₃×#121	C₂²	1	2	yes	complemented
29	C₂×C₁₃×#120	—	2	2	no	—
30	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₁₃×#117	—	2	1	no	—
34	C₂×C₁₃×#117	C₂²	1	2	yes	complemented
35	C₁₃×#486	C₂²	1	8	yes	complemented
36	C₁₃×#482	C₂²	1	16	yes	complemented
37	C₁₃×#476	C₂²	1	8	yes	complemented
38	C₁₃×#469	C₂²	1	16	yes	complemented
39	C₁₃×#459	C₂²	1	8	yes	complemented
40	C₁₃×#447	C₂²	1	16	yes	complemented
41	C₄×C₁₃×D₈	C₂²	1	8	yes	complemented
42	C₁₃×#436	C₂²	1	8	yes	complemented
43	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₁₃×#106	C₂²	1	2	yes	complemented
45	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
46	C₁₃×#418	C₂²	1	16	yes	complemented
47	C₂×C₁₃×#102	C₂²	1	2	yes	—
48	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
49	C₂×C₁₃×#102	C₂²	1	2	yes	complemented
50	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₁₃×#102	C₂²	1	2	yes	complemented
52	C₂×C₁₃×#102	C₂²	1	2	yes	complemented
53	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	complemented
54	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
55	C₂⁵×C₁₃	—	2	2	no	—
56	C₂²×Q₈×C₁₃	—	2	1	no	—
57	C₂²×D₄×C₁₃	—	2	8	no	—
58	C₂²×D₄×C₁₃	—	2	2	no	—
59	C₂²×D₄×C₁₃	—	2	2	no	—
60	C₂²×D₄×C₁₃	—	2	8	no	—
61	C₂²×D₄×C₁₃	—	2	2	no	—
62	C₂²×D₄×C₁₃	—	2	1	no	—
63	C₂²×D₄×C₁₃	—	2	4	no	—
64	C₂²×D₄×C₁₃	—	2	1	no	—
65	C₂²×D₄×C₁₃	—	4	4	no	—
66	C₂²×D₄×C₁₃	—	4	8	no	—
67	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
68	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
69	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
70	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
71	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₁₃	—	2	1	no	—
73	C₂³×C₄×C₁₃	—	2	1	no	—
74	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
75	C₂×C₁₃×D₈	—	2	4	no	—
76	C₂×C₁₃×D₈	—	4	4	no	—
77	C₂×C₁₃×D₈	C₂³	1	4	yes	—
78	C₂×C₁₃×D₈	C₂³	1	8	yes	complemented
79	C₂×C₁₃×M₁₆	—	4	4	no	—
80	C₂×C₁₃×M₁₆	C₂³	1	8	yes	complemented
81	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
84	C₁₃×C₄⋊Q₈	—	2	2	no	—
85	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	complemented
86	C₁₃×#127	—	2	2	no	—
87	C₁₃×#127	C₂³	1	4	yes	—
88	C₁₃×#124	—	2	16	no	—
89	C₁₃×#121	—	2	8	no	—
90	C₁₃×#121	—	2	4	no	—
91	C₁₃×#121	—	2	4	no	—
92	C₁₃×#121	—	2	8	no	—
93	C₁₃×#121	C₂³	1	8	yes	—
94	C₁₃×#121	C₂³	1	8	yes	complemented
95	C₁₃×#120	—	2	16	no	—
96	C₄×D₄×C₁₃	—	2	2	no	—
97	C₄×D₄×C₁₃	—	2	2	no	—
98	C₄×D₄×C₁₃	D₄	1	4	yes	—
99	C₄×D₄×C₁₃	C₂³	1	4	yes	—
100	C₄×D₄×C₁₃	C₂³	1	4	yes	—
101	C₄×D₄×C₁₃	C₂³	1	4	yes	complemented
102	C₁₃×#117	—	2	4	no	—
103	C₁₃×#117	—	2	8	no	—
104	C₁₃×#117	C₂³	1	8	yes	complemented
105	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
106	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
107	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
108	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
109	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
110	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
111	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
112	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
113	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
114	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
115	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
116	C₂×C₄²×C₁₃	—	2	2	no	—
117	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
118	C₁₃×#107	C₂³	1	4	yes	complemented
119	C₁₃×#106	C₂³	1	8	yes	complemented
120	C₁₃×C₄⋊C₈	C₂³	1	4	yes	complemented
121	C₁₃×#102	C₂³	1	4	yes	—
122	C₁₃×#102	C₂³	1	8	yes	—
123	C₁₃×#102	C₂³	1	8	yes	complemented
124	C₁₃×#102	C₂³	1	8	yes	complemented
125	C₁₃×#102	C₂³	1	4	yes	complemented
126	C₁₃×#102	C₂³	1	8	yes	complemented
127	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	complemented
128	C₄×C₈×C₁₃	C₂³	1	4	yes	complemented
129	C₂×#3325	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
130	C₂⁴×C₁₃	—	2	1	no	—
131	C₂⁴×C₁₃	—	2	1	no	—
132	C₂⁴×C₁₃	—	2	2	no	—
133	C₂⁴×C₁₃	—	2	8	no	—
134	C₂⁴×C₁₃	—	4	8	no	—
135	C₂⁴×C₁₃	—	4	8	no	—
136	C₂⁴×C₁₃	—	8	4	no	—
137	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
138	C₂×Q₈×C₁₃	—	2	4	no	—
139	C₂×Q₈×C₁₃	—	8	2	no	—
140	C₂×D₄×C₁₃	—	2	16	no	—
141	C₂×D₄×C₁₃	—	2	8	no	—
142	C₂×D₄×C₁₃	—	2	8	no	—
143	C₂×D₄×C₁₃	—	2	4	no	—
144	C₂×D₄×C₁₃	—	2	1	no	—
145	C₂×D₄×C₁₃	—	2	1	no	—
146	C₂×D₄×C₁₃	—	2	8	no	—
147	C₂×D₄×C₁₃	—	2	2	no	—
148	C₂×D₄×C₁₃	—	2	4	no	—
149	C₂×D₄×C₁₃	—	2	4	no	—
150	C₂×D₄×C₁₃	—	2	2	no	—
151	C₂×D₄×C₁₃	—	2	4	no	—
152	C₂×D₄×C₁₃	—	2	2	no	—
153	C₂×D₄×C₁₃	—	2	2	no	—
154	C₂×D₄×C₁₃	—	2	4	no	—
155	C₂×D₄×C₁₃	—	4	8	no	—
156	C₂×D₄×C₁₃	—	4	16	no	—
157	C₂×D₄×C₁₃	—	4	8	no	—
158	C₂×D₄×C₁₃	—	4	32	no	—
159	C₂×D₄×C₁₃	—	4	8	no	—
160	C₂×D₄×C₁₃	—	4	4	no	—
161	C₂×D₄×C₁₃	—	8	2	no	—
162	C₂×D₄×C₁₃	—	8	4	no	—
163	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
164	C₂×D₄×C₁₃	#41	1	4	yes	—
165	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
166	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
167	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
168	C₂²×C₄×C₁₃	—	2	4	no	—
169	C₂²×C₄×C₁₃	—	2	4	no	—
170	C₂²×C₄×C₁₃	—	2	1	no	—
171	C₂²×C₄×C₁₃	—	2	2	no	—
172	C₂²×C₄×C₁₃	—	2	1	no	—
173	C₂²×C₄×C₁₃	—	2	4	no	—
174	C₂²×C₄×C₁₃	—	2	4	no	—
175	C₂²×C₄×C₁₃	—	4	4	no	—
176	C₂²×C₄×C₁₃	—	4	4	no	—
177	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
178	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
179	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
180	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
181	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
182	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
183	C₁₃×D₈	—	2	8	no	—
184	C₁₃×D₈	—	4	8	no	—
185	C₁₃×M₁₆	—	4	8	no	—
186	C₂×C₈×C₁₃	—	2	2	no	—
187	C₂×C₈×C₁₃	—	2	2	no	—
188	C₂×C₈×C₁₃	—	2	4	no	—
189	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
190	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
191	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
192	C₁₃×C₄⋊C₄	—	2	4	no	—
193	C₁₃×C₄⋊C₄	—	2	1	no	—
194	C₁₃×C₄⋊C₄	—	2	2	no	—
195	C₁₃×C₄⋊C₄	—	2	1	no	—
196	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
197	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
198	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
199	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
200	C₁₃×C₂²⋊C₄	—	2	8	no	—
201	C₁₃×C₂²⋊C₄	—	2	8	no	—
202	C₁₃×C₂²⋊C₄	—	2	4	no	—
203	C₁₃×C₂²⋊C₄	—	2	4	no	—
204	C₁₃×C₂²⋊C₄	—	2	8	no	—
205	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
206	C₄²×C₁₃	—	2	8	no	—
207	C₄²×C₁₃	C₂×D₄	1	2	yes	—
208	C₄²×C₁₃	C₂⁴	1	2	yes	—
209	C₂×#555	C₂×C₁₃	1	1	yes	characteristic, complemented
210	C₂×D₄²	C₂×C₁₃	1	1	yes	characteristic, complemented
211	#3325	C₂×C₁₃	1	16	yes	direct product factor
212	C₂×#486	C₂×C₁₃	1	1	yes	characteristic, complemented
213	C₂×#482	C₂×C₁₃	1	2	yes	complemented
214	C₂×#476	C₂×C₁₃	1	1	yes	characteristic, complemented
215	C₂×#469	C₂×C₁₃	1	2	yes	complemented
216	C₂×#459	C₂×C₁₃	1	1	yes	characteristic, complemented
217	C₂×#447	C₂×C₁₃	1	2	yes	complemented
218	C₂×C₄×D₈	C₂×C₁₃	1	1	yes	characteristic, complemented
219	C₂×#436	C₂×C₁₃	1	1	yes	characteristic, complemented
220	C₂×#418	C₂×C₁₃	1	2	yes	complemented
221	C₂³×C₁₃	—	2	4	no	—
222	C₂³×C₁₃	—	2	4	no	—
223	C₂³×C₁₃	—	2	4	no	—
224	C₂³×C₁₃	—	2	4	no	—
225	C₂³×C₁₃	—	2	2	no	—
226	C₂³×C₁₃	—	2	2	no	—
227	C₂³×C₁₃	—	2	4	no	—
228	C₂³×C₁₃	—	4	16	no	—
229	C₂³×C₁₃	—	4	16	no	—
230	C₂³×C₁₃	—	4	2	no	—
231	C₂³×C₁₃	—	4	2	no	—
232	C₂³×C₁₃	—	4	4	no	—
233	C₂³×C₁₃	—	4	2	no	—
234	C₂³×C₁₃	—	4	2	no	—
235	C₂³×C₁₃	—	4	4	no	—
236	C₂³×C₁₃	—	4	2	no	—
237	C₂³×C₁₃	—	4	4	no	—
238	C₂³×C₁₃	—	8	8	no	—
239	C₂³×C₁₃	—	8	32	no	—
240	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
241	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
242	Q₈×C₁₃	—	8	4	no	—
243	D₄×C₁₃	—	2	4	no	—
244	D₄×C₁₃	—	2	8	no	—
245	D₄×C₁₃	—	2	2	no	—
246	D₄×C₁₃	—	2	4	no	—
247	D₄×C₁₃	—	2	2	no	—
248	D₄×C₁₃	—	2	2	no	—
249	D₄×C₁₃	—	2	4	no	—
250	D₄×C₁₃	—	4	16	no	—
251	D₄×C₁₃	—	4	16	no	—
252	D₄×C₁₃	—	4	2	no	—
253	D₄×C₁₃	—	4	4	no	—
254	D₄×C₁₃	—	4	8	no	—
255	D₄×C₁₃	—	8	4	no	—
256	D₄×C₁₃	—	8	8	no	—
257	D₄×C₁₃	C₂×#41	1	4	yes	—
258	C₂×C₄×C₁₃	—	2	4	no	—
259	C₂×C₄×C₁₃	—	2	2	no	—
260	C₂×C₄×C₁₃	—	2	8	no	—
261	C₂×C₄×C₁₃	—	2	4	no	—
262	C₂×C₄×C₁₃	—	2	4	no	—
263	C₂×C₄×C₁₃	—	2	2	no	—
264	C₂×C₄×C₁₃	—	2	4	no	—
265	C₂×C₄×C₁₃	—	2	2	no	—
266	C₂×C₄×C₁₃	—	4	2	no	—
267	C₂×C₄×C₁₃	—	4	2	no	—
268	C₂×C₄×C₁₃	—	4	4	no	—
269	C₂×C₄×C₁₃	—	4	8	no	—
270	C₂×C₄×C₁₃	—	4	8	no	—
271	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
272	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
273	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
274	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
275	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
276	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
277	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
278	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
279	C₈×C₁₃	—	2	2	no	—
280	C₈×C₁₃	—	2	2	no	—
281	C₈×C₁₃	—	2	4	no	—
282	C₂³×D₄	—	2	1	no	—
283	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
284	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
285	C₂²×D₈	C₂²×C₁₃	1	2	yes	complemented
286	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	complemented
287	#555	—	2	4	no	—
288	#555	C₂²×C₁₃	1	8	yes	complemented
289	D₄²	—	2	4	no	—
290	D₄²	C₂²×C₁₃	1	8	yes	complemented
291	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
292	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
293	C₂×#124	—	2	2	no	—
294	C₂×#121	—	2	1	no	—
295	C₂×#121	—	2	1	no	—
296	C₂×#121	C₂²×C₁₃	1	2	yes	—
297	C₂×#121	C₂²×C₁₃	1	2	yes	complemented
298	C₂×#120	—	2	2	no	—
299	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
300	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
301	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
302	C₂×#117	—	2	1	no	—
303	C₂×#117	C₂²×C₁₃	1	2	yes	complemented
304	#486	C₂²×C₁₃	1	8	yes	complemented
305	#482	C₂²×C₁₃	1	16	yes	complemented
306	#476	C₂²×C₁₃	1	8	yes	complemented
307	#469	C₂²×C₁₃	1	16	yes	complemented
308	#459	C₂²×C₁₃	1	8	yes	complemented
309	#447	C₂²×C₁₃	1	16	yes	complemented
310	C₄×D₈	C₂²×C₁₃	1	8	yes	complemented
311	#436	C₂²×C₁₃	1	8	yes	complemented
312	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic, complemented
313	C₂×#106	C₂²×C₁₃	1	2	yes	complemented
314	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
315	#418	C₂²×C₁₃	1	16	yes	complemented
316	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
317	C₂×#102	C₂²×C₁₃	1	2	yes	—
318	C₂×#102	C₂²×C₁₃	1	2	yes	complemented
319	C₂×#102	C₂²×C₁₃	1	2	yes	complemented
320	C₂×#102	C₂²×C₁₃	1	2	yes	complemented
321	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
322	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	complemented
323	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
324	C₂²×C₁₃	—	2	4	no	—
325	C₂²×C₁₃	—	2	4	no	—
326	C₂²×C₁₃	—	2	4	no	—
327	C₂²×C₁₃	—	2	4	no	—
328	C₂²×C₁₃	—	4	2	no	—
329	C₂²×C₁₃	—	4	8	no	—
330	C₂²×C₁₃	—	4	8	no	—
331	C₂²×C₁₃	—	4	2	no	—
332	C₂²×C₁₃	—	4	4	no	—
333	C₂²×C₁₃	—	4	2	no	—
334	C₂²×C₁₃	—	4	2	no	—
335	C₂²×C₁₃	—	4	4	no	—
336	C₂²×C₁₃	—	4	2	no	—
337	C₂²×C₁₃	—	4	4	no	—
338	C₂²×C₁₃	—	8	32	no	—
339	C₂²×C₁₃	—	8	4	no	—
340	C₂²×C₁₃	—	8	8	no	—
341	C₂²×C₁₃	#546	1	2	yes	—
342	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
343	C₂²×C₁₃	#576	1	2	yes	—
344	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
345	C₄×C₁₃	—	2	4	no	—
346	C₄×C₁₃	—	2	2	no	—
347	C₄×C₁₃	—	4	2	no	—
348	C₄×C₁₃	—	4	2	no	—
349	C₄×C₁₃	—	4	4	no	—
350	C₄×C₁₃	#546	1	2	yes	—
351	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
352	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
353	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
354	C₂⁵	—	2	2	no	—
355	C₂²×Q₈	—	2	1	no	—
356	C₂²×D₄	—	2	8	no	—
357	C₂²×D₄	—	2	2	no	—
358	C₂²×D₄	—	2	2	no	—
359	C₂²×D₄	—	2	8	no	—
360	C₂²×D₄	—	2	2	no	—
361	C₂²×D₄	—	2	1	no	—
362	C₂²×D₄	—	2	4	no	—
363	C₂²×D₄	—	2	1	no	—
364	C₂²×D₄	—	4	4	no	—
365	C₂²×D₄	—	4	8	no	—
366	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
367	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
368	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
369	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
370	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
371	C₂³×C₄	—	2	1	no	—
372	C₂³×C₄	—	2	1	no	—
373	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
374	C₂×D₈	—	2	4	no	—
375	C₂×D₈	—	4	4	no	—
376	C₂×D₈	C₂³×C₁₃	1	4	yes	—
377	C₂×D₈	C₂³×C₁₃	1	8	yes	complemented
378	C₂×M₁₆	—	4	4	no	—
379	C₂×M₁₆	C₂³×C₁₃	1	8	yes	complemented
380	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
381	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
382	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
383	C₄⋊Q₈	—	2	2	no	—
384	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	complemented
385	#127	—	2	2	no	—
386	#127	C₂³×C₁₃	1	4	yes	—
387	#124	—	2	16	no	—
388	#121	—	2	8	no	—
389	#121	—	2	4	no	—
390	#121	—	2	4	no	—
391	#121	—	2	8	no	—
392	#121	C₂³×C₁₃	1	8	yes	—
393	#121	C₂³×C₁₃	1	8	yes	complemented
394	#120	—	2	16	no	—
395	C₄×D₄	—	2	2	no	—
396	C₄×D₄	—	2	2	no	—
397	C₄×D₄	D₄×C₁₃	1	4	yes	—
398	C₄×D₄	C₂³×C₁₃	1	4	yes	—
399	C₄×D₄	C₂³×C₁₃	1	4	yes	—
400	C₄×D₄	C₂³×C₁₃	1	4	yes	complemented
401	#117	—	2	4	no	—
402	#117	—	2	8	no	—
403	#117	C₂³×C₁₃	1	8	yes	complemented
404	C₂×C₄⋊C₄	—	2	1	no	—
405	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
406	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
407	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
408	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
409	C₂×C₂²⋊C₄	—	2	2	no	—
410	C₂×C₂²⋊C₄	—	2	2	no	—
411	C₂×C₂²⋊C₄	—	2	1	no	—
412	C₂×C₂²⋊C₄	—	2	1	no	—
413	C₂×C₂²⋊C₄	—	2	2	no	—
414	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
415	C₂×C₄²	—	2	2	no	—
416	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
417	#107	C₂³×C₁₃	1	4	yes	complemented
418	#106	C₂³×C₁₃	1	8	yes	complemented
419	C₄⋊C₈	C₂³×C₁₃	1	4	yes	complemented
420	#102	C₂³×C₁₃	1	4	yes	—
421	#102	C₂³×C₁₃	1	8	yes	—
422	#102	C₂³×C₁₃	1	8	yes	complemented
423	#102	C₂³×C₁₃	1	8	yes	complemented
424	#102	C₂³×C₁₃	1	4	yes	complemented
425	#102	C₂³×C₁₃	1	8	yes	complemented
426	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	complemented
427	C₄×C₈	C₂³×C₁₃	1	4	yes	complemented
428	C₂×C₁₃	—	4	4	no	—
429	C₂×C₁₃	—	4	4	no	—
430	C₂×C₁₃	—	8	2	no	—
431	C₂×C₁₃	—	8	4	no	—
432	C₂×C₁₃	#3325	1	4	yes	direct product factor
433	C₂×C₁₃	C₂×#546	1	1	yes	characteristic
434	C₂×C₁₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
435	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
436	C₂⁴	—	2	1	no	—
437	C₂⁴	—	2	1	no	—
438	C₂⁴	—	2	2	no	—
439	C₂⁴	—	2	8	no	—
440	C₂⁴	—	4	8	no	—
441	C₂⁴	—	4	8	no	—
442	C₂⁴	—	8	4	no	—
443	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
444	C₂×Q₈	—	2	4	no	—
445	C₂×Q₈	—	8	2	no	—
446	C₂×D₄	—	2	16	no	—
447	C₂×D₄	—	2	8	no	—
448	C₂×D₄	—	2	8	no	—
449	C₂×D₄	—	2	4	no	—
450	C₂×D₄	—	2	1	no	—
451	C₂×D₄	—	2	1	no	—
452	C₂×D₄	—	2	8	no	—
453	C₂×D₄	—	2	2	no	—
454	C₂×D₄	—	2	4	no	—
455	C₂×D₄	—	2	4	no	—
456	C₂×D₄	—	2	2	no	—
457	C₂×D₄	—	2	4	no	—
458	C₂×D₄	—	2	2	no	—
459	C₂×D₄	—	2	2	no	—
460	C₂×D₄	—	2	4	no	—
461	C₂×D₄	—	4	8	no	—
462	C₂×D₄	—	4	16	no	—
463	C₂×D₄	—	4	8	no	—
464	C₂×D₄	—	4	32	no	—
465	C₂×D₄	—	4	8	no	—
466	C₂×D₄	—	4	4	no	—
467	C₂×D₄	—	8	2	no	—
468	C₂×D₄	—	8	4	no	—
469	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
470	C₂×D₄	C₁₃×#41	1	4	yes	—
471	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
472	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
473	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
474	C₂²×C₄	—	2	4	no	—
475	C₂²×C₄	—	2	4	no	—
476	C₂²×C₄	—	2	1	no	—
477	C₂²×C₄	—	2	2	no	—
478	C₂²×C₄	—	2	1	no	—
479	C₂²×C₄	—	2	4	no	—
480	C₂²×C₄	—	2	4	no	—
481	C₂²×C₄	—	4	4	no	—
482	C₂²×C₄	—	4	4	no	—
483	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
484	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
485	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
486	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
487	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
488	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
489	D₈	—	2	8	no	—
490	D₈	—	4	8	no	—
491	M₁₆	—	4	8	no	—
492	C₂×C₈	—	2	2	no	—
493	C₂×C₈	—	2	2	no	—
494	C₂×C₈	—	2	4	no	—
495	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
496	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
497	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
498	C₄⋊C₄	—	2	4	no	—
499	C₄⋊C₄	—	2	1	no	—
500	C₄⋊C₄	—	2	2	no	—
501	C₄⋊C₄	—	2	1	no	—
502	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
503	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
504	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
505	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
506	C₂²⋊C₄	—	2	8	no	—
507	C₂²⋊C₄	—	2	8	no	—
508	C₂²⋊C₄	—	2	4	no	—
509	C₂²⋊C₄	—	2	4	no	—
510	C₂²⋊C₄	—	2	8	no	—
511	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
512	C₄²	—	2	8	no	—
513	C₄²	C₂×D₄×C₁₃	1	2	yes	—
514	C₄²	C₂⁴×C₁₃	1	2	yes	—
515	C₁₃	C₂×#3325	1	1	yes	characteristic, direct product factor, Sylow
516	C₂³	—	2	4	no	—
517	C₂³	—	2	4	no	—
518	C₂³	—	2	4	no	—
519	C₂³	—	2	4	no	—
520	C₂³	—	2	2	no	—
521	C₂³	—	2	2	no	—
522	C₂³	—	2	4	no	—
523	C₂³	—	4	16	no	—
524	C₂³	—	4	16	no	—
525	C₂³	—	4	2	no	—
526	C₂³	—	4	2	no	—
527	C₂³	—	4	4	no	—
528	C₂³	—	4	2	no	—
529	C₂³	—	4	2	no	—
530	C₂³	—	4	4	no	—
531	C₂³	—	4	2	no	—
532	C₂³	—	4	4	no	—
533	C₂³	—	8	8	no	—
534	C₂³	—	8	32	no	—
535	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
536	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
537	Q₈	—	8	4	no	—
538	D₄	—	2	4	no	—
539	D₄	—	2	8	no	—
540	D₄	—	2	2	no	—
541	D₄	—	2	4	no	—
542	D₄	—	2	2	no	—
543	D₄	—	2	2	no	—
544	D₄	—	2	4	no	—
545	D₄	—	4	16	no	—
546	D₄	—	4	16	no	—
547	D₄	—	4	4	no	—
548	D₄	—	4	2	no	—
549	D₄	—	4	8	no	—
550	D₄	—	8	4	no	—
551	D₄	—	8	8	no	—
552	D₄	C₂×C₁₃×#41	1	4	yes	—
553	C₂×C₄	—	2	4	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	8	no	—
556	C₂×C₄	—	2	4	no	—
557	C₂×C₄	—	2	4	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	4	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	4	2	no	—
562	C₂×C₄	—	4	2	no	—
563	C₂×C₄	—	4	4	no	—
564	C₂×C₄	—	4	8	no	—
565	C₂×C₄	—	4	8	no	—
566	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
567	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
568	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
569	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
570	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
571	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
572	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
573	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
574	C₈	—	2	2	no	—
575	C₈	—	2	2	no	—
576	C₈	—	2	4	no	—
577	C₂²	—	2	4	no	—
578	C₂²	—	2	4	no	—
579	C₂²	—	2	4	no	—
580	C₂²	—	2	4	no	—
581	C₂²	—	4	2	no	—
582	C₂²	—	4	8	no	—
583	C₂²	—	4	8	no	—
584	C₂²	—	4	2	no	—
585	C₂²	—	4	2	no	—
586	C₂²	—	4	4	no	—
587	C₂²	—	4	2	no	—
588	C₂²	—	4	4	no	—
589	C₂²	—	4	4	no	—
590	C₂²	—	4	2	no	—
591	C₂²	—	8	32	no	—
592	C₂²	—	8	4	no	—
593	C₂²	—	8	8	no	—
594	C₂²	C₁₃×#546	1	2	yes	—
595	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
596	C₂²	C₁₃×#576	1	2	yes	—
597	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
598	C₄	—	2	2	no	—
599	C₄	—	2	4	no	—
600	C₄	—	4	2	no	—
601	C₄	—	4	2	no	—
602	C₄	—	4	4	no	—
603	C₄	C₁₃×#546	1	2	yes	—
604	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	4	yes	—
605	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
606	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
607	C₂	—	4	4	no	—
608	C₂	—	4	4	no	—
609	C₂	—	8	4	no	—
610	C₂	—	8	2	no	—
611	C₂	C₁₃×#3325	1	4	yes	direct product factor
612	C₂	C₂×C₁₃×#546	1	1	yes	characteristic
613	C₂	C₂²×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
614	C₂	C₂×C₁₃×#576	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. C₂×C₁₃×#555	C₂	semidirect
2. C₂×D₄²×C₁₃	C₂	semidirect
3. C₁₃×#3325	C₂	direct (N × H)
4. C₂×C₁₃×#486	C₂	semidirect
5. C₂×C₁₃×#482	C₂	semidirect
6. C₂×C₁₃×#476	C₂	semidirect
7. C₂×C₁₃×#469	C₂	semidirect
8. C₂×C₁₃×#459	C₂	semidirect
9. C₂×C₁₃×#447	C₂	semidirect
10. C₂×C₄×C₁₃×D₈	C₂	semidirect
11. C₂×C₁₃×#436	C₂	semidirect
12. C₂×C₁₃×#418	C₂	semidirect
16. C₂²×C₁₃×D₈	C₂²	semidirect
17. C₂²×C₁₃×M₁₆	C₂²	semidirect
19. C₁₃×#555	C₂²	semidirect
21. D₄²×C₁₃	C₂²	semidirect
22. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
28. C₂×C₁₃×#121	C₂²	semidirect
32. C₂×C₄×D₄×C₁₃	C₂²	semidirect
34. C₂×C₁₃×#117	C₂²	semidirect
35. C₁₃×#486	C₂²	semidirect
36. C₁₃×#482	C₂²	semidirect
37. C₁₃×#476	C₂²	semidirect
38. C₁₃×#469	C₂²	semidirect
39. C₁₃×#459	C₂²	semidirect
40. C₁₃×#447	C₂²	semidirect
41. C₄×C₁₃×D₈	C₂²	semidirect
42. C₁₃×#436	C₂²	semidirect
43. C₂×C₁₃×#107	C₂²	semidirect
44. C₂×C₁₃×#106	C₂²	semidirect
45. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
46. C₁₃×#418	C₂²	semidirect
49. C₂×C₁₃×#102	C₂²	semidirect
50. C₂×C₁₃×#102	C₂²	semidirect
51. C₂×C₁₃×#102	C₂²	semidirect
52. C₂×C₁₃×#102	C₂²	semidirect
53. C₂×C₁₃×C₂²⋊C₈	C₂²	semidirect
54. C₂×C₄×C₈×C₁₃	C₂²	semidirect
78. C₂×C₁₃×D₈	C₂³	semidirect
80. C₂×C₁₃×M₁₆	C₂³	semidirect
85. C₁₃×C₄⋊Q₈	C₂³	semidirect
94. C₁₃×#121	C₂³	semidirect
101. C₄×D₄×C₁₃	C₂³	semidirect
104. C₁₃×#117	C₂³	semidirect
118. C₁₃×#107	C₂³	semidirect
119. C₁₃×#106	C₂³	semidirect
120. C₁₃×C₄⋊C₈	C₂³	semidirect
123. C₁₃×#102	C₂³	semidirect
124. C₁₃×#102	C₂³	semidirect
125. C₁₃×#102	C₂³	semidirect
126. C₁₃×#102	C₂³	semidirect
127. C₁₃×C₂²⋊C₈	C₂³	semidirect
128. C₄×C₈×C₁₃	C₂³	semidirect
129. C₂×#3325	C₁₃	direct (N × H)
209. C₂×#555	C₂×C₁₃	semidirect
210. C₂×D₄²	C₂×C₁₃	semidirect
211. #3325	C₂×C₁₃	direct (N × H)
212. C₂×#486	C₂×C₁₃	semidirect
213. C₂×#482	C₂×C₁₃	semidirect
214. C₂×#476	C₂×C₁₃	semidirect
215. C₂×#469	C₂×C₁₃	semidirect
216. C₂×#459	C₂×C₁₃	semidirect
217. C₂×#447	C₂×C₁₃	semidirect
218. C₂×C₄×D₈	C₂×C₁₃	semidirect
219. C₂×#436	C₂×C₁₃	semidirect
220. C₂×#418	C₂×C₁₃	semidirect
285. C₂²×D₈	C₂²×C₁₃	semidirect
286. C₂²×M₁₆	C₂²×C₁₃	semidirect
288. #555	C₂²×C₁₃	semidirect
290. D₄²	C₂²×C₁₃	semidirect
291. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
297. C₂×#121	C₂²×C₁₃	semidirect
301. C₂×C₄×D₄	C₂²×C₁₃	semidirect
303. C₂×#117	C₂²×C₁₃	semidirect
304. #486	C₂²×C₁₃	semidirect
305. #482	C₂²×C₁₃	semidirect
306. #476	C₂²×C₁₃	semidirect
307. #469	C₂²×C₁₃	semidirect
308. #459	C₂²×C₁₃	semidirect
309. #447	C₂²×C₁₃	semidirect
310. C₄×D₈	C₂²×C₁₃	semidirect
311. #436	C₂²×C₁₃	semidirect
312. C₂×#107	C₂²×C₁₃	semidirect
313. C₂×#106	C₂²×C₁₃	semidirect
314. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
315. #418	C₂²×C₁₃	semidirect
318. C₂×#102	C₂²×C₁₃	semidirect
319. C₂×#102	C₂²×C₁₃	semidirect
320. C₂×#102	C₂²×C₁₃	semidirect
321. C₂×#102	C₂²×C₁₃	semidirect
322. C₂×C₂²⋊C₈	C₂²×C₁₃	semidirect
323. C₂×C₄×C₈	C₂²×C₁₃	semidirect
377. C₂×D₈	C₂³×C₁₃	semidirect
379. C₂×M₁₆	C₂³×C₁₃	semidirect
384. C₄⋊Q₈	C₂³×C₁₃	semidirect
393. #121	C₂³×C₁₃	semidirect
400. C₄×D₄	C₂³×C₁₃	semidirect
403. #117	C₂³×C₁₃	semidirect
417. #107	C₂³×C₁₃	semidirect
418. #106	C₂³×C₁₃	semidirect
419. C₄⋊C₈	C₂³×C₁₃	semidirect
422. #102	C₂³×C₁₃	semidirect
423. #102	C₂³×C₁₃	semidirect
424. #102	C₂³×C₁₃	semidirect
425. #102	C₂³×C₁₃	semidirect
426. C₂²⋊C₈	C₂³×C₁₃	semidirect
427. C₄×C₈	C₂³×C₁₃	semidirect
432. C₂×C₁₃	#3325	direct (N × H)
515. C₁₃	C₂×#3325	direct (N × H)
611. C₂	C₁₃×#3325	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×#555	2
C₂×D₄²×C₁₃	2
C₁₃×#3325	2
C₂×C₁₃×#486	2
C₂×C₁₃×#482	2
C₂×C₁₃×#476	2
C₂×C₁₃×#469	2
C₂×C₁₃×#459	2
C₂×C₁₃×#447	2
C₂×C₄×C₁₃×D₈	2
C₂×C₁₃×#436	2
C₂×C₁₃×#418	2
C₂×#3325	13

Subgroups — C2×C13×#3325 #15747484

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3325 #15747484