Subgroups — C₂×C₁₃×#3214 #15747126

Order 3328.

2446 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3214	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#496	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×#489	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#461	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#459	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#449	C₂	1	4	yes	maximal, complemented
9	C₂×C₁₃×#432	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₁₃×#41	—	2	1	no	—
11	C₂²×C₁₃×#41	C₂²	1	2	yes	—
12	C₂²×C₁₃×SD₁₆	C₂²	1	4	yes	—
13	C₂²×C₁₃×D₈	C₂²	1	4	yes	—
14	C₁₃×#532	—	2	4	no	—
15	C₁₃×#532	—	2	4	no	—
16	C₁₃×#532	C₂²	1	8	yes	complemented
17	C₁₃×#532	C₂²	1	8	yes	complemented
18	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#124	—	2	1	no	—
23	C₂×C₁₃×#124	C₂²	1	2	yes	—
24	C₂×C₁₃×#121	—	2	1	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×C₄×D₄×C₁₃	—	2	1	no	—
29	C₂×C₄×D₄×C₁₃	—	2	1	no	—
30	C₂×C₄×D₄×C₁₃	—	2	1	no	—
31	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
32	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
33	C₁₃×#496	C₂²	1	16	yes	complemented
34	C₁₃×#489	C₂²	1	16	yes	complemented
35	C₁₃×#461	C₂²	1	16	yes	complemented
36	C₁₃×#459	C₂²	1	16	yes	complemented
37	C₁₃×#449	C₂²	1	32	yes	complemented
38	C₁₃×#432	C₂²	1	8	yes	complemented
39	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
40	C₂×C₁₃×#103	C₂²	1	4	yes	—
41	C₂×C₁₃×#102	C₂²	1	4	yes	—
42	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
43	C₂×C₁₃×#97	C₂²	1	2	yes	—
44	C₂×C₁₃×#41	—	2	4	no	—
45	C₂×C₁₃×#41	—	2	8	no	—
46	C₂×C₁₃×#41	—	4	8	no	—
47	C₂×C₁₃×#41	—	4	8	no	—
48	C₂×C₁₃×#41	C₂³	1	8	yes	—
49	C₂²×Q₈×C₁₃	—	2	1	no	—
50	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
51	C₂²×D₄×C₁₃	—	2	2	no	—
52	C₂²×D₄×C₁₃	—	2	2	no	—
53	C₂²×D₄×C₁₃	—	2	1	no	—
54	C₂²×D₄×C₁₃	—	2	1	no	—
55	C₂²×D₄×C₁₃	—	2	1	no	—
56	C₂²×D₄×C₁₃	—	2	1	no	—
57	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
58	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
59	C₂³×C₄×C₁₃	—	2	2	no	—
60	C₂³×C₄×C₁₃	—	2	2	no	—
61	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
62	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
63	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
64	C₂×C₁₃×SD₁₆	—	4	8	no	—
65	C₂×C₁₃×SD₁₆	C₂³	1	16	yes	—
66	C₂×C₁₃×D₈	—	4	8	no	—
67	C₂×C₁₃×D₈	C₂³	1	16	yes	—
68	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
69	C₁₃×C₄⋊Q₈	—	2	2	no	—
70	C₁₃×C₄⋊Q₈	—	2	2	no	—
71	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
72	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
73	C₁₃×#127	—	2	2	no	—
74	C₁₃×#127	—	2	2	no	—
75	C₁₃×#127	C₂³	1	4	yes	—
76	C₁₃×#127	C₂³	1	4	yes	—
77	C₁₃×#124	—	2	8	no	—
78	C₁₃×#124	—	2	4	no	—
79	C₁₃×#124	C₂³	1	8	yes	—
80	C₁₃×#121	—	2	8	no	—
81	C₁₃×#121	—	2	8	no	—
82	C₁₃×#121	—	2	8	no	—
83	C₁₃×#121	—	2	4	no	—
84	C₁₃×#121	C₂³	1	8	yes	—
85	C₄×D₄×C₁₃	—	2	8	no	—
86	C₄×D₄×C₁₃	—	2	8	no	—
87	C₄×D₄×C₁₃	—	2	8	no	—
88	C₄×D₄×C₁₃	—	2	4	no	—
89	C₄×D₄×C₁₃	C₂³	1	8	yes	—
90	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
91	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
92	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
93	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
94	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
95	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
96	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
97	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
98	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
99	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
100	C₂×C₄²×C₁₃	D₄	1	4	yes	—
101	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
102	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
103	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
104	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
105	C₁₃×#103	C₂³	1	16	yes	—
106	C₁₃×#102	C₂³	1	16	yes	—
107	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
108	C₁₃×#97	C₂³	1	8	yes	—
109	C₂×#3214	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
110	C₂⁴×C₁₃	—	2	2	no	—
111	C₂⁴×C₁₃	—	2	2	no	—
112	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
113	C₁₃×#41	—	4	16	no	—
114	C₁₃×#41	—	4	16	no	—
115	C₁₃×#41	—	4	32	no	—
116	C₂×Q₈×C₁₃	—	2	2	no	—
117	C₂×Q₈×C₁₃	—	2	4	no	—
118	C₂×Q₈×C₁₃	—	2	8	no	—
119	C₂×Q₈×C₁₃	—	4	4	no	—
120	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
121	C₂×D₄×C₁₃	—	2	8	no	—
122	C₂×D₄×C₁₃	—	2	8	no	—
123	C₂×D₄×C₁₃	—	2	2	no	—
124	C₂×D₄×C₁₃	—	2	4	no	—
125	C₂×D₄×C₁₃	—	2	4	no	—
126	C₂×D₄×C₁₃	—	2	4	no	—
127	C₂×D₄×C₁₃	—	2	2	no	—
128	C₂×D₄×C₁₃	—	2	4	no	—
129	C₂×D₄×C₁₃	—	2	4	no	—
130	C₂×D₄×C₁₃	—	2	8	no	—
131	C₂×D₄×C₁₃	—	2	4	no	—
132	C₂×D₄×C₁₃	—	4	4	no	—
133	C₂×D₄×C₁₃	—	4	4	no	—
134	C₂×D₄×C₁₃	—	4	4	no	—
135	C₂×D₄×C₁₃	—	4	8	no	—
136	C₂×D₄×C₁₃	—	4	8	no	—
137	C₂×D₄×C₁₃	—	4	4	no	—
138	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
139	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
140	C₂²×C₄×C₁₃	—	2	4	no	—
141	C₂²×C₄×C₁₃	—	2	4	no	—
142	C₂²×C₄×C₁₃	—	2	2	no	—
143	C₂²×C₄×C₁₃	—	2	2	no	—
144	C₂²×C₄×C₁₃	—	2	8	no	—
145	C₂²×C₄×C₁₃	—	2	8	no	—
146	C₂²×C₄×C₁₃	—	4	2	no	—
147	C₂²×C₄×C₁₃	—	4	8	no	—
148	C₂²×C₄×C₁₃	—	4	8	no	—
149	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
150	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
151	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
156	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
158	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
159	C₁₃×SD₁₆	—	4	16	no	—
160	C₁₃×D₈	—	4	16	no	—
161	C₂×C₈×C₁₃	—	2	8	no	—
162	C₂×C₈×C₁₃	C₂⁴	1	8	yes	—
163	C₁₃×C₄⋊C₄	—	2	4	no	—
164	C₁₃×C₄⋊C₄	—	2	4	no	—
165	C₁₃×C₄⋊C₄	—	2	4	no	—
166	C₁₃×C₄⋊C₄	—	2	2	no	—
167	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
168	C₁₃×C₂²⋊C₄	—	2	8	no	—
169	C₁₃×C₂²⋊C₄	—	2	8	no	—
170	C₁₃×C₂²⋊C₄	—	2	8	no	—
171	C₁₃×C₂²⋊C₄	—	2	8	no	—
172	C₄²×C₁₃	C₂×D₄	1	4	yes	—
173	C₄²×C₁₃	C₂×D₄	1	4	yes	—
174	C₄²×C₁₃	C₂×D₄	1	2	yes	—
175	C₄²×C₁₃	C₂×D₄	1	2	yes	—
176	C₄²×C₁₃	C₂⁴	1	2	yes	—
177	C₄²×C₁₃	C₂⁴	1	2	yes	—
178	C₂×#532	C₂×C₁₃	1	1	yes	characteristic, complemented
179	C₂×#532	C₂×C₁₃	1	1	yes	characteristic, complemented
180	#3214	C₂×C₁₃	1	16	yes	direct product factor
181	C₂×#496	C₂×C₁₃	1	2	yes	complemented
182	C₂×#489	C₂×C₁₃	1	2	yes	complemented
183	C₂×#461	C₂×C₁₃	1	2	yes	complemented
184	C₂×#459	C₂×C₁₃	1	2	yes	complemented
185	C₂×#449	C₂×C₁₃	1	4	yes	complemented
186	C₂×#432	C₂×C₁₃	1	1	yes	characteristic, complemented
187	C₂³×C₁₃	—	2	2	no	—
188	C₂³×C₁₃	—	2	2	no	—
189	C₂³×C₁₃	—	2	2	no	—
190	C₂³×C₁₃	—	2	4	no	—
191	C₂³×C₁₃	—	2	4	no	—
192	C₂³×C₁₃	—	4	4	no	—
193	C₂³×C₁₃	—	4	4	no	—
194	C₂³×C₁₃	—	4	4	no	—
195	C₂³×C₁₃	—	4	4	no	—
196	C₂³×C₁₃	—	4	4	no	—
197	C₂³×C₁₃	—	4	4	no	—
198	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
199	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
200	Q₈×C₁₃	—	2	8	no	—
201	Q₈×C₁₃	—	4	8	no	—
202	Q₈×C₁₃	—	4	4	no	—
203	D₄×C₁₃	—	2	4	no	—
204	D₄×C₁₃	—	2	8	no	—
205	D₄×C₁₃	—	2	4	no	—
206	D₄×C₁₃	—	4	8	no	—
207	D₄×C₁₃	—	4	8	no	—
208	D₄×C₁₃	—	4	8	no	—
209	D₄×C₁₃	—	4	16	no	—
210	D₄×C₁₃	—	4	16	no	—
211	D₄×C₁₃	—	4	4	no	—
212	D₄×C₁₃	—	4	4	no	—
213	D₄×C₁₃	—	4	8	no	—
214	C₂×C₄×C₁₃	—	2	2	no	—
215	C₂×C₄×C₁₃	—	2	2	no	—
216	C₂×C₄×C₁₃	—	2	2	no	—
217	C₂×C₄×C₁₃	—	2	2	no	—
218	C₂×C₄×C₁₃	—	2	4	no	—
219	C₂×C₄×C₁₃	—	2	8	no	—
220	C₂×C₄×C₁₃	—	2	4	no	—
221	C₂×C₄×C₁₃	—	2	4	no	—
222	C₂×C₄×C₁₃	—	2	4	no	—
223	C₂×C₄×C₁₃	—	4	4	no	—
224	C₂×C₄×C₁₃	—	4	16	no	—
225	C₂×C₄×C₁₃	—	4	4	no	—
226	C₂×C₄×C₁₃	—	4	4	no	—
227	C₂×C₄×C₁₃	—	4	16	no	—
228	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
229	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
230	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
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	1	yes	characteristic
234	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
235	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
236	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
237	C₈×C₁₃	—	2	8	no	—
238	C₂²×#41	—	2	1	no	—
239	C₂²×#41	C₂²×C₁₃	1	2	yes	—
240	C₂²×SD₁₆	C₂²×C₁₃	1	4	yes	—
241	C₂²×D₈	C₂²×C₁₃	1	4	yes	—
242	#532	—	2	4	no	—
243	#532	—	2	4	no	—
244	#532	C₂²×C₁₃	1	8	yes	complemented
245	#532	C₂²×C₁₃	1	8	yes	complemented
246	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
247	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
248	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
249	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
250	C₂×#124	—	2	1	no	—
251	C₂×#124	C₂²×C₁₃	1	2	yes	—
252	C₂×#121	—	2	1	no	—
253	C₂×#121	—	2	1	no	—
254	C₂×#121	—	2	1	no	—
255	C₂×#121	C₂²×C₁₃	1	2	yes	—
256	C₂×C₄×D₄	—	2	1	no	—
257	C₂×C₄×D₄	—	2	1	no	—
258	C₂×C₄×D₄	—	2	1	no	—
259	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
260	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
261	#496	C₂²×C₁₃	1	16	yes	complemented
262	#489	C₂²×C₁₃	1	16	yes	complemented
263	#461	C₂²×C₁₃	1	16	yes	complemented
264	#459	C₂²×C₁₃	1	16	yes	complemented
265	#449	C₂²×C₁₃	1	32	yes	complemented
266	#432	C₂²×C₁₃	1	8	yes	complemented
267	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
268	C₂×#103	C₂²×C₁₃	1	4	yes	—
269	C₂×#102	C₂²×C₁₃	1	4	yes	—
270	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
271	C₂×#97	C₂²×C₁₃	1	2	yes	—
272	C₂²×C₁₃	—	2	2	no	—
273	C₂²×C₁₃	—	2	2	no	—
274	C₂²×C₁₃	—	2	2	no	—
275	C₂²×C₁₃	—	4	4	no	—
276	C₂²×C₁₃	—	4	4	no	—
277	C₂²×C₁₃	—	4	4	no	—
278	C₂²×C₁₃	—	4	4	no	—
279	C₂²×C₁₃	—	4	4	no	—
280	C₂²×C₁₃	—	4	4	no	—
281	C₂²×C₁₃	—	4	4	no	—
282	C₂²×C₁₃	—	8	8	no	—
283	C₂²×C₁₃	—	8	8	no	—
284	C₂²×C₁₃	#535	1	2	yes	—
285	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
286	C₂²×C₁₃	#575	1	2	yes	—
287	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
288	C₄×C₁₃	—	2	2	no	—
289	C₄×C₁₃	—	2	2	no	—
290	C₄×C₁₃	—	2	2	no	—
291	C₄×C₁₃	—	2	2	no	—
292	C₄×C₁₃	—	4	4	no	—
293	C₄×C₁₃	—	4	4	no	—
294	C₄×C₁₃	#535	1	2	yes	—
295	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
296	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
297	C₂×#41	—	2	4	no	—
298	C₂×#41	—	2	8	no	—
299	C₂×#41	—	4	8	no	—
300	C₂×#41	—	4	8	no	—
301	C₂×#41	C₂³×C₁₃	1	8	yes	—
302	C₂²×Q₈	—	2	1	no	—
303	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
304	C₂²×D₄	—	2	2	no	—
305	C₂²×D₄	—	2	2	no	—
306	C₂²×D₄	—	2	1	no	—
307	C₂²×D₄	—	2	1	no	—
308	C₂²×D₄	—	2	1	no	—
309	C₂²×D₄	—	2	1	no	—
310	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
311	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
312	C₂³×C₄	—	2	2	no	—
313	C₂³×C₄	—	2	2	no	—
314	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
315	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
316	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
317	C₂×SD₁₆	—	4	8	no	—
318	C₂×SD₁₆	C₂³×C₁₃	1	16	yes	—
319	C₂×D₈	—	4	8	no	—
320	C₂×D₈	C₂³×C₁₃	1	16	yes	—
321	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
322	C₄⋊Q₈	—	2	2	no	—
323	C₄⋊Q₈	—	2	2	no	—
324	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
325	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
326	#127	—	2	2	no	—
327	#127	—	2	2	no	—
328	#127	C₂³×C₁₃	1	4	yes	—
329	#127	C₂³×C₁₃	1	4	yes	—
330	#124	—	2	8	no	—
331	#124	—	2	4	no	—
332	#124	C₂³×C₁₃	1	8	yes	—
333	#121	—	2	8	no	—
334	#121	—	2	8	no	—
335	#121	—	2	8	no	—
336	#121	—	2	4	no	—
337	#121	C₂³×C₁₃	1	8	yes	—
338	C₄×D₄	—	2	8	no	—
339	C₄×D₄	—	2	8	no	—
340	C₄×D₄	—	2	8	no	—
341	C₄×D₄	—	2	4	no	—
342	C₄×D₄	C₂³×C₁₃	1	8	yes	—
343	C₂×C₄⋊C₄	—	2	1	no	—
344	C₂×C₄⋊C₄	—	2	1	no	—
345	C₂×C₄⋊C₄	—	2	1	no	—
346	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
347	C₂×C₂²⋊C₄	—	2	2	no	—
348	C₂×C₂²⋊C₄	—	2	2	no	—
349	C₂×C₂²⋊C₄	—	2	2	no	—
350	C₂×C₂²⋊C₄	—	2	2	no	—
351	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
352	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
353	C₂×C₄²	D₄×C₁₃	1	4	yes	—
354	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
355	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
356	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
357	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
358	#103	C₂³×C₁₃	1	16	yes	—
359	#102	C₂³×C₁₃	1	16	yes	—
360	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
361	#97	C₂³×C₁₃	1	8	yes	—
362	C₂×C₁₃	—	4	2	no	—
363	C₂×C₁₃	—	8	4	no	—
364	C₂×C₁₃	—	8	4	no	—
365	C₂×C₁₃	#3214	1	4	yes	direct product factor
366	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
367	C₂×C₁₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
368	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
369	C₂⁴	—	2	2	no	—
370	C₂⁴	—	2	2	no	—
371	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
372	#41	—	4	16	no	—
373	#41	—	4	16	no	—
374	#41	—	4	32	no	—
375	C₂×Q₈	—	2	2	no	—
376	C₂×Q₈	—	2	4	no	—
377	C₂×Q₈	—	2	8	no	—
378	C₂×Q₈	—	4	4	no	—
379	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
380	C₂×D₄	—	2	8	no	—
381	C₂×D₄	—	2	8	no	—
382	C₂×D₄	—	2	2	no	—
383	C₂×D₄	—	2	4	no	—
384	C₂×D₄	—	2	4	no	—
385	C₂×D₄	—	2	4	no	—
386	C₂×D₄	—	2	2	no	—
387	C₂×D₄	—	2	4	no	—
388	C₂×D₄	—	2	4	no	—
389	C₂×D₄	—	2	8	no	—
390	C₂×D₄	—	2	4	no	—
391	C₂×D₄	—	4	4	no	—
392	C₂×D₄	—	4	4	no	—
393	C₂×D₄	—	4	4	no	—
394	C₂×D₄	—	4	8	no	—
395	C₂×D₄	—	4	8	no	—
396	C₂×D₄	—	4	4	no	—
397	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
398	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
399	C₂²×C₄	—	2	4	no	—
400	C₂²×C₄	—	2	4	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	2	8	no	—
404	C₂²×C₄	—	2	8	no	—
405	C₂²×C₄	—	4	2	no	—
406	C₂²×C₄	—	4	8	no	—
407	C₂²×C₄	—	4	8	no	—
408	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
409	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
410	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
411	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
412	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
413	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
414	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
415	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
416	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
417	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
418	SD₁₆	—	4	16	no	—
419	D₈	—	4	16	no	—
420	C₂×C₈	—	2	8	no	—
421	C₂×C₈	C₂⁴×C₁₃	1	8	yes	—
422	C₄⋊C₄	—	2	4	no	—
423	C₄⋊C₄	—	2	4	no	—
424	C₄⋊C₄	—	2	4	no	—
425	C₄⋊C₄	—	2	2	no	—
426	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
427	C₂²⋊C₄	—	2	8	no	—
428	C₂²⋊C₄	—	2	8	no	—
429	C₂²⋊C₄	—	2	8	no	—
430	C₂²⋊C₄	—	2	8	no	—
431	C₄²	C₂×D₄×C₁₃	1	4	yes	—
432	C₄²	C₂×D₄×C₁₃	1	4	yes	—
433	C₄²	C₂×D₄×C₁₃	1	2	yes	—
434	C₄²	C₂×D₄×C₁₃	1	2	yes	—
435	C₄²	C₂⁴×C₁₃	1	2	yes	—
436	C₄²	C₂⁴×C₁₃	1	2	yes	—
437	C₁₃	C₂×#3214	1	1	yes	characteristic, direct product factor, Sylow
438	C₂³	—	2	2	no	—
439	C₂³	—	2	2	no	—
440	C₂³	—	2	2	no	—
441	C₂³	—	2	4	no	—
442	C₂³	—	2	4	no	—
443	C₂³	—	4	4	no	—
444	C₂³	—	4	4	no	—
445	C₂³	—	4	4	no	—
446	C₂³	—	4	4	no	—
447	C₂³	—	4	4	no	—
448	C₂³	—	4	4	no	—
449	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
450	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
451	Q₈	—	2	8	no	—
452	Q₈	—	4	8	no	—
453	Q₈	—	4	4	no	—
454	D₄	—	2	4	no	—
455	D₄	—	2	8	no	—
456	D₄	—	2	4	no	—
457	D₄	—	4	8	no	—
458	D₄	—	4	8	no	—
459	D₄	—	4	8	no	—
460	D₄	—	4	16	no	—
461	D₄	—	4	16	no	—
462	D₄	—	4	4	no	—
463	D₄	—	4	4	no	—
464	D₄	—	4	8	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	4	no	—
470	C₂×C₄	—	2	8	no	—
471	C₂×C₄	—	2	4	no	—
472	C₂×C₄	—	2	4	no	—
473	C₂×C₄	—	2	4	no	—
474	C₂×C₄	—	4	4	no	—
475	C₂×C₄	—	4	16	no	—
476	C₂×C₄	—	4	4	no	—
477	C₂×C₄	—	4	4	no	—
478	C₂×C₄	—	4	16	no	—
479	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
480	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
481	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
482	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
483	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
484	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
485	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
486	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
487	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
488	C₈	—	2	8	no	—
489	C₂²	—	2	2	no	—
490	C₂²	—	2	2	no	—
491	C₂²	—	2	2	no	—
492	C₂²	—	4	4	no	—
493	C₂²	—	4	4	no	—
494	C₂²	—	4	4	no	—
495	C₂²	—	4	4	no	—
496	C₂²	—	4	4	no	—
497	C₂²	—	4	4	no	—
498	C₂²	—	4	4	no	—
499	C₂²	—	8	8	no	—
500	C₂²	—	8	8	no	—
501	C₂²	C₁₃×#535	1	2	yes	—
502	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
503	C₂²	C₁₃×#575	1	2	yes	—
504	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
505	C₄	—	2	2	no	—
506	C₄	—	2	2	no	—
507	C₄	—	2	2	no	—
508	C₄	—	2	2	no	—
509	C₄	—	4	4	no	—
510	C₄	—	4	4	no	—
511	C₄	C₁₃×#535	1	2	yes	—
512	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	4	yes	—
513	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
514	C₂	—	4	2	no	—
515	C₂	—	8	4	no	—
516	C₂	—	8	4	no	—
517	C₂	C₁₃×#3214	1	4	yes	direct product factor
518	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
519	C₂	C₂²×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
520	C₂	C₂×C₁₃×#575	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. C₂×C₁₃×#532	C₂	semidirect
2. C₂×C₁₃×#532	C₂	semidirect
3. C₁₃×#3214	C₂	direct (N × H)
4. C₂×C₁₃×#496	C₂	semidirect
5. C₂×C₁₃×#489	C₂	semidirect
6. C₂×C₁₃×#461	C₂	semidirect
7. C₂×C₁₃×#459	C₂	semidirect
8. C₂×C₁₃×#449	C₂	semidirect
9. C₂×C₁₃×#432	C₂	semidirect
16. C₁₃×#532	C₂²	semidirect
17. C₁₃×#532	C₂²	semidirect
33. C₁₃×#496	C₂²	semidirect
34. C₁₃×#489	C₂²	semidirect
35. C₁₃×#461	C₂²	semidirect
36. C₁₃×#459	C₂²	semidirect
37. C₁₃×#449	C₂²	semidirect
38. C₁₃×#432	C₂²	semidirect
109. C₂×#3214	C₁₃	direct (N × H)
178. C₂×#532	C₂×C₁₃	semidirect
179. C₂×#532	C₂×C₁₃	semidirect
180. #3214	C₂×C₁₃	direct (N × H)
181. C₂×#496	C₂×C₁₃	semidirect
182. C₂×#489	C₂×C₁₃	semidirect
183. C₂×#461	C₂×C₁₃	semidirect
184. C₂×#459	C₂×C₁₃	semidirect
185. C₂×#449	C₂×C₁₃	semidirect
186. C₂×#432	C₂×C₁₃	semidirect
244. #532	C₂²×C₁₃	semidirect
245. #532	C₂²×C₁₃	semidirect
261. #496	C₂²×C₁₃	semidirect
262. #489	C₂²×C₁₃	semidirect
263. #461	C₂²×C₁₃	semidirect
264. #459	C₂²×C₁₃	semidirect
265. #449	C₂²×C₁₃	semidirect
266. #432	C₂²×C₁₃	semidirect
365. C₂×C₁₃	#3214	direct (N × H)
437. C₁₃	C₂×#3214	direct (N × H)
517. C₂	C₁₃×#3214	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×#532	2
C₁₃×#3214	2
C₂×C₁₃×#496	2
C₂×C₁₃×#489	2
C₂×C₁₃×#461	2
C₂×C₁₃×#459	2
C₂×C₁₃×#449	2
C₂×C₁₃×#432	2
C₂×#3214	13

Subgroups — C2×C13×#3214 #15747126

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3214 #15747126