Subgroups — C₂×C₁₃×#3221 #15747133

Order 3328.

2150 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#540	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#536	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3221	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#496	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#492	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#491	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#488	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#463	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₃×#461	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₃×#449	C₂	1	2	yes	maximal, complemented
11	C₂×C₁₃×#448	C₂	1	2	yes	maximal, complemented
12	C₂×C₁₃×#433	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
14	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
16	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
17	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
18	C₂²×C₁₃×D₈	C₂²	1	2	yes	—
19	C₁₃×#540	—	2	4	no	—
20	C₁₃×#540	C₂²	1	8	yes	complemented
21	C₁₃×#536	—	2	4	no	—
22	C₁₃×#536	C₂²	1	8	yes	complemented
23	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#123	—	2	2	no	—
30	C₂×C₁₃×#123	—	2	2	no	—
31	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
32	C₂×C₁₃×#121	—	2	2	no	—
33	C₂×C₁₃×#121	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
35	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
36	C₁₃×#496	C₂²	1	8	yes	complemented
37	C₁₃×#492	C₂²	1	8	yes	complemented
38	C₁₃×#491	C₂²	1	8	yes	complemented
39	C₁₃×#488	C₂²	1	8	yes	complemented
40	C₁₃×#463	C₂²	1	16	yes	complemented
41	C₁₃×#461	C₂²	1	16	yes	complemented
42	C₁₃×#449	C₂²	1	16	yes	complemented
43	C₁₃×#448	C₂²	1	16	yes	complemented
44	C₁₃×#433	C₂²	1	8	yes	complemented
45	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
46	C₂×C₁₃×#103	C₂²	1	2	yes	—
47	C₂×C₁₃×#103	C₂²	1	2	yes	—
48	C₂×C₁₃×#103	C₂²	1	2	yes	—
49	C₂×C₁₃×#102	C₂²	1	2	yes	—
50	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
51	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
52	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
53	C₂×C₁₃×#41	—	2	2	no	—
54	C₂×C₁₃×#41	—	4	4	no	—
55	C₂×C₁₃×#41	C₂³	1	4	yes	—
56	C₂²×Q₈×C₁₃	—	2	1	no	—
57	C₂²×Q₈×C₁₃	—	2	2	no	—
58	C₂²×Q₈×C₁₃	—	4	4	no	—
59	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
60	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
61	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
62	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
63	C₂²×D₄×C₁₃	—	2	1	no	—
64	C₂²×D₄×C₁₃	—	2	2	no	—
65	C₂²×D₄×C₁₃	—	2	2	no	—
66	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
67	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
68	C₂³×C₄×C₁₃	—	2	1	no	—
69	C₂³×C₄×C₁₃	—	2	1	no	—
70	C₂³×C₄×C₁₃	—	2	2	no	—
71	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
72	C₂×C₁₃×SD₁₆	—	4	4	no	—
73	C₂×C₁₃×SD₁₆	—	4	4	no	—
74	C₂×C₁₃×SD₁₆	—	4	4	no	—
75	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
76	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
77	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
78	C₂×C₁₃×D₈	—	4	4	no	—
79	C₂×C₁₃×D₈	C₂³	1	8	yes	—
80	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
81	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
82	C₁₃×C₄⋊Q₈	—	2	2	no	—
83	C₁₃×C₄⋊Q₈	—	2	2	no	—
84	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
85	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
86	C₁₃×#127	—	2	2	no	—
87	C₁₃×#127	C₂³	1	4	yes	—
88	C₁₃×#125	—	2	2	no	—
89	C₁₃×#125	C₂³	1	4	yes	—
90	C₁₃×#124	—	2	2	no	—
91	C₁₃×#124	—	2	2	no	—
92	C₁₃×#124	C₂³	1	4	yes	—
93	C₁₃×#124	C₂³	1	4	yes	—
94	C₁₃×#123	—	2	16	no	—
95	C₁₃×#123	—	2	16	no	—
96	C₁₃×C₂²⋊Q₈	—	2	16	no	—
97	C₁₃×#121	—	2	4	no	—
98	C₁₃×#121	—	2	16	no	—
99	C₁₃×#121	C₂³	1	8	yes	—
100	C₄×D₄×C₁₃	—	2	4	no	—
101	C₄×D₄×C₁₃	C₂³	1	8	yes	—
102	C₁₃×#117	D₄	1	4	yes	—
103	C₁₃×#117	C₂³	1	4	yes	—
104	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
105	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
106	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
107	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
108	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
109	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
110	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
111	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
112	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
113	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
114	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
115	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
116	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
117	C₁₃×#103	C₂³	1	8	yes	—
118	C₁₃×#103	C₂³	1	8	yes	—
119	C₁₃×#103	C₂³	1	8	yes	—
120	C₁₃×#102	C₂³	1	8	yes	—
121	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
122	C₁₃×#97	C₂³	1	4	yes	—
123	C₄×C₈×C₁₃	C₂³	1	4	yes	—
124	C₂×#3221	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
125	C₂⁴×C₁₃	—	2	1	no	—
126	C₂⁴×C₁₃	—	2	2	no	—
127	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
128	C₁₃×#41	—	4	8	no	—
129	C₁₃×#41	—	4	8	no	—
130	C₂×Q₈×C₁₃	—	2	4	no	—
131	C₂×Q₈×C₁₃	—	2	1	no	—
132	C₂×Q₈×C₁₃	—	2	1	no	—
133	C₂×Q₈×C₁₃	—	2	1	no	—
134	C₂×Q₈×C₁₃	—	2	4	no	—
135	C₂×Q₈×C₁₃	—	2	4	no	—
136	C₂×Q₈×C₁₃	—	2	4	no	—
137	C₂×Q₈×C₁₃	—	4	8	no	—
138	C₂×Q₈×C₁₃	—	4	4	no	—
139	C₂×Q₈×C₁₃	—	4	8	no	—
140	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
141	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
142	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
143	C₂×D₄×C₁₃	—	2	4	no	—
144	C₂×D₄×C₁₃	—	2	8	no	—
145	C₂×D₄×C₁₃	—	2	2	no	—
146	C₂×D₄×C₁₃	—	2	1	no	—
147	C₂×D₄×C₁₃	—	2	8	no	—
148	C₂×D₄×C₁₃	—	2	4	no	—
149	C₂×D₄×C₁₃	—	2	4	no	—
150	C₂×D₄×C₁₃	—	2	4	no	—
151	C₂×D₄×C₁₃	—	4	4	no	—
152	C₂×D₄×C₁₃	—	8	4	no	—
153	C₂×D₄×C₁₃	—	8	4	no	—
154	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
155	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
156	C₂²×C₄×C₁₃	—	2	4	no	—
157	C₂²×C₄×C₁₃	—	2	4	no	—
158	C₂²×C₄×C₁₃	—	2	2	no	—
159	C₂²×C₄×C₁₃	—	2	1	no	—
160	C₂²×C₄×C₁₃	—	2	1	no	—
161	C₂²×C₄×C₁₃	—	2	1	no	—
162	C₂²×C₄×C₁₃	—	2	4	no	—
163	C₂²×C₄×C₁₃	—	2	8	no	—
164	C₂²×C₄×C₁₃	—	4	4	no	—
165	C₂²×C₄×C₁₃	—	4	4	no	—
166	C₂²×C₄×C₁₃	—	8	4	no	—
167	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
168	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
169	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
170	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
172	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
173	C₁₃×SD₁₆	—	4	8	no	—
174	C₁₃×SD₁₆	—	4	8	no	—
175	C₁₃×SD₁₆	—	4	8	no	—
176	C₁₃×D₈	—	4	8	no	—
177	C₂×C₈×C₁₃	—	2	4	no	—
178	C₂×C₈×C₁₃	—	2	4	no	—
179	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
180	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
181	C₁₃×C₄⋊C₄	—	2	8	no	—
182	C₁₃×C₄⋊C₄	—	2	8	no	—
183	C₁₃×C₄⋊C₄	—	2	8	no	—
184	C₁₃×C₄⋊C₄	—	2	2	no	—
185	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
186	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
187	C₁₃×C₂²⋊C₄	—	2	8	no	—
188	C₁₃×C₂²⋊C₄	—	2	8	no	—
189	C₁₃×C₂²⋊C₄	—	2	8	no	—
190	C₁₃×C₂²⋊C₄	—	2	8	no	—
191	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
192	C₄²×C₁₃	C₂×D₄	1	2	yes	—
193	C₄²×C₁₃	C₂×D₄	1	2	yes	—
194	C₄²×C₁₃	C₂⁴	1	2	yes	—
195	C₄²×C₁₃	C₂⁴	1	2	yes	—
196	C₂×#540	C₂×C₁₃	1	1	yes	characteristic, complemented
197	C₂×#536	C₂×C₁₃	1	1	yes	characteristic, complemented
198	#3221	C₂×C₁₃	1	16	yes	direct product factor
199	C₂×#496	C₂×C₁₃	1	1	yes	characteristic, complemented
200	C₂×#492	C₂×C₁₃	1	1	yes	characteristic, complemented
201	C₂×#491	C₂×C₁₃	1	1	yes	characteristic, complemented
202	C₂×#488	C₂×C₁₃	1	1	yes	characteristic, complemented
203	C₂×#463	C₂×C₁₃	1	2	yes	complemented
204	C₂×#461	C₂×C₁₃	1	2	yes	complemented
205	C₂×#449	C₂×C₁₃	1	2	yes	complemented
206	C₂×#448	C₂×C₁₃	1	2	yes	complemented
207	C₂×#433	C₂×C₁₃	1	1	yes	characteristic, complemented
208	C₂³×C₁₃	—	2	2	no	—
209	C₂³×C₁₃	—	2	4	no	—
210	C₂³×C₁₃	—	2	2	no	—
211	C₂³×C₁₃	—	2	4	no	—
212	C₂³×C₁₃	—	4	2	no	—
213	C₂³×C₁₃	—	4	4	no	—
214	C₂³×C₁₃	—	4	4	no	—
215	C₂³×C₁₃	—	4	4	no	—
216	C₂³×C₁₃	—	4	4	no	—
217	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
218	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
219	Q₈×C₁₃	—	2	4	no	—
220	Q₈×C₁₃	—	2	4	no	—
221	Q₈×C₁₃	—	2	4	no	—
222	Q₈×C₁₃	—	4	8	no	—
223	Q₈×C₁₃	—	4	2	no	—
224	Q₈×C₁₃	—	4	2	no	—
225	Q₈×C₁₃	—	4	2	no	—
226	D₄×C₁₃	—	2	4	no	—
227	D₄×C₁₃	—	2	4	no	—
228	D₄×C₁₃	—	2	4	no	—
229	D₄×C₁₃	—	4	8	no	—
230	D₄×C₁₃	—	4	4	no	—
231	D₄×C₁₃	—	4	2	no	—
232	D₄×C₁₃	—	8	8	no	—
233	D₄×C₁₃	—	8	8	no	—
234	C₂×C₄×C₁₃	—	2	2	no	—
235	C₂×C₄×C₁₃	—	2	4	no	—
236	C₂×C₄×C₁₃	—	2	4	no	—
237	C₂×C₄×C₁₃	—	2	4	no	—
238	C₂×C₄×C₁₃	—	2	4	no	—
239	C₂×C₄×C₁₃	—	2	4	no	—
240	C₂×C₄×C₁₃	—	2	2	no	—
241	C₂×C₄×C₁₃	—	2	2	no	—
242	C₂×C₄×C₁₃	—	2	2	no	—
243	C₂×C₄×C₁₃	—	4	8	no	—
244	C₂×C₄×C₁₃	—	4	8	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	4	no	—
249	C₂×C₄×C₁₃	—	8	8	no	—
250	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
251	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
252	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
253	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
254	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
255	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
256	C₈×C₁₃	—	2	4	no	—
257	C₈×C₁₃	—	2	4	no	—
258	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
259	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
260	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
261	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
262	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
263	C₂²×D₈	C₂²×C₁₃	1	2	yes	—
264	#540	—	2	4	no	—
265	#540	C₂²×C₁₃	1	8	yes	complemented
266	#536	—	2	4	no	—
267	#536	C₂²×C₁₃	1	8	yes	complemented
268	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
269	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
270	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
271	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
272	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
273	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
274	C₂×#123	—	2	2	no	—
275	C₂×#123	—	2	2	no	—
276	C₂×C₂²⋊Q₈	—	2	2	no	—
277	C₂×#121	—	2	2	no	—
278	C₂×#121	C₂²×C₁₃	1	2	yes	—
279	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
280	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
281	#496	C₂²×C₁₃	1	8	yes	complemented
282	#492	C₂²×C₁₃	1	8	yes	complemented
283	#491	C₂²×C₁₃	1	8	yes	complemented
284	#488	C₂²×C₁₃	1	8	yes	complemented
285	#463	C₂²×C₁₃	1	16	yes	complemented
286	#461	C₂²×C₁₃	1	16	yes	complemented
287	#449	C₂²×C₁₃	1	16	yes	complemented
288	#448	C₂²×C₁₃	1	16	yes	complemented
289	#433	C₂²×C₁₃	1	8	yes	complemented
290	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
291	C₂×#103	C₂²×C₁₃	1	2	yes	—
292	C₂×#103	C₂²×C₁₃	1	2	yes	—
293	C₂×#103	C₂²×C₁₃	1	2	yes	—
294	C₂×#102	C₂²×C₁₃	1	2	yes	—
295	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
296	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
297	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
298	C₂²×C₁₃	—	2	2	no	—
299	C₂²×C₁₃	—	2	4	no	—
300	C₂²×C₁₃	—	4	4	no	—
301	C₂²×C₁₃	—	4	2	no	—
302	C₂²×C₁₃	—	4	4	no	—
303	C₂²×C₁₃	—	4	4	no	—
304	C₂²×C₁₃	—	4	4	no	—
305	C₂²×C₁₃	—	4	4	no	—
306	C₂²×C₁₃	—	8	4	no	—
307	C₂²×C₁₃	—	8	8	no	—
308	C₂²×C₁₃	#535	1	2	yes	—
309	C₂²×C₁₃	#577	1	4	yes	—
310	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
311	C₄×C₁₃	—	2	2	no	—
312	C₄×C₁₃	—	2	4	no	—
313	C₄×C₁₃	—	2	4	no	—
314	C₄×C₁₃	—	4	2	no	—
315	C₄×C₁₃	—	4	2	no	—
316	C₄×C₁₃	—	4	2	no	—
317	C₄×C₁₃	—	4	4	no	—
318	C₄×C₁₃	#535	1	2	yes	—
319	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
320	C₂×#41	—	2	2	no	—
321	C₂×#41	—	4	4	no	—
322	C₂×#41	C₂³×C₁₃	1	4	yes	—
323	C₂²×Q₈	—	2	1	no	—
324	C₂²×Q₈	—	2	2	no	—
325	C₂²×Q₈	—	4	4	no	—
326	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
327	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
328	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
329	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
330	C₂²×D₄	—	2	1	no	—
331	C₂²×D₄	—	2	2	no	—
332	C₂²×D₄	—	2	2	no	—
333	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
334	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
335	C₂³×C₄	—	2	1	no	—
336	C₂³×C₄	—	2	1	no	—
337	C₂³×C₄	—	2	2	no	—
338	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
339	C₂×SD₁₆	—	4	4	no	—
340	C₂×SD₁₆	—	4	4	no	—
341	C₂×SD₁₆	—	4	4	no	—
342	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
343	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
344	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
345	C₂×D₈	—	4	4	no	—
346	C₂×D₈	C₂³×C₁₃	1	8	yes	—
347	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
348	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
349	C₄⋊Q₈	—	2	2	no	—
350	C₄⋊Q₈	—	2	2	no	—
351	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
352	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
353	#127	—	2	2	no	—
354	#127	C₂³×C₁₃	1	4	yes	—
355	#125	—	2	2	no	—
356	#125	C₂³×C₁₃	1	4	yes	—
357	#124	—	2	2	no	—
358	#124	—	2	2	no	—
359	#124	C₂³×C₁₃	1	4	yes	—
360	#124	C₂³×C₁₃	1	4	yes	—
361	#123	—	2	16	no	—
362	#123	—	2	16	no	—
363	C₂²⋊Q₈	—	2	16	no	—
364	#121	—	2	4	no	—
365	#121	—	2	16	no	—
366	#121	C₂³×C₁₃	1	8	yes	—
367	C₄×D₄	—	2	4	no	—
368	C₄×D₄	C₂³×C₁₃	1	8	yes	—
369	#117	D₄×C₁₃	1	4	yes	—
370	#117	C₂³×C₁₃	1	4	yes	—
371	C₂×C₄⋊C₄	—	2	2	no	—
372	C₂×C₄⋊C₄	—	2	2	no	—
373	C₂×C₄⋊C₄	—	2	2	no	—
374	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
375	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
376	C₂×C₂²⋊C₄	—	2	2	no	—
377	C₂×C₂²⋊C₄	—	2	2	no	—
378	C₂×C₂²⋊C₄	—	2	2	no	—
379	C₂×C₂²⋊C₄	—	2	2	no	—
380	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
381	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
382	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
383	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
384	#103	C₂³×C₁₃	1	8	yes	—
385	#103	C₂³×C₁₃	1	8	yes	—
386	#103	C₂³×C₁₃	1	8	yes	—
387	#102	C₂³×C₁₃	1	8	yes	—
388	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
389	#97	C₂³×C₁₃	1	4	yes	—
390	C₄×C₈	C₂³×C₁₃	1	4	yes	—
391	C₂×C₁₃	—	4	2	no	—
392	C₂×C₁₃	—	8	2	no	—
393	C₂×C₁₃	—	8	4	no	—
394	C₂×C₁₃	#3221	1	4	yes	direct product factor
395	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
396	C₂×C₁₃	C₂×#577	1	2	yes	—
397	C₂⁴	—	2	1	no	—
398	C₂⁴	—	2	2	no	—
399	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
400	#41	—	4	8	no	—
401	#41	—	4	8	no	—
402	C₂×Q₈	—	2	4	no	—
403	C₂×Q₈	—	2	1	no	—
404	C₂×Q₈	—	2	1	no	—
405	C₂×Q₈	—	2	1	no	—
406	C₂×Q₈	—	2	4	no	—
407	C₂×Q₈	—	2	4	no	—
408	C₂×Q₈	—	2	4	no	—
409	C₂×Q₈	—	4	8	no	—
410	C₂×Q₈	—	4	4	no	—
411	C₂×Q₈	—	4	8	no	—
412	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
413	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
414	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
415	C₂×D₄	—	2	4	no	—
416	C₂×D₄	—	2	8	no	—
417	C₂×D₄	—	2	2	no	—
418	C₂×D₄	—	2	1	no	—
419	C₂×D₄	—	2	8	no	—
420	C₂×D₄	—	2	4	no	—
421	C₂×D₄	—	2	4	no	—
422	C₂×D₄	—	2	4	no	—
423	C₂×D₄	—	4	4	no	—
424	C₂×D₄	—	8	4	no	—
425	C₂×D₄	—	8	4	no	—
426	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
427	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
428	C₂²×C₄	—	2	4	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	2	4	no	—
434	C₂²×C₄	—	2	4	no	—
435	C₂²×C₄	—	2	8	no	—
436	C₂²×C₄	—	4	4	no	—
437	C₂²×C₄	—	4	4	no	—
438	C₂²×C₄	—	8	4	no	—
439	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
440	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
441	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
442	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
443	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
444	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
445	SD₁₆	—	4	8	no	—
446	SD₁₆	—	4	8	no	—
447	SD₁₆	—	4	8	no	—
448	D₈	—	4	8	no	—
449	C₂×C₈	—	2	4	no	—
450	C₂×C₈	—	2	4	no	—
451	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
452	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
453	C₄⋊C₄	—	2	8	no	—
454	C₄⋊C₄	—	2	8	no	—
455	C₄⋊C₄	—	2	8	no	—
456	C₄⋊C₄	—	2	2	no	—
457	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
458	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
459	C₂²⋊C₄	—	2	8	no	—
460	C₂²⋊C₄	—	2	8	no	—
461	C₂²⋊C₄	—	2	8	no	—
462	C₂²⋊C₄	—	2	8	no	—
463	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
464	C₄²	C₂×D₄×C₁₃	1	2	yes	—
465	C₄²	C₂×D₄×C₁₃	1	2	yes	—
466	C₄²	C₂⁴×C₁₃	1	2	yes	—
467	C₄²	C₂⁴×C₁₃	1	2	yes	—
468	C₁₃	C₂×#3221	1	1	yes	characteristic, direct product factor, Sylow
469	C₂³	—	2	2	no	—
470	C₂³	—	2	4	no	—
471	C₂³	—	2	2	no	—
472	C₂³	—	2	4	no	—
473	C₂³	—	4	2	no	—
474	C₂³	—	4	4	no	—
475	C₂³	—	4	4	no	—
476	C₂³	—	4	4	no	—
477	C₂³	—	4	4	no	—
478	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
479	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
480	Q₈	—	2	4	no	—
481	Q₈	—	2	4	no	—
482	Q₈	—	2	4	no	—
483	Q₈	—	4	8	no	—
484	Q₈	—	4	2	no	—
485	Q₈	—	4	2	no	—
486	Q₈	—	4	2	no	—
487	D₄	—	2	4	no	—
488	D₄	—	2	4	no	—
489	D₄	—	2	4	no	—
490	D₄	—	4	8	no	—
491	D₄	—	4	4	no	—
492	D₄	—	4	2	no	—
493	D₄	—	8	8	no	—
494	D₄	—	8	8	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	4	no	—
497	C₂×C₄	—	2	4	no	—
498	C₂×C₄	—	2	4	no	—
499	C₂×C₄	—	2	4	no	—
500	C₂×C₄	—	2	4	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	4	8	no	—
505	C₂×C₄	—	4	8	no	—
506	C₂×C₄	—	4	2	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	4	4	no	—
510	C₂×C₄	—	8	8	no	—
511	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
512	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
513	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
514	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
515	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
516	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
517	C₈	—	2	4	no	—
518	C₈	—	2	4	no	—
519	C₂²	—	2	4	no	—
520	C₂²	—	2	2	no	—
521	C₂²	—	4	4	no	—
522	C₂²	—	4	4	no	—
523	C₂²	—	4	4	no	—
524	C₂²	—	4	4	no	—
525	C₂²	—	4	2	no	—
526	C₂²	—	4	4	no	—
527	C₂²	—	8	4	no	—
528	C₂²	—	8	8	no	—
529	C₂²	C₁₃×#535	1	2	yes	—
530	C₂²	C₁₃×#577	1	4	yes	—
531	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
532	C₄	—	2	4	no	—
533	C₄	—	2	4	no	—
534	C₄	—	2	2	no	—
535	C₄	—	4	4	no	—
536	C₄	—	4	2	no	—
537	C₄	—	4	2	no	—
538	C₄	—	4	2	no	—
539	C₄	C₁₃×#535	1	2	yes	—
540	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
541	C₂	—	4	2	no	—
542	C₂	—	8	4	no	—
543	C₂	—	8	2	no	—
544	C₂	C₁₃×#3221	1	4	yes	direct product factor
545	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
546	C₂	C₂×C₁₃×#577	1	2	yes	—

	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×C₁₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#540	C₂	semidirect
2. C₂×C₁₃×#536	C₂	semidirect
3. C₁₃×#3221	C₂	direct (N × H)
4. C₂×C₁₃×#496	C₂	semidirect
5. C₂×C₁₃×#492	C₂	semidirect
6. C₂×C₁₃×#491	C₂	semidirect
7. C₂×C₁₃×#488	C₂	semidirect
8. C₂×C₁₃×#463	C₂	semidirect
9. C₂×C₁₃×#461	C₂	semidirect
10. C₂×C₁₃×#449	C₂	semidirect
11. C₂×C₁₃×#448	C₂	semidirect
12. C₂×C₁₃×#433	C₂	semidirect
20. C₁₃×#540	C₂²	semidirect
22. C₁₃×#536	C₂²	semidirect
36. C₁₃×#496	C₂²	semidirect
37. C₁₃×#492	C₂²	semidirect
38. C₁₃×#491	C₂²	semidirect
39. C₁₃×#488	C₂²	semidirect
40. C₁₃×#463	C₂²	semidirect
41. C₁₃×#461	C₂²	semidirect
42. C₁₃×#449	C₂²	semidirect
43. C₁₃×#448	C₂²	semidirect
44. C₁₃×#433	C₂²	semidirect
124. C₂×#3221	C₁₃	direct (N × H)
196. C₂×#540	C₂×C₁₃	semidirect
197. C₂×#536	C₂×C₁₃	semidirect
198. #3221	C₂×C₁₃	direct (N × H)
199. C₂×#496	C₂×C₁₃	semidirect
200. C₂×#492	C₂×C₁₃	semidirect
201. C₂×#491	C₂×C₁₃	semidirect
202. C₂×#488	C₂×C₁₃	semidirect
203. C₂×#463	C₂×C₁₃	semidirect
204. C₂×#461	C₂×C₁₃	semidirect
205. C₂×#449	C₂×C₁₃	semidirect
206. C₂×#448	C₂×C₁₃	semidirect
207. C₂×#433	C₂×C₁₃	semidirect
265. #540	C₂²×C₁₃	semidirect
267. #536	C₂²×C₁₃	semidirect
281. #496	C₂²×C₁₃	semidirect
282. #492	C₂²×C₁₃	semidirect
283. #491	C₂²×C₁₃	semidirect
284. #488	C₂²×C₁₃	semidirect
285. #463	C₂²×C₁₃	semidirect
286. #461	C₂²×C₁₃	semidirect
287. #449	C₂²×C₁₃	semidirect
288. #448	C₂²×C₁₃	semidirect
289. #433	C₂²×C₁₃	semidirect
394. C₂×C₁₃	#3221	direct (N × H)
468. C₁₃	C₂×#3221	direct (N × H)
544. C₂	C₁₃×#3221	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×#540	2
C₂×C₁₃×#536	2
C₁₃×#3221	2
C₂×C₁₃×#496	2
C₂×C₁₃×#492	2
C₂×C₁₃×#491	2
C₂×C₁₃×#488	2
C₂×C₁₃×#463	2
C₂×C₁₃×#461	2
C₂×C₁₃×#449	2
C₂×C₁₃×#448	2
C₂×C₁₃×#433	2
C₂×#3221	13

Subgroups — C2×C13×#3221 #15747133

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3221 #15747133