Subgroups — C₂×C₁₃×#3223 #15747134

Order 3328.

2022 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#541	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#536	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3223	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#497	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#494	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×#464	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₃×#462	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₃×#452	C₂	1	2	yes	maximal
11	C₂×C₁₃×#451	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×Q₁₆	C₂²	1	2	yes	—
16	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
17	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
18	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
19	C₁₃×#541	—	2	4	no	—
20	C₁₃×#541	C₂²	1	8	yes	complemented
21	C₁₃×#536	—	2	4	no	—
22	C₁₃×#536	C₂²	1	8	yes	—
23	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#126	—	2	2	no	—
27	C₂×C₁₃×#125	—	2	2	no	—
28	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#123	—	2	2	no	—
32	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
33	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
34	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
35	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
36	C₁₃×#497	C₂²	1	8	yes	complemented
37	C₁₃×#494	C₂²	1	8	yes	complemented
38	C₁₃×#491	C₂²	1	8	yes	complemented
39	C₁₃×#488	C₂²	1	8	yes	complemented
40	C₁₃×#464	C₂²	1	16	yes	complemented
41	C₁₃×#462	C₂²	1	16	yes	complemented
42	C₁₃×#452	C₂²	1	16	yes	—
43	C₁₃×#451	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	2	yes	—
63	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
64	C₂²×D₄×C₁₃	—	2	1	no	—
65	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₁₃	—	2	1	no	—
67	C₂³×C₄×C₁₃	—	2	1	no	—
68	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
69	C₂×C₁₃×Q₁₆	—	4	4	no	—
70	C₂×C₁₃×Q₁₆	—	4	4	no	—
71	C₂×C₁₃×Q₁₆	—	4	4	no	—
72	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	—
73	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	—
74	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	—
75	C₂×C₁₃×SD₁₆	—	4	4	no	—
76	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
77	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
78	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
79	C₁₃×C₄⋊Q₈	—	2	2	no	—
80	C₁₃×C₄⋊Q₈	—	2	2	no	—
81	C₁₃×C₄⋊Q₈	—	2	2	no	—
82	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
83	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
84	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
85	C₁₃×#126	—	2	16	no	—
86	C₁₃×#125	—	2	16	no	—
87	C₁₃×#125	—	2	2	no	—
88	C₁₃×#125	C₂³	1	4	yes	—
89	C₁₃×#124	—	2	2	no	—
90	C₁₃×#124	—	2	2	no	—
91	C₁₃×#124	C₂³	1	4	yes	—
92	C₁₃×#124	C₂³	1	4	yes	—
93	C₁₃×#123	—	2	16	no	—
94	C₁₃×C₂²⋊Q₈	—	2	4	no	—
95	C₁₃×C₂²⋊Q₈	—	2	16	no	—
96	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
97	C₄×Q₈×C₁₃	—	2	4	no	—
98	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
99	C₁₃×#117	D₄	1	4	yes	—
100	C₁₃×#117	C₂³	1	4	yes	—
101	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
102	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
103	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
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	D₄	1	2	yes	—
113	C₂×C₄²×C₁₃	—	2	2	no	—
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×#3223	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
125	C₂⁴×C₁₃	—	2	1	no	—
126	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
127	C₁₃×#41	—	4	8	no	—
128	C₁₃×#41	—	4	8	no	—
129	C₂×Q₈×C₁₃	—	2	2	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	—	2	4	no	—
138	C₂×Q₈×C₁₃	—	2	4	no	—
139	C₂×Q₈×C₁₃	—	4	8	no	—
140	C₂×Q₈×C₁₃	—	4	4	no	—
141	C₂×Q₈×C₁₃	—	4	8	no	—
142	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
143	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
144	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
145	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
146	C₂×D₄×C₁₃	—	2	4	no	—
147	C₂×D₄×C₁₃	—	2	1	no	—
148	C₂×D₄×C₁₃	—	2	4	no	—
149	C₂×D₄×C₁₃	—	4	4	no	—
150	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
151	C₂²×C₄×C₁₃	—	2	4	no	—
152	C₂²×C₄×C₁₃	—	2	4	no	—
153	C₂²×C₄×C₁₃	—	2	2	no	—
154	C₂²×C₄×C₁₃	—	2	2	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	—	4	4	no	—
161	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
162	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
163	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
164	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
166	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
167	C₁₃×Q₁₆	—	4	8	no	—
168	C₁₃×Q₁₆	—	4	8	no	—
169	C₁₃×Q₁₆	—	4	8	no	—
170	C₁₃×SD₁₆	—	4	8	no	—
171	C₂×C₈×C₁₃	—	2	4	no	—
172	C₂×C₈×C₁₃	—	2	4	no	—
173	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
174	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
175	C₁₃×C₄⋊C₄	—	2	8	no	—
176	C₁₃×C₄⋊C₄	—	2	8	no	—
177	C₁₃×C₄⋊C₄	—	2	8	no	—
178	C₁₃×C₄⋊C₄	—	2	8	no	—
179	C₁₃×C₄⋊C₄	—	2	8	no	—
180	C₁₃×C₄⋊C₄	—	2	8	no	—
181	C₁₃×C₄⋊C₄	—	2	2	no	—
182	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
183	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
184	C₁₃×C₂²⋊C₄	—	2	8	no	—
185	C₁₃×C₂²⋊C₄	—	2	8	no	—
186	C₁₃×C₂²⋊C₄	—	2	8	no	—
187	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
188	C₄²×C₁₃	—	2	8	no	—
189	C₄²×C₁₃	C₂×D₄	1	2	yes	—
190	C₄²×C₁₃	C₂×D₄	1	2	yes	—
191	C₄²×C₁₃	C₂⁴	1	2	yes	—
192	C₄²×C₁₃	C₂⁴	1	2	yes	—
193	C₂×#541	C₂×C₁₃	1	1	yes	characteristic, complemented
194	C₂×#536	C₂×C₁₃	1	1	yes	characteristic
195	#3223	C₂×C₁₃	1	16	yes	direct product factor
196	C₂×#497	C₂×C₁₃	1	1	yes	characteristic, complemented
197	C₂×#494	C₂×C₁₃	1	1	yes	characteristic, complemented
198	C₂×#491	C₂×C₁₃	1	1	yes	characteristic, complemented
199	C₂×#488	C₂×C₁₃	1	1	yes	characteristic, complemented
200	C₂×#464	C₂×C₁₃	1	2	yes	complemented
201	C₂×#462	C₂×C₁₃	1	2	yes	complemented
202	C₂×#452	C₂×C₁₃	1	2	yes	—
203	C₂×#451	C₂×C₁₃	1	2	yes	complemented
204	C₂×#433	C₂×C₁₃	1	1	yes	characteristic, complemented
205	C₂³×C₁₃	—	2	2	no	—
206	C₂³×C₁₃	—	2	4	no	—
207	C₂³×C₁₃	—	2	2	no	—
208	C₂³×C₁₃	—	4	2	no	—
209	C₂³×C₁₃	—	4	4	no	—
210	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
211	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
212	Q₈×C₁₃	—	2	4	no	—
213	Q₈×C₁₃	—	2	4	no	—
214	Q₈×C₁₃	—	2	4	no	—
215	Q₈×C₁₃	—	2	4	no	—
216	Q₈×C₁₃	—	2	4	no	—
217	Q₈×C₁₃	—	4	8	no	—
218	Q₈×C₁₃	—	4	4	no	—
219	Q₈×C₁₃	—	4	2	no	—
220	Q₈×C₁₃	—	4	2	no	—
221	Q₈×C₁₃	—	4	2	no	—
222	D₄×C₁₃	—	2	4	no	—
223	D₄×C₁₃	—	4	8	no	—
224	D₄×C₁₃	—	4	2	no	—
225	C₂×C₄×C₁₃	—	2	2	no	—
226	C₂×C₄×C₁₃	—	2	4	no	—
227	C₂×C₄×C₁₃	—	2	4	no	—
228	C₂×C₄×C₁₃	—	2	4	no	—
229	C₂×C₄×C₁₃	—	2	4	no	—
230	C₂×C₄×C₁₃	—	2	4	no	—
231	C₂×C₄×C₁₃	—	2	4	no	—
232	C₂×C₄×C₁₃	—	2	2	no	—
233	C₂×C₄×C₁₃	—	2	2	no	—
234	C₂×C₄×C₁₃	—	2	2	no	—
235	C₂×C₄×C₁₃	—	4	8	no	—
236	C₂×C₄×C₁₃	—	4	8	no	—
237	C₂×C₄×C₁₃	—	4	2	no	—
238	C₂×C₄×C₁₃	—	4	2	no	—
239	C₂×C₄×C₁₃	—	4	2	no	—
240	C₂×C₄×C₁₃	—	4	4	no	—
241	C₂×C₄×C₁₃	—	4	4	no	—
242	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
243	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
244	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
245	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
246	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
247	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
248	C₈×C₁₃	—	2	4	no	—
249	C₈×C₁₃	—	2	4	no	—
250	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
251	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
252	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
253	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
254	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
255	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
256	#541	—	2	4	no	—
257	#541	C₂²×C₁₃	1	8	yes	complemented
258	#536	—	2	4	no	—
259	#536	C₂²×C₁₃	1	8	yes	—
260	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
261	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
262	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
263	C₂×#126	—	2	2	no	—
264	C₂×#125	—	2	2	no	—
265	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
266	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
267	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
268	C₂×#123	—	2	2	no	—
269	C₂×C₂²⋊Q₈	—	2	2	no	—
270	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
271	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
272	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
273	#497	C₂²×C₁₃	1	8	yes	complemented
274	#494	C₂²×C₁₃	1	8	yes	complemented
275	#491	C₂²×C₁₃	1	8	yes	complemented
276	#488	C₂²×C₁₃	1	8	yes	complemented
277	#464	C₂²×C₁₃	1	16	yes	complemented
278	#462	C₂²×C₁₃	1	16	yes	complemented
279	#452	C₂²×C₁₃	1	16	yes	—
280	#451	C₂²×C₁₃	1	16	yes	complemented
281	#433	C₂²×C₁₃	1	8	yes	complemented
282	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
283	C₂×#103	C₂²×C₁₃	1	2	yes	—
284	C₂×#103	C₂²×C₁₃	1	2	yes	—
285	C₂×#103	C₂²×C₁₃	1	2	yes	—
286	C₂×#102	C₂²×C₁₃	1	2	yes	—
287	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
288	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
289	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
290	C₂²×C₁₃	—	2	2	no	—
291	C₂²×C₁₃	—	2	4	no	—
292	C₂²×C₁₃	—	4	4	no	—
293	C₂²×C₁₃	—	4	2	no	—
294	C₂²×C₁₃	—	4	4	no	—
295	C₂²×C₁₃	—	8	4	no	—
296	C₂²×C₁₃	#535	1	2	yes	—
297	C₂²×C₁₃	#578	1	4	yes	—
298	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
299	C₄×C₁₃	—	2	2	no	—
300	C₄×C₁₃	—	2	4	no	—
301	C₄×C₁₃	—	2	4	no	—
302	C₄×C₁₃	—	4	2	no	—
303	C₄×C₁₃	—	4	2	no	—
304	C₄×C₁₃	—	4	2	no	—
305	C₄×C₁₃	—	4	4	no	—
306	C₄×C₁₃	—	4	4	no	—
307	C₄×C₁₃	#535	1	2	yes	—
308	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
309	C₂×#41	—	2	2	no	—
310	C₂×#41	—	4	4	no	—
311	C₂×#41	C₂³×C₁₃	1	4	yes	—
312	C₂²×Q₈	—	2	1	no	—
313	C₂²×Q₈	—	2	2	no	—
314	C₂²×Q₈	—	4	4	no	—
315	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
316	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
317	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
318	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
319	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
320	C₂²×D₄	—	2	1	no	—
321	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
322	C₂³×C₄	—	2	1	no	—
323	C₂³×C₄	—	2	1	no	—
324	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
325	C₂×Q₁₆	—	4	4	no	—
326	C₂×Q₁₆	—	4	4	no	—
327	C₂×Q₁₆	—	4	4	no	—
328	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	—
329	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	—
330	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	—
331	C₂×SD₁₆	—	4	4	no	—
332	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
333	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
334	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
335	C₄⋊Q₈	—	2	2	no	—
336	C₄⋊Q₈	—	2	2	no	—
337	C₄⋊Q₈	—	2	2	no	—
338	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
339	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
340	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
341	#126	—	2	16	no	—
342	#125	—	2	16	no	—
343	#125	—	2	2	no	—
344	#125	C₂³×C₁₃	1	4	yes	—
345	#124	—	2	2	no	—
346	#124	—	2	2	no	—
347	#124	C₂³×C₁₃	1	4	yes	—
348	#124	C₂³×C₁₃	1	4	yes	—
349	#123	—	2	16	no	—
350	C₂²⋊Q₈	—	2	4	no	—
351	C₂²⋊Q₈	—	2	16	no	—
352	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
353	C₄×Q₈	—	2	4	no	—
354	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
355	#117	D₄×C₁₃	1	4	yes	—
356	#117	C₂³×C₁₃	1	4	yes	—
357	C₂×C₄⋊C₄	—	2	2	no	—
358	C₂×C₄⋊C₄	—	2	2	no	—
359	C₂×C₄⋊C₄	—	2	2	no	—
360	C₂×C₄⋊C₄	—	2	2	no	—
361	C₂×C₄⋊C₄	—	2	2	no	—
362	C₂×C₄⋊C₄	—	2	2	no	—
363	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
364	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
365	C₂×C₂²⋊C₄	—	2	2	no	—
366	C₂×C₂²⋊C₄	—	2	2	no	—
367	C₂×C₂²⋊C₄	—	2	2	no	—
368	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
369	C₂×C₄²	—	2	2	no	—
370	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
371	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
372	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
373	#103	C₂³×C₁₃	1	8	yes	—
374	#103	C₂³×C₁₃	1	8	yes	—
375	#103	C₂³×C₁₃	1	8	yes	—
376	#102	C₂³×C₁₃	1	8	yes	—
377	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
378	#97	C₂³×C₁₃	1	4	yes	—
379	C₄×C₈	C₂³×C₁₃	1	4	yes	—
380	C₂×C₁₃	—	4	2	no	—
381	C₂×C₁₃	—	8	2	no	—
382	C₂×C₁₃	#3223	1	4	yes	direct product factor
383	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
384	C₂×C₁₃	C₂×#578	1	2	yes	—
385	C₂⁴	—	2	1	no	—
386	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
387	#41	—	4	8	no	—
388	#41	—	4	8	no	—
389	C₂×Q₈	—	2	2	no	—
390	C₂×Q₈	—	2	4	no	—
391	C₂×Q₈	—	2	1	no	—
392	C₂×Q₈	—	2	1	no	—
393	C₂×Q₈	—	2	1	no	—
394	C₂×Q₈	—	2	4	no	—
395	C₂×Q₈	—	2	4	no	—
396	C₂×Q₈	—	2	4	no	—
397	C₂×Q₈	—	2	4	no	—
398	C₂×Q₈	—	2	4	no	—
399	C₂×Q₈	—	4	8	no	—
400	C₂×Q₈	—	4	4	no	—
401	C₂×Q₈	—	4	8	no	—
402	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
403	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
404	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
405	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
406	C₂×D₄	—	2	4	no	—
407	C₂×D₄	—	2	1	no	—
408	C₂×D₄	—	2	4	no	—
409	C₂×D₄	—	4	4	no	—
410	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
411	C₂²×C₄	—	2	4	no	—
412	C₂²×C₄	—	2	2	no	—
413	C₂²×C₄	—	2	2	no	—
414	C₂²×C₄	—	2	1	no	—
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	2	1	no	—
417	C₂²×C₄	—	2	4	no	—
418	C₂²×C₄	—	2	4	no	—
419	C₂²×C₄	—	4	4	no	—
420	C₂²×C₄	—	4	4	no	—
421	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
422	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
423	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
424	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
425	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
426	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
427	Q₁₆	—	4	8	no	—
428	Q₁₆	—	4	8	no	—
429	Q₁₆	—	4	8	no	—
430	SD₁₆	—	4	8	no	—
431	C₂×C₈	—	2	4	no	—
432	C₂×C₈	—	2	4	no	—
433	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
434	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
435	C₄⋊C₄	—	2	8	no	—
436	C₄⋊C₄	—	2	8	no	—
437	C₄⋊C₄	—	2	8	no	—
438	C₄⋊C₄	—	2	8	no	—
439	C₄⋊C₄	—	2	8	no	—
440	C₄⋊C₄	—	2	8	no	—
441	C₄⋊C₄	—	2	2	no	—
442	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
443	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
444	C₂²⋊C₄	—	2	8	no	—
445	C₂²⋊C₄	—	2	8	no	—
446	C₂²⋊C₄	—	2	8	no	—
447	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
448	C₄²	—	2	8	no	—
449	C₄²	C₂×D₄×C₁₃	1	2	yes	—
450	C₄²	C₂×D₄×C₁₃	1	2	yes	—
451	C₄²	C₂⁴×C₁₃	1	2	yes	—
452	C₄²	C₂⁴×C₁₃	1	2	yes	—
453	C₁₃	C₂×#3223	1	1	yes	characteristic, direct product factor, Sylow
454	C₂³	—	2	2	no	—
455	C₂³	—	2	4	no	—
456	C₂³	—	2	2	no	—
457	C₂³	—	4	2	no	—
458	C₂³	—	4	4	no	—
459	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
460	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
461	Q₈	—	2	4	no	—
462	Q₈	—	2	4	no	—
463	Q₈	—	2	4	no	—
464	Q₈	—	2	4	no	—
465	Q₈	—	2	4	no	—
466	Q₈	—	4	8	no	—
467	Q₈	—	4	2	no	—
468	Q₈	—	4	2	no	—
469	Q₈	—	4	2	no	—
470	Q₈	—	4	4	no	—
471	D₄	—	2	4	no	—
472	D₄	—	4	8	no	—
473	D₄	—	4	2	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	2	4	no	—
477	C₂×C₄	—	2	4	no	—
478	C₂×C₄	—	2	4	no	—
479	C₂×C₄	—	2	4	no	—
480	C₂×C₄	—	2	4	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	4	8	no	—
485	C₂×C₄	—	4	8	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	4	2	no	—
489	C₂×C₄	—	4	4	no	—
490	C₂×C₄	—	4	4	no	—
491	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
492	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
493	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
494	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
495	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
496	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
497	C₈	—	2	4	no	—
498	C₈	—	2	4	no	—
499	C₂²	—	2	4	no	—
500	C₂²	—	2	2	no	—
501	C₂²	—	4	4	no	—
502	C₂²	—	4	4	no	—
503	C₂²	—	4	2	no	—
504	C₂²	—	8	4	no	—
505	C₂²	C₁₃×#535	1	2	yes	—
506	C₂²	C₁₃×#578	1	4	yes	—
507	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
508	C₄	—	2	4	no	—
509	C₄	—	2	4	no	—
510	C₄	—	2	2	no	—
511	C₄	—	4	4	no	—
512	C₄	—	4	2	no	—
513	C₄	—	4	2	no	—
514	C₄	—	4	2	no	—
515	C₄	—	4	4	no	—
516	C₄	C₁₃×#535	1	2	yes	—
517	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
518	C₂	—	4	2	no	—
519	C₂	—	8	2	no	—
520	C₂	C₁₃×#3223	1	4	yes	direct product factor
521	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
522	C₂	C₂×C₁₃×#578	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂²×C₁₃×#41	C₂²
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×#541	C₂	semidirect
3. C₁₃×#3223	C₂	direct (N × H)
4. C₂×C₁₃×#497	C₂	semidirect
5. C₂×C₁₃×#494	C₂	semidirect
6. C₂×C₁₃×#491	C₂	semidirect
7. C₂×C₁₃×#488	C₂	semidirect
8. C₂×C₁₃×#464	C₂	semidirect
9. C₂×C₁₃×#462	C₂	semidirect
11. C₂×C₁₃×#451	C₂	semidirect
12. C₂×C₁₃×#433	C₂	semidirect
20. C₁₃×#541	C₂²	semidirect
36. C₁₃×#497	C₂²	semidirect
37. C₁₃×#494	C₂²	semidirect
38. C₁₃×#491	C₂²	semidirect
39. C₁₃×#488	C₂²	semidirect
40. C₁₃×#464	C₂²	semidirect
41. C₁₃×#462	C₂²	semidirect
43. C₁₃×#451	C₂²	semidirect
44. C₁₃×#433	C₂²	semidirect
124. C₂×#3223	C₁₃	direct (N × H)
193. C₂×#541	C₂×C₁₃	semidirect
195. #3223	C₂×C₁₃	direct (N × H)
196. C₂×#497	C₂×C₁₃	semidirect
197. C₂×#494	C₂×C₁₃	semidirect
198. C₂×#491	C₂×C₁₃	semidirect
199. C₂×#488	C₂×C₁₃	semidirect
200. C₂×#464	C₂×C₁₃	semidirect
201. C₂×#462	C₂×C₁₃	semidirect
203. C₂×#451	C₂×C₁₃	semidirect
204. C₂×#433	C₂×C₁₃	semidirect
257. #541	C₂²×C₁₃	semidirect
273. #497	C₂²×C₁₃	semidirect
274. #494	C₂²×C₁₃	semidirect
275. #491	C₂²×C₁₃	semidirect
276. #488	C₂²×C₁₃	semidirect
277. #464	C₂²×C₁₃	semidirect
278. #462	C₂²×C₁₃	semidirect
280. #451	C₂²×C₁₃	semidirect
281. #433	C₂²×C₁₃	semidirect
382. C₂×C₁₃	#3223	direct (N × H)
453. C₁₃	C₂×#3223	direct (N × H)
520. C₂	C₁₃×#3223	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×#541	2
C₂×C₁₃×#536	2
C₁₃×#3223	2
C₂×C₁₃×#497	2
C₂×C₁₃×#494	2
C₂×C₁₃×#491	2
C₂×C₁₃×#488	2
C₂×C₁₃×#464	2
C₂×C₁₃×#462	2
C₂×C₁₃×#452	2
C₂×C₁₃×#451	2
C₂×C₁₃×#433	2
C₂×#3223	13

Subgroups — C2×C13×#3223 #15747134

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3223 #15747134