Subgroups — C₂×C₁₃×#3215 #15747123

Order 3328.

2242 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×#124	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3215	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#497	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×#489	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#464	C₂	1	4	yes	maximal, complemented
7	C₂×C₁₃×#451	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#450	C₂	1	2	yes	maximal
9	C₂×C₁₃×#432	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
11	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
12	C₂²×C₁₃×Q₁₆	C₂²	1	4	yes	complemented
13	C₂²×C₁₃×SD₁₆	C₂²	1	4	yes	—
14	C₁₃×#533	—	2	4	no	—
15	C₁₃×#533	C₂²	1	8	yes	complemented
16	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
17	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
18	C₂×C₁₃×#125	—	2	1	no	—
19	C₂×C₁₃×#124	—	2	1	no	—
20	C₂×C₁₃×#124	—	2	1	no	—
21	C₂×C₁₃×#124	—	2	4	no	—
22	C₂×C₁₃×#124	C₂²	1	2	yes	—
23	C₂×C₁₃×#124	C₂²	1	2	yes	—
24	C₂×C₁₃×#124	C₂²	1	8	yes	—
25	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
26	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
27	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
28	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
29	C₂×C₁₃×#117	—	2	1	no	—
30	C₂²×C₁₃×C₂²⋊C₄	—	2	1	no	—
31	C₂²×C₁₃×C₂²⋊C₄	—	2	1	no	—
32	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
33	C₁₃×#497	C₂²	1	16	yes	complemented
34	C₁₃×#489	C₂²	1	16	yes	complemented
35	C₁₃×#464	C₂²	1	32	yes	complemented
36	C₁₃×#451	C₂²	1	16	yes	complemented
37	C₁₃×#450	C₂²	1	16	yes	—
38	C₁₃×#432	C₂²	1	8	yes	complemented
39	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	complemented
40	C₂×C₁₃×#103	C₂²	1	4	yes	complemented
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	complemented
44	C₂⁵×C₁₃	—	2	1	no	—
45	C₂²×Q₈×C₁₃	—	2	1	no	—
46	C₂²×Q₈×C₁₃	—	2	2	no	—
47	C₂²×Q₈×C₁₃	—	2	1	no	—
48	C₂²×Q₈×C₁₃	—	4	4	no	—
49	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
50	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
51	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
52	C₂²×D₄×C₁₃	—	2	2	no	—
53	C₂²×D₄×C₁₃	—	2	1	no	—
54	C₂²×D₄×C₁₃	—	4	4	no	—
55	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
56	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
57	C₂³×C₄×C₁₃	—	2	1	no	—
58	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
59	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
60	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
61	C₂×C₁₃×Q₁₆	—	4	8	no	—
62	C₂×C₁₃×Q₁₆	C₂³	1	16	yes	complemented
63	C₂×C₁₃×SD₁₆	—	4	8	no	—
64	C₂×C₁₃×SD₁₆	C₂³	1	16	yes	—
65	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
66	C₁₃×C₄⋊Q₈	—	2	2	no	—
67	C₁₃×C₄⋊Q₈	—	2	2	no	—
68	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	complemented
69	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	complemented
70	C₁₃×#125	—	2	8	no	—
71	C₁₃×#124	—	2	4	no	—
72	C₁₃×#124	—	2	8	no	—
73	C₁₃×#124	—	2	8	no	—
74	C₁₃×#124	—	2	4	no	—
75	C₁₃×#124	C₂³	1	8	yes	—
76	C₁₃×#124	C₂³	1	8	yes	—
77	C₁₃×C₂²⋊Q₈	—	2	8	no	—
78	C₁₃×C₂²⋊Q₈	—	2	4	no	—
79	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
80	C₄×Q₈×C₁₃	—	2	8	no	—
81	C₄×Q₈×C₁₃	—	2	4	no	—
82	C₄×Q₈×C₁₃	C₂³	1	8	yes	complemented
83	C₁₃×#117	—	2	8	no	—
84	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
85	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
86	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
87	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
88	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
89	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
90	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
91	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
92	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
93	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
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×C₄²×C₁₃	—	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	complemented
105	C₁₃×#103	C₂³	1	16	yes	complemented
106	C₁₃×#102	C₂³	1	16	yes	—
107	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
108	C₁₃×#97	C₂³	1	8	yes	complemented
109	C₂×#3215	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
110	C₂⁴×C₁₃	—	2	4	no	—
111	C₂⁴×C₁₃	—	2	2	no	—
112	C₂⁴×C₁₃	—	4	4	no	—
113	C₂⁴×C₁₃	—	4	4	no	—
114	C₂⁴×C₁₃	—	4	4	no	—
115	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
116	C₂×Q₈×C₁₃	—	2	2	no	—
117	C₂×Q₈×C₁₃	—	2	4	no	—
118	C₂×Q₈×C₁₃	—	2	4	no	—
119	C₂×Q₈×C₁₃	—	2	2	no	—
120	C₂×Q₈×C₁₃	—	2	8	no	—
121	C₂×Q₈×C₁₃	—	2	8	no	—
122	C₂×Q₈×C₁₃	—	4	8	no	—
123	C₂×Q₈×C₁₃	—	4	4	no	—
124	C₂×Q₈×C₁₃	—	4	4	no	—
125	C₂×Q₈×C₁₃	—	4	8	no	—
126	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
127	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
128	C₂×D₄×C₁₃	—	2	4	no	—
129	C₂×D₄×C₁₃	—	2	2	no	—
130	C₂×D₄×C₁₃	—	2	8	no	—
131	C₂×D₄×C₁₃	—	4	8	no	—
132	C₂×D₄×C₁₃	—	4	4	no	—
133	C₂×D₄×C₁₃	—	4	8	no	—
134	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
135	C₂²×C₄×C₁₃	—	2	4	no	—
136	C₂²×C₄×C₁₃	—	2	4	no	—
137	C₂²×C₄×C₁₃	—	2	4	no	—
138	C₂²×C₄×C₁₃	—	2	2	no	—
139	C₂²×C₄×C₁₃	—	2	2	no	—
140	C₂²×C₄×C₁₃	—	2	2	no	—
141	C₂²×C₄×C₁₃	—	4	2	no	—
142	C₂²×C₄×C₁₃	—	4	4	no	—
143	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
144	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
145	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
151	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
152	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
153	C₁₃×Q₁₆	—	4	16	no	—
154	C₁₃×SD₁₆	—	4	16	no	—
155	C₂×C₈×C₁₃	—	2	8	no	—
156	C₂×C₈×C₁₃	C₂⁴	1	8	yes	—
157	C₁₃×C₄⋊C₄	—	2	4	no	—
158	C₁₃×C₄⋊C₄	—	2	4	no	—
159	C₁₃×C₄⋊C₄	—	2	4	no	—
160	C₁₃×C₄⋊C₄	—	2	8	no	—
161	C₁₃×C₄⋊C₄	—	2	8	no	—
162	C₁₃×C₄⋊C₄	—	2	2	no	—
163	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
164	C₁₃×C₂²⋊C₄	—	2	8	no	—
165	C₁₃×C₂²⋊C₄	—	2	8	no	—
166	C₁₃×C₂²⋊C₄	—	2	8	no	—
167	C₁₃×C₂²⋊C₄	—	2	8	no	—
168	C₁₃×C₂²⋊C₄	—	2	8	no	—
169	C₄²×C₁₃	—	2	8	no	—
170	C₄²×C₁₃	C₂×D₄	1	4	yes	—
171	C₄²×C₁₃	C₂×D₄	1	2	yes	—
172	C₄²×C₁₃	C₂×D₄	1	4	yes	—
173	C₄²×C₁₃	C₂×D₄	1	2	yes	—
174	C₄²×C₁₃	C₂⁴	1	2	yes	—
175	C₄²×C₁₃	C₂⁴	1	2	yes	—
176	C₂×#533	C₂×C₁₃	1	1	yes	characteristic, complemented
177	C₂²×#124	C₂×C₁₃	1	1	yes	characteristic
178	#3215	C₂×C₁₃	1	16	yes	direct product factor
179	C₂×#497	C₂×C₁₃	1	2	yes	complemented
180	C₂×#489	C₂×C₁₃	1	2	yes	complemented
181	C₂×#464	C₂×C₁₃	1	4	yes	complemented
182	C₂×#451	C₂×C₁₃	1	2	yes	complemented
183	C₂×#450	C₂×C₁₃	1	2	yes	—
184	C₂×#432	C₂×C₁₃	1	1	yes	characteristic, complemented
185	C₂³×C₁₃	—	2	2	no	—
186	C₂³×C₁₃	—	2	2	no	—
187	C₂³×C₁₃	—	2	4	no	—
188	C₂³×C₁₃	—	4	8	no	—
189	C₂³×C₁₃	—	4	8	no	—
190	C₂³×C₁₃	—	4	4	no	—
191	C₂³×C₁₃	—	4	8	no	—
192	C₂³×C₁₃	—	4	4	no	—
193	C₂³×C₁₃	—	4	4	no	—
194	C₂³×C₁₃	—	8	16	no	—
195	C₂³×C₁₃	#137	1	4	yes	—
196	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
197	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
198	Q₈×C₁₃	—	2	8	no	—
199	Q₈×C₁₃	—	2	8	no	—
200	Q₈×C₁₃	—	4	8	no	—
201	Q₈×C₁₃	—	4	8	no	—
202	Q₈×C₁₃	—	4	4	no	—
203	Q₈×C₁₃	—	4	4	no	—
204	D₄×C₁₃	—	2	8	no	—
205	D₄×C₁₃	—	4	8	no	—
206	D₄×C₁₃	—	4	4	no	—
207	C₂×C₄×C₁₃	—	2	2	no	—
208	C₂×C₄×C₁₃	—	2	8	no	—
209	C₂×C₄×C₁₃	—	2	2	no	—
210	C₂×C₄×C₁₃	—	2	2	no	—
211	C₂×C₄×C₁₃	—	2	2	no	—
212	C₂×C₄×C₁₃	—	2	2	no	—
213	C₂×C₄×C₁₃	—	2	4	no	—
214	C₂×C₄×C₁₃	—	2	4	no	—
215	C₂×C₄×C₁₃	—	2	4	no	—
216	C₂×C₄×C₁₃	—	2	4	no	—
217	C₂×C₄×C₁₃	—	2	4	no	—
218	C₂×C₄×C₁₃	—	4	4	no	—
219	C₂×C₄×C₁₃	—	4	8	no	—
220	C₂×C₄×C₁₃	—	4	4	no	—
221	C₂×C₄×C₁₃	—	4	4	no	—
222	C₂×C₄×C₁₃	—	4	4	no	—
223	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
224	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
225	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
226	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
227	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
228	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
229	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
230	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
231	C₈×C₁₃	—	2	8	no	—
232	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
233	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
234	C₂²×Q₁₆	C₂²×C₁₃	1	4	yes	complemented
235	C₂²×SD₁₆	C₂²×C₁₃	1	4	yes	—
236	#533	—	2	4	no	—
237	#533	C₂²×C₁₃	1	8	yes	complemented
238	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
239	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
240	C₂×#125	—	2	1	no	—
241	C₂×#124	—	2	1	no	—
242	C₂×#124	—	2	1	no	—
243	C₂×#124	—	2	4	no	—
244	C₂×#124	C₂²×C₁₃	1	2	yes	—
245	C₂×#124	C₂²×C₁₃	1	8	yes	—
246	C₂×#124	C₂²×C₁₃	1	2	yes	—
247	C₂×C₂²⋊Q₈	—	2	1	no	—
248	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
249	C₂×C₄×Q₈	—	2	1	no	—
250	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
251	C₂×#117	—	2	1	no	—
252	C₂²×C₂²⋊C₄	—	2	1	no	—
253	C₂²×C₂²⋊C₄	—	2	1	no	—
254	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
255	#497	C₂²×C₁₃	1	16	yes	complemented
256	#489	C₂²×C₁₃	1	16	yes	complemented
257	#464	C₂²×C₁₃	1	32	yes	complemented
258	#451	C₂²×C₁₃	1	16	yes	complemented
259	#450	C₂²×C₁₃	1	16	yes	—
260	#432	C₂²×C₁₃	1	8	yes	complemented
261	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	complemented
262	C₂×#103	C₂²×C₁₃	1	4	yes	complemented
263	C₂×#102	C₂²×C₁₃	1	4	yes	—
264	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
265	C₂×#97	C₂²×C₁₃	1	2	yes	complemented
266	C₂²×C₁₃	—	2	2	no	—
267	C₂²×C₁₃	—	2	8	no	—
268	C₂²×C₁₃	—	2	2	no	—
269	C₂²×C₁₃	—	4	4	no	—
270	C₂²×C₁₃	—	4	4	no	—
271	C₂²×C₁₃	—	4	4	no	—
272	C₂²×C₁₃	—	8	16	no	—
273	C₂²×C₁₃	—	8	8	no	—
274	C₂²×C₁₃	#535	1	2	yes	—
275	C₂²×C₁₃	C₂×#137	1	4	yes	—
276	C₂²×C₁₃	C₂×#137	1	2	yes	—
277	C₂²×C₁₃	#575	1	2	yes	—
278	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
279	C₄×C₁₃	—	2	2	no	—
280	C₄×C₁₃	—	2	2	no	—
281	C₄×C₁₃	—	2	2	no	—
282	C₄×C₁₃	—	2	2	no	—
283	C₄×C₁₃	—	2	2	no	—
284	C₄×C₁₃	—	4	4	no	—
285	C₄×C₁₃	—	4	4	no	—
286	C₄×C₁₃	—	4	4	no	—
287	C₄×C₁₃	#535	1	2	yes	—
288	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
289	C₂⁵	—	2	1	no	—
290	C₂²×Q₈	—	2	1	no	—
291	C₂²×Q₈	—	2	1	no	—
292	C₂²×Q₈	—	2	2	no	—
293	C₂²×Q₈	—	4	4	no	—
294	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
295	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
296	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
297	C₂²×D₄	—	2	1	no	—
298	C₂²×D₄	—	2	2	no	—
299	C₂²×D₄	—	4	4	no	—
300	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
301	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
302	C₂³×C₄	—	2	1	no	—
303	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
304	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
305	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
306	C₂×Q₁₆	—	4	8	no	—
307	C₂×Q₁₆	C₂³×C₁₃	1	16	yes	complemented
308	C₂×SD₁₆	—	4	8	no	—
309	C₂×SD₁₆	C₂³×C₁₃	1	16	yes	—
310	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
311	C₄⋊Q₈	—	2	2	no	—
312	C₄⋊Q₈	—	2	2	no	—
313	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	complemented
314	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	complemented
315	#125	—	2	8	no	—
316	#124	—	2	8	no	—
317	#124	—	2	4	no	—
318	#124	—	2	8	no	—
319	#124	—	2	4	no	—
320	#124	C₂³×C₁₃	1	8	yes	—
321	#124	C₂³×C₁₃	1	8	yes	—
322	C₂²⋊Q₈	—	2	8	no	—
323	C₂²⋊Q₈	—	2	4	no	—
324	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
325	C₄×Q₈	—	2	8	no	—
326	C₄×Q₈	—	2	4	no	—
327	C₄×Q₈	C₂³×C₁₃	1	8	yes	complemented
328	#117	—	2	8	no	—
329	C₂×C₄⋊C₄	—	2	1	no	—
330	C₂×C₄⋊C₄	—	2	1	no	—
331	C₂×C₄⋊C₄	—	2	1	no	—
332	C₂×C₄⋊C₄	—	2	2	no	—
333	C₂×C₄⋊C₄	—	2	2	no	—
334	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
335	C₂×C₂²⋊C₄	—	2	2	no	—
336	C₂×C₂²⋊C₄	—	2	2	no	—
337	C₂×C₂²⋊C₄	—	2	2	no	—
338	C₂×C₂²⋊C₄	—	2	2	no	—
339	C₂×C₂²⋊C₄	—	2	2	no	—
340	C₂×C₂²⋊C₄	—	2	8	no	—
341	C₂×C₂²⋊C₄	—	2	8	no	—
342	C₂×C₄²	—	2	2	no	—
343	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
344	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
345	C₂×C₄²	D₄×C₁₃	1	4	yes	—
346	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
347	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
348	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
349	C₄⋊C₈	C₂³×C₁₃	1	8	yes	complemented
350	#103	C₂³×C₁₃	1	16	yes	complemented
351	#102	C₂³×C₁₃	1	16	yes	—
352	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
353	#97	C₂³×C₁₃	1	8	yes	complemented
354	C₂×C₁₃	—	2	4	no	—
355	C₂×C₁₃	—	8	4	no	—
356	C₂×C₁₃	#3215	1	4	yes	direct product factor
357	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
358	C₂×C₁₃	C₂²×#137	1	1	yes	characteristic
359	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
360	C₂⁴	—	2	4	no	—
361	C₂⁴	—	2	2	no	—
362	C₂⁴	—	4	4	no	—
363	C₂⁴	—	4	4	no	—
364	C₂⁴	—	4	4	no	—
365	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
366	C₂×Q₈	—	2	2	no	—
367	C₂×Q₈	—	2	4	no	—
368	C₂×Q₈	—	2	4	no	—
369	C₂×Q₈	—	2	2	no	—
370	C₂×Q₈	—	2	8	no	—
371	C₂×Q₈	—	2	8	no	—
372	C₂×Q₈	—	4	8	no	—
373	C₂×Q₈	—	4	4	no	—
374	C₂×Q₈	—	4	8	no	—
375	C₂×Q₈	—	4	4	no	—
376	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
377	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
378	C₂×D₄	—	2	4	no	—
379	C₂×D₄	—	2	2	no	—
380	C₂×D₄	—	2	8	no	—
381	C₂×D₄	—	4	8	no	—
382	C₂×D₄	—	4	4	no	—
383	C₂×D₄	—	4	8	no	—
384	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
385	C₂²×C₄	—	2	4	no	—
386	C₂²×C₄	—	2	4	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	4	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	4	2	no	—
392	C₂²×C₄	—	4	4	no	—
393	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
394	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
395	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
396	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
397	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
398	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
399	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
400	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
401	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
402	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
403	Q₁₆	—	4	16	no	—
404	SD₁₆	—	4	16	no	—
405	C₂×C₈	—	2	8	no	—
406	C₂×C₈	C₂⁴×C₁₃	1	8	yes	—
407	C₄⋊C₄	—	2	4	no	—
408	C₄⋊C₄	—	2	4	no	—
409	C₄⋊C₄	—	2	4	no	—
410	C₄⋊C₄	—	2	8	no	—
411	C₄⋊C₄	—	2	8	no	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
414	C₂²⋊C₄	—	2	8	no	—
415	C₂²⋊C₄	—	2	8	no	—
416	C₂²⋊C₄	—	2	8	no	—
417	C₂²⋊C₄	—	2	8	no	—
418	C₂²⋊C₄	—	2	8	no	—
419	C₄²	—	2	8	no	—
420	C₄²	C₂×D₄×C₁₃	1	4	yes	—
421	C₄²	C₂×D₄×C₁₃	1	2	yes	—
422	C₄²	C₂×D₄×C₁₃	1	4	yes	—
423	C₄²	C₂×D₄×C₁₃	1	2	yes	—
424	C₄²	C₂⁴×C₁₃	1	2	yes	—
425	C₄²	C₂⁴×C₁₃	1	2	yes	—
426	C₁₃	C₂×#3215	1	1	yes	characteristic, direct product factor, Sylow
427	C₂³	—	2	2	no	—
428	C₂³	—	2	2	no	—
429	C₂³	—	2	4	no	—
430	C₂³	—	4	8	no	—
431	C₂³	—	4	8	no	—
432	C₂³	—	4	4	no	—
433	C₂³	—	4	8	no	—
434	C₂³	—	4	4	no	—
435	C₂³	—	4	4	no	—
436	C₂³	—	8	16	no	—
437	C₂³	C₁₃×#137	1	4	yes	—
438	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
439	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
440	Q₈	—	2	8	no	—
441	Q₈	—	2	8	no	—
442	Q₈	—	4	8	no	—
443	Q₈	—	4	8	no	—
444	Q₈	—	4	4	no	—
445	Q₈	—	4	4	no	—
446	D₄	—	2	8	no	—
447	D₄	—	4	8	no	—
448	D₄	—	4	4	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	8	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	2	4	no	—
457	C₂×C₄	—	2	4	no	—
458	C₂×C₄	—	2	4	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	4	4	no	—
461	C₂×C₄	—	4	8	no	—
462	C₂×C₄	—	4	4	no	—
463	C₂×C₄	—	4	4	no	—
464	C₂×C₄	—	4	4	no	—
465	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
466	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
467	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
468	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
469	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
470	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
471	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
472	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
473	C₈	—	2	8	no	—
474	C₂²	—	2	2	no	—
475	C₂²	—	2	2	no	—
476	C₂²	—	2	8	no	—
477	C₂²	—	4	4	no	—
478	C₂²	—	4	4	no	—
479	C₂²	—	4	4	no	—
480	C₂²	—	8	16	no	—
481	C₂²	—	8	8	no	—
482	C₂²	C₁₃×#535	1	2	yes	—
483	C₂²	C₂×C₁₃×#137	1	4	yes	—
484	C₂²	C₂×C₁₃×#137	1	2	yes	—
485	C₂²	C₁₃×#575	1	2	yes	—
486	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
487	C₄	—	2	2	no	—
488	C₄	—	2	2	no	—
489	C₄	—	2	2	no	—
490	C₄	—	2	2	no	—
491	C₄	—	2	2	no	—
492	C₄	—	4	4	no	—
493	C₄	—	4	4	no	—
494	C₄	—	4	4	no	—
495	C₄	C₁₃×#535	1	2	yes	—
496	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
497	C₂	—	2	4	no	—
498	C₂	—	8	4	no	—
499	C₂	C₁₃×#3215	1	4	yes	direct product factor
500	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
501	C₂	C₂²×C₁₃×#137	1	1	yes	characteristic
502	C₂	C₂×C₁₃×#575	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂³×D₄×C₁₃	C₂²
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×#533	C₂	semidirect
3. C₁₃×#3215	C₂	direct (N × H)
4. C₂×C₁₃×#497	C₂	semidirect
5. C₂×C₁₃×#489	C₂	semidirect
6. C₂×C₁₃×#464	C₂	semidirect
7. C₂×C₁₃×#451	C₂	semidirect
9. C₂×C₁₃×#432	C₂	semidirect
12. C₂²×C₁₃×Q₁₆	C₂²	semidirect
15. C₁₃×#533	C₂²	semidirect
16. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
17. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
28. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
33. C₁₃×#497	C₂²	semidirect
34. C₁₃×#489	C₂²	semidirect
35. C₁₃×#464	C₂²	semidirect
36. C₁₃×#451	C₂²	semidirect
38. C₁₃×#432	C₂²	semidirect
39. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
40. C₂×C₁₃×#103	C₂²	semidirect
43. C₂×C₁₃×#97	C₂²	semidirect
62. C₂×C₁₃×Q₁₆	C₂³	semidirect
68. C₁₃×C₄⋊Q₈	C₂³	semidirect
69. C₁₃×C₄⋊Q₈	C₂³	semidirect
82. C₄×Q₈×C₁₃	C₂³	semidirect
104. C₁₃×C₄⋊C₈	C₂³	semidirect
105. C₁₃×#103	C₂³	semidirect
108. C₁₃×#97	C₂³	semidirect
109. C₂×#3215	C₁₃	direct (N × H)
176. C₂×#533	C₂×C₁₃	semidirect
178. #3215	C₂×C₁₃	direct (N × H)
179. C₂×#497	C₂×C₁₃	semidirect
180. C₂×#489	C₂×C₁₃	semidirect
181. C₂×#464	C₂×C₁₃	semidirect
182. C₂×#451	C₂×C₁₃	semidirect
184. C₂×#432	C₂×C₁₃	semidirect
234. C₂²×Q₁₆	C₂²×C₁₃	semidirect
237. #533	C₂²×C₁₃	semidirect
238. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
239. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
250. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
255. #497	C₂²×C₁₃	semidirect
256. #489	C₂²×C₁₃	semidirect
257. #464	C₂²×C₁₃	semidirect
258. #451	C₂²×C₁₃	semidirect
260. #432	C₂²×C₁₃	semidirect
261. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
262. C₂×#103	C₂²×C₁₃	semidirect
265. C₂×#97	C₂²×C₁₃	semidirect
307. C₂×Q₁₆	C₂³×C₁₃	semidirect
313. C₄⋊Q₈	C₂³×C₁₃	semidirect
314. C₄⋊Q₈	C₂³×C₁₃	semidirect
327. C₄×Q₈	C₂³×C₁₃	semidirect
349. C₄⋊C₈	C₂³×C₁₃	semidirect
350. #103	C₂³×C₁₃	semidirect
353. #97	C₂³×C₁₃	semidirect
356. C₂×C₁₃	#3215	direct (N × H)
426. C₁₃	C₂×#3215	direct (N × H)
499. C₂	C₁₃×#3215	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×#533	2
C₂²×C₁₃×#124	2
C₁₃×#3215	2
C₂×C₁₃×#497	2
C₂×C₁₃×#489	2
C₂×C₁₃×#464	2
C₂×C₁₃×#451	2
C₂×C₁₃×#450	2
C₂×C₁₃×#432	2
C₂×#3215	13

Subgroups — C2×C13×#3215 #15747123

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3215 #15747123