Subgroups — C₂×C₁₃×#3295 #15747452

Order 3328.

2642 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#554	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄²×C₁₃	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3295	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#486	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#481	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#476	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#465	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#460	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#450	C₂	1	2	yes	maximal, complemented
10	C₂×C₄×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₈×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×#102	C₂	1	2	yes	maximal, complemented
13	C₂³×D₄×C₁₃	—	2	1	no	—
14	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
15	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
16	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
17	C₂³×C₈×C₁₃	C₂²	1	2	yes	complemented
18	C₁₃×#554	—	2	4	no	—
19	C₁₃×#554	C₂²	1	8	yes	complemented
20	D₄²×C₁₃	—	2	4	no	—
21	D₄²×C₁₃	C₂²	1	8	yes	—
22	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#125	—	2	1	no	—
25	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
26	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
27	C₂×C₁₃×#121	—	2	1	no	—
28	C₂×C₁₃×#121	C₂²	1	2	yes	—
29	C₂×C₁₃×#120	—	2	2	no	—
30	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₄×D₄×C₁₃	—	2	1	no	—
32	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
34	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
35	C₁₃×#486	C₂²	1	8	yes	complemented
36	C₁₃×#481	C₂²	1	16	yes	complemented
37	C₁₃×#476	C₂²	1	8	yes	complemented
38	C₁₃×#465	C₂²	1	16	yes	complemented
39	C₁₃×#460	C₂²	1	8	yes	complemented
40	C₁₃×#450	C₂²	1	16	yes	complemented
41	C₄×C₁₃×SD₁₆	C₂²	1	8	yes	complemented
42	C₈×D₄×C₁₃	C₂²	1	8	yes	complemented
43	C₂×C₁₃×#106	C₂²	1	2	yes	complemented
44	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₁₃×#102	C₂²	1	2	yes	—
48	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
49	C₂×C₁₃×#102	C₂²	1	16	yes	complemented
50	C₂×C₁₃×#102	C₂²	1	2	yes	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×Q₈×C₁₃	C₂³	1	1	yes	characteristic
58	C₂²×D₄×C₁₃	—	2	8	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	8	yes	—
70	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₁₃	—	2	2	no	—
72	C₂³×C₄×C₁₃	—	2	1	no	—
73	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
74	C₂×C₁₃×SD₁₆	—	2	4	no	—
75	C₂×C₁₃×SD₁₆	—	4	4	no	—
76	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
77	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	complemented
78	C₂²×C₈×C₁₃	—	4	4	no	—
79	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
82	C₂²×C₈×C₁₃	C₂³	1	8	yes	complemented
83	C₁₃×C₄⋊Q₈	—	2	2	no	—
84	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	complemented
85	C₁₃×#127	—	2	2	no	—
86	C₁₃×#127	C₂³	1	4	yes	—
87	C₁₃×#125	—	2	8	no	—
88	C₁₃×C₂²⋊Q₈	—	2	4	no	—
89	C₁₃×C₂²⋊Q₈	—	2	16	no	—
90	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	complemented
91	C₁₃×#121	—	2	4	no	—
92	C₁₃×#121	—	2	8	no	—
93	C₁₃×#121	C₂³	1	8	yes	—
94	C₁₃×#120	—	2	16	no	—
95	C₄×Q₈×C₁₃	—	2	2	no	—
96	C₄×Q₈×C₁₃	C₂³	1	4	yes	complemented
97	C₄×D₄×C₁₃	—	2	8	no	—
98	C₄×D₄×C₁₃	—	2	2	no	—
99	C₄×D₄×C₁₃	D₄	1	4	yes	—
100	C₄×D₄×C₁₃	C₂³	1	4	yes	—
101	C₄×D₄×C₁₃	C₂³	1	4	yes	—
102	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
103	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
104	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
105	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
106	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
107	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
108	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
109	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
110	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
111	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	complemented
112	C₂×C₁₃×C₂²⋊C₄	—	2	2	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	1	no	—
117	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
118	C₁₃×#106	C₂³	1	4	yes	complemented
119	C₁₃×#106	C₂³	1	8	yes	complemented
120	C₁₃×C₄⋊C₈	C₂³	1	4	yes	complemented
121	C₁₃×#103	C₂³	1	4	yes	complemented
122	C₁₃×#102	C₂³	1	4	yes	—
123	C₁₃×#102	C₂³	1	8	yes	—
124	C₁₃×#102	C₂³	1	8	yes	complemented
125	C₁₃×#102	C₂³	1	8	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×#3295	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
130	C₂⁴×C₁₃	—	2	1	no	—
131	C₂⁴×C₁₃	—	2	2	no	—
132	C₂⁴×C₁₃	—	2	8	no	—
133	C₂⁴×C₁₃	—	4	8	no	—
134	C₂⁴×C₁₃	—	4	8	no	—
135	C₂⁴×C₁₃	—	8	4	no	—
136	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
137	C₂×Q₈×C₁₃	—	2	1	no	—
138	C₂×Q₈×C₁₃	—	2	4	no	—
139	C₂×Q₈×C₁₃	—	2	2	no	—
140	C₂×Q₈×C₁₃	—	2	2	no	—
141	C₂×Q₈×C₁₃	—	8	2	no	—
142	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
143	C₂×D₄×C₁₃	—	2	16	no	—
144	C₂×D₄×C₁₃	—	2	8	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	4	no	—
151	C₂×D₄×C₁₃	—	2	2	no	—
152	C₂×D₄×C₁₃	—	2	4	no	—
153	C₂×D₄×C₁₃	—	4	8	no	—
154	C₂×D₄×C₁₃	—	4	16	no	—
155	C₂×D₄×C₁₃	—	4	8	no	—
156	C₂×D₄×C₁₃	—	4	8	no	—
157	C₂×D₄×C₁₃	—	4	32	no	—
158	C₂×D₄×C₁₃	—	4	4	no	—
159	C₂×D₄×C₁₃	—	8	2	no	—
160	C₂×D₄×C₁₃	SD₁₆	1	8	yes	complemented
161	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
162	C₂×D₄×C₁₃	#41	1	4	yes	—
163	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
164	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
165	C₂²×C₄×C₁₃	—	2	4	no	—
166	C₂²×C₄×C₁₃	—	2	4	no	—
167	C₂²×C₄×C₁₃	—	2	1	no	—
168	C₂²×C₄×C₁₃	—	2	1	no	—
169	C₂²×C₄×C₁₃	—	2	1	no	—
170	C₂²×C₄×C₁₃	—	2	2	no	—
171	C₂²×C₄×C₁₃	—	2	8	no	—
172	C₂²×C₄×C₁₃	—	2	4	no	—
173	C₂²×C₄×C₁₃	—	4	4	no	—
174	C₂²×C₄×C₁₃	—	8	4	no	—
175	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
176	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
178	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
179	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
180	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
181	C₁₃×SD₁₆	—	2	8	no	—
182	C₁₃×SD₁₆	—	4	8	no	—
183	C₂×C₈×C₁₃	—	2	2	no	—
184	C₂×C₈×C₁₃	—	2	2	no	—
185	C₂×C₈×C₁₃	—	2	4	no	—
186	C₂×C₈×C₁₃	—	4	8	no	—
187	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
188	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
189	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
190	C₁₃×C₄⋊C₄	—	2	1	no	—
191	C₁₃×C₄⋊C₄	—	2	2	no	—
192	C₁₃×C₄⋊C₄	—	2	8	no	—
193	C₁₃×C₄⋊C₄	—	2	4	no	—
194	C₁₃×C₄⋊C₄	—	2	4	no	—
195	C₁₃×C₄⋊C₄	—	2	8	no	—
196	C₁₃×C₄⋊C₄	—	2	1	no	—
197	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
198	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
199	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
200	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
201	C₁₃×C₂²⋊C₄	—	2	8	no	—
202	C₁₃×C₂²⋊C₄	—	2	4	no	—
203	C₁₃×C₂²⋊C₄	—	2	8	no	—
204	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
205	C₄²×C₁₃	—	2	4	no	—
206	C₄²×C₁₃	C₂×D₄	1	2	yes	—
207	C₄²×C₁₃	C₂⁴	1	2	yes	—
208	C₂×#554	C₂×C₁₃	1	1	yes	characteristic, complemented
209	C₂×D₄²	C₂×C₁₃	1	1	yes	characteristic
210	#3295	C₂×C₁₃	1	16	yes	direct product factor
211	C₂×#486	C₂×C₁₃	1	1	yes	characteristic, complemented
212	C₂×#481	C₂×C₁₃	1	2	yes	complemented
213	C₂×#476	C₂×C₁₃	1	1	yes	characteristic, complemented
214	C₂×#465	C₂×C₁₃	1	2	yes	complemented
215	C₂×#460	C₂×C₁₃	1	1	yes	characteristic, complemented
216	C₂×#450	C₂×C₁₃	1	2	yes	complemented
217	C₂×C₄×SD₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
218	C₂×C₈×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
219	C₂²×#102	C₂×C₁₃	1	2	yes	complemented
220	C₂³×C₁₃	—	2	4	no	—
221	C₂³×C₁₃	—	2	4	no	—
222	C₂³×C₁₃	—	2	4	no	—
223	C₂³×C₁₃	—	2	2	no	—
224	C₂³×C₁₃	—	2	4	no	—
225	C₂³×C₁₃	—	4	16	no	—
226	C₂³×C₁₃	—	4	2	no	—
227	C₂³×C₁₃	—	4	2	no	—
228	C₂³×C₁₃	—	4	4	no	—
229	C₂³×C₁₃	—	4	16	no	—
230	C₂³×C₁₃	—	4	4	no	—
231	C₂³×C₁₃	—	4	4	no	—
232	C₂³×C₁₃	—	8	8	no	—
233	C₂³×C₁₃	—	8	32	no	—
234	C₂³×C₁₃	C₂×SD₁₆	1	8	yes	—
235	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
236	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
237	Q₈×C₁₃	—	2	2	no	—
238	Q₈×C₁₃	—	2	2	no	—
239	Q₈×C₁₃	—	4	2	no	—
240	Q₈×C₁₃	—	8	4	no	—
241	D₄×C₁₃	—	2	4	no	—
242	D₄×C₁₃	—	2	4	no	—
243	D₄×C₁₃	—	2	2	no	—
244	D₄×C₁₃	—	2	4	no	—
245	D₄×C₁₃	—	4	16	no	—
246	D₄×C₁₃	—	4	16	no	—
247	D₄×C₁₃	—	4	4	no	—
248	D₄×C₁₃	—	4	8	no	—
249	D₄×C₁₃	—	8	4	no	—
250	D₄×C₁₃	C₂×SD₁₆	1	16	yes	complemented
251	D₄×C₁₃	C₂×#41	1	4	yes	—
252	C₂×C₄×C₁₃	—	2	4	no	—
253	C₂×C₄×C₁₃	—	2	2	no	—
254	C₂×C₄×C₁₃	—	2	8	no	—
255	C₂×C₄×C₁₃	—	2	4	no	—
256	C₂×C₄×C₁₃	—	2	4	no	—
257	C₂×C₄×C₁₃	—	2	2	no	—
258	C₂×C₄×C₁₃	—	2	2	no	—
259	C₂×C₄×C₁₃	—	2	2	no	—
260	C₂×C₄×C₁₃	—	2	4	no	—
261	C₂×C₄×C₁₃	—	4	2	no	—
262	C₂×C₄×C₁₃	—	4	2	no	—
263	C₂×C₄×C₁₃	—	4	2	no	—
264	C₂×C₄×C₁₃	—	4	4	no	—
265	C₂×C₄×C₁₃	—	4	8	no	—
266	C₂×C₄×C₁₃	—	8	8	no	—
267	C₂×C₄×C₁₃	C₂×SD₁₆	1	4	yes	—
268	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
269	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
270	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
271	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
272	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
273	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
274	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
275	C₈×C₁₃	—	2	2	no	—
276	C₈×C₁₃	—	2	2	no	—
277	C₈×C₁₃	—	2	4	no	—
278	C₂³×D₄	—	2	1	no	—
279	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
280	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
281	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
282	C₂³×C₈	C₂²×C₁₃	1	2	yes	complemented
283	#554	—	2	4	no	—
284	#554	C₂²×C₁₃	1	8	yes	complemented
285	D₄²	—	2	4	no	—
286	D₄²	C₂²×C₁₃	1	8	yes	—
287	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
288	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
289	C₂×#125	—	2	1	no	—
290	C₂×C₂²⋊Q₈	—	2	2	no	—
291	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
292	C₂×#121	—	2	1	no	—
293	C₂×#121	C₂²×C₁₃	1	2	yes	—
294	C₂×#120	—	2	2	no	—
295	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
296	C₂×C₄×D₄	—	2	1	no	—
297	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
298	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
299	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
300	#486	C₂²×C₁₃	1	8	yes	complemented
301	#481	C₂²×C₁₃	1	16	yes	complemented
302	#476	C₂²×C₁₃	1	8	yes	complemented
303	#465	C₂²×C₁₃	1	16	yes	complemented
304	#460	C₂²×C₁₃	1	8	yes	complemented
305	#450	C₂²×C₁₃	1	16	yes	complemented
306	C₄×SD₁₆	C₂²×C₁₃	1	8	yes	complemented
307	C₈×D₄	C₂²×C₁₃	1	8	yes	complemented
308	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic, complemented
309	C₂×#106	C₂²×C₁₃	1	2	yes	complemented
310	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
311	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
312	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
313	C₂×#102	C₂²×C₁₃	1	2	yes	—
314	C₂×#102	C₂²×C₁₃	1	16	yes	complemented
315	C₂×#102	C₂²×C₁₃	1	2	yes	complemented
316	C₂×#102	C₂²×C₁₃	1	2	yes	complemented
317	C₂×#102	C₂²×C₁₃	1	2	yes	complemented
318	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	complemented
319	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
320	C₂²×C₁₃	—	2	4	no	—
321	C₂²×C₁₃	—	2	16	no	—
322	C₂²×C₁₃	—	2	4	no	—
323	C₂²×C₁₃	—	2	4	no	—
324	C₂²×C₁₃	—	4	8	no	—
325	C₂²×C₁₃	—	4	2	no	—
326	C₂²×C₁₃	—	4	2	no	—
327	C₂²×C₁₃	—	4	4	no	—
328	C₂²×C₁₃	—	4	4	no	—
329	C₂²×C₁₃	—	4	4	no	—
330	C₂²×C₁₃	—	8	32	no	—
331	C₂²×C₁₃	—	8	8	no	—
332	C₂²×C₁₃	#546	1	2	yes	—
333	C₂²×C₁₃	C₂²×SD₁₆	1	8	yes	—
334	C₂²×C₁₃	C₂²×SD₁₆	1	2	yes	—
335	C₂²×C₁₃	#576	1	2	yes	—
336	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
337	C₄×C₁₃	—	2	4	no	—
338	C₄×C₁₃	—	2	2	no	—
339	C₄×C₁₃	—	4	2	no	—
340	C₄×C₁₃	—	4	2	no	—
341	C₄×C₁₃	—	4	2	no	—
342	C₄×C₁₃	—	4	4	no	—
343	C₄×C₁₃	#546	1	2	yes	—
344	C₄×C₁₃	C₂²×SD₁₆	1	4	yes	—
345	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
346	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
347	C₂⁵	—	2	2	no	—
348	C₂²×Q₈	—	2	1	no	—
349	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
350	C₂²×D₄	—	2	8	no	—
351	C₂²×D₄	—	2	2	no	—
352	C₂²×D₄	—	2	8	no	—
353	C₂²×D₄	—	2	2	no	—
354	C₂²×D₄	—	2	1	no	—
355	C₂²×D₄	—	2	4	no	—
356	C₂²×D₄	—	2	1	no	—
357	C₂²×D₄	—	4	4	no	—
358	C₂²×D₄	—	4	8	no	—
359	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
360	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
361	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
362	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
363	C₂³×C₄	—	2	2	no	—
364	C₂³×C₄	—	2	1	no	—
365	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
366	C₂×SD₁₆	—	2	4	no	—
367	C₂×SD₁₆	—	4	4	no	—
368	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
369	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	complemented
370	C₂²×C₈	—	4	4	no	—
371	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
372	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
373	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
374	C₂²×C₈	C₂³×C₁₃	1	8	yes	complemented
375	C₄⋊Q₈	—	2	2	no	—
376	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	complemented
377	#127	—	2	2	no	—
378	#127	C₂³×C₁₃	1	4	yes	—
379	#125	—	2	8	no	—
380	C₂²⋊Q₈	—	2	4	no	—
381	C₂²⋊Q₈	—	2	16	no	—
382	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	complemented
383	#121	—	2	4	no	—
384	#121	—	2	8	no	—
385	#121	C₂³×C₁₃	1	8	yes	—
386	#120	—	2	16	no	—
387	C₄×Q₈	—	2	2	no	—
388	C₄×Q₈	C₂³×C₁₃	1	4	yes	complemented
389	C₄×D₄	—	2	8	no	—
390	C₄×D₄	—	2	2	no	—
391	C₄×D₄	D₄×C₁₃	1	4	yes	—
392	C₄×D₄	C₂³×C₁₃	1	4	yes	—
393	C₄×D₄	C₂³×C₁₃	1	4	yes	—
394	C₂×C₄⋊C₄	—	2	2	no	—
395	C₂×C₄⋊C₄	—	2	4	no	—
396	C₂×C₄⋊C₄	—	2	1	no	—
397	C₂×C₄⋊C₄	—	2	1	no	—
398	C₂×C₄⋊C₄	—	2	2	no	—
399	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
400	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
401	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
402	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
403	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	complemented
404	C₂×C₂²⋊C₄	—	2	2	no	—
405	C₂×C₂²⋊C₄	—	2	1	no	—
406	C₂×C₂²⋊C₄	—	2	2	no	—
407	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
408	C₂×C₄²	—	2	1	no	—
409	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
410	#106	C₂³×C₁₃	1	4	yes	complemented
411	#106	C₂³×C₁₃	1	8	yes	complemented
412	C₄⋊C₈	C₂³×C₁₃	1	4	yes	complemented
413	#103	C₂³×C₁₃	1	4	yes	complemented
414	#102	C₂³×C₁₃	1	4	yes	—
415	#102	C₂³×C₁₃	1	8	yes	—
416	#102	C₂³×C₁₃	1	8	yes	complemented
417	#102	C₂³×C₁₃	1	8	yes	complemented
418	#102	C₂³×C₁₃	1	8	yes	complemented
419	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	complemented
420	C₄×C₈	C₂³×C₁₃	1	4	yes	complemented
421	C₂×C₁₃	—	2	8	no	—
422	C₂×C₁₃	—	4	4	no	—
423	C₂×C₁₃	—	8	4	no	—
424	C₂×C₁₃	#3295	1	4	yes	direct product factor
425	C₂×C₁₃	C₂×#546	1	1	yes	characteristic
426	C₂×C₁₃	C₂³×SD₁₆	1	1	yes	characteristic
427	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
428	C₂⁴	—	2	1	no	—
429	C₂⁴	—	2	2	no	—
430	C₂⁴	—	2	8	no	—
431	C₂⁴	—	4	8	no	—
432	C₂⁴	—	4	8	no	—
433	C₂⁴	—	8	4	no	—
434	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
435	C₂×Q₈	—	2	1	no	—
436	C₂×Q₈	—	2	4	no	—
437	C₂×Q₈	—	2	2	no	—
438	C₂×Q₈	—	2	2	no	—
439	C₂×Q₈	—	8	2	no	—
440	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
441	C₂×D₄	—	2	16	no	—
442	C₂×D₄	—	2	8	no	—
443	C₂×D₄	—	2	1	no	—
444	C₂×D₄	—	2	8	no	—
445	C₂×D₄	—	2	2	no	—
446	C₂×D₄	—	2	4	no	—
447	C₂×D₄	—	2	4	no	—
448	C₂×D₄	—	2	4	no	—
449	C₂×D₄	—	2	2	no	—
450	C₂×D₄	—	2	4	no	—
451	C₂×D₄	—	4	8	no	—
452	C₂×D₄	—	4	16	no	—
453	C₂×D₄	—	4	8	no	—
454	C₂×D₄	—	4	8	no	—
455	C₂×D₄	—	4	32	no	—
456	C₂×D₄	—	4	4	no	—
457	C₂×D₄	—	8	2	no	—
458	C₂×D₄	C₁₃×SD₁₆	1	8	yes	complemented
459	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
460	C₂×D₄	C₁₃×#41	1	4	yes	—
461	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
462	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
463	C₂²×C₄	—	2	4	no	—
464	C₂²×C₄	—	2	4	no	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	2	no	—
469	C₂²×C₄	—	2	8	no	—
470	C₂²×C₄	—	2	4	no	—
471	C₂²×C₄	—	4	4	no	—
472	C₂²×C₄	—	8	4	no	—
473	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
474	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
475	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
476	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
477	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
478	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
479	SD₁₆	—	2	8	no	—
480	SD₁₆	—	4	8	no	—
481	C₂×C₈	—	2	2	no	—
482	C₂×C₈	—	2	2	no	—
483	C₂×C₈	—	2	4	no	—
484	C₂×C₈	—	4	8	no	—
485	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
486	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
487	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
488	C₄⋊C₄	—	2	1	no	—
489	C₄⋊C₄	—	2	2	no	—
490	C₄⋊C₄	—	2	8	no	—
491	C₄⋊C₄	—	2	4	no	—
492	C₄⋊C₄	—	2	4	no	—
493	C₄⋊C₄	—	2	8	no	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
496	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
497	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
498	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
499	C₂²⋊C₄	—	2	8	no	—
500	C₂²⋊C₄	—	2	4	no	—
501	C₂²⋊C₄	—	2	8	no	—
502	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
503	C₄²	—	2	4	no	—
504	C₄²	C₂×D₄×C₁₃	1	2	yes	—
505	C₄²	C₂⁴×C₁₃	1	2	yes	—
506	C₁₃	C₂×#3295	1	1	yes	characteristic, direct product factor, Sylow
507	C₂³	—	2	4	no	—
508	C₂³	—	2	4	no	—
509	C₂³	—	2	4	no	—
510	C₂³	—	2	2	no	—
511	C₂³	—	2	4	no	—
512	C₂³	—	4	16	no	—
513	C₂³	—	4	2	no	—
514	C₂³	—	4	2	no	—
515	C₂³	—	4	4	no	—
516	C₂³	—	4	16	no	—
517	C₂³	—	4	4	no	—
518	C₂³	—	4	4	no	—
519	C₂³	—	8	8	no	—
520	C₂³	—	8	32	no	—
521	C₂³	C₂×C₁₃×SD₁₆	1	8	yes	—
522	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
523	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
524	Q₈	—	2	2	no	—
525	Q₈	—	2	2	no	—
526	Q₈	—	4	2	no	—
527	Q₈	—	8	4	no	—
528	D₄	—	2	4	no	—
529	D₄	—	2	4	no	—
530	D₄	—	2	2	no	—
531	D₄	—	2	4	no	—
532	D₄	—	4	16	no	—
533	D₄	—	4	16	no	—
534	D₄	—	4	4	no	—
535	D₄	—	4	8	no	—
536	D₄	—	8	4	no	—
537	D₄	C₂×C₁₃×SD₁₆	1	16	yes	complemented
538	D₄	C₂×C₁₃×#41	1	4	yes	—
539	C₂×C₄	—	2	4	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	8	no	—
542	C₂×C₄	—	2	4	no	—
543	C₂×C₄	—	2	4	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	4	no	—
548	C₂×C₄	—	4	2	no	—
549	C₂×C₄	—	4	2	no	—
550	C₂×C₄	—	4	2	no	—
551	C₂×C₄	—	4	4	no	—
552	C₂×C₄	—	4	8	no	—
553	C₂×C₄	—	8	8	no	—
554	C₂×C₄	C₂×C₁₃×SD₁₆	1	4	yes	—
555	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
556	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
557	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
558	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
559	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
560	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
561	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
562	C₈	—	2	2	no	—
563	C₈	—	2	2	no	—
564	C₈	—	2	4	no	—
565	C₂²	—	2	16	no	—
566	C₂²	—	2	4	no	—
567	C₂²	—	2	4	no	—
568	C₂²	—	2	4	no	—
569	C₂²	—	4	8	no	—
570	C₂²	—	4	2	no	—
571	C₂²	—	4	2	no	—
572	C₂²	—	4	4	no	—
573	C₂²	—	4	4	no	—
574	C₂²	—	4	4	no	—
575	C₂²	—	8	32	no	—
576	C₂²	—	8	8	no	—
577	C₂²	C₁₃×#546	1	2	yes	—
578	C₂²	C₂²×C₁₃×SD₁₆	1	8	yes	—
579	C₂²	C₂²×C₁₃×SD₁₆	1	2	yes	—
580	C₂²	C₁₃×#576	1	2	yes	—
581	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
582	C₄	—	2	2	no	—
583	C₄	—	2	4	no	—
584	C₄	—	4	2	no	—
585	C₄	—	4	2	no	—
586	C₄	—	4	4	no	—
587	C₄	—	4	2	no	—
588	C₄	C₁₃×#546	1	2	yes	—
589	C₄	C₂²×C₁₃×SD₁₆	1	4	yes	—
590	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
591	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
592	C₂	—	2	8	no	—
593	C₂	—	4	4	no	—
594	C₂	—	8	4	no	—
595	C₂	C₁₃×#3295	1	4	yes	direct product factor
596	C₂	C₂×C₁₃×#546	1	1	yes	characteristic
597	C₂	C₂³×C₁₃×SD₁₆	1	1	yes	characteristic
598	C₂	C₂×C₁₃×#576	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂×D₄²×C₁₃	C₂
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×#554	C₂	semidirect
3. C₁₃×#3295	C₂	direct (N × H)
4. C₂×C₁₃×#486	C₂	semidirect
5. C₂×C₁₃×#481	C₂	semidirect
6. C₂×C₁₃×#476	C₂	semidirect
7. C₂×C₁₃×#465	C₂	semidirect
8. C₂×C₁₃×#460	C₂	semidirect
9. C₂×C₁₃×#450	C₂	semidirect
10. C₂×C₄×C₁₃×SD₁₆	C₂	semidirect
11. C₂×C₈×D₄×C₁₃	C₂	semidirect
12. C₂²×C₁₃×#102	C₂	semidirect
16. C₂²×C₁₃×SD₁₆	C₂²	semidirect
17. C₂³×C₈×C₁₃	C₂²	semidirect
19. C₁₃×#554	C₂²	semidirect
22. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
26. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
30. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
34. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
35. C₁₃×#486	C₂²	semidirect
36. C₁₃×#481	C₂²	semidirect
37. C₁₃×#476	C₂²	semidirect
38. C₁₃×#465	C₂²	semidirect
39. C₁₃×#460	C₂²	semidirect
40. C₁₃×#450	C₂²	semidirect
41. C₄×C₁₃×SD₁₆	C₂²	semidirect
42. C₈×D₄×C₁₃	C₂²	semidirect
43. C₂×C₁₃×#106	C₂²	semidirect
44. C₂×C₁₃×#106	C₂²	semidirect
45. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
46. C₂×C₁₃×#103	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
77. C₂×C₁₃×SD₁₆	C₂³	semidirect
82. C₂²×C₈×C₁₃	C₂³	semidirect
84. C₁₃×C₄⋊Q₈	C₂³	semidirect
90. C₁₃×C₂²⋊Q₈	C₂³	semidirect
96. C₄×Q₈×C₁₃	C₂³	semidirect
111. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
118. C₁₃×#106	C₂³	semidirect
119. C₁₃×#106	C₂³	semidirect
120. C₁₃×C₄⋊C₈	C₂³	semidirect
121. C₁₃×#103	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×#3295	C₁₃	direct (N × H)
160. C₂×D₄×C₁₃	SD₁₆	semidirect
208. C₂×#554	C₂×C₁₃	semidirect
210. #3295	C₂×C₁₃	direct (N × H)
211. C₂×#486	C₂×C₁₃	semidirect
212. C₂×#481	C₂×C₁₃	semidirect
213. C₂×#476	C₂×C₁₃	semidirect
214. C₂×#465	C₂×C₁₃	semidirect
215. C₂×#460	C₂×C₁₃	semidirect
216. C₂×#450	C₂×C₁₃	semidirect
217. C₂×C₄×SD₁₆	C₂×C₁₃	semidirect
218. C₂×C₈×D₄	C₂×C₁₃	semidirect
219. C₂²×#102	C₂×C₁₃	semidirect
250. D₄×C₁₃	C₂×SD₁₆	semidirect
281. C₂²×SD₁₆	C₂²×C₁₃	semidirect
282. C₂³×C₈	C₂²×C₁₃	semidirect
284. #554	C₂²×C₁₃	semidirect
287. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
291. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
295. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
299. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
300. #486	C₂²×C₁₃	semidirect
301. #481	C₂²×C₁₃	semidirect
302. #476	C₂²×C₁₃	semidirect
303. #465	C₂²×C₁₃	semidirect
304. #460	C₂²×C₁₃	semidirect
305. #450	C₂²×C₁₃	semidirect
306. C₄×SD₁₆	C₂²×C₁₃	semidirect
307. C₈×D₄	C₂²×C₁₃	semidirect
308. C₂×#106	C₂²×C₁₃	semidirect
309. C₂×#106	C₂²×C₁₃	semidirect
310. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
311. C₂×#103	C₂²×C₁₃	semidirect
314. C₂×#102	C₂²×C₁₃	semidirect
315. C₂×#102	C₂²×C₁₃	semidirect
316. C₂×#102	C₂²×C₁₃	semidirect
317. C₂×#102	C₂²×C₁₃	semidirect
318. C₂×C₂²⋊C₈	C₂²×C₁₃	semidirect
319. C₂×C₄×C₈	C₂²×C₁₃	semidirect
369. C₂×SD₁₆	C₂³×C₁₃	semidirect
374. C₂²×C₈	C₂³×C₁₃	semidirect
376. C₄⋊Q₈	C₂³×C₁₃	semidirect
382. C₂²⋊Q₈	C₂³×C₁₃	semidirect
388. C₄×Q₈	C₂³×C₁₃	semidirect
403. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
410. #106	C₂³×C₁₃	semidirect
411. #106	C₂³×C₁₃	semidirect
412. C₄⋊C₈	C₂³×C₁₃	semidirect
413. #103	C₂³×C₁₃	semidirect
416. #102	C₂³×C₁₃	semidirect
417. #102	C₂³×C₁₃	semidirect
418. #102	C₂³×C₁₃	semidirect
419. C₂²⋊C₈	C₂³×C₁₃	semidirect
420. C₄×C₈	C₂³×C₁₃	semidirect
424. C₂×C₁₃	#3295	direct (N × H)
458. C₂×D₄	C₁₃×SD₁₆	semidirect
506. C₁₃	C₂×#3295	direct (N × H)
537. D₄	C₂×C₁₃×SD₁₆	semidirect
595. C₂	C₁₃×#3295	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×#554	2
C₂×D₄²×C₁₃	2
C₁₃×#3295	2
C₂×C₁₃×#486	2
C₂×C₁₃×#481	2
C₂×C₁₃×#476	2
C₂×C₁₃×#465	2
C₂×C₁₃×#460	2
C₂×C₁₃×#450	2
C₂×C₄×C₁₃×SD₁₆	2
C₂×C₈×D₄×C₁₃	2
C₂²×C₁₃×#102	2
C₂×#3295	13

Subgroups — C2×C13×#3295 #15747452

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3295 #15747452