Subgroups — C₂×C₁₃×#3294 #15747451

Order 3328.

2858 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#547	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3294	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#486	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#480	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#474	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#466	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#459	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#447	C₂	1	2	yes	maximal, complemented
10	C₂×C₄×C₁₃×D₈	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	C₂²×C₁₃×#41	—	2	1	no	—
14	C₂³×D₄×C₁₃	—	2	1	no	—
15	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
16	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×D₈	C₂²	1	2	yes	complemented
18	C₂³×C₈×C₁₃	C₂²	1	2	yes	complemented
19	C₁₃×#547	—	2	4	no	—
20	C₁₃×#547	C₂²	1	8	yes	complemented
21	D₄²×C₁₃	—	2	4	no	—
22	D₄²×C₁₃	C₂²	1	8	yes	complemented
23	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#123	—	2	2	no	—
26	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
27	C₂×C₁₃×#121	—	2	1	no	—
28	C₂×C₁₃×#121	C₂²	1	2	yes	—
29	C₂×C₁₃×#121	C₂²	1	2	yes	complemented
30	C₂×C₁₃×#120	—	2	2	no	—
31	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
34	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
35	C₁₃×#486	C₂²	1	8	yes	complemented
36	C₁₃×#480	C₂²	1	16	yes	complemented
37	C₁₃×#474	C₂²	1	8	yes	complemented
38	C₁₃×#466	C₂²	1	16	yes	complemented
39	C₁₃×#459	C₂²	1	8	yes	complemented
40	C₁₃×#447	C₂²	1	16	yes	complemented
41	C₄×C₁₃×D₈	C₂²	1	8	yes	complemented
42	C₈×D₄×C₁₃	C₂²	1	8	yes	complemented
43	C₂×C₁₃×#107	C₂²	1	2	yes	complemented
44	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₁₃×#102	C₂²	1	2	yes	—
47	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
48	C₂×C₁₃×#102	C₂²	1	16	yes	complemented
49	C₂×C₁₃×#102	C₂²	1	2	yes	complemented
50	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic, 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	C₂×C₁₃×#41	—	2	8	no	—
57	C₂×C₁₃×#41	—	4	8	no	—
58	C₂²×Q₈×C₁₃	—	2	1	no	—
59	C₂²×D₄×C₁₃	—	2	8	no	—
60	C₂²×D₄×C₁₃	—	2	2	no	—
61	C₂²×D₄×C₁₃	—	2	2	no	—
62	C₂²×D₄×C₁₃	—	2	8	no	—
63	C₂²×D₄×C₁₃	—	2	2	no	—
64	C₂²×D₄×C₁₃	—	2	1	no	—
65	C₂²×D₄×C₁₃	—	2	4	no	—
66	C₂²×D₄×C₁₃	—	2	1	no	—
67	C₂²×D₄×C₁₃	—	4	4	no	—
68	C₂²×D₄×C₁₃	—	4	8	no	—
69	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
70	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
71	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
72	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
73	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₁₃	—	2	2	no	—
75	C₂³×C₄×C₁₃	—	2	1	no	—
76	C₂³×C₄×C₁₃	—	2	1	no	—
77	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
78	C₂×C₁₃×D₈	—	2	4	no	—
79	C₂×C₁₃×D₈	—	4	4	no	—
80	C₂×C₁₃×D₈	C₂³	1	4	yes	—
81	C₂×C₁₃×D₈	C₂³	1	8	yes	complemented
82	C₂²×C₈×C₁₃	—	4	4	no	—
83	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
86	C₂²×C₈×C₁₃	C₂³	1	8	yes	complemented
87	C₁₃×C₄⋊Q₈	—	2	2	no	—
88	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	complemented
89	C₁₃×#127	—	2	2	no	—
90	C₁₃×#127	C₂³	1	4	yes	—
91	C₁₃×#123	—	2	16	no	—
92	C₁₃×C₂²⋊Q₈	—	2	8	no	—
93	C₁₃×#121	—	2	4	no	—
94	C₁₃×#121	—	2	4	no	—
95	C₁₃×#121	—	2	8	no	—
96	C₁₃×#121	C₂³	1	8	yes	—
97	C₁₃×#121	C₂³	1	8	yes	complemented
98	C₁₃×#120	—	2	16	no	—
99	C₄×D₄×C₁₃	—	2	2	no	—
100	C₄×D₄×C₁₃	—	2	2	no	—
101	C₄×D₄×C₁₃	D₄	1	4	yes	—
102	C₄×D₄×C₁₃	C₂³	1	4	yes	—
103	C₄×D₄×C₁₃	C₂³	1	4	yes	—
104	C₄×D₄×C₁₃	C₂³	1	4	yes	complemented
105	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
106	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
107	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
108	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
109	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
110	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
111	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
112	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	complemented
113	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
114	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
115	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
116	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
117	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
118	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
119	C₁₃×#107	C₂³	1	4	yes	complemented
120	C₁₃×#107	C₂³	1	8	yes	complemented
121	C₁₃×C₄⋊C₈	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	4	yes	complemented
127	C₁₃×#102	C₂³	1	8	yes	complemented
128	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	complemented
129	C₄×C₈×C₁₃	C₂³	1	4	yes	complemented
130	C₂×#3294	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
131	C₂⁴×C₁₃	—	2	1	no	—
132	C₂⁴×C₁₃	—	2	1	no	—
133	C₂⁴×C₁₃	—	2	2	no	—
134	C₂⁴×C₁₃	—	2	8	no	—
135	C₂⁴×C₁₃	—	4	8	no	—
136	C₂⁴×C₁₃	—	4	8	no	—
137	C₂⁴×C₁₃	—	8	4	no	—
138	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
139	C₁₃×#41	—	4	32	no	—
140	C₂×Q₈×C₁₃	—	2	4	no	—
141	C₂×Q₈×C₁₃	—	4	4	no	—
142	C₂×D₄×C₁₃	—	2	16	no	—
143	C₂×D₄×C₁₃	—	2	8	no	—
144	C₂×D₄×C₁₃	—	2	8	no	—
145	C₂×D₄×C₁₃	—	2	1	no	—
146	C₂×D₄×C₁₃	—	2	1	no	—
147	C₂×D₄×C₁₃	—	2	8	no	—
148	C₂×D₄×C₁₃	—	2	2	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	—	2	2	no	—
154	C₂×D₄×C₁₃	—	2	2	no	—
155	C₂×D₄×C₁₃	—	2	4	no	—
156	C₂×D₄×C₁₃	—	4	8	no	—
157	C₂×D₄×C₁₃	—	4	16	no	—
158	C₂×D₄×C₁₃	—	4	8	no	—
159	C₂×D₄×C₁₃	—	4	8	no	—
160	C₂×D₄×C₁₃	—	4	8	no	—
161	C₂×D₄×C₁₃	—	4	32	no	—
162	C₂×D₄×C₁₃	—	4	4	no	—
163	C₂×D₄×C₁₃	—	8	2	no	—
164	C₂×D₄×C₁₃	D₈	1	8	yes	complemented
165	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
166	C₂×D₄×C₁₃	#41	1	4	yes	complemented
167	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
168	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
169	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
170	C₂²×C₄×C₁₃	—	2	4	no	—
171	C₂²×C₄×C₁₃	—	2	4	no	—
172	C₂²×C₄×C₁₃	—	2	8	no	—
173	C₂²×C₄×C₁₃	—	2	1	no	—
174	C₂²×C₄×C₁₃	—	2	1	no	—
175	C₂²×C₄×C₁₃	—	2	2	no	—
176	C₂²×C₄×C₁₃	—	2	4	no	—
177	C₂²×C₄×C₁₃	—	2	4	no	—
178	C₂²×C₄×C₁₃	—	4	8	no	—
179	C₂²×C₄×C₁₃	—	4	4	no	—
180	C₂²×C₄×C₁₃	—	4	4	no	—
181	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
182	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
183	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
184	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
185	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
186	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
187	C₁₃×D₈	—	2	8	no	—
188	C₁₃×D₈	—	4	8	no	—
189	C₂×C₈×C₁₃	—	2	2	no	—
190	C₂×C₈×C₁₃	—	2	2	no	—
191	C₂×C₈×C₁₃	—	2	4	no	—
192	C₂×C₈×C₁₃	—	4	8	no	—
193	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
194	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
195	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
196	C₁₃×C₄⋊C₄	—	2	1	no	—
197	C₁₃×C₄⋊C₄	—	2	2	no	—
198	C₁₃×C₄⋊C₄	—	2	8	no	—
199	C₁₃×C₄⋊C₄	—	2	4	no	—
200	C₁₃×C₄⋊C₄	—	2	1	no	—
201	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
202	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
203	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
204	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
205	C₁₃×C₂²⋊C₄	—	2	4	no	—
206	C₁₃×C₂²⋊C₄	—	2	4	no	—
207	C₁₃×C₂²⋊C₄	—	2	8	no	—
208	C₁₃×C₂²⋊C₄	—	2	8	no	—
209	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
210	C₄²×C₁₃	C₂×D₄	1	2	yes	—
211	C₄²×C₁₃	C₂⁴	1	2	yes	—
212	C₂×#547	C₂×C₁₃	1	1	yes	characteristic, complemented
213	C₂×D₄²	C₂×C₁₃	1	1	yes	characteristic, complemented
214	#3294	C₂×C₁₃	1	16	yes	direct product factor
215	C₂×#486	C₂×C₁₃	1	1	yes	characteristic, complemented
216	C₂×#480	C₂×C₁₃	1	2	yes	complemented
217	C₂×#474	C₂×C₁₃	1	1	yes	characteristic, complemented
218	C₂×#466	C₂×C₁₃	1	2	yes	complemented
219	C₂×#459	C₂×C₁₃	1	1	yes	characteristic, complemented
220	C₂×#447	C₂×C₁₃	1	2	yes	complemented
221	C₂×C₄×D₈	C₂×C₁₃	1	1	yes	characteristic, complemented
222	C₂×C₈×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
223	C₂²×#102	C₂×C₁₃	1	2	yes	complemented
224	C₂³×C₁₃	—	2	4	no	—
225	C₂³×C₁₃	—	2	4	no	—
226	C₂³×C₁₃	—	2	4	no	—
227	C₂³×C₁₃	—	2	2	no	—
228	C₂³×C₁₃	—	2	2	no	—
229	C₂³×C₁₃	—	2	4	no	—
230	C₂³×C₁₃	—	4	16	no	—
231	C₂³×C₁₃	—	4	2	no	—
232	C₂³×C₁₃	—	4	2	no	—
233	C₂³×C₁₃	—	4	4	no	—
234	C₂³×C₁₃	—	4	2	no	—
235	C₂³×C₁₃	—	4	2	no	—
236	C₂³×C₁₃	—	4	16	no	—
237	C₂³×C₁₃	—	4	4	no	—
238	C₂³×C₁₃	—	4	4	no	—
239	C₂³×C₁₃	—	4	2	no	—
240	C₂³×C₁₃	—	8	8	no	—
241	C₂³×C₁₃	—	8	32	no	—
242	C₂³×C₁₃	C₂×D₈	1	8	yes	—
243	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
244	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
245	Q₈×C₁₃	—	4	8	no	—
246	D₄×C₁₃	—	2	4	no	—
247	D₄×C₁₃	—	2	2	no	—
248	D₄×C₁₃	—	2	4	no	—
249	D₄×C₁₃	—	2	2	no	—
250	D₄×C₁₃	—	2	2	no	—
251	D₄×C₁₃	—	2	4	no	—
252	D₄×C₁₃	—	4	16	no	—
253	D₄×C₁₃	—	4	16	no	—
254	D₄×C₁₃	—	4	16	no	—
255	D₄×C₁₃	—	4	2	no	—
256	D₄×C₁₃	—	4	4	no	—
257	D₄×C₁₃	—	4	8	no	—
258	D₄×C₁₃	—	8	4	no	—
259	D₄×C₁₃	C₂×D₈	1	16	yes	complemented
260	D₄×C₁₃	C₂×#41	1	4	yes	complemented
261	C₂×C₄×C₁₃	—	2	4	no	—
262	C₂×C₄×C₁₃	—	2	2	no	—
263	C₂×C₄×C₁₃	—	2	8	no	—
264	C₂×C₄×C₁₃	—	2	4	no	—
265	C₂×C₄×C₁₃	—	2	4	no	—
266	C₂×C₄×C₁₃	—	2	2	no	—
267	C₂×C₄×C₁₃	—	2	2	no	—
268	C₂×C₄×C₁₃	—	2	4	no	—
269	C₂×C₄×C₁₃	—	4	2	no	—
270	C₂×C₄×C₁₃	—	4	2	no	—
271	C₂×C₄×C₁₃	—	4	4	no	—
272	C₂×C₄×C₁₃	—	4	16	no	—
273	C₂×C₄×C₁₃	—	4	8	no	—
274	C₂×C₄×C₁₃	—	4	8	no	—
275	C₂×C₄×C₁₃	C₂×D₈	1	4	yes	—
276	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
277	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
278	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
279	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
280	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
281	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
282	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
283	C₈×C₁₃	—	2	2	no	—
284	C₈×C₁₃	—	2	2	no	—
285	C₈×C₁₃	—	2	4	no	—
286	C₂²×#41	—	2	1	no	—
287	C₂³×D₄	—	2	1	no	—
288	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
289	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
290	C₂²×D₈	C₂²×C₁₃	1	2	yes	complemented
291	C₂³×C₈	C₂²×C₁₃	1	2	yes	complemented
292	#547	—	2	4	no	—
293	#547	C₂²×C₁₃	1	8	yes	complemented
294	D₄²	—	2	4	no	—
295	D₄²	C₂²×C₁₃	1	8	yes	complemented
296	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
297	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
298	C₂×#123	—	2	2	no	—
299	C₂×C₂²⋊Q₈	—	2	1	no	—
300	C₂×#121	—	2	1	no	—
301	C₂×#121	C₂²×C₁₃	1	2	yes	—
302	C₂×#121	C₂²×C₁₃	1	2	yes	complemented
303	C₂×#120	—	2	2	no	—
304	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
305	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
306	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
307	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
308	#486	C₂²×C₁₃	1	8	yes	complemented
309	#480	C₂²×C₁₃	1	16	yes	complemented
310	#474	C₂²×C₁₃	1	8	yes	complemented
311	#466	C₂²×C₁₃	1	16	yes	complemented
312	#459	C₂²×C₁₃	1	8	yes	complemented
313	#447	C₂²×C₁₃	1	16	yes	complemented
314	C₄×D₈	C₂²×C₁₃	1	8	yes	complemented
315	C₈×D₄	C₂²×C₁₃	1	8	yes	complemented
316	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic, complemented
317	C₂×#107	C₂²×C₁₃	1	2	yes	complemented
318	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
319	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
320	C₂×#102	C₂²×C₁₃	1	2	yes	—
321	C₂×#102	C₂²×C₁₃	1	16	yes	complemented
322	C₂×#102	C₂²×C₁₃	1	2	yes	complemented
323	C₂×#102	C₂²×C₁₃	1	2	yes	complemented
324	C₂×#102	C₂²×C₁₃	1	2	yes	complemented
325	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
326	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	complemented
327	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
328	C₂²×C₁₃	—	2	4	no	—
329	C₂²×C₁₃	—	2	16	no	—
330	C₂²×C₁₃	—	2	4	no	—
331	C₂²×C₁₃	—	2	4	no	—
332	C₂²×C₁₃	—	4	8	no	—
333	C₂²×C₁₃	—	4	2	no	—
334	C₂²×C₁₃	—	4	2	no	—
335	C₂²×C₁₃	—	4	4	no	—
336	C₂²×C₁₃	—	4	2	no	—
337	C₂²×C₁₃	—	4	2	no	—
338	C₂²×C₁₃	—	4	4	no	—
339	C₂²×C₁₃	—	4	4	no	—
340	C₂²×C₁₃	—	4	2	no	—
341	C₂²×C₁₃	—	8	32	no	—
342	C₂²×C₁₃	—	8	4	no	—
343	C₂²×C₁₃	—	8	8	no	—
344	C₂²×C₁₃	#546	1	2	yes	—
345	C₂²×C₁₃	C₂²×D₈	1	8	yes	—
346	C₂²×C₁₃	C₂²×D₈	1	2	yes	—
347	C₂²×C₁₃	#577	1	2	yes	—
348	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
349	C₄×C₁₃	—	2	4	no	—
350	C₄×C₁₃	—	2	2	no	—
351	C₄×C₁₃	—	4	2	no	—
352	C₄×C₁₃	—	4	2	no	—
353	C₄×C₁₃	—	4	4	no	—
354	C₄×C₁₃	#546	1	2	yes	—
355	C₄×C₁₃	C₂²×D₈	1	4	yes	—
356	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
357	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
358	C₂⁵	—	2	2	no	—
359	C₂×#41	—	2	8	no	—
360	C₂×#41	—	4	8	no	—
361	C₂²×Q₈	—	2	1	no	—
362	C₂²×D₄	—	2	8	no	—
363	C₂²×D₄	—	2	2	no	—
364	C₂²×D₄	—	2	2	no	—
365	C₂²×D₄	—	2	8	no	—
366	C₂²×D₄	—	2	2	no	—
367	C₂²×D₄	—	2	1	no	—
368	C₂²×D₄	—	2	4	no	—
369	C₂²×D₄	—	2	1	no	—
370	C₂²×D₄	—	4	4	no	—
371	C₂²×D₄	—	4	8	no	—
372	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
373	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
374	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
375	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
376	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
377	C₂³×C₄	—	2	2	no	—
378	C₂³×C₄	—	2	1	no	—
379	C₂³×C₄	—	2	1	no	—
380	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
381	C₂×D₈	—	2	4	no	—
382	C₂×D₈	—	4	4	no	—
383	C₂×D₈	C₂³×C₁₃	1	4	yes	—
384	C₂×D₈	C₂³×C₁₃	1	8	yes	complemented
385	C₂²×C₈	—	4	4	no	—
386	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
387	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
388	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
389	C₂²×C₈	C₂³×C₁₃	1	8	yes	complemented
390	C₄⋊Q₈	—	2	2	no	—
391	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	complemented
392	#127	—	2	2	no	—
393	#127	C₂³×C₁₃	1	4	yes	—
394	#123	—	2	16	no	—
395	C₂²⋊Q₈	—	2	8	no	—
396	#121	—	2	4	no	—
397	#121	—	2	4	no	—
398	#121	—	2	8	no	—
399	#121	C₂³×C₁₃	1	8	yes	—
400	#121	C₂³×C₁₃	1	8	yes	complemented
401	#120	—	2	16	no	—
402	C₄×D₄	—	2	2	no	—
403	C₄×D₄	—	2	2	no	—
404	C₄×D₄	D₄×C₁₃	1	4	yes	—
405	C₄×D₄	C₂³×C₁₃	1	4	yes	—
406	C₄×D₄	C₂³×C₁₃	1	4	yes	—
407	C₄×D₄	C₂³×C₁₃	1	4	yes	complemented
408	C₂×C₄⋊C₄	—	2	2	no	—
409	C₂×C₄⋊C₄	—	2	4	no	—
410	C₂×C₄⋊C₄	—	2	1	no	—
411	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
412	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
413	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
414	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
415	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	complemented
416	C₂×C₂²⋊C₄	—	2	1	no	—
417	C₂×C₂²⋊C₄	—	2	1	no	—
418	C₂×C₂²⋊C₄	—	2	2	no	—
419	C₂×C₂²⋊C₄	—	2	2	no	—
420	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
421	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
422	#107	C₂³×C₁₃	1	4	yes	complemented
423	#107	C₂³×C₁₃	1	8	yes	complemented
424	C₄⋊C₈	C₂³×C₁₃	1	4	yes	complemented
425	#102	C₂³×C₁₃	1	4	yes	—
426	#102	C₂³×C₁₃	1	8	yes	—
427	#102	C₂³×C₁₃	1	8	yes	complemented
428	#102	C₂³×C₁₃	1	8	yes	complemented
429	#102	C₂³×C₁₃	1	4	yes	complemented
430	#102	C₂³×C₁₃	1	8	yes	complemented
431	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	complemented
432	C₄×C₈	C₂³×C₁₃	1	4	yes	complemented
433	C₂×C₁₃	—	2	8	no	—
434	C₂×C₁₃	—	4	4	no	—
435	C₂×C₁₃	—	8	2	no	—
436	C₂×C₁₃	—	8	4	no	—
437	C₂×C₁₃	#3294	1	4	yes	direct product factor
438	C₂×C₁₃	C₂×#546	1	1	yes	characteristic
439	C₂×C₁₃	C₂³×D₈	1	1	yes	characteristic
440	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
441	C₂⁴	—	2	1	no	—
442	C₂⁴	—	2	1	no	—
443	C₂⁴	—	2	2	no	—
444	C₂⁴	—	2	8	no	—
445	C₂⁴	—	4	8	no	—
446	C₂⁴	—	4	8	no	—
447	C₂⁴	—	8	4	no	—
448	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
449	#41	—	4	32	no	—
450	C₂×Q₈	—	2	4	no	—
451	C₂×Q₈	—	4	4	no	—
452	C₂×D₄	—	2	16	no	—
453	C₂×D₄	—	2	8	no	—
454	C₂×D₄	—	2	8	no	—
455	C₂×D₄	—	2	1	no	—
456	C₂×D₄	—	2	1	no	—
457	C₂×D₄	—	2	8	no	—
458	C₂×D₄	—	2	2	no	—
459	C₂×D₄	—	2	4	no	—
460	C₂×D₄	—	2	4	no	—
461	C₂×D₄	—	2	2	no	—
462	C₂×D₄	—	2	4	no	—
463	C₂×D₄	—	2	2	no	—
464	C₂×D₄	—	2	2	no	—
465	C₂×D₄	—	2	4	no	—
466	C₂×D₄	—	4	8	no	—
467	C₂×D₄	—	4	16	no	—
468	C₂×D₄	—	4	8	no	—
469	C₂×D₄	—	4	8	no	—
470	C₂×D₄	—	4	8	no	—
471	C₂×D₄	—	4	32	no	—
472	C₂×D₄	—	4	4	no	—
473	C₂×D₄	—	8	2	no	—
474	C₂×D₄	C₁₃×D₈	1	8	yes	complemented
475	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
476	C₂×D₄	C₁₃×#41	1	4	yes	complemented
477	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
478	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
479	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
480	C₂²×C₄	—	2	4	no	—
481	C₂²×C₄	—	2	4	no	—
482	C₂²×C₄	—	2	1	no	—
483	C₂²×C₄	—	2	1	no	—
484	C₂²×C₄	—	2	2	no	—
485	C₂²×C₄	—	2	8	no	—
486	C₂²×C₄	—	2	4	no	—
487	C₂²×C₄	—	2	4	no	—
488	C₂²×C₄	—	4	8	no	—
489	C₂²×C₄	—	4	4	no	—
490	C₂²×C₄	—	4	4	no	—
491	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
492	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
493	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
494	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
495	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
496	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
497	D₈	—	2	8	no	—
498	D₈	—	4	8	no	—
499	C₂×C₈	—	2	2	no	—
500	C₂×C₈	—	2	2	no	—
501	C₂×C₈	—	2	4	no	—
502	C₂×C₈	—	4	8	no	—
503	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
504	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
505	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
506	C₄⋊C₄	—	2	1	no	—
507	C₄⋊C₄	—	2	2	no	—
508	C₄⋊C₄	—	2	8	no	—
509	C₄⋊C₄	—	2	4	no	—
510	C₄⋊C₄	—	2	1	no	—
511	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
512	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
513	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
514	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
515	C₂²⋊C₄	—	2	4	no	—
516	C₂²⋊C₄	—	2	4	no	—
517	C₂²⋊C₄	—	2	8	no	—
518	C₂²⋊C₄	—	2	8	no	—
519	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
520	C₄²	C₂×D₄×C₁₃	1	2	yes	—
521	C₄²	C₂⁴×C₁₃	1	2	yes	—
522	C₁₃	C₂×#3294	1	1	yes	characteristic, direct product factor, Sylow
523	C₂³	—	2	4	no	—
524	C₂³	—	2	4	no	—
525	C₂³	—	2	4	no	—
526	C₂³	—	2	2	no	—
527	C₂³	—	2	2	no	—
528	C₂³	—	2	4	no	—
529	C₂³	—	4	16	no	—
530	C₂³	—	4	2	no	—
531	C₂³	—	4	2	no	—
532	C₂³	—	4	4	no	—
533	C₂³	—	4	2	no	—
534	C₂³	—	4	2	no	—
535	C₂³	—	4	16	no	—
536	C₂³	—	4	4	no	—
537	C₂³	—	4	4	no	—
538	C₂³	—	4	2	no	—
539	C₂³	—	8	8	no	—
540	C₂³	—	8	32	no	—
541	C₂³	C₂×C₁₃×D₈	1	8	yes	—
542	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
543	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
544	Q₈	—	4	8	no	—
545	D₄	—	2	4	no	—
546	D₄	—	2	2	no	—
547	D₄	—	2	4	no	—
548	D₄	—	2	2	no	—
549	D₄	—	2	2	no	—
550	D₄	—	2	4	no	—
551	D₄	—	4	16	no	—
552	D₄	—	4	16	no	—
553	D₄	—	4	16	no	—
554	D₄	—	4	4	no	—
555	D₄	—	4	2	no	—
556	D₄	—	4	8	no	—
557	D₄	—	8	4	no	—
558	D₄	C₂×C₁₃×D₈	1	16	yes	complemented
559	D₄	C₂×C₁₃×#41	1	4	yes	complemented
560	C₂×C₄	—	2	4	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	8	no	—
563	C₂×C₄	—	2	4	no	—
564	C₂×C₄	—	2	4	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	4	no	—
568	C₂×C₄	—	4	2	no	—
569	C₂×C₄	—	4	2	no	—
570	C₂×C₄	—	4	4	no	—
571	C₂×C₄	—	4	16	no	—
572	C₂×C₄	—	4	8	no	—
573	C₂×C₄	—	4	8	no	—
574	C₂×C₄	C₂×C₁₃×D₈	1	4	yes	—
575	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
576	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
577	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
578	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
579	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
580	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
581	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
582	C₈	—	2	2	no	—
583	C₈	—	2	2	no	—
584	C₈	—	2	4	no	—
585	C₂²	—	2	16	no	—
586	C₂²	—	2	4	no	—
587	C₂²	—	2	4	no	—
588	C₂²	—	2	4	no	—
589	C₂²	—	4	8	no	—
590	C₂²	—	4	2	no	—
591	C₂²	—	4	2	no	—
592	C₂²	—	4	2	no	—
593	C₂²	—	4	4	no	—
594	C₂²	—	4	4	no	—
595	C₂²	—	4	2	no	—
596	C₂²	—	4	4	no	—
597	C₂²	—	4	2	no	—
598	C₂²	—	8	32	no	—
599	C₂²	—	8	4	no	—
600	C₂²	—	8	8	no	—
601	C₂²	C₁₃×#546	1	2	yes	—
602	C₂²	C₂²×C₁₃×D₈	1	8	yes	—
603	C₂²	C₂²×C₁₃×D₈	1	2	yes	—
604	C₂²	C₁₃×#577	1	2	yes	—
605	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
606	C₄	—	2	2	no	—
607	C₄	—	2	4	no	—
608	C₄	—	4	2	no	—
609	C₄	—	4	2	no	—
610	C₄	—	4	4	no	—
611	C₄	C₁₃×#546	1	2	yes	—
612	C₄	C₂²×C₁₃×D₈	1	4	yes	—
613	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
614	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
615	C₂	—	2	8	no	—
616	C₂	—	4	4	no	—
617	C₂	—	8	4	no	—
618	C₂	—	8	2	no	—
619	C₂	C₁₃×#3294	1	4	yes	direct product factor
620	C₂	C₂×C₁₃×#546	1	1	yes	characteristic
621	C₂	C₂³×C₁₃×D₈	1	1	yes	characteristic
622	C₂	C₂×C₁₃×#577	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 ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#547	C₂	semidirect
2. C₂×D₄²×C₁₃	C₂	semidirect
3. C₁₃×#3294	C₂	direct (N × H)
4. C₂×C₁₃×#486	C₂	semidirect
5. C₂×C₁₃×#480	C₂	semidirect
6. C₂×C₁₃×#474	C₂	semidirect
7. C₂×C₁₃×#466	C₂	semidirect
8. C₂×C₁₃×#459	C₂	semidirect
9. C₂×C₁₃×#447	C₂	semidirect
10. C₂×C₄×C₁₃×D₈	C₂	semidirect
11. C₂×C₈×D₄×C₁₃	C₂	semidirect
12. C₂²×C₁₃×#102	C₂	semidirect
17. C₂²×C₁₃×D₈	C₂²	semidirect
18. C₂³×C₈×C₁₃	C₂²	semidirect
20. C₁₃×#547	C₂²	semidirect
22. D₄²×C₁₃	C₂²	semidirect
23. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
29. C₂×C₁₃×#121	C₂²	semidirect
33. C₂×C₄×D₄×C₁₃	C₂²	semidirect
34. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
35. C₁₃×#486	C₂²	semidirect
36. C₁₃×#480	C₂²	semidirect
37. C₁₃×#474	C₂²	semidirect
38. C₁₃×#466	C₂²	semidirect
39. C₁₃×#459	C₂²	semidirect
40. C₁₃×#447	C₂²	semidirect
41. C₄×C₁₃×D₈	C₂²	semidirect
42. C₈×D₄×C₁₃	C₂²	semidirect
43. C₂×C₁₃×#107	C₂²	semidirect
44. C₂×C₁₃×#107	C₂²	semidirect
45. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
48. C₂×C₁₃×#102	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
81. C₂×C₁₃×D₈	C₂³	semidirect
86. C₂²×C₈×C₁₃	C₂³	semidirect
88. C₁₃×C₄⋊Q₈	C₂³	semidirect
97. C₁₃×#121	C₂³	semidirect
104. C₄×D₄×C₁₃	C₂³	semidirect
112. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
119. C₁₃×#107	C₂³	semidirect
120. C₁₃×#107	C₂³	semidirect
121. C₁₃×C₄⋊C₈	C₂³	semidirect
124. C₁₃×#102	C₂³	semidirect
125. C₁₃×#102	C₂³	semidirect
126. C₁₃×#102	C₂³	semidirect
127. C₁₃×#102	C₂³	semidirect
128. C₁₃×C₂²⋊C₈	C₂³	semidirect
129. C₄×C₈×C₁₃	C₂³	semidirect
130. C₂×#3294	C₁₃	direct (N × H)
164. C₂×D₄×C₁₃	D₈	semidirect
166. C₂×D₄×C₁₃	#41	semidirect
212. C₂×#547	C₂×C₁₃	semidirect
213. C₂×D₄²	C₂×C₁₃	semidirect
214. #3294	C₂×C₁₃	direct (N × H)
215. C₂×#486	C₂×C₁₃	semidirect
216. C₂×#480	C₂×C₁₃	semidirect
217. C₂×#474	C₂×C₁₃	semidirect
218. C₂×#466	C₂×C₁₃	semidirect
219. C₂×#459	C₂×C₁₃	semidirect
220. C₂×#447	C₂×C₁₃	semidirect
221. C₂×C₄×D₈	C₂×C₁₃	semidirect
222. C₂×C₈×D₄	C₂×C₁₃	semidirect
223. C₂²×#102	C₂×C₁₃	semidirect
259. D₄×C₁₃	C₂×D₈	semidirect
260. D₄×C₁₃	C₂×#41	semidirect
290. C₂²×D₈	C₂²×C₁₃	semidirect
291. C₂³×C₈	C₂²×C₁₃	semidirect
293. #547	C₂²×C₁₃	semidirect
295. D₄²	C₂²×C₁₃	semidirect
296. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
302. C₂×#121	C₂²×C₁₃	semidirect
306. C₂×C₄×D₄	C₂²×C₁₃	semidirect
307. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
308. #486	C₂²×C₁₃	semidirect
309. #480	C₂²×C₁₃	semidirect
310. #474	C₂²×C₁₃	semidirect
311. #466	C₂²×C₁₃	semidirect
312. #459	C₂²×C₁₃	semidirect
313. #447	C₂²×C₁₃	semidirect
314. C₄×D₈	C₂²×C₁₃	semidirect
315. C₈×D₄	C₂²×C₁₃	semidirect
316. C₂×#107	C₂²×C₁₃	semidirect
317. C₂×#107	C₂²×C₁₃	semidirect
318. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
321. C₂×#102	C₂²×C₁₃	semidirect
322. C₂×#102	C₂²×C₁₃	semidirect
323. C₂×#102	C₂²×C₁₃	semidirect
324. C₂×#102	C₂²×C₁₃	semidirect
325. C₂×#102	C₂²×C₁₃	semidirect
326. C₂×C₂²⋊C₈	C₂²×C₁₃	semidirect
327. C₂×C₄×C₈	C₂²×C₁₃	semidirect
384. C₂×D₈	C₂³×C₁₃	semidirect
389. C₂²×C₈	C₂³×C₁₃	semidirect
391. C₄⋊Q₈	C₂³×C₁₃	semidirect
400. #121	C₂³×C₁₃	semidirect
407. C₄×D₄	C₂³×C₁₃	semidirect
415. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
422. #107	C₂³×C₁₃	semidirect
423. #107	C₂³×C₁₃	semidirect
424. C₄⋊C₈	C₂³×C₁₃	semidirect
427. #102	C₂³×C₁₃	semidirect
428. #102	C₂³×C₁₃	semidirect
429. #102	C₂³×C₁₃	semidirect
430. #102	C₂³×C₁₃	semidirect
431. C₂²⋊C₈	C₂³×C₁₃	semidirect
432. C₄×C₈	C₂³×C₁₃	semidirect
437. C₂×C₁₃	#3294	direct (N × H)
474. C₂×D₄	C₁₃×D₈	semidirect
476. C₂×D₄	C₁₃×#41	semidirect
522. C₁₃	C₂×#3294	direct (N × H)
558. D₄	C₂×C₁₃×D₈	semidirect
559. D₄	C₂×C₁₃×#41	semidirect
619. C₂	C₁₃×#3294	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×#547	2
C₂×D₄²×C₁₃	2
C₁₃×#3294	2
C₂×C₁₃×#486	2
C₂×C₁₃×#480	2
C₂×C₁₃×#474	2
C₂×C₁₃×#466	2
C₂×C₁₃×#459	2
C₂×C₁₃×#447	2
C₂×C₄×C₁₃×D₈	2
C₂×C₈×D₄×C₁₃	2
C₂²×C₁₃×#102	2
C₂×#3294	13

Subgroups — C2×C13×#3294 #15747451

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3294 #15747451