Subgroups — C₂×C₁₃×#2814 #15722990

Order 3328.

2674 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	C₂²×C₁₃×#123	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2814	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#398	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#398	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#397	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#397	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#396	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₃×#395	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#394	C₂	1	2	yes	maximal
11	C₂×C₁₃×#393	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#380	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
15	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#123	—	2	8	no	—
17	C₂×C₁₃×#123	C₂²	1	8	yes	—
18	C₂×C₁₃×C₂²⋊Q₈	—	2	8	no	—
19	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	8	yes	complemented
20	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
22	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
25	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
26	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
27	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
28	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
29	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
30	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
32	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
33	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
34	C₁₃×#398	C₂²	1	8	yes	complemented
35	C₁₃×#398	C₂²	1	16	yes	complemented
36	C₁₃×#397	C₂²	1	8	yes	complemented
37	C₁₃×#397	C₂²	1	16	yes	complemented
38	C₁₃×#396	C₂²	1	16	yes	complemented
39	C₁₃×#395	C₂²	1	8	yes	complemented
40	C₁₃×#394	C₂²	1	16	yes	—
41	C₁₃×#393	C₂²	1	8	yes	complemented
42	C₁₃×#380	C₂²	1	8	yes	complemented
43	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
44	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×#95	C₂²	1	2	yes	—
46	C₂×C₁₃×#95	C₂²	1	2	yes	—
47	C₂×C₁₃×#95	C₂²	1	2	yes	—
48	C₂×C₁₃×#95	C₂²	1	2	yes	—
49	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
50	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
51	C₂²×Q₈×C₁₃	—	2	4	no	—
52	C₂²×Q₈×C₁₃	—	4	4	no	—
53	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
54	C₂²×D₄×C₁₃	—	2	4	no	—
55	C₂²×D₄×C₁₃	—	4	4	no	—
56	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
57	C₂³×C₄×C₁₃	—	4	4	no	—
58	C₂³×C₄×C₁₃	D₄	1	8	yes	—
59	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
61	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
62	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
63	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
64	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
69	C₁₃×#123	—	2	32	no	—
70	C₁₃×C₂²⋊Q₈	—	2	32	no	—
71	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
72	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
73	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
74	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
75	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
76	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
77	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
78	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
79	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
80	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
81	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
82	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
83	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
84	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
85	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
86	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
87	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
88	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
89	C₂×C₁₃×C₂²⋊C₄	—	4	4	no	—
90	C₂×C₁₃×C₂²⋊C₄	—	4	4	no	—
91	C₂×C₁₃×C₂²⋊C₄	—	4	4	no	—
92	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
93	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
94	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
95	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
96	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
97	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
98	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
99	C₁₃×#95	C₂³	1	4	yes	—
100	C₁₃×#95	C₂³	1	4	yes	—
101	C₁₃×#95	C₂³	1	8	yes	—
102	C₁₃×#95	C₂³	1	8	yes	—
103	C₁₃×#95	C₂³	1	8	yes	—
104	C₁₃×#95	C₂³	1	8	yes	—
105	C₂×#2814	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
106	C₂⁴×C₁₃	—	2	2	no	—
107	C₂⁴×C₁₃	—	2	4	no	—
108	C₂⁴×C₁₃	—	2	4	no	—
109	C₂⁴×C₁₃	—	2	2	no	—
110	C₂⁴×C₁₃	—	2	2	no	—
111	C₂⁴×C₁₃	—	2	2	no	—
112	C₂⁴×C₁₃	—	2	4	no	—
113	C₂⁴×C₁₃	—	2	4	no	—
114	C₂⁴×C₁₃	—	2	2	no	—
115	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
116	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
117	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
118	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
119	C₂×Q₈×C₁₃	—	2	8	no	—
120	C₂×Q₈×C₁₃	—	4	8	no	—
121	C₂×Q₈×C₁₃	—	4	16	no	—
122	C₂×D₄×C₁₃	—	2	8	no	—
123	C₂×D₄×C₁₃	—	4	8	no	—
124	C₂×D₄×C₁₃	—	4	16	no	—
125	C₂²×C₄×C₁₃	—	2	4	no	—
126	C₂²×C₄×C₁₃	—	2	4	no	—
127	C₂²×C₄×C₁₃	—	2	2	no	—
128	C₂²×C₄×C₁₃	—	2	2	no	—
129	C₂²×C₄×C₁₃	—	2	4	no	—
130	C₂²×C₄×C₁₃	—	2	4	no	—
131	C₂²×C₄×C₁₃	—	2	2	no	—
132	C₂²×C₄×C₁₃	—	2	4	no	—
133	C₂²×C₄×C₁₃	—	2	4	no	—
134	C₂²×C₄×C₁₃	—	2	4	no	—
135	C₂²×C₄×C₁₃	—	2	4	no	—
136	C₂²×C₄×C₁₃	—	2	4	no	—
137	C₂²×C₄×C₁₃	—	2	2	no	—
138	C₂²×C₄×C₁₃	—	2	4	no	—
139	C₂²×C₄×C₁₃	—	2	4	no	—
140	C₂²×C₄×C₁₃	—	2	4	no	—
141	C₂²×C₄×C₁₃	—	2	4	no	—
142	C₂²×C₄×C₁₃	—	2	2	no	—
143	C₂²×C₄×C₁₃	—	2	4	no	—
144	C₂²×C₄×C₁₃	—	2	4	no	—
145	C₂²×C₄×C₁₃	—	2	4	no	—
146	C₂²×C₄×C₁₃	—	4	16	no	—
147	C₂²×C₄×C₁₃	—	4	8	no	—
148	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
149	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
150	C₂²×C₄×C₁₃	C₂×D₄	1	16	yes	—
151	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
152	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
153	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
154	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
155	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
156	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
157	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
158	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
159	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
160	C₁₃×C₄⋊C₄	—	2	8	no	—
161	C₁₃×C₄⋊C₄	—	2	16	no	—
162	C₁₃×C₄⋊C₄	—	2	8	no	—
163	C₁₃×C₄⋊C₄	—	2	8	no	—
164	C₁₃×C₄⋊C₄	—	4	8	no	—
165	C₁₃×C₄⋊C₄	—	4	8	no	—
166	C₁₃×C₄⋊C₄	—	4	8	no	—
167	C₁₃×C₂²⋊C₄	—	2	16	no	—
168	C₁₃×C₂²⋊C₄	—	2	8	no	—
169	C₁₃×C₂²⋊C₄	—	2	8	no	—
170	C₁₃×C₂²⋊C₄	—	2	8	no	—
171	C₁₃×C₂²⋊C₄	—	4	8	no	—
172	C₁₃×C₂²⋊C₄	—	4	8	no	—
173	C₁₃×C₂²⋊C₄	—	4	8	no	—
174	C₂²×#123	C₂×C₁₃	1	1	yes	characteristic
175	C₂²×C₂²⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
176	#2814	C₂×C₁₃	1	16	yes	direct product factor
177	C₂×#398	C₂×C₁₃	1	1	yes	characteristic, complemented
178	C₂×#398	C₂×C₁₃	1	2	yes	complemented
179	C₂×#397	C₂×C₁₃	1	1	yes	characteristic, complemented
180	C₂×#397	C₂×C₁₃	1	2	yes	complemented
181	C₂×#396	C₂×C₁₃	1	2	yes	complemented
182	C₂×#395	C₂×C₁₃	1	1	yes	characteristic, complemented
183	C₂×#394	C₂×C₁₃	1	2	yes	—
184	C₂×#393	C₂×C₁₃	1	1	yes	characteristic, complemented
185	C₂×#380	C₂×C₁₃	1	1	yes	characteristic, complemented
186	C₂³×C₁₃	—	2	8	no	—
187	C₂³×C₁₃	—	2	8	no	—
188	C₂³×C₁₃	—	2	8	no	—
189	C₂³×C₁₃	—	2	2	no	—
190	C₂³×C₁₃	—	2	4	no	—
191	C₂³×C₁₃	—	2	4	no	—
192	C₂³×C₁₃	—	2	2	no	—
193	C₂³×C₁₃	—	2	2	no	—
194	C₂³×C₁₃	—	2	2	no	—
195	C₂³×C₁₃	—	2	4	no	—
196	C₂³×C₁₃	—	2	4	no	—
197	C₂³×C₁₃	—	2	2	no	—
198	C₂³×C₁₃	—	4	8	no	—
199	C₂³×C₁₃	—	4	8	no	—
200	C₂³×C₁₃	—	4	4	no	—
201	C₂³×C₁₃	—	4	4	no	—
202	C₂³×C₁₃	—	4	4	no	—
203	C₂³×C₁₃	—	4	8	no	—
204	C₂³×C₁₃	—	4	8	no	—
205	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
206	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
207	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
208	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
209	C₂³×C₁₃	2₋¹⁺⁴	1	4	yes	—
210	C₂³×C₁₃	2₋¹⁺⁴	1	2	yes	—
211	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
212	Q₈×C₁₃	—	4	16	no	—
213	D₄×C₁₃	—	4	16	no	—
214	C₂×C₄×C₁₃	—	2	8	no	—
215	C₂×C₄×C₁₃	—	2	8	no	—
216	C₂×C₄×C₁₃	—	2	4	no	—
217	C₂×C₄×C₁₃	—	2	4	no	—
218	C₂×C₄×C₁₃	—	2	2	no	—
219	C₂×C₄×C₁₃	—	2	2	no	—
220	C₂×C₄×C₁₃	—	2	4	no	—
221	C₂×C₄×C₁₃	—	2	4	no	—
222	C₂×C₄×C₁₃	—	2	2	no	—
223	C₂×C₄×C₁₃	—	2	4	no	—
224	C₂×C₄×C₁₃	—	2	4	no	—
225	C₂×C₄×C₁₃	—	2	4	no	—
226	C₂×C₄×C₁₃	—	2	4	no	—
227	C₂×C₄×C₁₃	—	2	4	no	—
228	C₂×C₄×C₁₃	—	2	2	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	4	no	—
233	C₂×C₄×C₁₃	—	2	2	no	—
234	C₂×C₄×C₁₃	—	2	4	no	—
235	C₂×C₄×C₁₃	—	2	4	no	—
236	C₂×C₄×C₁₃	—	2	4	no	—
237	C₂×C₄×C₁₃	—	4	16	no	—
238	C₂×C₄×C₁₃	—	4	4	no	—
239	C₂×C₄×C₁₃	—	4	8	no	—
240	C₂×C₄×C₁₃	—	4	4	no	—
241	C₂×C₄×C₁₃	—	4	4	no	—
242	C₂×C₄×C₁₃	—	4	8	no	—
243	C₂×C₄×C₁₃	—	4	8	no	—
244	C₂×C₄×C₁₃	—	4	8	no	—
245	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
246	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
247	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
248	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
249	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
250	C₂×#123	—	2	8	no	—
251	C₂×#123	C₂²×C₁₃	1	8	yes	—
252	C₂×C₂²⋊Q₈	—	2	8	no	—
253	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	8	yes	complemented
254	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
255	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
256	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
257	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
258	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
259	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
260	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
261	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
262	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
263	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
264	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
265	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
266	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
267	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
268	#398	C₂²×C₁₃	1	8	yes	complemented
269	#398	C₂²×C₁₃	1	16	yes	complemented
270	#397	C₂²×C₁₃	1	8	yes	complemented
271	#397	C₂²×C₁₃	1	16	yes	complemented
272	#396	C₂²×C₁₃	1	16	yes	complemented
273	#395	C₂²×C₁₃	1	8	yes	complemented
274	#394	C₂²×C₁₃	1	16	yes	—
275	#393	C₂²×C₁₃	1	8	yes	complemented
276	#380	C₂²×C₁₃	1	8	yes	complemented
277	C₂×#95	C₂²×C₁₃	1	2	yes	—
278	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
279	C₂×#95	C₂²×C₁₃	1	2	yes	—
280	C₂×#95	C₂²×C₁₃	1	2	yes	—
281	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
282	C₂×#95	C₂²×C₁₃	1	2	yes	—
283	C₂²×C₁₃	—	2	4	no	—
284	C₂²×C₁₃	—	2	4	no	—
285	C₂²×C₁₃	—	2	4	no	—
286	C₂²×C₁₃	—	4	4	no	—
287	C₂²×C₁₃	—	4	4	no	—
288	C₂²×C₁₃	—	4	16	no	—
289	C₂²×C₁₃	—	4	2	no	—
290	C₂²×C₁₃	—	4	2	no	—
291	C₂²×C₁₃	—	4	2	no	—
292	C₂²×C₁₃	—	4	4	no	—
293	C₂²×C₁₃	—	4	4	no	—
294	C₂²×C₁₃	—	8	8	no	—
295	C₂²×C₁₃	#534	1	4	yes	—
296	C₂²×C₁₃	#536	1	4	yes	—
297	C₂²×C₁₃	#537	1	4	yes	—
298	C₂²×C₁₃	#562	1	8	yes	—
299	C₂²×C₁₃	#563	1	8	yes	—
300	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
301	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
302	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
303	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
304	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
305	C₄×C₁₃	—	2	4	no	—
306	C₄×C₁₃	—	2	4	no	—
307	C₄×C₁₃	—	4	2	no	—
308	C₄×C₁₃	—	4	4	no	—
309	C₄×C₁₃	—	4	2	no	—
310	C₄×C₁₃	—	4	2	no	—
311	C₄×C₁₃	—	4	4	no	—
312	C₄×C₁₃	—	4	4	no	—
313	C₄×C₁₃	—	4	4	no	—
314	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
315	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
316	C₂²×Q₈	—	2	4	no	—
317	C₂²×Q₈	—	4	4	no	—
318	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
319	C₂²×D₄	—	2	4	no	—
320	C₂²×D₄	—	4	4	no	—
321	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
322	C₂³×C₄	—	4	4	no	—
323	C₂³×C₄	D₄×C₁₃	1	8	yes	—
324	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
325	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
326	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
327	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
328	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
329	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
330	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
331	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
332	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
333	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
334	#123	—	2	32	no	—
335	C₂²⋊Q₈	—	2	32	no	—
336	C₂×C₄⋊C₄	—	2	4	no	—
337	C₂×C₄⋊C₄	—	2	8	no	—
338	C₂×C₄⋊C₄	—	2	4	no	—
339	C₂×C₄⋊C₄	—	2	4	no	—
340	C₂×C₄⋊C₄	—	4	4	no	—
341	C₂×C₄⋊C₄	—	4	4	no	—
342	C₂×C₄⋊C₄	—	4	4	no	—
343	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
344	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
345	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
346	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
347	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
348	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
349	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
350	C₂×C₂²⋊C₄	—	2	8	no	—
351	C₂×C₂²⋊C₄	—	2	4	no	—
352	C₂×C₂²⋊C₄	—	2	4	no	—
353	C₂×C₂²⋊C₄	—	2	4	no	—
354	C₂×C₂²⋊C₄	—	4	4	no	—
355	C₂×C₂²⋊C₄	—	4	4	no	—
356	C₂×C₂²⋊C₄	—	4	4	no	—
357	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
358	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
359	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
360	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
361	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
362	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
363	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
364	#95	C₂³×C₁₃	1	4	yes	—
365	#95	C₂³×C₁₃	1	4	yes	—
366	#95	C₂³×C₁₃	1	8	yes	—
367	#95	C₂³×C₁₃	1	8	yes	—
368	#95	C₂³×C₁₃	1	8	yes	—
369	#95	C₂³×C₁₃	1	8	yes	—
370	C₂×C₁₃	—	4	4	no	—
371	C₂×C₁₃	—	8	2	no	—
372	C₂×C₁₃	#2814	1	8	yes	direct product factor
373	C₂×C₁₃	C₂×#534	1	1	yes	characteristic
374	C₂×C₁₃	C₂×#536	1	1	yes	characteristic
375	C₂×C₁₃	C₂×#537	1	1	yes	characteristic
376	C₂×C₁₃	C₂×#562	1	2	yes	—
377	C₂×C₁₃	C₂×#563	1	2	yes	—
378	C₂⁴	—	2	2	no	—
379	C₂⁴	—	2	4	no	—
380	C₂⁴	—	2	4	no	—
381	C₂⁴	—	2	2	no	—
382	C₂⁴	—	2	2	no	—
383	C₂⁴	—	2	2	no	—
384	C₂⁴	—	2	4	no	—
385	C₂⁴	—	2	4	no	—
386	C₂⁴	—	2	2	no	—
387	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
388	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
389	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
390	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
391	C₂×Q₈	—	2	8	no	—
392	C₂×Q₈	—	4	8	no	—
393	C₂×Q₈	—	4	16	no	—
394	C₂×D₄	—	2	8	no	—
395	C₂×D₄	—	4	8	no	—
396	C₂×D₄	—	4	16	no	—
397	C₂²×C₄	—	2	4	no	—
398	C₂²×C₄	—	2	4	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	2	4	no	—
402	C₂²×C₄	—	2	4	no	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	—	2	4	no	—
405	C₂²×C₄	—	2	4	no	—
406	C₂²×C₄	—	2	4	no	—
407	C₂²×C₄	—	2	4	no	—
408	C₂²×C₄	—	2	4	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	2	4	no	—
411	C₂²×C₄	—	2	4	no	—
412	C₂²×C₄	—	2	4	no	—
413	C₂²×C₄	—	2	4	no	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	4	no	—
416	C₂²×C₄	—	2	4	no	—
417	C₂²×C₄	—	2	4	no	—
418	C₂²×C₄	—	4	16	no	—
419	C₂²×C₄	—	4	8	no	—
420	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
421	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
422	C₂²×C₄	C₂×D₄×C₁₃	1	16	yes	—
423	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
424	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
425	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
426	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
427	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
428	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
429	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
430	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
431	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
432	C₄⋊C₄	—	2	8	no	—
433	C₄⋊C₄	—	2	16	no	—
434	C₄⋊C₄	—	2	8	no	—
435	C₄⋊C₄	—	2	8	no	—
436	C₄⋊C₄	—	4	8	no	—
437	C₄⋊C₄	—	4	8	no	—
438	C₄⋊C₄	—	4	8	no	—
439	C₂²⋊C₄	—	2	16	no	—
440	C₂²⋊C₄	—	2	8	no	—
441	C₂²⋊C₄	—	2	8	no	—
442	C₂²⋊C₄	—	2	8	no	—
443	C₂²⋊C₄	—	4	8	no	—
444	C₂²⋊C₄	—	4	8	no	—
445	C₂²⋊C₄	—	4	8	no	—
446	C₁₃	C₂×#2814	1	1	yes	characteristic, direct product factor, Sylow
447	C₂³	—	2	8	no	—
448	C₂³	—	2	8	no	—
449	C₂³	—	2	8	no	—
450	C₂³	—	2	2	no	—
451	C₂³	—	2	4	no	—
452	C₂³	—	2	4	no	—
453	C₂³	—	2	2	no	—
454	C₂³	—	2	2	no	—
455	C₂³	—	2	2	no	—
456	C₂³	—	2	4	no	—
457	C₂³	—	2	4	no	—
458	C₂³	—	2	2	no	—
459	C₂³	—	4	8	no	—
460	C₂³	—	4	8	no	—
461	C₂³	—	4	4	no	—
462	C₂³	—	4	4	no	—
463	C₂³	—	4	4	no	—
464	C₂³	—	4	8	no	—
465	C₂³	—	4	8	no	—
466	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
467	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
468	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
469	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
470	C₂³	C₁₃×2₋¹⁺⁴	1	4	yes	—
471	C₂³	C₁₃×2₋¹⁺⁴	1	2	yes	—
472	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
473	Q₈	—	4	16	no	—
474	D₄	—	4	16	no	—
475	C₂×C₄	—	2	8	no	—
476	C₂×C₄	—	2	8	no	—
477	C₂×C₄	—	2	4	no	—
478	C₂×C₄	—	2	4	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	4	no	—
482	C₂×C₄	—	2	4	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	4	no	—
485	C₂×C₄	—	2	4	no	—
486	C₂×C₄	—	2	4	no	—
487	C₂×C₄	—	2	4	no	—
488	C₂×C₄	—	2	4	no	—
489	C₂×C₄	—	2	4	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	4	no	—
492	C₂×C₄	—	2	4	no	—
493	C₂×C₄	—	2	4	no	—
494	C₂×C₄	—	2	4	no	—
495	C₂×C₄	—	2	4	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	4	no	—
498	C₂×C₄	—	4	16	no	—
499	C₂×C₄	—	4	4	no	—
500	C₂×C₄	—	4	8	no	—
501	C₂×C₄	—	4	4	no	—
502	C₂×C₄	—	4	4	no	—
503	C₂×C₄	—	4	8	no	—
504	C₂×C₄	—	4	8	no	—
505	C₂×C₄	—	4	8	no	—
506	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
507	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
508	C₂²	—	2	4	no	—
509	C₂²	—	2	4	no	—
510	C₂²	—	2	4	no	—
511	C₂²	—	4	4	no	—
512	C₂²	—	4	4	no	—
513	C₂²	—	4	16	no	—
514	C₂²	—	4	4	no	—
515	C₂²	—	4	4	no	—
516	C₂²	—	4	2	no	—
517	C₂²	—	4	2	no	—
518	C₂²	—	4	2	no	—
519	C₂²	—	8	8	no	—
520	C₂²	C₁₃×#534	1	4	yes	—
521	C₂²	C₁₃×#536	1	4	yes	—
522	C₂²	C₁₃×#537	1	4	yes	—
523	C₂²	C₁₃×#562	1	8	yes	—
524	C₂²	C₁₃×#563	1	8	yes	—
525	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
526	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
527	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
528	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
529	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
530	C₄	—	2	4	no	—
531	C₄	—	2	4	no	—
532	C₄	—	4	4	no	—
533	C₄	—	4	4	no	—
534	C₄	—	4	2	no	—
535	C₄	—	4	4	no	—
536	C₄	—	4	2	no	—
537	C₄	—	4	2	no	—
538	C₄	—	4	4	no	—
539	C₂	—	4	4	no	—
540	C₂	—	8	2	no	—
541	C₂	C₁₃×#2814	1	8	yes	direct product factor
542	C₂	C₂×C₁₃×#534	1	1	yes	characteristic
543	C₂	C₂×C₁₃×#536	1	1	yes	characteristic
544	C₂	C₂×C₁₃×#537	1	1	yes	characteristic
545	C₂	C₂×C₁₃×#562	1	2	yes	—
546	C₂	C₂×C₁₃×#563	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂³×D₄×C₁₃	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₁₃×C₂²⋊Q₈	C₂	semidirect
3. C₁₃×#2814	C₂	direct (N × H)
4. C₂×C₁₃×#398	C₂	semidirect
5. C₂×C₁₃×#398	C₂	semidirect
6. C₂×C₁₃×#397	C₂	semidirect
7. C₂×C₁₃×#397	C₂	semidirect
8. C₂×C₁₃×#396	C₂	semidirect
9. C₂×C₁₃×#395	C₂	semidirect
11. C₂×C₁₃×#393	C₂	semidirect
12. C₂×C₁₃×#380	C₂	semidirect
19. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
34. C₁₃×#398	C₂²	semidirect
35. C₁₃×#398	C₂²	semidirect
36. C₁₃×#397	C₂²	semidirect
37. C₁₃×#397	C₂²	semidirect
38. C₁₃×#396	C₂²	semidirect
39. C₁₃×#395	C₂²	semidirect
41. C₁₃×#393	C₂²	semidirect
42. C₁₃×#380	C₂²	semidirect
105. C₂×#2814	C₁₃	direct (N × H)
175. C₂²×C₂²⋊Q₈	C₂×C₁₃	semidirect
176. #2814	C₂×C₁₃	direct (N × H)
177. C₂×#398	C₂×C₁₃	semidirect
178. C₂×#398	C₂×C₁₃	semidirect
179. C₂×#397	C₂×C₁₃	semidirect
180. C₂×#397	C₂×C₁₃	semidirect
181. C₂×#396	C₂×C₁₃	semidirect
182. C₂×#395	C₂×C₁₃	semidirect
184. C₂×#393	C₂×C₁₃	semidirect
185. C₂×#380	C₂×C₁₃	semidirect
253. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
268. #398	C₂²×C₁₃	semidirect
269. #398	C₂²×C₁₃	semidirect
270. #397	C₂²×C₁₃	semidirect
271. #397	C₂²×C₁₃	semidirect
272. #396	C₂²×C₁₃	semidirect
273. #395	C₂²×C₁₃	semidirect
275. #393	C₂²×C₁₃	semidirect
276. #380	C₂²×C₁₃	semidirect
372. C₂×C₁₃	#2814	direct (N × H)
446. C₁₃	C₂×#2814	direct (N × H)
541. C₂	C₁₃×#2814	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₁₃×#123	2
C₂²×C₁₃×C₂²⋊Q₈	2
C₁₃×#2814	2
C₂×C₁₃×#398	2
C₂×C₁₃×#397	2
C₂×C₁₃×#396	2
C₂×C₁₃×#395	2
C₂×C₁₃×#394	2
C₂×C₁₃×#393	2
C₂×C₁₃×#380	2
C₂×#2814	13

Subgroups — C2×C13×#2814 #15722990

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2814 #15722990