Subgroups — C₂×C₁₃×#2323 #15720402

Order 3328.

3198 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₁₃×#117	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2323	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₁₃×#391	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#389	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#389	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#388	C₂	1	2	yes	maximal
9	C₂×C₁₃×#388	C₂	1	2	yes	maximal
10	C₂×C₁₃×#387	C₂	1	2	yes	maximal, complemented
11	C₂×C₁₃×#380	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×C₂²⋊Q₈	C₄	1	16	yes	complemented
16	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	8	yes	—
17	C₂×C₄×Q₈×C₁₃	—	2	8	no	—
18	C₂×C₄×Q₈×C₁₃	C₂²	1	8	yes	complemented
19	C₂×C₁₃×#117	—	2	8	no	—
20	C₂×C₁₃×#117	C₂²	1	8	yes	—
21	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
26	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
27	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₂²×C₁₃×C₄⋊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×C₄²×C₁₃	C₂²	1	2	yes	—
34	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
35	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
36	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
37	C₁₃×#391	C₂²	1	8	yes	complemented
38	C₁₃×#389	C₂²	1	16	yes	complemented
39	C₁₃×#389	C₂²	1	8	yes	complemented
40	C₁₃×#388	C₂²	1	16	yes	—
41	C₁₃×#388	C₂²	1	16	yes	—
42	C₁₃×#387	C₂²	1	16	yes	complemented
43	C₁₃×#380	C₂²	1	8	yes	—
44	C₄×C₁₃×C₄⋊C₄	C₂²	1	8	yes	complemented
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	C₂×C₁₃×#95	C₂²	1	2	yes	—
50	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
51	C₂²×Q₈×C₁₃	—	2	4	no	—
52	C₂²×Q₈×C₁₃	—	2	4	no	—
53	C₂²×Q₈×C₁₃	C₂×C₄	1	8	yes	—
54	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
55	C₂³×C₄×C₁₃	—	2	4	no	—
56	C₂³×C₄×C₁₃	—	2	4	no	—
57	C₂³×C₄×C₁₃	C₂×C₄	1	8	yes	—
58	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
59	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
60	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
62	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
63	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
64	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
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	1	yes	characteristic
69	C₁₃×C₂²⋊Q₈	C₂×C₄	1	64	yes	complemented
70	C₄×Q₈×C₁₃	—	2	32	no	—
71	C₁₃×#117	—	2	32	no	—
72	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
73	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
74	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
75	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
76	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
77	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
78	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	8	yes	—
79	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	16	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	4	yes	—
83	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
84	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
85	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
86	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
87	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
88	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
89	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
90	C₂×C₁₃×C₂²⋊C₄	—	4	4	no	—
91	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	16	yes	—
92	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
93	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
94	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
95	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
96	C₂×C₄²×C₁₃	—	2	4	no	—
97	C₂×C₄²×C₁₃	—	2	8	no	—
98	C₂×C₄²×C₁₃	—	4	4	no	—
99	C₂×C₄²×C₁₃	D₄	1	8	yes	—
100	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
101	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
102	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
103	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
104	C₁₃×#95	C₂³	1	8	yes	—
105	C₁₃×#95	C₂³	1	8	yes	—
106	C₁₃×#95	C₂³	1	8	yes	—
107	C₁₃×#95	C₂³	1	8	yes	—
108	C₁₃×#95	C₂³	1	8	yes	—
109	C₂×#2323	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
110	C₂⁴×C₁₃	—	2	2	no	—
111	C₂⁴×C₁₃	—	2	2	no	—
112	C₂⁴×C₁₃	—	2	2	no	—
113	C₂⁴×C₁₃	—	2	2	no	—
114	C₂⁴×C₁₃	—	2	2	no	—
115	C₂⁴×C₁₃	—	2	2	no	—
116	C₂⁴×C₁₃	C₂²×C₄	1	4	yes	—
117	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
118	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
119	C₂×Q₈×C₁₃	—	2	32	no	—
120	C₂×Q₈×C₁₃	—	2	8	no	—
121	C₂×Q₈×C₁₃	—	2	8	no	—
122	C₂×Q₈×C₁₃	C₂²×C₄	1	16	yes	—
123	C₂²×C₄×C₁₃	—	2	4	no	—
124	C₂²×C₄×C₁₃	—	2	2	no	—
125	C₂²×C₄×C₁₃	—	2	2	no	—
126	C₂²×C₄×C₁₃	—	2	4	no	—
127	C₂²×C₄×C₁₃	—	2	2	no	—
128	C₂²×C₄×C₁₃	—	2	4	no	—
129	C₂²×C₄×C₁₃	—	2	4	no	—
130	C₂²×C₄×C₁₃	—	2	2	no	—
131	C₂²×C₄×C₁₃	—	2	2	no	—
132	C₂²×C₄×C₁₃	—	2	2	no	—
133	C₂²×C₄×C₁₃	—	2	32	no	—
134	C₂²×C₄×C₁₃	—	2	8	no	—
135	C₂²×C₄×C₁₃	—	2	8	no	—
136	C₂²×C₄×C₁₃	—	2	2	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	2	no	—
144	C₂²×C₄×C₁₃	—	2	2	no	—
145	C₂²×C₄×C₁₃	—	2	2	no	—
146	C₂²×C₄×C₁₃	—	2	4	no	—
147	C₂²×C₄×C₁₃	—	2	4	no	—
148	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
149	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
150	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
151	C₂²×C₄×C₁₃	C₂²×C₄	1	16	yes	—
152	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
153	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
154	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
155	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
156	C₂²×C₄×C₁₃	#41	1	4	yes	—
157	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
158	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
159	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
160	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
161	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
162	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
163	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
164	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
165	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
166	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
167	C₁₃×C₄⋊C₄	—	2	8	no	—
168	C₁₃×C₄⋊C₄	—	2	8	no	—
169	C₁₃×C₄⋊C₄	—	2	16	no	—
170	C₁₃×C₄⋊C₄	—	2	8	no	—
171	C₁₃×C₄⋊C₄	—	2	8	no	—
172	C₁₃×C₄⋊C₄	—	4	8	no	—
173	C₁₃×C₄⋊C₄	C₂²×C₄	1	16	yes	—
174	C₁₃×C₄⋊C₄	C₂²×C₄	1	32	yes	—
175	C₁₃×C₂²⋊C₄	—	2	8	no	—
176	C₁₃×C₂²⋊C₄	—	2	8	no	—
177	C₁₃×C₂²⋊C₄	—	4	8	no	—
178	C₁₃×C₂²⋊C₄	C₂²×C₄	1	32	yes	—
179	C₄²×C₁₃	—	2	8	no	—
180	C₄²×C₁₃	—	2	16	no	—
181	C₄²×C₁₃	—	4	8	no	—
182	C₄²×C₁₃	C₂×D₄	1	16	yes	—
183	C₂²×C₂²⋊Q₈	C₂×C₁₃	1	1	yes	characteristic
184	C₂²×C₄×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
185	C₂²×#117	C₂×C₁₃	1	1	yes	characteristic
186	#2323	C₂×C₁₃	1	16	yes	direct product factor
187	C₂×#391	C₂×C₁₃	1	1	yes	characteristic, complemented
188	C₂×#389	C₂×C₁₃	1	2	yes	complemented
189	C₂×#389	C₂×C₁₃	1	1	yes	characteristic, complemented
190	C₂×#388	C₂×C₁₃	1	2	yes	—
191	C₂×#388	C₂×C₁₃	1	2	yes	—
192	C₂×#387	C₂×C₁₃	1	2	yes	complemented
193	C₂×#380	C₂×C₁₃	1	1	yes	characteristic
194	C₂×C₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
195	C₂³×C₁₃	—	2	8	no	—
196	C₂³×C₁₃	—	2	8	no	—
197	C₂³×C₁₃	—	2	8	no	—
198	C₂³×C₁₃	—	2	2	no	—
199	C₂³×C₁₃	—	2	2	no	—
200	C₂³×C₁₃	—	2	2	no	—
201	C₂³×C₁₃	—	2	2	no	—
202	C₂³×C₁₃	—	2	2	no	—
203	C₂³×C₁₃	—	2	2	no	—
204	C₂³×C₁₃	—	4	4	no	—
205	C₂³×C₁₃	—	4	4	no	—
206	C₂³×C₁₃	—	4	4	no	—
207	C₂³×C₁₃	—	4	4	no	—
208	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
209	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
210	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
211	C₂³×C₁₃	C₂×#41	1	2	yes	—
212	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
213	C₂³×C₁₃	2₋¹⁺⁴	1	2	yes	—
214	C₂³×C₁₃	2₋¹⁺⁴	1	2	yes	—
215	C₂³×C₁₃	2₋¹⁺⁴	1	2	yes	—
216	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
217	Q₈×C₁₃	—	2	32	no	—
218	C₂×C₄×C₁₃	—	2	8	no	—
219	C₂×C₄×C₁₃	—	2	16	no	—
220	C₂×C₄×C₁₃	—	2	16	no	—
221	C₂×C₄×C₁₃	—	2	8	no	—
222	C₂×C₄×C₁₃	—	2	8	no	—
223	C₂×C₄×C₁₃	—	2	4	no	—
224	C₂×C₄×C₁₃	—	2	2	no	—
225	C₂×C₄×C₁₃	—	2	2	no	—
226	C₂×C₄×C₁₃	—	2	4	no	—
227	C₂×C₄×C₁₃	—	2	2	no	—
228	C₂×C₄×C₁₃	—	2	4	no	—
229	C₂×C₄×C₁₃	—	2	4	no	—
230	C₂×C₄×C₁₃	—	2	2	no	—
231	C₂×C₄×C₁₃	—	2	2	no	—
232	C₂×C₄×C₁₃	—	2	2	no	—
233	C₂×C₄×C₁₃	—	2	32	no	—
234	C₂×C₄×C₁₃	—	2	2	no	—
235	C₂×C₄×C₁₃	—	2	2	no	—
236	C₂×C₄×C₁₃	—	2	4	no	—
237	C₂×C₄×C₁₃	—	2	4	no	—
238	C₂×C₄×C₁₃	—	2	4	no	—
239	C₂×C₄×C₁₃	—	2	4	no	—
240	C₂×C₄×C₁₃	—	2	2	no	—
241	C₂×C₄×C₁₃	—	2	2	no	—
242	C₂×C₄×C₁₃	—	2	2	no	—
243	C₂×C₄×C₁₃	—	2	2	no	—
244	C₂×C₄×C₁₃	—	2	4	no	—
245	C₂×C₄×C₁₃	—	2	4	no	—
246	C₂×C₄×C₁₃	—	4	4	no	—
247	C₂×C₄×C₁₃	—	4	4	no	—
248	C₂×C₄×C₁₃	—	4	8	no	—
249	C₂×C₄×C₁₃	—	4	8	no	—
250	C₂×C₄×C₁₃	C₄×D₄	1	16	yes	—
251	C₂×C₄×C₁₃	C₂³×C₄	1	8	yes	—
252	C₂×C₄×C₁₃	C₂³×C₄	1	8	yes	—
253	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
254	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
255	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
256	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
257	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
258	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
259	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
260	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
261	C₂×C₂²⋊Q₈	C₄×C₁₃	1	16	yes	complemented
262	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	8	yes	—
263	C₂×C₄×Q₈	—	2	8	no	—
264	C₂×C₄×Q₈	C₂²×C₁₃	1	8	yes	complemented
265	C₂×#117	—	2	8	no	—
266	C₂×#117	C₂²×C₁₃	1	8	yes	—
267	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
268	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
269	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
270	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
271	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
272	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
273	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
274	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
275	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
276	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
277	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
278	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
279	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
280	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
281	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
282	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
283	#391	C₂²×C₁₃	1	8	yes	complemented
284	#389	C₂²×C₁₃	1	16	yes	complemented
285	#389	C₂²×C₁₃	1	8	yes	complemented
286	#388	C₂²×C₁₃	1	16	yes	—
287	#388	C₂²×C₁₃	1	16	yes	—
288	#387	C₂²×C₁₃	1	16	yes	complemented
289	#380	C₂²×C₁₃	1	8	yes	—
290	C₄×C₄⋊C₄	C₂²×C₁₃	1	8	yes	complemented
291	C₂×#95	C₂²×C₁₃	1	2	yes	—
292	C₂×#95	C₂²×C₁₃	1	2	yes	—
293	C₂×#95	C₂²×C₁₃	1	2	yes	—
294	C₂×#95	C₂²×C₁₃	1	2	yes	—
295	C₂×#95	C₂²×C₁₃	1	2	yes	—
296	C₂²×C₁₃	—	2	4	no	—
297	C₂²×C₁₃	—	2	4	no	—
298	C₂²×C₁₃	—	2	4	no	—
299	C₂²×C₁₃	—	4	16	no	—
300	C₂²×C₁₃	—	4	2	no	—
301	C₂²×C₁₃	—	4	2	no	—
302	C₂²×C₁₃	—	4	2	no	—
303	C₂²×C₁₃	—	4	2	no	—
304	C₂²×C₁₃	C₂×C₄×D₄	1	4	yes	—
305	C₂²×C₁₃	#519	1	4	yes	—
306	C₂²×C₁₃	#520	1	4	yes	—
307	C₂²×C₁₃	#536	1	4	yes	—
308	C₂²×C₁₃	#537	1	4	yes	—
309	C₂²×C₁₃	#541	1	4	yes	—
310	C₂²×C₁₃	#542	1	4	yes	—
311	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
312	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
313	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
314	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
315	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
316	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
317	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
318	C₄×C₁₃	—	2	4	no	—
319	C₄×C₁₃	—	2	8	no	—
320	C₄×C₁₃	—	2	8	no	—
321	C₄×C₁₃	—	2	4	no	—
322	C₄×C₁₃	—	2	4	no	—
323	C₄×C₁₃	—	4	2	no	—
324	C₄×C₁₃	—	4	2	no	—
325	C₄×C₁₃	—	4	4	no	—
326	C₄×C₁₃	—	4	4	no	—
327	C₄×C₁₃	C₂×C₄×D₄	1	8	yes	—
328	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
329	C₂²×Q₈	—	2	4	no	—
330	C₂²×Q₈	—	2	4	no	—
331	C₂²×Q₈	C₂×C₄×C₁₃	1	8	yes	—
332	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
333	C₂³×C₄	—	2	4	no	—
334	C₂³×C₄	—	2	4	no	—
335	C₂³×C₄	C₂×C₄×C₁₃	1	8	yes	—
336	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
337	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
338	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
339	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
340	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
341	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
342	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
343	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
344	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
345	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
346	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
347	C₂²⋊Q₈	C₂×C₄×C₁₃	1	64	yes	complemented
348	C₄×Q₈	—	2	32	no	—
349	#117	—	2	32	no	—
350	C₂×C₄⋊C₄	—	2	4	no	—
351	C₂×C₄⋊C₄	—	2	4	no	—
352	C₂×C₄⋊C₄	—	2	8	no	—
353	C₂×C₄⋊C₄	—	2	4	no	—
354	C₂×C₄⋊C₄	—	2	4	no	—
355	C₂×C₄⋊C₄	—	4	4	no	—
356	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	8	yes	—
357	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	16	yes	—
358	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
359	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
360	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
361	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
362	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
363	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
364	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
365	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
366	C₂×C₂²⋊C₄	—	2	4	no	—
367	C₂×C₂²⋊C₄	—	2	4	no	—
368	C₂×C₂²⋊C₄	—	4	4	no	—
369	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	16	yes	—
370	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
371	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
372	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
373	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
374	C₂×C₄²	—	2	4	no	—
375	C₂×C₄²	—	2	8	no	—
376	C₂×C₄²	—	4	4	no	—
377	C₂×C₄²	D₄×C₁₃	1	8	yes	—
378	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
379	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
380	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
381	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
382	#95	C₂³×C₁₃	1	8	yes	—
383	#95	C₂³×C₁₃	1	8	yes	—
384	#95	C₂³×C₁₃	1	8	yes	—
385	#95	C₂³×C₁₃	1	8	yes	—
386	#95	C₂³×C₁₃	1	8	yes	—
387	C₂×C₁₃	—	4	4	no	—
388	C₂×C₁₃	#2323	1	8	yes	direct product factor
389	C₂×C₁₃	C₂²×C₄×D₄	1	1	yes	characteristic
390	C₂×C₁₃	C₂×#519	1	1	yes	characteristic
391	C₂×C₁₃	C₂×#520	1	1	yes	characteristic
392	C₂×C₁₃	C₂×#536	1	1	yes	characteristic
393	C₂×C₁₃	C₂×#537	1	1	yes	characteristic
394	C₂×C₁₃	C₂×#541	1	1	yes	characteristic
395	C₂×C₁₃	C₂×#542	1	1	yes	characteristic
396	C₂⁴	—	2	2	no	—
397	C₂⁴	—	2	2	no	—
398	C₂⁴	—	2	2	no	—
399	C₂⁴	—	2	2	no	—
400	C₂⁴	—	2	2	no	—
401	C₂⁴	—	2	2	no	—
402	C₂⁴	C₂²×C₄×C₁₃	1	4	yes	—
403	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
404	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
405	C₂×Q₈	—	2	32	no	—
406	C₂×Q₈	—	2	8	no	—
407	C₂×Q₈	—	2	8	no	—
408	C₂×Q₈	C₂²×C₄×C₁₃	1	16	yes	—
409	C₂²×C₄	—	2	4	no	—
410	C₂²×C₄	—	2	2	no	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	4	no	—
413	C₂²×C₄	—	2	2	no	—
414	C₂²×C₄	—	2	4	no	—
415	C₂²×C₄	—	2	4	no	—
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	—	2	2	no	—
418	C₂²×C₄	—	2	2	no	—
419	C₂²×C₄	—	2	32	no	—
420	C₂²×C₄	—	2	8	no	—
421	C₂²×C₄	—	2	8	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	—	2	4	no	—
425	C₂²×C₄	—	2	4	no	—
426	C₂²×C₄	—	2	4	no	—
427	C₂²×C₄	—	2	4	no	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	—	2	2	no	—
432	C₂²×C₄	—	2	4	no	—
433	C₂²×C₄	—	2	4	no	—
434	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
435	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
436	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
437	C₂²×C₄	C₂²×C₄×C₁₃	1	16	yes	—
438	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
439	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
440	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
441	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
442	C₂²×C₄	C₁₃×#41	1	4	yes	—
443	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
444	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
445	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
446	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
447	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
448	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
449	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
450	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
451	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
452	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
453	C₄⋊C₄	—	2	8	no	—
454	C₄⋊C₄	—	2	8	no	—
455	C₄⋊C₄	—	2	16	no	—
456	C₄⋊C₄	—	2	8	no	—
457	C₄⋊C₄	—	2	8	no	—
458	C₄⋊C₄	—	4	8	no	—
459	C₄⋊C₄	C₂²×C₄×C₁₃	1	16	yes	—
460	C₄⋊C₄	C₂²×C₄×C₁₃	1	32	yes	—
461	C₂²⋊C₄	—	2	8	no	—
462	C₂²⋊C₄	—	2	8	no	—
463	C₂²⋊C₄	—	4	8	no	—
464	C₂²⋊C₄	C₂²×C₄×C₁₃	1	32	yes	—
465	C₄²	—	2	8	no	—
466	C₄²	—	2	16	no	—
467	C₄²	—	4	8	no	—
468	C₄²	C₂×D₄×C₁₃	1	16	yes	—
469	C₁₃	C₂×#2323	1	1	yes	characteristic, direct product factor, Sylow
470	C₂³	—	2	8	no	—
471	C₂³	—	2	8	no	—
472	C₂³	—	2	8	no	—
473	C₂³	—	2	2	no	—
474	C₂³	—	2	2	no	—
475	C₂³	—	2	2	no	—
476	C₂³	—	2	2	no	—
477	C₂³	—	2	2	no	—
478	C₂³	—	2	2	no	—
479	C₂³	—	4	4	no	—
480	C₂³	—	4	4	no	—
481	C₂³	—	4	4	no	—
482	C₂³	—	4	4	no	—
483	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
484	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
485	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
486	C₂³	C₂×C₁₃×#41	1	2	yes	—
487	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
488	C₂³	C₁₃×2₋¹⁺⁴	1	2	yes	—
489	C₂³	C₁₃×2₋¹⁺⁴	1	2	yes	—
490	C₂³	C₁₃×2₋¹⁺⁴	1	2	yes	—
491	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
492	Q₈	—	2	32	no	—
493	C₂×C₄	—	2	8	no	—
494	C₂×C₄	—	2	16	no	—
495	C₂×C₄	—	2	16	no	—
496	C₂×C₄	—	2	8	no	—
497	C₂×C₄	—	2	8	no	—
498	C₂×C₄	—	2	4	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	4	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	4	no	—
504	C₂×C₄	—	2	4	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	32	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	4	no	—
512	C₂×C₄	—	2	4	no	—
513	C₂×C₄	—	2	4	no	—
514	C₂×C₄	—	2	4	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	4	no	—
520	C₂×C₄	—	2	4	no	—
521	C₂×C₄	—	4	4	no	—
522	C₂×C₄	—	4	4	no	—
523	C₂×C₄	—	4	8	no	—
524	C₂×C₄	—	4	8	no	—
525	C₂×C₄	C₄×D₄×C₁₃	1	16	yes	—
526	C₂×C₄	C₂³×C₄×C₁₃	1	8	yes	—
527	C₂×C₄	C₂³×C₄×C₁₃	1	8	yes	—
528	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
529	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
530	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
531	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
532	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
533	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
534	C₂²	—	2	4	no	—
535	C₂²	—	2	4	no	—
536	C₂²	—	2	4	no	—
537	C₂²	—	4	16	no	—
538	C₂²	—	4	2	no	—
539	C₂²	—	4	2	no	—
540	C₂²	—	4	2	no	—
541	C₂²	—	4	2	no	—
542	C₂²	C₂×C₄×D₄×C₁₃	1	4	yes	—
543	C₂²	C₁₃×#519	1	4	yes	—
544	C₂²	C₁₃×#520	1	4	yes	—
545	C₂²	C₁₃×#536	1	4	yes	—
546	C₂²	C₁₃×#537	1	4	yes	—
547	C₂²	C₁₃×#541	1	4	yes	—
548	C₂²	C₁₃×#542	1	4	yes	—
549	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
550	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
551	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
552	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
553	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
554	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
555	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
556	C₄	—	2	4	no	—
557	C₄	—	2	8	no	—
558	C₄	—	2	8	no	—
559	C₄	—	2	4	no	—
560	C₄	—	2	4	no	—
561	C₄	—	4	2	no	—
562	C₄	—	4	2	no	—
563	C₄	—	4	4	no	—
564	C₄	—	4	4	no	—
565	C₄	C₂×C₄×D₄×C₁₃	1	8	yes	—
566	C₂	—	4	4	no	—
567	C₂	C₁₃×#2323	1	8	yes	direct product factor
568	C₂	C₂²×C₄×D₄×C₁₃	1	1	yes	characteristic
569	C₂	C₂×C₁₃×#519	1	1	yes	characteristic
570	C₂	C₂×C₁₃×#520	1	1	yes	characteristic
571	C₂	C₂×C₁₃×#536	1	1	yes	characteristic
572	C₂	C₂×C₁₃×#537	1	1	yes	characteristic
573	C₂	C₂×C₁₃×#541	1	1	yes	characteristic
574	C₂	C₂×C₁₃×#542	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₃	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₁₃
Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂⁵×C₁₃	C₂³
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄×Q₈×C₁₃	C₂	semidirect
4. C₁₃×#2323	C₂	direct (N × H)
5. C₂×C₁₃×#391	C₂	semidirect
6. C₂×C₁₃×#389	C₂	semidirect
7. C₂×C₁₃×#389	C₂	semidirect
10. C₂×C₁₃×#387	C₂	semidirect
12. C₂×C₄×C₁₃×C₄⋊C₄	C₂	semidirect
15. C₂×C₁₃×C₂²⋊Q₈	C₄	semidirect
18. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
37. C₁₃×#391	C₂²	semidirect
38. C₁₃×#389	C₂²	semidirect
39. C₁₃×#389	C₂²	semidirect
42. C₁₃×#387	C₂²	semidirect
44. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
69. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
109. C₂×#2323	C₁₃	direct (N × H)
184. C₂²×C₄×Q₈	C₂×C₁₃	semidirect
186. #2323	C₂×C₁₃	direct (N × H)
187. C₂×#391	C₂×C₁₃	semidirect
188. C₂×#389	C₂×C₁₃	semidirect
189. C₂×#389	C₂×C₁₃	semidirect
192. C₂×#387	C₂×C₁₃	semidirect
194. C₂×C₄×C₄⋊C₄	C₂×C₁₃	semidirect
261. C₂×C₂²⋊Q₈	C₄×C₁₃	semidirect
264. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
283. #391	C₂²×C₁₃	semidirect
284. #389	C₂²×C₁₃	semidirect
285. #389	C₂²×C₁₃	semidirect
288. #387	C₂²×C₁₃	semidirect
290. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
347. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
388. C₂×C₁₃	#2323	direct (N × H)
469. C₁₃	C₂×#2323	direct (N × H)
567. C₂	C₁₃×#2323	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×C₂²⋊Q₈	2
C₂²×C₄×Q₈×C₁₃	2
C₂²×C₁₃×#117	2
C₁₃×#2323	2
C₂×C₁₃×#391	2
C₂×C₁₃×#389	2
C₂×C₁₃×#388	2
C₂×C₁₃×#387	2
C₂×C₁₃×#380	2
C₂×C₄×C₁₃×C₄⋊C₄	2
C₂×#2323	13

Subgroups — C2×C13×#2323 #15720402

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2323 #15720402