Subgroups — C₂×C₁₃×#3455 #15749024

Order 3328.

7302 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	C₁₃×#3455	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₁₃×#542	C₂	1	4	yes	maximal, complemented
3	C₂×C₁₃×#541	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₃×#540	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×#539	C₂	1	4	yes	maximal, complemented
6	C₂×C₁₃×#538	C₂	1	4	yes	maximal, complemented
7	C₂×C₁₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#529	C₂	1	8	yes	maximal, complemented
10	C₂×C₁₃×#525	C₂	1	2	yes	maximal, complemented
11	C₂×C₄×C₁₃×#41	C₂	1	2	yes	maximal, complemented
12	C₂²×C₁₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₁₃×#41	C₂²	1	2	yes	—
14	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
15	C₁₃×#542	C₂²	1	64	yes	complemented
16	C₁₃×#541	C₂²	1	32	yes	complemented
17	C₁₃×#540	C₂²	1	32	yes	complemented
18	C₁₃×#539	C₂²	1	64	yes	complemented
19	C₁₃×#538	C₂²	1	64	yes	complemented
20	C₁₃×#533	C₂²	1	16	yes	complemented
21	C₁₃×#532	C₂²	1	16	yes	complemented
22	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
24	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic, complemented
25	C₁₃×#529	C₂²	1	128	yes	complemented
26	C₂×C₁₃×#126	C₂²	1	8	yes	—
27	C₂×C₁₃×#126	C₂²	1	8	yes	complemented
28	C₂×C₁₃×#125	C₂²	1	8	yes	complemented
29	C₂×C₁₃×#125	C₂²	1	2	yes	complemented
30	C₂×C₁₃×#124	C₂²	1	8	yes	—
31	C₂×C₁₃×#124	C₂²	1	2	yes	complemented
32	C₁₃×#525	C₂²	1	32	yes	complemented
33	C₂×C₁₃×#123	C₂²	1	4	yes	—
34	C₂×C₁₃×#123	C₂²	1	8	yes	—
35	C₂×C₁₃×#123	C₂²	1	8	yes	complemented
36	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
37	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
38	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	8	yes	complemented
39	C₂×C₁₃×#121	C₂²	1	4	yes	—
40	C₂×C₁₃×#121	C₂²	1	8	yes	—
41	C₂×C₁₃×#121	C₂²	1	4	yes	—
42	C₂×C₁₃×#120	C₂²	1	4	yes	—
43	C₄×C₁₃×#41	C₂²	1	32	yes	complemented
44	C₂×C₄×Q₈×C₁₃	C₂²	1	4	yes	complemented
45	C₂×C₄×Q₈×C₁₃	C₂²	1	4	yes	complemented
46	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	—
47	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	—
48	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
49	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
50	C₂×C₁₃×#117	C₂²	1	4	yes	—
51	C₂×C₁₃×#117	C₂²	1	2	yes	—
52	C₂×C₁₃×#117	C₂²	1	2	yes	—
53	C₂×C₁₃×#117	C₂²	1	2	yes	—
54	C₂×C₁₃×#117	C₂²	1	16	yes	complemented
55	C₂×C₁₃×#117	C₂²	1	4	yes	complemented
56	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
57	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
58	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
59	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
60	C₂²×C₄²×C₁₃	C₂²	1	4	yes	complemented
61	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
62	C₂×C₁₃×#41	—	2	16	no	—
63	C₂×C₁₃×#41	C₂³	1	16	yes	—
64	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
65	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
66	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
67	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
68	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
69	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
70	C₂³×C₄×C₁₃	—	2	8	no	—
71	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
73	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
74	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
75	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
76	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
77	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
78	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
79	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
80	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	complemented
81	C₁₃×C₄⋊Q₈	C₂³	1	16	yes	complemented
82	C₁₃×#127	C₂³	1	8	yes	complemented
83	C₁₃×#126	C₂³	1	64	yes	—
84	C₁₃×#126	C₂³	1	64	yes	complemented
85	C₁₃×#125	C₂³	1	64	yes	complemented
86	C₁₃×#125	C₂³	1	16	yes	complemented
87	C₁₃×#124	C₂³	1	64	yes	—
88	C₁₃×#124	C₂³	1	16	yes	complemented
89	C₁₃×#123	C₂³	1	32	yes	—
90	C₁₃×#123	C₂³	1	64	yes	—
91	C₁₃×#123	C₂³	1	64	yes	complemented
92	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	—
93	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	—
94	C₁₃×C₂²⋊Q₈	C₂³	1	64	yes	complemented
95	C₁₃×#121	C₂³	1	32	yes	—
96	C₁₃×#121	C₂³	1	64	yes	—
97	C₁₃×#121	C₂³	1	32	yes	—
98	C₁₃×#120	C₂³	1	32	yes	—
99	C₄×Q₈×C₁₃	C₂³	1	32	yes	complemented
100	C₄×Q₈×C₁₃	C₂³	1	32	yes	complemented
101	C₄×D₄×C₁₃	C₂³	1	64	yes	—
102	C₄×D₄×C₁₃	C₂³	1	64	yes	—
103	C₄×D₄×C₁₃	C₂³	1	32	yes	complemented
104	C₄×D₄×C₁₃	C₂³	1	32	yes	complemented
105	C₁₃×#117	C₂³	1	32	yes	—
106	C₁₃×#117	C₂³	1	16	yes	—
107	C₁₃×#117	C₂³	1	16	yes	—
108	C₁₃×#117	C₂³	1	16	yes	—
109	C₁₃×#117	C₂³	1	32	yes	complemented
110	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
111	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
112	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	yes	—
113	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
114	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
115	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
116	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
117	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
118	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
119	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
120	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
121	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
122	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
123	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
124	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
125	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
126	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
127	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
128	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
129	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
130	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
131	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
132	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
133	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
134	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
135	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
136	C₂×C₄²×C₁₃	C₂³	1	32	yes	complemented
137	C₂×#3455	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
138	C₂⁴×C₁₃	—	2	4	no	—
139	C₂⁴×C₁₃	—	4	4	no	—
140	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
141	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
142	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
143	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
144	C₁₃×#41	—	2	64	no	—
145	C₂×Q₈×C₁₃	—	2	8	no	—
146	C₂×Q₈×C₁₃	—	4	8	no	—
147	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
148	C₂×Q₈×C₁₃	C₂⁴	1	16	yes	—
149	C₂×D₄×C₁₃	—	2	16	no	—
150	C₂×D₄×C₁₃	—	2	8	no	—
151	C₂×D₄×C₁₃	—	4	8	no	—
152	C₂×D₄×C₁₃	—	4	16	no	—
153	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
154	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
155	C₂×D₄×C₁₃	C₂⁴	1	32	yes	—
156	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
157	C₂²×C₄×C₁₃	—	2	4	no	—
158	C₂²×C₄×C₁₃	—	2	8	no	—
159	C₂²×C₄×C₁₃	—	2	8	no	—
160	C₂²×C₄×C₁₃	—	2	32	no	—
161	C₂²×C₄×C₁₃	—	2	16	no	—
162	C₂²×C₄×C₁₃	—	4	4	no	—
163	C₂²×C₄×C₁₃	—	4	16	no	—
164	C₂²×C₄×C₁₃	—	4	4	no	—
165	C₂²×C₄×C₁₃	#41	1	8	yes	—
166	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
167	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
168	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
169	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
170	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
171	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
172	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
173	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
174	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
175	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
176	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
177	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
178	C₂²×C₄×C₁₃	C₂⁴	1	32	yes	—
179	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
180	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
181	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
182	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
183	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
184	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
185	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	—
186	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	—
187	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
188	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	—
189	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
190	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
191	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
192	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
193	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
194	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
195	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
196	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
197	C₄²×C₁₃	C₂⁴	1	8	yes	—
198	C₄²×C₁₃	C₂⁴	1	8	yes	—
199	C₄²×C₁₃	C₂⁴	1	8	yes	—
200	C₄²×C₁₃	C₂⁴	1	4	yes	—
201	C₄²×C₁₃	C₂⁴	1	4	yes	—
202	C₄²×C₁₃	C₂⁴	1	16	yes	—
203	C₄²×C₁₃	C₂⁴	1	32	yes	—
204	#3455	C₂×C₁₃	1	32	yes	direct product factor
205	C₂×#542	C₂×C₁₃	1	4	yes	complemented
206	C₂×#541	C₂×C₁₃	1	2	yes	complemented
207	C₂×#540	C₂×C₁₃	1	2	yes	complemented
208	C₂×#539	C₂×C₁₃	1	4	yes	complemented
209	C₂×#538	C₂×C₁₃	1	4	yes	complemented
210	C₂×#533	C₂×C₁₃	1	1	yes	characteristic, complemented
211	C₂×#532	C₂×C₁₃	1	1	yes	characteristic, complemented
212	C₂×#529	C₂×C₁₃	1	8	yes	complemented
213	C₂×#525	C₂×C₁₃	1	2	yes	complemented
214	C₂×C₄×#41	C₂×C₁₃	1	2	yes	complemented
215	C₂²×#117	C₂×C₁₃	1	1	yes	characteristic, complemented
216	C₂³×C₁₃	—	2	4	no	—
217	C₂³×C₁₃	—	2	8	no	—
218	C₂³×C₁₃	—	2	4	no	—
219	C₂³×C₁₃	—	2	8	no	—
220	C₂³×C₁₃	—	2	16	no	—
221	C₂³×C₁₃	—	2	8	no	—
222	C₂³×C₁₃	—	4	8	no	—
223	C₂³×C₁₃	—	4	16	no	—
224	C₂³×C₁₃	C₂×#41	1	4	yes	—
225	C₂³×C₁₃	C₂⁵	1	4	yes	—
226	C₂³×C₁₃	C₂⁵	1	8	yes	—
227	C₂³×C₁₃	C₂⁵	1	2	yes	—
228	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
229	Q₈×C₁₃	—	2	16	no	—
230	Q₈×C₁₃	—	4	16	no	—
231	D₄×C₁₃	—	2	32	no	—
232	D₄×C₁₃	—	2	16	no	—
233	D₄×C₁₃	—	4	16	no	—
234	D₄×C₁₃	—	4	32	no	—
235	C₂×C₄×C₁₃	—	2	8	no	—
236	C₂×C₄×C₁₃	—	2	4	no	—
237	C₂×C₄×C₁₃	—	2	8	no	—
238	C₂×C₄×C₁₃	—	2	8	no	—
239	C₂×C₄×C₁₃	—	2	4	no	—
240	C₂×C₄×C₁₃	—	2	16	no	—
241	C₂×C₄×C₁₃	—	2	4	no	—
242	C₂×C₄×C₁₃	—	2	16	no	—
243	C₂×C₄×C₁₃	—	2	16	no	—
244	C₂×C₄×C₁₃	—	2	32	no	—
245	C₂×C₄×C₁₃	—	4	8	no	—
246	C₂×C₄×C₁₃	—	4	32	no	—
247	C₂×C₄×C₁₃	—	4	8	no	—
248	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
249	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
250	C₂×C₄×C₁₃	C₂×#41	1	16	yes	—
251	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
252	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
253	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
254	C₂×C₄×C₁₃	C₂⁵	1	16	yes	—
255	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
256	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
257	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
258	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
259	C₂²×#41	C₂²×C₁₃	1	2	yes	—
260	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
261	#542	C₂²×C₁₃	1	64	yes	complemented
262	#541	C₂²×C₁₃	1	32	yes	complemented
263	#540	C₂²×C₁₃	1	32	yes	complemented
264	#539	C₂²×C₁₃	1	64	yes	complemented
265	#538	C₂²×C₁₃	1	64	yes	complemented
266	#533	C₂²×C₁₃	1	16	yes	complemented
267	#532	C₂²×C₁₃	1	16	yes	complemented
268	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
269	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
270	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic, complemented
271	#529	C₂²×C₁₃	1	128	yes	complemented
272	C₂×#126	C₂²×C₁₃	1	8	yes	—
273	C₂×#126	C₂²×C₁₃	1	8	yes	complemented
274	C₂×#125	C₂²×C₁₃	1	8	yes	complemented
275	C₂×#125	C₂²×C₁₃	1	2	yes	complemented
276	C₂×#124	C₂²×C₁₃	1	8	yes	—
277	C₂×#124	C₂²×C₁₃	1	2	yes	complemented
278	#525	C₂²×C₁₃	1	32	yes	complemented
279	C₂×#123	C₂²×C₁₃	1	4	yes	—
280	C₂×#123	C₂²×C₁₃	1	8	yes	—
281	C₂×#123	C₂²×C₁₃	1	8	yes	complemented
282	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
283	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
284	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	8	yes	complemented
285	C₂×#121	C₂²×C₁₃	1	4	yes	—
286	C₂×#121	C₂²×C₁₃	1	8	yes	—
287	C₂×#121	C₂²×C₁₃	1	4	yes	—
288	C₂×#120	C₂²×C₁₃	1	4	yes	—
289	C₄×#41	C₂²×C₁₃	1	32	yes	complemented
290	C₂×C₄×Q₈	C₂²×C₁₃	1	4	yes	complemented
291	C₂×C₄×Q₈	C₂²×C₁₃	1	4	yes	complemented
292	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	—
293	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	—
294	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
295	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
296	C₂×#117	C₂²×C₁₃	1	4	yes	—
297	C₂×#117	C₂²×C₁₃	1	2	yes	—
298	C₂×#117	C₂²×C₁₃	1	2	yes	—
299	C₂×#117	C₂²×C₁₃	1	2	yes	—
300	C₂×#117	C₂²×C₁₃	1	16	yes	complemented
301	C₂×#117	C₂²×C₁₃	1	4	yes	complemented
302	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
303	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
304	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
305	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
306	C₂²×C₄²	C₂²×C₁₃	1	4	yes	complemented
307	C₂²×C₁₃	—	2	4	no	—
308	C₂²×C₁₃	—	2	8	no	—
309	C₂²×C₁₃	—	2	4	no	—
310	C₂²×C₁₃	—	2	8	no	—
311	C₂²×C₁₃	—	2	16	no	—
312	C₂²×C₁₃	—	2	8	no	—
313	C₂²×C₁₃	—	4	16	no	—
314	C₂²×C₁₃	—	4	16	no	—
315	C₂²×C₁₃	—	4	8	no	—
316	C₂²×C₁₃	C₂²×#41	1	4	yes	—
317	C₂²×C₁₃	C₂²×#41	1	2	yes	—
318	C₂²×C₁₃	#585	1	4	yes	—
319	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
320	C₄×C₁₃	—	2	4	no	—
321	C₄×C₁₃	—	2	8	no	—
322	C₄×C₁₃	—	2	8	no	—
323	C₄×C₁₃	—	2	4	no	—
324	C₄×C₁₃	—	2	16	no	—
325	C₄×C₁₃	—	2	4	no	—
326	C₄×C₁₃	C₂²×#41	1	4	yes	—
327	C₄×C₁₃	C₂²×#41	1	4	yes	—
328	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
329	C₂×#41	—	2	16	no	—
330	C₂×#41	C₂³×C₁₃	1	16	yes	—
331	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
332	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
333	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
334	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
335	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
336	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
337	C₂³×C₄	—	2	8	no	—
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	8	yes	—
342	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
343	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
344	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
345	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
346	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
347	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	complemented
348	C₄⋊Q₈	C₂³×C₁₃	1	16	yes	complemented
349	#127	C₂³×C₁₃	1	8	yes	complemented
350	#126	C₂³×C₁₃	1	64	yes	—
351	#126	C₂³×C₁₃	1	64	yes	complemented
352	#125	C₂³×C₁₃	1	64	yes	complemented
353	#125	C₂³×C₁₃	1	16	yes	complemented
354	#124	C₂³×C₁₃	1	64	yes	—
355	#124	C₂³×C₁₃	1	16	yes	complemented
356	#123	C₂³×C₁₃	1	32	yes	—
357	#123	C₂³×C₁₃	1	64	yes	—
358	#123	C₂³×C₁₃	1	64	yes	complemented
359	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	—
360	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	—
361	C₂²⋊Q₈	C₂³×C₁₃	1	64	yes	complemented
362	#121	C₂³×C₁₃	1	32	yes	—
363	#121	C₂³×C₁₃	1	64	yes	—
364	#121	C₂³×C₁₃	1	32	yes	—
365	#120	C₂³×C₁₃	1	32	yes	—
366	C₄×Q₈	C₂³×C₁₃	1	32	yes	complemented
367	C₄×Q₈	C₂³×C₁₃	1	32	yes	complemented
368	C₄×D₄	C₂³×C₁₃	1	64	yes	—
369	C₄×D₄	C₂³×C₁₃	1	64	yes	—
370	C₄×D₄	C₂³×C₁₃	1	32	yes	complemented
371	C₄×D₄	C₂³×C₁₃	1	32	yes	complemented
372	#117	C₂³×C₁₃	1	32	yes	—
373	#117	C₂³×C₁₃	1	16	yes	—
374	#117	C₂³×C₁₃	1	16	yes	—
375	#117	C₂³×C₁₃	1	16	yes	—
376	#117	C₂³×C₁₃	1	32	yes	complemented
377	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
378	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
379	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	yes	—
380	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
381	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
382	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
383	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
384	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
385	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
386	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
387	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
388	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
389	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
390	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
391	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
392	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
393	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
394	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
395	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
396	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
397	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
398	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
399	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
400	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
401	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
402	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
403	C₂×C₄²	C₂³×C₁₃	1	32	yes	complemented
404	C₂×C₁₃	—	2	4	no	—
405	C₂×C₁₃	—	4	8	no	—
406	C₂×C₁₃	—	4	4	no	—
407	C₂×C₁₃	#3455	1	4	yes	direct product factor
408	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
409	C₂×C₁₃	C₂×#585	1	2	yes	—
410	C₂⁴	—	2	4	no	—
411	C₂⁴	—	4	4	no	—
412	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
413	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
414	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
415	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
416	#41	—	2	64	no	—
417	C₂×Q₈	—	2	8	no	—
418	C₂×Q₈	—	4	8	no	—
419	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
420	C₂×Q₈	C₂⁴×C₁₃	1	16	yes	—
421	C₂×D₄	—	2	16	no	—
422	C₂×D₄	—	2	8	no	—
423	C₂×D₄	—	4	8	no	—
424	C₂×D₄	—	4	16	no	—
425	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
426	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
427	C₂×D₄	C₂⁴×C₁₃	1	32	yes	—
428	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
429	C₂²×C₄	—	2	4	no	—
430	C₂²×C₄	—	2	8	no	—
431	C₂²×C₄	—	2	8	no	—
432	C₂²×C₄	—	2	32	no	—
433	C₂²×C₄	—	2	16	no	—
434	C₂²×C₄	—	4	4	no	—
435	C₂²×C₄	—	4	16	no	—
436	C₂²×C₄	—	4	4	no	—
437	C₂²×C₄	C₁₃×#41	1	8	yes	—
438	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
439	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
440	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
441	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
442	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
443	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
444	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
445	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
446	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
447	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
448	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
449	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
450	C₂²×C₄	C₂⁴×C₁₃	1	32	yes	—
451	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
452	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
453	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
454	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
455	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
456	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
457	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	—
458	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	—
459	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
460	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	—
461	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
462	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
463	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
464	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
465	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
466	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
467	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
468	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
469	C₄²	C₂⁴×C₁₃	1	8	yes	—
470	C₄²	C₂⁴×C₁₃	1	8	yes	—
471	C₄²	C₂⁴×C₁₃	1	8	yes	—
472	C₄²	C₂⁴×C₁₃	1	4	yes	—
473	C₄²	C₂⁴×C₁₃	1	4	yes	—
474	C₄²	C₂⁴×C₁₃	1	16	yes	—
475	C₄²	C₂⁴×C₁₃	1	32	yes	—
476	C₁₃	C₂×#3455	1	1	yes	characteristic, direct product factor, Sylow
477	C₂³	—	2	4	no	—
478	C₂³	—	2	8	no	—
479	C₂³	—	2	4	no	—
480	C₂³	—	2	8	no	—
481	C₂³	—	2	16	no	—
482	C₂³	—	2	8	no	—
483	C₂³	—	4	8	no	—
484	C₂³	—	4	16	no	—
485	C₂³	C₂×C₁₃×#41	1	4	yes	—
486	C₂³	C₂⁵×C₁₃	1	4	yes	—
487	C₂³	C₂⁵×C₁₃	1	8	yes	—
488	C₂³	C₂⁵×C₁₃	1	2	yes	—
489	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
490	Q₈	—	2	16	no	—
491	Q₈	—	4	16	no	—
492	D₄	—	2	32	no	—
493	D₄	—	2	16	no	—
494	D₄	—	4	16	no	—
495	D₄	—	4	32	no	—
496	C₂×C₄	—	2	8	no	—
497	C₂×C₄	—	2	4	no	—
498	C₂×C₄	—	2	8	no	—
499	C₂×C₄	—	2	8	no	—
500	C₂×C₄	—	2	4	no	—
501	C₂×C₄	—	2	16	no	—
502	C₂×C₄	—	2	4	no	—
503	C₂×C₄	—	2	16	no	—
504	C₂×C₄	—	2	16	no	—
505	C₂×C₄	—	2	32	no	—
506	C₂×C₄	—	4	8	no	—
507	C₂×C₄	—	4	32	no	—
508	C₂×C₄	—	4	8	no	—
509	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
510	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
511	C₂×C₄	C₂×C₁₃×#41	1	16	yes	—
512	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
513	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
514	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
515	C₂×C₄	C₂⁵×C₁₃	1	16	yes	—
516	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
517	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
518	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
519	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
520	C₂²	—	2	4	no	—
521	C₂²	—	2	8	no	—
522	C₂²	—	2	4	no	—
523	C₂²	—	2	8	no	—
524	C₂²	—	2	16	no	—
525	C₂²	—	2	8	no	—
526	C₂²	—	4	16	no	—
527	C₂²	—	4	16	no	—
528	C₂²	—	4	8	no	—
529	C₂²	C₂²×C₁₃×#41	1	4	yes	—
530	C₂²	C₂²×C₁₃×#41	1	2	yes	—
531	C₂²	C₁₃×#585	1	4	yes	—
532	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
533	C₄	—	2	4	no	—
534	C₄	—	2	8	no	—
535	C₄	—	2	8	no	—
536	C₄	—	2	4	no	—
537	C₄	—	2	16	no	—
538	C₄	—	2	4	no	—
539	C₄	C₂²×C₁₃×#41	1	4	yes	—
540	C₄	C₂²×C₁₃×#41	1	4	yes	—
541	C₂	—	2	4	no	—
542	C₂	—	4	4	no	—
543	C₂	—	4	8	no	—
544	C₂	C₁₃×#3455	1	4	yes	direct product factor
545	C₂	C₂³×C₁₃×#41	1	1	yes	characteristic
546	C₂	C₂×C₁₃×#585	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₃
socle	C₂³×C₁₃	C₂⁵
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3455	C₂	direct (N × H)
2. C₂×C₁₃×#542	C₂	semidirect
3. C₂×C₁₃×#541	C₂	semidirect
4. C₂×C₁₃×#540	C₂	semidirect
5. C₂×C₁₃×#539	C₂	semidirect
6. C₂×C₁₃×#538	C₂	semidirect
7. C₂×C₁₃×#533	C₂	semidirect
8. C₂×C₁₃×#532	C₂	semidirect
9. C₂×C₁₃×#529	C₂	semidirect
10. C₂×C₁₃×#525	C₂	semidirect
11. C₂×C₄×C₁₃×#41	C₂	semidirect
12. C₂²×C₁₃×#117	C₂	semidirect
15. C₁₃×#542	C₂²	semidirect
16. C₁₃×#541	C₂²	semidirect
17. C₁₃×#540	C₂²	semidirect
18. C₁₃×#539	C₂²	semidirect
19. C₁₃×#538	C₂²	semidirect
20. C₁₃×#533	C₂²	semidirect
21. C₁₃×#532	C₂²	semidirect
22. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
23. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
24. C₂×C₁₃×#127	C₂²	semidirect
25. C₁₃×#529	C₂²	semidirect
27. C₂×C₁₃×#126	C₂²	semidirect
28. C₂×C₁₃×#125	C₂²	semidirect
29. C₂×C₁₃×#125	C₂²	semidirect
31. C₂×C₁₃×#124	C₂²	semidirect
32. C₁₃×#525	C₂²	semidirect
35. C₂×C₁₃×#123	C₂²	semidirect
38. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
43. C₄×C₁₃×#41	C₂²	semidirect
44. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
45. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
48. C₂×C₄×D₄×C₁₃	C₂²	semidirect
49. C₂×C₄×D₄×C₁₃	C₂²	semidirect
54. C₂×C₁₃×#117	C₂²	semidirect
55. C₂×C₁₃×#117	C₂²	semidirect
60. C₂²×C₄²×C₁₃	C₂²	semidirect
80. C₁₃×C₄⋊Q₈	C₂³	semidirect
81. C₁₃×C₄⋊Q₈	C₂³	semidirect
82. C₁₃×#127	C₂³	semidirect
84. C₁₃×#126	C₂³	semidirect
85. C₁₃×#125	C₂³	semidirect
86. C₁₃×#125	C₂³	semidirect
88. C₁₃×#124	C₂³	semidirect
91. C₁₃×#123	C₂³	semidirect
94. C₁₃×C₂²⋊Q₈	C₂³	semidirect
99. C₄×Q₈×C₁₃	C₂³	semidirect
100. C₄×Q₈×C₁₃	C₂³	semidirect
103. C₄×D₄×C₁₃	C₂³	semidirect
104. C₄×D₄×C₁₃	C₂³	semidirect
109. C₁₃×#117	C₂³	semidirect
136. C₂×C₄²×C₁₃	C₂³	semidirect
137. C₂×#3455	C₁₃	direct (N × H)
204. #3455	C₂×C₁₃	direct (N × H)
205. C₂×#542	C₂×C₁₃	semidirect
206. C₂×#541	C₂×C₁₃	semidirect
207. C₂×#540	C₂×C₁₃	semidirect
208. C₂×#539	C₂×C₁₃	semidirect
209. C₂×#538	C₂×C₁₃	semidirect
210. C₂×#533	C₂×C₁₃	semidirect
211. C₂×#532	C₂×C₁₃	semidirect
212. C₂×#529	C₂×C₁₃	semidirect
213. C₂×#525	C₂×C₁₃	semidirect
214. C₂×C₄×#41	C₂×C₁₃	semidirect
215. C₂²×#117	C₂×C₁₃	semidirect
261. #542	C₂²×C₁₃	semidirect
262. #541	C₂²×C₁₃	semidirect
263. #540	C₂²×C₁₃	semidirect
264. #539	C₂²×C₁₃	semidirect
265. #538	C₂²×C₁₃	semidirect
266. #533	C₂²×C₁₃	semidirect
267. #532	C₂²×C₁₃	semidirect
268. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
269. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
270. C₂×#127	C₂²×C₁₃	semidirect
271. #529	C₂²×C₁₃	semidirect
273. C₂×#126	C₂²×C₁₃	semidirect
274. C₂×#125	C₂²×C₁₃	semidirect
275. C₂×#125	C₂²×C₁₃	semidirect
277. C₂×#124	C₂²×C₁₃	semidirect
278. #525	C₂²×C₁₃	semidirect
281. C₂×#123	C₂²×C₁₃	semidirect
284. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
289. C₄×#41	C₂²×C₁₃	semidirect
290. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
291. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
294. C₂×C₄×D₄	C₂²×C₁₃	semidirect
295. C₂×C₄×D₄	C₂²×C₁₃	semidirect
300. C₂×#117	C₂²×C₁₃	semidirect
301. C₂×#117	C₂²×C₁₃	semidirect
306. C₂²×C₄²	C₂²×C₁₃	semidirect
347. C₄⋊Q₈	C₂³×C₁₃	semidirect
348. C₄⋊Q₈	C₂³×C₁₃	semidirect
349. #127	C₂³×C₁₃	semidirect
351. #126	C₂³×C₁₃	semidirect
352. #125	C₂³×C₁₃	semidirect
353. #125	C₂³×C₁₃	semidirect
355. #124	C₂³×C₁₃	semidirect
358. #123	C₂³×C₁₃	semidirect
361. C₂²⋊Q₈	C₂³×C₁₃	semidirect
366. C₄×Q₈	C₂³×C₁₃	semidirect
367. C₄×Q₈	C₂³×C₁₃	semidirect
370. C₄×D₄	C₂³×C₁₃	semidirect
371. C₄×D₄	C₂³×C₁₃	semidirect
376. #117	C₂³×C₁₃	semidirect
403. C₂×C₄²	C₂³×C₁₃	semidirect
407. C₂×C₁₃	#3455	direct (N × H)
476. C₁₃	C₂×#3455	direct (N × H)
544. C₂	C₁₃×#3455	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#3455	2
C₂×C₁₃×#542	2
C₂×C₁₃×#541	2
C₂×C₁₃×#540	2
C₂×C₁₃×#539	2
C₂×C₁₃×#538	2
C₂×C₁₃×#533	2
C₂×C₁₃×#532	2
C₂×C₁₃×#529	2
C₂×C₁₃×#525	2
C₂×C₄×C₁₃×#41	2
C₂²×C₁₃×#117	2
C₂×#3455	13

Subgroups — C2×C13×#3455 #15749024

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3455 #15749024