Subgroups — C₂×C₁₃×#3498 #15749134

Order 3328.

12982 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×H(5,𝔽₂)	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3498	C₂	1	32	yes	maximal, direct product factor
3	C₂×C₁₃×#550	C₂	1	4	yes	maximal, complemented
4	C₂×D₄²×C₁₃	C₂	1	12	yes	maximal, complemented
5	C₂×C₁₃×#535	C₂	1	6	yes	maximal, complemented
6	C₂×C₁₃×#532	C₂	1	3	yes	maximal, complemented
7	C₂²×C₁₃×#127	C₂	1	3	yes	maximal, complemented
8	C₂×C₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×H(5,𝔽₂)	—	2	32	no	—
10	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	32	yes	complemented
11	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
12	C₂²×C₁₃×#41	C₂²	1	6	yes	complemented
13	C₂²×C₁₃×#41	C₂²	1	4	yes	complemented
14	C₂³×D₄×C₁₃	C₂²	1	6	yes	complemented
15	C₂³×D₄×C₁₃	C₂²	1	12	yes	complemented
16	C₂³×D₄×C₁₃	C₂²	1	12	yes	complemented
17	C₁₃×#550	C₂²	1	64	yes	complemented
18	D₄²×C₁₃	C₂²	1	192	yes	complemented
19	C₁₃×#535	C₂²	1	96	yes	complemented
20	C₁₃×#532	C₂²	1	48	yes	complemented
21	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₁₃×#127	C₂²	1	3	yes	complemented
23	C₂×C₁₃×#127	C₂²	1	6	yes	complemented
24	C₂×C₁₃×#127	C₂²	1	12	yes	complemented
25	C₂×C₁₃×#127	C₂²	1	48	yes	complemented
26	C₂×C₁₃×#124	C₂²	1	6	yes	complemented
27	C₂×C₁₃×#121	C₂²	1	12	yes	complemented
28	C₂×C₁₃×#121	C₂²	1	24	yes	complemented
29	C₂×C₁₃×#120	C₂²	1	24	yes	complemented
30	C₄×C₁₃×#41	C₂²	1	16	yes	complemented
31	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
32	C₂×C₄×D₄×C₁₃	C₂²	1	6	yes	complemented
33	C₂×C₄×D₄×C₁₃	C₂²	1	12	yes	complemented
34	C₂×C₁₃×#117	C₂²	1	3	yes	complemented
35	C₂²×C₄²×C₁₃	C₂²	1	3	yes	complemented
36	C₂⁵×C₁₃	C₂³	1	12	yes	—
37	C₁₃×H(5,𝔽₂)	—	2	256	no	—
38	C₂×C₁₃×#41	—	2	32	no	—
39	C₂×C₁₃×#41	—	2	48	no	—
40	C₂×C₁₃×#41	D₄	1	16	yes	complemented
41	C₂×C₁₃×#41	C₂³	1	8	yes	—
42	C₂×C₁₃×#41	C₂³	1	48	yes	complemented
43	C₂×C₁₃×#41	C₂³	1	32	yes	complemented
44	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
45	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
46	C₂²×D₄×C₁₃	—	2	96	no	—
47	C₂²×D₄×C₁₃	—	2	48	no	—
48	C₂²×D₄×C₁₃	—	4	48	no	—
49	C₂²×D₄×C₁₃	C₂³	1	12	yes	—
50	C₂²×D₄×C₁₃	C₂³	1	12	yes	—
51	C₂²×D₄×C₁₃	C₂³	1	12	yes	—
52	C₂²×D₄×C₁₃	C₂³	1	6	yes	—
53	C₂²×D₄×C₁₃	C₂³	1	24	yes	—
54	C₂²×D₄×C₁₃	C₂³	1	3	yes	—
55	C₂²×D₄×C₁₃	C₂³	1	48	yes	complemented
56	C₂²×D₄×C₁₃	C₂³	1	96	yes	complemented
57	C₂²×D₄×C₁₃	C₂³	1	96	yes	complemented
58	C₂³×C₄×C₁₃	C₂³	1	6	yes	—
59	C₂³×C₄×C₁₃	C₂³	1	12	yes	—
60	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
61	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	complemented
62	C₁₃×#127	C₂³	1	24	yes	complemented
63	C₁₃×#127	C₂³	1	48	yes	complemented
64	C₁₃×#127	C₂³	1	96	yes	complemented
65	C₁₃×#124	C₂³	1	48	yes	complemented
66	C₁₃×#121	C₂³	1	96	yes	complemented
67	C₁₃×#121	C₂³	1	192	yes	complemented
68	C₁₃×#120	C₂³	1	192	yes	complemented
69	C₄×Q₈×C₁₃	C₂³	1	16	yes	complemented
70	C₄×D₄×C₁₃	C₂³	1	48	yes	complemented
71	C₄×D₄×C₁₃	C₂³	1	96	yes	complemented
72	C₁₃×#117	C₂³	1	24	yes	complemented
73	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
74	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
75	C₂×C₁₃×C₂²⋊C₄	C₂³	1	6	yes	—
76	C₂×C₁₃×C₂²⋊C₄	C₂³	1	24	yes	—
77	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
79	C₂×C₄²×C₁₃	C₂³	1	6	yes	—
80	C₂×C₄²×C₁₃	C₂³	1	24	yes	complemented
81	C₂×#3498	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
82	C₂⁴×C₁₃	—	2	48	no	—
83	C₂⁴×C₁₃	—	4	48	no	—
84	C₂⁴×C₁₃	C₂⁴	1	12	yes	—
85	C₂⁴×C₁₃	C₂⁴	1	3	yes	—
86	C₂⁴×C₁₃	C₂⁴	1	48	yes	—
87	C₁₃×#41	—	2	128	no	—
88	C₁₃×#41	—	2	192	no	—
89	C₁₃×#41	C₂×D₄	1	64	yes	complemented
90	C₂×Q₈×C₁₃	—	2	8	no	—
91	C₂×Q₈×C₁₃	C₂×D₄	1	8	yes	complemented
92	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
93	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
94	C₂×D₄×C₁₃	—	2	48	no	—
95	C₂×D₄×C₁₃	—	2	384	no	—
96	C₂×D₄×C₁₃	—	2	48	no	—
97	C₂×D₄×C₁₃	—	2	24	no	—
98	C₂×D₄×C₁₃	—	2	192	no	—
99	C₂×D₄×C₁₃	—	2	48	no	—
100	C₂×D₄×C₁₃	—	4	192	no	—
101	C₂×D₄×C₁₃	—	4	48	no	—
102	C₂×D₄×C₁₃	C₂×D₄	1	24	yes	complemented
103	C₂×D₄×C₁₃	C₂⁴	1	48	yes	—
104	C₂×D₄×C₁₃	C₂⁴	1	48	yes	—
105	C₂×D₄×C₁₃	C₂⁴	1	48	yes	—
106	C₂×D₄×C₁₃	C₂⁴	1	24	yes	—
107	C₂×D₄×C₁₃	C₂⁴	1	96	yes	—
108	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
109	C₂²×C₄×C₁₃	—	2	48	no	—
110	C₂²×C₄×C₁₃	—	2	24	no	—
111	C₂²×C₄×C₁₃	C₂×D₄	1	24	yes	complemented
112	C₂²×C₄×C₁₃	C₂⁴	1	24	yes	—
113	C₂²×C₄×C₁₃	C₂⁴	1	48	yes	—
114	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
115	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
116	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
118	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
119	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
120	C₁₃×C₄⋊C₄	C₂⁴	1	24	yes	—
121	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
122	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
123	C₁₃×C₂²⋊C₄	C₂⁴	1	96	yes	—
124	C₄²×C₁₃	C₂⁴	1	4	yes	—
125	C₄²×C₁₃	C₂⁴	1	12	yes	—
126	C₄²×C₁₃	C₂⁴	1	24	yes	—
127	C₂²×H(5,𝔽₂)	C₂×C₁₃	1	2	yes	complemented
128	#3498	C₂×C₁₃	1	32	yes	direct product factor
129	C₂×#550	C₂×C₁₃	1	4	yes	complemented
130	C₂×D₄²	C₂×C₁₃	1	12	yes	complemented
131	C₂×#535	C₂×C₁₃	1	6	yes	complemented
132	C₂×#532	C₂×C₁₃	1	3	yes	complemented
133	C₂²×#127	C₂×C₁₃	1	3	yes	complemented
134	C₂×C₄×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
135	C₂³×C₁₃	—	2	12	no	—
136	C₂³×C₁₃	—	2	24	no	—
137	C₂³×C₁₃	—	2	48	no	—
138	C₂³×C₁₃	—	2	96	no	—
139	C₂³×C₁₃	—	4	96	no	—
140	C₂³×C₁₃	—	8	96	no	—
141	C₂³×C₁₃	C₂²×D₄	1	12	yes	—
142	C₂³×C₁₃	C₂⁵	1	24	yes	—
143	C₂³×C₁₃	C₂⁵	1	6	yes	—
144	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
145	Q₈×C₁₃	—	2	16	no	—
146	Q₈×C₁₃	C₂²×D₄	1	16	yes	complemented
147	D₄×C₁₃	—	2	96	no	—
148	D₄×C₁₃	—	2	96	no	—
149	D₄×C₁₃	—	2	48	no	—
150	D₄×C₁₃	—	2	96	no	—
151	D₄×C₁₃	—	4	96	no	—
152	D₄×C₁₃	C₂²×D₄	1	48	yes	complemented
153	C₂×C₄×C₁₃	—	2	8	no	—
154	C₂×C₄×C₁₃	—	2	12	no	—
155	C₂×C₄×C₁₃	—	2	96	no	—
156	C₂×C₄×C₁₃	—	2	48	no	—
157	C₂×C₄×C₁₃	C₂²×D₄	1	12	yes	—
158	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
159	C₂×C₄×C₁₃	C₂²×D₄	1	48	yes	complemented
160	C₂×C₄×C₁₃	H(5,𝔽₂)	1	8	yes	complemented
161	C₂×C₄×C₁₃	C₂⁵	1	12	yes	—
162	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
163	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
164	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
165	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
166	C₂×H(5,𝔽₂)	—	2	32	no	—
167	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	32	yes	complemented
168	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
169	C₂²×#41	C₂²×C₁₃	1	6	yes	complemented
170	C₂²×#41	C₂²×C₁₃	1	4	yes	complemented
171	C₂³×D₄	C₂²×C₁₃	1	6	yes	complemented
172	C₂³×D₄	C₂²×C₁₃	1	12	yes	complemented
173	C₂³×D₄	C₂²×C₁₃	1	12	yes	complemented
174	#550	C₂²×C₁₃	1	64	yes	complemented
175	D₄²	C₂²×C₁₃	1	192	yes	complemented
176	#535	C₂²×C₁₃	1	96	yes	complemented
177	#532	C₂²×C₁₃	1	48	yes	complemented
178	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
179	C₂×#127	C₂²×C₁₃	1	3	yes	complemented
180	C₂×#127	C₂²×C₁₃	1	6	yes	complemented
181	C₂×#127	C₂²×C₁₃	1	12	yes	complemented
182	C₂×#127	C₂²×C₁₃	1	48	yes	complemented
183	C₂×#124	C₂²×C₁₃	1	6	yes	complemented
184	C₂×#121	C₂²×C₁₃	1	12	yes	complemented
185	C₂×#121	C₂²×C₁₃	1	24	yes	complemented
186	C₂×#120	C₂²×C₁₃	1	24	yes	complemented
187	C₄×#41	C₂²×C₁₃	1	16	yes	complemented
188	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
189	C₂×C₄×D₄	C₂²×C₁₃	1	6	yes	complemented
190	C₂×C₄×D₄	C₂²×C₁₃	1	12	yes	complemented
191	C₂×#117	C₂²×C₁₃	1	3	yes	complemented
192	C₂²×C₄²	C₂²×C₁₃	1	3	yes	complemented
193	C₂²×C₁₃	—	2	12	no	—
194	C₂²×C₁₃	—	2	24	no	—
195	C₂²×C₁₃	—	2	24	no	—
196	C₂²×C₁₃	—	2	48	no	—
197	C₂²×C₁₃	—	4	48	no	—
198	C₂²×C₁₃	—	8	96	no	—
199	C₂²×C₁₃	C₂³×D₄	1	12	yes	—
200	C₂²×C₁₃	C₂³×D₄	1	2	yes	—
201	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
202	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
203	C₄×C₁₃	—	2	8	no	—
204	C₄×C₁₃	—	2	12	no	—
205	C₄×C₁₃	C₂³×D₄	1	12	yes	—
206	C₄×C₁₃	C₂³×D₄	1	4	yes	—
207	C₄×C₁₃	C₂×H(5,𝔽₂)	1	8	yes	complemented
208	C₂⁵	C₂³×C₁₃	1	12	yes	—
209	H(5,𝔽₂)	—	2	256	no	—
210	C₂×#41	—	2	32	no	—
211	C₂×#41	—	2	48	no	—
212	C₂×#41	D₄×C₁₃	1	16	yes	complemented
213	C₂×#41	C₂³×C₁₃	1	8	yes	—
214	C₂×#41	C₂³×C₁₃	1	48	yes	complemented
215	C₂×#41	C₂³×C₁₃	1	32	yes	complemented
216	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
217	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
218	C₂²×D₄	—	2	96	no	—
219	C₂²×D₄	—	2	48	no	—
220	C₂²×D₄	—	4	48	no	—
221	C₂²×D₄	C₂³×C₁₃	1	12	yes	—
222	C₂²×D₄	C₂³×C₁₃	1	12	yes	—
223	C₂²×D₄	C₂³×C₁₃	1	12	yes	—
224	C₂²×D₄	C₂³×C₁₃	1	6	yes	—
225	C₂²×D₄	C₂³×C₁₃	1	24	yes	—
226	C₂²×D₄	C₂³×C₁₃	1	3	yes	—
227	C₂²×D₄	C₂³×C₁₃	1	48	yes	complemented
228	C₂²×D₄	C₂³×C₁₃	1	96	yes	complemented
229	C₂²×D₄	C₂³×C₁₃	1	96	yes	complemented
230	C₂³×C₄	C₂³×C₁₃	1	6	yes	—
231	C₂³×C₄	C₂³×C₁₃	1	12	yes	—
232	C₂³×C₄	C₂³×C₁₃	1	3	yes	—
233	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	complemented
234	#127	C₂³×C₁₃	1	24	yes	complemented
235	#127	C₂³×C₁₃	1	48	yes	complemented
236	#127	C₂³×C₁₃	1	96	yes	complemented
237	#124	C₂³×C₁₃	1	48	yes	complemented
238	#121	C₂³×C₁₃	1	96	yes	complemented
239	#121	C₂³×C₁₃	1	192	yes	complemented
240	#120	C₂³×C₁₃	1	192	yes	complemented
241	C₄×Q₈	C₂³×C₁₃	1	16	yes	complemented
242	C₄×D₄	C₂³×C₁₃	1	48	yes	complemented
243	C₄×D₄	C₂³×C₁₃	1	96	yes	complemented
244	#117	C₂³×C₁₃	1	24	yes	complemented
245	C₂×C₄⋊C₄	C₂³×C₁₃	1	6	yes	—
246	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
247	C₂×C₂²⋊C₄	C₂³×C₁₃	1	6	yes	—
248	C₂×C₂²⋊C₄	C₂³×C₁₃	1	24	yes	—
249	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
250	C₂×C₄²	C₂³×C₁₃	1	6	yes	—
251	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
252	C₂×C₄²	C₂³×C₁₃	1	24	yes	complemented
253	C₂×C₁₃	—	2	12	no	—
254	C₂×C₁₃	—	4	24	no	—
255	C₂×C₁₃	#3498	1	4	yes	direct product factor
256	C₂×C₁₃	C₂⁴×D₄	1	1	yes	characteristic
257	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	2	yes	—
258	C₂⁴	—	2	48	no	—
259	C₂⁴	—	4	48	no	—
260	C₂⁴	C₂⁴×C₁₃	1	12	yes	—
261	C₂⁴	C₂⁴×C₁₃	1	3	yes	—
262	C₂⁴	C₂⁴×C₁₃	1	48	yes	—
263	#41	—	2	128	no	—
264	#41	—	2	192	no	—
265	#41	C₂×D₄×C₁₃	1	64	yes	complemented
266	C₂×Q₈	—	2	8	no	—
267	C₂×Q₈	C₂×D₄×C₁₃	1	8	yes	complemented
268	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
269	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
270	C₂×D₄	—	2	48	no	—
271	C₂×D₄	—	2	384	no	—
272	C₂×D₄	—	2	48	no	—
273	C₂×D₄	—	2	24	no	—
274	C₂×D₄	—	2	192	no	—
275	C₂×D₄	—	2	48	no	—
276	C₂×D₄	—	4	192	no	—
277	C₂×D₄	—	4	48	no	—
278	C₂×D₄	C₂×D₄×C₁₃	1	24	yes	complemented
279	C₂×D₄	C₂⁴×C₁₃	1	48	yes	—
280	C₂×D₄	C₂⁴×C₁₃	1	48	yes	—
281	C₂×D₄	C₂⁴×C₁₃	1	48	yes	—
282	C₂×D₄	C₂⁴×C₁₃	1	24	yes	—
283	C₂×D₄	C₂⁴×C₁₃	1	96	yes	—
284	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
285	C₂²×C₄	—	2	48	no	—
286	C₂²×C₄	—	2	24	no	—
287	C₂²×C₄	C₂×D₄×C₁₃	1	24	yes	complemented
288	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
289	C₂²×C₄	C₂⁴×C₁₃	1	24	yes	—
290	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
291	C₂²×C₄	C₂⁴×C₁₃	1	48	yes	—
292	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
293	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
294	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
295	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
296	C₄⋊C₄	C₂⁴×C₁₃	1	24	yes	—
297	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
298	C₂²⋊C₄	C₂⁴×C₁₃	1	24	yes	—
299	C₂²⋊C₄	C₂⁴×C₁₃	1	96	yes	—
300	C₄²	C₂⁴×C₁₃	1	4	yes	—
301	C₄²	C₂⁴×C₁₃	1	12	yes	—
302	C₄²	C₂⁴×C₁₃	1	24	yes	—
303	C₁₃	C₂×#3498	1	1	yes	characteristic, direct product factor, Sylow
304	C₂³	—	2	12	no	—
305	C₂³	—	2	24	no	—
306	C₂³	—	2	48	no	—
307	C₂³	—	2	96	no	—
308	C₂³	—	4	96	no	—
309	C₂³	—	8	96	no	—
310	C₂³	C₂²×D₄×C₁₃	1	12	yes	—
311	C₂³	C₂⁵×C₁₃	1	24	yes	—
312	C₂³	C₂⁵×C₁₃	1	6	yes	—
313	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
314	Q₈	—	2	16	no	—
315	Q₈	C₂²×D₄×C₁₃	1	16	yes	complemented
316	D₄	—	2	96	no	—
317	D₄	—	2	96	no	—
318	D₄	—	2	48	no	—
319	D₄	—	2	96	no	—
320	D₄	—	4	96	no	—
321	D₄	C₂²×D₄×C₁₃	1	48	yes	complemented
322	C₂×C₄	—	2	8	no	—
323	C₂×C₄	—	2	12	no	—
324	C₂×C₄	—	2	96	no	—
325	C₂×C₄	—	2	48	no	—
326	C₂×C₄	C₂²×D₄×C₁₃	1	12	yes	—
327	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
328	C₂×C₄	C₂²×D₄×C₁₃	1	48	yes	complemented
329	C₂×C₄	C₁₃×H(5,𝔽₂)	1	8	yes	complemented
330	C₂×C₄	C₂⁵×C₁₃	1	12	yes	—
331	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
332	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
333	C₂×C₄	C₂⁵×C₁₃	1	6	yes	—
334	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
335	C₂²	—	2	12	no	—
336	C₂²	—	2	24	no	—
337	C₂²	—	2	24	no	—
338	C₂²	—	2	48	no	—
339	C₂²	—	4	48	no	—
340	C₂²	—	8	96	no	—
341	C₂²	C₂³×D₄×C₁₃	1	12	yes	—
342	C₂²	C₂³×D₄×C₁₃	1	2	yes	—
343	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	4	yes	—
344	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
345	C₄	—	2	8	no	—
346	C₄	—	2	12	no	—
347	C₄	C₂³×D₄×C₁₃	1	12	yes	—
348	C₄	C₂³×D₄×C₁₃	1	4	yes	—
349	C₄	C₂×C₁₃×H(5,𝔽₂)	1	8	yes	complemented
350	C₂	—	2	12	no	—
351	C₂	—	4	24	no	—
352	C₂	C₁₃×#3498	1	4	yes	direct product factor
353	C₂	C₂⁴×D₄×C₁₃	1	1	yes	characteristic
354	C₂	C₂²×C₁₃×H(5,𝔽₂)	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₃×H(5,𝔽₂)	C₂	semidirect
2. C₁₃×#3498	C₂	direct (N × H)
3. C₂×C₁₃×#550	C₂	semidirect
4. C₂×D₄²×C₁₃	C₂	semidirect
5. C₂×C₁₃×#535	C₂	semidirect
6. C₂×C₁₃×#532	C₂	semidirect
7. C₂²×C₁₃×#127	C₂	semidirect
8. C₂×C₄×C₁₃×#41	C₂	semidirect
10. C₂×C₁₃×H(5,𝔽₂)	C₂²	semidirect
12. C₂²×C₁₃×#41	C₂²	semidirect
13. C₂²×C₁₃×#41	C₂²	semidirect
14. C₂³×D₄×C₁₃	C₂²	semidirect
15. C₂³×D₄×C₁₃	C₂²	semidirect
16. C₂³×D₄×C₁₃	C₂²	semidirect
17. C₁₃×#550	C₂²	semidirect
18. D₄²×C₁₃	C₂²	semidirect
19. C₁₃×#535	C₂²	semidirect
20. C₁₃×#532	C₂²	semidirect
21. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
22. C₂×C₁₃×#127	C₂²	semidirect
23. C₂×C₁₃×#127	C₂²	semidirect
24. C₂×C₁₃×#127	C₂²	semidirect
25. C₂×C₁₃×#127	C₂²	semidirect
26. C₂×C₁₃×#124	C₂²	semidirect
27. C₂×C₁₃×#121	C₂²	semidirect
28. C₂×C₁₃×#121	C₂²	semidirect
29. C₂×C₁₃×#120	C₂²	semidirect
30. C₄×C₁₃×#41	C₂²	semidirect
31. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
32. C₂×C₄×D₄×C₁₃	C₂²	semidirect
33. C₂×C₄×D₄×C₁₃	C₂²	semidirect
34. C₂×C₁₃×#117	C₂²	semidirect
35. C₂²×C₄²×C₁₃	C₂²	semidirect
40. C₂×C₁₃×#41	D₄	semidirect
42. C₂×C₁₃×#41	C₂³	semidirect
43. C₂×C₁₃×#41	C₂³	semidirect
55. C₂²×D₄×C₁₃	C₂³	semidirect
56. C₂²×D₄×C₁₃	C₂³	semidirect
57. C₂²×D₄×C₁₃	C₂³	semidirect
61. C₁₃×C₄⋊Q₈	C₂³	semidirect
62. C₁₃×#127	C₂³	semidirect
63. C₁₃×#127	C₂³	semidirect
64. C₁₃×#127	C₂³	semidirect
65. C₁₃×#124	C₂³	semidirect
66. C₁₃×#121	C₂³	semidirect
67. C₁₃×#121	C₂³	semidirect
68. C₁₃×#120	C₂³	semidirect
69. C₄×Q₈×C₁₃	C₂³	semidirect
70. C₄×D₄×C₁₃	C₂³	semidirect
71. C₄×D₄×C₁₃	C₂³	semidirect
72. C₁₃×#117	C₂³	semidirect
80. C₂×C₄²×C₁₃	C₂³	semidirect
81. C₂×#3498	C₁₃	direct (N × H)
89. C₁₃×#41	C₂×D₄	semidirect
91. C₂×Q₈×C₁₃	C₂×D₄	semidirect
102. C₂×D₄×C₁₃	C₂×D₄	semidirect
111. C₂²×C₄×C₁₃	C₂×D₄	semidirect
127. C₂²×H(5,𝔽₂)	C₂×C₁₃	semidirect
128. #3498	C₂×C₁₃	direct (N × H)
129. C₂×#550	C₂×C₁₃	semidirect
130. C₂×D₄²	C₂×C₁₃	semidirect
131. C₂×#535	C₂×C₁₃	semidirect
132. C₂×#532	C₂×C₁₃	semidirect
133. C₂²×#127	C₂×C₁₃	semidirect
134. C₂×C₄×#41	C₂×C₁₃	semidirect
146. Q₈×C₁₃	C₂²×D₄	semidirect
152. D₄×C₁₃	C₂²×D₄	semidirect
159. C₂×C₄×C₁₃	C₂²×D₄	semidirect
160. C₂×C₄×C₁₃	H(5,𝔽₂)	semidirect
167. C₂×H(5,𝔽₂)	C₂²×C₁₃	semidirect
169. C₂²×#41	C₂²×C₁₃	semidirect
170. C₂²×#41	C₂²×C₁₃	semidirect
171. C₂³×D₄	C₂²×C₁₃	semidirect
172. C₂³×D₄	C₂²×C₁₃	semidirect
173. C₂³×D₄	C₂²×C₁₃	semidirect
174. #550	C₂²×C₁₃	semidirect
175. D₄²	C₂²×C₁₃	semidirect
176. #535	C₂²×C₁₃	semidirect
177. #532	C₂²×C₁₃	semidirect
178. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
179. C₂×#127	C₂²×C₁₃	semidirect
180. C₂×#127	C₂²×C₁₃	semidirect
181. C₂×#127	C₂²×C₁₃	semidirect
182. C₂×#127	C₂²×C₁₃	semidirect
183. C₂×#124	C₂²×C₁₃	semidirect
184. C₂×#121	C₂²×C₁₃	semidirect
185. C₂×#121	C₂²×C₁₃	semidirect
186. C₂×#120	C₂²×C₁₃	semidirect
187. C₄×#41	C₂²×C₁₃	semidirect
188. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
189. C₂×C₄×D₄	C₂²×C₁₃	semidirect
190. C₂×C₄×D₄	C₂²×C₁₃	semidirect
191. C₂×#117	C₂²×C₁₃	semidirect
192. C₂²×C₄²	C₂²×C₁₃	semidirect
207. C₄×C₁₃	C₂×H(5,𝔽₂)	semidirect
212. C₂×#41	D₄×C₁₃	semidirect
214. C₂×#41	C₂³×C₁₃	semidirect
215. C₂×#41	C₂³×C₁₃	semidirect
227. C₂²×D₄	C₂³×C₁₃	semidirect
228. C₂²×D₄	C₂³×C₁₃	semidirect
229. C₂²×D₄	C₂³×C₁₃	semidirect
233. C₄⋊Q₈	C₂³×C₁₃	semidirect
234. #127	C₂³×C₁₃	semidirect
235. #127	C₂³×C₁₃	semidirect
236. #127	C₂³×C₁₃	semidirect
237. #124	C₂³×C₁₃	semidirect
238. #121	C₂³×C₁₃	semidirect
239. #121	C₂³×C₁₃	semidirect
240. #120	C₂³×C₁₃	semidirect
241. C₄×Q₈	C₂³×C₁₃	semidirect
242. C₄×D₄	C₂³×C₁₃	semidirect
243. C₄×D₄	C₂³×C₁₃	semidirect
244. #117	C₂³×C₁₃	semidirect
252. C₂×C₄²	C₂³×C₁₃	semidirect
255. C₂×C₁₃	#3498	direct (N × H)
265. #41	C₂×D₄×C₁₃	semidirect
267. C₂×Q₈	C₂×D₄×C₁₃	semidirect
278. C₂×D₄	C₂×D₄×C₁₃	semidirect
287. C₂²×C₄	C₂×D₄×C₁₃	semidirect
303. C₁₃	C₂×#3498	direct (N × H)
315. Q₈	C₂²×D₄×C₁₃	semidirect
321. D₄	C₂²×D₄×C₁₃	semidirect
328. C₂×C₄	C₂²×D₄×C₁₃	semidirect
329. C₂×C₄	C₁₃×H(5,𝔽₂)	semidirect
349. C₄	C₂×C₁₃×H(5,𝔽₂)	semidirect
352. C₂	C₁₃×#3498	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×H(5,𝔽₂)	2
C₁₃×#3498	2
C₂×C₁₃×#550	2
C₂×D₄²×C₁₃	2
C₂×C₁₃×#535	2
C₂×C₁₃×#532	2
C₂²×C₁₃×#127	2
C₂×C₄×C₁₃×#41	2
C₂×#3498	13

Subgroups — C2×C13×#3498 #15749134

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3498 #15749134