Subgroups — C₂×C₁₃×#3486 #15749121

Order 3328.

11254 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×C₁₃×2₋¹⁺⁴	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂⁴×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3486	C₂	1	32	yes	maximal, direct product factor
4	C₂×D₄×Q₈×C₁₃	C₂	1	8	yes	maximal, complemented
5	C₂×C₁₃×#548	C₂	1	8	yes	maximal, complemented
6	C₂×C₁₃×#536	C₂	1	6	yes	maximal, complemented
7	C₂×C₁₃×#525	C₂	1	6	yes	maximal, complemented
8	C₂×C₁₃×#519	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×2₋¹⁺⁴	—	2	16	no	—
10	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	16	yes	complemented
11	C₂²×C₁₃×#41	C₂²	1	6	yes	—
12	C₂²×C₁₃×#41	C₂²	1	4	yes	complemented
13	C₂³×Q₈×C₁₃	—	2	16	no	—
14	C₂³×Q₈×C₁₃	C₂²	1	3	yes	—
15	C₂³×Q₈×C₁₃	C₂²	1	8	yes	—
16	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
17	C₂³×Q₈×C₁₃	C₂²	1	16	yes	complemented
18	C₂³×Q₈×C₁₃	C₂²	1	4	yes	complemented
19	C₂⁴×C₄×C₁₃	C₂²	1	3	yes	—
20	D₄×Q₈×C₁₃	C₂²	1	128	yes	complemented
21	C₁₃×#548	C₂²	1	128	yes	complemented
22	C₁₃×#536	C₂²	1	96	yes	complemented
23	C₂×C₁₃×C₄⋊Q₈	C₂²	1	12	yes	complemented
24	C₂×C₁₃×#124	C₂²	1	12	yes	complemented
25	C₁₃×#525	C₂²	1	96	yes	complemented
26	C₂×C₁₃×#123	C₂²	1	12	yes	—
27	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	12	yes	—
28	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	24	yes	complemented
29	C₂×C₁₃×#121	C₂²	1	12	yes	—
30	C₂×C₁₃×#120	C₂²	1	4	yes	—
31	C₁₃×#519	C₂²	1	16	yes	complemented
32	C₂×C₄×Q₈×C₁₃	C₂²	1	8	yes	complemented
33	C₂×C₄×D₄×C₁₃	C₂²	1	24	yes	—
34	C₂×C₁₃×#117	C₂²	1	6	yes	—
35	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
36	C₁₃×2₋¹⁺⁴	—	2	128	no	—
37	C₂×C₁₃×#41	—	2	32	no	—
38	C₂×C₁₃×#41	—	2	48	no	—
39	C₂×C₁₃×#41	C₂³	1	48	yes	—
40	C₂×C₁₃×#41	C₂³	1	32	yes	complemented
41	C₂²×Q₈×C₁₃	—	2	64	no	—
42	C₂²×Q₈×C₁₃	—	2	32	no	—
43	C₂²×Q₈×C₁₃	—	2	128	no	—
44	C₂²×Q₈×C₁₃	—	2	24	no	—
45	C₂²×Q₈×C₁₃	D₄	1	16	yes	complemented
46	C₂²×Q₈×C₁₃	C₂³	1	6	yes	—
47	C₂²×Q₈×C₁₃	C₂³	1	12	yes	—
48	C₂²×Q₈×C₁₃	C₂³	1	24	yes	—
49	C₂²×Q₈×C₁₃	C₂³	1	64	yes	—
50	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
51	C₂²×Q₈×C₁₃	C₂³	1	8	yes	—
52	C₂²×Q₈×C₁₃	C₂³	1	32	yes	complemented
53	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
54	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
55	C₂²×D₄×C₁₃	C₂³	1	6	yes	—
56	C₂³×C₄×C₁₃	—	2	24	no	—
57	C₂³×C₄×C₁₃	C₂³	1	12	yes	—
58	C₂³×C₄×C₁₃	C₂³	1	12	yes	—
59	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
60	C₂³×C₄×C₁₃	C₂³	1	24	yes	—
61	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
62	C₁₃×C₄⋊Q₈	C₂³	1	96	yes	complemented
63	C₁₃×#124	C₂³	1	96	yes	complemented
64	C₁₃×#123	C₂³	1	96	yes	—
65	C₁₃×C₂²⋊Q₈	C₂³	1	96	yes	—
66	C₁₃×C₂²⋊Q₈	C₂³	1	192	yes	complemented
67	C₁₃×#121	C₂³	1	96	yes	—
68	C₁₃×#120	C₂³	1	32	yes	—
69	C₄×Q₈×C₁₃	C₂³	1	64	yes	complemented
70	C₄×D₄×C₁₃	C₂³	1	192	yes	—
71	C₁₃×#117	C₂³	1	48	yes	—
72	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	—
73	C₂×C₁₃×C₄⋊C₄	C₂³	1	24	yes	—
74	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
75	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
76	C₂×C₁₃×C₂²⋊C₄	C₂³	1	24	yes	—
77	C₂×C₄²×C₁₃	C₂³	1	12	yes	—
78	C₂×#3486	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
79	C₂⁴×C₁₃	—	2	4	no	—
80	C₂⁴×C₁₃	—	2	8	no	—
81	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
82	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
83	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
84	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
85	C₁₃×#41	—	2	128	no	—
86	C₁₃×#41	—	2	192	no	—
87	C₂×Q₈×C₁₃	—	2	256	no	—
88	C₂×Q₈×C₁₃	—	2	128	no	—
89	C₂×Q₈×C₁₃	—	2	48	no	—
90	C₂×Q₈×C₁₃	—	2	96	no	—
91	C₂×Q₈×C₁₃	—	2	24	no	—
92	C₂×Q₈×C₁₃	C₂×D₄	1	32	yes	—
93	C₂×Q₈×C₁₃	C₂×D₄	1	64	yes	complemented
94	C₂×Q₈×C₁₃	C₂⁴	1	24	yes	—
95	C₂×Q₈×C₁₃	C₂⁴	1	48	yes	—
96	C₂×Q₈×C₁₃	C₂⁴	1	16	yes	—
97	C₂×D₄×C₁₃	—	2	16	no	—
98	C₂×D₄×C₁₃	—	2	32	no	—
99	C₂×D₄×C₁₃	—	2	24	no	—
100	C₂×D₄×C₁₃	C₂⁴	1	32	yes	—
101	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
102	C₂×D₄×C₁₃	C₂⁴	1	24	yes	—
103	C₂²×C₄×C₁₃	—	2	12	no	—
104	C₂²×C₄×C₁₃	—	2	48	no	—
105	C₂²×C₄×C₁₃	—	2	96	no	—
106	C₂²×C₄×C₁₃	—	2	48	no	—
107	C₂²×C₄×C₁₃	C₂×D₄	1	24	yes	—
108	C₂²×C₄×C₁₃	C₂⁴	1	48	yes	—
109	C₂²×C₄×C₁₃	C₂⁴	1	48	yes	—
110	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
111	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
112	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
113	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
114	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
115	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
116	C₁₃×C₄⋊C₄	C₂⁴	1	48	yes	—
117	C₁₃×C₄⋊C₄	C₂⁴	1	96	yes	—
118	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
119	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
120	C₁₃×C₂²⋊C₄	C₂⁴	1	96	yes	—
121	C₄²×C₁₃	C₂⁴	1	48	yes	—
122	C₂²×2₋¹⁺⁴	C₂×C₁₃	1	1	yes	characteristic, complemented
123	C₂⁴×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
124	#3486	C₂×C₁₃	1	32	yes	direct product factor
125	C₂×D₄×Q₈	C₂×C₁₃	1	8	yes	complemented
126	C₂×#548	C₂×C₁₃	1	8	yes	complemented
127	C₂×#536	C₂×C₁₃	1	6	yes	complemented
128	C₂×#525	C₂×C₁₃	1	6	yes	complemented
129	C₂×#519	C₂×C₁₃	1	1	yes	characteristic, complemented
130	C₂³×C₁₃	—	2	32	no	—
131	C₂³×C₁₃	—	2	8	no	—
132	C₂³×C₁₃	—	2	4	no	—
133	C₂³×C₁₃	—	2	4	no	—
134	C₂³×C₁₃	—	2	4	no	—
135	C₂³×C₁₃	—	2	16	no	—
136	C₂³×C₁₃	—	2	8	no	—
137	C₂³×C₁₃	—	2	16	no	—
138	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
139	C₂³×C₁₃	2₋¹⁺⁴	1	8	yes	complemented
140	C₂³×C₁₃	C₂⁵	1	8	yes	—
141	C₂³×C₁₃	C₂⁵	1	2	yes	—
142	C₂³×C₁₃	C₂⁵	1	4	yes	—
143	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
144	Q₈×C₁₃	—	2	96	no	—
145	Q₈×C₁₃	—	2	48	no	—
146	Q₈×C₁₃	C₂²×D₄	1	64	yes	—
147	D₄×C₁₃	—	2	32	no	—
148	D₄×C₁₃	—	2	64	no	—
149	D₄×C₁₃	—	2	48	no	—
150	C₂×C₄×C₁₃	—	2	8	no	—
151	C₂×C₄×C₁₃	—	2	24	no	—
152	C₂×C₄×C₁₃	—	2	12	no	—
153	C₂×C₄×C₁₃	—	2	16	no	—
154	C₂×C₄×C₁₃	—	2	96	no	—
155	C₂×C₄×C₁₃	—	2	96	no	—
156	C₂×C₄×C₁₃	C₂²×D₄	1	24	yes	—
157	C₂×C₄×C₁₃	C₂²×D₄	1	48	yes	—
158	C₂×C₄×C₁₃	C₂⁵	1	16	yes	—
159	C₂×C₄×C₁₃	C₂⁵	1	12	yes	—
160	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
161	C₂×C₄×C₁₃	C₂⁵	1	12	yes	—
162	C₂×2₋¹⁺⁴	—	2	16	no	—
163	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	16	yes	complemented
164	C₂²×#41	C₂²×C₁₃	1	6	yes	—
165	C₂²×#41	C₂²×C₁₃	1	4	yes	complemented
166	C₂³×Q₈	—	2	16	no	—
167	C₂³×Q₈	C₂²×C₁₃	1	3	yes	—
168	C₂³×Q₈	C₂²×C₁₃	1	8	yes	—
169	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
170	C₂³×Q₈	C₂²×C₁₃	1	16	yes	complemented
171	C₂³×Q₈	C₂²×C₁₃	1	4	yes	complemented
172	C₂⁴×C₄	C₂²×C₁₃	1	3	yes	—
173	D₄×Q₈	C₂²×C₁₃	1	128	yes	complemented
174	#548	C₂²×C₁₃	1	128	yes	complemented
175	#536	C₂²×C₁₃	1	96	yes	complemented
176	C₂×C₄⋊Q₈	C₂²×C₁₃	1	12	yes	complemented
177	C₂×#124	C₂²×C₁₃	1	12	yes	complemented
178	#525	C₂²×C₁₃	1	96	yes	complemented
179	C₂×#123	C₂²×C₁₃	1	12	yes	—
180	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	12	yes	—
181	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	24	yes	complemented
182	C₂×#121	C₂²×C₁₃	1	12	yes	—
183	C₂×#120	C₂²×C₁₃	1	4	yes	—
184	#519	C₂²×C₁₃	1	16	yes	complemented
185	C₂×C₄×Q₈	C₂²×C₁₃	1	8	yes	complemented
186	C₂×C₄×D₄	C₂²×C₁₃	1	24	yes	—
187	C₂×#117	C₂²×C₁₃	1	6	yes	—
188	C₂²×C₁₃	—	2	32	no	—
189	C₂²×C₁₃	—	2	4	no	—
190	C₂²×C₁₃	—	2	4	no	—
191	C₂²×C₁₃	—	2	4	no	—
192	C₂²×C₁₃	—	2	8	no	—
193	C₂²×C₁₃	—	2	16	no	—
194	C₂²×C₁₃	—	2	8	no	—
195	C₂²×C₁₃	—	2	16	no	—
196	C₂²×C₁₃	—	4	16	no	—
197	C₂²×C₁₃	C₂³×D₄	1	4	yes	—
198	C₂²×C₁₃	C₂³×D₄	1	2	yes	—
199	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	4	yes	—
200	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	8	yes	complemented
201	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
202	C₄×C₁₃	—	2	8	no	—
203	C₄×C₁₃	—	2	12	no	—
204	C₄×C₁₃	—	2	16	no	—
205	C₄×C₁₃	C₂³×D₄	1	24	yes	—
206	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
207	2₋¹⁺⁴	—	2	128	no	—
208	C₂×#41	—	2	32	no	—
209	C₂×#41	—	2	48	no	—
210	C₂×#41	C₂³×C₁₃	1	48	yes	—
211	C₂×#41	C₂³×C₁₃	1	32	yes	complemented
212	C₂²×Q₈	—	2	64	no	—
213	C₂²×Q₈	—	2	32	no	—
214	C₂²×Q₈	—	2	128	no	—
215	C₂²×Q₈	—	2	24	no	—
216	C₂²×Q₈	D₄×C₁₃	1	16	yes	complemented
217	C₂²×Q₈	C₂³×C₁₃	1	6	yes	—
218	C₂²×Q₈	C₂³×C₁₃	1	12	yes	—
219	C₂²×Q₈	C₂³×C₁₃	1	24	yes	—
220	C₂²×Q₈	C₂³×C₁₃	1	64	yes	—
221	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
222	C₂²×Q₈	C₂³×C₁₃	1	8	yes	—
223	C₂²×Q₈	C₂³×C₁₃	1	32	yes	complemented
224	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
225	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
226	C₂²×D₄	C₂³×C₁₃	1	6	yes	—
227	C₂³×C₄	—	2	24	no	—
228	C₂³×C₄	C₂³×C₁₃	1	12	yes	—
229	C₂³×C₄	C₂³×C₁₃	1	12	yes	—
230	C₂³×C₄	C₂³×C₁₃	1	3	yes	—
231	C₂³×C₄	C₂³×C₁₃	1	24	yes	—
232	C₂³×C₄	C₂³×C₁₃	1	3	yes	—
233	C₄⋊Q₈	C₂³×C₁₃	1	96	yes	complemented
234	#124	C₂³×C₁₃	1	96	yes	complemented
235	#123	C₂³×C₁₃	1	96	yes	—
236	C₂²⋊Q₈	C₂³×C₁₃	1	96	yes	—
237	C₂²⋊Q₈	C₂³×C₁₃	1	192	yes	complemented
238	#121	C₂³×C₁₃	1	96	yes	—
239	#120	C₂³×C₁₃	1	32	yes	—
240	C₄×Q₈	C₂³×C₁₃	1	64	yes	complemented
241	C₄×D₄	C₂³×C₁₃	1	192	yes	—
242	#117	C₂³×C₁₃	1	48	yes	—
243	C₂×C₄⋊C₄	C₂³×C₁₃	1	12	yes	—
244	C₂×C₄⋊C₄	C₂³×C₁₃	1	24	yes	—
245	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
246	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
247	C₂×C₂²⋊C₄	C₂³×C₁₃	1	24	yes	—
248	C₂×C₄²	C₂³×C₁₃	1	12	yes	—
249	C₂×C₁₃	—	2	4	no	—
250	C₂×C₁₃	—	2	8	no	—
251	C₂×C₁₃	—	4	8	no	—
252	C₂×C₁₃	#3486	1	4	yes	direct product factor
253	C₂×C₁₃	C₂⁴×D₄	1	1	yes	characteristic
254	C₂×C₁₃	C₂²×2₋¹⁺⁴	1	2	yes	—
255	C₂⁴	—	2	4	no	—
256	C₂⁴	—	2	8	no	—
257	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
258	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
259	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
260	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
261	#41	—	2	128	no	—
262	#41	—	2	192	no	—
263	C₂×Q₈	—	2	256	no	—
264	C₂×Q₈	—	2	128	no	—
265	C₂×Q₈	—	2	48	no	—
266	C₂×Q₈	—	2	96	no	—
267	C₂×Q₈	—	2	24	no	—
268	C₂×Q₈	C₂×D₄×C₁₃	1	32	yes	—
269	C₂×Q₈	C₂×D₄×C₁₃	1	64	yes	complemented
270	C₂×Q₈	C₂⁴×C₁₃	1	24	yes	—
271	C₂×Q₈	C₂⁴×C₁₃	1	48	yes	—
272	C₂×Q₈	C₂⁴×C₁₃	1	16	yes	—
273	C₂×D₄	—	2	16	no	—
274	C₂×D₄	—	2	32	no	—
275	C₂×D₄	—	2	24	no	—
276	C₂×D₄	C₂⁴×C₁₃	1	32	yes	—
277	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
278	C₂×D₄	C₂⁴×C₁₃	1	24	yes	—
279	C₂²×C₄	—	2	12	no	—
280	C₂²×C₄	—	2	48	no	—
281	C₂²×C₄	—	2	96	no	—
282	C₂²×C₄	—	2	48	no	—
283	C₂²×C₄	C₂×D₄×C₁₃	1	24	yes	—
284	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
285	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
286	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
287	C₂²×C₄	C₂⁴×C₁₃	1	48	yes	—
288	C₂²×C₄	C₂⁴×C₁₃	1	48	yes	—
289	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
290	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
291	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
292	C₄⋊C₄	C₂⁴×C₁₃	1	48	yes	—
293	C₄⋊C₄	C₂⁴×C₁₃	1	96	yes	—
294	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
295	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
296	C₂²⋊C₄	C₂⁴×C₁₃	1	96	yes	—
297	C₄²	C₂⁴×C₁₃	1	48	yes	—
298	C₁₃	C₂×#3486	1	1	yes	characteristic, direct product factor, Sylow
299	C₂³	—	2	32	no	—
300	C₂³	—	2	8	no	—
301	C₂³	—	2	4	no	—
302	C₂³	—	2	4	no	—
303	C₂³	—	2	4	no	—
304	C₂³	—	2	16	no	—
305	C₂³	—	2	8	no	—
306	C₂³	—	2	16	no	—
307	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
308	C₂³	C₁₃×2₋¹⁺⁴	1	8	yes	complemented
309	C₂³	C₂⁵×C₁₃	1	8	yes	—
310	C₂³	C₂⁵×C₁₃	1	2	yes	—
311	C₂³	C₂⁵×C₁₃	1	4	yes	—
312	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
313	Q₈	—	2	96	no	—
314	Q₈	—	2	48	no	—
315	Q₈	C₂²×D₄×C₁₃	1	64	yes	—
316	D₄	—	2	32	no	—
317	D₄	—	2	64	no	—
318	D₄	—	2	48	no	—
319	C₂×C₄	—	2	8	no	—
320	C₂×C₄	—	2	24	no	—
321	C₂×C₄	—	2	12	no	—
322	C₂×C₄	—	2	16	no	—
323	C₂×C₄	—	2	96	no	—
324	C₂×C₄	—	2	96	no	—
325	C₂×C₄	C₂²×D₄×C₁₃	1	24	yes	—
326	C₂×C₄	C₂²×D₄×C₁₃	1	48	yes	—
327	C₂×C₄	C₂⁵×C₁₃	1	16	yes	—
328	C₂×C₄	C₂⁵×C₁₃	1	12	yes	—
329	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
330	C₂×C₄	C₂⁵×C₁₃	1	12	yes	—
331	C₂²	—	2	32	no	—
332	C₂²	—	2	4	no	—
333	C₂²	—	2	4	no	—
334	C₂²	—	2	4	no	—
335	C₂²	—	2	8	no	—
336	C₂²	—	2	16	no	—
337	C₂²	—	2	8	no	—
338	C₂²	—	2	16	no	—
339	C₂²	—	4	16	no	—
340	C₂²	C₂³×D₄×C₁₃	1	4	yes	—
341	C₂²	C₂³×D₄×C₁₃	1	2	yes	—
342	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	4	yes	—
343	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	8	yes	complemented
344	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
345	C₄	—	2	8	no	—
346	C₄	—	2	12	no	—
347	C₄	—	2	16	no	—
348	C₄	C₂³×D₄×C₁₃	1	24	yes	—
349	C₂	—	2	4	no	—
350	C₂	—	2	8	no	—
351	C₂	—	4	8	no	—
352	C₂	C₁₃×#3486	1	4	yes	direct product factor
353	C₂	C₂⁴×D₄×C₁₃	1	1	yes	characteristic
354	C₂	C₂²×C₁₃×2₋¹⁺⁴	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×C₁₃×2₋¹⁺⁴	C₂	semidirect
2. C₂⁴×Q₈×C₁₃	C₂	semidirect
3. C₁₃×#3486	C₂	direct (N × H)
4. C₂×D₄×Q₈×C₁₃	C₂	semidirect
5. C₂×C₁₃×#548	C₂	semidirect
6. C₂×C₁₃×#536	C₂	semidirect
7. C₂×C₁₃×#525	C₂	semidirect
8. C₂×C₁₃×#519	C₂	semidirect
10. C₂×C₁₃×2₋¹⁺⁴	C₂²	semidirect
12. C₂²×C₁₃×#41	C₂²	semidirect
17. C₂³×Q₈×C₁₃	C₂²	semidirect
18. C₂³×Q₈×C₁₃	C₂²	semidirect
20. D₄×Q₈×C₁₃	C₂²	semidirect
21. C₁₃×#548	C₂²	semidirect
22. C₁₃×#536	C₂²	semidirect
23. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
24. C₂×C₁₃×#124	C₂²	semidirect
25. C₁₃×#525	C₂²	semidirect
28. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
31. C₁₃×#519	C₂²	semidirect
32. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
40. C₂×C₁₃×#41	C₂³	semidirect
45. C₂²×Q₈×C₁₃	D₄	semidirect
52. C₂²×Q₈×C₁₃	C₂³	semidirect
62. C₁₃×C₄⋊Q₈	C₂³	semidirect
63. C₁₃×#124	C₂³	semidirect
66. C₁₃×C₂²⋊Q₈	C₂³	semidirect
69. C₄×Q₈×C₁₃	C₂³	semidirect
78. C₂×#3486	C₁₃	direct (N × H)
93. C₂×Q₈×C₁₃	C₂×D₄	semidirect
122. C₂²×2₋¹⁺⁴	C₂×C₁₃	semidirect
123. C₂⁴×Q₈	C₂×C₁₃	semidirect
124. #3486	C₂×C₁₃	direct (N × H)
125. C₂×D₄×Q₈	C₂×C₁₃	semidirect
126. C₂×#548	C₂×C₁₃	semidirect
127. C₂×#536	C₂×C₁₃	semidirect
128. C₂×#525	C₂×C₁₃	semidirect
129. C₂×#519	C₂×C₁₃	semidirect
139. C₂³×C₁₃	2₋¹⁺⁴	semidirect
163. C₂×2₋¹⁺⁴	C₂²×C₁₃	semidirect
165. C₂²×#41	C₂²×C₁₃	semidirect
170. C₂³×Q₈	C₂²×C₁₃	semidirect
171. C₂³×Q₈	C₂²×C₁₃	semidirect
173. D₄×Q₈	C₂²×C₁₃	semidirect
174. #548	C₂²×C₁₃	semidirect
175. #536	C₂²×C₁₃	semidirect
176. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
177. C₂×#124	C₂²×C₁₃	semidirect
178. #525	C₂²×C₁₃	semidirect
181. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
184. #519	C₂²×C₁₃	semidirect
185. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
200. C₂²×C₁₃	C₂×2₋¹⁺⁴	semidirect
211. C₂×#41	C₂³×C₁₃	semidirect
216. C₂²×Q₈	D₄×C₁₃	semidirect
223. C₂²×Q₈	C₂³×C₁₃	semidirect
233. C₄⋊Q₈	C₂³×C₁₃	semidirect
234. #124	C₂³×C₁₃	semidirect
237. C₂²⋊Q₈	C₂³×C₁₃	semidirect
240. C₄×Q₈	C₂³×C₁₃	semidirect
252. C₂×C₁₃	#3486	direct (N × H)
269. C₂×Q₈	C₂×D₄×C₁₃	semidirect
298. C₁₃	C₂×#3486	direct (N × H)
308. C₂³	C₁₃×2₋¹⁺⁴	semidirect
343. C₂²	C₂×C₁₃×2₋¹⁺⁴	semidirect
352. C₂	C₁₃×#3486	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×C₁₃×2₋¹⁺⁴	2
C₂⁴×Q₈×C₁₃	2
C₁₃×#3486	2
C₂×D₄×Q₈×C₁₃	2
C₂×C₁₃×#548	2
C₂×C₁₃×#536	2
C₂×C₁₃×#525	2
C₂×C₁₃×#519	2
C₂×#3486	13

Subgroups — C2×C13×#3486 #15749121

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3486 #15749121