Subgroups — C₂×C₁₃×#3568 #15749075

Order 3328.

6726 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3568	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₁₃×#563	C₂	1	3	yes	maximal, complemented
3	C₂×C₁₃×H(3,𝔽₄)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×#556	C₂	1	6	yes	maximal, complemented
5	C₂×C₁₃×#551	C₂	1	6	yes	maximal, complemented
6	C₂×C₁₃×#542	C₂	1	6	yes	maximal, complemented
7	C₂×C₁₃×#538	C₂	1	6	yes	maximal, complemented
8	C₂×C₁₃×#529	C₂	1	3	yes	maximal, complemented
9	C₁₃×#563	C₂²	1	48	yes	complemented
10	C₁₃×H(3,𝔽₄)	C₂²	1	16	yes	complemented
11	C₁₃×#556	C₂²	1	96	yes	complemented
12	C₁₃×#551	C₂²	1	96	yes	complemented
13	C₁₃×#542	C₂²	1	96	yes	complemented
14	C₁₃×#538	C₂²	1	96	yes	complemented
15	C₂×C₁₃×C₄⋊Q₈	C₂²	1	6	yes	complemented
16	C₁₃×#529	C₂²	1	48	yes	complemented
17	C₂×C₁₃×#126	C₂²	1	6	yes	complemented
18	C₂×C₁₃×#126	C₂²	1	6	yes	complemented
19	C₂×C₁₃×#126	C₂²	1	6	yes	complemented
20	C₂×C₁₃×#126	C₂²	1	6	yes	complemented
21	C₂×C₁₃×#126	C₂²	1	2	yes	complemented
22	C₂×C₁₃×#125	C₂²	1	3	yes	complemented
23	C₂×C₁₃×#124	C₂²	1	3	yes	—
24	C₂×C₁₃×#124	C₂²	1	6	yes	—
25	C₂×C₁₃×#124	C₂²	1	6	yes	—
26	C₂×C₁₃×#124	C₂²	1	6	yes	complemented
27	C₂×C₁₃×#123	C₂²	1	6	yes	—
28	C₂×C₁₃×#123	C₂²	1	6	yes	—
29	C₂×C₁₃×#123	C₂²	1	6	yes	complemented
30	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	6	yes	complemented
31	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	6	yes	complemented
32	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	3	yes	complemented
33	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	6	yes	complemented
34	C₂×C₁₃×#121	C₂²	1	3	yes	—
35	C₂×C₁₃×#121	C₂²	1	6	yes	—
36	C₂×C₁₃×#120	C₂²	1	6	yes	—
37	C₂×C₁₃×#120	C₂²	1	2	yes	complemented
38	C₂×C₄×Q₈×C₁₃	C₂²	1	3	yes	complemented
39	C₂×C₄×Q₈×C₁₃	C₂²	1	6	yes	complemented
40	C₂×C₄×D₄×C₁₃	C₂²	1	3	yes	—
41	C₂×C₄×D₄×C₁₃	C₂²	1	6	yes	—
42	C₂×C₄×D₄×C₁₃	C₂²	1	6	yes	complemented
43	C₂×C₁₃×#117	C₂²	1	6	yes	complemented
44	C₂×C₁₃×#117	C₂²	1	6	yes	complemented
45	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	6	yes	complemented
46	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
47	C₂⁵×C₁₃	C₂³	1	2	yes	—
48	C₂²×Q₈×C₁₃	C₂³	1	6	yes	—
49	C₂²×Q₈×C₁₃	C₂³	1	3	yes	—
50	C₂²×D₄×C₁₃	C₂³	1	3	yes	—
51	C₂²×D₄×C₁₃	C₂³	1	6	yes	—
52	C₂²×D₄×C₁₃	C₂³	1	6	yes	—
53	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
54	C₂³×C₄×C₁₃	C₂³	1	6	yes	—
55	C₂³×C₄×C₁₃	C₂³	1	6	yes	—
56	C₁₃×C₄⋊Q₈	C₂³	1	48	yes	complemented
57	C₁₃×#126	C₂³	1	48	yes	complemented
58	C₁₃×#126	C₂³	1	48	yes	complemented
59	C₁₃×#126	C₂³	1	48	yes	complemented
60	C₁₃×#126	C₂³	1	16	yes	complemented
61	C₁₃×#126	C₂³	1	48	yes	complemented
62	C₁₃×#125	C₂³	1	24	yes	complemented
63	C₁₃×#124	C₂³	1	24	yes	—
64	C₁₃×#124	C₂³	1	48	yes	—
65	C₁₃×#124	C₂³	1	48	yes	—
66	C₁₃×#124	C₂³	1	48	yes	complemented
67	C₁₃×#123	C₂³	1	48	yes	—
68	C₁₃×#123	C₂³	1	48	yes	—
69	C₁₃×#123	C₂³	1	48	yes	complemented
70	C₁₃×C₂²⋊Q₈	C₂³	1	24	yes	complemented
71	C₁₃×C₂²⋊Q₈	C₂³	1	48	yes	complemented
72	C₁₃×C₂²⋊Q₈	C₂³	1	48	yes	complemented
73	C₁₃×C₂²⋊Q₈	C₂³	1	48	yes	complemented
74	C₁₃×#121	C₂³	1	24	yes	—
75	C₁₃×#121	C₂³	1	48	yes	—
76	C₁₃×#120	C₂³	1	48	yes	—
77	C₁₃×#120	C₂³	1	16	yes	complemented
78	C₄×Q₈×C₁₃	C₂³	1	24	yes	complemented
79	C₄×Q₈×C₁₃	C₂³	1	48	yes	complemented
80	C₄×D₄×C₁₃	C₂³	1	24	yes	—
81	C₄×D₄×C₁₃	C₂³	1	48	yes	—
82	C₄×D₄×C₁₃	C₂³	1	48	yes	complemented
83	C₁₃×#117	C₂³	1	48	yes	complemented
84	C₁₃×#117	C₂³	1	48	yes	complemented
85	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
86	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
87	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
88	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
89	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
90	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
91	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
92	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
93	C₂×C₁₃×C₂²⋊C₄	C₂³	1	6	yes	—
94	C₂×C₁₃×C₂²⋊C₄	C₂³	1	6	yes	—
95	C₂×C₁₃×C₂²⋊C₄	C₂³	1	6	yes	—
96	C₂×C₁₃×C₂²⋊C₄	C₂³	1	6	yes	—
97	C₂×C₁₃×C₂²⋊C₄	C₂³	1	6	yes	—
98	C₂×C₁₃×C₂²⋊C₄	C₂³	1	6	yes	—
99	C₂×C₁₃×C₂²⋊C₄	C₂³	1	6	yes	—
100	C₂×C₁₃×C₂²⋊C₄	C₂³	1	6	yes	—
101	C₂×C₁₃×C₂²⋊C₄	C₂³	1	6	yes	—
102	C₂×C₁₃×C₂²⋊C₄	C₂³	1	48	yes	complemented
103	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
104	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
105	C₂×C₄²×C₁₃	C₂³	1	6	yes	—
106	C₂×C₄²×C₁₃	C₂³	1	6	yes	—
107	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
108	C₂×C₄²×C₁₃	C₂³	1	8	yes	complemented
109	C₂×#3568	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
110	C₂⁴×C₁₃	—	4	12	no	—
111	C₂⁴×C₁₃	C₂⁴	1	6	yes	—
112	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
113	C₂⁴×C₁₃	C₂⁴	1	8	yes	—
114	C₂×Q₈×C₁₃	—	4	12	no	—
115	C₂×Q₈×C₁₃	—	4	6	no	—
116	C₂×Q₈×C₁₃	C₂⁴	1	24	yes	—
117	C₂×Q₈×C₁₃	C₂⁴	1	12	yes	—
118	C₂×D₄×C₁₃	—	4	12	no	—
119	C₂×D₄×C₁₃	—	4	6	no	—
120	C₂×D₄×C₁₃	—	4	12	no	—
121	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
122	C₂×D₄×C₁₃	C₂⁴	1	24	yes	—
123	C₂×D₄×C₁₃	C₂⁴	1	24	yes	—
124	C₂²×C₄×C₁₃	—	4	12	no	—
125	C₂²×C₄×C₁₃	—	4	6	no	—
126	C₂²×C₄×C₁₃	—	4	12	no	—
127	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
128	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
129	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
130	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
131	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
132	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
133	C₂²×C₄×C₁₃	C₂⁴	1	24	yes	—
134	C₂²×C₄×C₁₃	C₂⁴	1	24	yes	—
135	C₁₃×C₄⋊C₄	C₂⁴	1	24	yes	—
136	C₁₃×C₄⋊C₄	C₂⁴	1	24	yes	—
137	C₁₃×C₄⋊C₄	C₂⁴	1	24	yes	—
138	C₁₃×C₄⋊C₄	C₂⁴	1	24	yes	—
139	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
140	C₁₃×C₄⋊C₄	C₂⁴	1	24	yes	—
141	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
142	C₁₃×C₄⋊C₄	C₂⁴	1	24	yes	—
143	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
144	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
145	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
146	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
147	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
148	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
149	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
150	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
151	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
152	C₄²×C₁₃	C₂⁴	1	12	yes	—
153	C₄²×C₁₃	C₂⁴	1	4	yes	—
154	C₄²×C₁₃	C₂⁴	1	24	yes	—
155	C₄²×C₁₃	C₂⁴	1	24	yes	—
156	C₄²×C₁₃	C₂⁴	1	8	yes	—
157	#3568	C₂×C₁₃	1	32	yes	direct product factor
158	C₂×#563	C₂×C₁₃	1	3	yes	complemented
159	C₂×H(3,𝔽₄)	C₂×C₁₃	1	1	yes	characteristic, complemented
160	C₂×#556	C₂×C₁₃	1	6	yes	complemented
161	C₂×#551	C₂×C₁₃	1	6	yes	complemented
162	C₂×#542	C₂×C₁₃	1	6	yes	complemented
163	C₂×#538	C₂×C₁₃	1	6	yes	complemented
164	C₂×#529	C₂×C₁₃	1	3	yes	complemented
165	C₂³×C₁₃	—	2	6	no	—
166	C₂³×C₁₃	—	2	12	no	—
167	C₂³×C₁₃	—	2	12	no	—
168	C₂³×C₁₃	—	2	12	no	—
169	C₂³×C₁₃	—	4	24	no	—
170	C₂³×C₁₃	—	8	16	no	—
171	C₂³×C₁₃	C₂⁵	1	12	yes	—
172	C₂³×C₁₃	C₂⁵	1	2	yes	—
173	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
174	Q₈×C₁₃	—	4	24	no	—
175	Q₈×C₁₃	—	4	12	no	—
176	D₄×C₁₃	—	4	24	no	—
177	D₄×C₁₃	—	4	12	no	—
178	D₄×C₁₃	—	4	24	no	—
179	C₂×C₄×C₁₃	—	2	6	no	—
180	C₂×C₄×C₁₃	—	2	12	no	—
181	C₂×C₄×C₁₃	—	2	6	no	—
182	C₂×C₄×C₁₃	—	2	12	no	—
183	C₂×C₄×C₁₃	—	2	12	no	—
184	C₂×C₄×C₁₃	—	4	24	no	—
185	C₂×C₄×C₁₃	—	4	12	no	—
186	C₂×C₄×C₁₃	—	4	24	no	—
187	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
188	C₂×C₄×C₁₃	C₂⁵	1	12	yes	—
189	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
190	C₂×C₄×C₁₃	C₂⁵	1	12	yes	—
191	C₂×C₄×C₁₃	C₂⁵	1	12	yes	—
192	#563	C₂²×C₁₃	1	48	yes	complemented
193	H(3,𝔽₄)	C₂²×C₁₃	1	16	yes	complemented
194	#556	C₂²×C₁₃	1	96	yes	complemented
195	#551	C₂²×C₁₃	1	96	yes	complemented
196	#542	C₂²×C₁₃	1	96	yes	complemented
197	#538	C₂²×C₁₃	1	96	yes	complemented
198	C₂×C₄⋊Q₈	C₂²×C₁₃	1	6	yes	complemented
199	#529	C₂²×C₁₃	1	48	yes	complemented
200	C₂×#126	C₂²×C₁₃	1	6	yes	complemented
201	C₂×#126	C₂²×C₁₃	1	6	yes	complemented
202	C₂×#126	C₂²×C₁₃	1	6	yes	complemented
203	C₂×#126	C₂²×C₁₃	1	2	yes	complemented
204	C₂×#126	C₂²×C₁₃	1	6	yes	complemented
205	C₂×#125	C₂²×C₁₃	1	3	yes	complemented
206	C₂×#124	C₂²×C₁₃	1	3	yes	—
207	C₂×#124	C₂²×C₁₃	1	6	yes	—
208	C₂×#124	C₂²×C₁₃	1	6	yes	—
209	C₂×#124	C₂²×C₁₃	1	6	yes	complemented
210	C₂×#123	C₂²×C₁₃	1	6	yes	—
211	C₂×#123	C₂²×C₁₃	1	6	yes	—
212	C₂×#123	C₂²×C₁₃	1	6	yes	complemented
213	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	3	yes	complemented
214	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	6	yes	complemented
215	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	6	yes	complemented
216	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	6	yes	complemented
217	C₂×#121	C₂²×C₁₃	1	3	yes	—
218	C₂×#121	C₂²×C₁₃	1	6	yes	—
219	C₂×#120	C₂²×C₁₃	1	6	yes	—
220	C₂×#120	C₂²×C₁₃	1	2	yes	complemented
221	C₂×C₄×Q₈	C₂²×C₁₃	1	3	yes	complemented
222	C₂×C₄×Q₈	C₂²×C₁₃	1	6	yes	complemented
223	C₂×C₄×D₄	C₂²×C₁₃	1	3	yes	—
224	C₂×C₄×D₄	C₂²×C₁₃	1	6	yes	—
225	C₂×C₄×D₄	C₂²×C₁₃	1	6	yes	complemented
226	C₂×#117	C₂²×C₁₃	1	6	yes	complemented
227	C₂×#117	C₂²×C₁₃	1	6	yes	complemented
228	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	6	yes	complemented
229	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic, complemented
230	C₂²×C₁₃	—	2	6	no	—
231	C₂²×C₁₃	—	2	12	no	—
232	C₂²×C₁₃	—	2	12	no	—
233	C₂²×C₁₃	—	2	12	no	—
234	C₂²×C₁₃	—	4	4	no	—
235	C₂²×C₁₃	—	4	24	no	—
236	C₂²×C₁₃	—	8	16	no	—
237	C₂²×C₁₃	#585	1	6	yes	—
238	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
239	C₄×C₁₃	—	2	6	no	—
240	C₄×C₁₃	—	2	12	no	—
241	C₄×C₁₃	—	2	6	no	—
242	C₄×C₁₃	—	2	12	no	—
243	C₄×C₁₃	—	2	12	no	—
244	C₂⁵	C₂³×C₁₃	1	2	yes	—
245	C₂²×Q₈	C₂³×C₁₃	1	6	yes	—
246	C₂²×Q₈	C₂³×C₁₃	1	3	yes	—
247	C₂²×D₄	C₂³×C₁₃	1	3	yes	—
248	C₂²×D₄	C₂³×C₁₃	1	6	yes	—
249	C₂²×D₄	C₂³×C₁₃	1	6	yes	—
250	C₂³×C₄	C₂³×C₁₃	1	6	yes	—
251	C₂³×C₄	C₂³×C₁₃	1	6	yes	—
252	C₂³×C₄	C₂³×C₁₃	1	3	yes	—
253	C₄⋊Q₈	C₂³×C₁₃	1	48	yes	complemented
254	#126	C₂³×C₁₃	1	48	yes	complemented
255	#126	C₂³×C₁₃	1	48	yes	complemented
256	#126	C₂³×C₁₃	1	48	yes	complemented
257	#126	C₂³×C₁₃	1	16	yes	complemented
258	#126	C₂³×C₁₃	1	48	yes	complemented
259	#125	C₂³×C₁₃	1	24	yes	complemented
260	#124	C₂³×C₁₃	1	24	yes	—
261	#124	C₂³×C₁₃	1	48	yes	—
262	#124	C₂³×C₁₃	1	48	yes	—
263	#124	C₂³×C₁₃	1	48	yes	complemented
264	#123	C₂³×C₁₃	1	48	yes	—
265	#123	C₂³×C₁₃	1	48	yes	—
266	#123	C₂³×C₁₃	1	48	yes	complemented
267	C₂²⋊Q₈	C₂³×C₁₃	1	24	yes	complemented
268	C₂²⋊Q₈	C₂³×C₁₃	1	48	yes	complemented
269	C₂²⋊Q₈	C₂³×C₁₃	1	48	yes	complemented
270	C₂²⋊Q₈	C₂³×C₁₃	1	48	yes	complemented
271	#121	C₂³×C₁₃	1	24	yes	—
272	#121	C₂³×C₁₃	1	48	yes	—
273	#120	C₂³×C₁₃	1	48	yes	—
274	#120	C₂³×C₁₃	1	16	yes	complemented
275	C₄×Q₈	C₂³×C₁₃	1	24	yes	complemented
276	C₄×Q₈	C₂³×C₁₃	1	48	yes	complemented
277	C₄×D₄	C₂³×C₁₃	1	24	yes	—
278	C₄×D₄	C₂³×C₁₃	1	48	yes	—
279	C₄×D₄	C₂³×C₁₃	1	48	yes	complemented
280	#117	C₂³×C₁₃	1	48	yes	complemented
281	#117	C₂³×C₁₃	1	48	yes	complemented
282	C₂×C₄⋊C₄	C₂³×C₁₃	1	6	yes	—
283	C₂×C₄⋊C₄	C₂³×C₁₃	1	6	yes	—
284	C₂×C₄⋊C₄	C₂³×C₁₃	1	6	yes	—
285	C₂×C₄⋊C₄	C₂³×C₁₃	1	6	yes	—
286	C₂×C₄⋊C₄	C₂³×C₁₃	1	3	yes	—
287	C₂×C₄⋊C₄	C₂³×C₁₃	1	6	yes	—
288	C₂×C₄⋊C₄	C₂³×C₁₃	1	3	yes	—
289	C₂×C₄⋊C₄	C₂³×C₁₃	1	6	yes	—
290	C₂×C₂²⋊C₄	C₂³×C₁₃	1	6	yes	—
291	C₂×C₂²⋊C₄	C₂³×C₁₃	1	6	yes	—
292	C₂×C₂²⋊C₄	C₂³×C₁₃	1	6	yes	—
293	C₂×C₂²⋊C₄	C₂³×C₁₃	1	6	yes	—
294	C₂×C₂²⋊C₄	C₂³×C₁₃	1	6	yes	—
295	C₂×C₂²⋊C₄	C₂³×C₁₃	1	6	yes	—
296	C₂×C₂²⋊C₄	C₂³×C₁₃	1	6	yes	—
297	C₂×C₂²⋊C₄	C₂³×C₁₃	1	6	yes	—
298	C₂×C₂²⋊C₄	C₂³×C₁₃	1	6	yes	—
299	C₂×C₂²⋊C₄	C₂³×C₁₃	1	48	yes	complemented
300	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
301	C₂×C₄²	C₂³×C₁₃	1	6	yes	—
302	C₂×C₄²	C₂³×C₁₃	1	6	yes	—
303	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
304	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
305	C₂×C₄²	C₂³×C₁₃	1	8	yes	complemented
306	C₂×C₁₃	—	4	2	no	—
307	C₂×C₁₃	—	4	12	no	—
308	C₂×C₁₃	#3568	1	4	yes	direct product factor
309	C₂×C₁₃	C₂×#585	1	3	yes	—
310	C₂⁴	—	4	12	no	—
311	C₂⁴	C₂⁴×C₁₃	1	6	yes	—
312	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
313	C₂⁴	C₂⁴×C₁₃	1	8	yes	—
314	C₂×Q₈	—	4	12	no	—
315	C₂×Q₈	—	4	6	no	—
316	C₂×Q₈	C₂⁴×C₁₃	1	24	yes	—
317	C₂×Q₈	C₂⁴×C₁₃	1	12	yes	—
318	C₂×D₄	—	4	12	no	—
319	C₂×D₄	—	4	6	no	—
320	C₂×D₄	—	4	12	no	—
321	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
322	C₂×D₄	C₂⁴×C₁₃	1	24	yes	—
323	C₂×D₄	C₂⁴×C₁₃	1	24	yes	—
324	C₂²×C₄	—	4	12	no	—
325	C₂²×C₄	—	4	6	no	—
326	C₂²×C₄	—	4	12	no	—
327	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
328	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
329	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
330	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
331	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
332	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
333	C₂²×C₄	C₂⁴×C₁₃	1	24	yes	—
334	C₂²×C₄	C₂⁴×C₁₃	1	24	yes	—
335	C₄⋊C₄	C₂⁴×C₁₃	1	24	yes	—
336	C₄⋊C₄	C₂⁴×C₁₃	1	24	yes	—
337	C₄⋊C₄	C₂⁴×C₁₃	1	24	yes	—
338	C₄⋊C₄	C₂⁴×C₁₃	1	24	yes	—
339	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
340	C₄⋊C₄	C₂⁴×C₁₃	1	24	yes	—
341	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
342	C₄⋊C₄	C₂⁴×C₁₃	1	24	yes	—
343	C₂²⋊C₄	C₂⁴×C₁₃	1	24	yes	—
344	C₂²⋊C₄	C₂⁴×C₁₃	1	24	yes	—
345	C₂²⋊C₄	C₂⁴×C₁₃	1	24	yes	—
346	C₂²⋊C₄	C₂⁴×C₁₃	1	24	yes	—
347	C₂²⋊C₄	C₂⁴×C₁₃	1	24	yes	—
348	C₂²⋊C₄	C₂⁴×C₁₃	1	24	yes	—
349	C₂²⋊C₄	C₂⁴×C₁₃	1	24	yes	—
350	C₂²⋊C₄	C₂⁴×C₁₃	1	24	yes	—
351	C₂²⋊C₄	C₂⁴×C₁₃	1	24	yes	—
352	C₄²	C₂⁴×C₁₃	1	12	yes	—
353	C₄²	C₂⁴×C₁₃	1	4	yes	—
354	C₄²	C₂⁴×C₁₃	1	24	yes	—
355	C₄²	C₂⁴×C₁₃	1	24	yes	—
356	C₄²	C₂⁴×C₁₃	1	8	yes	—
357	C₁₃	C₂×#3568	1	1	yes	characteristic, direct product factor, Sylow
358	C₂³	—	2	6	no	—
359	C₂³	—	2	12	no	—
360	C₂³	—	2	12	no	—
361	C₂³	—	2	12	no	—
362	C₂³	—	4	24	no	—
363	C₂³	—	8	16	no	—
364	C₂³	C₂⁵×C₁₃	1	12	yes	—
365	C₂³	C₂⁵×C₁₃	1	2	yes	—
366	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
367	Q₈	—	4	24	no	—
368	Q₈	—	4	12	no	—
369	D₄	—	4	24	no	—
370	D₄	—	4	12	no	—
371	D₄	—	4	24	no	—
372	C₂×C₄	—	2	6	no	—
373	C₂×C₄	—	2	12	no	—
374	C₂×C₄	—	2	6	no	—
375	C₂×C₄	—	2	12	no	—
376	C₂×C₄	—	2	12	no	—
377	C₂×C₄	—	4	24	no	—
378	C₂×C₄	—	4	12	no	—
379	C₂×C₄	—	4	24	no	—
380	C₂×C₄	C₂⁵×C₁₃	1	6	yes	—
381	C₂×C₄	C₂⁵×C₁₃	1	12	yes	—
382	C₂×C₄	C₂⁵×C₁₃	1	6	yes	—
383	C₂×C₄	C₂⁵×C₁₃	1	12	yes	—
384	C₂×C₄	C₂⁵×C₁₃	1	12	yes	—
385	C₂²	—	2	6	no	—
386	C₂²	—	2	12	no	—
387	C₂²	—	2	12	no	—
388	C₂²	—	2	12	no	—
389	C₂²	—	4	4	no	—
390	C₂²	—	4	24	no	—
391	C₂²	—	8	16	no	—
392	C₂²	C₁₃×#585	1	6	yes	—
393	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
394	C₄	—	2	6	no	—
395	C₄	—	2	12	no	—
396	C₄	—	2	6	no	—
397	C₄	—	2	12	no	—
398	C₄	—	2	12	no	—
399	C₂	—	4	12	no	—
400	C₂	—	4	2	no	—
401	C₂	C₁₃×#3568	1	4	yes	direct product factor
402	C₂	C₂×C₁₃×#585	1	3	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. C₁₃×#3568	C₂	direct (N × H)
2. C₂×C₁₃×#563	C₂	semidirect
3. C₂×C₁₃×H(3,𝔽₄)	C₂	semidirect
4. C₂×C₁₃×#556	C₂	semidirect
5. C₂×C₁₃×#551	C₂	semidirect
6. C₂×C₁₃×#542	C₂	semidirect
7. C₂×C₁₃×#538	C₂	semidirect
8. C₂×C₁₃×#529	C₂	semidirect
9. C₁₃×#563	C₂²	semidirect
10. C₁₃×H(3,𝔽₄)	C₂²	semidirect
11. C₁₃×#556	C₂²	semidirect
12. C₁₃×#551	C₂²	semidirect
13. C₁₃×#542	C₂²	semidirect
14. C₁₃×#538	C₂²	semidirect
15. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
16. C₁₃×#529	C₂²	semidirect
17. C₂×C₁₃×#126	C₂²	semidirect
18. C₂×C₁₃×#126	C₂²	semidirect
19. C₂×C₁₃×#126	C₂²	semidirect
20. C₂×C₁₃×#126	C₂²	semidirect
21. C₂×C₁₃×#126	C₂²	semidirect
22. C₂×C₁₃×#125	C₂²	semidirect
26. C₂×C₁₃×#124	C₂²	semidirect
29. C₂×C₁₃×#123	C₂²	semidirect
30. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
31. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
32. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
33. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
37. C₂×C₁₃×#120	C₂²	semidirect
38. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
39. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
42. C₂×C₄×D₄×C₁₃	C₂²	semidirect
43. C₂×C₁₃×#117	C₂²	semidirect
44. C₂×C₁₃×#117	C₂²	semidirect
45. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
46. C₂²×C₄²×C₁₃	C₂²	semidirect
56. C₁₃×C₄⋊Q₈	C₂³	semidirect
57. C₁₃×#126	C₂³	semidirect
58. C₁₃×#126	C₂³	semidirect
59. C₁₃×#126	C₂³	semidirect
60. C₁₃×#126	C₂³	semidirect
61. C₁₃×#126	C₂³	semidirect
62. C₁₃×#125	C₂³	semidirect
66. C₁₃×#124	C₂³	semidirect
69. C₁₃×#123	C₂³	semidirect
70. C₁₃×C₂²⋊Q₈	C₂³	semidirect
71. C₁₃×C₂²⋊Q₈	C₂³	semidirect
72. C₁₃×C₂²⋊Q₈	C₂³	semidirect
73. C₁₃×C₂²⋊Q₈	C₂³	semidirect
77. C₁₃×#120	C₂³	semidirect
78. C₄×Q₈×C₁₃	C₂³	semidirect
79. C₄×Q₈×C₁₃	C₂³	semidirect
82. C₄×D₄×C₁₃	C₂³	semidirect
83. C₁₃×#117	C₂³	semidirect
84. C₁₃×#117	C₂³	semidirect
102. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
108. C₂×C₄²×C₁₃	C₂³	semidirect
109. C₂×#3568	C₁₃	direct (N × H)
157. #3568	C₂×C₁₃	direct (N × H)
158. C₂×#563	C₂×C₁₃	semidirect
159. C₂×H(3,𝔽₄)	C₂×C₁₃	semidirect
160. C₂×#556	C₂×C₁₃	semidirect
161. C₂×#551	C₂×C₁₃	semidirect
162. C₂×#542	C₂×C₁₃	semidirect
163. C₂×#538	C₂×C₁₃	semidirect
164. C₂×#529	C₂×C₁₃	semidirect
192. #563	C₂²×C₁₃	semidirect
193. H(3,𝔽₄)	C₂²×C₁₃	semidirect
194. #556	C₂²×C₁₃	semidirect
195. #551	C₂²×C₁₃	semidirect
196. #542	C₂²×C₁₃	semidirect
197. #538	C₂²×C₁₃	semidirect
198. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
199. #529	C₂²×C₁₃	semidirect
200. C₂×#126	C₂²×C₁₃	semidirect
201. C₂×#126	C₂²×C₁₃	semidirect
202. C₂×#126	C₂²×C₁₃	semidirect
203. C₂×#126	C₂²×C₁₃	semidirect
204. C₂×#126	C₂²×C₁₃	semidirect
205. C₂×#125	C₂²×C₁₃	semidirect
209. C₂×#124	C₂²×C₁₃	semidirect
212. C₂×#123	C₂²×C₁₃	semidirect
213. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
214. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
215. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
216. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
220. C₂×#120	C₂²×C₁₃	semidirect
221. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
222. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
225. C₂×C₄×D₄	C₂²×C₁₃	semidirect
226. C₂×#117	C₂²×C₁₃	semidirect
227. C₂×#117	C₂²×C₁₃	semidirect
228. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
229. C₂²×C₄²	C₂²×C₁₃	semidirect
253. C₄⋊Q₈	C₂³×C₁₃	semidirect
254. #126	C₂³×C₁₃	semidirect
255. #126	C₂³×C₁₃	semidirect
256. #126	C₂³×C₁₃	semidirect
257. #126	C₂³×C₁₃	semidirect
258. #126	C₂³×C₁₃	semidirect
259. #125	C₂³×C₁₃	semidirect
263. #124	C₂³×C₁₃	semidirect
266. #123	C₂³×C₁₃	semidirect
267. C₂²⋊Q₈	C₂³×C₁₃	semidirect
268. C₂²⋊Q₈	C₂³×C₁₃	semidirect
269. C₂²⋊Q₈	C₂³×C₁₃	semidirect
270. C₂²⋊Q₈	C₂³×C₁₃	semidirect
274. #120	C₂³×C₁₃	semidirect
275. C₄×Q₈	C₂³×C₁₃	semidirect
276. C₄×Q₈	C₂³×C₁₃	semidirect
279. C₄×D₄	C₂³×C₁₃	semidirect
280. #117	C₂³×C₁₃	semidirect
281. #117	C₂³×C₁₃	semidirect
299. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
305. C₂×C₄²	C₂³×C₁₃	semidirect
308. C₂×C₁₃	#3568	direct (N × H)
357. C₁₃	C₂×#3568	direct (N × H)
401. C₂	C₁₃×#3568	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×#3568	2
C₂×C₁₃×#563	2
C₂×C₁₃×H(3,𝔽₄)	2
C₂×C₁₃×#556	2
C₂×C₁₃×#551	2
C₂×C₁₃×#542	2
C₂×C₁₃×#538	2
C₂×C₁₃×#529	2
C₂×#3568	13

Subgroups — C2×C13×#3568 #15749075

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3568 #15749075