Subgroups — C₂²×C₁₃×#542 #15749017

Order 3328.

7974 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#542	C₂	1	48	yes	maximal, direct product factor
2	C₂²×C₁₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₁₃×#126	C₂	1	2	yes	maximal, complemented
4	C₂²×C₁₃×#124	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₁₃×#124	C₂	1	2	yes	maximal, complemented
6	C₂²×C₁₃×#123	C₂	1	2	yes	maximal, complemented
7	C₂²×C₁₃×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
8	C₂²×C₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₁₃×#121	C₂	1	1	yes	maximal, characteristic
10	C₂²×C₄×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₂³×Q₈×C₁₃	C₂²	1	2	yes	—
15	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
16	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
17	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
19	C₁₃×#542	C₂²	1	256	yes	direct product factor
20	C₂×C₁₃×C₄⋊Q₈	C₂²	1	24	yes	complemented
21	C₂×C₁₃×#126	C₂²	1	48	yes	complemented
22	C₂×C₁₃×#124	C₂²	1	24	yes	complemented
23	C₂×C₁₃×#124	C₂²	1	48	yes	complemented
24	C₂×C₁₃×#123	C₂²	1	48	yes	complemented
25	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	48	yes	complemented
26	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	24	yes	complemented
27	C₂×C₁₃×#121	C₂²	1	24	yes	—
28	C₂×C₄×Q₈×C₁₃	C₂²	1	24	yes	complemented
29	C₂×C₄×D₄×C₁₃	C₂²	1	24	yes	complemented
30	C₂×C₁₃×#117	C₂²	1	24	yes	complemented
31	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
32	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
36	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
37	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
38	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
39	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
40	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
41	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
42	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
43	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
44	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
45	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
46	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
47	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
48	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
49	C₂⁵×C₁₃	C₂³	1	2	yes	—
50	C₂²×Q₈×C₁₃	—	2	8	no	—
51	C₂²×Q₈×C₁₃	—	4	8	no	—
52	C₂²×Q₈×C₁₃	C₂³	1	12	yes	—
53	C₂²×Q₈×C₁₃	C₂³	1	24	yes	—
54	C₂²×D₄×C₁₃	—	2	8	no	—
55	C₂²×D₄×C₁₃	—	4	8	no	—
56	C₂²×D₄×C₁₃	C₂³	1	12	yes	—
57	C₂²×D₄×C₁₃	C₂³	1	24	yes	—
58	C₂³×C₄×C₁₃	—	2	8	no	—
59	C₂³×C₄×C₁₃	—	4	8	no	—
60	C₂³×C₄×C₁₃	C₂³	1	12	yes	—
61	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
64	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
67	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
69	C₂³×C₄×C₁₃	C₂³	1	24	yes	—
70	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
71	C₁₃×C₄⋊Q₈	C₂³	1	64	yes	complemented
72	C₁₃×#126	C₂³	1	128	yes	complemented
73	C₁₃×#124	C₂³	1	64	yes	complemented
74	C₁₃×#124	C₂³	1	128	yes	complemented
75	C₁₃×#123	C₂³	1	128	yes	complemented
76	C₁₃×C₂²⋊Q₈	C₂³	1	128	yes	complemented
77	C₁₃×C₂²⋊Q₈	C₂³	1	64	yes	complemented
78	C₁₃×#121	C₂³	1	64	yes	—
79	C₄×Q₈×C₁₃	C₂³	1	64	yes	complemented
80	C₄×D₄×C₁₃	C₂³	1	64	yes	complemented
81	C₁₃×#117	C₂³	1	64	yes	complemented
82	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	—
83	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	—
84	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	—
85	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	—
86	C₂×C₁₃×C₄⋊C₄	C₂³	1	24	yes	—
87	C₂×C₁₃×C₄⋊C₄	C₂³	1	24	yes	—
88	C₂×C₁₃×C₄⋊C₄	C₂³	1	24	yes	—
89	C₂×C₁₃×C₂²⋊C₄	C₂³	1	12	yes	—
90	C₂×C₁₃×C₂²⋊C₄	C₂³	1	12	yes	—
91	C₂×C₁₃×C₂²⋊C₄	C₂³	1	24	yes	—
92	C₂×C₁₃×C₂²⋊C₄	C₂³	1	24	yes	—
93	C₂×C₁₃×C₂²⋊C₄	C₂³	1	24	yes	—
94	C₂×C₁₃×C₂²⋊C₄	C₂³	1	24	yes	—
95	C₂×C₁₃×C₂²⋊C₄	C₂³	1	24	yes	—
96	C₂×C₄²×C₁₃	C₂³	1	12	yes	—
97	C₂×C₄²×C₁₃	C₂³	1	12	yes	—
98	C₂×C₄²×C₁₃	C₂³	1	24	yes	—
99	C₂²×#542	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
100	C₂⁴×C₁₃	—	2	4	no	—
101	C₂⁴×C₁₃	—	2	8	no	—
102	C₂⁴×C₁₃	—	2	8	no	—
103	C₂⁴×C₁₃	—	2	4	no	—
104	C₂⁴×C₁₃	—	2	4	no	—
105	C₂⁴×C₁₃	—	2	8	no	—
106	C₂⁴×C₁₃	C₂⁴	1	6	yes	—
107	C₂⁴×C₁₃	C₂⁴	1	12	yes	—
108	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
109	C₂×Q₈×C₁₃	—	2	48	no	—
110	C₂×Q₈×C₁₃	—	4	48	no	—
111	C₂×Q₈×C₁₃	C₂⁴	1	16	yes	—
112	C₂×Q₈×C₁₃	C₂⁴	1	32	yes	—
113	C₂×D₄×C₁₃	—	2	48	no	—
114	C₂×D₄×C₁₃	—	4	48	no	—
115	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
116	C₂×D₄×C₁₃	C₂⁴	1	32	yes	—
117	C₂²×C₄×C₁₃	—	2	4	no	—
118	C₂²×C₄×C₁₃	—	2	8	no	—
119	C₂²×C₄×C₁₃	—	2	4	no	—
120	C₂²×C₄×C₁₃	—	2	8	no	—
121	C₂²×C₄×C₁₃	—	2	8	no	—
122	C₂²×C₄×C₁₃	—	2	4	no	—
123	C₂²×C₄×C₁₃	—	2	4	no	—
124	C₂²×C₄×C₁₃	—	2	4	no	—
125	C₂²×C₄×C₁₃	—	2	48	no	—
126	C₂²×C₄×C₁₃	—	4	48	no	—
127	C₂²×C₄×C₁₃	#41	1	8	yes	—
128	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
129	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
130	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
131	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
132	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
133	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
134	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
135	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
136	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
137	C₂²×C₄×C₁₃	C₂⁴	1	32	yes	—
138	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
139	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
140	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
141	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
142	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
143	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	—
144	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	—
145	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	—
146	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
147	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
148	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
149	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
150	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
151	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
152	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
153	C₄²×C₁₃	C₂⁴	1	16	yes	—
154	C₄²×C₁₃	C₂⁴	1	16	yes	—
155	C₄²×C₁₃	C₂⁴	1	32	yes	—
156	C₂×#542	C₂×C₁₃	1	48	yes	direct product factor
157	C₂²×C₄⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
158	C₂²×#126	C₂×C₁₃	1	2	yes	complemented
159	C₂²×#124	C₂×C₁₃	1	2	yes	complemented
160	C₂²×#124	C₂×C₁₃	1	1	yes	characteristic, complemented
161	C₂²×#123	C₂×C₁₃	1	2	yes	complemented
162	C₂²×C₂²⋊Q₈	C₂×C₁₃	1	2	yes	complemented
163	C₂²×C₂²⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
164	C₂²×#121	C₂×C₁₃	1	1	yes	characteristic
165	C₂²×C₄×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
166	C₂²×C₄×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
167	C₂²×#117	C₂×C₁₃	1	1	yes	characteristic, complemented
168	C₂³×C₁₃	—	2	12	no	—
169	C₂³×C₁₃	—	2	24	no	—
170	C₂³×C₁₃	—	2	24	no	—
171	C₂³×C₁₃	—	2	12	no	—
172	C₂³×C₁₃	—	2	12	no	—
173	C₂³×C₁₃	—	2	24	no	—
174	C₂³×C₁₃	—	4	16	no	—
175	C₂³×C₁₃	—	4	32	no	—
176	C₂³×C₁₃	C₂×#41	1	4	yes	—
177	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
178	C₂³×C₁₃	2₋¹⁺⁴	1	4	yes	—
179	C₂³×C₁₃	C₂⁵	1	4	yes	—
180	C₂³×C₁₃	C₂⁵	1	8	yes	—
181	C₂³×C₁₃	C₂⁵	1	3	yes	—
182	Q₈×C₁₃	—	2	32	no	—
183	Q₈×C₁₃	—	4	32	no	—
184	D₄×C₁₃	—	2	32	no	—
185	D₄×C₁₃	—	4	32	no	—
186	C₂×C₄×C₁₃	—	2	12	no	—
187	C₂×C₄×C₁₃	—	2	24	no	—
188	C₂×C₄×C₁₃	—	2	12	no	—
189	C₂×C₄×C₁₃	—	2	24	no	—
190	C₂×C₄×C₁₃	—	2	24	no	—
191	C₂×C₄×C₁₃	—	2	12	no	—
192	C₂×C₄×C₁₃	—	2	12	no	—
193	C₂×C₄×C₁₃	—	2	12	no	—
194	C₂×C₄×C₁₃	—	2	32	no	—
195	C₂×C₄×C₁₃	—	4	32	no	—
196	C₂×C₄×C₁₃	C₂×#41	1	24	yes	—
197	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
198	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
199	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
200	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
201	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
202	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
203	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
204	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
205	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
206	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
207	C₂³×Q₈	C₂²×C₁₃	1	2	yes	—
208	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
209	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
210	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
211	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	—
212	#542	C₂²×C₁₃	1	256	yes	direct product factor
213	C₂×C₄⋊Q₈	C₂²×C₁₃	1	24	yes	complemented
214	C₂×#126	C₂²×C₁₃	1	48	yes	complemented
215	C₂×#124	C₂²×C₁₃	1	24	yes	complemented
216	C₂×#124	C₂²×C₁₃	1	48	yes	complemented
217	C₂×#123	C₂²×C₁₃	1	48	yes	complemented
218	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	48	yes	complemented
219	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	24	yes	complemented
220	C₂×#121	C₂²×C₁₃	1	24	yes	—
221	C₂×C₄×Q₈	C₂²×C₁₃	1	24	yes	complemented
222	C₂×C₄×D₄	C₂²×C₁₃	1	24	yes	complemented
223	C₂×#117	C₂²×C₁₃	1	24	yes	complemented
224	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
225	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
226	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
227	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
228	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
229	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
230	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
231	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
232	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
233	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
234	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
235	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
236	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
237	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
238	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
239	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
240	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
241	C₂²×C₁₃	—	2	4	no	—
242	C₂²×C₁₃	—	2	8	no	—
243	C₂²×C₁₃	—	2	8	no	—
244	C₂²×C₁₃	—	2	4	no	—
245	C₂²×C₁₃	—	2	4	no	—
246	C₂²×C₁₃	—	2	8	no	—
247	C₂²×C₁₃	—	4	24	no	—
248	C₂²×C₁₃	—	4	48	no	—
249	C₂²×C₁₃	#542	1	16	yes	direct product factor
250	C₂²×C₁₃	C₂²×#41	1	6	yes	—
251	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	6	yes	—
252	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	6	yes	—
253	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
254	C₄×C₁₃	—	2	4	no	—
255	C₄×C₁₃	—	2	8	no	—
256	C₄×C₁₃	—	2	4	no	—
257	C₄×C₁₃	—	2	8	no	—
258	C₄×C₁₃	—	2	8	no	—
259	C₄×C₁₃	—	2	4	no	—
260	C₄×C₁₃	—	2	4	no	—
261	C₄×C₁₃	—	2	4	no	—
262	C₄×C₁₃	C₂²×#41	1	8	yes	—
263	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
264	C₂⁵	C₂³×C₁₃	1	2	yes	—
265	C₂²×Q₈	—	2	8	no	—
266	C₂²×Q₈	—	4	8	no	—
267	C₂²×Q₈	C₂³×C₁₃	1	12	yes	—
268	C₂²×Q₈	C₂³×C₁₃	1	24	yes	—
269	C₂²×D₄	—	2	8	no	—
270	C₂²×D₄	—	4	8	no	—
271	C₂²×D₄	C₂³×C₁₃	1	12	yes	—
272	C₂²×D₄	C₂³×C₁₃	1	24	yes	—
273	C₂³×C₄	—	2	8	no	—
274	C₂³×C₄	—	4	8	no	—
275	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
276	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
277	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
278	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
279	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
280	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
281	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
282	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
283	C₂³×C₄	C₂³×C₁₃	1	12	yes	—
284	C₂³×C₄	C₂³×C₁₃	1	24	yes	—
285	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
286	C₄⋊Q₈	C₂³×C₁₃	1	64	yes	complemented
287	#126	C₂³×C₁₃	1	128	yes	complemented
288	#124	C₂³×C₁₃	1	64	yes	complemented
289	#124	C₂³×C₁₃	1	128	yes	complemented
290	#123	C₂³×C₁₃	1	128	yes	complemented
291	C₂²⋊Q₈	C₂³×C₁₃	1	128	yes	complemented
292	C₂²⋊Q₈	C₂³×C₁₃	1	64	yes	complemented
293	#121	C₂³×C₁₃	1	64	yes	—
294	C₄×Q₈	C₂³×C₁₃	1	64	yes	complemented
295	C₄×D₄	C₂³×C₁₃	1	64	yes	complemented
296	#117	C₂³×C₁₃	1	64	yes	complemented
297	C₂×C₄⋊C₄	C₂³×C₁₃	1	12	yes	—
298	C₂×C₄⋊C₄	C₂³×C₁₃	1	12	yes	—
299	C₂×C₄⋊C₄	C₂³×C₁₃	1	12	yes	—
300	C₂×C₄⋊C₄	C₂³×C₁₃	1	12	yes	—
301	C₂×C₄⋊C₄	C₂³×C₁₃	1	24	yes	—
302	C₂×C₄⋊C₄	C₂³×C₁₃	1	24	yes	—
303	C₂×C₄⋊C₄	C₂³×C₁₃	1	24	yes	—
304	C₂×C₂²⋊C₄	C₂³×C₁₃	1	12	yes	—
305	C₂×C₂²⋊C₄	C₂³×C₁₃	1	12	yes	—
306	C₂×C₂²⋊C₄	C₂³×C₁₃	1	24	yes	—
307	C₂×C₂²⋊C₄	C₂³×C₁₃	1	24	yes	—
308	C₂×C₂²⋊C₄	C₂³×C₁₃	1	24	yes	—
309	C₂×C₂²⋊C₄	C₂³×C₁₃	1	24	yes	—
310	C₂×C₂²⋊C₄	C₂³×C₁₃	1	24	yes	—
311	C₂×C₄²	C₂³×C₁₃	1	12	yes	—
312	C₂×C₄²	C₂³×C₁₃	1	12	yes	—
313	C₂×C₄²	C₂³×C₁₃	1	24	yes	—
314	C₂×C₁₃	—	4	4	no	—
315	C₂×C₁₃	—	4	8	no	—
316	C₂×C₁₃	C₂×#542	1	12	yes	direct product factor
317	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
318	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
319	C₂×C₁₃	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
320	C₂⁴	—	2	4	no	—
321	C₂⁴	—	2	8	no	—
322	C₂⁴	—	2	8	no	—
323	C₂⁴	—	2	4	no	—
324	C₂⁴	—	2	4	no	—
325	C₂⁴	—	2	8	no	—
326	C₂⁴	C₂⁴×C₁₃	1	6	yes	—
327	C₂⁴	C₂⁴×C₁₃	1	12	yes	—
328	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
329	C₂×Q₈	—	2	48	no	—
330	C₂×Q₈	—	4	48	no	—
331	C₂×Q₈	C₂⁴×C₁₃	1	16	yes	—
332	C₂×Q₈	C₂⁴×C₁₃	1	32	yes	—
333	C₂×D₄	—	2	48	no	—
334	C₂×D₄	—	4	48	no	—
335	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
336	C₂×D₄	C₂⁴×C₁₃	1	32	yes	—
337	C₂²×C₄	—	2	4	no	—
338	C₂²×C₄	—	2	8	no	—
339	C₂²×C₄	—	2	4	no	—
340	C₂²×C₄	—	2	8	no	—
341	C₂²×C₄	—	2	8	no	—
342	C₂²×C₄	—	2	4	no	—
343	C₂²×C₄	—	2	4	no	—
344	C₂²×C₄	—	2	4	no	—
345	C₂²×C₄	—	2	48	no	—
346	C₂²×C₄	—	4	48	no	—
347	C₂²×C₄	C₁₃×#41	1	8	yes	—
348	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
349	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
350	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
351	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
352	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
353	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
354	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
355	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
356	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
357	C₂²×C₄	C₂⁴×C₁₃	1	32	yes	—
358	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
359	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
360	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
361	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
362	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
363	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	—
364	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	—
365	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	—
366	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
367	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
368	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
369	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
370	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
371	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
372	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
373	C₄²	C₂⁴×C₁₃	1	16	yes	—
374	C₄²	C₂⁴×C₁₃	1	16	yes	—
375	C₄²	C₂⁴×C₁₃	1	32	yes	—
376	C₁₃	C₂²×#542	1	1	yes	characteristic, direct product factor, Sylow
377	C₂³	—	2	12	no	—
378	C₂³	—	2	24	no	—
379	C₂³	—	2	24	no	—
380	C₂³	—	2	12	no	—
381	C₂³	—	2	12	no	—
382	C₂³	—	2	24	no	—
383	C₂³	—	4	16	no	—
384	C₂³	—	4	32	no	—
385	C₂³	C₂×C₁₃×#41	1	4	yes	—
386	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
387	C₂³	C₁₃×2₋¹⁺⁴	1	4	yes	—
388	C₂³	C₂⁵×C₁₃	1	4	yes	—
389	C₂³	C₂⁵×C₁₃	1	8	yes	—
390	C₂³	C₂⁵×C₁₃	1	3	yes	—
391	Q₈	—	2	32	no	—
392	Q₈	—	4	32	no	—
393	D₄	—	2	32	no	—
394	D₄	—	4	32	no	—
395	C₂×C₄	—	2	12	no	—
396	C₂×C₄	—	2	24	no	—
397	C₂×C₄	—	2	12	no	—
398	C₂×C₄	—	2	24	no	—
399	C₂×C₄	—	2	24	no	—
400	C₂×C₄	—	2	12	no	—
401	C₂×C₄	—	2	12	no	—
402	C₂×C₄	—	2	12	no	—
403	C₂×C₄	—	2	32	no	—
404	C₂×C₄	—	4	32	no	—
405	C₂×C₄	C₂×C₁₃×#41	1	24	yes	—
406	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
407	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
408	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
409	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
410	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
411	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
412	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
413	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
414	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
415	C₂²	—	2	4	no	—
416	C₂²	—	2	8	no	—
417	C₂²	—	2	8	no	—
418	C₂²	—	2	4	no	—
419	C₂²	—	2	4	no	—
420	C₂²	—	2	8	no	—
421	C₂²	—	4	24	no	—
422	C₂²	—	4	48	no	—
423	C₂²	C₁₃×#542	1	16	yes	direct product factor
424	C₂²	C₂²×C₁₃×#41	1	6	yes	—
425	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	6	yes	—
426	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	6	yes	—
427	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
428	C₄	—	2	4	no	—
429	C₄	—	2	8	no	—
430	C₄	—	2	4	no	—
431	C₄	—	2	8	no	—
432	C₄	—	2	8	no	—
433	C₄	—	2	4	no	—
434	C₄	—	2	4	no	—
435	C₄	—	2	4	no	—
436	C₄	C₂²×C₁₃×#41	1	8	yes	—
437	C₂	—	4	4	no	—
438	C₂	—	4	8	no	—
439	C₂	C₂×C₁₃×#542	1	12	yes	direct product factor
440	C₂	C₂³×C₁₃×#41	1	1	yes	characteristic
441	C₂	C₂²×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
442	C₂	C₂²×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₃
prime radical	C₂²×C₁₃×#121	C₂
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
1. C₂×C₁₃×#542	C₂	direct (N × H)
2. C₂²×C₁₃×C₄⋊Q₈	C₂	semidirect
3. C₂²×C₁₃×#126	C₂	semidirect
4. C₂²×C₁₃×#124	C₂	semidirect
5. C₂²×C₁₃×#124	C₂	semidirect
6. C₂²×C₁₃×#123	C₂	semidirect
7. C₂²×C₁₃×C₂²⋊Q₈	C₂	semidirect
8. C₂²×C₁₃×C₂²⋊Q₈	C₂	semidirect
10. C₂²×C₄×Q₈×C₁₃	C₂	semidirect
11. C₂²×C₄×D₄×C₁₃	C₂	semidirect
12. C₂²×C₁₃×#117	C₂	semidirect
19. C₁₃×#542	C₂²	direct (N × H)
20. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
21. C₂×C₁₃×#126	C₂²	semidirect
22. C₂×C₁₃×#124	C₂²	semidirect
23. C₂×C₁₃×#124	C₂²	semidirect
24. C₂×C₁₃×#123	C₂²	semidirect
25. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
26. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
28. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
29. C₂×C₄×D₄×C₁₃	C₂²	semidirect
30. C₂×C₁₃×#117	C₂²	semidirect
71. C₁₃×C₄⋊Q₈	C₂³	semidirect
72. C₁₃×#126	C₂³	semidirect
73. C₁₃×#124	C₂³	semidirect
74. C₁₃×#124	C₂³	semidirect
75. C₁₃×#123	C₂³	semidirect
76. C₁₃×C₂²⋊Q₈	C₂³	semidirect
77. C₁₃×C₂²⋊Q₈	C₂³	semidirect
79. C₄×Q₈×C₁₃	C₂³	semidirect
80. C₄×D₄×C₁₃	C₂³	semidirect
81. C₁₃×#117	C₂³	semidirect
99. C₂²×#542	C₁₃	direct (N × H)
156. C₂×#542	C₂×C₁₃	direct (N × H)
157. C₂²×C₄⋊Q₈	C₂×C₁₃	semidirect
158. C₂²×#126	C₂×C₁₃	semidirect
159. C₂²×#124	C₂×C₁₃	semidirect
160. C₂²×#124	C₂×C₁₃	semidirect
161. C₂²×#123	C₂×C₁₃	semidirect
162. C₂²×C₂²⋊Q₈	C₂×C₁₃	semidirect
163. C₂²×C₂²⋊Q₈	C₂×C₁₃	semidirect
165. C₂²×C₄×Q₈	C₂×C₁₃	semidirect
166. C₂²×C₄×D₄	C₂×C₁₃	semidirect
167. C₂²×#117	C₂×C₁₃	semidirect
212. #542	C₂²×C₁₃	direct (N × H)
213. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
214. C₂×#126	C₂²×C₁₃	semidirect
215. C₂×#124	C₂²×C₁₃	semidirect
216. C₂×#124	C₂²×C₁₃	semidirect
217. C₂×#123	C₂²×C₁₃	semidirect
218. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
219. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
221. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
222. C₂×C₄×D₄	C₂²×C₁₃	semidirect
223. C₂×#117	C₂²×C₁₃	semidirect
249. C₂²×C₁₃	#542	direct (N × H)
286. C₄⋊Q₈	C₂³×C₁₃	semidirect
287. #126	C₂³×C₁₃	semidirect
288. #124	C₂³×C₁₃	semidirect
289. #124	C₂³×C₁₃	semidirect
290. #123	C₂³×C₁₃	semidirect
291. C₂²⋊Q₈	C₂³×C₁₃	semidirect
292. C₂²⋊Q₈	C₂³×C₁₃	semidirect
294. C₄×Q₈	C₂³×C₁₃	semidirect
295. C₄×D₄	C₂³×C₁₃	semidirect
296. #117	C₂³×C₁₃	semidirect
316. C₂×C₁₃	C₂×#542	direct (N × H)
376. C₁₃	C₂²×#542	direct (N × H)
423. C₂²	C₁₃×#542	direct (N × H)
439. C₂	C₂×C₁₃×#542	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#542	2
C₂²×C₁₃×C₄⋊Q₈	2
C₂²×C₁₃×#126	2
C₂²×C₁₃×#124	2
C₂²×C₁₃×#123	2
C₂²×C₁₃×C₂²⋊Q₈	2
C₂²×C₁₃×#121	2
C₂²×C₄×Q₈×C₁₃	2
C₂²×C₄×D₄×C₁₃	2
C₂²×C₁₃×#117	2
C₂²×#542	13

Subgroups — C22×C13×#542 #15749017

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₁₃×#542 #15749017