Subgroups — C₂×C₁₃×#3492 #15749107

Order 3328.

7910 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3492	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₁₃×#554	C₂	1	4	yes	maximal, complemented
3	C₂×C₁₃×#553	C₂	1	4	yes	maximal, complemented
4	C₂×C₁₃×#552	C₂	1	4	yes	maximal, complemented
5	C₂×C₁₃×#547	C₂	1	4	yes	maximal, complemented
6	C₂×C₁₃×#544	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#539	C₂	1	4	yes	maximal, complemented
8	C₂×C₁₃×#537	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#525	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₃×#525	C₂	1	4	yes	maximal, complemented
11	C₂×C₁₃×#520	C₂	1	2	yes	maximal, complemented
12	C₂³×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₁₃×#41	C₂²	1	2	yes	—
14	C₂²×C₁₃×#41	C₂²	1	4	yes	—
15	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
16	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
17	C₁₃×#554	C₂²	1	64	yes	complemented
18	C₁₃×#553	C₂²	1	64	yes	complemented
19	C₁₃×#552	C₂²	1	64	yes	complemented
20	C₁₃×#547	C₂²	1	64	yes	complemented
21	C₁₃×#544	C₂²	1	16	yes	complemented
22	C₁₃×#539	C₂²	1	64	yes	complemented
23	C₁₃×#537	C₂²	1	16	yes	complemented
24	C₂×C₁₃×C₄⋊Q₈	C₂²	1	4	yes	complemented
25	C₂×C₁₃×#126	C₂²	1	8	yes	complemented
26	C₂×C₁₃×#125	C₂²	1	8	yes	complemented
27	C₂×C₁₃×#125	C₂²	1	4	yes	complemented
28	C₁₃×#525	C₂²	1	32	yes	complemented
29	C₁₃×#525	C₂²	1	64	yes	complemented
30	C₂×C₁₃×#123	C₂²	1	4	yes	—
31	C₂×C₁₃×#123	C₂²	1	8	yes	—
32	C₂×C₁₃×#123	C₂²	1	8	yes	complemented
33	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
34	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
35	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
36	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
37	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
38	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	8	yes	complemented
39	C₂×C₁₃×#121	C₂²	1	4	yes	—
40	C₂×C₁₃×#121	C₂²	1	2	yes	—
41	C₂×C₁₃×#121	C₂²	1	4	yes	—
42	C₂×C₁₃×#121	C₂²	1	2	yes	—
43	C₂×C₁₃×#121	C₂²	1	4	yes	complemented
44	C₂×C₁₃×#120	C₂²	1	4	yes	—
45	C₁₃×#520	C₂²	1	32	yes	complemented
46	C₂×C₄×Q₈×C₁₃	C₂²	1	4	yes	complemented
47	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	—
48	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
49	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	—
50	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
51	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
52	C₂×C₁₃×#117	C₂²	1	2	yes	—
53	C₂×C₁₃×#117	C₂²	1	4	yes	—
54	C₂×C₁₃×#117	C₂²	1	4	yes	complemented
55	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
56	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
57	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
58	C₂²×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
59	C₂²×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
60	C₂²×C₁₃×C₄⋊C₄	C₂²	1	16	yes	complemented
61	C₂²×C₁₃×C₄⋊C₄	C₂²	1	4	yes	complemented
62	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
63	C₂×C₁₃×#41	—	2	16	no	—
64	C₂×C₁₃×#41	—	4	16	no	—
65	C₂×C₁₃×#41	C₂³	1	16	yes	—
66	C₂×C₁₃×#41	C₂³	1	32	yes	—
67	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
68	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
69	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
70	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
71	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
72	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
73	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
74	C₂³×C₄×C₁₃	—	2	8	no	—
75	C₂³×C₄×C₁₃	—	4	8	no	—
76	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
77	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
78	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
79	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
80	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
81	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
82	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
83	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
84	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
85	C₂³×C₄×C₁₃	C₂³	1	16	yes	—
86	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
87	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
88	C₁₃×C₄⋊Q₈	C₂³	1	32	yes	complemented
89	C₁₃×#126	C₂³	1	64	yes	complemented
90	C₁₃×#125	C₂³	1	64	yes	complemented
91	C₁₃×#125	C₂³	1	32	yes	complemented
92	C₁₃×#123	C₂³	1	32	yes	—
93	C₁₃×#123	C₂³	1	64	yes	—
94	C₁₃×#123	C₂³	1	64	yes	complemented
95	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	—
96	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
97	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
98	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	—
99	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	complemented
100	C₁₃×C₂²⋊Q₈	C₂³	1	64	yes	complemented
101	C₁₃×#121	C₂³	1	32	yes	—
102	C₁₃×#121	C₂³	1	16	yes	—
103	C₁₃×#121	C₂³	1	32	yes	—
104	C₁₃×#121	C₂³	1	16	yes	—
105	C₁₃×#121	C₂³	1	32	yes	complemented
106	C₁₃×#120	C₂³	1	32	yes	—
107	C₄×Q₈×C₁₃	C₂³	1	32	yes	complemented
108	C₄×D₄×C₁₃	C₂³	1	64	yes	—
109	C₄×D₄×C₁₃	C₂³	1	32	yes	—
110	C₄×D₄×C₁₃	C₂³	1	64	yes	—
111	C₄×D₄×C₁₃	C₂³	1	32	yes	—
112	C₄×D₄×C₁₃	C₂³	1	32	yes	complemented
113	C₁₃×#117	C₂³	1	16	yes	—
114	C₁₃×#117	C₂³	1	32	yes	—
115	C₁₃×#117	C₂³	1	32	yes	complemented
116	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
117	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
118	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
119	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
120	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
121	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	yes	—
122	C₂×C₁₃×C₄⋊C₄	C₂³	1	32	yes	—
123	C₂×C₁₃×C₄⋊C₄	C₂³	1	32	yes	—
124	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
125	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
126	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
127	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
128	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
129	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
130	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
131	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
132	C₂×C₁₃×C₄⋊C₄	C₂³	1	32	yes	complemented
133	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
134	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
135	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
136	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
137	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
138	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
139	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
140	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
141	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
142	C₂×#3492	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
143	C₂⁴×C₁₃	—	2	4	no	—
144	C₂⁴×C₁₃	—	2	4	no	—
145	C₂⁴×C₁₃	—	2	4	no	—
146	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
147	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
148	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
149	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
150	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
151	C₁₃×#41	—	2	64	no	—
152	C₁₃×#41	—	4	64	no	—
153	C₂×Q₈×C₁₃	—	2	8	no	—
154	C₂×Q₈×C₁₃	—	4	8	no	—
155	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
156	C₂×Q₈×C₁₃	C₂⁴	1	16	yes	—
157	C₂×D₄×C₁₃	—	2	16	no	—
158	C₂×D₄×C₁₃	—	2	16	no	—
159	C₂×D₄×C₁₃	—	2	16	no	—
160	C₂×D₄×C₁₃	—	2	8	no	—
161	C₂×D₄×C₁₃	—	4	8	no	—
162	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
163	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
164	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
165	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
166	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
167	C₂²×C₄×C₁₃	—	2	4	no	—
168	C₂²×C₄×C₁₃	—	2	16	no	—
169	C₂²×C₄×C₁₃	—	2	8	no	—
170	C₂²×C₄×C₁₃	—	2	8	no	—
171	C₂²×C₄×C₁₃	—	2	16	no	—
172	C₂²×C₄×C₁₃	—	2	32	no	—
173	C₂²×C₄×C₁₃	—	4	4	no	—
174	C₂²×C₄×C₁₃	—	4	8	no	—
175	C₂²×C₄×C₁₃	—	4	4	no	—
176	C₂²×C₄×C₁₃	—	4	32	no	—
177	C₂²×C₄×C₁₃	—	4	16	no	—
178	C₂²×C₄×C₁₃	#41	1	8	yes	complemented
179	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
180	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
181	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
182	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
183	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
184	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
185	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
186	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
187	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
188	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
189	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
190	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
191	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
192	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
193	C₂²×C₄×C₁₃	C₂⁴	1	32	yes	—
194	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
195	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
196	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
197	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
198	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	—
199	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
200	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	—
201	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
202	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
203	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
204	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
205	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	—
206	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
207	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
208	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
209	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
210	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
211	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
212	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
213	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
214	C₄²×C₁₃	C₂⁴	1	32	yes	—
215	C₄²×C₁₃	C₂⁴	1	16	yes	—
216	#3492	C₂×C₁₃	1	32	yes	direct product factor
217	C₂×#554	C₂×C₁₃	1	4	yes	complemented
218	C₂×#553	C₂×C₁₃	1	4	yes	complemented
219	C₂×#552	C₂×C₁₃	1	4	yes	complemented
220	C₂×#547	C₂×C₁₃	1	4	yes	complemented
221	C₂×#544	C₂×C₁₃	1	1	yes	characteristic, complemented
222	C₂×#539	C₂×C₁₃	1	4	yes	complemented
223	C₂×#537	C₂×C₁₃	1	1	yes	characteristic, complemented
224	C₂×#525	C₂×C₁₃	1	2	yes	complemented
225	C₂×#525	C₂×C₁₃	1	4	yes	complemented
226	C₂×#520	C₂×C₁₃	1	2	yes	complemented
227	C₂³×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
228	C₂³×C₁₃	—	2	32	no	—
229	C₂³×C₁₃	—	2	8	no	—
230	C₂³×C₁₃	—	2	2	no	—
231	C₂³×C₁₃	—	2	2	no	—
232	C₂³×C₁₃	—	2	8	no	—
233	C₂³×C₁₃	—	2	2	no	—
234	C₂³×C₁₃	—	2	2	no	—
235	C₂³×C₁₃	—	2	8	no	—
236	C₂³×C₁₃	—	2	2	no	—
237	C₂³×C₁₃	—	2	2	no	—
238	C₂³×C₁₃	—	2	8	no	—
239	C₂³×C₁₃	—	2	8	no	—
240	C₂³×C₁₃	—	2	8	no	—
241	C₂³×C₁₃	C₂×#41	1	4	yes	—
242	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
243	C₂³×C₁₃	2₋¹⁺⁴	1	4	yes	—
244	C₂³×C₁₃	C₂⁵	1	8	yes	—
245	C₂³×C₁₃	C₂⁵	1	2	yes	—
246	C₂³×C₁₃	C₂⁵	1	2	yes	—
247	C₂³×C₁₃	C₂⁵	1	2	yes	—
248	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
249	Q₈×C₁₃	—	2	16	no	—
250	Q₈×C₁₃	—	4	16	no	—
251	D₄×C₁₃	—	2	32	no	—
252	D₄×C₁₃	—	2	32	no	—
253	D₄×C₁₃	—	2	32	no	—
254	D₄×C₁₃	—	2	16	no	—
255	D₄×C₁₃	—	4	16	no	—
256	C₂×C₄×C₁₃	—	2	8	no	—
257	C₂×C₄×C₁₃	—	2	4	no	—
258	C₂×C₄×C₁₃	—	2	8	no	—
259	C₂×C₄×C₁₃	—	2	8	no	—
260	C₂×C₄×C₁₃	—	2	8	no	—
261	C₂×C₄×C₁₃	—	2	32	no	—
262	C₂×C₄×C₁₃	—	2	8	no	—
263	C₂×C₄×C₁₃	—	2	8	no	—
264	C₂×C₄×C₁₃	—	2	16	no	—
265	C₂×C₄×C₁₃	—	2	16	no	—
266	C₂×C₄×C₁₃	—	2	32	no	—
267	C₂×C₄×C₁₃	—	4	8	no	—
268	C₂×C₄×C₁₃	—	4	16	no	—
269	C₂×C₄×C₁₃	—	4	8	no	—
270	C₂×C₄×C₁₃	—	4	32	no	—
271	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
272	C₂×C₄×C₁₃	C₂×#41	1	16	yes	complemented
273	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
274	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
275	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
276	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
277	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
278	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
279	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
280	C₂²×#41	C₂²×C₁₃	1	2	yes	—
281	C₂²×#41	C₂²×C₁₃	1	4	yes	—
282	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
283	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	—
284	#554	C₂²×C₁₃	1	64	yes	complemented
285	#553	C₂²×C₁₃	1	64	yes	complemented
286	#552	C₂²×C₁₃	1	64	yes	complemented
287	#547	C₂²×C₁₃	1	64	yes	complemented
288	#544	C₂²×C₁₃	1	16	yes	complemented
289	#539	C₂²×C₁₃	1	64	yes	complemented
290	#537	C₂²×C₁₃	1	16	yes	complemented
291	C₂×C₄⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
292	C₂×#126	C₂²×C₁₃	1	8	yes	complemented
293	C₂×#125	C₂²×C₁₃	1	8	yes	complemented
294	C₂×#125	C₂²×C₁₃	1	4	yes	complemented
295	#525	C₂²×C₁₃	1	32	yes	complemented
296	#525	C₂²×C₁₃	1	64	yes	complemented
297	C₂×#123	C₂²×C₁₃	1	4	yes	—
298	C₂×#123	C₂²×C₁₃	1	8	yes	—
299	C₂×#123	C₂²×C₁₃	1	8	yes	complemented
300	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
301	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
302	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
303	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
304	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
305	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	8	yes	complemented
306	C₂×#121	C₂²×C₁₃	1	4	yes	—
307	C₂×#121	C₂²×C₁₃	1	2	yes	—
308	C₂×#121	C₂²×C₁₃	1	4	yes	—
309	C₂×#121	C₂²×C₁₃	1	2	yes	—
310	C₂×#121	C₂²×C₁₃	1	4	yes	complemented
311	C₂×#120	C₂²×C₁₃	1	4	yes	—
312	#520	C₂²×C₁₃	1	32	yes	complemented
313	C₂×C₄×Q₈	C₂²×C₁₃	1	4	yes	complemented
314	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	—
315	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
316	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	—
317	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
318	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
319	C₂×#117	C₂²×C₁₃	1	2	yes	—
320	C₂×#117	C₂²×C₁₃	1	4	yes	—
321	C₂×#117	C₂²×C₁₃	1	4	yes	complemented
322	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
323	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
324	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
325	C₂²×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
326	C₂²×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
327	C₂²×C₄⋊C₄	C₂²×C₁₃	1	16	yes	complemented
328	C₂²×C₄⋊C₄	C₂²×C₁₃	1	4	yes	complemented
329	C₂²×C₁₃	—	2	32	no	—
330	C₂²×C₁₃	—	2	2	no	—
331	C₂²×C₁₃	—	2	2	no	—
332	C₂²×C₁₃	—	2	2	no	—
333	C₂²×C₁₃	—	2	2	no	—
334	C₂²×C₁₃	—	2	2	no	—
335	C₂²×C₁₃	—	2	2	no	—
336	C₂²×C₁₃	—	2	8	no	—
337	C₂²×C₁₃	—	2	8	no	—
338	C₂²×C₁₃	—	2	8	no	—
339	C₂²×C₁₃	—	2	8	no	—
340	C₂²×C₁₃	—	2	8	no	—
341	C₂²×C₁₃	—	2	8	no	—
342	C₂²×C₁₃	—	4	16	no	—
343	C₂²×C₁₃	C₂²×#41	1	4	yes	—
344	C₂²×C₁₃	C₂²×#41	1	2	yes	—
345	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
346	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
347	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	4	yes	—
348	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
349	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
350	C₄×C₁₃	—	2	4	no	—
351	C₄×C₁₃	—	2	8	no	—
352	C₄×C₁₃	—	2	8	no	—
353	C₄×C₁₃	—	2	8	no	—
354	C₄×C₁₃	—	2	8	no	—
355	C₄×C₁₃	—	2	8	no	—
356	C₄×C₁₃	C₂²×#41	1	8	yes	—
357	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
358	C₂×#41	—	2	16	no	—
359	C₂×#41	—	4	16	no	—
360	C₂×#41	C₂³×C₁₃	1	16	yes	—
361	C₂×#41	C₂³×C₁₃	1	32	yes	—
362	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
363	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
364	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
365	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
366	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
367	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
368	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
369	C₂³×C₄	—	2	8	no	—
370	C₂³×C₄	—	4	8	no	—
371	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
372	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
373	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
374	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
375	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
376	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
377	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
378	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
379	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
380	C₂³×C₄	C₂³×C₁₃	1	16	yes	—
381	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
382	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
383	C₄⋊Q₈	C₂³×C₁₃	1	32	yes	complemented
384	#126	C₂³×C₁₃	1	64	yes	complemented
385	#125	C₂³×C₁₃	1	64	yes	complemented
386	#125	C₂³×C₁₃	1	32	yes	complemented
387	#123	C₂³×C₁₃	1	32	yes	—
388	#123	C₂³×C₁₃	1	64	yes	—
389	#123	C₂³×C₁₃	1	64	yes	complemented
390	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	—
391	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
392	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
393	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	—
394	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	complemented
395	C₂²⋊Q₈	C₂³×C₁₃	1	64	yes	complemented
396	#121	C₂³×C₁₃	1	32	yes	—
397	#121	C₂³×C₁₃	1	16	yes	—
398	#121	C₂³×C₁₃	1	32	yes	—
399	#121	C₂³×C₁₃	1	16	yes	—
400	#121	C₂³×C₁₃	1	32	yes	complemented
401	#120	C₂³×C₁₃	1	32	yes	—
402	C₄×Q₈	C₂³×C₁₃	1	32	yes	complemented
403	C₄×D₄	C₂³×C₁₃	1	64	yes	—
404	C₄×D₄	C₂³×C₁₃	1	32	yes	—
405	C₄×D₄	C₂³×C₁₃	1	64	yes	—
406	C₄×D₄	C₂³×C₁₃	1	32	yes	—
407	C₄×D₄	C₂³×C₁₃	1	32	yes	complemented
408	#117	C₂³×C₁₃	1	16	yes	—
409	#117	C₂³×C₁₃	1	32	yes	—
410	#117	C₂³×C₁₃	1	32	yes	complemented
411	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
412	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
413	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
414	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
415	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
416	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	yes	—
417	C₂×C₄⋊C₄	C₂³×C₁₃	1	32	yes	—
418	C₂×C₄⋊C₄	C₂³×C₁₃	1	32	yes	—
419	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
420	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
421	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
422	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
423	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
424	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
425	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
426	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
427	C₂×C₄⋊C₄	C₂³×C₁₃	1	32	yes	complemented
428	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
429	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
430	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
431	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
432	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
433	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
434	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
435	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
436	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
437	C₂×C₁₃	—	2	4	no	—
438	C₂×C₁₃	—	2	4	no	—
439	C₂×C₁₃	—	2	4	no	—
440	C₂×C₁₃	—	4	8	no	—
441	C₂×C₁₃	#3492	1	4	yes	direct product factor
442	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
443	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
444	C₂×C₁₃	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
445	C₂⁴	—	2	4	no	—
446	C₂⁴	—	2	4	no	—
447	C₂⁴	—	2	4	no	—
448	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
449	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
450	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
451	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
452	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
453	#41	—	2	64	no	—
454	#41	—	4	64	no	—
455	C₂×Q₈	—	2	8	no	—
456	C₂×Q₈	—	4	8	no	—
457	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
458	C₂×Q₈	C₂⁴×C₁₃	1	16	yes	—
459	C₂×D₄	—	2	16	no	—
460	C₂×D₄	—	2	16	no	—
461	C₂×D₄	—	2	16	no	—
462	C₂×D₄	—	2	8	no	—
463	C₂×D₄	—	4	8	no	—
464	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
465	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
466	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
467	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
468	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
469	C₂²×C₄	—	2	4	no	—
470	C₂²×C₄	—	2	16	no	—
471	C₂²×C₄	—	2	8	no	—
472	C₂²×C₄	—	2	8	no	—
473	C₂²×C₄	—	2	16	no	—
474	C₂²×C₄	—	2	32	no	—
475	C₂²×C₄	—	4	4	no	—
476	C₂²×C₄	—	4	8	no	—
477	C₂²×C₄	—	4	4	no	—
478	C₂²×C₄	—	4	32	no	—
479	C₂²×C₄	—	4	16	no	—
480	C₂²×C₄	C₁₃×#41	1	8	yes	complemented
481	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
482	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
483	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
484	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
485	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
486	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
487	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
488	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
489	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
490	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
491	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
492	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
493	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
494	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
495	C₂²×C₄	C₂⁴×C₁₃	1	32	yes	—
496	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
497	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
498	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
499	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
500	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	—
501	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
502	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	—
503	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
504	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
505	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
506	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
507	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	—
508	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
509	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
510	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
511	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
512	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
513	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
514	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
515	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
516	C₄²	C₂⁴×C₁₃	1	32	yes	—
517	C₄²	C₂⁴×C₁₃	1	16	yes	—
518	C₁₃	C₂×#3492	1	1	yes	characteristic, direct product factor, Sylow
519	C₂³	—	2	32	no	—
520	C₂³	—	2	8	no	—
521	C₂³	—	2	2	no	—
522	C₂³	—	2	2	no	—
523	C₂³	—	2	8	no	—
524	C₂³	—	2	2	no	—
525	C₂³	—	2	2	no	—
526	C₂³	—	2	8	no	—
527	C₂³	—	2	2	no	—
528	C₂³	—	2	2	no	—
529	C₂³	—	2	8	no	—
530	C₂³	—	2	8	no	—
531	C₂³	—	2	8	no	—
532	C₂³	C₂×C₁₃×#41	1	4	yes	—
533	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
534	C₂³	C₁₃×2₋¹⁺⁴	1	4	yes	—
535	C₂³	C₂⁵×C₁₃	1	8	yes	—
536	C₂³	C₂⁵×C₁₃	1	2	yes	—
537	C₂³	C₂⁵×C₁₃	1	2	yes	—
538	C₂³	C₂⁵×C₁₃	1	2	yes	—
539	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
540	Q₈	—	2	16	no	—
541	Q₈	—	4	16	no	—
542	D₄	—	2	32	no	—
543	D₄	—	2	32	no	—
544	D₄	—	2	32	no	—
545	D₄	—	2	16	no	—
546	D₄	—	4	16	no	—
547	C₂×C₄	—	2	8	no	—
548	C₂×C₄	—	2	4	no	—
549	C₂×C₄	—	2	8	no	—
550	C₂×C₄	—	2	8	no	—
551	C₂×C₄	—	2	8	no	—
552	C₂×C₄	—	2	32	no	—
553	C₂×C₄	—	2	8	no	—
554	C₂×C₄	—	2	8	no	—
555	C₂×C₄	—	2	16	no	—
556	C₂×C₄	—	2	16	no	—
557	C₂×C₄	—	2	32	no	—
558	C₂×C₄	—	4	8	no	—
559	C₂×C₄	—	4	16	no	—
560	C₂×C₄	—	4	8	no	—
561	C₂×C₄	—	4	32	no	—
562	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
563	C₂×C₄	C₂×C₁₃×#41	1	16	yes	complemented
564	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
565	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
566	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
567	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
568	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
569	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
570	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
571	C₂²	—	2	32	no	—
572	C₂²	—	2	2	no	—
573	C₂²	—	2	2	no	—
574	C₂²	—	2	2	no	—
575	C₂²	—	2	2	no	—
576	C₂²	—	2	2	no	—
577	C₂²	—	2	2	no	—
578	C₂²	—	2	8	no	—
579	C₂²	—	2	8	no	—
580	C₂²	—	2	8	no	—
581	C₂²	—	2	8	no	—
582	C₂²	—	2	8	no	—
583	C₂²	—	2	8	no	—
584	C₂²	—	4	16	no	—
585	C₂²	C₂²×C₁₃×#41	1	4	yes	—
586	C₂²	C₂²×C₁₃×#41	1	2	yes	—
587	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	4	yes	—
588	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
589	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	4	yes	—
590	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
591	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
592	C₄	—	2	4	no	—
593	C₄	—	2	8	no	—
594	C₄	—	2	8	no	—
595	C₄	—	2	8	no	—
596	C₄	—	2	8	no	—
597	C₄	—	2	8	no	—
598	C₄	C₂²×C₁₃×#41	1	8	yes	—
599	C₂	—	2	4	no	—
600	C₂	—	2	4	no	—
601	C₂	—	2	4	no	—
602	C₂	—	4	8	no	—
603	C₂	C₁₃×#3492	1	4	yes	direct product factor
604	C₂	C₂³×C₁₃×#41	1	1	yes	characteristic
605	C₂	C₂²×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
606	C₂	C₂²×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic

	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×#3492	C₂	direct (N × H)
2. C₂×C₁₃×#554	C₂	semidirect
3. C₂×C₁₃×#553	C₂	semidirect
4. C₂×C₁₃×#552	C₂	semidirect
5. C₂×C₁₃×#547	C₂	semidirect
6. C₂×C₁₃×#544	C₂	semidirect
7. C₂×C₁₃×#539	C₂	semidirect
8. C₂×C₁₃×#537	C₂	semidirect
9. C₂×C₁₃×#525	C₂	semidirect
10. C₂×C₁₃×#525	C₂	semidirect
11. C₂×C₁₃×#520	C₂	semidirect
12. C₂³×C₁₃×C₄⋊C₄	C₂	semidirect
17. C₁₃×#554	C₂²	semidirect
18. C₁₃×#553	C₂²	semidirect
19. C₁₃×#552	C₂²	semidirect
20. C₁₃×#547	C₂²	semidirect
21. C₁₃×#544	C₂²	semidirect
22. C₁₃×#539	C₂²	semidirect
23. C₁₃×#537	C₂²	semidirect
24. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
25. C₂×C₁₃×#126	C₂²	semidirect
26. C₂×C₁₃×#125	C₂²	semidirect
27. C₂×C₁₃×#125	C₂²	semidirect
28. C₁₃×#525	C₂²	semidirect
29. C₁₃×#525	C₂²	semidirect
32. C₂×C₁₃×#123	C₂²	semidirect
37. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
38. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
43. C₂×C₁₃×#121	C₂²	semidirect
45. C₁₃×#520	C₂²	semidirect
46. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
51. C₂×C₄×D₄×C₁₃	C₂²	semidirect
54. C₂×C₁₃×#117	C₂²	semidirect
60. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
61. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
88. C₁₃×C₄⋊Q₈	C₂³	semidirect
89. C₁₃×#126	C₂³	semidirect
90. C₁₃×#125	C₂³	semidirect
91. C₁₃×#125	C₂³	semidirect
94. C₁₃×#123	C₂³	semidirect
99. C₁₃×C₂²⋊Q₈	C₂³	semidirect
100. C₁₃×C₂²⋊Q₈	C₂³	semidirect
105. C₁₃×#121	C₂³	semidirect
107. C₄×Q₈×C₁₃	C₂³	semidirect
112. C₄×D₄×C₁₃	C₂³	semidirect
115. C₁₃×#117	C₂³	semidirect
132. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
142. C₂×#3492	C₁₃	direct (N × H)
178. C₂²×C₄×C₁₃	#41	semidirect
216. #3492	C₂×C₁₃	direct (N × H)
217. C₂×#554	C₂×C₁₃	semidirect
218. C₂×#553	C₂×C₁₃	semidirect
219. C₂×#552	C₂×C₁₃	semidirect
220. C₂×#547	C₂×C₁₃	semidirect
221. C₂×#544	C₂×C₁₃	semidirect
222. C₂×#539	C₂×C₁₃	semidirect
223. C₂×#537	C₂×C₁₃	semidirect
224. C₂×#525	C₂×C₁₃	semidirect
225. C₂×#525	C₂×C₁₃	semidirect
226. C₂×#520	C₂×C₁₃	semidirect
227. C₂³×C₄⋊C₄	C₂×C₁₃	semidirect
272. C₂×C₄×C₁₃	C₂×#41	semidirect
284. #554	C₂²×C₁₃	semidirect
285. #553	C₂²×C₁₃	semidirect
286. #552	C₂²×C₁₃	semidirect
287. #547	C₂²×C₁₃	semidirect
288. #544	C₂²×C₁₃	semidirect
289. #539	C₂²×C₁₃	semidirect
290. #537	C₂²×C₁₃	semidirect
291. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
292. C₂×#126	C₂²×C₁₃	semidirect
293. C₂×#125	C₂²×C₁₃	semidirect
294. C₂×#125	C₂²×C₁₃	semidirect
295. #525	C₂²×C₁₃	semidirect
296. #525	C₂²×C₁₃	semidirect
299. C₂×#123	C₂²×C₁₃	semidirect
304. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
305. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
310. C₂×#121	C₂²×C₁₃	semidirect
312. #520	C₂²×C₁₃	semidirect
313. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
318. C₂×C₄×D₄	C₂²×C₁₃	semidirect
321. C₂×#117	C₂²×C₁₃	semidirect
327. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
328. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
383. C₄⋊Q₈	C₂³×C₁₃	semidirect
384. #126	C₂³×C₁₃	semidirect
385. #125	C₂³×C₁₃	semidirect
386. #125	C₂³×C₁₃	semidirect
389. #123	C₂³×C₁₃	semidirect
394. C₂²⋊Q₈	C₂³×C₁₃	semidirect
395. C₂²⋊Q₈	C₂³×C₁₃	semidirect
400. #121	C₂³×C₁₃	semidirect
402. C₄×Q₈	C₂³×C₁₃	semidirect
407. C₄×D₄	C₂³×C₁₃	semidirect
410. #117	C₂³×C₁₃	semidirect
427. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
441. C₂×C₁₃	#3492	direct (N × H)
480. C₂²×C₄	C₁₃×#41	semidirect
518. C₁₃	C₂×#3492	direct (N × H)
563. C₂×C₄	C₂×C₁₃×#41	semidirect
603. C₂	C₁₃×#3492	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×#3492	2
C₂×C₁₃×#554	2
C₂×C₁₃×#553	2
C₂×C₁₃×#552	2
C₂×C₁₃×#547	2
C₂×C₁₃×#544	2
C₂×C₁₃×#539	2
C₂×C₁₃×#537	2
C₂×C₁₃×#525	2
C₂×C₁₃×#520	2
C₂³×C₁₃×C₄⋊C₄	2
C₂×#3492	13

Subgroups — C2×C13×#3492 #15749107

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3492 #15749107