Group #44478166 — subgroups

Subgroups — C₂×C₅×D₃×C₁₃×C₁₃⋊C₃ #44478166

Order 30420.

256 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₁₃×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₃×C₁₃×C₁₃⋊C₃	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₅×D₃×C₁₃²	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₅×C₁₃×C₁₃⋊C₃	—	3	1	no	maximal
5	C₃×C₅×C₁₃×C₁₃⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×D₃×C₁₃×C₁₃⋊C₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₅×D₃×C₁₃²	C₂×C₃	1	2	yes	complemented
8	C₂×C₅×C₁₃×C₁₃⋊C₃	—	2	1	no	—
9	C₂×C₅×C₁₃×C₁₃⋊C₃	—	3	2	no	—
10	C₂×C₅×C₁₃×C₁₃⋊C₃	D₃	1	1	yes	characteristic, direct product factor
11	C₂×C₃×C₅×C₁₃²	C₂×C₃	1	1	yes	characteristic, complemented
12	C₂²×C₅×C₁₃²	—	3	1	no	Hall
13	C₂×C₃×C₁₃×C₁₃⋊C₃	C₂×C₅	1	1	yes	characteristic, complemented
14	D₃×C₁₃×C₁₃⋊C₃	C₂×C₅	1	2	yes	direct product factor
15	C₅×C₁₃×C₁₃⋊C₃	—	2	1	no	—
16	C₅×C₁₃×C₁₃⋊C₃	C₂×D₃	1	1	yes	characteristic, direct product factor
17	C₃×C₅×C₁₃²	C₂²×C₃	1	1	yes	characteristic, complemented
18	C₂×C₃×C₅×D₃×C₁₃	—	13	1	no	maximal
19	C₂×C₅×D₃×C₁₃⋊C₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor
20	C₂×D₃×C₁₃²	C₃×C₅	1	1	yes	characteristic, complemented
21	C₂²×C₁₃×C₁₃⋊C₃	—	3	1	no	—
22	C₂×C₅×C₁₃²	—	3	2	no	—
23	C₂×C₅×C₁₃²	C₃×D₃	1	1	yes	characteristic, complemented
24	C₃×C₁₃×C₁₃⋊C₃	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
25	C₂×C₃²×C₅×C₁₃	—	13	1	no	—
26	C₃×C₅×D₃×C₁₃	—	13	2	no	—
27	C₂×C₃×C₅×C₁₃⋊C₃	C₂×C₁₃	1	1	yes	characteristic, complemented
28	C₅×D₃×C₁₃⋊C₃	C₂×C₁₃	1	2	yes	direct product factor
29	C₂×C₃×C₁₃²	C₂×C₃×C₅	1	1	yes	characteristic, complemented
30	D₃×C₁₃²	C₂×C₃×C₅	1	2	yes	complemented
31	C₂×C₁₃×C₁₃⋊C₃	—	2	1	no	—
32	C₂×C₁₃×C₁₃⋊C₃	—	3	2	no	—
33	C₂×C₁₃×C₁₃⋊C₃	C₅×D₃	1	1	yes	characteristic, direct product factor
34	C₅×C₁₃²	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
35	C₂²×C₃×C₅×C₁₃	—	39	1	no	—
36	C₂×C₅×D₃×C₁₃	—	3	4	no	—
37	C₂×C₅×D₃×C₁₃	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
38	C₂×C₅×D₃×C₁₃	C₃×C₁₃	1	1	yes	characteristic, complemented
39	C₂²×C₅×C₁₃⋊C₃	—	3	1	no	—
40	C₂²×C₁₃²	—	3	1	no	Hall
41	C₃²×C₅×C₁₃	—	13	1	no	—
42	C₃×C₅×C₁₃⋊C₃	C₂²×C₁₃	1	1	yes	characteristic, complemented
43	C₃×C₁₃²	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
44	C₁₃×C₁₃⋊C₃	—	2	1	no	—
45	C₁₃×C₁₃⋊C₃	C₂×C₅×D₃	1	1	yes	characteristic, direct product factor
46	C₂×C₃×D₃×C₁₃	—	13	1	no	—
47	C₂×D₃×C₁₃⋊C₃	C₅×C₁₃	1	1	yes	characteristic, direct product factor
48	C₂×C₃×C₅×C₁₃	—	3	4	no	—
49	C₂×C₃×C₅×C₁₃	—	13	1	no	—
50	C₂×C₃×C₅×C₁₃	—	26	1	no	—
51	C₂×C₃×C₅×C₁₃	—	39	2	no	—
52	C₂×C₃×C₅×C₁₃	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented
53	C₂×C₃×C₅×C₁₃	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented
54	C₅×D₃×C₁₃	—	3	8	no	—
55	C₅×D₃×C₁₃	C₂×C₁₃⋊C₃	1	2	yes	direct product factor
56	C₅×D₃×C₁₃	C₂×C₃×C₁₃	1	2	yes	complemented
57	C₂×C₅×C₁₃⋊C₃	—	2	1	no	—
58	C₂×C₅×C₁₃⋊C₃	—	3	2	no	—
59	C₂×C₅×C₁₃⋊C₃	D₃×C₁₃	1	1	yes	characteristic, direct product factor
60	C₂×C₁₃²	—	3	2	no	—
61	C₂×C₁₃²	C₃×C₅×D₃	1	1	yes	characteristic, complemented
62	C₂²×C₅×C₁₃	—	3	1	no	—
63	C₂²×C₅×C₁₃	—	3	1	no	—
64	C₂²×C₅×C₁₃	—	9	4	no	—
65	C₂×C₃²×C₁₃	—	13	1	no	—
66	C₃×D₃×C₁₃	—	13	2	no	—
67	C₂×C₃×C₁₃⋊C₃	C₂×C₅×C₁₃	1	1	yes	characteristic, complemented
68	D₃×C₁₃⋊C₃	C₂×C₅×C₁₃	1	2	yes	direct product factor
69	C₃×C₅×C₁₃	—	3	4	no	—
70	C₃×C₅×C₁₃	—	13	1	no	—
71	C₃×C₅×C₁₃	—	26	1	no	—
72	C₃×C₅×C₁₃	C₂²×C₁₃⋊C₃	1	1	yes	characteristic, complemented
73	C₃×C₅×C₁₃	C₂²×C₃×C₁₃	1	1	yes	characteristic, complemented
74	C₅×C₁₃⋊C₃	—	2	1	no	—
75	C₅×C₁₃⋊C₃	C₂×D₃×C₁₃	1	1	yes	characteristic, direct product factor
76	C₂×C₃×C₅×D₃	—	13	1	no	Hall
77	C₁₃²	C₂×C₃×C₅×D₃	1	1	yes	characteristic, complemented, Sylow
78	C₂²×C₃×C₁₃	—	39	1	no	—
79	C₂×D₃×C₁₃	—	3	4	no	—
80	C₂×D₃×C₁₃	C₅×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
81	C₂×D₃×C₁₃	C₃×C₅×C₁₃	1	1	yes	characteristic, complemented
82	C₂²×C₁₃⋊C₃	—	3	1	no	—
83	C₂×C₅×C₁₃	—	3	2	no	—
84	C₂×C₅×C₁₃	—	3	2	no	—
85	C₂×C₅×C₁₃	—	3	4	no	—
86	C₂×C₅×C₁₃	—	9	8	no	—
87	C₂×C₅×C₁₃	D₃×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
88	C₂×C₅×C₁₃	C₃×D₃×C₁₃	1	1	yes	characteristic, complemented
89	C₃²×C₁₃	—	13	1	no	—
90	C₃×C₁₃⋊C₃	C₂²×C₅×C₁₃	1	1	yes	characteristic, complemented
91	C₂×C₃²×C₅	—	13	1	no	—
92	C₃×C₅×D₃	—	13	2	no	—
93	C₂×C₃×C₁₃	—	3	4	no	—
94	C₂×C₃×C₁₃	—	13	1	no	—
95	C₂×C₃×C₁₃	—	26	1	no	—
96	C₂×C₃×C₁₃	—	39	2	no	—
97	C₂×C₃×C₁₃	C₂×C₅×C₁₃⋊C₃	1	1	yes	characteristic, complemented
98	C₂×C₃×C₁₃	C₂×C₃×C₅×C₁₃	1	1	yes	characteristic, complemented
99	D₃×C₁₃	—	3	8	no	—
100	D₃×C₁₃	C₂×C₅×C₁₃⋊C₃	1	2	yes	direct product factor
101	D₃×C₁₃	C₂×C₃×C₅×C₁₃	1	2	yes	complemented
102	C₂×C₁₃⋊C₃	—	2	1	no	—
103	C₂×C₁₃⋊C₃	—	3	2	no	—
104	C₂×C₁₃⋊C₃	C₅×D₃×C₁₃	1	1	yes	characteristic, direct product factor
105	C₅×C₁₃	—	3	4	no	—
106	C₅×C₁₃	C₂×D₃×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
107	C₅×C₁₃	C₂×C₃×D₃×C₁₃	1	1	yes	characteristic, complemented
108	C₂²×C₃×C₅	—	39	1	no	—
109	C₂×C₅×D₃	C₁₃×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
110	C₂²×C₁₃	—	3	1	no	—
111	C₂²×C₁₃	—	3	1	no	—
112	C₂²×C₁₃	—	9	4	no	—
113	C₃²×C₅	—	13	1	no	Hall
114	C₃×C₁₃	—	3	4	no	—
115	C₃×C₁₃	—	13	1	no	—
116	C₃×C₁₃	—	26	1	no	—
117	C₃×C₁₃	C₂²×C₅×C₁₃⋊C₃	1	1	yes	characteristic, complemented
118	C₃×C₁₃	C₂²×C₃×C₅×C₁₃	1	1	yes	characteristic, complemented
119	C₁₃⋊C₃	—	2	1	no	—
120	C₁₃⋊C₃	C₂×C₅×D₃×C₁₃	1	1	yes	characteristic, direct product factor
121	C₂×C₃×D₃	—	13	1	no	Hall
122	C₂×C₃×C₅	—	13	1	no	—
123	C₂×C₃×C₅	—	26	1	no	—
124	C₂×C₃×C₅	—	39	2	no	—
125	C₂×C₃×C₅	C₂×C₁₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented
126	C₅×D₃	C₂×C₁₃×C₁₃⋊C₃	1	2	yes	direct product factor
127	C₂×C₁₃	—	3	2	no	—
128	C₂×C₁₃	—	3	2	no	—
129	C₂×C₁₃	—	3	4	no	—
130	C₂×C₁₃	—	9	8	no	—
131	C₂×C₁₃	C₅×D₃×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
132	C₂×C₁₃	C₃×C₅×D₃×C₁₃	1	1	yes	characteristic, complemented
133	C₂²×C₅	—	3	1	no	Hall
134	C₂×C₃²	—	13	1	no	—
135	C₃×D₃	—	13	2	no	—
136	C₃×C₅	—	13	1	no	—
137	C₃×C₅	—	26	1	no	—
138	C₃×C₅	C₂²×C₁₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented
139	C₁₃	—	3	4	no	—
140	C₁₃	C₂×C₅×D₃×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
141	C₁₃	C₂×C₃×C₅×D₃×C₁₃	1	1	yes	characteristic, complemented
142	C₂²×C₃	—	39	1	no	—
143	C₂×D₃	C₅×C₁₃×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
144	C₂×C₅	—	3	2	no	—
145	C₂×C₅	D₃×C₁₃×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
146	C₃²	—	13	1	no	Sylow
147	C₂×C₃	—	13	1	no	—
148	C₂×C₃	—	26	1	no	—
149	C₂×C₃	—	39	2	no	—
150	C₂×C₃	C₂×C₅×C₁₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented
151	D₃	C₂×C₅×C₁₃×C₁₃⋊C₃	1	2	yes	direct product factor
152	C₅	C₂×D₃×C₁₃×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
153	C₂²	—	3	1	no	Sylow
154	C₃	—	13	1	no	—
155	C₃	—	26	1	no	—
156	C₃	C₂²×C₅×C₁₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented
157	C₂	—	3	2	no	—
158	C₂	C₅×D₃×C₁₃×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₃×C₅×C₁₃×C₁₃⋊C₃

C₂

yes

maximal, characteristic, complemented

C₅×D₃×C₁₃×C₁₃⋊C₃

C₂

yes

maximal, direct product factor

C₂×C₅×D₃×C₁₃²

C₃

yes

maximal, characteristic, complemented

C₂²×C₅×C₁₃×C₁₃⋊C₃

—

maximal

C₃×C₅×C₁₃×C₁₃⋊C₃

C₂²

yes

characteristic, complemented, Hall

C₂×D₃×C₁₃×C₁₃⋊C₃

C₅

yes

maximal, characteristic, direct product factor, Hall

C₅×D₃×C₁₃²

C₂×C₃

yes

complemented

C₂×C₅×C₁₃×C₁₃⋊C₃

—

C₂×C₅×C₁₃×C₁₃⋊C₃

—

C₂×C₅×C₁₃×C₁₃⋊C₃

D₃

yes

characteristic, direct product factor

C₂×C₃×C₅×C₁₃²

C₂×C₃

yes

characteristic, complemented

C₂²×C₅×C₁₃²

—

Hall

C₂×C₃×C₁₃×C₁₃⋊C₃

C₂×C₅

yes

characteristic, complemented

D₃×C₁₃×C₁₃⋊C₃

C₂×C₅

yes

direct product factor

C₅×C₁₃×C₁₃⋊C₃

—

C₅×C₁₃×C₁₃⋊C₃

C₂×D₃

yes

characteristic, direct product factor

C₃×C₅×C₁₃²

C₂²×C₃

yes

characteristic, complemented

C₂×C₃×C₅×D₃×C₁₃

—

maximal

C₂×C₅×D₃×C₁₃⋊C₃

C₁₃

yes

maximal, characteristic, direct product factor

C₂×D₃×C₁₃²

C₃×C₅

yes

characteristic, complemented

C₂²×C₁₃×C₁₃⋊C₃

—

C₂×C₅×C₁₃²

—

C₂×C₅×C₁₃²

C₃×D₃

yes

characteristic, complemented

C₃×C₁₃×C₁₃⋊C₃

C₂²×C₅

yes

characteristic, complemented, Hall

C₂×C₃²×C₅×C₁₃

—

C₃×C₅×D₃×C₁₃

—

C₂×C₃×C₅×C₁₃⋊C₃

C₂×C₁₃

yes

characteristic, complemented

C₅×D₃×C₁₃⋊C₃

C₂×C₁₃

yes

direct product factor

C₂×C₃×C₁₃²

C₂×C₃×C₅

yes

characteristic, complemented

D₃×C₁₃²

C₂×C₃×C₅

yes

complemented

C₂×C₁₃×C₁₃⋊C₃

—

C₂×C₁₃×C₁₃⋊C₃

—

C₂×C₁₃×C₁₃⋊C₃

C₅×D₃

yes

characteristic, direct product factor

C₅×C₁₃²

C₂×C₃×D₃

yes

characteristic, complemented, Hall

C₂²×C₃×C₅×C₁₃

—

C₂×C₅×D₃×C₁₃

—

C₂×C₅×D₃×C₁₃

C₁₃⋊C₃

yes

characteristic, direct product factor

C₂×C₅×D₃×C₁₃

C₃×C₁₃

yes

characteristic, complemented

C₂²×C₅×C₁₃⋊C₃

—

C₂²×C₁₃²

—

Hall

C₃²×C₅×C₁₃

—

C₃×C₅×C₁₃⋊C₃

C₂²×C₁₃

yes

characteristic, complemented

C₃×C₁₃²

C₂²×C₃×C₅

yes

characteristic, complemented

C₁₃×C₁₃⋊C₃

—

C₁₃×C₁₃⋊C₃

C₂×C₅×D₃

yes

characteristic, direct product factor

C₂×C₃×D₃×C₁₃

—

C₂×D₃×C₁₃⋊C₃

C₅×C₁₃

yes

characteristic, direct product factor

C₂×C₃×C₅×C₁₃

—

C₂×C₃×C₅×C₁₃

—

C₂×C₃×C₅×C₁₃

—

C₂×C₃×C₅×C₁₃

—

C₂×C₃×C₅×C₁₃

C₂×C₁₃⋊C₃

yes

characteristic, complemented

C₂×C₃×C₅×C₁₃

C₂×C₃×C₁₃

yes

characteristic, complemented

C₅×D₃×C₁₃

—

C₅×D₃×C₁₃

C₂×C₁₃⋊C₃

yes

direct product factor

C₅×D₃×C₁₃

C₂×C₃×C₁₃

yes

complemented

C₂×C₅×C₁₃⋊C₃

—

C₂×C₅×C₁₃⋊C₃

—

C₂×C₅×C₁₃⋊C₃

D₃×C₁₃

yes

characteristic, direct product factor

C₂×C₁₃²

—

C₂×C₁₃²

C₃×C₅×D₃

yes

characteristic, complemented

C₂²×C₅×C₁₃

—

C₂²×C₅×C₁₃

—

C₂²×C₅×C₁₃

—

C₂×C₃²×C₁₃

—

C₃×D₃×C₁₃

—

C₂×C₃×C₁₃⋊C₃

C₂×C₅×C₁₃

yes

characteristic, complemented

D₃×C₁₃⋊C₃

C₂×C₅×C₁₃

yes

direct product factor

C₃×C₅×C₁₃

—

C₃×C₅×C₁₃

—

C₃×C₅×C₁₃

—

C₃×C₅×C₁₃

C₂²×C₁₃⋊C₃

yes

characteristic, complemented

C₃×C₅×C₁₃

C₂²×C₃×C₁₃

yes

characteristic, complemented

C₅×C₁₃⋊C₃

—

C₅×C₁₃⋊C₃

C₂×D₃×C₁₃

yes

characteristic, direct product factor

C₂×C₃×C₅×D₃

—

Hall

C₁₃²

C₂×C₃×C₅×D₃

yes

characteristic, complemented, Sylow

C₂²×C₃×C₁₃

—

C₂×D₃×C₁₃

—

C₂×D₃×C₁₃

C₅×C₁₃⋊C₃

yes

characteristic, direct product factor

C₂×D₃×C₁₃

C₃×C₅×C₁₃

yes

characteristic, complemented

C₂²×C₁₃⋊C₃

—

C₂×C₅×C₁₃

—

C₂×C₅×C₁₃

—

C₂×C₅×C₁₃

—

C₂×C₅×C₁₃

—

C₂×C₅×C₁₃

D₃×C₁₃⋊C₃

yes

characteristic, direct product factor

C₂×C₅×C₁₃

C₃×D₃×C₁₃

yes

characteristic, complemented

C₃²×C₁₃

—

C₃×C₁₃⋊C₃

C₂²×C₅×C₁₃

yes

characteristic, complemented

C₂×C₃²×C₅

—

C₃×C₅×D₃

—

C₂×C₃×C₁₃

—

C₂×C₃×C₁₃

—

C₂×C₃×C₁₃

—

C₂×C₃×C₁₃

—

C₂×C₃×C₁₃

C₂×C₅×C₁₃⋊C₃

yes

characteristic, complemented

C₂×C₃×C₁₃

C₂×C₃×C₅×C₁₃

yes

characteristic, complemented

D₃×C₁₃

—

100

D₃×C₁₃

C₂×C₅×C₁₃⋊C₃

yes

direct product factor

101

D₃×C₁₃

C₂×C₃×C₅×C₁₃

yes

complemented

102

C₂×C₁₃⋊C₃

—

103

C₂×C₁₃⋊C₃

—

104

C₂×C₁₃⋊C₃

C₅×D₃×C₁₃

yes

characteristic, direct product factor

105

C₅×C₁₃

—

106

C₅×C₁₃

C₂×D₃×C₁₃⋊C₃

yes

characteristic, direct product factor

107

C₅×C₁₃

C₂×C₃×D₃×C₁₃

yes

characteristic, complemented

108

C₂²×C₃×C₅

—

109

C₂×C₅×D₃

C₁₃×C₁₃⋊C₃

yes

characteristic, direct product factor

110

C₂²×C₁₃

—

111

C₂²×C₁₃

—

112

C₂²×C₁₃

—

113

C₃²×C₅

—

Hall

114

C₃×C₁₃

—

115

C₃×C₁₃

—

116

C₃×C₁₃

—

117

C₃×C₁₃

C₂²×C₅×C₁₃⋊C₃

yes

characteristic, complemented

118

C₃×C₁₃

C₂²×C₃×C₅×C₁₃

yes

characteristic, complemented

119

C₁₃⋊C₃

—

120

C₁₃⋊C₃

C₂×C₅×D₃×C₁₃

yes

characteristic, direct product factor

121

C₂×C₃×D₃

—

Hall

122

C₂×C₃×C₅

—

123

C₂×C₃×C₅

—

124

C₂×C₃×C₅

—

125

C₂×C₃×C₅

C₂×C₁₃×C₁₃⋊C₃

yes

characteristic, complemented

126

C₅×D₃

C₂×C₁₃×C₁₃⋊C₃

yes

direct product factor

127

C₂×C₁₃

—

128

C₂×C₁₃

—

129

C₂×C₁₃

—

130

C₂×C₁₃

—

131

C₂×C₁₃

C₅×D₃×C₁₃⋊C₃

yes

characteristic, direct product factor

132

C₂×C₁₃

C₃×C₅×D₃×C₁₃

yes

characteristic, complemented

133

C₂²×C₅

—

Hall

134

C₂×C₃²

—

135

C₃×D₃

—

136

C₃×C₅

—

137

C₃×C₅

—

138

C₃×C₅

C₂²×C₁₃×C₁₃⋊C₃

yes

characteristic, complemented

139

C₁₃

—

140

C₁₃

C₂×C₅×D₃×C₁₃⋊C₃

yes

characteristic, direct product factor

141

C₁₃

C₂×C₃×C₅×D₃×C₁₃

yes

characteristic, complemented

142

C₂²×C₃

—

143

C₂×D₃

C₅×C₁₃×C₁₃⋊C₃

yes

characteristic, direct product factor

144

C₂×C₅

—

145

C₂×C₅

D₃×C₁₃×C₁₃⋊C₃

yes

characteristic, direct product factor

146

C₃²

—

Sylow

147

C₂×C₃

—

148

C₂×C₃

—

149

C₂×C₃

—

150

C₂×C₃

C₂×C₅×C₁₃×C₁₃⋊C₃

yes

characteristic, complemented

151

D₃

C₂×C₅×C₁₃×C₁₃⋊C₃

yes

direct product factor

152

C₅

C₂×D₃×C₁₃×C₁₃⋊C₃

yes

characteristic, direct product factor, Sylow

153

C₂²

—

Sylow

154

C₃

—

155

C₃

—

156

C₃

C₂²×C₅×C₁₃×C₁₃⋊C₃

yes

characteristic, complemented

157

C₂

—

158

C₂

C₅×D₃×C₁₃×C₁₃⋊C₃

yes

characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅×C₁₃	D₃×C₁₃⋊C₃
commutator, cosocle, hypocenter	C₃×C₁₃	C₂²×C₃×C₅×C₁₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₁₃²	C₂×C₃
LCS	G ▷ C₃×C₁₃
UCS	C₁ ◁ C₂×C₅×C₁₃

subgroup

G/H

center, hypercenter

C₂×C₅×C₁₃

D₃×C₁₃⋊C₃

commutator, cosocle, hypocenter

C₃×C₁₃

C₂²×C₃×C₅×C₁₃

Frattini

C₁

Fitting, socle

C₂×C₃×C₅×C₁₃²

C₂×C₃

LCS

G ▷ C₃×C₁₃

UCS

C₁ ◁ C₂×C₅×C₁₃

N	H ≅ G/N	type
1. C₂×C₃×C₅×C₁₃×C₁₃⋊C₃	C₂	semidirect
2. C₅×D₃×C₁₃×C₁₃⋊C₃	C₂	direct (N × H)
3. C₂×C₅×D₃×C₁₃²	C₃	semidirect
5. C₃×C₅×C₁₃×C₁₃⋊C₃	C₂²	semidirect
6. C₂×D₃×C₁₃×C₁₃⋊C₃	C₅	direct (N × H)
7. C₅×D₃×C₁₃²	C₂×C₃	semidirect
10. C₂×C₅×C₁₃×C₁₃⋊C₃	D₃	direct (N × H)
11. C₂×C₃×C₅×C₁₃²	C₂×C₃	semidirect
13. C₂×C₃×C₁₃×C₁₃⋊C₃	C₂×C₅	semidirect
14. D₃×C₁₃×C₁₃⋊C₃	C₂×C₅	direct (N × H)
16. C₅×C₁₃×C₁₃⋊C₃	C₂×D₃	direct (N × H)
17. C₃×C₅×C₁₃²	C₂²×C₃	semidirect
19. C₂×C₅×D₃×C₁₃⋊C₃	C₁₃	direct (N × H)
20. C₂×D₃×C₁₃²	C₃×C₅	semidirect
23. C₂×C₅×C₁₃²	C₃×D₃	semidirect
24. C₃×C₁₃×C₁₃⋊C₃	C₂²×C₅	semidirect
27. C₂×C₃×C₅×C₁₃⋊C₃	C₂×C₁₃	semidirect
28. C₅×D₃×C₁₃⋊C₃	C₂×C₁₃	direct (N × H)
29. C₂×C₃×C₁₃²	C₂×C₃×C₅	semidirect
30. D₃×C₁₃²	C₂×C₃×C₅	semidirect
33. C₂×C₁₃×C₁₃⋊C₃	C₅×D₃	direct (N × H)
34. C₅×C₁₃²	C₂×C₃×D₃	semidirect
37. C₂×C₅×D₃×C₁₃	C₁₃⋊C₃	direct (N × H)
38. C₂×C₅×D₃×C₁₃	C₃×C₁₃	semidirect
42. C₃×C₅×C₁₃⋊C₃	C₂²×C₁₃	semidirect
43. C₃×C₁₃²	C₂²×C₃×C₅	semidirect
45. C₁₃×C₁₃⋊C₃	C₂×C₅×D₃	direct (N × H)
47. C₂×D₃×C₁₃⋊C₃	C₅×C₁₃	direct (N × H)
52. C₂×C₃×C₅×C₁₃	C₂×C₁₃⋊C₃	semidirect
53. C₂×C₃×C₅×C₁₃	C₂×C₃×C₁₃	semidirect
55. C₅×D₃×C₁₃	C₂×C₁₃⋊C₃	direct (N × H)
56. C₅×D₃×C₁₃	C₂×C₃×C₁₃	semidirect
59. C₂×C₅×C₁₃⋊C₃	D₃×C₁₃	direct (N × H)
61. C₂×C₁₃²	C₃×C₅×D₃	semidirect
67. C₂×C₃×C₁₃⋊C₃	C₂×C₅×C₁₃	semidirect
68. D₃×C₁₃⋊C₃	C₂×C₅×C₁₃	direct (N × H)
72. C₃×C₅×C₁₃	C₂²×C₁₃⋊C₃	semidirect
73. C₃×C₅×C₁₃	C₂²×C₃×C₁₃	semidirect
75. C₅×C₁₃⋊C₃	C₂×D₃×C₁₃	direct (N × H)
77. C₁₃²	C₂×C₃×C₅×D₃	semidirect
80. C₂×D₃×C₁₃	C₅×C₁₃⋊C₃	direct (N × H)
81. C₂×D₃×C₁₃	C₃×C₅×C₁₃	semidirect
87. C₂×C₅×C₁₃	D₃×C₁₃⋊C₃	direct (N × H)
88. C₂×C₅×C₁₃	C₃×D₃×C₁₃	semidirect
90. C₃×C₁₃⋊C₃	C₂²×C₅×C₁₃	semidirect
97. C₂×C₃×C₁₃	C₂×C₅×C₁₃⋊C₃	semidirect
98. C₂×C₃×C₁₃	C₂×C₃×C₅×C₁₃	semidirect
100. D₃×C₁₃	C₂×C₅×C₁₃⋊C₃	direct (N × H)
101. D₃×C₁₃	C₂×C₃×C₅×C₁₃	semidirect
104. C₂×C₁₃⋊C₃	C₅×D₃×C₁₃	direct (N × H)
106. C₅×C₁₃	C₂×D₃×C₁₃⋊C₃	direct (N × H)
107. C₅×C₁₃	C₂×C₃×D₃×C₁₃	semidirect
109. C₂×C₅×D₃	C₁₃×C₁₃⋊C₃	direct (N × H)
117. C₃×C₁₃	C₂²×C₅×C₁₃⋊C₃	semidirect
118. C₃×C₁₃	C₂²×C₃×C₅×C₁₃	semidirect
120. C₁₃⋊C₃	C₂×C₅×D₃×C₁₃	direct (N × H)
125. C₂×C₃×C₅	C₂×C₁₃×C₁₃⋊C₃	semidirect
126. C₅×D₃	C₂×C₁₃×C₁₃⋊C₃	direct (N × H)
131. C₂×C₁₃	C₅×D₃×C₁₃⋊C₃	direct (N × H)
132. C₂×C₁₃	C₃×C₅×D₃×C₁₃	semidirect
138. C₃×C₅	C₂²×C₁₃×C₁₃⋊C₃	semidirect
140. C₁₃	C₂×C₅×D₃×C₁₃⋊C₃	direct (N × H)
141. C₁₃	C₂×C₃×C₅×D₃×C₁₃	semidirect
143. C₂×D₃	C₅×C₁₃×C₁₃⋊C₃	direct (N × H)
145. C₂×C₅	D₃×C₁₃×C₁₃⋊C₃	direct (N × H)
150. C₂×C₃	C₂×C₅×C₁₃×C₁₃⋊C₃	semidirect
151. D₃	C₂×C₅×C₁₃×C₁₃⋊C₃	direct (N × H)
152. C₅	C₂×D₃×C₁₃×C₁₃⋊C₃	direct (N × H)
156. C₃	C₂²×C₅×C₁₃×C₁₃⋊C₃	semidirect
158. C₂	C₅×D₃×C₁₃×C₁₃⋊C₃	direct (N × H)

H ≅ G/N

type

1. C₂×C₃×C₅×C₁₃×C₁₃⋊C₃

C₂

semidirect

2. C₅×D₃×C₁₃×C₁₃⋊C₃

C₂

direct (N × H)

3. C₂×C₅×D₃×C₁₃²

C₃

semidirect

5. C₃×C₅×C₁₃×C₁₃⋊C₃

C₂²

semidirect

6. C₂×D₃×C₁₃×C₁₃⋊C₃

C₅

direct (N × H)

7. C₅×D₃×C₁₃²

C₂×C₃

semidirect

10. C₂×C₅×C₁₃×C₁₃⋊C₃

D₃

direct (N × H)

11. C₂×C₃×C₅×C₁₃²

C₂×C₃

semidirect

13. C₂×C₃×C₁₃×C₁₃⋊C₃

C₂×C₅

semidirect

14. D₃×C₁₃×C₁₃⋊C₃

C₂×C₅

direct (N × H)

16. C₅×C₁₃×C₁₃⋊C₃

C₂×D₃

direct (N × H)

17. C₃×C₅×C₁₃²

C₂²×C₃

semidirect

19. C₂×C₅×D₃×C₁₃⋊C₃

C₁₃

direct (N × H)

20. C₂×D₃×C₁₃²

C₃×C₅

semidirect

23. C₂×C₅×C₁₃²

C₃×D₃

semidirect

24. C₃×C₁₃×C₁₃⋊C₃

C₂²×C₅

semidirect

27. C₂×C₃×C₅×C₁₃⋊C₃

C₂×C₁₃

semidirect

28. C₅×D₃×C₁₃⋊C₃

C₂×C₁₃

direct (N × H)

29. C₂×C₃×C₁₃²

C₂×C₃×C₅

semidirect

30. D₃×C₁₃²

C₂×C₃×C₅

semidirect

33. C₂×C₁₃×C₁₃⋊C₃

C₅×D₃

direct (N × H)

34. C₅×C₁₃²

C₂×C₃×D₃

semidirect

37. C₂×C₅×D₃×C₁₃

C₁₃⋊C₃

direct (N × H)

38. C₂×C₅×D₃×C₁₃

C₃×C₁₃

semidirect

42. C₃×C₅×C₁₃⋊C₃

C₂²×C₁₃

semidirect

43. C₃×C₁₃²

C₂²×C₃×C₅

semidirect

45. C₁₃×C₁₃⋊C₃

C₂×C₅×D₃

direct (N × H)

47. C₂×D₃×C₁₃⋊C₃

C₅×C₁₃

direct (N × H)

52. C₂×C₃×C₅×C₁₃

C₂×C₁₃⋊C₃

semidirect

53. C₂×C₃×C₅×C₁₃

C₂×C₃×C₁₃

semidirect

55. C₅×D₃×C₁₃

C₂×C₁₃⋊C₃

direct (N × H)

56. C₅×D₃×C₁₃

C₂×C₃×C₁₃

semidirect

59. C₂×C₅×C₁₃⋊C₃

D₃×C₁₃

direct (N × H)

61. C₂×C₁₃²

C₃×C₅×D₃

semidirect

67. C₂×C₃×C₁₃⋊C₃

C₂×C₅×C₁₃

semidirect

68. D₃×C₁₃⋊C₃

C₂×C₅×C₁₃

direct (N × H)

72. C₃×C₅×C₁₃

C₂²×C₁₃⋊C₃

semidirect

73. C₃×C₅×C₁₃

C₂²×C₃×C₁₃

semidirect

75. C₅×C₁₃⋊C₃

C₂×D₃×C₁₃

direct (N × H)

77. C₁₃²

C₂×C₃×C₅×D₃

semidirect

80. C₂×D₃×C₁₃

C₅×C₁₃⋊C₃

direct (N × H)

81. C₂×D₃×C₁₃

C₃×C₅×C₁₃

semidirect

87. C₂×C₅×C₁₃

D₃×C₁₃⋊C₃

direct (N × H)

88. C₂×C₅×C₁₃

C₃×D₃×C₁₃

semidirect

90. C₃×C₁₃⋊C₃

C₂²×C₅×C₁₃

semidirect

97. C₂×C₃×C₁₃

C₂×C₅×C₁₃⋊C₃

semidirect

98. C₂×C₃×C₁₃

C₂×C₃×C₅×C₁₃

semidirect

100. D₃×C₁₃

C₂×C₅×C₁₃⋊C₃

direct (N × H)

101. D₃×C₁₃

C₂×C₃×C₅×C₁₃

semidirect

104. C₂×C₁₃⋊C₃

C₅×D₃×C₁₃

direct (N × H)

106. C₅×C₁₃

C₂×D₃×C₁₃⋊C₃

direct (N × H)

107. C₅×C₁₃

C₂×C₃×D₃×C₁₃

semidirect

109. C₂×C₅×D₃

C₁₃×C₁₃⋊C₃

direct (N × H)

117. C₃×C₁₃

C₂²×C₅×C₁₃⋊C₃

semidirect

118. C₃×C₁₃

C₂²×C₃×C₅×C₁₃

semidirect

120. C₁₃⋊C₃

C₂×C₅×D₃×C₁₃

direct (N × H)

125. C₂×C₃×C₅

C₂×C₁₃×C₁₃⋊C₃

semidirect

126. C₅×D₃

C₂×C₁₃×C₁₃⋊C₃

direct (N × H)

131. C₂×C₁₃

C₅×D₃×C₁₃⋊C₃

direct (N × H)

132. C₂×C₁₃

C₃×C₅×D₃×C₁₃

semidirect

138. C₃×C₅

C₂²×C₁₃×C₁₃⋊C₃

semidirect

140. C₁₃

C₂×C₅×D₃×C₁₃⋊C₃

direct (N × H)

141. C₁₃

C₂×C₃×C₅×D₃×C₁₃

semidirect

143. C₂×D₃

C₅×C₁₃×C₁₃⋊C₃

direct (N × H)

145. C₂×C₅

D₃×C₁₃×C₁₃⋊C₃

direct (N × H)

150. C₂×C₃

C₂×C₅×C₁₃×C₁₃⋊C₃

semidirect

151. D₃

C₂×C₅×C₁₃×C₁₃⋊C₃

direct (N × H)

152. C₅

C₂×D₃×C₁₃×C₁₃⋊C₃

direct (N × H)

156. C₃

C₂²×C₅×C₁₃×C₁₃⋊C₃

semidirect

158. C₂

C₅×D₃×C₁₃×C₁₃⋊C₃

direct (N × H)

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

subgroup	index
C₂×C₃×C₅×C₁₃×C₁₃⋊C₃	2
C₅×D₃×C₁₃×C₁₃⋊C₃	2
C₂×C₅×D₃×C₁₃²	3
C₂²×C₅×C₁₃×C₁₃⋊C₃	3
C₂×D₃×C₁₃×C₁₃⋊C₃	5
C₂×C₃×C₅×D₃×C₁₃	13
C₂×C₅×D₃×C₁₃⋊C₃	13

subgroup

index

C₂×C₃×C₅×C₁₃×C₁₃⋊C₃

C₅×D₃×C₁₃×C₁₃⋊C₃

C₂×C₅×D₃×C₁₃²

C₂²×C₅×C₁₃×C₁₃⋊C₃

C₂×D₃×C₁₃×C₁₃⋊C₃

C₂×C₃×C₅×D₃×C₁₃

C₂×C₅×D₃×C₁₃⋊C₃

Subgroups — C₂×C₅×D₃×C₁₃×C₁₃⋊C₃ #44478166

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×C5×D3×C13×C13⋊C3 #44478166

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×D₃×C₁₃×C₁₃⋊C₃ #44478166