Subgroups — C₂₉×#17977 #20312877

Order 7424.

590 conjugacy classes of subgroups.

The subgroup lattice has 248 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3170	C₂	1	1	yes	maximal, characteristic
2	C₂₉×#2960	C₂	1	2	yes	maximal
3	C₂₉×#1584	C₂	1	8	yes	maximal, complemented
4	C₂₉×#1567	C₂	1	1	yes	maximal, characteristic
5	C₂₉×#1493	C₂	1	2	yes	maximal
6	C₂×C₂₉×#322	C₂	1	1	yes	maximal, characteristic
7	C₂₉×#533	C₂²	1	2	yes	—
8	C₂₉×#500	C₄	1	1	yes	characteristic
9	C₂₉×#494	C₄	1	1	yes	characteristic
10	C₂₉×#487	C₄	1	2	yes	—
11	C₂₉×#467	C₄	1	4	yes	—
12	C₂₉×#446	—	2	2	no	—
13	C₂₉×#446	C₂²	1	4	yes	—
14	C₈×Q₈×C₂₉	—	2	2	no	—
15	C₈×Q₈×C₂₉	C₂²	1	4	yes	—
16	C₄×Q₁₆×C₂₉	C₂²	1	4	yes	—
17	C₂₉×#424	—	2	2	no	—
18	C₂₉×#423	C₂²	1	2	yes	—
19	C₂₉×#405	—	2	2	no	—
20	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
23	C₂₉×#335	C₂²	1	4	yes	—
24	C₂₉×Q₈⋊C₈	C₂²	1	8	yes	—
25	C₂₉×#322	C₂²	1	4	yes	—
26	C₂×Q₁₆×C₂₉	C₂×C₄	1	4	yes	—
27	C₂×M₁₆×C₂₉	—	2	2	no	—
28	C₂²×C₈×C₂₉	—	2	1	no	—
29	C₂²×C₈×C₂₉	C₂×C₄	1	2	yes	—
30	C₂²×C₈×C₂₉	D₄	1	1	yes	characteristic
31	C₂²×C₈×C₂₉	D₄	1	1	yes	characteristic
32	C₂₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
33	C₂₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
34	C₂₉×#125	—	2	2	no	—
35	C₂₉×C₂²⋊Q₈	—	2	2	no	—
36	C₂₉×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
37	C₄×Q₈×C₂₉	—	2	2	no	—
38	C₄×Q₈×C₂₉	C₂³	1	4	yes	—
39	C₂₉×#117	—	2	2	no	—
40	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
41	C₂₉×#107	C₂×C₄	1	4	yes	—
42	C₂₉×C₄⋊C₈	—	2	4	no	—
43	C₂₉×C₄⋊C₈	—	2	4	no	—
44	C₂₉×C₄⋊C₈	—	2	2	no	—
45	C₂₉×C₄⋊C₈	C₂³	1	4	yes	—
46	C₂₉×#103	C₂×C₄	1	8	yes	—
47	C₂₉×#97	—	2	4	no	—
48	C₄×C₈×C₂₉	—	2	4	no	—
49	C₄×C₈×C₂₉	—	2	1	no	—
50	C₄×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
51	C₄×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
52	C₄×C₈×C₂₉	D₄	1	2	yes	—
53	C₄×C₈×C₂₉	C₂³	1	2	yes	—
54	C₄×C₈×C₂₉	C₂³	1	2	yes	—
55	C₄×C₈×C₂₉	C₂³	1	2	yes	—
56	C₂×Q₈×C₂₉	—	2	2	no	—
57	C₂×Q₈×C₂₉	C₂²×C₄	1	4	yes	—
58	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
59	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
60	C₂²×C₄×C₂₉	#41	1	1	yes	characteristic
61	Q₁₆×C₂₉	—	4	4	no	—
62	M₁₆×C₂₉	—	4	4	no	—
63	C₂×C₈×C₂₉	—	2	2	no	—
64	C₂×C₈×C₂₉	—	2	4	no	—
65	C₂×C₈×C₂₉	—	2	2	no	—
66	C₂×C₈×C₂₉	—	4	2	no	—
67	C₂×C₈×C₂₉	—	4	2	no	—
68	C₂×C₈×C₂₉	Q₁₆	1	4	yes	complemented
69	C₂×C₈×C₂₉	C₂²×C₄	1	2	yes	—
70	C₂×C₈×C₂₉	C₂²×C₄	1	2	yes	—
71	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
72	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
73	C₄⋊C₄×C₂₉	—	2	2	no	—
74	C₄⋊C₄×C₂₉	—	2	2	no	—
75	C₄⋊C₄×C₂₉	—	2	2	no	—
76	C₄⋊C₄×C₂₉	—	2	4	no	—
77	C₄⋊C₄×C₂₉	—	2	4	no	—
78	C₄⋊C₄×C₂₉	C₂²×C₄	1	4	yes	—
79	C₂²⋊C₄×C₂₉	—	2	4	no	—
80	C₄²×C₂₉	—	2	4	no	—
81	C₄²×C₂₉	C₂²×C₄	1	1	yes	characteristic
82	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
83	C₄²×C₂₉	#41	1	1	yes	characteristic
84	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
85	#17977	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
86	C₂³×C₂₉	C₄×D₄	1	1	yes	characteristic
87	Q₈×C₂₉	—	2	8	no	—
88	Q₈×C₂₉	—	4	4	no	—
89	C₂×C₄×C₂₉	—	2	2	no	—
90	C₂×C₄×C₂₉	—	2	2	no	—
91	C₂×C₄×C₂₉	—	2	4	no	—
92	C₂×C₄×C₂₉	—	2	4	no	—
93	C₂×C₄×C₂₉	C₄×D₄	1	1	yes	characteristic
94	C₂×C₄×C₂₉	C₄×D₄	1	1	yes	characteristic
95	C₂×C₄×C₂₉	C₄×D₄	1	1	yes	characteristic
96	C₂×C₄×C₂₉	C₂×Q₁₆	1	2	yes	—
97	C₂×C₄×C₂₉	#135	1	2	yes	—
98	C₂×C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
99	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
100	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
101	C₈×C₂₉	—	2	2	no	—
102	C₈×C₂₉	—	2	2	no	—
103	C₈×C₂₉	—	2	2	no	—
104	C₈×C₂₉	—	4	2	no	—
105	C₈×C₂₉	—	4	4	no	—
106	C₈×C₂₉	C₂×Q₁₆	1	4	yes	—
107	#3170	C₂×C₂₉	1	1	yes	characteristic
108	#2960	C₂×C₂₉	1	2	yes	—
109	#1584	C₂×C₂₉	1	8	yes	complemented
110	#1567	C₂×C₂₉	1	1	yes	characteristic
111	#1493	C₂×C₂₉	1	2	yes	—
112	C₂×#322	C₂×C₂₉	1	1	yes	characteristic
113	C₂²×C₂₉	—	2	1	no	—
114	C₂²×C₂₉	—	2	1	no	—
115	C₂²×C₂₉	C₄×Q₁₆	1	2	yes	—
116	C₂²×C₂₉	C₂×C₄×D₄	1	1	yes	characteristic
117	C₄×C₂₉	—	2	1	no	—
118	C₄×C₂₉	—	2	1	no	—
119	C₄×C₂₉	—	4	4	no	—
120	C₄×C₂₉	—	4	4	no	—
121	C₄×C₂₉	C₄×Q₁₆	1	2	yes	—
122	C₄×C₂₉	#444	1	2	yes	—
123	C₄×C₂₉	#568	1	2	yes	—
124	C₄×C₂₉	C₂²×Q₁₆	1	1	yes	characteristic
125	C₄×C₂₉	C₂×#135	1	1	yes	characteristic
126	#533	C₂²×C₂₉	1	2	yes	—
127	#500	C₄×C₂₉	1	1	yes	characteristic
128	#494	C₄×C₂₉	1	1	yes	characteristic
129	#487	C₄×C₂₉	1	2	yes	—
130	#467	C₄×C₂₉	1	4	yes	—
131	#446	—	2	2	no	—
132	#446	C₂²×C₂₉	1	4	yes	—
133	C₈×Q₈	—	2	2	no	—
134	C₈×Q₈	C₂²×C₂₉	1	4	yes	—
135	C₄×Q₁₆	C₂²×C₂₉	1	4	yes	—
136	#424	—	2	2	no	—
137	#423	C₂²×C₂₉	1	2	yes	—
138	#405	—	2	2	no	—
139	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
140	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
141	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
142	#335	C₂²×C₂₉	1	4	yes	—
143	Q₈⋊C₈	C₂²×C₂₉	1	8	yes	—
144	#322	C₂²×C₂₉	1	4	yes	—
145	C₂×C₂₉	—	2	2	no	—
146	C₂×C₂₉	#2932	1	1	yes	characteristic
147	C₂×C₂₉	C₂×C₄×Q₁₆	1	1	yes	characteristic
148	C₂×C₂₉	C₂×#444	1	1	yes	characteristic
149	C₂×Q₁₆	C₂×C₄×C₂₉	1	4	yes	—
150	C₂×M₁₆	—	2	2	no	—
151	C₂²×C₈	—	2	1	no	—
152	C₂²×C₈	C₂×C₄×C₂₉	1	2	yes	—
153	C₂²×C₈	D₄×C₂₉	1	1	yes	characteristic
154	C₂²×C₈	D₄×C₂₉	1	1	yes	characteristic
155	C₄⋊Q₈	C₂×C₄×C₂₉	1	2	yes	—
156	C₄⋊Q₈	C₂×C₄×C₂₉	1	2	yes	—
157	#125	—	2	2	no	—
158	C₂²⋊Q₈	—	2	2	no	—
159	C₂²⋊Q₈	C₂×C₄×C₂₉	1	4	yes	—
160	C₄×Q₈	—	2	2	no	—
161	C₄×Q₈	C₂³×C₂₉	1	4	yes	—
162	#117	—	2	2	no	—
163	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
164	#107	C₂×C₄×C₂₉	1	4	yes	—
165	C₄⋊C₈	—	2	4	no	—
166	C₄⋊C₈	—	2	4	no	—
167	C₄⋊C₈	—	2	2	no	—
168	C₄⋊C₈	C₂³×C₂₉	1	4	yes	—
169	#103	C₂×C₄×C₂₉	1	8	yes	—
170	#97	—	2	4	no	—
171	C₄×C₈	—	2	4	no	—
172	C₄×C₈	—	2	1	no	—
173	C₄×C₈	C₂×C₄×C₂₉	1	1	yes	characteristic
174	C₄×C₈	C₂×C₄×C₂₉	1	1	yes	characteristic
175	C₄×C₈	D₄×C₂₉	1	2	yes	—
176	C₄×C₈	C₂³×C₂₉	1	2	yes	—
177	C₄×C₈	C₂³×C₂₉	1	2	yes	—
178	C₄×C₈	C₂³×C₂₉	1	2	yes	—
179	C₂₉	#17977	1	1	yes	characteristic, direct product factor, Sylow
180	C₂×Q₈	—	2	2	no	—
181	C₂×Q₈	C₂²×C₄×C₂₉	1	4	yes	—
182	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
183	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
184	C₂²×C₄	#41×C₂₉	1	1	yes	characteristic
185	Q₁₆	—	4	4	no	—
186	M₁₆	—	4	4	no	—
187	C₂×C₈	—	2	2	no	—
188	C₂×C₈	—	2	4	no	—
189	C₂×C₈	—	2	2	no	—
190	C₂×C₈	—	4	2	no	—
191	C₂×C₈	—	4	2	no	—
192	C₂×C₈	Q₁₆×C₂₉	1	4	yes	complemented
193	C₂×C₈	C₂²×C₄×C₂₉	1	2	yes	—
194	C₂×C₈	C₂²×C₄×C₂₉	1	2	yes	—
195	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
196	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
197	C₄⋊C₄	—	2	2	no	—
198	C₄⋊C₄	—	2	2	no	—
199	C₄⋊C₄	—	2	2	no	—
200	C₄⋊C₄	—	2	4	no	—
201	C₄⋊C₄	—	2	4	no	—
202	C₄⋊C₄	C₂²×C₄×C₂₉	1	4	yes	—
203	C₂²⋊C₄	—	2	4	no	—
204	C₄²	—	2	4	no	—
205	C₄²	C₂²×C₄×C₂₉	1	1	yes	characteristic
206	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
207	C₄²	#41×C₂₉	1	1	yes	characteristic
208	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
209	C₂³	C₄×D₄×C₂₉	1	1	yes	characteristic
210	Q₈	—	2	8	no	—
211	Q₈	—	4	4	no	—
212	C₂×C₄	—	2	2	no	—
213	C₂×C₄	—	2	2	no	—
214	C₂×C₄	—	2	4	no	—
215	C₂×C₄	—	2	4	no	—
216	C₂×C₄	C₄×D₄×C₂₉	1	1	yes	characteristic
217	C₂×C₄	C₄×D₄×C₂₉	1	1	yes	characteristic
218	C₂×C₄	C₄×D₄×C₂₉	1	1	yes	characteristic
219	C₂×C₄	C₂×Q₁₆×C₂₉	1	2	yes	—
220	C₂×C₄	C₂₉×#135	1	2	yes	—
221	C₂×C₄	C₂³×C₄×C₂₉	1	1	yes	characteristic
222	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
223	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
224	C₈	—	2	2	no	—
225	C₈	—	2	2	no	—
226	C₈	—	2	2	no	—
227	C₈	—	4	2	no	—
228	C₈	—	4	4	no	—
229	C₈	C₂×Q₁₆×C₂₉	1	4	yes	—
230	C₂²	—	2	1	no	—
231	C₂²	—	2	1	no	—
232	C₂²	C₄×Q₁₆×C₂₉	1	2	yes	—
233	C₂²	C₂×C₄×D₄×C₂₉	1	1	yes	characteristic
234	C₄	—	2	1	no	—
235	C₄	—	2	1	no	—
236	C₄	—	4	4	no	—
237	C₄	—	4	4	no	—
238	C₄	C₄×Q₁₆×C₂₉	1	2	yes	—
239	C₄	C₂₉×#444	1	2	yes	—
240	C₄	C₂₉×#568	1	2	yes	—
241	C₄	C₂²×Q₁₆×C₂₉	1	1	yes	characteristic
242	C₄	C₂×C₂₉×#135	1	1	yes	characteristic
243	C₂	—	2	2	no	—
244	C₂	C₂₉×#2932	1	1	yes	characteristic
245	C₂	C₂×C₄×Q₁₆×C₂₉	1	1	yes	characteristic
246	C₂	C₂×C₂₉×#444	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₂₉
Frattini, cosocle	C₄²	C₂⁴×C₂₉
socle	C₂²×C₂₉	C₂×C₄×D₄
prime radical	C₂³×C₂₉	C₄×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₉ ◁ C₂×C₄×C₈×C₂₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
3. C₂₉×#1584	C₂	semidirect
68. C₂×C₈×C₂₉	Q₁₆	semidirect
85. #17977	C₂₉	direct (N × H)
109. #1584	C₂×C₂₉	semidirect
179. C₂₉	#17977	direct (N × H)
192. C₂×C₈	Q₁₆×C₂₉	semidirect

Maximal subgroups

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

subgroup	index
C₂₉×#3170	2
C₂₉×#2960	2
C₂₉×#1584	2
C₂₉×#1567	2
C₂₉×#1493	2
C₂×C₂₉×#322	2
#17977	29

Subgroups — C29×#17977 #20312877

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#17977 #20312877