Group #20305249 — subgroups

Subgroups — C₂₉×#10349 #20305249

Order 7424.

504 conjugacy classes of subgroups; only the 154 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 154 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	C₂₉×#2551	C₂	1	1	yes	maximal, characteristic
2	C₂₉×#1987	C₂	1	2	yes	maximal
3	C₂₉×#1956	C₂	1	1	yes	maximal, characteristic
4	C₂₉×#1296	C₂	1	1	yes	maximal, characteristic
5	C₂₉×#1279	C₂	1	2	yes	maximal
6	C₂×C₂₉×C₄⋊Q₈	—	2	2	no	—
7	C₂×C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
8	C₂×C₂₉×C₄⋊C₈	C₂²	1	2	yes	—
9	C₂×C₂₉×#103	—	2	2	no	—
10	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
11	C₂₉×#395	—	2	2	no	—
12	C₂₉×#389	—	2	2	no	—
13	C₂₉×#384	C₂²	1	1	yes	characteristic
14	C₄×C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
15	C₂₉×#340	—	2	2	no	—
16	C₂₉×#340	—	2	2	no	—
17	C₂²×Q₈×C₂₉	—	2	2	no	—
18	C₂²×Q₈×C₂₉	—	2	1	no	—
19	C₂²×C₈×C₂₉	—	2	1	no	—
20	C₂²×C₈×C₂₉	—	2	2	no	—
21	C₂₉×C₄⋊Q₈	—	2	2	no	—
22	C₂₉×C₄⋊Q₈	—	2	1	no	—
23	C₂₉×C₄⋊Q₈	—	4	4	no	—
24	C₂₉×C₄⋊Q₈	—	4	4	no	—
25	C₂₉×C₄⋊Q₈	Q₈	1	2	yes	complemented
26	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
27	C₂×C₄⋊C₄×C₂₉	—	2	4	no	—
28	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
29	C₂×C₄⋊C₄×C₂₉	D₄	1	2	yes	—
30	C₂×C₄⋊C₄×C₂₉	D₄	1	2	yes	—
31	C₂×C₄⋊C₄×C₂₉	D₄	1	2	yes	—
32	C₂×C₄²×C₂₉	—	2	2	no	—
33	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
34	C₂₉×C₄⋊C₈	—	2	2	no	—
35	C₂₉×C₄⋊C₈	—	2	2	no	—
36	C₂₉×#103	—	4	4	no	—
37	C₄×C₈×C₂₉	—	2	2	no	—
38	C₂₉×#95	—	2	2	no	—
39	C₂₉×#95	—	2	2	no	—
40	C₂×Q₈×C₂₉	—	2	2	no	—
41	C₂×Q₈×C₂₉	—	4	8	no	—
42	C₂×Q₈×C₂₉	—	4	2	no	—
43	C₂×Q₈×C₂₉	—	4	2	no	—
44	C₂×Q₈×C₂₉	—	4	1	no	—
45	C₂×Q₈×C₂₉	—	8	2	no	—
46	C₂²×C₄×C₂₉	—	2	2	no	—
47	C₂²×C₄×C₂₉	—	2	2	no	—
48	C₂²×C₄×C₂₉	—	2	2	no	—
49	C₂²×C₄×C₂₉	—	4	1	no	—
50	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
51	C₂²×C₄×C₂₉	C₂×D₄	1	2	yes	—
52	C₂×C₈×C₂₉	—	2	2	no	—
53	C₂×C₈×C₂₉	—	4	1	no	—
54	C₂×C₈×C₂₉	—	4	1	no	—
55	C₂×C₈×C₂₉	—	4	2	no	—
56	C₂×C₈×C₂₉	—	4	2	no	—
57	C₂×C₈×C₂₉	—	4	2	no	—
58	C₄⋊C₄×C₂₉	—	2	2	no	—
59	C₄⋊C₄×C₂₉	—	2	2	no	—
60	C₄⋊C₄×C₂₉	—	2	4	no	—
61	C₄⋊C₄×C₂₉	—	4	2	no	—
62	C₄⋊C₄×C₂₉	—	4	8	no	—
63	C₄⋊C₄×C₂₉	—	4	2	no	—
64	C₄⋊C₄×C₂₉	—	4	2	no	—
65	C₄⋊C₄×C₂₉	—	4	2	no	—
66	C₄⋊C₄×C₂₉	SD₁₆	1	4	yes	—
67	C₄⋊C₄×C₂₉	Q₁₆	1	4	yes	—
68	C₄²×C₂₉	—	4	2	no	—
69	C₄²×C₂₉	—	4	2	no	—
70	C₄²×C₂₉	C₂×Q₈	1	1	yes	characteristic
71	C₄²×C₂₉	#41	1	2	yes	—
72	C₄²×C₂₉	#41	1	1	yes	characteristic
73	#10349	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
74	C₂³×C₂₉	#120	1	1	yes	characteristic
75	Q₈×C₂₉	—	4	4	no	—
76	Q₈×C₂₉	—	8	2	no	—
77	Q₈×C₂₉	—	8	8	no	—
78	C₂×C₄×C₂₉	—	2	1	no	—
79	C₂×C₄×C₂₉	—	2	1	no	—
80	C₂×C₄×C₂₉	—	2	4	no	—
81	C₂×C₄×C₂₉	—	2	4	no	—
82	C₂×C₄×C₂₉	—	4	2	no	—
83	C₂×C₄×C₂₉	—	4	2	no	—
84	C₂×C₄×C₂₉	—	4	2	no	—
85	C₂×C₄×C₂₉	—	4	2	no	—
86	C₂×C₄×C₂₉	—	4	2	no	—
87	C₂×C₄×C₂₉	—	4	4	no	—
88	C₂×C₄×C₂₉	—	4	2	no	—
89	C₂×C₄×C₂₉	—	8	1	no	—
90	C₂×C₄×C₂₉	—	8	1	no	—
91	C₂×C₄×C₂₉	C₂²⋊Q₈	1	1	yes	characteristic
92	C₂×C₄×C₂₉	C₂²⋊Q₈	1	2	yes	—
93	C₂×C₄×C₂₉	#124	1	1	yes	characteristic
94	C₂×C₄×C₂₉	#124	1	2	yes	—
95	C₂×C₄×C₂₉	C₂×SD₁₆	1	2	yes	—
96	C₂×C₄×C₂₉	C₂×Q₁₆	1	2	yes	—
97	C₂×C₄×C₂₉	AGL(1,ℤ/8)	1	2	yes	—
98	C₂×C₄×C₂₉	#137	1	2	yes	—
99	C₈×C₂₉	—	4	2	no	—
100	C₈×C₂₉	—	8	2	no	—
101	#2551	C₂×C₂₉	1	1	yes	characteristic
102	#1987	C₂×C₂₉	1	2	yes	—
103	#1956	C₂×C₂₉	1	1	yes	characteristic
104	#1296	C₂×C₂₉	1	1	yes	characteristic
105	#1279	C₂×C₂₉	1	2	yes	—
106	C₂²×C₂₉	#393	1	1	yes	characteristic
107	C₂²×C₂₉	#450	1	2	yes	—
108	C₂²×C₂₉	#451	1	2	yes	—
109	C₂²×C₂₉	#453	1	1	yes	characteristic
110	C₂²×C₂₉	#454	1	1	yes	characteristic
111	C₄×C₂₉	—	2	1	no	—
112	C₄×C₂₉	—	2	1	no	—
113	C₄×C₂₉	—	4	4	no	—
114	C₄×C₂₉	—	4	4	no	—
115	C₄×C₂₉	—	8	2	no	—
116	C₄×C₂₉	—	8	2	no	—
117	C₄×C₂₉	#475	1	2	yes	—
118	C₄×C₂₉	#477	1	2	yes	—
119	C₄×C₂₉	#487	1	2	yes	—
120	C₄×C₂₉	#489	1	2	yes	—
121	C₂×C₄⋊Q₈	—	2	2	no	—
122	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
123	C₂×C₄⋊C₈	C₂²×C₂₉	1	2	yes	—
124	C₂×#103	—	2	2	no	—
125	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
126	#395	—	2	2	no	—
127	#389	—	2	2	no	—
128	#384	C₂²×C₂₉	1	1	yes	characteristic
129	C₄×C₄⋊C₄	C₂²×C₂₉	1	2	yes	—
130	#340	—	2	2	no	—
131	#340	—	2	2	no	—
132	C₂×C₂₉	#1629	1	1	yes	characteristic
133	C₂×C₂₉	#1633	1	1	yes	characteristic
134	C₂×C₂₉	#1637	1	2	yes	—
135	C₂×C₂₉	#2024	1	2	yes	—
136	C₂×C₂₉	#2027	1	1	yes	characteristic
137	C₂²×Q₈	—	2	2	no	—
138	C₂²×Q₈	—	2	1	no	—
139	C₂²×C₈	—	2	1	no	—
140	C₂²×C₈	—	2	2	no	—
141	C₄⋊Q₈	—	2	2	no	—
142	C₄⋊Q₈	—	2	1	no	—
143	C₄⋊Q₈	—	4	4	no	—
144	C₄⋊Q₈	—	4	4	no	—
145	C₄⋊Q₈	Q₈×C₂₉	1	2	yes	complemented
146	C₂×C₄⋊C₄	—	2	2	no	—
147	C₂×C₄⋊C₄	—	2	4	no	—
148	C₂×C₄⋊C₄	—	2	2	no	—
149	C₂×C₄⋊C₄	D₄×C₂₉	1	2	yes	—
150	C₂×C₄⋊C₄	D₄×C₂₉	1	2	yes	—
151	C₂×C₄⋊C₄	D₄×C₂₉	1	2	yes	—
152	C₂×C₄²	—	2	2	no	—
153	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
154	C₄⋊C₈	—	2	2	no	—
155	C₄⋊C₈	—	2	2	no	—
156	#103	—	4	4	no	—
157	C₄×C₈	—	2	2	no	—
158	#95	—	2	2	no	—
159	#95	—	2	2	no	—
160	C₂₉	#10349	1	1	yes	characteristic, direct product factor, Sylow
161	C₂×Q₈	—	2	2	no	—
162	C₂×Q₈	—	4	8	no	—
163	C₂×Q₈	—	4	2	no	—
164	C₂×Q₈	—	4	2	no	—
165	C₂×Q₈	—	4	1	no	—
166	C₂×Q₈	—	8	2	no	—
167	C₂²×C₄	—	2	2	no	—
168	C₂²×C₄	—	2	2	no	—
169	C₂²×C₄	—	2	2	no	—
170	C₂²×C₄	—	4	1	no	—
171	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
172	C₂²×C₄	C₂×D₄×C₂₉	1	2	yes	—
173	C₂×C₈	—	2	2	no	—
174	C₂×C₈	—	4	1	no	—
175	C₂×C₈	—	4	1	no	—
176	C₂×C₈	—	4	2	no	—
177	C₂×C₈	—	4	2	no	—
178	C₂×C₈	—	4	2	no	—
179	C₄⋊C₄	—	2	2	no	—
180	C₄⋊C₄	—	2	2	no	—
181	C₄⋊C₄	—	2	4	no	—
182	C₄⋊C₄	—	4	2	no	—
183	C₄⋊C₄	—	4	8	no	—
184	C₄⋊C₄	—	4	2	no	—
185	C₄⋊C₄	—	4	2	no	—
186	C₄⋊C₄	—	4	2	no	—
187	C₄⋊C₄	SD₁₆×C₂₉	1	4	yes	—
188	C₄⋊C₄	Q₁₆×C₂₉	1	4	yes	—
189	C₄²	—	4	2	no	—
190	C₄²	—	4	2	no	—
191	C₄²	C₂×Q₈×C₂₉	1	1	yes	characteristic
192	C₄²	#41×C₂₉	1	2	yes	—
193	C₄²	#41×C₂₉	1	1	yes	characteristic
194	C₂³	C₂₉×#120	1	1	yes	characteristic
195	Q₈	—	4	4	no	—
196	Q₈	—	8	2	no	—
197	Q₈	—	8	8	no	—
198	C₂×C₄	—	2	1	no	—
199	C₂×C₄	—	2	1	no	—
200	C₂×C₄	—	2	4	no	—
201	C₂×C₄	—	2	4	no	—
202	C₂×C₄	—	4	2	no	—
203	C₂×C₄	—	4	2	no	—
204	C₂×C₄	—	4	2	no	—
205	C₂×C₄	—	4	2	no	—
206	C₂×C₄	—	4	4	no	—
207	C₂×C₄	—	4	2	no	—
208	C₂×C₄	—	4	2	no	—
209	C₂×C₄	—	8	1	no	—
210	C₂×C₄	—	8	1	no	—
211	C₂×C₄	C₂₉×C₂²⋊Q₈	1	1	yes	characteristic
212	C₂×C₄	C₂₉×C₂²⋊Q₈	1	2	yes	—
213	C₂×C₄	C₂₉×#124	1	1	yes	characteristic
214	C₂×C₄	C₂₉×#124	1	2	yes	—
215	C₂×C₄	C₂×SD₁₆×C₂₉	1	2	yes	—
216	C₂×C₄	C₂×Q₁₆×C₂₉	1	2	yes	—
217	C₂×C₄	C₂₉×AGL(1,ℤ/8)	1	2	yes	—
218	C₂×C₄	C₂₉×#137	1	2	yes	—
219	C₈	—	4	2	no	—
220	C₈	—	8	2	no	—
221	C₂²	C₂₉×#393	1	1	yes	characteristic
222	C₂²	C₂₉×#450	1	2	yes	—
223	C₂²	C₂₉×#451	1	2	yes	—
224	C₂²	C₂₉×#453	1	1	yes	characteristic
225	C₂²	C₂₉×#454	1	1	yes	characteristic
226	C₄	—	2	1	no	—
227	C₄	—	2	1	no	—
228	C₄	—	4	4	no	—
229	C₄	—	4	4	no	—
230	C₄	—	8	2	no	—
231	C₄	—	8	2	no	—
232	C₄	C₂₉×#475	1	2	yes	—
233	C₄	C₂₉×#477	1	2	yes	—
234	C₄	C₂₉×#487	1	2	yes	—
235	C₄	C₂₉×#489	1	2	yes	—
236	C₂	C₂₉×#1629	1	1	yes	characteristic
237	C₂	C₂₉×#1633	1	1	yes	characteristic
238	C₂	C₂₉×#1637	1	2	yes	—
239	C₂	C₂₉×#2024	1	2	yes	—
240	C₂	C₂₉×#2027	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂₉×#2551

C₂

yes

maximal, characteristic

C₂₉×#1987

C₂

yes

maximal

C₂₉×#1956

C₂

yes

maximal, characteristic

C₂₉×#1296

C₂

yes

maximal, characteristic

C₂₉×#1279

C₂

yes

maximal

C₂×C₂₉×C₄⋊Q₈

—

C₂×C₂₉×C₄⋊Q₈

C₂²

yes

characteristic

C₂×C₂₉×C₄⋊C₈

C₂²

yes

—

C₂×C₂₉×#103

—

C₂×C₄×C₈×C₂₉

C₂²

yes

characteristic

C₂₉×#395

—

C₂₉×#389

—

C₂₉×#384

C₂²

yes

characteristic

C₄×C₄⋊C₄×C₂₉

C₂²

yes

—

C₂₉×#340

—

C₂₉×#340

—

C₂²×Q₈×C₂₉

—

C₂²×Q₈×C₂₉

—

C₂²×C₈×C₂₉

—

C₂²×C₈×C₂₉

—

C₂₉×C₄⋊Q₈

—

C₂₉×C₄⋊Q₈

—

C₂₉×C₄⋊Q₈

—

C₂₉×C₄⋊Q₈

—

C₂₉×C₄⋊Q₈

Q₈

yes

complemented

C₂×C₄⋊C₄×C₂₉

—

C₂×C₄⋊C₄×C₂₉

—

C₂×C₄⋊C₄×C₂₉

—

C₂×C₄⋊C₄×C₂₉

D₄

yes

—

C₂×C₄⋊C₄×C₂₉

D₄

yes

—

C₂×C₄⋊C₄×C₂₉

D₄

yes

—

C₂×C₄²×C₂₉

—

C₂×C₄²×C₂₉

C₂³

yes

characteristic

C₂₉×C₄⋊C₈

—

C₂₉×C₄⋊C₈

—

C₂₉×#103

—

C₄×C₈×C₂₉

—

C₂₉×#95

—

C₂₉×#95

—

C₂×Q₈×C₂₉

—

C₂×Q₈×C₂₉

—

C₂×Q₈×C₂₉

—

C₂×Q₈×C₂₉

—

C₂×Q₈×C₂₉

—

C₂×Q₈×C₂₉

—

C₂²×C₄×C₂₉

—

C₂²×C₄×C₂₉

—

C₂²×C₄×C₂₉

—

C₂²×C₄×C₂₉

—

C₂²×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₂₉

C₂×D₄

yes

—

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

SD₁₆

yes

—

C₄⋊C₄×C₂₉

Q₁₆

yes

—

C₄²×C₂₉

—

C₄²×C₂₉

—

C₄²×C₂₉

C₂×Q₈

yes

characteristic

C₄²×C₂₉

#41

yes

—

C₄²×C₂₉

#41

yes

characteristic

#10349

C₂₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₂₉

#120

yes

characteristic

Q₈×C₂₉

—

Q₈×C₂₉

—

Q₈×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₂₉

C₂²⋊Q₈

yes

—

C₂×C₄×C₂₉

#124

yes

characteristic

C₂×C₄×C₂₉

#124

yes

—

C₂×C₄×C₂₉

C₂×SD₁₆

yes

—

C₂×C₄×C₂₉

C₂×Q₁₆

yes

—

C₂×C₄×C₂₉

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₂₉

#137

yes

—

C₈×C₂₉

—

100

C₈×C₂₉

—

101

#2551

C₂×C₂₉

yes

characteristic

102

#1987

C₂×C₂₉

yes

—

103

#1956

C₂×C₂₉

yes

characteristic

104

#1296

C₂×C₂₉

yes

characteristic

105

#1279

C₂×C₂₉

yes

—

106

C₂²×C₂₉

#393

yes

characteristic

107

C₂²×C₂₉

#450

yes

—

108

C₂²×C₂₉

#451

yes

—

109

C₂²×C₂₉

#453

yes

characteristic

110

C₂²×C₂₉

#454

yes

characteristic

111

C₄×C₂₉

—

112

C₄×C₂₉

—

113

C₄×C₂₉

—

114

C₄×C₂₉

—

115

C₄×C₂₉

—

116

C₄×C₂₉

—

117

C₄×C₂₉

#475

yes

—

118

C₄×C₂₉

#477

yes

—

119

C₄×C₂₉

#487

yes

—

120

C₄×C₂₉

#489

yes

—

121

C₂×C₄⋊Q₈

—

122

C₂×C₄⋊Q₈

C₂²×C₂₉

yes

characteristic

123

C₂×C₄⋊C₈

C₂²×C₂₉

yes

—

124

C₂×#103

—

125

C₂×C₄×C₈

C₂²×C₂₉

yes

characteristic

126

#395

—

127

#389

—

128

#384

C₂²×C₂₉

yes

characteristic

129

C₄×C₄⋊C₄

C₂²×C₂₉

yes

—

130

#340

—

131

#340

—

132

C₂×C₂₉

#1629

yes

characteristic

133

C₂×C₂₉

#1633

yes

characteristic

134

C₂×C₂₉

#1637

yes

—

135

C₂×C₂₉

#2024

yes

—

136

C₂×C₂₉

#2027

yes

characteristic

137

C₂²×Q₈

—

138

C₂²×Q₈

—

139

C₂²×C₈

—

140

C₂²×C₈

—

141

C₄⋊Q₈

—

142

C₄⋊Q₈

—

143

C₄⋊Q₈

—

144

C₄⋊Q₈

—

145

C₄⋊Q₈

Q₈×C₂₉

yes

complemented

146

C₂×C₄⋊C₄

—

147

C₂×C₄⋊C₄

—

148

C₂×C₄⋊C₄

—

149

C₂×C₄⋊C₄

D₄×C₂₉

yes

—

150

C₂×C₄⋊C₄

D₄×C₂₉

yes

—

151

C₂×C₄⋊C₄

D₄×C₂₉

yes

—

152

C₂×C₄²

—

153

C₂×C₄²

C₂³×C₂₉

yes

characteristic

154

C₄⋊C₈

—

155

C₄⋊C₈

—

156

#103

—

157

C₄×C₈

—

158

#95

—

159

#95

—

160

C₂₉

#10349

yes

characteristic, direct product factor, Sylow

161

C₂×Q₈

—

162

C₂×Q₈

—

163

C₂×Q₈

—

164

C₂×Q₈

—

165

C₂×Q₈

—

166

C₂×Q₈

—

167

C₂²×C₄

—

168

C₂²×C₄

—

169

C₂²×C₄

—

170

C₂²×C₄

—

171

C₂²×C₄

C₂×D₄×C₂₉

yes

characteristic

172

C₂²×C₄

C₂×D₄×C₂₉

yes

—

173

C₂×C₈

—

174

C₂×C₈

—

175

C₂×C₈

—

176

C₂×C₈

—

177

C₂×C₈

—

178

C₂×C₈

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

181

C₄⋊C₄

—

182

C₄⋊C₄

—

183

C₄⋊C₄

—

184

C₄⋊C₄

—

185

C₄⋊C₄

—

186

C₄⋊C₄

—

187

C₄⋊C₄

SD₁₆×C₂₉

yes

—

188

C₄⋊C₄

Q₁₆×C₂₉

yes

—

189

C₄²

—

190

C₄²

—

191

C₄²

C₂×Q₈×C₂₉

yes

characteristic

192

C₄²

#41×C₂₉

yes

—

193

C₄²

#41×C₂₉

yes

characteristic

194

C₂³

C₂₉×#120

yes

characteristic

195

Q₈

—

196

Q₈

—

197

Q₈

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

C₂₉×C₂²⋊Q₈

yes

characteristic

212

C₂×C₄

C₂₉×C₂²⋊Q₈

yes

—

213

C₂×C₄

C₂₉×#124

yes

characteristic

214

C₂×C₄

C₂₉×#124

yes

—

215

C₂×C₄

C₂×SD₁₆×C₂₉

yes

—

216

C₂×C₄

C₂×Q₁₆×C₂₉

yes

—

217

C₂×C₄

C₂₉×AGL(1,ℤ/8)

yes

—

218

C₂×C₄

C₂₉×#137

yes

—

219

C₈

—

220

C₈

—

221

C₂²

C₂₉×#393

yes

characteristic

222

C₂²

C₂₉×#450

yes

—

223

C₂²

C₂₉×#451

yes

—

224

C₂²

C₂₉×#453

yes

characteristic

225

C₂²

C₂₉×#454

yes

characteristic

226

C₄

—

227

C₄

—

228

C₄

—

229

C₄

—

230

C₄

—

231

C₄

—

232

C₄

C₂₉×#475

yes

—

233

C₄

C₂₉×#477

yes

—

234

C₄

C₂₉×#487

yes

—

235

C₄

C₂₉×#489

yes

—

236

C₂

C₂₉×#1629

yes

characteristic

237

C₂

C₂₉×#1633

yes

characteristic

238

C₂

C₂₉×#1637

yes

—

239

C₂

C₂₉×#2024

yes

—

240

C₂

C₂₉×#2027

yes

characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₂₉	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₂₉
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ C₂×C₄²×C₂₉ ◁ G

subgroup

G/H

center, socle, prime radical

C₂³×C₂₉

#120

commutator, Frattini, cosocle

C₂×C₄²

C₂³×C₂₉

LCS

G ▷ C₂×C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂³×C₂₉ ◁ C₂×C₄²×C₂₉ ◁ G

N	H ≅ G/N	type
25. C₂₉×C₄⋊Q₈	Q₈	semidirect
73. #10349	C₂₉	direct (N × H)
145. C₄⋊Q₈	Q₈×C₂₉	semidirect
160. C₂₉	#10349	direct (N × H)

H ≅ G/N

type

25. C₂₉×C₄⋊Q₈

Q₈

semidirect

73. #10349

C₂₉

direct (N × H)

145. C₄⋊Q₈

Q₈×C₂₉

semidirect

160. C₂₉

#10349

direct (N × H)

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

subgroup	index
C₂₉×#2551	2
C₂₉×#1987	2
C₂₉×#1956	2
C₂₉×#1296	2
C₂₉×#1279	2
#10349	29

subgroup

index

C₂₉×#2551

C₂₉×#1987

C₂₉×#1956

C₂₉×#1296

C₂₉×#1279

#10349

Subgroups — C₂₉×#10349 #20305249

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C29×#10349 #20305249

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#10349 #20305249