Subgroups — C₂×C₂₉×#2404 #20329628

Order 7424.

7222 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#41×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₂₉×#120	C₂	1	2	yes	maximal, complemented
3	C₂³×C₂²⋊C₄×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#2404	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₂₉×#393	C₂	1	2	yes	maximal, complemented
6	C₂×C₂₉×#392	C₂	1	2	yes	maximal, complemented
7	C₂×C₂₉×#386	C₂	1	4	yes	maximal, complemented
8	C₂×C₂₉×#386	C₂	1	2	yes	maximal, complemented
9	C₂×C₂₉×#381	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂⁶×C₂₉	C₂²	1	1	yes	characteristic
11	C₂²×#41×C₂₉	—	2	16	no	—
12	C₂²×#41×C₂₉	—	2	8	no	—
13	C₂²×#41×C₂₉	C₂²	1	8	yes	complemented
14	C₂³×Q₈×C₂₉	C₂²	1	1	yes	characteristic, complemented
15	C₂³×D₄×C₂₉	C₂²	1	4	yes	—
16	C₂³×D₄×C₂₉	C₂²	1	2	yes	—
17	C₂³×D₄×C₂₉	C₂²	1	1	yes	characteristic, complemented
18	C₂⁴×C₄×C₂₉	C₂²	1	1	yes	characteristic
19	C₂⁴×C₄×C₂₉	C₂²	1	1	yes	characteristic
20	C₂⁴×C₄×C₂₉	C₂²	1	2	yes	complemented
21	C₂×C₂₉×#120	—	2	16	no	—
22	C₂×C₂₉×#120	C₂²	1	16	yes	complemented
23	C₂²×C₂²⋊C₄×C₂₉	—	2	8	no	—
24	C₂²×C₂²⋊C₄×C₂₉	C₂²	1	2	yes	—
25	C₂²×C₂²⋊C₄×C₂₉	C₂²	1	2	yes	—
26	C₂²×C₂²⋊C₄×C₂₉	C₂²	1	4	yes	—
27	C₂²×C₂²⋊C₄×C₂₉	C₂²	1	2	yes	—
28	C₂²×C₂²⋊C₄×C₂₉	C₂²	1	8	yes	complemented
29	C₂²×C₂²⋊C₄×C₂₉	C₂²	1	4	yes	complemented
30	C₂₉×#393	C₂²	1	16	yes	complemented
31	C₂₉×#392	C₂²	1	16	yes	complemented
32	C₂₉×#386	C₂²	1	32	yes	complemented
33	C₂₉×#386	C₂²	1	16	yes	complemented
34	C₂₉×#381	C₂²	1	8	yes	complemented
35	C₂×C₂₉×#95	C₂²	1	2	yes	complemented
36	C₂×C₂₉×#95	C₂²	1	2	yes	complemented
37	C₂×C₂₉×#95	C₂²	1	4	yes	complemented
38	C₂⁵×C₂₉	—	2	4	no	—
39	C₂⁵×C₂₉	—	2	8	no	—
40	C₂⁵×C₂₉	—	2	8	no	—
41	C₂⁵×C₂₉	—	4	4	no	—
42	C₂⁵×C₂₉	C₂³	1	2	yes	—
43	C₂⁵×C₂₉	C₂³	1	2	yes	—
44	C₂⁵×C₂₉	C₂³	1	4	yes	—
45	C₂⁵×C₂₉	C₂³	1	1	yes	characteristic
46	C₂×#41×C₂₉	—	2	128	no	—
47	C₂×#41×C₂₉	—	2	64	no	—
48	C₂×#41×C₂₉	—	2	32	no	—
49	C₂²×Q₈×C₂₉	—	2	8	no	—
50	C₂²×Q₈×C₂₉	—	2	4	no	—
51	C₂²×Q₈×C₂₉	C₂³	1	4	yes	complemented
52	C₂²×D₄×C₂₉	—	2	8	no	—
53	C₂²×D₄×C₂₉	—	2	8	no	—
54	C₂²×D₄×C₂₉	—	2	8	no	—
55	C₂²×D₄×C₂₉	—	2	16	no	—
56	C₂²×D₄×C₂₉	—	2	16	no	—
57	C₂²×D₄×C₂₉	—	2	4	no	—
58	C₂²×D₄×C₂₉	—	4	8	no	—
59	C₂²×D₄×C₂₉	D₄	1	16	yes	complemented
60	C₂²×D₄×C₂₉	C₂³	1	16	yes	—
61	C₂²×D₄×C₂₉	C₂³	1	8	yes	—
62	C₂²×D₄×C₂₉	C₂³	1	4	yes	complemented
63	C₂³×C₄×C₂₉	—	2	8	no	—
64	C₂³×C₄×C₂₉	—	2	8	no	—
65	C₂³×C₄×C₂₉	—	2	8	no	—
66	C₂³×C₄×C₂₉	—	2	8	no	—
67	C₂³×C₄×C₂₉	—	2	4	no	—
68	C₂³×C₄×C₂₉	—	4	4	no	—
69	C₂³×C₄×C₂₉	D₄	1	8	yes	complemented
70	C₂³×C₄×C₂₉	C₂³	1	2	yes	—
71	C₂³×C₄×C₂₉	C₂³	1	4	yes	—
72	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₂₉	C₂³	1	2	yes	—
75	C₂³×C₄×C₂₉	C₂³	1	4	yes	—
76	C₂³×C₄×C₂₉	C₂³	1	4	yes	—
77	C₂³×C₄×C₂₉	C₂³	1	8	yes	complemented
78	C₂₉×#120	—	2	64	no	—
79	C₂×C₂²⋊C₄×C₂₉	—	2	8	no	—
80	C₂×C₂²⋊C₄×C₂₉	—	2	8	no	—
81	C₂×C₂²⋊C₄×C₂₉	—	2	8	no	—
82	C₂×C₂²⋊C₄×C₂₉	—	2	16	no	—
83	C₂×C₂²⋊C₄×C₂₉	—	2	32	no	—
84	C₂×C₂²⋊C₄×C₂₉	—	4	8	no	—
85	C₂×C₂²⋊C₄×C₂₉	C₂³	1	8	yes	—
86	C₂×C₂²⋊C₄×C₂₉	C₂³	1	8	yes	—
87	C₂×C₂²⋊C₄×C₂₉	C₂³	1	8	yes	—
88	C₂×C₂²⋊C₄×C₂₉	C₂³	1	16	yes	—
89	C₂×C₂²⋊C₄×C₂₉	C₂³	1	16	yes	complemented
90	C₂₉×#95	C₂³	1	8	yes	complemented
91	C₂₉×#95	C₂³	1	8	yes	complemented
92	C₂₉×#95	C₂³	1	16	yes	complemented
93	C₂⁴×C₂₉	—	2	4	no	—
94	C₂⁴×C₂₉	—	2	4	no	—
95	C₂⁴×C₂₉	—	2	32	no	—
96	C₂⁴×C₂₉	—	2	8	no	—
97	C₂⁴×C₂₉	—	2	4	no	—
98	C₂⁴×C₂₉	—	2	8	no	—
99	C₂⁴×C₂₉	—	2	4	no	—
100	C₂⁴×C₂₉	—	2	4	no	—
101	C₂⁴×C₂₉	—	2	8	no	—
102	C₂⁴×C₂₉	—	2	4	no	—
103	C₂⁴×C₂₉	—	2	16	no	—
104	C₂⁴×C₂₉	—	2	8	no	—
105	C₂⁴×C₂₉	—	2	8	no	—
106	C₂⁴×C₂₉	—	2	16	no	—
107	C₂⁴×C₂₉	—	4	8	no	—
108	C₂⁴×C₂₉	—	4	64	no	—
109	C₂⁴×C₂₉	—	4	16	no	—
110	C₂⁴×C₂₉	—	4	16	no	—
111	C₂⁴×C₂₉	C₂×D₄	1	8	yes	—
112	C₂⁴×C₂₉	C₂×D₄	1	8	yes	—
113	C₂⁴×C₂₉	C₂×D₄	1	4	yes	—
114	C₂⁴×C₂₉	#41	1	8	yes	complemented
115	C₂⁴×C₂₉	C₂⁴	1	4	yes	—
116	C₂⁴×C₂₉	C₂⁴	1	4	yes	—
117	C₂⁴×C₂₉	C₂⁴	1	2	yes	—
118	C₂⁴×C₂₉	C₂⁴	1	1	yes	characteristic
119	#41×C₂₉	—	2	256	no	—
120	C₂×Q₈×C₂₉	—	2	32	no	—
121	C₂×Q₈×C₂₉	—	2	16	no	—
122	C₂×Q₈×C₂₉	—	2	8	no	—
123	C₂×D₄×C₂₉	—	2	32	no	—
124	C₂×D₄×C₂₉	—	2	64	no	—
125	C₂×D₄×C₂₉	—	2	16	no	—
126	C₂×D₄×C₂₉	—	2	16	no	—
127	C₂×D₄×C₂₉	—	2	16	no	—
128	C₂×D₄×C₂₉	—	2	32	no	—
129	C₂×D₄×C₂₉	—	2	32	no	—
130	C₂×D₄×C₂₉	—	2	8	no	—
131	C₂×D₄×C₂₉	—	4	16	no	—
132	C₂×D₄×C₂₉	—	4	64	no	—
133	C₂×D₄×C₂₉	C₂×D₄	1	32	yes	complemented
134	C₂²×C₄×C₂₉	—	2	64	no	—
135	C₂²×C₄×C₂₉	—	2	32	no	—
136	C₂²×C₄×C₂₉	—	2	4	no	—
137	C₂²×C₄×C₂₉	—	2	4	no	—
138	C₂²×C₄×C₂₉	—	2	4	no	—
139	C₂²×C₄×C₂₉	—	2	4	no	—
140	C₂²×C₄×C₂₉	—	2	16	no	—
141	C₂²×C₄×C₂₉	—	2	16	no	—
142	C₂²×C₄×C₂₉	—	2	16	no	—
143	C₂²×C₄×C₂₉	—	2	16	no	—
144	C₂²×C₄×C₂₉	—	2	8	no	—
145	C₂²×C₄×C₂₉	—	2	4	no	—
146	C₂²×C₄×C₂₉	—	2	8	no	—
147	C₂²×C₄×C₂₉	—	2	8	no	—
148	C₂²×C₄×C₂₉	—	2	8	no	—
149	C₂²×C₄×C₂₉	—	2	8	no	—
150	C₂²×C₄×C₂₉	—	4	8	no	—
151	C₂²×C₄×C₂₉	—	4	16	no	—
152	C₂²×C₄×C₂₉	C₂×D₄	1	4	yes	—
153	C₂²×C₄×C₂₉	C₂×D₄	1	8	yes	—
154	C₂²×C₄×C₂₉	C₂×D₄	1	4	yes	—
155	C₂²×C₄×C₂₉	C₂×D₄	1	16	yes	complemented
156	C₂²×C₄×C₂₉	C₂⁴	1	4	yes	—
157	C₂²×C₄×C₂₉	C₂⁴	1	8	yes	—
158	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
159	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
160	C₂²×C₄×C₂₉	C₂⁴	1	4	yes	—
161	C₂²⋊C₄×C₂₉	—	2	16	no	—
162	C₂²⋊C₄×C₂₉	—	2	16	no	—
163	C₂²⋊C₄×C₂₉	—	2	16	no	—
164	C₂²⋊C₄×C₂₉	—	2	32	no	—
165	C₂²⋊C₄×C₂₉	—	4	16	no	—
166	C₂×#2404	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
167	C₂³×C₂₉	—	2	8	no	—
168	C₂³×C₂₉	—	2	8	no	—
169	C₂³×C₂₉	—	2	32	no	—
170	C₂³×C₂₉	—	2	4	no	—
171	C₂³×C₂₉	—	2	4	no	—
172	C₂³×C₂₉	—	2	32	no	—
173	C₂³×C₂₉	—	2	16	no	—
174	C₂³×C₂₉	—	2	16	no	—
175	C₂³×C₂₉	—	2	32	no	—
176	C₂³×C₂₉	—	2	32	no	—
177	C₂³×C₂₉	—	2	4	no	—
178	C₂³×C₂₉	—	2	8	no	—
179	C₂³×C₂₉	—	2	4	no	—
180	C₂³×C₂₉	—	2	4	no	—
181	C₂³×C₂₉	—	2	8	no	—
182	C₂³×C₂₉	—	2	4	no	—
183	C₂³×C₂₉	—	2	8	no	—
184	C₂³×C₂₉	—	2	8	no	—
185	C₂³×C₂₉	—	4	64	no	—
186	C₂³×C₂₉	—	4	128	no	—
187	C₂³×C₂₉	—	4	16	no	—
188	C₂³×C₂₉	—	4	16	no	—
189	C₂³×C₂₉	—	4	8	no	—
190	C₂³×C₂₉	—	4	8	no	—
191	C₂³×C₂₉	—	4	8	no	—
192	C₂³×C₂₉	—	4	8	no	—
193	C₂³×C₂₉	—	4	16	no	—
194	C₂³×C₂₉	—	4	16	no	—
195	C₂³×C₂₉	#120	1	16	yes	—
196	C₂³×C₂₉	C₂²×D₄	1	8	yes	—
197	C₂³×C₂₉	C₂²×D₄	1	8	yes	—
198	C₂³×C₂₉	C₂²×D₄	1	4	yes	—
199	C₂³×C₂₉	C₂²×D₄	1	2	yes	—
200	C₂³×C₂₉	C₂²×D₄	1	4	yes	—
201	C₂³×C₂₉	C₂×#41	1	4	yes	—
202	C₂³×C₂₉	C₂×#41	1	8	yes	complemented
203	C₂³×C₂₉	H(5,𝔽₂)	1	4	yes	—
204	C₂³×C₂₉	C₂⁵	1	1	yes	characteristic
205	Q₈×C₂₉	—	2	32	no	—
206	D₄×C₂₉	—	2	32	no	—
207	D₄×C₂₉	—	2	64	no	—
208	D₄×C₂₉	—	4	64	no	—
209	C₂×C₄×C₂₉	—	2	64	no	—
210	C₂×C₄×C₂₉	—	2	8	no	—
211	C₂×C₄×C₂₉	—	2	16	no	—
212	C₂×C₄×C₂₉	—	2	8	no	—
213	C₂×C₄×C₂₉	—	2	32	no	—
214	C₂×C₄×C₂₉	—	2	4	no	—
215	C₂×C₄×C₂₉	—	2	4	no	—
216	C₂×C₄×C₂₉	—	2	4	no	—
217	C₂×C₄×C₂₉	—	2	4	no	—
218	C₂×C₄×C₂₉	—	2	4	no	—
219	C₂×C₄×C₂₉	—	2	8	no	—
220	C₂×C₄×C₂₉	—	2	8	no	—
221	C₂×C₄×C₂₉	—	2	8	no	—
222	C₂×C₄×C₂₉	—	2	8	no	—
223	C₂×C₄×C₂₉	—	4	16	no	—
224	C₂×C₄×C₂₉	—	4	8	no	—
225	C₂×C₄×C₂₉	—	4	16	no	—
226	C₂×C₄×C₂₉	C₂²×D₄	1	4	yes	—
227	C₂×C₄×C₂₉	C₂²×D₄	1	8	yes	—
228	C₂×C₄×C₂₉	C₂²×D₄	1	4	yes	—
229	C₂³×#41	C₂×C₂₉	1	1	yes	characteristic, complemented
230	C₂²×#120	C₂×C₂₉	1	2	yes	complemented
231	C₂³×C₂²⋊C₄	C₂×C₂₉	1	1	yes	characteristic, complemented
232	#2404	C₂×C₂₉	1	16	yes	direct product factor
233	C₂×#393	C₂×C₂₉	1	2	yes	complemented
234	C₂×#392	C₂×C₂₉	1	2	yes	complemented
235	C₂×#386	C₂×C₂₉	1	4	yes	complemented
236	C₂×#386	C₂×C₂₉	1	2	yes	complemented
237	C₂×#381	C₂×C₂₉	1	1	yes	characteristic, complemented
238	C₂²×C₂₉	—	2	32	no	—
239	C₂²×C₂₉	—	2	4	no	—
240	C₂²×C₂₉	—	2	4	no	—
241	C₂²×C₂₉	—	2	16	no	—
242	C₂²×C₂₉	—	2	8	no	—
243	C₂²×C₂₉	—	2	8	no	—
244	C₂²×C₂₉	—	2	16	no	—
245	C₂²×C₂₉	—	2	16	no	—
246	C₂²×C₂₉	—	4	64	no	—
247	C₂²×C₂₉	—	4	32	no	—
248	C₂²×C₂₉	—	4	32	no	—
249	C₂²×C₂₉	—	4	4	no	—
250	C₂²×C₂₉	—	4	4	no	—
251	C₂²×C₂₉	—	4	4	no	—
252	C₂²×C₂₉	—	4	4	no	—
253	C₂²×C₂₉	—	4	8	no	—
254	C₂²×C₂₉	—	4	8	no	—
255	C₂²×C₂₉	C₂×#120	1	8	yes	—
256	C₂²×C₂₉	C₂×#120	1	4	yes	—
257	C₂²×C₂₉	#525	1	4	yes	—
258	C₂²×C₂₉	#535	1	4	yes	—
259	C₂²×C₂₉	#546	1	16	yes	—
260	C₂²×C₂₉	C₂³×D₄	1	1	yes	characteristic
261	C₂²×C₂₉	C₂³×D₄	1	2	yes	—
262	C₂²×C₂₉	C₂²×#41	1	2	yes	—
263	C₂²×C₂₉	C₂×H(5,𝔽₂)	1	2	yes	—
264	C₄×C₂₉	—	2	4	no	—
265	C₄×C₂₉	—	2	8	no	—
266	C₄×C₂₉	—	2	4	no	—
267	C₄×C₂₉	—	4	4	no	—
268	C₄×C₂₉	—	4	8	no	—
269	C₂⁶	C₂²×C₂₉	1	1	yes	characteristic
270	C₂²×#41	—	2	16	no	—
271	C₂²×#41	—	2	8	no	—
272	C₂²×#41	C₂²×C₂₉	1	8	yes	complemented
273	C₂³×Q₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
274	C₂³×D₄	C₂²×C₂₉	1	4	yes	—
275	C₂³×D₄	C₂²×C₂₉	1	2	yes	—
276	C₂³×D₄	C₂²×C₂₉	1	1	yes	characteristic, complemented
277	C₂⁴×C₄	C₂²×C₂₉	1	1	yes	characteristic
278	C₂⁴×C₄	C₂²×C₂₉	1	1	yes	characteristic
279	C₂⁴×C₄	C₂²×C₂₉	1	2	yes	complemented
280	C₂×#120	—	2	16	no	—
281	C₂×#120	C₂²×C₂₉	1	16	yes	complemented
282	C₂²×C₂²⋊C₄	—	2	8	no	—
283	C₂²×C₂²⋊C₄	C₂²×C₂₉	1	2	yes	—
284	C₂²×C₂²⋊C₄	C₂²×C₂₉	1	4	yes	—
285	C₂²×C₂²⋊C₄	C₂²×C₂₉	1	2	yes	—
286	C₂²×C₂²⋊C₄	C₂²×C₂₉	1	2	yes	—
287	C₂²×C₂²⋊C₄	C₂²×C₂₉	1	8	yes	complemented
288	C₂²×C₂²⋊C₄	C₂²×C₂₉	1	4	yes	complemented
289	#393	C₂²×C₂₉	1	16	yes	complemented
290	#392	C₂²×C₂₉	1	16	yes	complemented
291	#386	C₂²×C₂₉	1	32	yes	complemented
292	#386	C₂²×C₂₉	1	16	yes	complemented
293	#381	C₂²×C₂₉	1	8	yes	complemented
294	C₂×#95	C₂²×C₂₉	1	2	yes	complemented
295	C₂×#95	C₂²×C₂₉	1	4	yes	complemented
296	C₂×#95	C₂²×C₂₉	1	2	yes	complemented
297	C₂×C₂₉	—	2	8	no	—
298	C₂×C₂₉	—	4	8	no	—
299	C₂×C₂₉	—	4	8	no	—
300	C₂×C₂₉	#2404	1	8	yes	direct product factor
301	C₂×C₂₉	C₂²×#120	1	1	yes	characteristic
302	C₂×C₂₉	C₂×#525	1	1	yes	characteristic
303	C₂×C₂₉	C₂×#535	1	1	yes	characteristic
304	C₂×C₂₉	C₂×#546	1	4	yes	—
305	C₂⁵	—	2	4	no	—
306	C₂⁵	—	2	8	no	—
307	C₂⁵	—	2	8	no	—
308	C₂⁵	—	4	4	no	—
309	C₂⁵	C₂³×C₂₉	1	2	yes	—
310	C₂⁵	C₂³×C₂₉	1	2	yes	—
311	C₂⁵	C₂³×C₂₉	1	4	yes	—
312	C₂⁵	C₂³×C₂₉	1	1	yes	characteristic
313	C₂×#41	—	2	128	no	—
314	C₂×#41	—	2	64	no	—
315	C₂×#41	—	2	32	no	—
316	C₂²×Q₈	—	2	8	no	—
317	C₂²×Q₈	—	2	4	no	—
318	C₂²×Q₈	C₂³×C₂₉	1	4	yes	complemented
319	C₂²×D₄	—	2	8	no	—
320	C₂²×D₄	—	2	8	no	—
321	C₂²×D₄	—	2	8	no	—
322	C₂²×D₄	—	2	16	no	—
323	C₂²×D₄	—	2	16	no	—
324	C₂²×D₄	—	2	4	no	—
325	C₂²×D₄	—	4	8	no	—
326	C₂²×D₄	D₄×C₂₉	1	16	yes	complemented
327	C₂²×D₄	C₂³×C₂₉	1	16	yes	—
328	C₂²×D₄	C₂³×C₂₉	1	8	yes	—
329	C₂²×D₄	C₂³×C₂₉	1	4	yes	complemented
330	C₂³×C₄	—	2	8	no	—
331	C₂³×C₄	—	2	8	no	—
332	C₂³×C₄	—	2	8	no	—
333	C₂³×C₄	—	2	8	no	—
334	C₂³×C₄	—	2	4	no	—
335	C₂³×C₄	—	4	4	no	—
336	C₂³×C₄	D₄×C₂₉	1	8	yes	complemented
337	C₂³×C₄	C₂³×C₂₉	1	2	yes	—
338	C₂³×C₄	C₂³×C₂₉	1	4	yes	—
339	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
340	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
341	C₂³×C₄	C₂³×C₂₉	1	2	yes	—
342	C₂³×C₄	C₂³×C₂₉	1	4	yes	—
343	C₂³×C₄	C₂³×C₂₉	1	4	yes	—
344	C₂³×C₄	C₂³×C₂₉	1	8	yes	complemented
345	#120	—	2	64	no	—
346	C₂×C₂²⋊C₄	—	2	8	no	—
347	C₂×C₂²⋊C₄	—	2	8	no	—
348	C₂×C₂²⋊C₄	—	2	8	no	—
349	C₂×C₂²⋊C₄	—	2	16	no	—
350	C₂×C₂²⋊C₄	—	2	32	no	—
351	C₂×C₂²⋊C₄	—	4	8	no	—
352	C₂×C₂²⋊C₄	C₂³×C₂₉	1	8	yes	—
353	C₂×C₂²⋊C₄	C₂³×C₂₉	1	8	yes	—
354	C₂×C₂²⋊C₄	C₂³×C₂₉	1	8	yes	—
355	C₂×C₂²⋊C₄	C₂³×C₂₉	1	16	yes	—
356	C₂×C₂²⋊C₄	C₂³×C₂₉	1	16	yes	complemented
357	#95	C₂³×C₂₉	1	8	yes	complemented
358	#95	C₂³×C₂₉	1	8	yes	complemented
359	#95	C₂³×C₂₉	1	16	yes	complemented
360	C₂₉	C₂×#2404	1	1	yes	characteristic, direct product factor, Sylow
361	C₂⁴	—	2	4	no	—
362	C₂⁴	—	2	4	no	—
363	C₂⁴	—	2	32	no	—
364	C₂⁴	—	2	8	no	—
365	C₂⁴	—	2	4	no	—
366	C₂⁴	—	2	8	no	—
367	C₂⁴	—	2	4	no	—
368	C₂⁴	—	2	4	no	—
369	C₂⁴	—	2	8	no	—
370	C₂⁴	—	2	4	no	—
371	C₂⁴	—	2	16	no	—
372	C₂⁴	—	2	8	no	—
373	C₂⁴	—	2	8	no	—
374	C₂⁴	—	2	16	no	—
375	C₂⁴	—	4	8	no	—
376	C₂⁴	—	4	64	no	—
377	C₂⁴	—	4	16	no	—
378	C₂⁴	—	4	16	no	—
379	C₂⁴	C₂×D₄×C₂₉	1	8	yes	—
380	C₂⁴	C₂×D₄×C₂₉	1	8	yes	—
381	C₂⁴	C₂×D₄×C₂₉	1	4	yes	—
382	C₂⁴	#41×C₂₉	1	8	yes	complemented
383	C₂⁴	C₂⁴×C₂₉	1	4	yes	—
384	C₂⁴	C₂⁴×C₂₉	1	4	yes	—
385	C₂⁴	C₂⁴×C₂₉	1	2	yes	—
386	C₂⁴	C₂⁴×C₂₉	1	1	yes	characteristic
387	#41	—	2	256	no	—
388	C₂×Q₈	—	2	32	no	—
389	C₂×Q₈	—	2	16	no	—
390	C₂×Q₈	—	2	8	no	—
391	C₂×D₄	—	2	32	no	—
392	C₂×D₄	—	2	64	no	—
393	C₂×D₄	—	2	16	no	—
394	C₂×D₄	—	2	16	no	—
395	C₂×D₄	—	2	16	no	—
396	C₂×D₄	—	2	32	no	—
397	C₂×D₄	—	2	32	no	—
398	C₂×D₄	—	2	8	no	—
399	C₂×D₄	—	4	16	no	—
400	C₂×D₄	—	4	64	no	—
401	C₂×D₄	C₂×D₄×C₂₉	1	32	yes	complemented
402	C₂²×C₄	—	2	64	no	—
403	C₂²×C₄	—	2	32	no	—
404	C₂²×C₄	—	2	4	no	—
405	C₂²×C₄	—	2	4	no	—
406	C₂²×C₄	—	2	4	no	—
407	C₂²×C₄	—	2	4	no	—
408	C₂²×C₄	—	2	16	no	—
409	C₂²×C₄	—	2	16	no	—
410	C₂²×C₄	—	2	16	no	—
411	C₂²×C₄	—	2	16	no	—
412	C₂²×C₄	—	2	8	no	—
413	C₂²×C₄	—	2	4	no	—
414	C₂²×C₄	—	2	8	no	—
415	C₂²×C₄	—	2	8	no	—
416	C₂²×C₄	—	2	8	no	—
417	C₂²×C₄	—	2	8	no	—
418	C₂²×C₄	—	4	8	no	—
419	C₂²×C₄	—	4	16	no	—
420	C₂²×C₄	C₂×D₄×C₂₉	1	4	yes	—
421	C₂²×C₄	C₂×D₄×C₂₉	1	8	yes	—
422	C₂²×C₄	C₂×D₄×C₂₉	1	4	yes	—
423	C₂²×C₄	C₂×D₄×C₂₉	1	16	yes	complemented
424	C₂²×C₄	C₂⁴×C₂₉	1	8	yes	—
425	C₂²×C₄	C₂⁴×C₂₉	1	4	yes	—
426	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
427	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
428	C₂²×C₄	C₂⁴×C₂₉	1	4	yes	—
429	C₂²⋊C₄	—	2	16	no	—
430	C₂²⋊C₄	—	2	16	no	—
431	C₂²⋊C₄	—	2	16	no	—
432	C₂²⋊C₄	—	2	32	no	—
433	C₂²⋊C₄	—	4	16	no	—
434	C₂³	—	2	8	no	—
435	C₂³	—	2	8	no	—
436	C₂³	—	2	32	no	—
437	C₂³	—	2	4	no	—
438	C₂³	—	2	4	no	—
439	C₂³	—	2	32	no	—
440	C₂³	—	2	16	no	—
441	C₂³	—	2	16	no	—
442	C₂³	—	2	32	no	—
443	C₂³	—	2	32	no	—
444	C₂³	—	2	4	no	—
445	C₂³	—	2	8	no	—
446	C₂³	—	2	4	no	—
447	C₂³	—	2	4	no	—
448	C₂³	—	2	8	no	—
449	C₂³	—	2	4	no	—
450	C₂³	—	2	8	no	—
451	C₂³	—	2	8	no	—
452	C₂³	—	4	64	no	—
453	C₂³	—	4	16	no	—
454	C₂³	—	4	128	no	—
455	C₂³	—	4	16	no	—
456	C₂³	—	4	8	no	—
457	C₂³	—	4	8	no	—
458	C₂³	—	4	8	no	—
459	C₂³	—	4	8	no	—
460	C₂³	—	4	16	no	—
461	C₂³	—	4	16	no	—
462	C₂³	C₂₉×#120	1	16	yes	—
463	C₂³	C₂²×D₄×C₂₉	1	8	yes	—
464	C₂³	C₂²×D₄×C₂₉	1	8	yes	—
465	C₂³	C₂²×D₄×C₂₉	1	4	yes	—
466	C₂³	C₂²×D₄×C₂₉	1	2	yes	—
467	C₂³	C₂²×D₄×C₂₉	1	4	yes	—
468	C₂³	C₂×#41×C₂₉	1	4	yes	—
469	C₂³	C₂×#41×C₂₉	1	8	yes	complemented
470	C₂³	C₂₉×H(5,𝔽₂)	1	4	yes	—
471	C₂³	C₂⁵×C₂₉	1	1	yes	characteristic
472	Q₈	—	2	32	no	—
473	D₄	—	2	32	no	—
474	D₄	—	2	64	no	—
475	D₄	—	4	64	no	—
476	C₂×C₄	—	2	64	no	—
477	C₂×C₄	—	2	8	no	—
478	C₂×C₄	—	2	16	no	—
479	C₂×C₄	—	2	8	no	—
480	C₂×C₄	—	2	32	no	—
481	C₂×C₄	—	2	4	no	—
482	C₂×C₄	—	2	4	no	—
483	C₂×C₄	—	2	4	no	—
484	C₂×C₄	—	2	4	no	—
485	C₂×C₄	—	2	4	no	—
486	C₂×C₄	—	2	8	no	—
487	C₂×C₄	—	2	8	no	—
488	C₂×C₄	—	2	8	no	—
489	C₂×C₄	—	2	8	no	—
490	C₂×C₄	—	4	16	no	—
491	C₂×C₄	—	4	8	no	—
492	C₂×C₄	—	4	16	no	—
493	C₂×C₄	C₂²×D₄×C₂₉	1	4	yes	—
494	C₂×C₄	C₂²×D₄×C₂₉	1	8	yes	—
495	C₂×C₄	C₂²×D₄×C₂₉	1	4	yes	—
496	C₂²	—	2	4	no	—
497	C₂²	—	2	16	no	—
498	C₂²	—	2	32	no	—
499	C₂²	—	2	4	no	—
500	C₂²	—	2	16	no	—
501	C₂²	—	2	16	no	—
502	C₂²	—	2	8	no	—
503	C₂²	—	2	8	no	—
504	C₂²	—	4	64	no	—
505	C₂²	—	4	4	no	—
506	C₂²	—	4	4	no	—
507	C₂²	—	4	8	no	—
508	C₂²	—	4	8	no	—
509	C₂²	—	4	32	no	—
510	C₂²	—	4	32	no	—
511	C₂²	—	4	4	no	—
512	C₂²	—	4	4	no	—
513	C₂²	C₂×C₂₉×#120	1	8	yes	—
514	C₂²	C₂×C₂₉×#120	1	4	yes	—
515	C₂²	C₂₉×#525	1	4	yes	—
516	C₂²	C₂₉×#535	1	4	yes	—
517	C₂²	C₂₉×#546	1	16	yes	—
518	C₂²	C₂³×D₄×C₂₉	1	1	yes	characteristic
519	C₂²	C₂³×D₄×C₂₉	1	2	yes	—
520	C₂²	C₂²×#41×C₂₉	1	2	yes	—
521	C₂²	C₂×C₂₉×H(5,𝔽₂)	1	2	yes	—
522	C₄	—	2	4	no	—
523	C₄	—	2	8	no	—
524	C₄	—	2	4	no	—
525	C₄	—	4	4	no	—
526	C₄	—	4	8	no	—
527	C₂	—	2	8	no	—
528	C₂	—	4	8	no	—
529	C₂	—	4	8	no	—
530	C₂	C₂₉×#2404	1	8	yes	direct product factor
531	C₂	C₂²×C₂₉×#120	1	1	yes	characteristic
532	C₂	C₂×C₂₉×#525	1	1	yes	characteristic
533	C₂	C₂×C₂₉×#535	1	1	yes	characteristic
534	C₂	C₂×C₂₉×#546	1	4	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₂₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₂₉
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×#41×C₂₉	C₂	semidirect
2. C₂²×C₂₉×#120	C₂	semidirect
3. C₂³×C₂²⋊C₄×C₂₉	C₂	semidirect
4. C₂₉×#2404	C₂	direct (N × H)
5. C₂×C₂₉×#393	C₂	semidirect
6. C₂×C₂₉×#392	C₂	semidirect
7. C₂×C₂₉×#386	C₂	semidirect
8. C₂×C₂₉×#386	C₂	semidirect
9. C₂×C₂₉×#381	C₂	semidirect
13. C₂²×#41×C₂₉	C₂²	semidirect
14. C₂³×Q₈×C₂₉	C₂²	semidirect
17. C₂³×D₄×C₂₉	C₂²	semidirect
20. C₂⁴×C₄×C₂₉	C₂²	semidirect
22. C₂×C₂₉×#120	C₂²	semidirect
28. C₂²×C₂²⋊C₄×C₂₉	C₂²	semidirect
29. C₂²×C₂²⋊C₄×C₂₉	C₂²	semidirect
30. C₂₉×#393	C₂²	semidirect
31. C₂₉×#392	C₂²	semidirect
32. C₂₉×#386	C₂²	semidirect
33. C₂₉×#386	C₂²	semidirect
34. C₂₉×#381	C₂²	semidirect
35. C₂×C₂₉×#95	C₂²	semidirect
36. C₂×C₂₉×#95	C₂²	semidirect
37. C₂×C₂₉×#95	C₂²	semidirect
51. C₂²×Q₈×C₂₉	C₂³	semidirect
59. C₂²×D₄×C₂₉	D₄	semidirect
62. C₂²×D₄×C₂₉	C₂³	semidirect
69. C₂³×C₄×C₂₉	D₄	semidirect
77. C₂³×C₄×C₂₉	C₂³	semidirect
89. C₂×C₂²⋊C₄×C₂₉	C₂³	semidirect
90. C₂₉×#95	C₂³	semidirect
91. C₂₉×#95	C₂³	semidirect
92. C₂₉×#95	C₂³	semidirect
114. C₂⁴×C₂₉	#41	semidirect
133. C₂×D₄×C₂₉	C₂×D₄	semidirect
155. C₂²×C₄×C₂₉	C₂×D₄	semidirect
166. C₂×#2404	C₂₉	direct (N × H)
202. C₂³×C₂₉	C₂×#41	semidirect
229. C₂³×#41	C₂×C₂₉	semidirect
230. C₂²×#120	C₂×C₂₉	semidirect
231. C₂³×C₂²⋊C₄	C₂×C₂₉	semidirect
232. #2404	C₂×C₂₉	direct (N × H)
233. C₂×#393	C₂×C₂₉	semidirect
234. C₂×#392	C₂×C₂₉	semidirect
235. C₂×#386	C₂×C₂₉	semidirect
236. C₂×#386	C₂×C₂₉	semidirect
237. C₂×#381	C₂×C₂₉	semidirect
272. C₂²×#41	C₂²×C₂₉	semidirect
273. C₂³×Q₈	C₂²×C₂₉	semidirect
276. C₂³×D₄	C₂²×C₂₉	semidirect
279. C₂⁴×C₄	C₂²×C₂₉	semidirect
281. C₂×#120	C₂²×C₂₉	semidirect
287. C₂²×C₂²⋊C₄	C₂²×C₂₉	semidirect
288. C₂²×C₂²⋊C₄	C₂²×C₂₉	semidirect
289. #393	C₂²×C₂₉	semidirect
290. #392	C₂²×C₂₉	semidirect
291. #386	C₂²×C₂₉	semidirect
292. #386	C₂²×C₂₉	semidirect
293. #381	C₂²×C₂₉	semidirect
294. C₂×#95	C₂²×C₂₉	semidirect
295. C₂×#95	C₂²×C₂₉	semidirect
296. C₂×#95	C₂²×C₂₉	semidirect
300. C₂×C₂₉	#2404	direct (N × H)
318. C₂²×Q₈	C₂³×C₂₉	semidirect
326. C₂²×D₄	D₄×C₂₉	semidirect
329. C₂²×D₄	C₂³×C₂₉	semidirect
336. C₂³×C₄	D₄×C₂₉	semidirect
344. C₂³×C₄	C₂³×C₂₉	semidirect
356. C₂×C₂²⋊C₄	C₂³×C₂₉	semidirect
357. #95	C₂³×C₂₉	semidirect
358. #95	C₂³×C₂₉	semidirect
359. #95	C₂³×C₂₉	semidirect
360. C₂₉	C₂×#2404	direct (N × H)
382. C₂⁴	#41×C₂₉	semidirect
401. C₂×D₄	C₂×D₄×C₂₉	semidirect
423. C₂²×C₄	C₂×D₄×C₂₉	semidirect
469. C₂³	C₂×#41×C₂₉	semidirect
530. C₂	C₂₉×#2404	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×#41×C₂₉	2
C₂²×C₂₉×#120	2
C₂³×C₂²⋊C₄×C₂₉	2
C₂₉×#2404	2
C₂×C₂₉×#393	2
C₂×C₂₉×#392	2
C₂×C₂₉×#386	2
C₂×C₂₉×#381	2
C₂×#2404	29

Subgroups — C2×C29×#2404 #20329628

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₉×#2404 #20329628