Subgroups — C₂₉×#25315 #20320215

Order 7424.

732 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3138	C₂	1	1	yes	maximal, characteristic
2	C₂₉×#3078	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₉×#460	C₂	1	1	yes	maximal, characteristic
4	C₂₉×#2962	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#2063	C₂	1	2	yes	maximal, complemented
6	C₂₉×#2046	C₂	1	2	yes	maximal, complemented
7	C₂₉×#1977	C₂	1	2	yes	maximal, complemented
8	C₂₉×#1965	C₂	1	1	yes	maximal, characteristic
9	C₂₉×#1950	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1931	C₂	1	2	yes	maximal, complemented
11	C₄×C₂₉×#101	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₂₉	C₂²	1	2	yes	—
13	C₂₉×#533	C₂²	1	1	yes	characteristic
14	C₂×C₂₉×#127	C₂²	1	1	yes	characteristic
15	C₂×C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
16	C₂₉×#490	—	2	2	no	—
17	C₂₉×#486	—	2	1	no	—
18	C₂₉×#486	—	2	1	no	—
19	C₂₉×#479	—	2	2	no	—
20	C₂₉×#477	—	2	1	no	—
21	C₂₉×#475	—	2	1	no	—
22	C₂₉×#460	—	2	1	no	—
23	C₂₉×#460	—	2	1	no	—
24	C₂₉×#460	—	2	2	no	—
25	C₂₉×#446	—	2	1	no	—
26	C₂₉×#446	—	2	2	no	—
27	C₈×Q₈×C₂₉	—	2	1	no	—
28	C₂×C₂₉×#108	C₂²	1	2	yes	—
29	C₂₉×#428	C₂²	1	2	yes	—
30	C₂₉×#424	C₂²	1	2	yes	—
31	C₂₉×#423	C₂²	1	1	yes	characteristic
32	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	C₂₉×#419	C₂²	1	2	yes	—
34	C₂₉×#418	C₂²	1	2	yes	—
35	C₂₉×#418	C₂²	1	2	yes	—
36	C₂×C₂₉×#102	C₂²	1	2	yes	—
37	C₂×C₂₉×#101	C₂²	1	1	yes	characteristic
38	C₂×C₂₉×#101	C₂²	1	1	yes	characteristic
39	C₂×C₂₉×#100	C₂²	1	2	yes	—
40	C₂×C₂₉×#100	C₂²	1	2	yes	—
41	C₂₉×#405	C₂²	1	2	yes	—
42	C₄×M₁₆×C₂₉	C₂²	1	1	yes	characteristic
43	C₄×M₁₆×C₂₉	C₂²	1	1	yes	characteristic
44	C₂₉×#343	C₂²	1	1	yes	characteristic
45	C₂₉×#343	C₂²	1	1	yes	characteristic
46	C₂₉×#341	C₂²	1	2	yes	—
47	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
48	C₂²×D₄×C₂₉	—	2	1	no	—
49	C₂²×D₄×C₂₉	—	2	1	no	—
50	C₂²×D₄×C₂₉	C₂³	1	2	yes	—
51	C₂×SD₁₆×C₂₉	—	2	4	no	—
52	C₂×SD₁₆×C₂₉	—	2	2	no	—
53	C₂×SD₁₆×C₂₉	—	2	2	no	—
54	C₂×SD₁₆×C₂₉	—	4	2	no	—
55	C₂×M₁₆×C₂₉	C₂³	1	2	yes	—
56	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
57	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
58	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
59	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
60	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
61	C₂₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
62	C₂₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
63	C₂₉×#127	—	2	1	no	—
64	C₂₉×#127	—	2	1	no	—
65	C₂₉×#127	—	2	1	no	—
66	C₂₉×#127	—	2	1	no	—
67	C₂₉×#125	D₄	1	2	yes	—
68	C₂₉×C₂²⋊Q₈	—	2	1	no	—
69	C₂₉×C₂²⋊Q₈	—	2	1	no	—
70	C₄×Q₈×C₂₉	—	2	1	no	—
71	C₄×Q₈×C₂₉	—	2	1	no	—
72	C₄×Q₈×C₂₉	—	2	1	no	—
73	C₄×Q₈×C₂₉	—	2	1	no	—
74	C₄×Q₈×C₂₉	—	2	1	no	—
75	C₄×Q₈×C₂₉	—	2	1	no	—
76	C₂₉×#117	C₂³	1	2	yes	—
77	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
78	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₂₉	—	2	1	no	—
80	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
81	C₂₉×#108	—	4	2	no	—
82	C₂₉×#107	—	2	2	no	—
83	C₂₉×#106	—	2	2	no	—
84	C₂₉×C₄⋊C₈	—	2	2	no	—
85	C₂₉×C₄⋊C₈	—	2	2	no	—
86	C₂₉×C₄⋊C₈	—	2	1	no	—
87	C₂₉×C₄⋊C₈	—	2	1	no	—
88	C₂₉×C₄⋊C₈	D₄	1	1	yes	characteristic
89	C₂₉×C₄⋊C₈	D₄	1	1	yes	characteristic
90	C₂₉×C₄⋊C₈	D₄	1	2	yes	—
91	C₂₉×#103	—	2	2	no	—
92	C₂₉×#103	—	2	2	no	—
93	C₂₉×#102	—	2	2	no	—
94	C₂₉×#102	—	2	2	no	—
95	C₂₉×#102	—	2	2	no	—
96	C₂₉×#102	—	2	2	no	—
97	C₂₉×#102	—	2	2	no	—
98	C₂₉×#102	—	2	2	no	—
99	C₂₉×#101	—	2	2	no	—
100	C₂₉×#101	—	2	2	no	—
101	C₂₉×#100	—	2	4	no	—
102	C₂₉×#100	—	4	2	no	—
103	C₂₉×#97	—	2	2	no	—
104	C₂₉×#97	—	2	1	no	—
105	C₂₉×#97	—	2	1	no	—
106	C₄×C₈×C₂₉	—	2	2	no	—
107	C₄×C₈×C₂₉	—	2	1	no	—
108	C₄×C₈×C₂₉	—	2	1	no	—
109	C₂⁴×C₂₉	—	2	2	no	—
110	C₂×Q₈×C₂₉	—	2	1	no	—
111	C₂×Q₈×C₂₉	—	2	1	no	—
112	C₂×Q₈×C₂₉	—	2	1	no	—
113	C₂×Q₈×C₂₉	—	2	1	no	—
114	C₂×Q₈×C₂₉	—	2	1	no	—
115	C₂×Q₈×C₂₉	—	2	1	no	—
116	C₂×Q₈×C₂₉	—	2	1	no	—
117	C₂×Q₈×C₂₉	#41	1	2	yes	—
118	C₂×D₄×C₂₉	—	2	2	no	—
119	C₂×D₄×C₂₉	—	2	2	no	—
120	C₂×D₄×C₂₉	—	2	2	no	—
121	C₂×D₄×C₂₉	—	2	2	no	—
122	C₂×D₄×C₂₉	—	2	2	no	—
123	C₂×D₄×C₂₉	—	2	2	no	—
124	C₂×D₄×C₂₉	—	4	1	no	—
125	C₂×D₄×C₂₉	—	4	1	no	—
126	C₂×D₄×C₂₉	—	4	1	no	—
127	C₂×D₄×C₂₉	—	4	1	no	—
128	C₂×D₄×C₂₉	—	8	2	no	—
129	C₂×D₄×C₂₉	—	8	2	no	—
130	C₂²×C₄×C₂₉	—	2	1	no	—
131	C₂²×C₄×C₂₉	—	2	1	no	—
132	C₂²×C₄×C₂₉	#41	1	1	yes	characteristic
133	C₂²×C₄×C₂₉	#41	1	1	yes	characteristic
134	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
135	SD₁₆×C₂₉	—	4	4	no	—
136	SD₁₆×C₂₉	—	4	4	no	—
137	M₁₆×C₂₉	—	2	1	no	—
138	M₁₆×C₂₉	—	2	2	no	—
139	M₁₆×C₂₉	—	2	1	no	—
140	M₁₆×C₂₉	—	2	1	no	—
141	M₁₆×C₂₉	—	2	1	no	—
142	M₁₆×C₂₉	—	2	1	no	—
143	M₁₆×C₂₉	—	2	2	no	—
144	M₁₆×C₂₉	—	2	1	no	—
145	M₁₆×C₂₉	—	2	1	no	—
146	M₁₆×C₂₉	#41	1	2	yes	—
147	C₂×C₈×C₂₉	—	2	1	no	—
148	C₂×C₈×C₂₉	—	2	2	no	—
149	C₂×C₈×C₂₉	—	2	2	no	—
150	C₂×C₈×C₂₉	—	2	1	no	—
151	C₂×C₈×C₂₉	—	2	1	no	—
152	C₂×C₈×C₂₉	—	2	1	no	—
153	C₂×C₈×C₂₉	—	2	2	no	—
154	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
155	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
156	C₄⋊C₄×C₂₉	—	2	2	no	—
157	C₄⋊C₄×C₂₉	—	2	2	no	—
158	C₄⋊C₄×C₂₉	—	2	1	no	—
159	C₄⋊C₄×C₂₉	—	2	1	no	—
160	C₄⋊C₄×C₂₉	—	2	1	no	—
161	C₄⋊C₄×C₂₉	—	2	1	no	—
162	C₄⋊C₄×C₂₉	—	4	1	no	—
163	C₄⋊C₄×C₂₉	—	4	1	no	—
164	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
165	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
166	C₂²⋊C₄×C₂₉	—	2	2	no	—
167	C₄²×C₂₉	—	2	2	no	—
168	C₄²×C₂₉	—	4	1	no	—
169	C₄²×C₂₉	—	4	1	no	—
170	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
171	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
172	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
173	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
174	#25315	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
175	C₂³×C₂₉	—	4	2	no	—
176	C₂³×C₂₉	—	4	2	no	—
177	C₂³×C₂₉	—	4	2	no	—
178	C₂³×C₂₉	—	8	2	no	—
179	C₂³×C₂₉	—	8	2	no	—
180	C₂³×C₂₉	C₂×#41	1	1	yes	characteristic
181	Q₈×C₂₉	—	2	2	no	—
182	Q₈×C₂₉	—	2	2	no	—
183	Q₈×C₂₉	—	4	1	no	—
184	Q₈×C₂₉	—	4	1	no	—
185	Q₈×C₂₉	—	4	2	no	—
186	Q₈×C₂₉	—	8	1	no	—
187	D₄×C₂₉	—	4	2	no	—
188	D₄×C₂₉	—	4	2	no	—
189	D₄×C₂₉	—	4	2	no	—
190	D₄×C₂₉	—	4	2	no	—
191	D₄×C₂₉	—	8	2	no	—
192	D₄×C₂₉	—	8	2	no	—
193	D₄×C₂₉	—	8	2	no	—
194	D₄×C₂₉	—	8	2	no	—
195	C₂×C₄×C₂₉	—	2	2	no	—
196	C₂×C₄×C₂₉	—	2	2	no	—
197	C₂×C₄×C₂₉	—	2	2	no	—
198	C₂×C₄×C₂₉	—	2	2	no	—
199	C₂×C₄×C₂₉	—	4	1	no	—
200	C₂×C₄×C₂₉	—	4	1	no	—
201	C₂×C₄×C₂₉	—	4	1	no	—
202	C₂×C₄×C₂₉	—	4	1	no	—
203	C₂×C₄×C₂₉	—	8	1	no	—
204	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
205	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
206	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
207	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
208	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
209	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
210	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
211	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
212	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
213	C₂×C₄×C₂₉	2₋¹⁺⁴	1	1	yes	characteristic
214	C₈×C₂₉	—	2	2	no	—
215	C₈×C₂₉	—	2	2	no	—
216	C₈×C₂₉	—	2	2	no	—
217	C₈×C₂₉	—	4	1	no	—
218	C₈×C₂₉	—	4	1	no	—
219	C₈×C₂₉	—	4	1	no	—
220	C₈×C₂₉	—	4	2	no	—
221	#3138	C₂×C₂₉	1	1	yes	characteristic
222	#3078	C₂×C₂₉	1	1	yes	characteristic, complemented
223	C₂×#460	C₂×C₂₉	1	1	yes	characteristic
224	#2962	C₂×C₂₉	1	1	yes	characteristic, complemented
225	#2063	C₂×C₂₉	1	2	yes	complemented
226	#2046	C₂×C₂₉	1	2	yes	complemented
227	#1977	C₂×C₂₉	1	2	yes	complemented
228	#1965	C₂×C₂₉	1	1	yes	characteristic
229	#1950	C₂×C₂₉	1	1	yes	characteristic, complemented
230	#1931	C₂×C₂₉	1	2	yes	complemented
231	C₄×#101	C₂×C₂₉	1	1	yes	characteristic, complemented
232	C₂²×C₂₉	—	2	1	no	—
233	C₂²×C₂₉	—	2	1	no	—
234	C₂²×C₂₉	—	8	2	no	—
235	C₂²×C₂₉	—	8	2	no	—
236	C₂²×C₂₉	—	8	2	no	—
237	C₂²×C₂₉	—	16	2	no	—
238	C₂²×C₂₉	—	16	2	no	—
239	C₂²×C₂₉	C₂×#121	1	1	yes	characteristic
240	C₂²×C₂₉	#529	1	1	yes	characteristic
241	C₂²×C₂₉	#542	1	1	yes	characteristic
242	C₄×C₂₉	—	2	1	no	—
243	C₄×C₂₉	—	2	1	no	—
244	C₄×C₂₉	—	2	1	no	—
245	C₄×C₂₉	—	4	2	no	—
246	C₄×C₂₉	—	4	2	no	—
247	C₄×C₂₉	—	4	2	no	—
248	C₄×C₂₉	—	8	1	no	—
249	C₄×C₂₉	#471	1	2	yes	—
250	C₄×C₂₉	#546	1	1	yes	characteristic
251	C₄×C₂₉	#548	1	1	yes	characteristic
252	C₄×C₂₉	#548	1	1	yes	characteristic
253	C₄×C₂₉	#550	1	1	yes	characteristic
254	C₂²×SD₁₆	C₂²×C₂₉	1	2	yes	—
255	#533	C₂²×C₂₉	1	1	yes	characteristic
256	C₂×#127	C₂²×C₂₉	1	1	yes	characteristic
257	C₂×C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
258	#490	—	2	2	no	—
259	#486	—	2	1	no	—
260	#486	—	2	1	no	—
261	#479	—	2	2	no	—
262	#477	—	2	1	no	—
263	#475	—	2	1	no	—
264	#460	—	2	1	no	—
265	#460	—	2	2	no	—
266	#460	—	2	1	no	—
267	#446	—	2	2	no	—
268	#446	—	2	1	no	—
269	C₈×Q₈	—	2	1	no	—
270	C₂×#108	C₂²×C₂₉	1	2	yes	—
271	#428	C₂²×C₂₉	1	2	yes	—
272	#424	C₂²×C₂₉	1	2	yes	—
273	#423	C₂²×C₂₉	1	1	yes	characteristic
274	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
275	#419	C₂²×C₂₉	1	2	yes	—
276	#418	C₂²×C₂₉	1	2	yes	—
277	#418	C₂²×C₂₉	1	2	yes	—
278	C₂×#102	C₂²×C₂₉	1	2	yes	—
279	C₂×#101	C₂²×C₂₉	1	1	yes	characteristic
280	C₂×#101	C₂²×C₂₉	1	1	yes	characteristic
281	C₂×#100	C₂²×C₂₉	1	2	yes	—
282	C₂×#100	C₂²×C₂₉	1	2	yes	—
283	#405	C₂²×C₂₉	1	2	yes	—
284	C₄×M₁₆	C₂²×C₂₉	1	1	yes	characteristic
285	C₄×M₁₆	C₂²×C₂₉	1	1	yes	characteristic
286	#343	C₂²×C₂₉	1	1	yes	characteristic
287	#343	C₂²×C₂₉	1	1	yes	characteristic
288	#341	C₂²×C₂₉	1	2	yes	—
289	C₂×C₂₉	—	2	1	no	—
290	C₂×C₂₉	—	2	1	no	—
291	C₂×C₂₉	—	16	2	no	—
292	C₂×C₂₉	#2426	1	1	yes	characteristic
293	C₂×C₂₉	C₂×#471	1	1	yes	characteristic
294	C₂×C₂₉	#3068	1	1	yes	characteristic
295	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
296	C₂²×D₄	—	2	1	no	—
297	C₂²×D₄	—	2	1	no	—
298	C₂²×D₄	C₂³×C₂₉	1	2	yes	—
299	C₂×SD₁₆	—	2	4	no	—
300	C₂×SD₁₆	—	2	2	no	—
301	C₂×SD₁₆	—	2	2	no	—
302	C₂×SD₁₆	—	4	2	no	—
303	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
304	C₂×M₁₆	C₂³×C₂₉	1	2	yes	—
305	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
306	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
307	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
308	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
309	C₄⋊Q₈	D₄×C₂₉	1	1	yes	characteristic
310	C₄⋊Q₈	D₄×C₂₉	1	1	yes	characteristic
311	#127	—	2	1	no	—
312	#127	—	2	1	no	—
313	#127	—	2	1	no	—
314	#127	—	2	1	no	—
315	#125	D₄×C₂₉	1	2	yes	—
316	C₂²⋊Q₈	—	2	1	no	—
317	C₂²⋊Q₈	—	2	1	no	—
318	C₄×Q₈	—	2	1	no	—
319	C₄×Q₈	—	2	1	no	—
320	C₄×Q₈	—	2	1	no	—
321	C₄×Q₈	—	2	1	no	—
322	C₄×Q₈	—	2	1	no	—
323	C₄×Q₈	—	2	1	no	—
324	#117	C₂³×C₂₉	1	2	yes	—
325	C₂×C₄⋊C₄	—	2	1	no	—
326	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
327	C₂×C₄²	—	2	1	no	—
328	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
329	#108	—	4	2	no	—
330	#107	—	2	2	no	—
331	#106	—	2	2	no	—
332	C₄⋊C₈	—	2	2	no	—
333	C₄⋊C₈	—	2	2	no	—
334	C₄⋊C₈	—	2	1	no	—
335	C₄⋊C₈	—	2	1	no	—
336	C₄⋊C₈	D₄×C₂₉	1	1	yes	characteristic
337	C₄⋊C₈	D₄×C₂₉	1	1	yes	characteristic
338	C₄⋊C₈	D₄×C₂₉	1	2	yes	—
339	#103	—	2	2	no	—
340	#103	—	2	2	no	—
341	#102	—	2	2	no	—
342	#102	—	2	2	no	—
343	#102	—	2	2	no	—
344	#102	—	2	2	no	—
345	#102	—	2	2	no	—
346	#102	—	2	2	no	—
347	#101	—	2	2	no	—
348	#101	—	2	2	no	—
349	#100	—	2	4	no	—
350	#100	—	4	2	no	—
351	#97	—	2	2	no	—
352	#97	—	2	1	no	—
353	#97	—	2	1	no	—
354	C₄×C₈	—	2	2	no	—
355	C₄×C₈	—	2	1	no	—
356	C₄×C₈	—	2	1	no	—
357	C₂₉	#25315	1	1	yes	characteristic, direct product factor, Sylow
358	C₂⁴	—	2	2	no	—
359	C₂×Q₈	—	2	1	no	—
360	C₂×Q₈	—	2	1	no	—
361	C₂×Q₈	—	2	1	no	—
362	C₂×Q₈	—	2	1	no	—
363	C₂×Q₈	—	2	1	no	—
364	C₂×Q₈	—	2	1	no	—
365	C₂×Q₈	—	2	1	no	—
366	C₂×Q₈	#41×C₂₉	1	2	yes	—
367	C₂×D₄	—	2	2	no	—
368	C₂×D₄	—	2	2	no	—
369	C₂×D₄	—	2	2	no	—
370	C₂×D₄	—	2	2	no	—
371	C₂×D₄	—	2	2	no	—
372	C₂×D₄	—	2	2	no	—
373	C₂×D₄	—	4	1	no	—
374	C₂×D₄	—	4	1	no	—
375	C₂×D₄	—	4	1	no	—
376	C₂×D₄	—	4	1	no	—
377	C₂×D₄	—	8	2	no	—
378	C₂×D₄	—	8	2	no	—
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	#41×C₂₉	1	1	yes	characteristic
382	C₂²×C₄	#41×C₂₉	1	1	yes	characteristic
383	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
384	SD₁₆	—	4	4	no	—
385	SD₁₆	—	4	4	no	—
386	M₁₆	—	2	1	no	—
387	M₁₆	—	2	2	no	—
388	M₁₆	—	2	1	no	—
389	M₁₆	—	2	1	no	—
390	M₁₆	—	2	1	no	—
391	M₁₆	—	2	1	no	—
392	M₁₆	—	2	2	no	—
393	M₁₆	—	2	1	no	—
394	M₁₆	—	2	1	no	—
395	M₁₆	#41×C₂₉	1	2	yes	—
396	C₂×C₈	—	2	1	no	—
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	—	2	2	no	—
399	C₂×C₈	—	2	1	no	—
400	C₂×C₈	—	2	1	no	—
401	C₂×C₈	—	2	1	no	—
402	C₂×C₈	—	2	2	no	—
403	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
404	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	2	1	no	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	2	1	no	—
410	C₄⋊C₄	—	2	1	no	—
411	C₄⋊C₄	—	4	1	no	—
412	C₄⋊C₄	—	4	1	no	—
413	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
414	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
415	C₂²⋊C₄	—	2	2	no	—
416	C₄²	—	2	2	no	—
417	C₄²	—	4	1	no	—
418	C₄²	—	4	1	no	—
419	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
420	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
421	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
422	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
423	C₂³	—	4	2	no	—
424	C₂³	—	4	2	no	—
425	C₂³	—	4	2	no	—
426	C₂³	—	8	2	no	—
427	C₂³	—	8	2	no	—
428	C₂³	C₂×#41×C₂₉	1	1	yes	characteristic
429	Q₈	—	2	2	no	—
430	Q₈	—	2	2	no	—
431	Q₈	—	4	2	no	—
432	Q₈	—	4	1	no	—
433	Q₈	—	4	1	no	—
434	Q₈	—	8	1	no	—
435	D₄	—	4	2	no	—
436	D₄	—	4	2	no	—
437	D₄	—	4	2	no	—
438	D₄	—	4	2	no	—
439	D₄	—	8	2	no	—
440	D₄	—	8	2	no	—
441	D₄	—	8	2	no	—
442	D₄	—	8	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	4	1	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	—	8	1	no	—
452	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
453	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
454	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
455	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
456	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
457	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
458	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
459	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
460	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
461	C₂×C₄	C₂₉×2₋¹⁺⁴	1	1	yes	characteristic
462	C₈	—	2	2	no	—
463	C₈	—	2	2	no	—
464	C₈	—	2	2	no	—
465	C₈	—	4	1	no	—
466	C₈	—	4	1	no	—
467	C₈	—	4	1	no	—
468	C₈	—	4	2	no	—
469	C₂²	—	2	1	no	—
470	C₂²	—	2	1	no	—
471	C₂²	—	8	2	no	—
472	C₂²	—	8	2	no	—
473	C₂²	—	8	2	no	—
474	C₂²	—	16	2	no	—
475	C₂²	—	16	2	no	—
476	C₂²	C₂×C₂₉×#121	1	1	yes	characteristic
477	C₂²	C₂₉×#529	1	1	yes	characteristic
478	C₂²	C₂₉×#542	1	1	yes	characteristic
479	C₄	—	2	1	no	—
480	C₄	—	2	1	no	—
481	C₄	—	2	1	no	—
482	C₄	—	4	2	no	—
483	C₄	—	4	2	no	—
484	C₄	—	4	2	no	—
485	C₄	—	8	1	no	—
486	C₄	C₂₉×#471	1	2	yes	—
487	C₄	C₂₉×#546	1	1	yes	characteristic
488	C₄	C₂₉×#548	1	1	yes	characteristic
489	C₄	C₂₉×#548	1	1	yes	characteristic
490	C₄	C₂₉×#550	1	1	yes	characteristic
491	C₂	—	2	1	no	—
492	C₂	—	2	1	no	—
493	C₂	—	16	2	no	—
494	C₂	C₂₉×#2426	1	1	yes	characteristic
495	C₂	C₂×C₂₉×#471	1	1	yes	characteristic
496	C₂	C₂₉×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₉
prime radical	C₂×C₂₉×#127	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂×C₄²×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₉×#3078	C₂	semidirect
4. C₂₉×#2962	C₂	semidirect
5. C₂₉×#2063	C₂	semidirect
6. C₂₉×#2046	C₂	semidirect
7. C₂₉×#1977	C₂	semidirect
9. C₂₉×#1950	C₂	semidirect
10. C₂₉×#1931	C₂	semidirect
11. C₄×C₂₉×#101	C₂	semidirect
174. #25315	C₂₉	direct (N × H)
222. #3078	C₂×C₂₉	semidirect
224. #2962	C₂×C₂₉	semidirect
225. #2063	C₂×C₂₉	semidirect
226. #2046	C₂×C₂₉	semidirect
227. #1977	C₂×C₂₉	semidirect
229. #1950	C₂×C₂₉	semidirect
230. #1931	C₂×C₂₉	semidirect
231. C₄×#101	C₂×C₂₉	semidirect
357. C₂₉	#25315	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₉×#3138	2
C₂₉×#3078	2
C₂×C₂₉×#460	2
C₂₉×#2962	2
C₂₉×#2063	2
C₂₉×#2046	2
C₂₉×#1977	2
C₂₉×#1965	2
C₂₉×#1950	2
C₂₉×#1931	2
C₄×C₂₉×#101	2
#25315	29

Subgroups — C29×#25315 #20320215

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#25315 #20320215