Subgroups — C₂×C₂₉×#1976 #20316143

Order 7424.

1474 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂₉×#135	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₉×#427	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₉×#421	C₂	1	2	yes	maximal, complemented
4	C₂×C₂₉×#410	C₂	1	2	yes	maximal, complemented
5	C₂×C₂₉×#405	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#1976	C₂	1	8	yes	maximal, direct product factor
7	C₂²×#41×C₂₉	C₂²	1	2	yes	—
8	C₂×C₂₉×#135	—	2	1	no	—
9	C₂×C₂₉×#135	—	2	1	no	—
10	C₂×C₂₉×#135	—	2	2	no	—
11	C₂×C₂₉×#135	—	2	1	no	—
12	C₂×C₂₉×#135	—	2	1	no	—
13	C₂×C₂₉×#135	—	2	2	no	—
14	C₂×C₂₉×#135	C₄	1	4	yes	complemented
15	C₂×C₂₉×#135	C₂²	1	4	yes	—
16	C₂²×Q₁₆×C₂₉	C₄	1	1	yes	characteristic, complemented
17	C₂²×SD₁₆×C₂₉	C₄	1	2	yes	complemented
18	C₂²×D₈×C₂₉	C₄	1	1	yes	characteristic, complemented
19	C₂²×M₁₆×C₂₉	C₂²	1	1	yes	characteristic
20	C₂³×C₈×C₂₉	C₂²	1	1	yes	characteristic
21	C₂×C₂₉×#117	C₂²	1	2	yes	—
22	C₂×C₂₉×#117	C₂²	1	1	yes	characteristic
23	C₂₉×#427	—	2	2	no	—
24	C₂₉×#427	C₂²	1	4	yes	complemented
25	C₂×C₂₉×#107	—	2	1	no	—
26	C₂×C₂₉×#106	—	2	1	no	—
27	C₂₉×#421	—	2	4	no	—
28	C₂₉×#421	C₂²	1	8	yes	complemented
29	C₂×C₂₉×#104	—	2	4	no	—
30	C₂₉×#410	—	2	4	no	—
31	C₂₉×#410	C₂²	1	8	yes	complemented
32	C₂×C₂₉×#99	—	2	4	no	—
33	C₂₉×#405	—	2	2	no	—
34	C₂₉×#405	C₂²	1	4	yes	complemented
35	C₂×C₂₉×#97	—	2	1	no	—
36	C₂×C₄×C₈×C₂₉	—	2	1	no	—
37	C₂×#41×C₂₉	—	2	2	no	—
38	C₂×#41×C₂₉	—	2	2	no	—
39	C₂×#41×C₂₉	—	2	2	no	—
40	C₂×#41×C₂₉	—	2	2	no	—
41	C₂×#41×C₂₉	—	2	2	no	—
42	C₂×#41×C₂₉	—	2	2	no	—
43	C₂×#41×C₂₉	—	2	2	no	—
44	C₂×#41×C₂₉	—	2	2	no	—
45	C₂×#41×C₂₉	—	2	2	no	—
46	C₂×#41×C₂₉	—	2	2	no	—
47	C₂×#41×C₂₉	C₂×C₄	1	4	yes	—
48	C₂×#41×C₂₉	C₂³	1	4	yes	—
49	C₂²×Q₈×C₂₉	C₂×C₄	1	2	yes	—
50	C₂²×D₄×C₂₉	—	2	2	no	—
51	C₂²×D₄×C₂₉	C₂×C₄	1	2	yes	—
52	C₂³×C₄×C₂₉	—	2	2	no	—
53	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
54	C₂₉×#135	—	2	4	no	—
55	C₂₉×#135	—	2	4	no	—
56	C₂₉×#135	—	2	4	no	—
57	C₂₉×#135	—	2	4	no	—
58	C₂₉×#135	—	2	4	no	—
59	C₂₉×#135	—	2	4	no	—
60	C₂₉×#135	—	2	4	no	—
61	C₂₉×#135	—	2	4	no	—
62	C₂×Q₁₆×C₂₉	—	2	1	no	—
63	C₂×Q₁₆×C₂₉	—	2	1	no	—
64	C₂×Q₁₆×C₂₉	—	2	2	no	—
65	C₂×Q₁₆×C₂₉	C₂×C₄	1	4	yes	complemented
66	C₂×SD₁₆×C₂₉	—	2	2	no	—
67	C₂×SD₁₆×C₂₉	—	2	2	no	—
68	C₂×SD₁₆×C₂₉	—	2	4	no	—
69	C₂×SD₁₆×C₂₉	C₂×C₄	1	8	yes	complemented
70	C₂×D₈×C₂₉	—	2	1	no	—
71	C₂×D₈×C₂₉	—	2	1	no	—
72	C₂×D₈×C₂₉	—	2	2	no	—
73	C₂×D₈×C₂₉	C₂×C₄	1	4	yes	complemented
74	C₂×M₁₆×C₂₉	—	2	1	no	—
75	C₂×M₁₆×C₂₉	—	2	1	no	—
76	C₂×M₁₆×C₂₉	—	2	1	no	—
77	C₂×M₁₆×C₂₉	D₄	1	2	yes	—
78	C₂×M₁₆×C₂₉	D₄	1	2	yes	—
79	C₂×M₁₆×C₂₉	C₂³	1	2	yes	—
80	C₂²×C₈×C₂₉	—	2	1	no	—
81	C₂²×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
82	C₂²×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
83	C₂²×C₈×C₂₉	C₂×C₄	1	2	yes	—
84	C₂²×C₈×C₂₉	D₄	1	1	yes	characteristic
85	C₂²×C₈×C₂₉	D₄	1	1	yes	characteristic
86	C₂²×C₈×C₂₉	D₄	1	2	yes	—
87	C₂²×C₈×C₂₉	D₄	1	1	yes	characteristic
88	C₂²×C₈×C₂₉	D₄	1	1	yes	characteristic
89	C₂²×C₈×C₂₉	D₄	1	2	yes	—
90	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
91	C₂₉×#117	—	2	1	no	—
92	C₂₉×#117	—	2	1	no	—
93	C₂₉×#117	—	2	2	no	—
94	C₂₉×#117	—	2	2	no	—
95	C₂₉×#117	—	2	2	no	—
96	C₂₉×#117	D₄	1	2	yes	—
97	C₂₉×#117	C₂³	1	4	yes	—
98	C₂₉×#117	C₂³	1	2	yes	—
99	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
100	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
101	C₂×C₂²⋊C₄×C₂₉	—	2	2	no	—
102	C₂×C₂²⋊C₄×C₂₉	D₄	1	2	yes	—
103	C₂×C₄²×C₂₉	—	2	1	no	—
104	C₂×C₄²×C₂₉	—	2	2	no	—
105	C₂₉×#107	—	2	4	no	—
106	C₂₉×#106	—	2	4	no	—
107	C₂₉×#104	—	2	16	no	—
108	C₂₉×#99	—	2	16	no	—
109	C₂₉×#97	—	2	4	no	—
110	C₄×C₈×C₂₉	—	2	4	no	—
111	C₂⁴×C₂₉	—	2	2	no	—
112	C₂⁴×C₂₉	C₂×D₄	1	1	yes	characteristic
113	#41×C₂₉	—	2	4	no	—
114	#41×C₂₉	—	2	4	no	—
115	#41×C₂₉	—	2	4	no	—
116	#41×C₂₉	—	2	4	no	—
117	#41×C₂₉	—	2	4	no	—
118	#41×C₂₉	—	2	4	no	—
119	#41×C₂₉	—	2	4	no	—
120	#41×C₂₉	—	2	4	no	—
121	#41×C₂₉	—	4	2	no	—
122	#41×C₂₉	—	4	2	no	—
123	#41×C₂₉	—	4	2	no	—
124	#41×C₂₉	—	4	2	no	—
125	#41×C₂₉	—	4	2	no	—
126	#41×C₂₉	—	4	2	no	—
127	#41×C₂₉	—	4	2	no	—
128	#41×C₂₉	—	4	2	no	—
129	C₂×Q₈×C₂₉	—	2	2	no	—
130	C₂×Q₈×C₂₉	—	2	2	no	—
131	C₂×Q₈×C₂₉	—	2	2	no	—
132	C₂×Q₈×C₂₉	—	2	2	no	—
133	C₂×Q₈×C₂₉	—	2	2	no	—
134	C₂×Q₈×C₂₉	C₂²×C₄	1	4	yes	—
135	C₂×D₄×C₂₉	—	2	4	no	—
136	C₂×D₄×C₂₉	—	2	4	no	—
137	C₂×D₄×C₂₉	—	2	2	no	—
138	C₂×D₄×C₂₉	—	2	2	no	—
139	C₂×D₄×C₂₉	—	2	2	no	—
140	C₂×D₄×C₂₉	—	2	2	no	—
141	C₂×D₄×C₂₉	—	2	2	no	—
142	C₂×D₄×C₂₉	—	4	2	no	—
143	C₂×D₄×C₂₉	—	4	2	no	—
144	C₂×D₄×C₂₉	—	4	2	no	—
145	C₂×D₄×C₂₉	—	4	2	no	—
146	C₂×D₄×C₂₉	C₂²×C₄	1	4	yes	—
147	C₂²×C₄×C₂₉	—	2	2	no	—
148	C₂²×C₄×C₂₉	—	2	2	no	—
149	C₂²×C₄×C₂₉	—	2	4	no	—
150	C₂²×C₄×C₂₉	—	2	4	no	—
151	C₂²×C₄×C₂₉	—	4	2	no	—
152	C₂²×C₄×C₂₉	—	4	2	no	—
153	C₂²×C₄×C₂₉	—	4	2	no	—
154	C₂²×C₄×C₂₉	—	4	2	no	—
155	C₂²×C₄×C₂₉	—	4	2	no	—
156	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
157	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
158	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₂₉	#41	1	1	yes	characteristic
166	C₂²×C₄×C₂₉	#41	1	1	yes	characteristic
167	C₂²×C₄×C₂₉	#41	1	1	yes	characteristic
168	C₂²×C₄×C₂₉	#41	1	1	yes	characteristic
169	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
170	Q₁₆×C₂₉	—	2	4	no	—
171	Q₁₆×C₂₉	—	2	4	no	—
172	SD₁₆×C₂₉	—	2	8	no	—
173	SD₁₆×C₂₉	—	2	8	no	—
174	D₈×C₂₉	—	2	4	no	—
175	D₈×C₂₉	—	2	4	no	—
176	M₁₆×C₂₉	—	2	2	no	—
177	M₁₆×C₂₉	—	2	2	no	—
178	M₁₆×C₂₉	—	2	2	no	—
179	M₁₆×C₂₉	C₂×D₄	1	4	yes	—
180	C₂×C₈×C₂₉	—	2	2	no	—
181	C₂×C₈×C₂₉	—	2	2	no	—
182	C₂×C₈×C₂₉	—	2	2	no	—
183	C₂×C₈×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
184	C₂×C₈×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
185	C₂×C₈×C₂₉	C₂²⋊C₄	1	2	yes	—
186	C₂×C₈×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
187	C₂×C₈×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
188	C₂×C₈×C₂₉	C₂²⋊C₄	1	2	yes	—
189	C₂×C₈×C₂₉	C₂²⋊C₄	1	2	yes	—
190	C₂×C₈×C₂₉	C₂²⋊C₄	1	2	yes	—
191	C₂×C₈×C₂₉	C₂²⋊C₄	1	2	yes	—
192	C₂×C₈×C₂₉	C₂²⋊C₄	1	2	yes	—
193	C₂×C₈×C₂₉	C₂²×C₄	1	2	yes	—
194	C₂×C₈×C₂₉	C₂²×C₄	1	2	yes	—
195	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
196	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
197	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
198	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
199	C₄⋊C₄×C₂₉	—	2	2	no	—
200	C₄⋊C₄×C₂₉	—	2	2	no	—
201	C₄⋊C₄×C₂₉	—	2	4	no	—
202	C₄⋊C₄×C₂₉	—	4	2	no	—
203	C₂²⋊C₄×C₂₉	—	2	2	no	—
204	C₂²⋊C₄×C₂₉	—	2	4	no	—
205	C₂²⋊C₄×C₂₉	—	4	2	no	—
206	C₂²⋊C₄×C₂₉	C₂×D₄	1	4	yes	—
207	C₄²×C₂₉	—	2	2	no	—
208	C₄²×C₂₉	—	2	2	no	—
209	C₄²×C₂₉	—	2	4	no	—
210	C₄²×C₂₉	—	4	2	no	—
211	C₂×#1976	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
212	C₂³×C₂₉	—	2	4	no	—
213	C₂³×C₂₉	—	4	2	no	—
214	C₂³×C₂₉	—	4	2	no	—
215	C₂³×C₂₉	—	4	2	no	—
216	C₂³×C₂₉	—	8	4	no	—
217	C₂³×C₂₉	C₄×D₄	1	1	yes	characteristic
218	C₂³×C₂₉	C₄×D₄	1	1	yes	characteristic
219	C₂³×C₂₉	#121	1	1	yes	characteristic
220	C₂³×C₂₉	#121	1	1	yes	characteristic
221	C₂³×C₂₉	#127	1	1	yes	characteristic
222	C₂³×C₂₉	#127	1	1	yes	characteristic
223	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
224	Q₈×C₂₉	—	2	4	no	—
225	Q₈×C₂₉	—	2	4	no	—
226	Q₈×C₂₉	—	4	2	no	—
227	Q₈×C₂₉	—	4	2	no	—
228	D₄×C₂₉	—	2	4	no	—
229	D₄×C₂₉	—	2	4	no	—
230	D₄×C₂₉	—	4	4	no	—
231	D₄×C₂₉	—	4	4	no	—
232	D₄×C₂₉	—	4	4	no	—
233	D₄×C₂₉	—	4	4	no	—
234	D₄×C₂₉	—	4	2	no	—
235	D₄×C₂₉	—	4	2	no	—
236	C₂×C₄×C₂₉	—	2	4	no	—
237	C₂×C₄×C₂₉	—	2	4	no	—
238	C₂×C₄×C₂₉	—	4	4	no	—
239	C₂×C₄×C₂₉	—	4	2	no	—
240	C₂×C₄×C₂₉	—	4	2	no	—
241	C₂×C₄×C₂₉	—	4	4	no	—
242	C₂×C₄×C₂₉	—	4	4	no	—
243	C₂×C₄×C₂₉	—	4	4	no	—
244	C₂×C₄×C₂₉	—	4	4	no	—
245	C₂×C₄×C₂₉	—	4	4	no	—
246	C₂×C₄×C₂₉	—	8	4	no	—
247	C₂×C₄×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
248	C₂×C₄×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
249	C₂×C₄×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
250	C₂×C₄×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
251	C₂×C₄×C₂₉	C₄×D₄	1	1	yes	characteristic
252	C₂×C₄×C₂₉	C₄×D₄	1	1	yes	characteristic
253	C₂×C₄×C₂₉	C₄×D₄	1	1	yes	characteristic
254	C₂×C₄×C₂₉	C₄×D₄	1	1	yes	characteristic
255	C₂×C₄×C₂₉	C₄×D₄	1	1	yes	characteristic
256	C₂×C₄×C₂₉	C₄×D₄	1	1	yes	characteristic
257	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
258	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
259	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
260	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
261	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
262	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
263	C₂×C₄×C₂₉	#124	1	1	yes	characteristic
264	C₂×C₄×C₂₉	#124	1	1	yes	characteristic
265	C₂×C₄×C₂₉	#124	1	1	yes	characteristic
266	C₂×C₄×C₂₉	#124	1	1	yes	characteristic
267	C₂×C₄×C₂₉	#127	1	1	yes	characteristic
268	C₂×C₄×C₂₉	#127	1	1	yes	characteristic
269	C₂×C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
270	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
271	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
272	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
273	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
274	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
275	C₈×C₂₉	—	2	4	no	—
276	C₈×C₂₉	C₂×C₂²⋊C₄	1	2	yes	—
277	C₈×C₂₉	C₂×C₂²⋊C₄	1	2	yes	—
278	C₈×C₂₉	C₂×C₂²⋊C₄	1	2	yes	—
279	C₈×C₂₉	C₂×C₂²⋊C₄	1	2	yes	—
280	C₂²×#135	C₂×C₂₉	1	1	yes	characteristic
281	C₂×#427	C₂×C₂₉	1	1	yes	characteristic, complemented
282	C₂×#421	C₂×C₂₉	1	2	yes	complemented
283	C₂×#410	C₂×C₂₉	1	2	yes	complemented
284	C₂×#405	C₂×C₂₉	1	1	yes	characteristic, complemented
285	#1976	C₂×C₂₉	1	8	yes	direct product factor
286	C₂²×C₂₉	—	2	2	no	—
287	C₂²×C₂₉	—	2	2	no	—
288	C₂²×C₂₉	—	2	2	no	—
289	C₂²×C₂₉	—	4	1	no	—
290	C₂²×C₂₉	—	4	1	no	—
291	C₂²×C₂₉	—	4	1	no	—
292	C₂²×C₂₉	—	4	1	no	—
293	C₂²×C₂₉	—	4	4	no	—
294	C₂²×C₂₉	—	8	4	no	—
295	C₂²×C₂₉	—	8	4	no	—
296	C₂²×C₂₉	—	8	4	no	—
297	C₂²×C₂₉	#390	1	1	yes	characteristic
298	C₂²×C₂₉	#390	1	1	yes	characteristic
299	C₂²×C₂₉	#390	1	1	yes	characteristic
300	C₂²×C₂₉	#390	1	1	yes	characteristic
301	C₂²×C₂₉	C₂×C₄×D₄	1	1	yes	characteristic
302	C₂²×C₂₉	C₂×#121	1	1	yes	characteristic
303	C₂²×C₂₉	C₂×#127	1	1	yes	characteristic
304	C₄×C₂₉	—	4	4	no	—
305	C₄×C₂₉	—	4	4	no	—
306	C₄×C₂₉	—	8	4	no	—
307	C₄×C₂₉	#390	1	1	yes	characteristic
308	C₄×C₂₉	#390	1	1	yes	characteristic
309	C₄×C₂₉	#390	1	1	yes	characteristic
310	C₄×C₂₉	#390	1	1	yes	characteristic
311	C₄×C₂₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
312	C₄×C₂₉	C₂×C₄×D₄	1	1	yes	characteristic
313	C₄×C₂₉	C₂×#121	1	1	yes	characteristic
314	C₄×C₂₉	C₂×#124	1	1	yes	characteristic
315	C₂²×#41	C₂²×C₂₉	1	2	yes	—
316	C₂×#135	—	2	1	no	—
317	C₂×#135	—	2	1	no	—
318	C₂×#135	—	2	2	no	—
319	C₂×#135	—	2	1	no	—
320	C₂×#135	—	2	1	no	—
321	C₂×#135	—	2	2	no	—
322	C₂×#135	C₄×C₂₉	1	4	yes	complemented
323	C₂×#135	C₂²×C₂₉	1	4	yes	—
324	C₂²×Q₁₆	C₄×C₂₉	1	1	yes	characteristic, complemented
325	C₂²×SD₁₆	C₄×C₂₉	1	2	yes	complemented
326	C₂²×D₈	C₄×C₂₉	1	1	yes	characteristic, complemented
327	C₂²×M₁₆	C₂²×C₂₉	1	1	yes	characteristic
328	C₂³×C₈	C₂²×C₂₉	1	1	yes	characteristic
329	C₂×#117	C₂²×C₂₉	1	2	yes	—
330	C₂×#117	C₂²×C₂₉	1	1	yes	characteristic
331	#427	—	2	2	no	—
332	#427	C₂²×C₂₉	1	4	yes	complemented
333	C₂×#107	—	2	1	no	—
334	C₂×#106	—	2	1	no	—
335	#421	—	2	4	no	—
336	#421	C₂²×C₂₉	1	8	yes	complemented
337	C₂×#104	—	2	4	no	—
338	#410	—	2	4	no	—
339	#410	C₂²×C₂₉	1	8	yes	complemented
340	C₂×#99	—	2	4	no	—
341	#405	—	2	2	no	—
342	#405	C₂²×C₂₉	1	4	yes	complemented
343	C₂×#97	—	2	1	no	—
344	C₂×C₄×C₈	—	2	1	no	—
345	C₂×C₂₉	—	2	1	no	—
346	C₂×C₂₉	—	2	1	no	—
347	C₂×C₂₉	—	2	1	no	—
348	C₂×C₂₉	—	2	1	no	—
349	C₂×C₂₉	—	2	1	no	—
350	C₂×C₂₉	—	2	1	no	—
351	C₂×C₂₉	—	8	4	no	—
352	C₂×C₂₉	#1976	1	2	yes	direct product factor
353	C₂×C₂₉	C₂×#390	1	1	yes	characteristic
354	C₂×#41	—	2	2	no	—
355	C₂×#41	—	2	2	no	—
356	C₂×#41	—	2	2	no	—
357	C₂×#41	—	2	2	no	—
358	C₂×#41	—	2	2	no	—
359	C₂×#41	—	2	2	no	—
360	C₂×#41	—	2	2	no	—
361	C₂×#41	—	2	2	no	—
362	C₂×#41	—	2	2	no	—
363	C₂×#41	—	2	2	no	—
364	C₂×#41	C₂×C₄×C₂₉	1	4	yes	—
365	C₂×#41	C₂³×C₂₉	1	4	yes	—
366	C₂²×Q₈	C₂×C₄×C₂₉	1	2	yes	—
367	C₂²×D₄	—	2	2	no	—
368	C₂²×D₄	C₂×C₄×C₂₉	1	2	yes	—
369	C₂³×C₄	—	2	2	no	—
370	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
371	#135	—	2	4	no	—
372	#135	—	2	4	no	—
373	#135	—	2	4	no	—
374	#135	—	2	4	no	—
375	#135	—	2	4	no	—
376	#135	—	2	4	no	—
377	#135	—	2	4	no	—
378	#135	—	2	4	no	—
379	C₂×Q₁₆	—	2	1	no	—
380	C₂×Q₁₆	—	2	1	no	—
381	C₂×Q₁₆	—	2	2	no	—
382	C₂×Q₁₆	C₂×C₄×C₂₉	1	4	yes	complemented
383	C₂×SD₁₆	—	2	2	no	—
384	C₂×SD₁₆	—	2	2	no	—
385	C₂×SD₁₆	—	2	4	no	—
386	C₂×SD₁₆	C₂×C₄×C₂₉	1	8	yes	complemented
387	C₂×D₈	—	2	1	no	—
388	C₂×D₈	—	2	1	no	—
389	C₂×D₈	—	2	2	no	—
390	C₂×D₈	C₂×C₄×C₂₉	1	4	yes	complemented
391	C₂×M₁₆	—	2	1	no	—
392	C₂×M₁₆	—	2	1	no	—
393	C₂×M₁₆	—	2	1	no	—
394	C₂×M₁₆	D₄×C₂₉	1	2	yes	—
395	C₂×M₁₆	D₄×C₂₉	1	2	yes	—
396	C₂×M₁₆	C₂³×C₂₉	1	2	yes	—
397	C₂²×C₈	—	2	1	no	—
398	C₂²×C₈	C₂×C₄×C₂₉	1	1	yes	characteristic
399	C₂²×C₈	C₂×C₄×C₂₉	1	1	yes	characteristic
400	C₂²×C₈	C₂×C₄×C₂₉	1	2	yes	—
401	C₂²×C₈	D₄×C₂₉	1	1	yes	characteristic
402	C₂²×C₈	D₄×C₂₉	1	1	yes	characteristic
403	C₂²×C₈	D₄×C₂₉	1	2	yes	—
404	C₂²×C₈	D₄×C₂₉	1	1	yes	characteristic
405	C₂²×C₈	D₄×C₂₉	1	1	yes	characteristic
406	C₂²×C₈	D₄×C₂₉	1	2	yes	—
407	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
408	#117	—	2	1	no	—
409	#117	—	2	1	no	—
410	#117	—	2	2	no	—
411	#117	—	2	2	no	—
412	#117	—	2	2	no	—
413	#117	D₄×C₂₉	1	2	yes	—
414	#117	C₂³×C₂₉	1	4	yes	—
415	#117	C₂³×C₂₉	1	2	yes	—
416	C₂×C₄⋊C₄	—	2	1	no	—
417	C₂×C₄⋊C₄	—	2	2	no	—
418	C₂×C₂²⋊C₄	—	2	2	no	—
419	C₂×C₂²⋊C₄	D₄×C₂₉	1	2	yes	—
420	C₂×C₄²	—	2	1	no	—
421	C₂×C₄²	—	2	2	no	—
422	#107	—	2	4	no	—
423	#106	—	2	4	no	—
424	#104	—	2	16	no	—
425	#99	—	2	16	no	—
426	#97	—	2	4	no	—
427	C₄×C₈	—	2	4	no	—
428	C₂₉	C₂×#1976	1	1	yes	characteristic, direct product factor, Sylow
429	C₂⁴	—	2	2	no	—
430	C₂⁴	C₂×D₄×C₂₉	1	1	yes	characteristic
431	#41	—	2	4	no	—
432	#41	—	2	4	no	—
433	#41	—	2	4	no	—
434	#41	—	2	4	no	—
435	#41	—	2	4	no	—
436	#41	—	2	4	no	—
437	#41	—	2	4	no	—
438	#41	—	2	4	no	—
439	#41	—	4	2	no	—
440	#41	—	4	2	no	—
441	#41	—	4	2	no	—
442	#41	—	4	2	no	—
443	#41	—	4	2	no	—
444	#41	—	4	2	no	—
445	#41	—	4	2	no	—
446	#41	—	4	2	no	—
447	C₂×Q₈	—	2	2	no	—
448	C₂×Q₈	—	2	2	no	—
449	C₂×Q₈	—	2	2	no	—
450	C₂×Q₈	—	2	2	no	—
451	C₂×Q₈	—	2	2	no	—
452	C₂×Q₈	C₂²×C₄×C₂₉	1	4	yes	—
453	C₂×D₄	—	2	4	no	—
454	C₂×D₄	—	2	4	no	—
455	C₂×D₄	—	2	2	no	—
456	C₂×D₄	—	2	2	no	—
457	C₂×D₄	—	2	2	no	—
458	C₂×D₄	—	2	2	no	—
459	C₂×D₄	—	2	2	no	—
460	C₂×D₄	—	4	2	no	—
461	C₂×D₄	—	4	2	no	—
462	C₂×D₄	—	4	2	no	—
463	C₂×D₄	—	4	2	no	—
464	C₂×D₄	C₂²×C₄×C₂₉	1	4	yes	—
465	C₂²×C₄	—	2	2	no	—
466	C₂²×C₄	—	2	2	no	—
467	C₂²×C₄	—	2	4	no	—
468	C₂²×C₄	—	2	4	no	—
469	C₂²×C₄	—	4	2	no	—
470	C₂²×C₄	—	4	2	no	—
471	C₂²×C₄	—	4	2	no	—
472	C₂²×C₄	—	4	2	no	—
473	C₂²×C₄	—	4	2	no	—
474	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
475	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
476	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
477	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
478	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
479	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
480	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
481	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
482	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
483	C₂²×C₄	#41×C₂₉	1	1	yes	characteristic
484	C₂²×C₄	#41×C₂₉	1	1	yes	characteristic
485	C₂²×C₄	#41×C₂₉	1	1	yes	characteristic
486	C₂²×C₄	#41×C₂₉	1	1	yes	characteristic
487	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
488	Q₁₆	—	2	4	no	—
489	Q₁₆	—	2	4	no	—
490	SD₁₆	—	2	8	no	—
491	SD₁₆	—	2	8	no	—
492	D₈	—	2	4	no	—
493	D₈	—	2	4	no	—
494	M₁₆	—	2	2	no	—
495	M₁₆	—	2	2	no	—
496	M₁₆	—	2	2	no	—
497	M₁₆	C₂×D₄×C₂₉	1	4	yes	—
498	C₂×C₈	—	2	2	no	—
499	C₂×C₈	—	2	2	no	—
500	C₂×C₈	—	2	2	no	—
501	C₂×C₈	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
502	C₂×C₈	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
503	C₂×C₈	C₂²⋊C₄×C₂₉	1	2	yes	—
504	C₂×C₈	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
505	C₂×C₈	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
506	C₂×C₈	C₂²⋊C₄×C₂₉	1	2	yes	—
507	C₂×C₈	C₂²⋊C₄×C₂₉	1	2	yes	—
508	C₂×C₈	C₂²⋊C₄×C₂₉	1	2	yes	—
509	C₂×C₈	C₂²⋊C₄×C₂₉	1	2	yes	—
510	C₂×C₈	C₂²⋊C₄×C₂₉	1	2	yes	—
511	C₂×C₈	C₂²×C₄×C₂₉	1	2	yes	—
512	C₂×C₈	C₂²×C₄×C₂₉	1	2	yes	—
513	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
514	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
515	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
516	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
517	C₄⋊C₄	—	2	2	no	—
518	C₄⋊C₄	—	2	2	no	—
519	C₄⋊C₄	—	2	4	no	—
520	C₄⋊C₄	—	4	2	no	—
521	C₂²⋊C₄	—	2	2	no	—
522	C₂²⋊C₄	—	2	4	no	—
523	C₂²⋊C₄	—	4	2	no	—
524	C₂²⋊C₄	C₂×D₄×C₂₉	1	4	yes	—
525	C₄²	—	2	2	no	—
526	C₄²	—	2	2	no	—
527	C₄²	—	2	4	no	—
528	C₄²	—	4	2	no	—
529	C₂³	—	2	4	no	—
530	C₂³	—	4	2	no	—
531	C₂³	—	4	2	no	—
532	C₂³	—	4	2	no	—
533	C₂³	—	8	4	no	—
534	C₂³	C₄×D₄×C₂₉	1	1	yes	characteristic
535	C₂³	C₄×D₄×C₂₉	1	1	yes	characteristic
536	C₂³	C₂₉×#121	1	1	yes	characteristic
537	C₂³	C₂₉×#121	1	1	yes	characteristic
538	C₂³	C₂₉×#127	1	1	yes	characteristic
539	C₂³	C₂₉×#127	1	1	yes	characteristic
540	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
541	Q₈	—	2	4	no	—
542	Q₈	—	2	4	no	—
543	Q₈	—	4	2	no	—
544	Q₈	—	4	2	no	—
545	D₄	—	2	4	no	—
546	D₄	—	2	4	no	—
547	D₄	—	4	4	no	—
548	D₄	—	4	4	no	—
549	D₄	—	4	4	no	—
550	D₄	—	4	4	no	—
551	D₄	—	4	2	no	—
552	D₄	—	4	2	no	—
553	C₂×C₄	—	2	4	no	—
554	C₂×C₄	—	2	4	no	—
555	C₂×C₄	—	4	4	no	—
556	C₂×C₄	—	4	2	no	—
557	C₂×C₄	—	4	2	no	—
558	C₂×C₄	—	4	4	no	—
559	C₂×C₄	—	4	4	no	—
560	C₂×C₄	—	4	4	no	—
561	C₂×C₄	—	4	4	no	—
562	C₂×C₄	—	4	4	no	—
563	C₂×C₄	—	8	4	no	—
564	C₂×C₄	C₂×C₂²⋊C₄×C₂₉	1	1	yes	characteristic
565	C₂×C₄	C₂×C₂²⋊C₄×C₂₉	1	1	yes	characteristic
566	C₂×C₄	C₂×C₂²⋊C₄×C₂₉	1	1	yes	characteristic
567	C₂×C₄	C₂×C₂²⋊C₄×C₂₉	1	1	yes	characteristic
568	C₂×C₄	C₄×D₄×C₂₉	1	1	yes	characteristic
569	C₂×C₄	C₄×D₄×C₂₉	1	1	yes	characteristic
570	C₂×C₄	C₄×D₄×C₂₉	1	1	yes	characteristic
571	C₂×C₄	C₄×D₄×C₂₉	1	1	yes	characteristic
572	C₂×C₄	C₄×D₄×C₂₉	1	1	yes	characteristic
573	C₂×C₄	C₄×D₄×C₂₉	1	1	yes	characteristic
574	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
575	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
576	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
577	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
578	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
579	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
580	C₂×C₄	C₂₉×#124	1	1	yes	characteristic
581	C₂×C₄	C₂₉×#124	1	1	yes	characteristic
582	C₂×C₄	C₂₉×#124	1	1	yes	characteristic
583	C₂×C₄	C₂₉×#124	1	1	yes	characteristic
584	C₂×C₄	C₂₉×#127	1	1	yes	characteristic
585	C₂×C₄	C₂₉×#127	1	1	yes	characteristic
586	C₂×C₄	C₂³×C₄×C₂₉	1	1	yes	characteristic
587	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
588	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
589	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
590	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
591	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
592	C₈	—	2	4	no	—
593	C₈	C₂×C₂²⋊C₄×C₂₉	1	2	yes	—
594	C₈	C₂×C₂²⋊C₄×C₂₉	1	2	yes	—
595	C₈	C₂×C₂²⋊C₄×C₂₉	1	2	yes	—
596	C₈	C₂×C₂²⋊C₄×C₂₉	1	2	yes	—
597	C₂²	—	2	2	no	—
598	C₂²	—	2	2	no	—
599	C₂²	—	2	2	no	—
600	C₂²	—	4	1	no	—
601	C₂²	—	4	1	no	—
602	C₂²	—	4	1	no	—
603	C₂²	—	4	1	no	—
604	C₂²	—	4	4	no	—
605	C₂²	—	8	4	no	—
606	C₂²	—	8	4	no	—
607	C₂²	—	8	4	no	—
608	C₂²	C₂₉×#390	1	1	yes	characteristic
609	C₂²	C₂₉×#390	1	1	yes	characteristic
610	C₂²	C₂₉×#390	1	1	yes	characteristic
611	C₂²	C₂₉×#390	1	1	yes	characteristic
612	C₂²	C₂×C₄×D₄×C₂₉	1	1	yes	characteristic
613	C₂²	C₂×C₂₉×#121	1	1	yes	characteristic
614	C₂²	C₂×C₂₉×#127	1	1	yes	characteristic
615	C₄	—	4	4	no	—
616	C₄	—	4	4	no	—
617	C₄	—	8	4	no	—
618	C₄	C₂₉×#390	1	1	yes	characteristic
619	C₄	C₂₉×#390	1	1	yes	characteristic
620	C₄	C₂₉×#390	1	1	yes	characteristic
621	C₄	C₂₉×#390	1	1	yes	characteristic
622	C₄	C₂²×C₂²⋊C₄×C₂₉	1	1	yes	characteristic
623	C₄	C₂×C₄×D₄×C₂₉	1	1	yes	characteristic
624	C₄	C₂×C₂₉×#121	1	1	yes	characteristic
625	C₄	C₂×C₂₉×#124	1	1	yes	characteristic
626	C₂	—	2	1	no	—
627	C₂	—	2	1	no	—
628	C₂	—	2	1	no	—
629	C₂	—	2	1	no	—
630	C₂	—	2	1	no	—
631	C₂	—	2	1	no	—
632	C₂	—	8	4	no	—
633	C₂	C₂₉×#1976	1	2	yes	direct product factor
634	C₂	C₂×C₂₉×#390	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₉	#121
commutator	C₂×C₄	C₂³×C₄×C₂₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₉
socle	C₂²×C₂₉	#390
prime radical	C₂²×C₂₉×#135	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₉ ◁ C₂³×C₄×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₂₉×#427	C₂	semidirect
3. C₂×C₂₉×#421	C₂	semidirect
4. C₂×C₂₉×#410	C₂	semidirect
5. C₂×C₂₉×#405	C₂	semidirect
6. C₂₉×#1976	C₂	direct (N × H)
14. C₂×C₂₉×#135	C₄	semidirect
16. C₂²×Q₁₆×C₂₉	C₄	semidirect
17. C₂²×SD₁₆×C₂₉	C₄	semidirect
18. C₂²×D₈×C₂₉	C₄	semidirect
24. C₂₉×#427	C₂²	semidirect
28. C₂₉×#421	C₂²	semidirect
31. C₂₉×#410	C₂²	semidirect
34. C₂₉×#405	C₂²	semidirect
65. C₂×Q₁₆×C₂₉	C₂×C₄	semidirect
69. C₂×SD₁₆×C₂₉	C₂×C₄	semidirect
73. C₂×D₈×C₂₉	C₂×C₄	semidirect
211. C₂×#1976	C₂₉	direct (N × H)
281. C₂×#427	C₂×C₂₉	semidirect
282. C₂×#421	C₂×C₂₉	semidirect
283. C₂×#410	C₂×C₂₉	semidirect
284. C₂×#405	C₂×C₂₉	semidirect
285. #1976	C₂×C₂₉	direct (N × H)
322. C₂×#135	C₄×C₂₉	semidirect
324. C₂²×Q₁₆	C₄×C₂₉	semidirect
325. C₂²×SD₁₆	C₄×C₂₉	semidirect
326. C₂²×D₈	C₄×C₂₉	semidirect
332. #427	C₂²×C₂₉	semidirect
336. #421	C₂²×C₂₉	semidirect
339. #410	C₂²×C₂₉	semidirect
342. #405	C₂²×C₂₉	semidirect
352. C₂×C₂₉	#1976	direct (N × H)
382. C₂×Q₁₆	C₂×C₄×C₂₉	semidirect
386. C₂×SD₁₆	C₂×C₄×C₂₉	semidirect
390. C₂×D₈	C₂×C₄×C₂₉	semidirect
428. C₂₉	C₂×#1976	direct (N × H)
633. C₂	C₂₉×#1976	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₂₉×#135	2
C₂×C₂₉×#427	2
C₂×C₂₉×#421	2
C₂×C₂₉×#410	2
C₂×C₂₉×#405	2
C₂₉×#1976	2
C₂×#1976	29

Subgroups — C2×C29×#1976 #20316143

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₉×#1976 #20316143