Subgroups — C₂×C₂₉×#3175 #20355579

Order 7424.

1970 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#542	C₂	1	2	yes	maximal, complemented
2	C₂₉×#3175	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₂₉×#500	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₂₉×#495	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₂₉×#489	C₂	1	2	yes	maximal, complemented
6	C₂×C₂₉×#468	C₂	1	2	yes	maximal, complemented
7	C₂×C₂₉×#467	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₂₉×#466	C₂	1	1	yes	maximal, characteristic
9	C₂×C₂₉×#440	C₂	1	2	yes	maximal, complemented
10	C₂×C₄×Q₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄×D₈×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₂₉×#405	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×Q₁₆×C₂₉	C₂²	1	1	yes	characteristic
14	C₂²×SD₁₆×C₂₉	C₂²	1	2	yes	—
15	C₂²×D₈×C₂₉	C₂²	1	1	yes	characteristic
16	C₂²×M₁₆×C₂₉	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₂₉	C₂²	1	1	yes	characteristic
18	C₂₉×#542	—	2	8	no	—
19	C₂₉×#542	C₂²	1	16	yes	complemented
20	C₂×C₂₉×C₄⋊Q₈	C₂²	1	2	yes	—
21	C₂×C₂₉×#126	—	2	2	no	—
22	C₂×C₂₉×#124	—	2	2	no	—
23	C₂×C₂₉×#124	C₂²	1	2	yes	—
24	C₂×C₂₉×#123	—	2	2	no	—
25	C₂×C₂₉×C₂²⋊Q₈	—	2	2	no	—
26	C₂×C₂₉×C₂²⋊Q₈	C₂²	1	2	yes	—
27	C₂×C₂₉×#121	C₂²	1	2	yes	—
28	C₂×C₄×Q₈×C₂₉	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₂₉	C₂²	1	2	yes	—
30	C₂×C₂₉×#117	C₂²	1	1	yes	characteristic
31	C₂₉×#500	C₂²	1	8	yes	complemented
32	C₂₉×#495	C₂²	1	8	yes	complemented
33	C₂₉×#489	C₂²	1	16	yes	complemented
34	C₂₉×#468	C₂²	1	16	yes	complemented
35	C₂₉×#467	C₂²	1	8	yes	complemented
36	C₂₉×#466	C₂²	1	8	yes	—
37	C₂₉×#440	C₂²	1	16	yes	complemented
38	C₄×Q₁₆×C₂₉	C₂²	1	8	yes	complemented
39	C₄×D₈×C₂₉	C₂²	1	8	yes	complemented
40	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic
41	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic
42	C₂×C₂₉×#107	C₂²	1	2	yes	—
43	C₂×C₂₉×#103	C₂²	1	2	yes	—
44	C₂×C₂₉×#103	C₂²	1	2	yes	—
45	C₂×C₂₉×#102	C₂²	1	2	yes	—
46	C₂×C₂₉×#102	C₂²	1	2	yes	—
47	C₂₉×#405	C₂²	1	8	yes	complemented
48	C₂×C₂₉×#97	C₂²	1	1	yes	characteristic
49	C₂×C₂₉×#97	C₂²	1	1	yes	characteristic
50	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
51	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
52	C₂²×Q₈×C₂₉	—	2	2	no	—
53	C₂²×Q₈×C₂₉	C₂³	1	2	yes	—
54	C₂²×D₄×C₂₉	—	2	2	no	—
55	C₂²×D₄×C₂₉	C₂³	1	2	yes	—
56	C₂³×C₄×C₂₉	—	2	2	no	—
57	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
58	C₂×Q₁₆×C₂₉	—	2	4	no	—
59	C₂×Q₁₆×C₂₉	C₂³	1	4	yes	—
60	C₂×SD₁₆×C₂₉	—	2	8	no	—
61	C₂×SD₁₆×C₂₉	C₂³	1	8	yes	—
62	C₂×D₈×C₂₉	—	2	4	no	—
63	C₂×D₈×C₂₉	C₂³	1	4	yes	—
64	C₂×M₁₆×C₂₉	—	2	4	no	—
65	C₂×M₁₆×C₂₉	C₂³	1	4	yes	—
66	C₂²×C₈×C₂₉	—	2	4	no	—
67	C₂²×C₈×C₂₉	C₂³	1	4	yes	—
68	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
72	C₂₉×C₄⋊Q₈	—	2	4	no	—
73	C₂₉×C₄⋊Q₈	C₂³	1	8	yes	—
74	C₂₉×#126	—	2	16	no	—
75	C₂₉×#124	—	2	16	no	—
76	C₂₉×#124	—	2	4	no	—
77	C₂₉×#124	C₂³	1	8	yes	—
78	C₂₉×#123	—	2	16	no	—
79	C₂₉×C₂²⋊Q₈	—	2	4	no	—
80	C₂₉×C₂²⋊Q₈	—	2	16	no	—
81	C₂₉×C₂²⋊Q₈	C₂³	1	8	yes	—
82	C₂₉×#121	—	2	4	no	—
83	C₂₉×#121	C₂³	1	8	yes	—
84	C₄×Q₈×C₂₉	—	2	4	no	—
85	C₄×Q₈×C₂₉	C₂³	1	8	yes	—
86	C₄×D₄×C₂₉	—	2	4	no	—
87	C₄×D₄×C₂₉	C₂³	1	8	yes	—
88	C₂₉×#117	D₄	1	4	yes	—
89	C₂₉×#117	C₂³	1	4	yes	—
90	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
91	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
92	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
93	C₂×C₄⋊C₄×C₂₉	D₄	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₂₉	D₄	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
96	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
97	C₂×C₂²⋊C₄×C₂₉	—	2	2	no	—
98	C₂×C₂²⋊C₄×C₂₉	—	2	2	no	—
99	C₂×C₂²⋊C₄×C₂₉	—	2	2	no	—
100	C₂×C₂²⋊C₄×C₂₉	—	2	2	no	—
101	C₂×C₂²⋊C₄×C₂₉	—	2	2	no	—
102	C₂×C₂²⋊C₄×C₂₉	D₄	1	1	yes	characteristic
103	C₂×C₂²⋊C₄×C₂₉	D₄	1	1	yes	characteristic
104	C₂×C₄²×C₂₉	—	2	2	no	—
105	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
107	C₂₉×#107	C₂³	1	4	yes	—
108	C₂₉×#107	C₂³	1	4	yes	—
109	C₂₉×#107	C₂³	1	8	yes	—
110	C₂₉×#103	C₂³	1	8	yes	—
111	C₂₉×#103	C₂³	1	8	yes	—
112	C₂₉×#102	C₂³	1	8	yes	—
113	C₂₉×#102	C₂³	1	8	yes	—
114	C₂₉×#97	C₂³	1	4	yes	—
115	C₂₉×#97	C₂³	1	4	yes	—
116	C₄×C₈×C₂₉	C₂³	1	4	yes	—
117	C₄×C₈×C₂₉	C₂³	1	4	yes	—
118	C₂⁴×C₂₉	—	2	2	no	—
119	C₂⁴×C₂₉	C₂×D₄	1	1	yes	characteristic
120	C₂×Q₈×C₂₉	—	2	2	no	—
121	C₂×Q₈×C₂₉	—	2	8	no	—
122	C₂×Q₈×C₂₉	—	2	4	no	—
123	C₂×Q₈×C₂₉	—	2	4	no	—
124	C₂×Q₈×C₂₉	—	8	4	no	—
125	C₂×Q₈×C₂₉	C₂⁴	1	4	yes	—
126	C₂×D₄×C₂₉	—	2	8	no	—
127	C₂×D₄×C₂₉	—	2	2	no	—
128	C₂×D₄×C₂₉	—	2	4	no	—
129	C₂×D₄×C₂₉	—	2	4	no	—
130	C₂×D₄×C₂₉	—	8	4	no	—
131	C₂×D₄×C₂₉	C₂⁴	1	4	yes	—
132	C₂²×C₄×C₂₉	—	2	2	no	—
133	C₂²×C₄×C₂₉	—	2	2	no	—
134	C₂²×C₄×C₂₉	—	2	2	no	—
135	C₂²×C₄×C₂₉	—	2	2	no	—
136	C₂²×C₄×C₂₉	—	2	2	no	—
137	C₂²×C₄×C₂₉	—	2	8	no	—
138	C₂²×C₄×C₂₉	—	8	4	no	—
139	C₂²×C₄×C₂₉	C₂×D₄	1	2	yes	—
140	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
146	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
147	Q₁₆×C₂₉	—	2	8	no	—
148	SD₁₆×C₂₉	—	2	16	no	—
149	D₈×C₂₉	—	2	8	no	—
150	M₁₆×C₂₉	—	2	8	no	—
151	C₂×C₈×C₂₉	—	2	2	no	—
152	C₂×C₈×C₂₉	—	2	2	no	—
153	C₂×C₈×C₂₉	—	2	8	no	—
154	C₂×C₈×C₂₉	#41	1	4	yes	—
155	C₂×C₈×C₂₉	#41	1	4	yes	—
156	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
157	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
158	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
159	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
160	C₄⋊C₄×C₂₉	—	2	8	no	—
161	C₄⋊C₄×C₂₉	—	2	8	no	—
162	C₄⋊C₄×C₂₉	—	2	8	no	—
163	C₄⋊C₄×C₂₉	—	2	2	no	—
164	C₄⋊C₄×C₂₉	—	2	2	no	—
165	C₄⋊C₄×C₂₉	C₂×D₄	1	4	yes	—
166	C₄⋊C₄×C₂₉	C₂×D₄	1	4	yes	—
167	C₄⋊C₄×C₂₉	C₂⁴	1	4	yes	—
168	C₄⋊C₄×C₂₉	C₂⁴	1	4	yes	—
169	C₂²⋊C₄×C₂₉	—	2	8	no	—
170	C₂²⋊C₄×C₂₉	—	2	8	no	—
171	C₂²⋊C₄×C₂₉	—	2	8	no	—
172	C₂²⋊C₄×C₂₉	—	2	8	no	—
173	C₂²⋊C₄×C₂₉	—	2	8	no	—
174	C₂²⋊C₄×C₂₉	C₂×D₄	1	4	yes	—
175	C₂²⋊C₄×C₂₉	C₂×D₄	1	4	yes	—
176	C₄²×C₂₉	—	2	8	no	—
177	C₄²×C₂₉	C₂×D₄	1	2	yes	—
178	C₄²×C₂₉	C₂×D₄	1	2	yes	—
179	C₄²×C₂₉	C₂⁴	1	2	yes	—
180	C₄²×C₂₉	C₂⁴	1	2	yes	—
181	C₂×#3175	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
182	C₂³×C₂₉	—	2	2	no	—
183	C₂³×C₂₉	—	2	2	no	—
184	C₂³×C₂₉	—	2	2	no	—
185	C₂³×C₂₉	—	2	4	no	—
186	C₂³×C₂₉	—	4	4	no	—
187	C₂³×C₂₉	—	4	4	no	—
188	C₂³×C₂₉	—	4	4	no	—
189	C₂³×C₂₉	C₂²×D₄	1	2	yes	—
190	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
191	Q₈×C₂₉	—	2	4	no	—
192	Q₈×C₂₉	—	2	4	no	—
193	Q₈×C₂₉	—	4	4	no	—
194	Q₈×C₂₉	—	8	8	no	—
195	D₄×C₂₉	—	2	4	no	—
196	D₄×C₂₉	—	2	4	no	—
197	D₄×C₂₉	—	4	4	no	—
198	D₄×C₂₉	—	8	8	no	—
199	C₂×C₄×C₂₉	—	2	2	no	—
200	C₂×C₄×C₂₉	—	2	2	no	—
201	C₂×C₄×C₂₉	—	2	2	no	—
202	C₂×C₄×C₂₉	—	2	2	no	—
203	C₂×C₄×C₂₉	—	2	2	no	—
204	C₂×C₄×C₂₉	—	2	4	no	—
205	C₂×C₄×C₂₉	—	2	2	no	—
206	C₂×C₄×C₂₉	—	2	2	no	—
207	C₂×C₄×C₂₉	—	2	4	no	—
208	C₂×C₄×C₂₉	—	2	4	no	—
209	C₂×C₄×C₂₉	—	2	4	no	—
210	C₂×C₄×C₂₉	—	4	4	no	—
211	C₂×C₄×C₂₉	—	4	4	no	—
212	C₂×C₄×C₂₉	—	4	4	no	—
213	C₂×C₄×C₂₉	—	8	8	no	—
214	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
215	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
216	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
217	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
218	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
219	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
220	C₂×C₄×C₂₉	C₂×#41	1	2	yes	—
221	C₂×C₄×C₂₉	C₂×#41	1	2	yes	—
222	C₂×C₄×C₂₉	C₂⁵	1	1	yes	characteristic
223	C₈×C₂₉	—	2	2	no	—
224	C₈×C₂₉	—	2	2	no	—
225	C₈×C₂₉	C₂×#41	1	4	yes	—
226	C₈×C₂₉	C₂×#41	1	4	yes	—
227	C₂×#542	C₂×C₂₉	1	2	yes	complemented
228	#3175	C₂×C₂₉	1	16	yes	direct product factor
229	C₂×#500	C₂×C₂₉	1	1	yes	characteristic, complemented
230	C₂×#495	C₂×C₂₉	1	1	yes	characteristic, complemented
231	C₂×#489	C₂×C₂₉	1	2	yes	complemented
232	C₂×#468	C₂×C₂₉	1	2	yes	complemented
233	C₂×#467	C₂×C₂₉	1	1	yes	characteristic, complemented
234	C₂×#466	C₂×C₂₉	1	1	yes	characteristic
235	C₂×#440	C₂×C₂₉	1	2	yes	complemented
236	C₂×C₄×Q₁₆	C₂×C₂₉	1	1	yes	characteristic, complemented
237	C₂×C₄×D₈	C₂×C₂₉	1	1	yes	characteristic, complemented
238	C₂×#405	C₂×C₂₉	1	1	yes	characteristic, complemented
239	C₂²×C₂₉	—	2	2	no	—
240	C₂²×C₂₉	—	2	2	no	—
241	C₂²×C₂₉	—	2	2	no	—
242	C₂²×C₂₉	—	4	4	no	—
243	C₂²×C₂₉	—	4	4	no	—
244	C₂²×C₂₉	—	4	4	no	—
245	C₂²×C₂₉	—	4	4	no	—
246	C₂²×C₂₉	—	8	8	no	—
247	C₂²×C₂₉	#532	1	2	yes	—
248	C₂²×C₂₉	#576	1	2	yes	—
249	C₂²×C₂₉	#578	1	2	yes	—
250	C₂²×C₂₉	C₂³×D₄	1	1	yes	characteristic
251	C₄×C₂₉	—	2	2	no	—
252	C₄×C₂₉	—	2	2	no	—
253	C₄×C₂₉	—	2	2	no	—
254	C₄×C₂₉	—	2	2	no	—
255	C₄×C₂₉	—	2	2	no	—
256	C₄×C₂₉	—	4	4	no	—
257	C₄×C₂₉	—	4	4	no	—
258	C₄×C₂₉	—	4	4	no	—
259	C₄×C₂₉	#532	1	2	yes	—
260	C₄×C₂₉	C₂²×#41	1	1	yes	characteristic
261	C₄×C₂₉	C₂²×#41	1	1	yes	characteristic
262	C₂²×Q₁₆	C₂²×C₂₉	1	1	yes	characteristic
263	C₂²×SD₁₆	C₂²×C₂₉	1	2	yes	—
264	C₂²×D₈	C₂²×C₂₉	1	1	yes	characteristic
265	C₂²×M₁₆	C₂²×C₂₉	1	1	yes	characteristic
266	C₂³×C₈	C₂²×C₂₉	1	1	yes	characteristic
267	#542	—	2	8	no	—
268	#542	C₂²×C₂₉	1	16	yes	complemented
269	C₂×C₄⋊Q₈	C₂²×C₂₉	1	2	yes	—
270	C₂×#126	—	2	2	no	—
271	C₂×#124	—	2	2	no	—
272	C₂×#124	C₂²×C₂₉	1	2	yes	—
273	C₂×#123	—	2	2	no	—
274	C₂×C₂²⋊Q₈	—	2	2	no	—
275	C₂×C₂²⋊Q₈	C₂²×C₂₉	1	2	yes	—
276	C₂×#121	C₂²×C₂₉	1	2	yes	—
277	C₂×C₄×Q₈	C₂²×C₂₉	1	2	yes	—
278	C₂×C₄×D₄	C₂²×C₂₉	1	2	yes	—
279	C₂×#117	C₂²×C₂₉	1	1	yes	characteristic
280	#500	C₂²×C₂₉	1	8	yes	complemented
281	#495	C₂²×C₂₉	1	8	yes	complemented
282	#489	C₂²×C₂₉	1	16	yes	complemented
283	#468	C₂²×C₂₉	1	16	yes	complemented
284	#467	C₂²×C₂₉	1	8	yes	complemented
285	#466	C₂²×C₂₉	1	8	yes	—
286	#440	C₂²×C₂₉	1	16	yes	complemented
287	C₄×Q₁₆	C₂²×C₂₉	1	8	yes	complemented
288	C₄×D₈	C₂²×C₂₉	1	8	yes	complemented
289	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
290	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
291	C₂×#107	C₂²×C₂₉	1	2	yes	—
292	C₂×#103	C₂²×C₂₉	1	2	yes	—
293	C₂×#103	C₂²×C₂₉	1	2	yes	—
294	C₂×#102	C₂²×C₂₉	1	2	yes	—
295	C₂×#102	C₂²×C₂₉	1	2	yes	—
296	#405	C₂²×C₂₉	1	8	yes	complemented
297	C₂×#97	C₂²×C₂₉	1	1	yes	characteristic
298	C₂×#97	C₂²×C₂₉	1	1	yes	characteristic
299	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
300	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
301	C₂×C₂₉	—	4	2	no	—
302	C₂×C₂₉	—	8	4	no	—
303	C₂×C₂₉	#3175	1	4	yes	direct product factor
304	C₂×C₂₉	C₂×#532	1	1	yes	characteristic
305	C₂×C₂₉	C₂×#576	1	1	yes	characteristic
306	C₂×C₂₉	C₂×#578	1	1	yes	characteristic
307	C₂²×Q₈	—	2	2	no	—
308	C₂²×Q₈	C₂³×C₂₉	1	2	yes	—
309	C₂²×D₄	—	2	2	no	—
310	C₂²×D₄	C₂³×C₂₉	1	2	yes	—
311	C₂³×C₄	—	2	2	no	—
312	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
313	C₂×Q₁₆	—	2	4	no	—
314	C₂×Q₁₆	C₂³×C₂₉	1	4	yes	—
315	C₂×SD₁₆	—	2	8	no	—
316	C₂×SD₁₆	C₂³×C₂₉	1	8	yes	—
317	C₂×D₈	—	2	4	no	—
318	C₂×D₈	C₂³×C₂₉	1	4	yes	—
319	C₂×M₁₆	—	2	4	no	—
320	C₂×M₁₆	C₂³×C₂₉	1	4	yes	—
321	C₂²×C₈	—	2	4	no	—
322	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
323	C₂²×C₈	C₂³×C₂₉	1	4	yes	—
324	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
325	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
326	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
327	C₄⋊Q₈	—	2	4	no	—
328	C₄⋊Q₈	C₂³×C₂₉	1	8	yes	—
329	#126	—	2	16	no	—
330	#124	—	2	16	no	—
331	#124	—	2	4	no	—
332	#124	C₂³×C₂₉	1	8	yes	—
333	#123	—	2	16	no	—
334	C₂²⋊Q₈	—	2	4	no	—
335	C₂²⋊Q₈	—	2	16	no	—
336	C₂²⋊Q₈	C₂³×C₂₉	1	8	yes	—
337	#121	—	2	4	no	—
338	#121	C₂³×C₂₉	1	8	yes	—
339	C₄×Q₈	—	2	4	no	—
340	C₄×Q₈	C₂³×C₂₉	1	8	yes	—
341	C₄×D₄	—	2	4	no	—
342	C₄×D₄	C₂³×C₂₉	1	8	yes	—
343	#117	D₄×C₂₉	1	4	yes	—
344	#117	C₂³×C₂₉	1	4	yes	—
345	C₂×C₄⋊C₄	—	2	2	no	—
346	C₂×C₄⋊C₄	—	2	2	no	—
347	C₂×C₄⋊C₄	—	2	2	no	—
348	C₂×C₄⋊C₄	D₄×C₂₉	1	1	yes	characteristic
349	C₂×C₄⋊C₄	D₄×C₂₉	1	1	yes	characteristic
350	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
351	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
352	C₂×C₂²⋊C₄	—	2	2	no	—
353	C₂×C₂²⋊C₄	—	2	2	no	—
354	C₂×C₂²⋊C₄	—	2	2	no	—
355	C₂×C₂²⋊C₄	—	2	2	no	—
356	C₂×C₂²⋊C₄	—	2	2	no	—
357	C₂×C₂²⋊C₄	D₄×C₂₉	1	1	yes	characteristic
358	C₂×C₂²⋊C₄	D₄×C₂₉	1	1	yes	characteristic
359	C₂×C₄²	—	2	2	no	—
360	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
361	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
362	#107	C₂³×C₂₉	1	4	yes	—
363	#107	C₂³×C₂₉	1	4	yes	—
364	#107	C₂³×C₂₉	1	8	yes	—
365	#103	C₂³×C₂₉	1	8	yes	—
366	#103	C₂³×C₂₉	1	8	yes	—
367	#102	C₂³×C₂₉	1	8	yes	—
368	#102	C₂³×C₂₉	1	8	yes	—
369	#97	C₂³×C₂₉	1	4	yes	—
370	#97	C₂³×C₂₉	1	4	yes	—
371	C₄×C₈	C₂³×C₂₉	1	4	yes	—
372	C₄×C₈	C₂³×C₂₉	1	4	yes	—
373	C₂₉	C₂×#3175	1	1	yes	characteristic, direct product factor, Sylow
374	C₂⁴	—	2	2	no	—
375	C₂⁴	C₂×D₄×C₂₉	1	1	yes	characteristic
376	C₂×Q₈	—	2	2	no	—
377	C₂×Q₈	—	2	8	no	—
378	C₂×Q₈	—	2	4	no	—
379	C₂×Q₈	—	2	4	no	—
380	C₂×Q₈	—	8	4	no	—
381	C₂×Q₈	C₂⁴×C₂₉	1	4	yes	—
382	C₂×D₄	—	2	8	no	—
383	C₂×D₄	—	2	2	no	—
384	C₂×D₄	—	2	4	no	—
385	C₂×D₄	—	2	4	no	—
386	C₂×D₄	—	8	4	no	—
387	C₂×D₄	C₂⁴×C₂₉	1	4	yes	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	8	no	—
394	C₂²×C₄	—	8	4	no	—
395	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
396	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
397	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
398	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
399	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
400	C₂²×C₄	C₂×D₄×C₂₉	1	2	yes	—
401	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
402	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
403	Q₁₆	—	2	8	no	—
404	SD₁₆	—	2	16	no	—
405	D₈	—	2	8	no	—
406	M₁₆	—	2	8	no	—
407	C₂×C₈	—	2	2	no	—
408	C₂×C₈	—	2	2	no	—
409	C₂×C₈	—	2	8	no	—
410	C₂×C₈	#41×C₂₉	1	4	yes	—
411	C₂×C₈	#41×C₂₉	1	4	yes	—
412	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
413	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
414	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
415	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
416	C₄⋊C₄	—	2	8	no	—
417	C₄⋊C₄	—	2	8	no	—
418	C₄⋊C₄	—	2	8	no	—
419	C₄⋊C₄	—	2	2	no	—
420	C₄⋊C₄	—	2	2	no	—
421	C₄⋊C₄	C₂×D₄×C₂₉	1	4	yes	—
422	C₄⋊C₄	C₂×D₄×C₂₉	1	4	yes	—
423	C₄⋊C₄	C₂⁴×C₂₉	1	4	yes	—
424	C₄⋊C₄	C₂⁴×C₂₉	1	4	yes	—
425	C₂²⋊C₄	—	2	8	no	—
426	C₂²⋊C₄	—	2	8	no	—
427	C₂²⋊C₄	—	2	8	no	—
428	C₂²⋊C₄	—	2	8	no	—
429	C₂²⋊C₄	—	2	8	no	—
430	C₂²⋊C₄	C₂×D₄×C₂₉	1	4	yes	—
431	C₂²⋊C₄	C₂×D₄×C₂₉	1	4	yes	—
432	C₄²	—	2	8	no	—
433	C₄²	C₂×D₄×C₂₉	1	2	yes	—
434	C₄²	C₂×D₄×C₂₉	1	2	yes	—
435	C₄²	C₂⁴×C₂₉	1	2	yes	—
436	C₄²	C₂⁴×C₂₉	1	2	yes	—
437	C₂³	—	2	2	no	—
438	C₂³	—	2	2	no	—
439	C₂³	—	2	2	no	—
440	C₂³	—	2	4	no	—
441	C₂³	—	4	4	no	—
442	C₂³	—	4	4	no	—
443	C₂³	—	4	4	no	—
444	C₂³	C₂²×D₄×C₂₉	1	2	yes	—
445	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
446	Q₈	—	2	4	no	—
447	Q₈	—	2	4	no	—
448	Q₈	—	4	4	no	—
449	Q₈	—	8	8	no	—
450	D₄	—	2	4	no	—
451	D₄	—	2	4	no	—
452	D₄	—	4	4	no	—
453	D₄	—	8	8	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	4	no	—
463	C₂×C₄	—	2	4	no	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	4	4	no	—
466	C₂×C₄	—	4	4	no	—
467	C₂×C₄	—	4	4	no	—
468	C₂×C₄	—	8	8	no	—
469	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
470	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
471	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
472	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
473	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
474	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
475	C₂×C₄	C₂×#41×C₂₉	1	2	yes	—
476	C₂×C₄	C₂×#41×C₂₉	1	2	yes	—
477	C₂×C₄	C₂⁵×C₂₉	1	1	yes	characteristic
478	C₈	—	2	2	no	—
479	C₈	—	2	2	no	—
480	C₈	C₂×#41×C₂₉	1	4	yes	—
481	C₈	C₂×#41×C₂₉	1	4	yes	—
482	C₂²	—	2	2	no	—
483	C₂²	—	2	2	no	—
484	C₂²	—	2	2	no	—
485	C₂²	—	4	4	no	—
486	C₂²	—	4	4	no	—
487	C₂²	—	4	4	no	—
488	C₂²	—	4	4	no	—
489	C₂²	—	8	8	no	—
490	C₂²	C₂₉×#532	1	2	yes	—
491	C₂²	C₂₉×#576	1	2	yes	—
492	C₂²	C₂₉×#578	1	2	yes	—
493	C₂²	C₂³×D₄×C₂₉	1	1	yes	characteristic
494	C₄	—	2	2	no	—
495	C₄	—	2	2	no	—
496	C₄	—	2	2	no	—
497	C₄	—	2	2	no	—
498	C₄	—	2	2	no	—
499	C₄	—	4	4	no	—
500	C₄	—	4	4	no	—
501	C₄	—	4	4	no	—
502	C₄	C₂₉×#532	1	2	yes	—
503	C₄	C₂²×#41×C₂₉	1	1	yes	characteristic
504	C₄	C₂²×#41×C₂₉	1	1	yes	characteristic
505	C₂	—	4	2	no	—
506	C₂	—	8	4	no	—
507	C₂	C₂₉×#3175	1	4	yes	direct product factor
508	C₂	C₂×C₂₉×#532	1	1	yes	characteristic
509	C₂	C₂×C₂₉×#576	1	1	yes	characteristic
510	C₂	C₂×C₂₉×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₉
prime radical	C₂×C₂₉×#466	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ C₂×C₂₉×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₉×#542	C₂	semidirect
2. C₂₉×#3175	C₂	direct (N × H)
3. C₂×C₂₉×#500	C₂	semidirect
4. C₂×C₂₉×#495	C₂	semidirect
5. C₂×C₂₉×#489	C₂	semidirect
6. C₂×C₂₉×#468	C₂	semidirect
7. C₂×C₂₉×#467	C₂	semidirect
9. C₂×C₂₉×#440	C₂	semidirect
10. C₂×C₄×Q₁₆×C₂₉	C₂	semidirect
11. C₂×C₄×D₈×C₂₉	C₂	semidirect
12. C₂×C₂₉×#405	C₂	semidirect
19. C₂₉×#542	C₂²	semidirect
31. C₂₉×#500	C₂²	semidirect
32. C₂₉×#495	C₂²	semidirect
33. C₂₉×#489	C₂²	semidirect
34. C₂₉×#468	C₂²	semidirect
35. C₂₉×#467	C₂²	semidirect
37. C₂₉×#440	C₂²	semidirect
38. C₄×Q₁₆×C₂₉	C₂²	semidirect
39. C₄×D₈×C₂₉	C₂²	semidirect
47. C₂₉×#405	C₂²	semidirect
181. C₂×#3175	C₂₉	direct (N × H)
227. C₂×#542	C₂×C₂₉	semidirect
228. #3175	C₂×C₂₉	direct (N × H)
229. C₂×#500	C₂×C₂₉	semidirect
230. C₂×#495	C₂×C₂₉	semidirect
231. C₂×#489	C₂×C₂₉	semidirect
232. C₂×#468	C₂×C₂₉	semidirect
233. C₂×#467	C₂×C₂₉	semidirect
235. C₂×#440	C₂×C₂₉	semidirect
236. C₂×C₄×Q₁₆	C₂×C₂₉	semidirect
237. C₂×C₄×D₈	C₂×C₂₉	semidirect
238. C₂×#405	C₂×C₂₉	semidirect
268. #542	C₂²×C₂₉	semidirect
280. #500	C₂²×C₂₉	semidirect
281. #495	C₂²×C₂₉	semidirect
282. #489	C₂²×C₂₉	semidirect
283. #468	C₂²×C₂₉	semidirect
284. #467	C₂²×C₂₉	semidirect
286. #440	C₂²×C₂₉	semidirect
287. C₄×Q₁₆	C₂²×C₂₉	semidirect
288. C₄×D₈	C₂²×C₂₉	semidirect
296. #405	C₂²×C₂₉	semidirect
303. C₂×C₂₉	#3175	direct (N × H)
373. C₂₉	C₂×#3175	direct (N × H)
507. C₂	C₂₉×#3175	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₂₉×#542	2
C₂₉×#3175	2
C₂×C₂₉×#500	2
C₂×C₂₉×#495	2
C₂×C₂₉×#489	2
C₂×C₂₉×#468	2
C₂×C₂₉×#467	2
C₂×C₂₉×#466	2
C₂×C₂₉×#440	2
C₂×C₄×Q₁₆×C₂₉	2
C₂×C₄×D₈×C₂₉	2
C₂×C₂₉×#405	2
C₂×#3175	29

Subgroups — C2×C29×#3175 #20355579

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₉×#3175 #20355579