Subgroups — C₂×C₂₉×#3197 #20355640

Order 7424.

2362 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#525	C₂	1	2	yes	maximal, complemented
2	C₂₉×#3197	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₂₉×#485	C₂	1	2	yes	maximal, complemented
4	C₂×C₂₉×#482	C₂	1	2	yes	maximal, complemented
5	C₂×C₂₉×#470	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₂₉×#469	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₂₉×#468	C₂	1	2	yes	maximal, complemented
8	C₂×C₂₉×#452	C₂	1	2	yes	maximal, complemented
9	C₂×C₂₉×#449	C₂	1	2	yes	maximal, complemented
10	C₂×C₂₉×#407	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×#41×C₂₉	C₂²	1	2	yes	—
12	C₂⁴×C₄×C₂₉	C₂²	1	1	yes	characteristic
13	C₂²×Q₁₆×C₂₉	C₂²	1	1	yes	characteristic, complemented
14	C₂²×SD₁₆×C₂₉	C₂²	1	2	yes	complemented
15	C₂²×D₈×C₂₉	C₂²	1	1	yes	characteristic, complemented
16	C₂²×M₁₆×C₂₉	C₂²	1	1	yes	characteristic
17	C₂²×M₁₆×C₂₉	C₂²	1	1	yes	characteristic
18	C₂₉×#525	—	2	8	no	—
19	C₂₉×#525	C₂²	1	16	yes	complemented
20	C₂×C₂₉×#123	—	2	2	no	—
21	C₂×C₂₉×C₂²⋊Q₈	C₂²	1	2	yes	—
22	C₂×C₂₉×C₂²⋊Q₈	C₂²	1	2	yes	—
23	C₂×C₂₉×#121	C₂²	1	2	yes	—
24	C₂×C₂₉×#121	C₂²	1	2	yes	—
25	C₂×C₂₉×#120	—	2	2	no	—
26	C₂×C₄×D₄×C₂₉	—	2	2	no	—
27	C₂×C₄×D₄×C₂₉	—	2	2	no	—
28	C₂×C₂₉×#117	C₂²	1	2	yes	—
29	C₂₉×#485	C₂²	1	16	yes	complemented
30	C₂₉×#482	C₂²	1	16	yes	complemented
31	C₂₉×#470	C₂²	1	8	yes	complemented
32	C₂₉×#469	C₂²	1	8	yes	complemented
33	C₂₉×#468	C₂²	1	16	yes	complemented
34	C₂₉×#452	C₂²	1	16	yes	complemented
35	C₂₉×#449	C₂²	1	16	yes	complemented
36	C₂×C₂₉×#107	C₂²	1	2	yes	complemented
37	C₂×C₂₉×#106	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₂₉×#106	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₂₉×#103	C₂²	1	2	yes	complemented
40	C₂×C₂₉×#103	C₂²	1	2	yes	complemented
41	C₂×C₂₉×#102	C₂²	1	2	yes	complemented
42	C₂×C₂₉×#102	C₂²	1	2	yes	complemented
43	C₂₉×#407	C₂²	1	8	yes	complemented
44	C₂×C₂₉×C₂²⋊C₈	C₂²	1	2	yes	—
45	C₂×C₂₉×C₂²⋊C₈	C₂²	1	2	yes	—
46	C₂⁵×C₂₉	D₄	1	1	yes	characteristic
47	C₂×#41×C₂₉	—	2	4	no	—
48	C₂×#41×C₂₉	—	4	4	no	—
49	C₂×#41×C₂₉	—	4	4	no	—
50	C₂×#41×C₂₉	C₂³	1	8	yes	—
51	C₂²×Q₈×C₂₉	C₂³	1	2	yes	—
52	C₂²×D₄×C₂₉	—	2	2	no	—
53	C₂²×D₄×C₂₉	—	2	2	no	—
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	—	4	2	no	—
58	C₂³×C₄×C₂₉	—	4	2	no	—
59	C₂³×C₄×C₂₉	D₄	1	1	yes	characteristic
60	C₂³×C₄×C₂₉	D₄	1	2	yes	—
61	C₂³×C₄×C₂₉	D₄	1	4	yes	—
62	C₂³×C₄×C₂₉	C₂³	1	2	yes	—
63	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₂₉	C₂³	1	4	yes	—
65	C₂×Q₁₆×C₂₉	—	4	2	no	—
66	C₂×Q₁₆×C₂₉	C₂³	1	4	yes	complemented
67	C₂×SD₁₆×C₂₉	—	4	4	no	—
68	C₂×SD₁₆×C₂₉	C₂³	1	8	yes	complemented
69	C₂×D₈×C₂₉	—	4	2	no	—
70	C₂×D₈×C₂₉	C₂³	1	4	yes	complemented
71	C₂×M₁₆×C₂₉	—	4	2	no	—
72	C₂×M₁₆×C₂₉	—	4	2	no	—
73	C₂×M₁₆×C₂₉	C₂³	1	4	yes	—
74	C₂×M₁₆×C₂₉	C₂³	1	4	yes	—
75	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
78	C₂₉×#123	—	2	16	no	—
79	C₂₉×C₂²⋊Q₈	—	2	4	no	—
80	C₂₉×C₂²⋊Q₈	—	2	4	no	—
81	C₂₉×C₂²⋊Q₈	C₂³	1	8	yes	—
82	C₂₉×C₂²⋊Q₈	C₂³	1	8	yes	—
83	C₂₉×#121	—	2	4	no	—
84	C₂₉×#121	—	2	4	no	—
85	C₂₉×#121	C₂³	1	8	yes	—
86	C₂₉×#121	C₂³	1	8	yes	—
87	C₂₉×#120	—	2	16	no	—
88	C₄×D₄×C₂₉	—	2	16	no	—
89	C₄×D₄×C₂₉	—	2	16	no	—
90	C₂₉×#117	—	2	4	no	—
91	C₂₉×#117	C₂³	1	8	yes	—
92	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
93	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
94	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
95	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
96	C₂×C₂²⋊C₄×C₂₉	—	2	2	no	—
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×C₄²×C₂₉	—	2	2	no	—
102	C₂₉×#107	C₂³	1	8	yes	complemented
103	C₂₉×#106	C₂³	1	4	yes	complemented
104	C₂₉×#106	C₂³	1	4	yes	complemented
105	C₂₉×#103	C₂³	1	8	yes	complemented
106	C₂₉×#103	C₂³	1	8	yes	complemented
107	C₂₉×#102	C₂³	1	8	yes	complemented
108	C₂₉×#102	C₂³	1	8	yes	complemented
109	C₂₉×C₂²⋊C₈	C₂³	1	8	yes	—
110	C₂₉×C₂²⋊C₈	C₂³	1	8	yes	—
111	C₂⁴×C₂₉	—	2	2	no	—
112	C₂⁴×C₂₉	—	4	2	no	—
113	C₂⁴×C₂₉	—	4	4	no	—
114	C₂⁴×C₂₉	C₂×D₄	1	2	yes	—
115	C₂⁴×C₂₉	C₂×D₄	1	1	yes	characteristic
116	C₂⁴×C₂₉	C₂×D₄	1	4	yes	—
117	#41×C₂₉	—	4	8	no	—
118	#41×C₂₉	—	4	8	no	—
119	#41×C₂₉	—	4	16	no	—
120	C₂×Q₈×C₂₉	—	2	2	no	—
121	C₂×Q₈×C₂₉	—	2	4	no	—
122	C₂×Q₈×C₂₉	—	2	4	no	—
123	C₂×Q₈×C₂₉	C₂⁴	1	4	yes	—
124	C₂×D₄×C₂₉	—	2	8	no	—
125	C₂×D₄×C₂₉	—	2	8	no	—
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	—	4	8	no	—
131	C₂×D₄×C₂₉	—	4	8	no	—
132	C₂×D₄×C₂₉	—	4	8	no	—
133	C₂×D₄×C₂₉	C₂⁴	1	4	yes	—
134	C₂²×C₄×C₂₉	—	2	2	no	—
135	C₂²×C₄×C₂₉	—	2	2	no	—
136	C₂²×C₄×C₂₉	—	2	4	no	—
137	C₂²×C₄×C₂₉	—	2	4	no	—
138	C₂²×C₄×C₂₉	—	2	2	no	—
139	C₂²×C₄×C₂₉	—	2	2	no	—
140	C₂²×C₄×C₂₉	—	2	2	no	—
141	C₂²×C₄×C₂₉	—	2	8	no	—
142	C₂²×C₄×C₂₉	—	4	8	no	—
143	C₂²×C₄×C₂₉	—	4	4	no	—
144	C₂²×C₄×C₂₉	—	4	4	no	—
145	C₂²×C₄×C₂₉	—	4	2	no	—
146	C₂²×C₄×C₂₉	—	4	4	no	—
147	C₂²×C₄×C₂₉	—	4	8	no	—
148	C₂²×C₄×C₂₉	C₂×D₄	1	4	yes	—
149	C₂²×C₄×C₂₉	C₂×D₄	1	2	yes	—
150	C₂²×C₄×C₂₉	C₂×D₄	1	2	yes	—
151	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₂₉	C₂×D₄	1	4	yes	—
153	C₂²×C₄×C₂₉	C₂×D₄	1	8	yes	—
154	C₂²×C₄×C₂₉	C₂⁴	1	4	yes	—
155	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
156	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
157	Q₁₆×C₂₉	—	4	4	no	—
158	SD₁₆×C₂₉	—	4	8	no	—
159	D₈×C₂₉	—	4	4	no	—
160	M₁₆×C₂₉	—	4	4	no	—
161	M₁₆×C₂₉	—	4	4	no	—
162	C₂×C₈×C₂₉	—	2	2	no	—
163	C₂×C₈×C₂₉	—	2	4	no	—
164	C₂×C₈×C₂₉	—	2	2	no	—
165	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
166	C₂×C₈×C₂₉	C₂⁴	1	4	yes	—
167	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
168	C₄⋊C₄×C₂₉	—	2	8	no	—
169	C₄⋊C₄×C₂₉	—	2	8	no	—
170	C₄⋊C₄×C₂₉	—	2	2	no	—
171	C₄⋊C₄×C₂₉	—	2	2	no	—
172	C₄⋊C₄×C₂₉	C₂⁴	1	4	yes	—
173	C₄⋊C₄×C₂₉	C₂⁴	1	4	yes	—
174	C₂²⋊C₄×C₂₉	—	2	8	no	—
175	C₂²⋊C₄×C₂₉	—	2	8	no	—
176	C₂²⋊C₄×C₂₉	—	2	8	no	—
177	C₂²⋊C₄×C₂₉	—	2	8	no	—
178	C₂²⋊C₄×C₂₉	—	2	8	no	—
179	C₄²×C₂₉	—	2	8	no	—
180	C₂×#3197	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
181	C₂³×C₂₉	—	2	4	no	—
182	C₂³×C₂₉	—	2	2	no	—
183	C₂³×C₂₉	—	2	4	no	—
184	C₂³×C₂₉	—	2	4	no	—
185	C₂³×C₂₉	—	2	4	no	—
186	C₂³×C₂₉	—	2	4	no	—
187	C₂³×C₂₉	—	4	4	no	—
188	C₂³×C₂₉	—	4	8	no	—
189	C₂³×C₂₉	—	4	16	no	—
190	C₂³×C₂₉	—	4	4	no	—
191	C₂³×C₂₉	—	4	4	no	—
192	C₂³×C₂₉	—	4	4	no	—
193	C₂³×C₂₉	C₂²×D₄	1	4	yes	—
194	C₂³×C₂₉	C₂²×D₄	1	2	yes	—
195	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
196	Q₈×C₂₉	—	2	4	no	—
197	Q₈×C₂₉	—	2	4	no	—
198	Q₈×C₂₉	—	4	4	no	—
199	D₄×C₂₉	—	2	4	no	—
200	D₄×C₂₉	—	2	4	no	—
201	D₄×C₂₉	—	4	16	no	—
202	D₄×C₂₉	—	4	16	no	—
203	D₄×C₂₉	—	4	16	no	—
204	D₄×C₂₉	—	4	4	no	—
205	C₂×C₄×C₂₉	—	2	4	no	—
206	C₂×C₄×C₂₉	—	2	2	no	—
207	C₂×C₄×C₂₉	—	2	4	no	—
208	C₂×C₄×C₂₉	—	2	8	no	—
209	C₂×C₄×C₂₉	—	2	2	no	—
210	C₂×C₄×C₂₉	—	2	2	no	—
211	C₂×C₄×C₂₉	—	2	4	no	—
212	C₂×C₄×C₂₉	—	2	4	no	—
213	C₂×C₄×C₂₉	—	2	4	no	—
214	C₂×C₄×C₂₉	—	2	4	no	—
215	C₂×C₄×C₂₉	—	2	4	no	—
216	C₂×C₄×C₂₉	—	4	4	no	—
217	C₂×C₄×C₂₉	—	4	8	no	—
218	C₂×C₄×C₂₉	—	4	16	no	—
219	C₂×C₄×C₂₉	—	4	4	no	—
220	C₂×C₄×C₂₉	—	4	4	no	—
221	C₂×C₄×C₂₉	—	4	4	no	—
222	C₂×C₄×C₂₉	C₂²×D₄	1	4	yes	—
223	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
224	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
225	C₂×C₄×C₂₉	H(5,𝔽₂)	1	2	yes	—
226	C₂×C₄×C₂₉	H(5,𝔽₂)	1	2	yes	—
227	C₂×C₄×C₂₉	C₂⁵	1	1	yes	characteristic
228	C₈×C₂₉	—	2	2	no	—
229	C₈×C₂₉	—	2	4	no	—
230	C₈×C₂₉	—	2	2	no	—
231	C₂×#525	C₂×C₂₉	1	2	yes	complemented
232	#3197	C₂×C₂₉	1	16	yes	direct product factor
233	C₂×#485	C₂×C₂₉	1	2	yes	complemented
234	C₂×#482	C₂×C₂₉	1	2	yes	complemented
235	C₂×#470	C₂×C₂₉	1	1	yes	characteristic, complemented
236	C₂×#469	C₂×C₂₉	1	1	yes	characteristic, complemented
237	C₂×#468	C₂×C₂₉	1	2	yes	complemented
238	C₂×#452	C₂×C₂₉	1	2	yes	complemented
239	C₂×#449	C₂×C₂₉	1	2	yes	complemented
240	C₂×#407	C₂×C₂₉	1	1	yes	characteristic, complemented
241	C₂²×C₂₉	—	2	4	no	—
242	C₂²×C₂₉	—	2	2	no	—
243	C₂²×C₂₉	—	2	4	no	—
244	C₂²×C₂₉	—	2	4	no	—
245	C₂²×C₂₉	—	2	4	no	—
246	C₂²×C₂₉	—	4	16	no	—
247	C₂²×C₂₉	—	4	8	no	—
248	C₂²×C₂₉	—	4	4	no	—
249	C₂²×C₂₉	—	4	4	no	—
250	C₂²×C₂₉	—	4	4	no	—
251	C₂²×C₂₉	—	4	4	no	—
252	C₂²×C₂₉	—	8	8	no	—
253	C₂²×C₂₉	#534	1	2	yes	—
254	C₂²×C₂₉	#575	1	4	yes	—
255	C₂²×C₂₉	C₂³×D₄	1	1	yes	characteristic
256	C₄×C₂₉	—	2	4	no	—
257	C₄×C₂₉	—	2	2	no	—
258	C₄×C₂₉	—	4	4	no	—
259	C₄×C₂₉	—	4	4	no	—
260	C₄×C₂₉	—	4	4	no	—
261	C₄×C₂₉	#534	1	2	yes	—
262	C₄×C₂₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
263	C₄×C₂₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
264	C₂²×#41	C₂²×C₂₉	1	2	yes	—
265	C₂⁴×C₄	C₂²×C₂₉	1	1	yes	characteristic
266	C₂²×Q₁₆	C₂²×C₂₉	1	1	yes	characteristic, complemented
267	C₂²×SD₁₆	C₂²×C₂₉	1	2	yes	complemented
268	C₂²×D₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
269	C₂²×M₁₆	C₂²×C₂₉	1	1	yes	characteristic
270	C₂²×M₁₆	C₂²×C₂₉	1	1	yes	characteristic
271	#525	—	2	8	no	—
272	#525	C₂²×C₂₉	1	16	yes	complemented
273	C₂×#123	—	2	2	no	—
274	C₂×C₂²⋊Q₈	C₂²×C₂₉	1	2	yes	—
275	C₂×C₂²⋊Q₈	C₂²×C₂₉	1	2	yes	—
276	C₂×#121	C₂²×C₂₉	1	2	yes	—
277	C₂×#121	C₂²×C₂₉	1	2	yes	—
278	C₂×#120	—	2	2	no	—
279	C₂×C₄×D₄	—	2	2	no	—
280	C₂×C₄×D₄	—	2	2	no	—
281	C₂×#117	C₂²×C₂₉	1	2	yes	—
282	#485	C₂²×C₂₉	1	16	yes	complemented
283	#482	C₂²×C₂₉	1	16	yes	complemented
284	#470	C₂²×C₂₉	1	8	yes	complemented
285	#469	C₂²×C₂₉	1	8	yes	complemented
286	#468	C₂²×C₂₉	1	16	yes	complemented
287	#452	C₂²×C₂₉	1	16	yes	complemented
288	#449	C₂²×C₂₉	1	16	yes	complemented
289	C₂×#107	C₂²×C₂₉	1	2	yes	complemented
290	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic, complemented
291	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic, complemented
292	C₂×#103	C₂²×C₂₉	1	2	yes	complemented
293	C₂×#103	C₂²×C₂₉	1	2	yes	complemented
294	C₂×#102	C₂²×C₂₉	1	2	yes	complemented
295	C₂×#102	C₂²×C₂₉	1	2	yes	complemented
296	#407	C₂²×C₂₉	1	8	yes	complemented
297	C₂×C₂²⋊C₈	C₂²×C₂₉	1	2	yes	—
298	C₂×C₂²⋊C₈	C₂²×C₂₉	1	2	yes	—
299	C₂×C₂₉	—	4	4	no	—
300	C₂×C₂₉	—	4	2	no	—
301	C₂×C₂₉	—	8	4	no	—
302	C₂×C₂₉	#3197	1	4	yes	direct product factor
303	C₂×C₂₉	C₂×#534	1	1	yes	characteristic
304	C₂×C₂₉	C₂×#575	1	2	yes	—
305	C₂⁵	D₄×C₂₉	1	1	yes	characteristic
306	C₂×#41	—	2	4	no	—
307	C₂×#41	—	4	4	no	—
308	C₂×#41	—	4	4	no	—
309	C₂×#41	C₂³×C₂₉	1	8	yes	—
310	C₂²×Q₈	C₂³×C₂₉	1	2	yes	—
311	C₂²×D₄	—	2	2	no	—
312	C₂²×D₄	—	2	2	no	—
313	C₂²×D₄	—	2	2	no	—
314	C₂²×D₄	C₂³×C₂₉	1	2	yes	—
315	C₂³×C₄	—	2	2	no	—
316	C₂³×C₄	—	4	2	no	—
317	C₂³×C₄	—	4	2	no	—
318	C₂³×C₄	D₄×C₂₉	1	1	yes	characteristic
319	C₂³×C₄	D₄×C₂₉	1	2	yes	—
320	C₂³×C₄	D₄×C₂₉	1	4	yes	—
321	C₂³×C₄	C₂³×C₂₉	1	2	yes	—
322	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
323	C₂³×C₄	C₂³×C₂₉	1	4	yes	—
324	C₂×Q₁₆	—	4	2	no	—
325	C₂×Q₁₆	C₂³×C₂₉	1	4	yes	complemented
326	C₂×SD₁₆	—	4	4	no	—
327	C₂×SD₁₆	C₂³×C₂₉	1	8	yes	complemented
328	C₂×D₈	—	4	2	no	—
329	C₂×D₈	C₂³×C₂₉	1	4	yes	complemented
330	C₂×M₁₆	—	4	2	no	—
331	C₂×M₁₆	—	4	2	no	—
332	C₂×M₁₆	C₂³×C₂₉	1	4	yes	—
333	C₂×M₁₆	C₂³×C₂₉	1	4	yes	—
334	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
335	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
336	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
337	#123	—	2	16	no	—
338	C₂²⋊Q₈	—	2	4	no	—
339	C₂²⋊Q₈	—	2	4	no	—
340	C₂²⋊Q₈	C₂³×C₂₉	1	8	yes	—
341	C₂²⋊Q₈	C₂³×C₂₉	1	8	yes	—
342	#121	—	2	4	no	—
343	#121	—	2	4	no	—
344	#121	C₂³×C₂₉	1	8	yes	—
345	#121	C₂³×C₂₉	1	8	yes	—
346	#120	—	2	16	no	—
347	C₄×D₄	—	2	16	no	—
348	C₄×D₄	—	2	16	no	—
349	#117	—	2	4	no	—
350	#117	C₂³×C₂₉	1	8	yes	—
351	C₂×C₄⋊C₄	—	2	2	no	—
352	C₂×C₄⋊C₄	—	2	2	no	—
353	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
354	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
355	C₂×C₂²⋊C₄	—	2	2	no	—
356	C₂×C₂²⋊C₄	—	2	2	no	—
357	C₂×C₂²⋊C₄	—	2	2	no	—
358	C₂×C₂²⋊C₄	—	2	2	no	—
359	C₂×C₂²⋊C₄	—	2	2	no	—
360	C₂×C₄²	—	2	2	no	—
361	#107	C₂³×C₂₉	1	8	yes	complemented
362	#106	C₂³×C₂₉	1	4	yes	complemented
363	#106	C₂³×C₂₉	1	4	yes	complemented
364	#103	C₂³×C₂₉	1	8	yes	complemented
365	#103	C₂³×C₂₉	1	8	yes	complemented
366	#102	C₂³×C₂₉	1	8	yes	complemented
367	#102	C₂³×C₂₉	1	8	yes	complemented
368	C₂²⋊C₈	C₂³×C₂₉	1	8	yes	—
369	C₂²⋊C₈	C₂³×C₂₉	1	8	yes	—
370	C₂₉	C₂×#3197	1	1	yes	characteristic, direct product factor, Sylow
371	C₂⁴	—	2	2	no	—
372	C₂⁴	—	4	2	no	—
373	C₂⁴	—	4	4	no	—
374	C₂⁴	C₂×D₄×C₂₉	1	2	yes	—
375	C₂⁴	C₂×D₄×C₂₉	1	1	yes	characteristic
376	C₂⁴	C₂×D₄×C₂₉	1	4	yes	—
377	#41	—	4	8	no	—
378	#41	—	4	8	no	—
379	#41	—	4	16	no	—
380	C₂×Q₈	—	2	2	no	—
381	C₂×Q₈	—	2	4	no	—
382	C₂×Q₈	—	2	4	no	—
383	C₂×Q₈	C₂⁴×C₂₉	1	4	yes	—
384	C₂×D₄	—	2	8	no	—
385	C₂×D₄	—	2	8	no	—
386	C₂×D₄	—	2	8	no	—
387	C₂×D₄	—	2	2	no	—
388	C₂×D₄	—	2	4	no	—
389	C₂×D₄	—	2	4	no	—
390	C₂×D₄	—	4	8	no	—
391	C₂×D₄	—	4	8	no	—
392	C₂×D₄	—	4	8	no	—
393	C₂×D₄	C₂⁴×C₂₉	1	4	yes	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	2	4	no	—
397	C₂²×C₄	—	2	4	no	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	2	8	no	—
402	C₂²×C₄	—	4	8	no	—
403	C₂²×C₄	—	4	4	no	—
404	C₂²×C₄	—	4	4	no	—
405	C₂²×C₄	—	4	2	no	—
406	C₂²×C₄	—	4	4	no	—
407	C₂²×C₄	—	4	8	no	—
408	C₂²×C₄	C₂×D₄×C₂₉	1	2	yes	—
409	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
410	C₂²×C₄	C₂×D₄×C₂₉	1	4	yes	—
411	C₂²×C₄	C₂×D₄×C₂₉	1	2	yes	—
412	C₂²×C₄	C₂×D₄×C₂₉	1	4	yes	—
413	C₂²×C₄	C₂×D₄×C₂₉	1	8	yes	—
414	C₂²×C₄	C₂⁴×C₂₉	1	4	yes	—
415	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
416	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
417	Q₁₆	—	4	4	no	—
418	SD₁₆	—	4	8	no	—
419	D₈	—	4	4	no	—
420	M₁₆	—	4	4	no	—
421	M₁₆	—	4	4	no	—
422	C₂×C₈	—	2	2	no	—
423	C₂×C₈	—	2	4	no	—
424	C₂×C₈	—	2	2	no	—
425	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
426	C₂×C₈	C₂⁴×C₂₉	1	4	yes	—
427	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
428	C₄⋊C₄	—	2	8	no	—
429	C₄⋊C₄	—	2	8	no	—
430	C₄⋊C₄	—	2	2	no	—
431	C₄⋊C₄	—	2	2	no	—
432	C₄⋊C₄	C₂⁴×C₂₉	1	4	yes	—
433	C₄⋊C₄	C₂⁴×C₂₉	1	4	yes	—
434	C₂²⋊C₄	—	2	8	no	—
435	C₂²⋊C₄	—	2	8	no	—
436	C₂²⋊C₄	—	2	8	no	—
437	C₂²⋊C₄	—	2	8	no	—
438	C₂²⋊C₄	—	2	8	no	—
439	C₄²	—	2	8	no	—
440	C₂³	—	2	4	no	—
441	C₂³	—	2	2	no	—
442	C₂³	—	2	4	no	—
443	C₂³	—	2	4	no	—
444	C₂³	—	2	4	no	—
445	C₂³	—	2	4	no	—
446	C₂³	—	4	4	no	—
447	C₂³	—	4	8	no	—
448	C₂³	—	4	16	no	—
449	C₂³	—	4	4	no	—
450	C₂³	—	4	4	no	—
451	C₂³	—	4	4	no	—
452	C₂³	C₂²×D₄×C₂₉	1	4	yes	—
453	C₂³	C₂²×D₄×C₂₉	1	2	yes	—
454	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
455	Q₈	—	2	4	no	—
456	Q₈	—	2	4	no	—
457	Q₈	—	4	4	no	—
458	D₄	—	2	4	no	—
459	D₄	—	2	4	no	—
460	D₄	—	4	16	no	—
461	D₄	—	4	16	no	—
462	D₄	—	4	16	no	—
463	D₄	—	4	4	no	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	8	no	—
467	C₂×C₄	—	2	4	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	4	no	—
471	C₂×C₄	—	2	4	no	—
472	C₂×C₄	—	2	4	no	—
473	C₂×C₄	—	2	4	no	—
474	C₂×C₄	—	2	4	no	—
475	C₂×C₄	—	4	4	no	—
476	C₂×C₄	—	4	8	no	—
477	C₂×C₄	—	4	16	no	—
478	C₂×C₄	—	4	4	no	—
479	C₂×C₄	—	4	4	no	—
480	C₂×C₄	—	4	4	no	—
481	C₂×C₄	C₂²×D₄×C₂₉	1	4	yes	—
482	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
483	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
484	C₂×C₄	C₂₉×H(5,𝔽₂)	1	2	yes	—
485	C₂×C₄	C₂₉×H(5,𝔽₂)	1	2	yes	—
486	C₂×C₄	C₂⁵×C₂₉	1	1	yes	characteristic
487	C₈	—	2	2	no	—
488	C₈	—	2	4	no	—
489	C₈	—	2	2	no	—
490	C₂²	—	2	4	no	—
491	C₂²	—	2	2	no	—
492	C₂²	—	2	4	no	—
493	C₂²	—	2	4	no	—
494	C₂²	—	2	4	no	—
495	C₂²	—	4	16	no	—
496	C₂²	—	4	8	no	—
497	C₂²	—	4	4	no	—
498	C₂²	—	4	4	no	—
499	C₂²	—	4	4	no	—
500	C₂²	—	4	4	no	—
501	C₂²	—	8	8	no	—
502	C₂²	C₂₉×#534	1	2	yes	—
503	C₂²	C₂₉×#575	1	4	yes	—
504	C₂²	C₂³×D₄×C₂₉	1	1	yes	characteristic
505	C₄	—	2	4	no	—
506	C₄	—	2	2	no	—
507	C₄	—	4	4	no	—
508	C₄	—	4	4	no	—
509	C₄	—	4	4	no	—
510	C₄	C₂₉×#534	1	2	yes	—
511	C₄	C₂×C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
512	C₄	C₂×C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
513	C₂	—	4	4	no	—
514	C₂	—	4	2	no	—
515	C₂	—	8	4	no	—
516	C₂	C₂₉×#3197	1	4	yes	direct product factor
517	C₂	C₂×C₂₉×#534	1	1	yes	characteristic
518	C₂	C₂×C₂₉×#575	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₂₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ C₂⁴×C₄×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₉×#525	C₂	semidirect
2. C₂₉×#3197	C₂	direct (N × H)
3. C₂×C₂₉×#485	C₂	semidirect
4. C₂×C₂₉×#482	C₂	semidirect
5. C₂×C₂₉×#470	C₂	semidirect
6. C₂×C₂₉×#469	C₂	semidirect
7. C₂×C₂₉×#468	C₂	semidirect
8. C₂×C₂₉×#452	C₂	semidirect
9. C₂×C₂₉×#449	C₂	semidirect
10. C₂×C₂₉×#407	C₂	semidirect
13. C₂²×Q₁₆×C₂₉	C₂²	semidirect
14. C₂²×SD₁₆×C₂₉	C₂²	semidirect
15. C₂²×D₈×C₂₉	C₂²	semidirect
19. C₂₉×#525	C₂²	semidirect
29. C₂₉×#485	C₂²	semidirect
30. C₂₉×#482	C₂²	semidirect
31. C₂₉×#470	C₂²	semidirect
32. C₂₉×#469	C₂²	semidirect
33. C₂₉×#468	C₂²	semidirect
34. C₂₉×#452	C₂²	semidirect
35. C₂₉×#449	C₂²	semidirect
36. C₂×C₂₉×#107	C₂²	semidirect
37. C₂×C₂₉×#106	C₂²	semidirect
38. C₂×C₂₉×#106	C₂²	semidirect
39. C₂×C₂₉×#103	C₂²	semidirect
40. C₂×C₂₉×#103	C₂²	semidirect
41. C₂×C₂₉×#102	C₂²	semidirect
42. C₂×C₂₉×#102	C₂²	semidirect
43. C₂₉×#407	C₂²	semidirect
66. C₂×Q₁₆×C₂₉	C₂³	semidirect
68. C₂×SD₁₆×C₂₉	C₂³	semidirect
70. C₂×D₈×C₂₉	C₂³	semidirect
102. C₂₉×#107	C₂³	semidirect
103. C₂₉×#106	C₂³	semidirect
104. C₂₉×#106	C₂³	semidirect
105. C₂₉×#103	C₂³	semidirect
106. C₂₉×#103	C₂³	semidirect
107. C₂₉×#102	C₂³	semidirect
108. C₂₉×#102	C₂³	semidirect
180. C₂×#3197	C₂₉	direct (N × H)
231. C₂×#525	C₂×C₂₉	semidirect
232. #3197	C₂×C₂₉	direct (N × H)
233. C₂×#485	C₂×C₂₉	semidirect
234. C₂×#482	C₂×C₂₉	semidirect
235. C₂×#470	C₂×C₂₉	semidirect
236. C₂×#469	C₂×C₂₉	semidirect
237. C₂×#468	C₂×C₂₉	semidirect
238. C₂×#452	C₂×C₂₉	semidirect
239. C₂×#449	C₂×C₂₉	semidirect
240. C₂×#407	C₂×C₂₉	semidirect
266. C₂²×Q₁₆	C₂²×C₂₉	semidirect
267. C₂²×SD₁₆	C₂²×C₂₉	semidirect
268. C₂²×D₈	C₂²×C₂₉	semidirect
272. #525	C₂²×C₂₉	semidirect
282. #485	C₂²×C₂₉	semidirect
283. #482	C₂²×C₂₉	semidirect
284. #470	C₂²×C₂₉	semidirect
285. #469	C₂²×C₂₉	semidirect
286. #468	C₂²×C₂₉	semidirect
287. #452	C₂²×C₂₉	semidirect
288. #449	C₂²×C₂₉	semidirect
289. C₂×#107	C₂²×C₂₉	semidirect
290. C₂×#106	C₂²×C₂₉	semidirect
291. C₂×#106	C₂²×C₂₉	semidirect
292. C₂×#103	C₂²×C₂₉	semidirect
293. C₂×#103	C₂²×C₂₉	semidirect
294. C₂×#102	C₂²×C₂₉	semidirect
295. C₂×#102	C₂²×C₂₉	semidirect
296. #407	C₂²×C₂₉	semidirect
302. C₂×C₂₉	#3197	direct (N × H)
325. C₂×Q₁₆	C₂³×C₂₉	semidirect
327. C₂×SD₁₆	C₂³×C₂₉	semidirect
329. C₂×D₈	C₂³×C₂₉	semidirect
361. #107	C₂³×C₂₉	semidirect
362. #106	C₂³×C₂₉	semidirect
363. #106	C₂³×C₂₉	semidirect
364. #103	C₂³×C₂₉	semidirect
365. #103	C₂³×C₂₉	semidirect
366. #102	C₂³×C₂₉	semidirect
367. #102	C₂³×C₂₉	semidirect
370. C₂₉	C₂×#3197	direct (N × H)
516. C₂	C₂₉×#3197	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×#525	2
C₂₉×#3197	2
C₂×C₂₉×#485	2
C₂×C₂₉×#482	2
C₂×C₂₉×#470	2
C₂×C₂₉×#469	2
C₂×C₂₉×#468	2
C₂×C₂₉×#452	2
C₂×C₂₉×#449	2
C₂×C₂₉×#407	2
C₂×#3197	29

Subgroups — C2×C29×#3197 #20355640

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₉×#3197 #20355640