Subgroups — C₂×C₂₉×#3554 #20357646

Order 7424.

7182 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3554	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₂₉×#562	C₂	1	4	yes	maximal, complemented
3	C₂×C₂₉×#559	C₂	1	2	yes	maximal, complemented
4	C₂×C₂₉×#559	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₂₉×#557	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₂₉×#554	C₂	1	2	yes	maximal, complemented
7	C₂×C₂₉×#550	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×D₄×Q₈×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₂₉×#548	C₂	1	2	yes	maximal, complemented
10	C₂×C₂₉×#547	C₂	1	2	yes	maximal, complemented
11	C₂×C₂₉×#542	C₂	1	2	yes	maximal, complemented
12	C₂×C₂₉×#542	C₂	1	2	yes	maximal, complemented
13	C₂×C₂₉×#540	C₂	1	2	yes	maximal, complemented
14	C₂×C₂₉×#539	C₂	1	4	yes	maximal, complemented
15	C₂×C₂₉×#536	C₂	1	2	yes	maximal, complemented
16	C₂×C₂₉×#533	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₂₉×#532	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₂₉×#529	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×#41×C₂₉	C₂²	1	2	yes	—
20	C₂²×#41×C₂₉	C₂²	1	2	yes	—
21	C₂³×Q₈×C₂₉	C₂²	1	2	yes	—
22	C₂₉×#562	C₂²	1	64	yes	complemented
23	C₂₉×#559	C₂²	1	32	yes	complemented
24	C₂₉×#559	C₂²	1	16	yes	complemented
25	C₂₉×#557	C₂²	1	16	yes	complemented
26	C₂₉×#554	C₂²	1	32	yes	complemented
27	C₂₉×#550	C₂²	1	16	yes	complemented
28	D₄×Q₈×C₂₉	C₂²	1	16	yes	complemented
29	C₂₉×#548	C₂²	1	32	yes	complemented
30	C₂₉×#547	C₂²	1	32	yes	complemented
31	C₂₉×#542	C₂²	1	32	yes	complemented
32	C₂₉×#542	C₂²	1	32	yes	complemented
33	C₂₉×#540	C₂²	1	32	yes	complemented
34	C₂₉×#539	C₂²	1	64	yes	complemented
35	C₂₉×#536	C₂²	1	32	yes	complemented
36	C₂₉×#533	C₂²	1	16	yes	complemented
37	C₂₉×#532	C₂²	1	16	yes	complemented
38	C₂×C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
39	C₂×C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
40	C₂×C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
41	C₂×C₂₉×C₄⋊Q₈	C₂²	1	2	yes	—
42	C₂×C₂₉×C₄⋊Q₈	C₂²	1	2	yes	—
43	C₂×C₂₉×#127	C₂²	1	1	yes	characteristic
44	C₂×C₂₉×#127	C₂²	1	2	yes	—
45	C₂₉×#529	C₂²	1	16	yes	complemented
46	C₂×C₂₉×#126	C₂²	1	2	yes	—
47	C₂×C₂₉×#126	C₂²	1	4	yes	—
48	C₂×C₂₉×#125	C₂²	1	1	yes	characteristic
49	C₂×C₂₉×#125	C₂²	1	2	yes	—
50	C₂×C₂₉×#125	C₂²	1	4	yes	—
51	C₂×C₂₉×#125	C₂²	1	2	yes	—
52	C₂×C₂₉×#124	C₂²	1	1	yes	characteristic
53	C₂×C₂₉×#124	C₂²	1	2	yes	—
54	C₂×C₂₉×#124	C₂²	1	2	yes	—
55	C₂×C₂₉×#124	C₂²	1	4	yes	—
56	C₂×C₂₉×#124	C₂²	1	2	yes	—
57	C₂×C₂₉×#124	C₂²	1	4	yes	—
58	C₂×C₂₉×#123	C₂²	1	2	yes	—
59	C₂×C₂₉×#123	C₂²	1	4	yes	—
60	C₂×C₂₉×#123	C₂²	1	4	yes	—
61	C₂×C₂₉×#123	C₂²	1	4	yes	—
62	C₂×C₂₉×#123	C₂²	1	4	yes	—
63	C₂×C₂₉×#123	C₂²	1	4	yes	—
64	C₂×C₂₉×#123	C₂²	1	4	yes	—
65	C₂×C₂₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
66	C₂×C₂₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
67	C₂×C₂₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
68	C₂×C₂₉×C₂²⋊Q₈	C₂²	1	2	yes	—
69	C₂×C₂₉×C₂²⋊Q₈	C₂²	1	4	yes	—
70	C₂×C₂₉×C₂²⋊Q₈	C₂²	1	4	yes	—
71	C₂×C₂₉×C₂²⋊Q₈	C₂²	1	4	yes	—
72	C₂×C₂₉×C₂²⋊Q₈	C₂²	1	4	yes	—
73	C₂×C₂₉×C₂²⋊Q₈	C₂²	1	2	yes	—
74	C₂×C₂₉×C₂²⋊Q₈	C₂²	1	4	yes	—
75	C₂×C₂₉×#121	C₂²	1	1	yes	characteristic
76	C₂×C₂₉×#121	C₂²	1	2	yes	—
77	C₂×C₂₉×#121	C₂²	1	2	yes	—
78	C₂×C₂₉×#121	C₂²	1	4	yes	—
79	C₂×C₂₉×#121	C₂²	1	4	yes	—
80	C₂×C₂₉×#121	C₂²	1	4	yes	—
81	C₂×C₂₉×#121	C₂²	1	2	yes	—
82	C₂×C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
83	C₂×C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
84	C₂×C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
85	C₂×C₄×Q₈×C₂₉	C₂²	1	2	yes	—
86	C₂×C₄×Q₈×C₂₉	C₂²	1	2	yes	—
87	C₂×C₄×Q₈×C₂₉	C₂²	1	2	yes	—
88	C₂×C₄×D₄×C₂₉	C₂²	1	2	yes	—
89	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
90	C₂×C₄×D₄×C₂₉	C₂²	1	2	yes	—
91	C₂×C₄×D₄×C₂₉	C₂²	1	2	yes	—
92	C₂×C₄×D₄×C₂₉	C₂²	1	4	yes	—
93	C₂×C₄×D₄×C₂₉	C₂²	1	2	yes	—
94	C₂×C₄×D₄×C₂₉	C₂²	1	2	yes	—
95	C₂×C₄×D₄×C₂₉	C₂²	1	2	yes	—
96	C₂×C₄×D₄×C₂₉	C₂²	1	2	yes	—
97	C₂×C₂₉×#117	C₂²	1	2	yes	—
98	C₂×C₂₉×#117	C₂²	1	2	yes	—
99	C₂²×C₄⋊C₄×C₂₉	C₂²	1	4	yes	—
100	C₂²×C₄²×C₂₉	C₂²	1	1	yes	characteristic
101	C₂×#41×C₂₉	—	4	8	no	—
102	C₂×#41×C₂₉	—	4	8	no	—
103	C₂×#41×C₂₉	C₂³	1	16	yes	—
104	C₂×#41×C₂₉	C₂³	1	16	yes	—
105	C₂²×Q₈×C₂₉	—	4	8	no	—
106	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
107	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₂₉	C₂³	1	2	yes	—
109	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
110	C₂²×Q₈×C₂₉	C₂³	1	2	yes	—
111	C₂²×Q₈×C₂₉	C₂³	1	4	yes	—
112	C₂²×Q₈×C₂₉	C₂³	1	16	yes	—
113	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
114	C₂²×D₄×C₂₉	C₂³	1	2	yes	—
115	C₂²×D₄×C₂₉	C₂³	1	2	yes	—
116	C₂²×D₄×C₂₉	C₂³	1	2	yes	—
117	C₂²×D₄×C₂₉	C₂³	1	2	yes	—
118	C₂²×D₄×C₂₉	C₂³	1	4	yes	—
119	C₂²×D₄×C₂₉	C₂³	1	4	yes	—
120	C₂²×D₄×C₂₉	C₂³	1	4	yes	—
121	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
122	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
123	C₂³×C₄×C₂₉	C₂³	1	2	yes	—
124	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
125	C₂³×C₄×C₂₉	C₂³	1	4	yes	—
126	C₂³×C₄×C₂₉	C₂³	1	4	yes	—
127	C₂³×C₄×C₂₉	C₂³	1	4	yes	—
128	C₂³×C₄×C₂₉	C₂³	1	4	yes	—
129	C₂₉×C₄⋊Q₈	C₂³	1	8	yes	—
130	C₂₉×C₄⋊Q₈	C₂³	1	8	yes	—
131	C₂₉×C₄⋊Q₈	C₂³	1	8	yes	—
132	C₂₉×C₄⋊Q₈	C₂³	1	16	yes	—
133	C₂₉×C₄⋊Q₈	C₂³	1	16	yes	—
134	C₂₉×#127	C₂³	1	8	yes	—
135	C₂₉×#127	C₂³	1	16	yes	—
136	C₂₉×#126	C₂³	1	16	yes	—
137	C₂₉×#126	C₂³	1	32	yes	—
138	C₂₉×#125	C₂³	1	8	yes	—
139	C₂₉×#125	C₂³	1	16	yes	—
140	C₂₉×#125	C₂³	1	32	yes	—
141	C₂₉×#125	C₂³	1	16	yes	—
142	C₂₉×#124	C₂³	1	8	yes	—
143	C₂₉×#124	C₂³	1	16	yes	—
144	C₂₉×#124	C₂³	1	16	yes	—
145	C₂₉×#124	C₂³	1	32	yes	—
146	C₂₉×#124	C₂³	1	16	yes	—
147	C₂₉×#124	C₂³	1	32	yes	—
148	C₂₉×#123	C₂³	1	16	yes	—
149	C₂₉×#123	C₂³	1	32	yes	—
150	C₂₉×#123	C₂³	1	32	yes	—
151	C₂₉×#123	C₂³	1	32	yes	—
152	C₂₉×#123	C₂³	1	32	yes	—
153	C₂₉×#123	C₂³	1	32	yes	—
154	C₂₉×#123	C₂³	1	32	yes	—
155	C₂₉×C₂²⋊Q₈	C₂³	1	8	yes	—
156	C₂₉×C₂²⋊Q₈	C₂³	1	8	yes	—
157	C₂₉×C₂²⋊Q₈	C₂³	1	8	yes	—
158	C₂₉×C₂²⋊Q₈	C₂³	1	16	yes	—
159	C₂₉×C₂²⋊Q₈	C₂³	1	32	yes	—
160	C₂₉×C₂²⋊Q₈	C₂³	1	32	yes	—
161	C₂₉×C₂²⋊Q₈	C₂³	1	32	yes	—
162	C₂₉×C₂²⋊Q₈	C₂³	1	32	yes	—
163	C₂₉×C₂²⋊Q₈	C₂³	1	16	yes	—
164	C₂₉×C₂²⋊Q₈	C₂³	1	32	yes	—
165	C₂₉×#121	C₂³	1	8	yes	—
166	C₂₉×#121	C₂³	1	16	yes	—
167	C₂₉×#121	C₂³	1	16	yes	—
168	C₂₉×#121	C₂³	1	32	yes	—
169	C₂₉×#121	C₂³	1	32	yes	—
170	C₂₉×#121	C₂³	1	32	yes	—
171	C₂₉×#121	C₂³	1	16	yes	—
172	C₄×Q₈×C₂₉	C₂³	1	8	yes	—
173	C₄×Q₈×C₂₉	C₂³	1	8	yes	—
174	C₄×Q₈×C₂₉	C₂³	1	8	yes	—
175	C₄×Q₈×C₂₉	C₂³	1	16	yes	—
176	C₄×Q₈×C₂₉	C₂³	1	16	yes	—
177	C₄×Q₈×C₂₉	C₂³	1	16	yes	—
178	C₄×D₄×C₂₉	C₂³	1	16	yes	—
179	C₄×D₄×C₂₉	C₂³	1	8	yes	—
180	C₄×D₄×C₂₉	C₂³	1	16	yes	—
181	C₄×D₄×C₂₉	C₂³	1	16	yes	—
182	C₄×D₄×C₂₉	C₂³	1	32	yes	—
183	C₄×D₄×C₂₉	C₂³	1	16	yes	—
184	C₄×D₄×C₂₉	C₂³	1	16	yes	—
185	C₄×D₄×C₂₉	C₂³	1	16	yes	—
186	C₄×D₄×C₂₉	C₂³	1	16	yes	—
187	C₂₉×#117	C₂³	1	16	yes	—
188	C₂₉×#117	C₂³	1	16	yes	—
189	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
190	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
191	C₂×C₄⋊C₄×C₂₉	C₂³	1	4	yes	—
192	C₂×C₄⋊C₄×C₂₉	C₂³	1	4	yes	—
193	C₂×C₄⋊C₄×C₂₉	C₂³	1	32	yes	—
194	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
195	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
196	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
197	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
198	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
199	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
200	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
201	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
202	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
203	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
204	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
205	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
206	C₂×C₄⋊C₄×C₂₉	C₂³	1	4	yes	—
207	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
208	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
209	C₂×C₄⋊C₄×C₂₉	C₂³	1	4	yes	—
210	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
211	C₂×C₂²⋊C₄×C₂₉	C₂³	1	2	yes	—
212	C₂×C₂²⋊C₄×C₂₉	C₂³	1	2	yes	—
213	C₂×C₂²⋊C₄×C₂₉	C₂³	1	2	yes	—
214	C₂×C₂²⋊C₄×C₂₉	C₂³	1	2	yes	—
215	C₂×C₂²⋊C₄×C₂₉	C₂³	1	2	yes	—
216	C₂×C₂²⋊C₄×C₂₉	C₂³	1	2	yes	—
217	C₂×C₂²⋊C₄×C₂₉	C₂³	1	4	yes	—
218	C₂×C₂²⋊C₄×C₂₉	C₂³	1	4	yes	—
219	C₂×C₂²⋊C₄×C₂₉	C₂³	1	4	yes	—
220	C₂×C₂²⋊C₄×C₂₉	C₂³	1	4	yes	—
221	C₂×C₂²⋊C₄×C₂₉	C₂³	1	4	yes	—
222	C₂×C₂²⋊C₄×C₂₉	C₂³	1	2	yes	—
223	C₂×C₂²⋊C₄×C₂₉	C₂³	1	4	yes	—
224	C₂×C₂²⋊C₄×C₂₉	C₂³	1	4	yes	—
225	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
226	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
227	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
228	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
229	C₂×C₄²×C₂₉	C₂³	1	8	yes	—
230	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
231	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
232	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
233	C₂×C₄²×C₂₉	C₂³	1	4	yes	—
234	C₂⁴×C₂₉	C₂⁴	1	2	yes	—
235	C₂⁴×C₂₉	C₂⁴	1	1	yes	characteristic
236	C₂⁴×C₂₉	C₂⁴	1	4	yes	—
237	#41×C₂₉	—	4	32	no	—
238	#41×C₂₉	—	4	32	no	—
239	C₂×Q₈×C₂₉	—	2	4	no	—
240	C₂×Q₈×C₂₉	—	2	8	no	—
241	C₂×Q₈×C₂₉	—	2	4	no	—
242	C₂×Q₈×C₂₉	—	2	4	no	—
243	C₂×Q₈×C₂₉	—	4	8	no	—
244	C₂×Q₈×C₂₉	—	4	4	no	—
245	C₂×Q₈×C₂₉	—	4	32	no	—
246	C₂×Q₈×C₂₉	C₂⁴	1	4	yes	—
247	C₂×Q₈×C₂₉	C₂⁴	1	4	yes	—
248	C₂×Q₈×C₂₉	C₂⁴	1	8	yes	—
249	C₂×Q₈×C₂₉	C₂⁴	1	4	yes	—
250	C₂×Q₈×C₂₉	C₂⁴	1	8	yes	—
251	C₂×Q₈×C₂₉	C₂⁴	1	16	yes	—
252	C₂×D₄×C₂₉	—	2	8	no	—
253	C₂×D₄×C₂₉	—	2	4	no	—
254	C₂×D₄×C₂₉	—	2	8	no	—
255	C₂×D₄×C₂₉	—	4	4	no	—
256	C₂×D₄×C₂₉	—	4	4	no	—
257	C₂×D₄×C₂₉	—	4	8	no	—
258	C₂×D₄×C₂₉	—	4	8	no	—
259	C₂×D₄×C₂₉	—	4	8	no	—
260	C₂×D₄×C₂₉	C₂⁴	1	4	yes	—
261	C₂×D₄×C₂₉	C₂⁴	1	8	yes	—
262	C₂×D₄×C₂₉	C₂⁴	1	8	yes	—
263	C₂×D₄×C₂₉	C₂⁴	1	8	yes	—
264	C₂×D₄×C₂₉	C₂⁴	1	8	yes	—
265	C₂×D₄×C₂₉	C₂⁴	1	16	yes	—
266	C₂×D₄×C₂₉	C₂⁴	1	16	yes	—
267	C₂×D₄×C₂₉	C₂⁴	1	16	yes	—
268	C₂²×C₄×C₂₉	—	2	8	no	—
269	C₂²×C₄×C₂₉	—	2	4	no	—
270	C₂²×C₄×C₂₉	—	2	4	no	—
271	C₂²×C₄×C₂₉	—	4	8	no	—
272	C₂²×C₄×C₂₉	—	4	2	no	—
273	C₂²×C₄×C₂₉	—	4	8	no	—
274	C₂²×C₄×C₂₉	—	4	8	no	—
275	C₂²×C₄×C₂₉	—	4	8	no	—
276	C₂²×C₄×C₂₉	C₂⁴	1	4	yes	—
277	C₂²×C₄×C₂₉	C₂⁴	1	4	yes	—
278	C₂²×C₄×C₂₉	C₂⁴	1	8	yes	—
279	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
280	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
281	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
282	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
284	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
285	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
286	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
287	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
288	C₂²×C₄×C₂₉	C₂⁴	1	4	yes	—
289	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
290	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
291	C₂²×C₄×C₂₉	C₂⁴	1	4	yes	—
292	C₂²×C₄×C₂₉	C₂⁴	1	16	yes	—
293	C₂²×C₄×C₂₉	C₂⁴	1	16	yes	—
294	C₂²×C₄×C₂₉	C₂⁴	1	16	yes	—
295	C₂²×C₄×C₂₉	C₂⁴	1	16	yes	—
296	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
297	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
298	C₄⋊C₄×C₂₉	C₂⁴	1	8	yes	—
299	C₄⋊C₄×C₂₉	C₂⁴	1	8	yes	—
300	C₄⋊C₄×C₂₉	C₂⁴	1	16	yes	—
301	C₄⋊C₄×C₂₉	C₂⁴	1	16	yes	—
302	C₄⋊C₄×C₂₉	C₂⁴	1	8	yes	—
303	C₄⋊C₄×C₂₉	C₂⁴	1	8	yes	—
304	C₄⋊C₄×C₂₉	C₂⁴	1	8	yes	—
305	C₄⋊C₄×C₂₉	C₂⁴	1	8	yes	—
306	C₄⋊C₄×C₂₉	C₂⁴	1	4	yes	—
307	C₄⋊C₄×C₂₉	C₂⁴	1	4	yes	—
308	C₄⋊C₄×C₂₉	C₂⁴	1	8	yes	—
309	C₄⋊C₄×C₂₉	C₂⁴	1	8	yes	—
310	C₄⋊C₄×C₂₉	C₂⁴	1	4	yes	—
311	C₄⋊C₄×C₂₉	C₂⁴	1	8	yes	—
312	C₄⋊C₄×C₂₉	C₂⁴	1	4	yes	—
313	C₄⋊C₄×C₂₉	C₂⁴	1	8	yes	—
314	C₄⋊C₄×C₂₉	C₂⁴	1	16	yes	—
315	C₄⋊C₄×C₂₉	C₂⁴	1	8	yes	—
316	C₄⋊C₄×C₂₉	C₂⁴	1	8	yes	—
317	C₄⋊C₄×C₂₉	C₂⁴	1	16	yes	—
318	C₄⋊C₄×C₂₉	C₂⁴	1	8	yes	—
319	C₂²⋊C₄×C₂₉	C₂⁴	1	8	yes	—
320	C₂²⋊C₄×C₂₉	C₂⁴	1	8	yes	—
321	C₂²⋊C₄×C₂₉	C₂⁴	1	8	yes	—
322	C₂²⋊C₄×C₂₉	C₂⁴	1	8	yes	—
323	C₂²⋊C₄×C₂₉	C₂⁴	1	8	yes	—
324	C₂²⋊C₄×C₂₉	C₂⁴	1	8	yes	—
325	C₂²⋊C₄×C₂₉	C₂⁴	1	16	yes	—
326	C₂²⋊C₄×C₂₉	C₂⁴	1	16	yes	—
327	C₂²⋊C₄×C₂₉	C₂⁴	1	16	yes	—
328	C₂²⋊C₄×C₂₉	C₂⁴	1	16	yes	—
329	C₂²⋊C₄×C₂₉	C₂⁴	1	16	yes	—
330	C₂²⋊C₄×C₂₉	C₂⁴	1	8	yes	—
331	C₂²⋊C₄×C₂₉	C₂⁴	1	16	yes	—
332	C₂²⋊C₄×C₂₉	C₂⁴	1	16	yes	—
333	C₄²×C₂₉	C₂⁴	1	4	yes	—
334	C₄²×C₂₉	C₂⁴	1	4	yes	—
335	C₄²×C₂₉	C₂⁴	1	4	yes	—
336	C₄²×C₂₉	C₂⁴	1	4	yes	—
337	C₄²×C₂₉	C₂⁴	1	8	yes	—
338	C₄²×C₂₉	C₂⁴	1	8	yes	—
339	C₄²×C₂₉	C₂⁴	1	8	yes	—
340	C₄²×C₂₉	C₂⁴	1	16	yes	—
341	C₂×#3554	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
342	C₂³×C₂₉	—	2	4	no	—
343	C₂³×C₂₉	—	2	2	no	—
344	C₂³×C₂₉	—	2	8	no	—
345	C₂³×C₂₉	—	2	2	no	—
346	C₂³×C₂₉	—	2	4	no	—
347	C₂³×C₂₉	—	2	8	no	—
348	C₂³×C₂₉	—	2	2	no	—
349	C₂³×C₂₉	—	2	8	no	—
350	C₂³×C₂₉	—	2	4	no	—
351	C₂³×C₂₉	C₂⁵	1	4	yes	—
352	C₂³×C₂₉	C₂⁵	1	2	yes	—
353	C₂³×C₂₉	C₂⁵	1	8	yes	—
354	C₂³×C₂₉	C₂⁵	1	1	yes	characteristic
355	Q₈×C₂₉	—	2	8	no	—
356	Q₈×C₂₉	—	2	16	no	—
357	Q₈×C₂₉	—	2	8	no	—
358	Q₈×C₂₉	—	2	8	no	—
359	Q₈×C₂₉	—	4	16	no	—
360	Q₈×C₂₉	—	4	8	no	—
361	D₄×C₂₉	—	2	16	no	—
362	D₄×C₂₉	—	2	8	no	—
363	D₄×C₂₉	—	2	16	no	—
364	D₄×C₂₉	—	4	8	no	—
365	D₄×C₂₉	—	4	8	no	—
366	D₄×C₂₉	—	4	16	no	—
367	D₄×C₂₉	—	4	16	no	—
368	D₄×C₂₉	—	4	16	no	—
369	C₂×C₄×C₂₉	—	2	2	no	—
370	C₂×C₄×C₂₉	—	2	4	no	—
371	C₂×C₄×C₂₉	—	2	4	no	—
372	C₂×C₄×C₂₉	—	2	8	no	—
373	C₂×C₄×C₂₉	—	2	4	no	—
374	C₂×C₄×C₂₉	—	2	2	no	—
375	C₂×C₄×C₂₉	—	2	4	no	—
376	C₂×C₄×C₂₉	—	2	4	no	—
377	C₂×C₄×C₂₉	—	2	4	no	—
378	C₂×C₄×C₂₉	—	2	2	no	—
379	C₂×C₄×C₂₉	—	2	2	no	—
380	C₂×C₄×C₂₉	—	2	4	no	—
381	C₂×C₄×C₂₉	—	2	16	no	—
382	C₂×C₄×C₂₉	—	2	8	no	—
383	C₂×C₄×C₂₉	—	2	8	no	—
384	C₂×C₄×C₂₉	—	4	16	no	—
385	C₂×C₄×C₂₉	—	4	4	no	—
386	C₂×C₄×C₂₉	—	4	16	no	—
387	C₂×C₄×C₂₉	—	4	16	no	—
388	C₂×C₄×C₂₉	—	4	16	no	—
389	C₂×C₄×C₂₉	H(5,𝔽₂)	1	4	yes	—
390	C₂×C₄×C₂₉	2₋¹⁺⁴	1	4	yes	—
391	C₂×C₄×C₂₉	C₂⁵	1	4	yes	—
392	C₂×C₄×C₂₉	C₂⁵	1	4	yes	—
393	C₂×C₄×C₂₉	C₂⁵	1	2	yes	—
394	C₂×C₄×C₂₉	C₂⁵	1	2	yes	—
395	C₂×C₄×C₂₉	C₂⁵	1	2	yes	—
396	C₂×C₄×C₂₉	C₂⁵	1	2	yes	—
397	C₂×C₄×C₂₉	C₂⁵	1	4	yes	—
398	C₂×C₄×C₂₉	C₂⁵	1	4	yes	—
399	C₂×C₄×C₂₉	C₂⁵	1	4	yes	—
400	C₂×C₄×C₂₉	C₂⁵	1	8	yes	—
401	C₂×C₄×C₂₉	C₂⁵	1	4	yes	—
402	C₂×C₄×C₂₉	C₂⁵	1	4	yes	—
403	C₂×C₄×C₂₉	C₂⁵	1	2	yes	—
404	C₂×C₄×C₂₉	C₂⁵	1	2	yes	—
405	#3554	C₂×C₂₉	1	32	yes	direct product factor
406	C₂×#562	C₂×C₂₉	1	4	yes	complemented
407	C₂×#559	C₂×C₂₉	1	2	yes	complemented
408	C₂×#559	C₂×C₂₉	1	1	yes	characteristic, complemented
409	C₂×#557	C₂×C₂₉	1	1	yes	characteristic, complemented
410	C₂×#554	C₂×C₂₉	1	2	yes	complemented
411	C₂×#550	C₂×C₂₉	1	1	yes	characteristic, complemented
412	C₂×D₄×Q₈	C₂×C₂₉	1	1	yes	characteristic, complemented
413	C₂×#548	C₂×C₂₉	1	2	yes	complemented
414	C₂×#547	C₂×C₂₉	1	2	yes	complemented
415	C₂×#542	C₂×C₂₉	1	2	yes	complemented
416	C₂×#542	C₂×C₂₉	1	2	yes	complemented
417	C₂×#540	C₂×C₂₉	1	2	yes	complemented
418	C₂×#539	C₂×C₂₉	1	4	yes	complemented
419	C₂×#536	C₂×C₂₉	1	2	yes	complemented
420	C₂×#533	C₂×C₂₉	1	1	yes	characteristic, complemented
421	C₂×#532	C₂×C₂₉	1	1	yes	characteristic, complemented
422	C₂×#529	C₂×C₂₉	1	1	yes	characteristic, complemented
423	C₂²×C₂₉	—	2	4	no	—
424	C₂²×C₂₉	—	2	2	no	—
425	C₂²×C₂₉	—	2	8	no	—
426	C₂²×C₂₉	—	2	2	no	—
427	C₂²×C₂₉	—	2	4	no	—
428	C₂²×C₂₉	—	2	8	no	—
429	C₂²×C₂₉	—	2	2	no	—
430	C₂²×C₂₉	—	2	8	no	—
431	C₂²×C₂₉	—	2	4	no	—
432	C₂²×C₂₉	—	4	8	no	—
433	C₂²×C₂₉	—	4	4	no	—
434	C₂²×C₂₉	—	4	16	no	—
435	C₂²×C₂₉	C₂×H(5,𝔽₂)	1	2	yes	—
436	C₂²×C₂₉	C₂×2₋¹⁺⁴	1	2	yes	—
437	C₂²×C₂₉	#585	1	2	yes	—
438	C₂²×C₂₉	C₂⁶	1	1	yes	characteristic
439	C₄×C₂₉	—	2	2	no	—
440	C₄×C₂₉	—	2	4	no	—
441	C₄×C₂₉	—	2	4	no	—
442	C₄×C₂₉	—	2	8	no	—
443	C₄×C₂₉	—	2	4	no	—
444	C₄×C₂₉	—	2	2	no	—
445	C₄×C₂₉	—	2	4	no	—
446	C₄×C₂₉	—	2	4	no	—
447	C₄×C₂₉	—	2	4	no	—
448	C₄×C₂₉	—	2	2	no	—
449	C₄×C₂₉	—	2	2	no	—
450	C₄×C₂₉	—	2	4	no	—
451	C₄×C₂₉	C₂×H(5,𝔽₂)	1	4	yes	—
452	C₄×C₂₉	C₂×2₋¹⁺⁴	1	4	yes	—
453	C₂²×#41	C₂²×C₂₉	1	2	yes	—
454	C₂²×#41	C₂²×C₂₉	1	2	yes	—
455	C₂³×Q₈	C₂²×C₂₉	1	2	yes	—
456	#562	C₂²×C₂₉	1	64	yes	complemented
457	#559	C₂²×C₂₉	1	32	yes	complemented
458	#559	C₂²×C₂₉	1	16	yes	complemented
459	#557	C₂²×C₂₉	1	16	yes	complemented
460	#554	C₂²×C₂₉	1	32	yes	complemented
461	#550	C₂²×C₂₉	1	16	yes	complemented
462	D₄×Q₈	C₂²×C₂₉	1	16	yes	complemented
463	#548	C₂²×C₂₉	1	32	yes	complemented
464	#547	C₂²×C₂₉	1	32	yes	complemented
465	#542	C₂²×C₂₉	1	32	yes	complemented
466	#542	C₂²×C₂₉	1	32	yes	complemented
467	#540	C₂²×C₂₉	1	32	yes	complemented
468	#539	C₂²×C₂₉	1	64	yes	complemented
469	#536	C₂²×C₂₉	1	32	yes	complemented
470	#533	C₂²×C₂₉	1	16	yes	complemented
471	#532	C₂²×C₂₉	1	16	yes	complemented
472	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
473	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
474	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
475	C₂×C₄⋊Q₈	C₂²×C₂₉	1	2	yes	—
476	C₂×C₄⋊Q₈	C₂²×C₂₉	1	2	yes	—
477	C₂×#127	C₂²×C₂₉	1	1	yes	characteristic
478	C₂×#127	C₂²×C₂₉	1	2	yes	—
479	#529	C₂²×C₂₉	1	16	yes	complemented
480	C₂×#126	C₂²×C₂₉	1	2	yes	—
481	C₂×#126	C₂²×C₂₉	1	4	yes	—
482	C₂×#125	C₂²×C₂₉	1	1	yes	characteristic
483	C₂×#125	C₂²×C₂₉	1	2	yes	—
484	C₂×#125	C₂²×C₂₉	1	4	yes	—
485	C₂×#125	C₂²×C₂₉	1	2	yes	—
486	C₂×#124	C₂²×C₂₉	1	1	yes	characteristic
487	C₂×#124	C₂²×C₂₉	1	2	yes	—
488	C₂×#124	C₂²×C₂₉	1	2	yes	—
489	C₂×#124	C₂²×C₂₉	1	4	yes	—
490	C₂×#124	C₂²×C₂₉	1	2	yes	—
491	C₂×#124	C₂²×C₂₉	1	4	yes	—
492	C₂×#123	C₂²×C₂₉	1	2	yes	—
493	C₂×#123	C₂²×C₂₉	1	4	yes	—
494	C₂×#123	C₂²×C₂₉	1	4	yes	—
495	C₂×#123	C₂²×C₂₉	1	4	yes	—
496	C₂×#123	C₂²×C₂₉	1	4	yes	—
497	C₂×#123	C₂²×C₂₉	1	4	yes	—
498	C₂×#123	C₂²×C₂₉	1	4	yes	—
499	C₂×C₂²⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
500	C₂×C₂²⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
501	C₂×C₂²⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
502	C₂×C₂²⋊Q₈	C₂²×C₂₉	1	2	yes	—
503	C₂×C₂²⋊Q₈	C₂²×C₂₉	1	4	yes	—
504	C₂×C₂²⋊Q₈	C₂²×C₂₉	1	4	yes	—
505	C₂×C₂²⋊Q₈	C₂²×C₂₉	1	4	yes	—
506	C₂×C₂²⋊Q₈	C₂²×C₂₉	1	4	yes	—
507	C₂×C₂²⋊Q₈	C₂²×C₂₉	1	2	yes	—
508	C₂×C₂²⋊Q₈	C₂²×C₂₉	1	4	yes	—
509	C₂×#121	C₂²×C₂₉	1	1	yes	characteristic
510	C₂×#121	C₂²×C₂₉	1	2	yes	—
511	C₂×#121	C₂²×C₂₉	1	2	yes	—
512	C₂×#121	C₂²×C₂₉	1	4	yes	—
513	C₂×#121	C₂²×C₂₉	1	4	yes	—
514	C₂×#121	C₂²×C₂₉	1	4	yes	—
515	C₂×#121	C₂²×C₂₉	1	2	yes	—
516	C₂×C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
517	C₂×C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
518	C₂×C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
519	C₂×C₄×Q₈	C₂²×C₂₉	1	2	yes	—
520	C₂×C₄×Q₈	C₂²×C₂₉	1	2	yes	—
521	C₂×C₄×Q₈	C₂²×C₂₉	1	2	yes	—
522	C₂×C₄×D₄	C₂²×C₂₉	1	2	yes	—
523	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
524	C₂×C₄×D₄	C₂²×C₂₉	1	2	yes	—
525	C₂×C₄×D₄	C₂²×C₂₉	1	2	yes	—
526	C₂×C₄×D₄	C₂²×C₂₉	1	4	yes	—
527	C₂×C₄×D₄	C₂²×C₂₉	1	2	yes	—
528	C₂×C₄×D₄	C₂²×C₂₉	1	2	yes	—
529	C₂×C₄×D₄	C₂²×C₂₉	1	2	yes	—
530	C₂×C₄×D₄	C₂²×C₂₉	1	2	yes	—
531	C₂×#117	C₂²×C₂₉	1	2	yes	—
532	C₂×#117	C₂²×C₂₉	1	2	yes	—
533	C₂²×C₄⋊C₄	C₂²×C₂₉	1	4	yes	—
534	C₂²×C₄²	C₂²×C₂₉	1	1	yes	characteristic
535	C₂×C₂₉	—	4	4	no	—
536	C₂×C₂₉	—	4	2	no	—
537	C₂×C₂₉	—	4	8	no	—
538	C₂×C₂₉	#3554	1	4	yes	direct product factor
539	C₂×C₂₉	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
540	C₂×C₂₉	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
541	C₂×C₂₉	C₂×#585	1	1	yes	characteristic
542	C₂×#41	—	4	8	no	—
543	C₂×#41	—	4	8	no	—
544	C₂×#41	C₂³×C₂₉	1	16	yes	—
545	C₂×#41	C₂³×C₂₉	1	16	yes	—
546	C₂²×Q₈	—	4	8	no	—
547	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
548	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
549	C₂²×Q₈	C₂³×C₂₉	1	2	yes	—
550	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
551	C₂²×Q₈	C₂³×C₂₉	1	2	yes	—
552	C₂²×Q₈	C₂³×C₂₉	1	4	yes	—
553	C₂²×Q₈	C₂³×C₂₉	1	16	yes	—
554	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
555	C₂²×D₄	C₂³×C₂₉	1	2	yes	—
556	C₂²×D₄	C₂³×C₂₉	1	2	yes	—
557	C₂²×D₄	C₂³×C₂₉	1	2	yes	—
558	C₂²×D₄	C₂³×C₂₉	1	2	yes	—
559	C₂²×D₄	C₂³×C₂₉	1	4	yes	—
560	C₂²×D₄	C₂³×C₂₉	1	4	yes	—
561	C₂²×D₄	C₂³×C₂₉	1	4	yes	—
562	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
563	C₂³×C₄	C₂³×C₂₉	1	2	yes	—
564	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
565	C₂³×C₄	C₂³×C₂₉	1	4	yes	—
566	C₂³×C₄	C₂³×C₂₉	1	4	yes	—
567	C₂³×C₄	C₂³×C₂₉	1	4	yes	—
568	C₂³×C₄	C₂³×C₂₉	1	4	yes	—
569	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
570	C₄⋊Q₈	C₂³×C₂₉	1	8	yes	—
571	C₄⋊Q₈	C₂³×C₂₉	1	8	yes	—
572	C₄⋊Q₈	C₂³×C₂₉	1	8	yes	—
573	C₄⋊Q₈	C₂³×C₂₉	1	16	yes	—
574	C₄⋊Q₈	C₂³×C₂₉	1	16	yes	—
575	#127	C₂³×C₂₉	1	8	yes	—
576	#127	C₂³×C₂₉	1	16	yes	—
577	#126	C₂³×C₂₉	1	16	yes	—
578	#126	C₂³×C₂₉	1	32	yes	—
579	#125	C₂³×C₂₉	1	8	yes	—
580	#125	C₂³×C₂₉	1	16	yes	—
581	#125	C₂³×C₂₉	1	32	yes	—
582	#125	C₂³×C₂₉	1	16	yes	—
583	#124	C₂³×C₂₉	1	8	yes	—
584	#124	C₂³×C₂₉	1	16	yes	—
585	#124	C₂³×C₂₉	1	16	yes	—
586	#124	C₂³×C₂₉	1	32	yes	—
587	#124	C₂³×C₂₉	1	16	yes	—
588	#124	C₂³×C₂₉	1	32	yes	—
589	#123	C₂³×C₂₉	1	16	yes	—
590	#123	C₂³×C₂₉	1	32	yes	—
591	#123	C₂³×C₂₉	1	32	yes	—
592	#123	C₂³×C₂₉	1	32	yes	—
593	#123	C₂³×C₂₉	1	32	yes	—
594	#123	C₂³×C₂₉	1	32	yes	—
595	#123	C₂³×C₂₉	1	32	yes	—
596	C₂²⋊Q₈	C₂³×C₂₉	1	8	yes	—
597	C₂²⋊Q₈	C₂³×C₂₉	1	8	yes	—
598	C₂²⋊Q₈	C₂³×C₂₉	1	8	yes	—
599	C₂²⋊Q₈	C₂³×C₂₉	1	16	yes	—
600	C₂²⋊Q₈	C₂³×C₂₉	1	32	yes	—
601	C₂²⋊Q₈	C₂³×C₂₉	1	32	yes	—
602	C₂²⋊Q₈	C₂³×C₂₉	1	32	yes	—
603	C₂²⋊Q₈	C₂³×C₂₉	1	32	yes	—
604	C₂²⋊Q₈	C₂³×C₂₉	1	16	yes	—
605	C₂²⋊Q₈	C₂³×C₂₉	1	32	yes	—
606	#121	C₂³×C₂₉	1	8	yes	—
607	#121	C₂³×C₂₉	1	16	yes	—
608	#121	C₂³×C₂₉	1	16	yes	—
609	#121	C₂³×C₂₉	1	32	yes	—
610	#121	C₂³×C₂₉	1	32	yes	—
611	#121	C₂³×C₂₉	1	32	yes	—
612	#121	C₂³×C₂₉	1	16	yes	—
613	C₄×Q₈	C₂³×C₂₉	1	8	yes	—
614	C₄×Q₈	C₂³×C₂₉	1	8	yes	—
615	C₄×Q₈	C₂³×C₂₉	1	8	yes	—
616	C₄×Q₈	C₂³×C₂₉	1	16	yes	—
617	C₄×Q₈	C₂³×C₂₉	1	16	yes	—
618	C₄×Q₈	C₂³×C₂₉	1	16	yes	—
619	C₄×D₄	C₂³×C₂₉	1	16	yes	—
620	C₄×D₄	C₂³×C₂₉	1	8	yes	—
621	C₄×D₄	C₂³×C₂₉	1	16	yes	—
622	C₄×D₄	C₂³×C₂₉	1	16	yes	—
623	C₄×D₄	C₂³×C₂₉	1	32	yes	—
624	C₄×D₄	C₂³×C₂₉	1	16	yes	—
625	C₄×D₄	C₂³×C₂₉	1	16	yes	—
626	C₄×D₄	C₂³×C₂₉	1	16	yes	—
627	C₄×D₄	C₂³×C₂₉	1	16	yes	—
628	#117	C₂³×C₂₉	1	16	yes	—
629	#117	C₂³×C₂₉	1	16	yes	—
630	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
631	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
632	C₂×C₄⋊C₄	C₂³×C₂₉	1	4	yes	—
633	C₂×C₄⋊C₄	C₂³×C₂₉	1	4	yes	—
634	C₂×C₄⋊C₄	C₂³×C₂₉	1	32	yes	—
635	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
636	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
637	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
638	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
639	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
640	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
641	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
642	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
643	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
644	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
645	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
646	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
647	C₂×C₄⋊C₄	C₂³×C₂₉	1	4	yes	—
648	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
649	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
650	C₂×C₄⋊C₄	C₂³×C₂₉	1	4	yes	—
651	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
652	C₂×C₂²⋊C₄	C₂³×C₂₉	1	2	yes	—
653	C₂×C₂²⋊C₄	C₂³×C₂₉	1	2	yes	—
654	C₂×C₂²⋊C₄	C₂³×C₂₉	1	2	yes	—
655	C₂×C₂²⋊C₄	C₂³×C₂₉	1	2	yes	—
656	C₂×C₂²⋊C₄	C₂³×C₂₉	1	2	yes	—
657	C₂×C₂²⋊C₄	C₂³×C₂₉	1	2	yes	—
658	C₂×C₂²⋊C₄	C₂³×C₂₉	1	4	yes	—
659	C₂×C₂²⋊C₄	C₂³×C₂₉	1	4	yes	—
660	C₂×C₂²⋊C₄	C₂³×C₂₉	1	4	yes	—
661	C₂×C₂²⋊C₄	C₂³×C₂₉	1	4	yes	—
662	C₂×C₂²⋊C₄	C₂³×C₂₉	1	4	yes	—
663	C₂×C₂²⋊C₄	C₂³×C₂₉	1	2	yes	—
664	C₂×C₂²⋊C₄	C₂³×C₂₉	1	4	yes	—
665	C₂×C₂²⋊C₄	C₂³×C₂₉	1	4	yes	—
666	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
667	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
668	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
669	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
670	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
671	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
672	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
673	C₂×C₄²	C₂³×C₂₉	1	4	yes	—
674	C₂×C₄²	C₂³×C₂₉	1	8	yes	—
675	C₂₉	C₂×#3554	1	1	yes	characteristic, direct product factor, Sylow
676	C₂⁴	C₂⁴×C₂₉	1	2	yes	—
677	C₂⁴	C₂⁴×C₂₉	1	1	yes	characteristic
678	C₂⁴	C₂⁴×C₂₉	1	4	yes	—
679	#41	—	4	32	no	—
680	#41	—	4	32	no	—
681	C₂×Q₈	—	2	4	no	—
682	C₂×Q₈	—	2	8	no	—
683	C₂×Q₈	—	2	4	no	—
684	C₂×Q₈	—	2	4	no	—
685	C₂×Q₈	—	4	8	no	—
686	C₂×Q₈	—	4	4	no	—
687	C₂×Q₈	—	4	32	no	—
688	C₂×Q₈	C₂⁴×C₂₉	1	4	yes	—
689	C₂×Q₈	C₂⁴×C₂₉	1	4	yes	—
690	C₂×Q₈	C₂⁴×C₂₉	1	8	yes	—
691	C₂×Q₈	C₂⁴×C₂₉	1	4	yes	—
692	C₂×Q₈	C₂⁴×C₂₉	1	8	yes	—
693	C₂×Q₈	C₂⁴×C₂₉	1	16	yes	—
694	C₂×D₄	—	2	8	no	—
695	C₂×D₄	—	2	4	no	—
696	C₂×D₄	—	2	8	no	—
697	C₂×D₄	—	4	8	no	—
698	C₂×D₄	—	4	8	no	—
699	C₂×D₄	—	4	4	no	—
700	C₂×D₄	—	4	4	no	—
701	C₂×D₄	—	4	8	no	—
702	C₂×D₄	C₂⁴×C₂₉	1	4	yes	—
703	C₂×D₄	C₂⁴×C₂₉	1	8	yes	—
704	C₂×D₄	C₂⁴×C₂₉	1	8	yes	—
705	C₂×D₄	C₂⁴×C₂₉	1	8	yes	—
706	C₂×D₄	C₂⁴×C₂₉	1	8	yes	—
707	C₂×D₄	C₂⁴×C₂₉	1	16	yes	—
708	C₂×D₄	C₂⁴×C₂₉	1	16	yes	—
709	C₂×D₄	C₂⁴×C₂₉	1	16	yes	—
710	C₂²×C₄	—	2	8	no	—
711	C₂²×C₄	—	2	4	no	—
712	C₂²×C₄	—	2	4	no	—
713	C₂²×C₄	—	4	8	no	—
714	C₂²×C₄	—	4	8	no	—
715	C₂²×C₄	—	4	8	no	—
716	C₂²×C₄	—	4	8	no	—
717	C₂²×C₄	—	4	2	no	—
718	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
719	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
720	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
721	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
722	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
723	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
724	C₂²×C₄	C₂⁴×C₂₉	1	4	yes	—
725	C₂²×C₄	C₂⁴×C₂₉	1	4	yes	—
726	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
727	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
728	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
729	C₂²×C₄	C₂⁴×C₂₉	1	4	yes	—
730	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
731	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
732	C₂²×C₄	C₂⁴×C₂₉	1	8	yes	—
733	C₂²×C₄	C₂⁴×C₂₉	1	4	yes	—
734	C₂²×C₄	C₂⁴×C₂₉	1	16	yes	—
735	C₂²×C₄	C₂⁴×C₂₉	1	16	yes	—
736	C₂²×C₄	C₂⁴×C₂₉	1	16	yes	—
737	C₂²×C₄	C₂⁴×C₂₉	1	16	yes	—
738	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
739	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
740	C₄⋊C₄	C₂⁴×C₂₉	1	8	yes	—
741	C₄⋊C₄	C₂⁴×C₂₉	1	8	yes	—
742	C₄⋊C₄	C₂⁴×C₂₉	1	16	yes	—
743	C₄⋊C₄	C₂⁴×C₂₉	1	16	yes	—
744	C₄⋊C₄	C₂⁴×C₂₉	1	8	yes	—
745	C₄⋊C₄	C₂⁴×C₂₉	1	8	yes	—
746	C₄⋊C₄	C₂⁴×C₂₉	1	8	yes	—
747	C₄⋊C₄	C₂⁴×C₂₉	1	8	yes	—
748	C₄⋊C₄	C₂⁴×C₂₉	1	4	yes	—
749	C₄⋊C₄	C₂⁴×C₂₉	1	4	yes	—
750	C₄⋊C₄	C₂⁴×C₂₉	1	8	yes	—
751	C₄⋊C₄	C₂⁴×C₂₉	1	8	yes	—
752	C₄⋊C₄	C₂⁴×C₂₉	1	4	yes	—
753	C₄⋊C₄	C₂⁴×C₂₉	1	8	yes	—
754	C₄⋊C₄	C₂⁴×C₂₉	1	4	yes	—
755	C₄⋊C₄	C₂⁴×C₂₉	1	8	yes	—
756	C₄⋊C₄	C₂⁴×C₂₉	1	16	yes	—
757	C₄⋊C₄	C₂⁴×C₂₉	1	8	yes	—
758	C₄⋊C₄	C₂⁴×C₂₉	1	8	yes	—
759	C₄⋊C₄	C₂⁴×C₂₉	1	16	yes	—
760	C₄⋊C₄	C₂⁴×C₂₉	1	8	yes	—
761	C₂²⋊C₄	C₂⁴×C₂₉	1	8	yes	—
762	C₂²⋊C₄	C₂⁴×C₂₉	1	8	yes	—
763	C₂²⋊C₄	C₂⁴×C₂₉	1	8	yes	—
764	C₂²⋊C₄	C₂⁴×C₂₉	1	8	yes	—
765	C₂²⋊C₄	C₂⁴×C₂₉	1	8	yes	—
766	C₂²⋊C₄	C₂⁴×C₂₉	1	8	yes	—
767	C₂²⋊C₄	C₂⁴×C₂₉	1	16	yes	—
768	C₂²⋊C₄	C₂⁴×C₂₉	1	16	yes	—
769	C₂²⋊C₄	C₂⁴×C₂₉	1	16	yes	—
770	C₂²⋊C₄	C₂⁴×C₂₉	1	16	yes	—
771	C₂²⋊C₄	C₂⁴×C₂₉	1	16	yes	—
772	C₂²⋊C₄	C₂⁴×C₂₉	1	8	yes	—
773	C₂²⋊C₄	C₂⁴×C₂₉	1	16	yes	—
774	C₂²⋊C₄	C₂⁴×C₂₉	1	16	yes	—
775	C₄²	C₂⁴×C₂₉	1	4	yes	—
776	C₄²	C₂⁴×C₂₉	1	4	yes	—
777	C₄²	C₂⁴×C₂₉	1	4	yes	—
778	C₄²	C₂⁴×C₂₉	1	4	yes	—
779	C₄²	C₂⁴×C₂₉	1	8	yes	—
780	C₄²	C₂⁴×C₂₉	1	8	yes	—
781	C₄²	C₂⁴×C₂₉	1	8	yes	—
782	C₄²	C₂⁴×C₂₉	1	16	yes	—
783	C₂³	—	2	4	no	—
784	C₂³	—	2	2	no	—
785	C₂³	—	2	8	no	—
786	C₂³	—	2	2	no	—
787	C₂³	—	2	4	no	—
788	C₂³	—	2	8	no	—
789	C₂³	—	2	2	no	—
790	C₂³	—	2	8	no	—
791	C₂³	—	2	4	no	—
792	C₂³	C₂⁵×C₂₉	1	4	yes	—
793	C₂³	C₂⁵×C₂₉	1	2	yes	—
794	C₂³	C₂⁵×C₂₉	1	8	yes	—
795	C₂³	C₂⁵×C₂₉	1	1	yes	characteristic
796	Q₈	—	2	8	no	—
797	Q₈	—	2	16	no	—
798	Q₈	—	2	8	no	—
799	Q₈	—	2	8	no	—
800	Q₈	—	4	16	no	—
801	Q₈	—	4	8	no	—
802	D₄	—	2	16	no	—
803	D₄	—	2	8	no	—
804	D₄	—	2	16	no	—
805	D₄	—	4	16	no	—
806	D₄	—	4	16	no	—
807	D₄	—	4	8	no	—
808	D₄	—	4	8	no	—
809	D₄	—	4	16	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	4	no	—
812	C₂×C₄	—	2	4	no	—
813	C₂×C₄	—	2	8	no	—
814	C₂×C₄	—	2	4	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	4	no	—
817	C₂×C₄	—	2	4	no	—
818	C₂×C₄	—	2	4	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	4	no	—
822	C₂×C₄	—	2	16	no	—
823	C₂×C₄	—	2	8	no	—
824	C₂×C₄	—	2	8	no	—
825	C₂×C₄	—	4	16	no	—
826	C₂×C₄	—	4	16	no	—
827	C₂×C₄	—	4	16	no	—
828	C₂×C₄	—	4	16	no	—
829	C₂×C₄	—	4	4	no	—
830	C₂×C₄	C₂₉×H(5,𝔽₂)	1	4	yes	—
831	C₂×C₄	C₂₉×2₋¹⁺⁴	1	4	yes	—
832	C₂×C₄	C₂⁵×C₂₉	1	4	yes	—
833	C₂×C₄	C₂⁵×C₂₉	1	4	yes	—
834	C₂×C₄	C₂⁵×C₂₉	1	2	yes	—
835	C₂×C₄	C₂⁵×C₂₉	1	2	yes	—
836	C₂×C₄	C₂⁵×C₂₉	1	2	yes	—
837	C₂×C₄	C₂⁵×C₂₉	1	2	yes	—
838	C₂×C₄	C₂⁵×C₂₉	1	4	yes	—
839	C₂×C₄	C₂⁵×C₂₉	1	4	yes	—
840	C₂×C₄	C₂⁵×C₂₉	1	4	yes	—
841	C₂×C₄	C₂⁵×C₂₉	1	8	yes	—
842	C₂×C₄	C₂⁵×C₂₉	1	4	yes	—
843	C₂×C₄	C₂⁵×C₂₉	1	4	yes	—
844	C₂×C₄	C₂⁵×C₂₉	1	2	yes	—
845	C₂×C₄	C₂⁵×C₂₉	1	2	yes	—
846	C₂²	—	2	4	no	—
847	C₂²	—	2	2	no	—
848	C₂²	—	2	8	no	—
849	C₂²	—	2	2	no	—
850	C₂²	—	2	4	no	—
851	C₂²	—	2	8	no	—
852	C₂²	—	2	2	no	—
853	C₂²	—	2	8	no	—
854	C₂²	—	2	4	no	—
855	C₂²	—	4	8	no	—
856	C₂²	—	4	4	no	—
857	C₂²	—	4	16	no	—
858	C₂²	C₂×C₂₉×H(5,𝔽₂)	1	2	yes	—
859	C₂²	C₂×C₂₉×2₋¹⁺⁴	1	2	yes	—
860	C₂²	C₂₉×#585	1	2	yes	—
861	C₂²	C₂⁶×C₂₉	1	1	yes	characteristic
862	C₄	—	2	2	no	—
863	C₄	—	2	4	no	—
864	C₄	—	2	4	no	—
865	C₄	—	2	8	no	—
866	C₄	—	2	4	no	—
867	C₄	—	2	2	no	—
868	C₄	—	2	4	no	—
869	C₄	—	2	4	no	—
870	C₄	—	2	4	no	—
871	C₄	—	2	2	no	—
872	C₄	—	2	2	no	—
873	C₄	—	2	4	no	—
874	C₄	C₂×C₂₉×H(5,𝔽₂)	1	4	yes	—
875	C₄	C₂×C₂₉×2₋¹⁺⁴	1	4	yes	—
876	C₂	—	4	4	no	—
877	C₂	—	4	2	no	—
878	C₂	—	4	8	no	—
879	C₂	C₂₉×#3554	1	4	yes	direct product factor
880	C₂	C₂²×C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
881	C₂	C₂²×C₂₉×2₋¹⁺⁴	1	1	yes	characteristic
882	C₂	C₂×C₂₉×#585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₉	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₂₉
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₉×#3554	C₂	direct (N × H)
2. C₂×C₂₉×#562	C₂	semidirect
3. C₂×C₂₉×#559	C₂	semidirect
4. C₂×C₂₉×#559	C₂	semidirect
5. C₂×C₂₉×#557	C₂	semidirect
6. C₂×C₂₉×#554	C₂	semidirect
7. C₂×C₂₉×#550	C₂	semidirect
8. C₂×D₄×Q₈×C₂₉	C₂	semidirect
9. C₂×C₂₉×#548	C₂	semidirect
10. C₂×C₂₉×#547	C₂	semidirect
11. C₂×C₂₉×#542	C₂	semidirect
12. C₂×C₂₉×#542	C₂	semidirect
13. C₂×C₂₉×#540	C₂	semidirect
14. C₂×C₂₉×#539	C₂	semidirect
15. C₂×C₂₉×#536	C₂	semidirect
16. C₂×C₂₉×#533	C₂	semidirect
17. C₂×C₂₉×#532	C₂	semidirect
18. C₂×C₂₉×#529	C₂	semidirect
22. C₂₉×#562	C₂²	semidirect
23. C₂₉×#559	C₂²	semidirect
24. C₂₉×#559	C₂²	semidirect
25. C₂₉×#557	C₂²	semidirect
26. C₂₉×#554	C₂²	semidirect
27. C₂₉×#550	C₂²	semidirect
28. D₄×Q₈×C₂₉	C₂²	semidirect
29. C₂₉×#548	C₂²	semidirect
30. C₂₉×#547	C₂²	semidirect
31. C₂₉×#542	C₂²	semidirect
32. C₂₉×#542	C₂²	semidirect
33. C₂₉×#540	C₂²	semidirect
34. C₂₉×#539	C₂²	semidirect
35. C₂₉×#536	C₂²	semidirect
36. C₂₉×#533	C₂²	semidirect
37. C₂₉×#532	C₂²	semidirect
45. C₂₉×#529	C₂²	semidirect
341. C₂×#3554	C₂₉	direct (N × H)
405. #3554	C₂×C₂₉	direct (N × H)
406. C₂×#562	C₂×C₂₉	semidirect
407. C₂×#559	C₂×C₂₉	semidirect
408. C₂×#559	C₂×C₂₉	semidirect
409. C₂×#557	C₂×C₂₉	semidirect
410. C₂×#554	C₂×C₂₉	semidirect
411. C₂×#550	C₂×C₂₉	semidirect
412. C₂×D₄×Q₈	C₂×C₂₉	semidirect
413. C₂×#548	C₂×C₂₉	semidirect
414. C₂×#547	C₂×C₂₉	semidirect
415. C₂×#542	C₂×C₂₉	semidirect
416. C₂×#542	C₂×C₂₉	semidirect
417. C₂×#540	C₂×C₂₉	semidirect
418. C₂×#539	C₂×C₂₉	semidirect
419. C₂×#536	C₂×C₂₉	semidirect
420. C₂×#533	C₂×C₂₉	semidirect
421. C₂×#532	C₂×C₂₉	semidirect
422. C₂×#529	C₂×C₂₉	semidirect
456. #562	C₂²×C₂₉	semidirect
457. #559	C₂²×C₂₉	semidirect
458. #559	C₂²×C₂₉	semidirect
459. #557	C₂²×C₂₉	semidirect
460. #554	C₂²×C₂₉	semidirect
461. #550	C₂²×C₂₉	semidirect
462. D₄×Q₈	C₂²×C₂₉	semidirect
463. #548	C₂²×C₂₉	semidirect
464. #547	C₂²×C₂₉	semidirect
465. #542	C₂²×C₂₉	semidirect
466. #542	C₂²×C₂₉	semidirect
467. #540	C₂²×C₂₉	semidirect
468. #539	C₂²×C₂₉	semidirect
469. #536	C₂²×C₂₉	semidirect
470. #533	C₂²×C₂₉	semidirect
471. #532	C₂²×C₂₉	semidirect
479. #529	C₂²×C₂₉	semidirect
538. C₂×C₂₉	#3554	direct (N × H)
675. C₂₉	C₂×#3554	direct (N × H)
879. C₂	C₂₉×#3554	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×#3554	2
C₂×C₂₉×#562	2
C₂×C₂₉×#559	2
C₂×C₂₉×#557	2
C₂×C₂₉×#554	2
C₂×C₂₉×#550	2
C₂×D₄×Q₈×C₂₉	2
C₂×C₂₉×#548	2
C₂×C₂₉×#547	2
C₂×C₂₉×#542	2
C₂×C₂₉×#540	2
C₂×C₂₉×#539	2
C₂×C₂₉×#536	2
C₂×C₂₉×#533	2
C₂×C₂₉×#532	2
C₂×C₂₉×#529	2
C₂×#3554	29

Subgroups — C2×C29×#3554 #20357646

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₉×#3554 #20357646