Subgroups — C₂×C₂₉×#3545 #20357653

Order 7424.

7430 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3545	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₂₉×#563	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₉×#562	C₂	1	2	yes	maximal, complemented
4	C₂×C₂₉×H(3,𝔽₄)	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₂₉×#555	C₂	1	2	yes	maximal, complemented
6	C₂×C₂₉×#551	C₂	1	2	yes	maximal, complemented
7	C₂×C₂₉×#551	C₂	1	4	yes	maximal, complemented
8	C₂×C₂₉×#546	C₂	1	4	yes	maximal, complemented
9	C₂×C₂₉×#542	C₂	1	4	yes	maximal, complemented
10	C₂×C₂₉×#538	C₂	1	4	yes	maximal, complemented
11	C₂×C₂₉×#536	C₂	1	2	yes	maximal, complemented
12	C₂×C₂₉×#534	C₂	1	2	yes	maximal, complemented
13	C₂×C₂₉×#529	C₂	1	2	yes	maximal, complemented
14	C₂²×C₂₉×#124	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#41×C₂₉	C₂²	1	2	yes	—
16	C₂³×Q₈×C₂₉	C₂²	1	1	yes	characteristic, complemented
17	C₂³×D₄×C₂₉	C₂²	1	1	yes	characteristic
18	C₂³×D₄×C₂₉	C₂²	1	2	yes	complemented
19	C₂₉×#563	C₂²	1	16	yes	complemented
20	C₂₉×#562	C₂²	1	32	yes	complemented
21	C₂₉×H(3,𝔽₄)	C₂²	1	16	yes	complemented
22	C₂₉×#555	C₂²	1	32	yes	complemented
23	C₂₉×#551	C₂²	1	32	yes	complemented
24	C₂₉×#551	C₂²	1	64	yes	complemented
25	C₂₉×#546	C₂²	1	64	yes	complemented
26	C₂₉×#542	C₂²	1	64	yes	complemented
27	C₂₉×#538	C₂²	1	64	yes	complemented
28	C₂₉×#536	C₂²	1	32	yes	complemented
29	C₂₉×#534	C₂²	1	32	yes	complemented
30	C₂×C₂₉×C₄⋊Q₈	C₂²	1	2	yes	complemented
31	C₂×C₂₉×C₄⋊Q₈	C₂²	1	2	yes	complemented
32	C₂₉×#529	C₂²	1	32	yes	complemented
33	C₂×C₂₉×#126	C₂²	1	4	yes	complemented
34	C₂×C₂₉×#126	C₂²	1	4	yes	complemented
35	C₂×C₂₉×#126	C₂²	1	4	yes	complemented
36	C₂×C₂₉×#125	C₂²	1	2	yes	complemented
37	C₂×C₂₉×#124	C₂²	1	1	yes	characteristic
38	C₂×C₂₉×#124	C₂²	1	1	yes	characteristic
39	C₂×C₂₉×#124	C₂²	1	2	yes	complemented
40	C₂×C₂₉×#124	C₂²	1	2	yes	complemented
41	C₂×C₂₉×#124	C₂²	1	2	yes	complemented
42	C₂×C₂₉×#124	C₂²	1	4	yes	complemented
43	C₂×C₂₉×#124	C₂²	1	4	yes	complemented
44	C₂×C₂₉×#124	C₂²	1	4	yes	complemented
45	C₂×C₂₉×#124	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₂₉×#124	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₂₉×#124	C₂²	1	16	yes	complemented
48	C₂×C₂₉×#123	C₂²	1	2	yes	—
49	C₂×C₂₉×#123	C₂²	1	4	yes	complemented
50	C₂×C₂₉×#123	C₂²	1	2	yes	complemented
51	C₂×C₂₉×#123	C₂²	1	4	yes	complemented
52	C₂×C₂₉×#123	C₂²	1	4	yes	complemented
53	C₂×C₂₉×#123	C₂²	1	4	yes	complemented
54	C₂×C₂₉×#123	C₂²	1	4	yes	complemented
55	C₂×C₂₉×C₂²⋊Q₈	C₂²	1	2	yes	complemented
56	C₂×C₂₉×C₂²⋊Q₈	C₂²	1	4	yes	complemented
57	C₂×C₂₉×C₂²⋊Q₈	C₂²	1	4	yes	complemented
58	C₂×C₂₉×C₂²⋊Q₈	C₂²	1	4	yes	complemented
59	C₂×C₂₉×C₂²⋊Q₈	C₂²	1	4	yes	complemented
60	C₂×C₂₉×#121	C₂²	1	2	yes	—
61	C₂×C₂₉×#121	C₂²	1	4	yes	—
62	C₂×C₂₉×#121	C₂²	1	4	yes	complemented
63	C₂×C₂₉×#121	C₂²	1	4	yes	complemented
64	C₂×C₂₉×#121	C₂²	1	4	yes	complemented
65	C₂×C₂₉×#120	C₂²	1	4	yes	—
66	C₂×C₂₉×#120	C₂²	1	2	yes	—
67	C₂×C₂₉×#120	C₂²	1	2	yes	complemented
68	C₂×C₂₉×#120	C₂²	1	4	yes	complemented
69	C₂×C₄×Q₈×C₂₉	C₂²	1	2	yes	complemented
70	C₂×C₄×D₄×C₂₉	C₂²	1	2	yes	complemented
71	C₂×C₄×D₄×C₂₉	C₂²	1	4	yes	complemented
72	C₂×C₄×D₄×C₂₉	C₂²	1	4	yes	complemented
73	C₂×C₄×D₄×C₂₉	C₂²	1	4	yes	complemented
74	C₂×C₂₉×#117	C₂²	1	4	yes	complemented
75	C₂×C₂₉×#117	C₂²	1	2	yes	complemented
76	C₂×C₂₉×#117	C₂²	1	4	yes	complemented
77	C₂²×C₂²⋊C₄×C₂₉	C₂²	1	2	yes	complemented
78	C₂²×C₂²⋊C₄×C₂₉	C₂²	1	4	yes	complemented
79	C₂²×C₂²⋊C₄×C₂₉	C₂²	1	4	yes	complemented
80	C₂²×C₄²×C₂₉	C₂²	1	1	yes	characteristic, complemented
81	C₂⁵×C₂₉	C₂³	1	2	yes	—
82	C₂⁵×C₂₉	C₂³	1	2	yes	—
83	C₂×#41×C₂₉	—	4	8	no	—
84	C₂×#41×C₂₉	C₂³	1	16	yes	—
85	C₂²×Q₈×C₂₉	—	4	4	no	—
86	C₂²×Q₈×C₂₉	C₂³	1	2	yes	—
87	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
88	C₂²×Q₈×C₂₉	C₂³	1	2	yes	—
89	C₂²×Q₈×C₂₉	C₂³	1	2	yes	—
90	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
91	C₂²×Q₈×C₂₉	C₂³	1	8	yes	complemented
92	C₂²×D₄×C₂₉	—	4	4	no	—
93	C₂²×D₄×C₂₉	—	4	8	no	—
94	C₂²×D₄×C₂₉	C₂³	1	4	yes	—
95	C₂²×D₄×C₂₉	C₂³	1	4	yes	—
96	C₂²×D₄×C₂₉	C₂³	1	4	yes	—
97	C₂²×D₄×C₂₉	C₂³	1	2	yes	—
98	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
99	C₂²×D₄×C₂₉	C₂³	1	2	yes	—
100	C₂²×D₄×C₂₉	C₂³	1	2	yes	—
101	C₂²×D₄×C₂₉	C₂³	1	4	yes	—
102	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
103	C₂²×D₄×C₂₉	C₂³	1	8	yes	—
104	C₂²×D₄×C₂₉	C₂³	1	16	yes	complemented
105	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₂₉	C₂³	1	2	yes	—
107	C₂³×C₄×C₂₉	C₂³	1	2	yes	—
108	C₂³×C₄×C₂₉	C₂³	1	4	yes	—
109	C₂³×C₄×C₂₉	C₂³	1	4	yes	—
110	C₂³×C₄×C₂₉	C₂³	1	4	yes	—
111	C₂³×C₄×C₂₉	C₂³	1	2	yes	—
112	C₂₉×C₄⋊Q₈	C₂³	1	16	yes	complemented
113	C₂₉×C₄⋊Q₈	C₂³	1	16	yes	complemented
114	C₂₉×#126	C₂³	1	32	yes	complemented
115	C₂₉×#126	C₂³	1	32	yes	complemented
116	C₂₉×#126	C₂³	1	32	yes	complemented
117	C₂₉×#125	C₂³	1	16	yes	complemented
118	C₂₉×#124	C₂³	1	8	yes	—
119	C₂₉×#124	C₂³	1	8	yes	—
120	C₂₉×#124	C₂³	1	32	yes	complemented
121	C₂₉×#124	C₂³	1	8	yes	complemented
122	C₂₉×#124	C₂³	1	8	yes	complemented
123	C₂₉×#124	C₂³	1	16	yes	complemented
124	C₂₉×#124	C₂³	1	16	yes	complemented
125	C₂₉×#124	C₂³	1	16	yes	complemented
126	C₂₉×#124	C₂³	1	32	yes	complemented
127	C₂₉×#124	C₂³	1	32	yes	complemented
128	C₂₉×#123	C₂³	1	16	yes	—
129	C₂₉×#123	C₂³	1	32	yes	complemented
130	C₂₉×#123	C₂³	1	16	yes	complemented
131	C₂₉×#123	C₂³	1	32	yes	complemented
132	C₂₉×#123	C₂³	1	32	yes	complemented
133	C₂₉×#123	C₂³	1	32	yes	complemented
134	C₂₉×#123	C₂³	1	32	yes	complemented
135	C₂₉×C₂²⋊Q₈	C₂³	1	16	yes	complemented
136	C₂₉×C₂²⋊Q₈	C₂³	1	32	yes	complemented
137	C₂₉×C₂²⋊Q₈	C₂³	1	32	yes	complemented
138	C₂₉×C₂²⋊Q₈	C₂³	1	32	yes	complemented
139	C₂₉×C₂²⋊Q₈	C₂³	1	32	yes	complemented
140	C₂₉×#121	C₂³	1	16	yes	—
141	C₂₉×#121	C₂³	1	32	yes	—
142	C₂₉×#121	C₂³	1	32	yes	complemented
143	C₂₉×#121	C₂³	1	32	yes	complemented
144	C₂₉×#121	C₂³	1	32	yes	complemented
145	C₂₉×#120	C₂³	1	32	yes	—
146	C₂₉×#120	C₂³	1	16	yes	—
147	C₂₉×#120	C₂³	1	16	yes	complemented
148	C₂₉×#120	C₂³	1	32	yes	complemented
149	C₄×Q₈×C₂₉	C₂³	1	16	yes	complemented
150	C₄×D₄×C₂₉	C₂³	1	16	yes	complemented
151	C₄×D₄×C₂₉	C₂³	1	32	yes	complemented
152	C₄×D₄×C₂₉	C₂³	1	32	yes	complemented
153	C₄×D₄×C₂₉	C₂³	1	32	yes	complemented
154	C₂₉×#117	C₂³	1	32	yes	complemented
155	C₂₉×#117	C₂³	1	16	yes	complemented
156	C₂₉×#117	C₂³	1	32	yes	complemented
157	C₂×C₄⋊C₄×C₂₉	C₂³	1	4	yes	—
158	C₂×C₄⋊C₄×C₂₉	C₂³	1	4	yes	—
159	C₂×C₄⋊C₄×C₂₉	C₂³	1	4	yes	—
160	C₂×C₄⋊C₄×C₂₉	C₂³	1	4	yes	—
161	C₂×C₄⋊C₄×C₂₉	C₂³	1	4	yes	—
162	C₂×C₄⋊C₄×C₂₉	C₂³	1	4	yes	—
163	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
165	C₂×C₄⋊C₄×C₂₉	C₂³	1	4	yes	—
166	C₂×C₂²⋊C₄×C₂₉	C₂³	1	4	yes	—
167	C₂×C₂²⋊C₄×C₂₉	C₂³	1	4	yes	—
168	C₂×C₂²⋊C₄×C₂₉	C₂³	1	4	yes	—
169	C₂×C₂²⋊C₄×C₂₉	C₂³	1	4	yes	—
170	C₂×C₂²⋊C₄×C₂₉	C₂³	1	4	yes	—
171	C₂×C₂²⋊C₄×C₂₉	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄×C₂₉	C₂³	1	4	yes	—
173	C₂×C₂²⋊C₄×C₂₉	C₂³	1	2	yes	—
174	C₂×C₂²⋊C₄×C₂₉	C₂³	1	4	yes	—
175	C₂×C₂²⋊C₄×C₂₉	C₂³	1	4	yes	—
176	C₂×C₂²⋊C₄×C₂₉	C₂³	1	4	yes	—
177	C₂×C₂²⋊C₄×C₂₉	C₂³	1	4	yes	—
178	C₂×C₂²⋊C₄×C₂₉	C₂³	1	4	yes	—
179	C₂×C₂²⋊C₄×C₂₉	C₂³	1	4	yes	—
180	C₂×C₂²⋊C₄×C₂₉	C₂³	1	4	yes	—
181	C₂×C₂²⋊C₄×C₂₉	C₂³	1	32	yes	complemented
182	C₂×C₂²⋊C₄×C₂₉	C₂³	1	16	yes	complemented
183	C₂×C₂²⋊C₄×C₂₉	C₂³	1	32	yes	complemented
184	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
185	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
186	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
187	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
188	C₂×C₄²×C₂₉	C₂³	1	4	yes	—
189	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
190	C₂×C₄²×C₂₉	C₂³	1	8	yes	complemented
191	C₂⁴×C₂₉	—	2	8	no	—
192	C₂⁴×C₂₉	—	4	4	no	—
193	C₂⁴×C₂₉	—	4	8	no	—
194	C₂⁴×C₂₉	—	4	8	no	—
195	C₂⁴×C₂₉	C₂⁴	1	2	yes	—
196	C₂⁴×C₂₉	C₂⁴	1	4	yes	—
197	C₂⁴×C₂₉	C₂⁴	1	2	yes	—
198	C₂⁴×C₂₉	C₂⁴	1	1	yes	characteristic
199	C₂⁴×C₂₉	C₂⁴	1	8	yes	—
200	C₂⁴×C₂₉	C₂⁴	1	8	yes	—
201	#41×C₂₉	—	4	32	no	—
202	C₂×Q₈×C₂₉	—	4	2	no	—
203	C₂×Q₈×C₂₉	—	4	4	no	—
204	C₂×Q₈×C₂₉	—	4	2	no	—
205	C₂×Q₈×C₂₉	—	4	16	no	—
206	C₂×Q₈×C₂₉	—	4	4	no	—
207	C₂×Q₈×C₂₉	—	4	4	no	—
208	C₂×Q₈×C₂₉	C₂⁴	1	8	yes	—
209	C₂×Q₈×C₂₉	C₂⁴	1	4	yes	—
210	C₂×Q₈×C₂₉	C₂⁴	1	8	yes	—
211	C₂×Q₈×C₂₉	C₂⁴	1	8	yes	—
212	C₂×Q₈×C₂₉	C₂⁴	1	4	yes	—
213	C₂×D₄×C₂₉	—	2	16	no	—
214	C₂×D₄×C₂₉	—	4	2	no	—
215	C₂×D₄×C₂₉	—	4	4	no	—
216	C₂×D₄×C₂₉	—	4	2	no	—
217	C₂×D₄×C₂₉	—	4	16	no	—
218	C₂×D₄×C₂₉	—	4	8	no	—
219	C₂×D₄×C₂₉	—	4	8	no	—
220	C₂×D₄×C₂₉	—	4	8	no	—
221	C₂×D₄×C₂₉	—	4	4	no	—
222	C₂×D₄×C₂₉	—	4	4	no	—
223	C₂×D₄×C₂₉	—	4	32	no	—
224	C₂×D₄×C₂₉	C₂⁴	1	16	yes	—
225	C₂×D₄×C₂₉	C₂⁴	1	16	yes	—
226	C₂×D₄×C₂₉	C₂⁴	1	16	yes	—
227	C₂×D₄×C₂₉	C₂⁴	1	8	yes	—
228	C₂×D₄×C₂₉	C₂⁴	1	4	yes	—
229	C₂×D₄×C₂₉	C₂⁴	1	8	yes	—
230	C₂×D₄×C₂₉	C₂⁴	1	8	yes	—
231	C₂×D₄×C₂₉	C₂⁴	1	16	yes	—
232	C₂×D₄×C₂₉	C₂⁴	1	4	yes	—
233	C₂²×C₄×C₂₉	—	2	4	no	—
234	C₂²×C₄×C₂₉	—	2	8	no	—
235	C₂²×C₄×C₂₉	—	4	8	no	—
236	C₂²×C₄×C₂₉	—	4	4	no	—
237	C₂²×C₄×C₂₉	—	4	8	no	—
238	C₂²×C₄×C₂₉	—	4	4	no	—
239	C₂²×C₄×C₂₉	—	4	8	no	—
240	C₂²×C₄×C₂₉	C₂⁴	1	4	yes	—
241	C₂²×C₄×C₂₉	C₂⁴	1	8	yes	—
242	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₂₉	C₂⁴	1	4	yes	—
245	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
247	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
248	C₂²×C₄×C₂₉	C₂⁴	1	4	yes	—
249	C₂²×C₄×C₂₉	C₂⁴	1	4	yes	—
250	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
251	C₂²×C₄×C₂₉	C₂⁴	1	8	yes	—
252	C₂²×C₄×C₂₉	C₂⁴	1	16	yes	—
253	C₂²×C₄×C₂₉	C₂⁴	1	16	yes	—
254	C₂²×C₄×C₂₉	C₂⁴	1	16	yes	—
255	C₂²×C₄×C₂₉	C₂⁴	1	8	yes	—
256	C₄⋊C₄×C₂₉	C₂⁴	1	16	yes	—
257	C₄⋊C₄×C₂₉	C₂⁴	1	16	yes	—
258	C₄⋊C₄×C₂₉	C₂⁴	1	16	yes	—
259	C₄⋊C₄×C₂₉	C₂⁴	1	16	yes	—
260	C₄⋊C₄×C₂₉	C₂⁴	1	16	yes	—
261	C₄⋊C₄×C₂₉	C₂⁴	1	16	yes	—
262	C₄⋊C₄×C₂₉	C₂⁴	1	8	yes	—
263	C₄⋊C₄×C₂₉	C₂⁴	1	8	yes	—
264	C₄⋊C₄×C₂₉	C₂⁴	1	16	yes	—
265	C₂²⋊C₄×C₂₉	C₂⁴	1	16	yes	—
266	C₂²⋊C₄×C₂₉	C₂⁴	1	16	yes	—
267	C₂²⋊C₄×C₂₉	C₂⁴	1	16	yes	—
268	C₂²⋊C₄×C₂₉	C₂⁴	1	16	yes	—
269	C₂²⋊C₄×C₂₉	C₂⁴	1	16	yes	—
270	C₂²⋊C₄×C₂₉	C₂⁴	1	8	yes	—
271	C₂²⋊C₄×C₂₉	C₂⁴	1	16	yes	—
272	C₂²⋊C₄×C₂₉	C₂⁴	1	8	yes	—
273	C₂²⋊C₄×C₂₉	C₂⁴	1	16	yes	—
274	C₂²⋊C₄×C₂₉	C₂⁴	1	16	yes	—
275	C₂²⋊C₄×C₂₉	C₂⁴	1	16	yes	—
276	C₂²⋊C₄×C₂₉	C₂⁴	1	16	yes	—
277	C₂²⋊C₄×C₂₉	C₂⁴	1	16	yes	—
278	C₂²⋊C₄×C₂₉	C₂⁴	1	16	yes	—
279	C₂²⋊C₄×C₂₉	C₂⁴	1	16	yes	—
280	C₄²×C₂₉	C₂⁴	1	4	yes	—
281	C₄²×C₂₉	C₂⁴	1	8	yes	—
282	C₄²×C₂₉	C₂⁴	1	4	yes	—
283	C₄²×C₂₉	C₂⁴	1	8	yes	—
284	C₄²×C₂₉	C₂⁴	1	16	yes	—
285	C₄²×C₂₉	C₂⁴	1	8	yes	—
286	C₂×#3545	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
287	C₂³×C₂₉	—	2	4	no	—
288	C₂³×C₂₉	—	2	8	no	—
289	C₂³×C₂₉	—	2	4	no	—
290	C₂³×C₂₉	—	2	4	no	—
291	C₂³×C₂₉	—	2	8	no	—
292	C₂³×C₂₉	—	2	8	no	—
293	C₂³×C₂₉	—	2	8	no	—
294	C₂³×C₂₉	—	2	8	no	—
295	C₂³×C₂₉	—	2	16	no	—
296	C₂³×C₂₉	—	4	8	no	—
297	C₂³×C₂₉	—	4	16	no	—
298	C₂³×C₂₉	—	4	16	no	—
299	C₂³×C₂₉	—	8	16	no	—
300	C₂³×C₂₉	—	8	16	no	—
301	C₂³×C₂₉	H(5,𝔽₂)	1	4	yes	—
302	C₂³×C₂₉	C₂⁵	1	4	yes	—
303	C₂³×C₂₉	C₂⁵	1	8	yes	—
304	C₂³×C₂₉	C₂⁵	1	4	yes	—
305	C₂³×C₂₉	C₂⁵	1	2	yes	—
306	C₂³×C₂₉	C₂⁵	1	1	yes	characteristic
307	Q₈×C₂₉	—	4	4	no	—
308	Q₈×C₂₉	—	4	8	no	—
309	Q₈×C₂₉	—	4	4	no	—
310	Q₈×C₂₉	—	4	8	no	—
311	Q₈×C₂₉	—	4	8	no	—
312	D₄×C₂₉	—	2	32	no	—
313	D₄×C₂₉	—	4	4	no	—
314	D₄×C₂₉	—	4	8	no	—
315	D₄×C₂₉	—	4	4	no	—
316	D₄×C₂₉	—	4	16	no	—
317	D₄×C₂₉	—	4	16	no	—
318	D₄×C₂₉	—	4	16	no	—
319	D₄×C₂₉	—	4	8	no	—
320	D₄×C₂₉	—	4	8	no	—
321	C₂×C₄×C₂₉	—	2	4	no	—
322	C₂×C₄×C₂₉	—	2	8	no	—
323	C₂×C₄×C₂₉	—	2	2	no	—
324	C₂×C₄×C₂₉	—	2	2	no	—
325	C₂×C₄×C₂₉	—	2	4	no	—
326	C₂×C₄×C₂₉	—	2	16	no	—
327	C₂×C₄×C₂₉	—	2	8	no	—
328	C₂×C₄×C₂₉	—	2	4	no	—
329	C₂×C₄×C₂₉	—	2	8	no	—
330	C₂×C₄×C₂₉	—	2	4	no	—
331	C₂×C₄×C₂₉	—	2	8	no	—
332	C₂×C₄×C₂₉	—	4	16	no	—
333	C₂×C₄×C₂₉	—	4	8	no	—
334	C₂×C₄×C₂₉	—	4	16	no	—
335	C₂×C₄×C₂₉	—	4	8	no	—
336	C₂×C₄×C₂₉	—	4	16	no	—
337	C₂×C₄×C₂₉	C₂⁵	1	4	yes	—
338	C₂×C₄×C₂₉	C₂⁵	1	4	yes	—
339	C₂×C₄×C₂₉	C₂⁵	1	8	yes	—
340	C₂×C₄×C₂₉	C₂⁵	1	4	yes	—
341	C₂×C₄×C₂₉	C₂⁵	1	2	yes	—
342	C₂×C₄×C₂₉	C₂⁵	1	2	yes	—
343	C₂×C₄×C₂₉	C₂⁵	1	8	yes	—
344	C₂×C₄×C₂₉	C₂⁵	1	8	yes	—
345	C₂×C₄×C₂₉	C₂⁵	1	4	yes	—
346	#3545	C₂×C₂₉	1	32	yes	direct product factor
347	C₂×#563	C₂×C₂₉	1	1	yes	characteristic, complemented
348	C₂×#562	C₂×C₂₉	1	2	yes	complemented
349	C₂×H(3,𝔽₄)	C₂×C₂₉	1	1	yes	characteristic, complemented
350	C₂×#555	C₂×C₂₉	1	2	yes	complemented
351	C₂×#551	C₂×C₂₉	1	2	yes	complemented
352	C₂×#551	C₂×C₂₉	1	4	yes	complemented
353	C₂×#546	C₂×C₂₉	1	4	yes	complemented
354	C₂×#542	C₂×C₂₉	1	4	yes	complemented
355	C₂×#538	C₂×C₂₉	1	4	yes	complemented
356	C₂×#536	C₂×C₂₉	1	2	yes	complemented
357	C₂×#534	C₂×C₂₉	1	2	yes	complemented
358	C₂×#529	C₂×C₂₉	1	2	yes	complemented
359	C₂²×#124	C₂×C₂₉	1	1	yes	characteristic, complemented
360	C₂²×C₂₉	—	2	4	no	—
361	C₂²×C₂₉	—	2	8	no	—
362	C₂²×C₂₉	—	2	8	no	—
363	C₂²×C₂₉	—	2	4	no	—
364	C₂²×C₂₉	—	2	4	no	—
365	C₂²×C₂₉	—	2	8	no	—
366	C₂²×C₂₉	—	2	8	no	—
367	C₂²×C₂₉	—	2	8	no	—
368	C₂²×C₂₉	—	2	8	no	—
369	C₂²×C₂₉	—	4	16	no	—
370	C₂²×C₂₉	—	4	8	no	—
371	C₂²×C₂₉	—	4	8	no	—
372	C₂²×C₂₉	—	8	16	no	—
373	C₂²×C₂₉	—	8	16	no	—
374	C₂²×C₂₉	C₂×H(5,𝔽₂)	1	4	yes	—
375	C₂²×C₂₉	C₂×H(5,𝔽₂)	1	2	yes	—
376	C₂²×C₂₉	#585	1	4	yes	—
377	C₂²×C₂₉	C₂⁶	1	1	yes	characteristic
378	C₄×C₂₉	—	2	4	no	—
379	C₄×C₂₉	—	2	2	no	—
380	C₄×C₂₉	—	2	2	no	—
381	C₄×C₂₉	—	2	4	no	—
382	C₄×C₂₉	—	2	8	no	—
383	C₄×C₂₉	—	2	4	no	—
384	C₄×C₂₉	—	2	8	no	—
385	C₄×C₂₉	—	2	4	no	—
386	C₄×C₂₉	—	2	8	no	—
387	C₂²×#41	C₂²×C₂₉	1	2	yes	—
388	C₂³×Q₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
389	C₂³×D₄	C₂²×C₂₉	1	1	yes	characteristic
390	C₂³×D₄	C₂²×C₂₉	1	2	yes	complemented
391	#563	C₂²×C₂₉	1	16	yes	complemented
392	#562	C₂²×C₂₉	1	32	yes	complemented
393	H(3,𝔽₄)	C₂²×C₂₉	1	16	yes	complemented
394	#555	C₂²×C₂₉	1	32	yes	complemented
395	#551	C₂²×C₂₉	1	32	yes	complemented
396	#551	C₂²×C₂₉	1	64	yes	complemented
397	#546	C₂²×C₂₉	1	64	yes	complemented
398	#542	C₂²×C₂₉	1	64	yes	complemented
399	#538	C₂²×C₂₉	1	64	yes	complemented
400	#536	C₂²×C₂₉	1	32	yes	complemented
401	#534	C₂²×C₂₉	1	32	yes	complemented
402	C₂×C₄⋊Q₈	C₂²×C₂₉	1	2	yes	complemented
403	C₂×C₄⋊Q₈	C₂²×C₂₉	1	2	yes	complemented
404	#529	C₂²×C₂₉	1	32	yes	complemented
405	C₂×#126	C₂²×C₂₉	1	4	yes	complemented
406	C₂×#126	C₂²×C₂₉	1	4	yes	complemented
407	C₂×#126	C₂²×C₂₉	1	4	yes	complemented
408	C₂×#125	C₂²×C₂₉	1	2	yes	complemented
409	C₂×#124	C₂²×C₂₉	1	1	yes	characteristic
410	C₂×#124	C₂²×C₂₉	1	1	yes	characteristic
411	C₂×#124	C₂²×C₂₉	1	4	yes	complemented
412	C₂×#124	C₂²×C₂₉	1	1	yes	characteristic, complemented
413	C₂×#124	C₂²×C₂₉	1	1	yes	characteristic, complemented
414	C₂×#124	C₂²×C₂₉	1	2	yes	complemented
415	C₂×#124	C₂²×C₂₉	1	2	yes	complemented
416	C₂×#124	C₂²×C₂₉	1	2	yes	complemented
417	C₂×#124	C₂²×C₂₉	1	4	yes	complemented
418	C₂×#124	C₂²×C₂₉	1	4	yes	complemented
419	C₂×#124	C₂²×C₂₉	1	16	yes	complemented
420	C₂×#123	C₂²×C₂₉	1	2	yes	—
421	C₂×#123	C₂²×C₂₉	1	4	yes	complemented
422	C₂×#123	C₂²×C₂₉	1	2	yes	complemented
423	C₂×#123	C₂²×C₂₉	1	4	yes	complemented
424	C₂×#123	C₂²×C₂₉	1	4	yes	complemented
425	C₂×#123	C₂²×C₂₉	1	4	yes	complemented
426	C₂×#123	C₂²×C₂₉	1	4	yes	complemented
427	C₂×C₂²⋊Q₈	C₂²×C₂₉	1	2	yes	complemented
428	C₂×C₂²⋊Q₈	C₂²×C₂₉	1	4	yes	complemented
429	C₂×C₂²⋊Q₈	C₂²×C₂₉	1	4	yes	complemented
430	C₂×C₂²⋊Q₈	C₂²×C₂₉	1	4	yes	complemented
431	C₂×C₂²⋊Q₈	C₂²×C₂₉	1	4	yes	complemented
432	C₂×#121	C₂²×C₂₉	1	2	yes	—
433	C₂×#121	C₂²×C₂₉	1	4	yes	—
434	C₂×#121	C₂²×C₂₉	1	4	yes	complemented
435	C₂×#121	C₂²×C₂₉	1	4	yes	complemented
436	C₂×#121	C₂²×C₂₉	1	4	yes	complemented
437	C₂×#120	C₂²×C₂₉	1	4	yes	—
438	C₂×#120	C₂²×C₂₉	1	2	yes	—
439	C₂×#120	C₂²×C₂₉	1	2	yes	complemented
440	C₂×#120	C₂²×C₂₉	1	4	yes	complemented
441	C₂×C₄×Q₈	C₂²×C₂₉	1	2	yes	complemented
442	C₂×C₄×D₄	C₂²×C₂₉	1	2	yes	complemented
443	C₂×C₄×D₄	C₂²×C₂₉	1	4	yes	complemented
444	C₂×C₄×D₄	C₂²×C₂₉	1	4	yes	complemented
445	C₂×C₄×D₄	C₂²×C₂₉	1	4	yes	complemented
446	C₂×#117	C₂²×C₂₉	1	4	yes	complemented
447	C₂×#117	C₂²×C₂₉	1	2	yes	complemented
448	C₂×#117	C₂²×C₂₉	1	4	yes	complemented
449	C₂²×C₂²⋊C₄	C₂²×C₂₉	1	4	yes	complemented
450	C₂²×C₂²⋊C₄	C₂²×C₂₉	1	2	yes	complemented
451	C₂²×C₂²⋊C₄	C₂²×C₂₉	1	4	yes	complemented
452	C₂²×C₄²	C₂²×C₂₉	1	1	yes	characteristic, complemented
453	C₂×C₂₉	—	2	4	no	—
454	C₂×C₂₉	—	4	8	no	—
455	C₂×C₂₉	—	4	4	no	—
456	C₂×C₂₉	—	4	4	no	—
457	C₂×C₂₉	#3545	1	4	yes	direct product factor
458	C₂×C₂₉	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
459	C₂×C₂₉	C₂×#585	1	2	yes	—
460	C₂⁵	C₂³×C₂₉	1	2	yes	—
461	C₂⁵	C₂³×C₂₉	1	2	yes	—
462	C₂×#41	—	4	8	no	—
463	C₂×#41	C₂³×C₂₉	1	16	yes	—
464	C₂²×Q₈	—	4	4	no	—
465	C₂²×Q₈	C₂³×C₂₉	1	2	yes	—
466	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
467	C₂²×Q₈	C₂³×C₂₉	1	2	yes	—
468	C₂²×Q₈	C₂³×C₂₉	1	2	yes	—
469	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
470	C₂²×Q₈	C₂³×C₂₉	1	8	yes	complemented
471	C₂²×D₄	—	4	4	no	—
472	C₂²×D₄	—	4	8	no	—
473	C₂²×D₄	C₂³×C₂₉	1	4	yes	—
474	C₂²×D₄	C₂³×C₂₉	1	4	yes	—
475	C₂²×D₄	C₂³×C₂₉	1	4	yes	—
476	C₂²×D₄	C₂³×C₂₉	1	2	yes	—
477	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
478	C₂²×D₄	C₂³×C₂₉	1	2	yes	—
479	C₂²×D₄	C₂³×C₂₉	1	2	yes	—
480	C₂²×D₄	C₂³×C₂₉	1	4	yes	—
481	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
482	C₂²×D₄	C₂³×C₂₉	1	8	yes	—
483	C₂²×D₄	C₂³×C₂₉	1	16	yes	complemented
484	C₂³×C₄	C₂³×C₂₉	1	2	yes	—
485	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
486	C₂³×C₄	C₂³×C₂₉	1	2	yes	—
487	C₂³×C₄	C₂³×C₂₉	1	4	yes	—
488	C₂³×C₄	C₂³×C₂₉	1	4	yes	—
489	C₂³×C₄	C₂³×C₂₉	1	4	yes	—
490	C₂³×C₄	C₂³×C₂₉	1	2	yes	—
491	C₄⋊Q₈	C₂³×C₂₉	1	16	yes	complemented
492	C₄⋊Q₈	C₂³×C₂₉	1	16	yes	complemented
493	#126	C₂³×C₂₉	1	32	yes	complemented
494	#126	C₂³×C₂₉	1	32	yes	complemented
495	#126	C₂³×C₂₉	1	32	yes	complemented
496	#125	C₂³×C₂₉	1	16	yes	complemented
497	#124	C₂³×C₂₉	1	8	yes	—
498	#124	C₂³×C₂₉	1	8	yes	—
499	#124	C₂³×C₂₉	1	32	yes	complemented
500	#124	C₂³×C₂₉	1	8	yes	complemented
501	#124	C₂³×C₂₉	1	8	yes	complemented
502	#124	C₂³×C₂₉	1	16	yes	complemented
503	#124	C₂³×C₂₉	1	16	yes	complemented
504	#124	C₂³×C₂₉	1	16	yes	complemented
505	#124	C₂³×C₂₉	1	32	yes	complemented
506	#124	C₂³×C₂₉	1	32	yes	complemented
507	#123	C₂³×C₂₉	1	16	yes	—
508	#123	C₂³×C₂₉	1	32	yes	complemented
509	#123	C₂³×C₂₉	1	16	yes	complemented
510	#123	C₂³×C₂₉	1	32	yes	complemented
511	#123	C₂³×C₂₉	1	32	yes	complemented
512	#123	C₂³×C₂₉	1	32	yes	complemented
513	#123	C₂³×C₂₉	1	32	yes	complemented
514	C₂²⋊Q₈	C₂³×C₂₉	1	16	yes	complemented
515	C₂²⋊Q₈	C₂³×C₂₉	1	32	yes	complemented
516	C₂²⋊Q₈	C₂³×C₂₉	1	32	yes	complemented
517	C₂²⋊Q₈	C₂³×C₂₉	1	32	yes	complemented
518	C₂²⋊Q₈	C₂³×C₂₉	1	32	yes	complemented
519	#121	C₂³×C₂₉	1	16	yes	—
520	#121	C₂³×C₂₉	1	32	yes	—
521	#121	C₂³×C₂₉	1	32	yes	complemented
522	#121	C₂³×C₂₉	1	32	yes	complemented
523	#121	C₂³×C₂₉	1	32	yes	complemented
524	#120	C₂³×C₂₉	1	32	yes	—
525	#120	C₂³×C₂₉	1	16	yes	—
526	#120	C₂³×C₂₉	1	16	yes	complemented
527	#120	C₂³×C₂₉	1	32	yes	complemented
528	C₄×Q₈	C₂³×C₂₉	1	16	yes	complemented
529	C₄×D₄	C₂³×C₂₉	1	16	yes	complemented
530	C₄×D₄	C₂³×C₂₉	1	32	yes	complemented
531	C₄×D₄	C₂³×C₂₉	1	32	yes	complemented
532	C₄×D₄	C₂³×C₂₉	1	32	yes	complemented
533	#117	C₂³×C₂₉	1	32	yes	complemented
534	#117	C₂³×C₂₉	1	16	yes	complemented
535	#117	C₂³×C₂₉	1	32	yes	complemented
536	C₂×C₄⋊C₄	C₂³×C₂₉	1	4	yes	—
537	C₂×C₄⋊C₄	C₂³×C₂₉	1	4	yes	—
538	C₂×C₄⋊C₄	C₂³×C₂₉	1	4	yes	—
539	C₂×C₄⋊C₄	C₂³×C₂₉	1	4	yes	—
540	C₂×C₄⋊C₄	C₂³×C₂₉	1	4	yes	—
541	C₂×C₄⋊C₄	C₂³×C₂₉	1	4	yes	—
542	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
543	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
544	C₂×C₄⋊C₄	C₂³×C₂₉	1	4	yes	—
545	C₂×C₂²⋊C₄	C₂³×C₂₉	1	4	yes	—
546	C₂×C₂²⋊C₄	C₂³×C₂₉	1	4	yes	—
547	C₂×C₂²⋊C₄	C₂³×C₂₉	1	4	yes	—
548	C₂×C₂²⋊C₄	C₂³×C₂₉	1	4	yes	—
549	C₂×C₂²⋊C₄	C₂³×C₂₉	1	4	yes	—
550	C₂×C₂²⋊C₄	C₂³×C₂₉	1	2	yes	—
551	C₂×C₂²⋊C₄	C₂³×C₂₉	1	4	yes	—
552	C₂×C₂²⋊C₄	C₂³×C₂₉	1	2	yes	—
553	C₂×C₂²⋊C₄	C₂³×C₂₉	1	4	yes	—
554	C₂×C₂²⋊C₄	C₂³×C₂₉	1	4	yes	—
555	C₂×C₂²⋊C₄	C₂³×C₂₉	1	4	yes	—
556	C₂×C₂²⋊C₄	C₂³×C₂₉	1	4	yes	—
557	C₂×C₂²⋊C₄	C₂³×C₂₉	1	4	yes	—
558	C₂×C₂²⋊C₄	C₂³×C₂₉	1	4	yes	—
559	C₂×C₂²⋊C₄	C₂³×C₂₉	1	4	yes	—
560	C₂×C₂²⋊C₄	C₂³×C₂₉	1	32	yes	complemented
561	C₂×C₂²⋊C₄	C₂³×C₂₉	1	16	yes	complemented
562	C₂×C₂²⋊C₄	C₂³×C₂₉	1	32	yes	complemented
563	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
564	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
565	C₂×C₄²	C₂³×C₂₉	1	4	yes	—
566	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
567	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
568	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
569	C₂×C₄²	C₂³×C₂₉	1	8	yes	complemented
570	C₂₉	C₂×#3545	1	1	yes	characteristic, direct product factor, Sylow
571	C₂⁴	—	2	8	no	—
572	C₂⁴	—	4	4	no	—
573	C₂⁴	—	4	8	no	—
574	C₂⁴	—	4	8	no	—
575	C₂⁴	C₂⁴×C₂₉	1	2	yes	—
576	C₂⁴	C₂⁴×C₂₉	1	4	yes	—
577	C₂⁴	C₂⁴×C₂₉	1	2	yes	—
578	C₂⁴	C₂⁴×C₂₉	1	1	yes	characteristic
579	C₂⁴	C₂⁴×C₂₉	1	8	yes	—
580	C₂⁴	C₂⁴×C₂₉	1	8	yes	—
581	#41	—	4	32	no	—
582	C₂×Q₈	—	4	2	no	—
583	C₂×Q₈	—	4	4	no	—
584	C₂×Q₈	—	4	2	no	—
585	C₂×Q₈	—	4	16	no	—
586	C₂×Q₈	—	4	4	no	—
587	C₂×Q₈	—	4	4	no	—
588	C₂×Q₈	C₂⁴×C₂₉	1	8	yes	—
589	C₂×Q₈	C₂⁴×C₂₉	1	4	yes	—
590	C₂×Q₈	C₂⁴×C₂₉	1	8	yes	—
591	C₂×Q₈	C₂⁴×C₂₉	1	8	yes	—
592	C₂×Q₈	C₂⁴×C₂₉	1	4	yes	—
593	C₂×D₄	—	2	16	no	—
594	C₂×D₄	—	4	2	no	—
595	C₂×D₄	—	4	4	no	—
596	C₂×D₄	—	4	2	no	—
597	C₂×D₄	—	4	16	no	—
598	C₂×D₄	—	4	8	no	—
599	C₂×D₄	—	4	4	no	—
600	C₂×D₄	—	4	8	no	—
601	C₂×D₄	—	4	8	no	—
602	C₂×D₄	—	4	4	no	—
603	C₂×D₄	—	4	32	no	—
604	C₂×D₄	C₂⁴×C₂₉	1	16	yes	—
605	C₂×D₄	C₂⁴×C₂₉	1	16	yes	—
606	C₂×D₄	C₂⁴×C₂₉	1	16	yes	—
607	C₂×D₄	C₂⁴×C₂₉	1	8	yes	—
608	C₂×D₄	C₂⁴×C₂₉	1	4	yes	—
609	C₂×D₄	C₂⁴×C₂₉	1	8	yes	—
610	C₂×D₄	C₂⁴×C₂₉	1	8	yes	—
611	C₂×D₄	C₂⁴×C₂₉	1	16	yes	—
612	C₂×D₄	C₂⁴×C₂₉	1	4	yes	—
613	C₂²×C₄	—	2	4	no	—
614	C₂²×C₄	—	2	8	no	—
615	C₂²×C₄	—	4	4	no	—
616	C₂²×C₄	—	4	8	no	—
617	C₂²×C₄	—	4	8	no	—
618	C₂²×C₄	—	4	4	no	—
619	C₂²×C₄	—	4	8	no	—
620	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
621	C₂²×C₄	C₂⁴×C₂₉	1	4	yes	—
622	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
623	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
624	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
625	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
626	C₂²×C₄	C₂⁴×C₂₉	1	4	yes	—
627	C₂²×C₄	C₂⁴×C₂₉	1	4	yes	—
628	C₂²×C₄	C₂⁴×C₂₉	1	4	yes	—
629	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
630	C₂²×C₄	C₂⁴×C₂₉	1	8	yes	—
631	C₂²×C₄	C₂⁴×C₂₉	1	8	yes	—
632	C₂²×C₄	C₂⁴×C₂₉	1	16	yes	—
633	C₂²×C₄	C₂⁴×C₂₉	1	16	yes	—
634	C₂²×C₄	C₂⁴×C₂₉	1	16	yes	—
635	C₂²×C₄	C₂⁴×C₂₉	1	8	yes	—
636	C₄⋊C₄	C₂⁴×C₂₉	1	16	yes	—
637	C₄⋊C₄	C₂⁴×C₂₉	1	16	yes	—
638	C₄⋊C₄	C₂⁴×C₂₉	1	16	yes	—
639	C₄⋊C₄	C₂⁴×C₂₉	1	16	yes	—
640	C₄⋊C₄	C₂⁴×C₂₉	1	16	yes	—
641	C₄⋊C₄	C₂⁴×C₂₉	1	16	yes	—
642	C₄⋊C₄	C₂⁴×C₂₉	1	8	yes	—
643	C₄⋊C₄	C₂⁴×C₂₉	1	8	yes	—
644	C₄⋊C₄	C₂⁴×C₂₉	1	16	yes	—
645	C₂²⋊C₄	C₂⁴×C₂₉	1	16	yes	—
646	C₂²⋊C₄	C₂⁴×C₂₉	1	16	yes	—
647	C₂²⋊C₄	C₂⁴×C₂₉	1	16	yes	—
648	C₂²⋊C₄	C₂⁴×C₂₉	1	16	yes	—
649	C₂²⋊C₄	C₂⁴×C₂₉	1	16	yes	—
650	C₂²⋊C₄	C₂⁴×C₂₉	1	8	yes	—
651	C₂²⋊C₄	C₂⁴×C₂₉	1	16	yes	—
652	C₂²⋊C₄	C₂⁴×C₂₉	1	8	yes	—
653	C₂²⋊C₄	C₂⁴×C₂₉	1	16	yes	—
654	C₂²⋊C₄	C₂⁴×C₂₉	1	16	yes	—
655	C₂²⋊C₄	C₂⁴×C₂₉	1	16	yes	—
656	C₂²⋊C₄	C₂⁴×C₂₉	1	16	yes	—
657	C₂²⋊C₄	C₂⁴×C₂₉	1	16	yes	—
658	C₂²⋊C₄	C₂⁴×C₂₉	1	16	yes	—
659	C₂²⋊C₄	C₂⁴×C₂₉	1	16	yes	—
660	C₄²	C₂⁴×C₂₉	1	4	yes	—
661	C₄²	C₂⁴×C₂₉	1	8	yes	—
662	C₄²	C₂⁴×C₂₉	1	4	yes	—
663	C₄²	C₂⁴×C₂₉	1	8	yes	—
664	C₄²	C₂⁴×C₂₉	1	16	yes	—
665	C₄²	C₂⁴×C₂₉	1	8	yes	—
666	C₂³	—	2	4	no	—
667	C₂³	—	2	8	no	—
668	C₂³	—	2	4	no	—
669	C₂³	—	2	4	no	—
670	C₂³	—	2	8	no	—
671	C₂³	—	2	8	no	—
672	C₂³	—	2	8	no	—
673	C₂³	—	2	8	no	—
674	C₂³	—	2	16	no	—
675	C₂³	—	4	8	no	—
676	C₂³	—	4	16	no	—
677	C₂³	—	4	16	no	—
678	C₂³	—	8	16	no	—
679	C₂³	—	8	16	no	—
680	C₂³	C₂₉×H(5,𝔽₂)	1	4	yes	—
681	C₂³	C₂⁵×C₂₉	1	4	yes	—
682	C₂³	C₂⁵×C₂₉	1	8	yes	—
683	C₂³	C₂⁵×C₂₉	1	4	yes	—
684	C₂³	C₂⁵×C₂₉	1	2	yes	—
685	C₂³	C₂⁵×C₂₉	1	1	yes	characteristic
686	Q₈	—	4	4	no	—
687	Q₈	—	4	8	no	—
688	Q₈	—	4	4	no	—
689	Q₈	—	4	8	no	—
690	Q₈	—	4	8	no	—
691	D₄	—	2	32	no	—
692	D₄	—	4	4	no	—
693	D₄	—	4	8	no	—
694	D₄	—	4	4	no	—
695	D₄	—	4	16	no	—
696	D₄	—	4	8	no	—
697	D₄	—	4	16	no	—
698	D₄	—	4	16	no	—
699	D₄	—	4	8	no	—
700	C₂×C₄	—	2	4	no	—
701	C₂×C₄	—	2	8	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	4	no	—
705	C₂×C₄	—	2	16	no	—
706	C₂×C₄	—	2	8	no	—
707	C₂×C₄	—	2	4	no	—
708	C₂×C₄	—	2	8	no	—
709	C₂×C₄	—	2	4	no	—
710	C₂×C₄	—	2	8	no	—
711	C₂×C₄	—	4	8	no	—
712	C₂×C₄	—	4	16	no	—
713	C₂×C₄	—	4	16	no	—
714	C₂×C₄	—	4	8	no	—
715	C₂×C₄	—	4	16	no	—
716	C₂×C₄	C₂⁵×C₂₉	1	4	yes	—
717	C₂×C₄	C₂⁵×C₂₉	1	4	yes	—
718	C₂×C₄	C₂⁵×C₂₉	1	8	yes	—
719	C₂×C₄	C₂⁵×C₂₉	1	4	yes	—
720	C₂×C₄	C₂⁵×C₂₉	1	2	yes	—
721	C₂×C₄	C₂⁵×C₂₉	1	2	yes	—
722	C₂×C₄	C₂⁵×C₂₉	1	8	yes	—
723	C₂×C₄	C₂⁵×C₂₉	1	8	yes	—
724	C₂×C₄	C₂⁵×C₂₉	1	4	yes	—
725	C₂²	—	2	8	no	—
726	C₂²	—	2	4	no	—
727	C₂²	—	2	8	no	—
728	C₂²	—	2	4	no	—
729	C₂²	—	2	4	no	—
730	C₂²	—	2	8	no	—
731	C₂²	—	2	8	no	—
732	C₂²	—	2	8	no	—
733	C₂²	—	2	8	no	—
734	C₂²	—	4	8	no	—
735	C₂²	—	4	16	no	—
736	C₂²	—	4	8	no	—
737	C₂²	—	8	16	no	—
738	C₂²	—	8	16	no	—
739	C₂²	C₂×C₂₉×H(5,𝔽₂)	1	4	yes	—
740	C₂²	C₂×C₂₉×H(5,𝔽₂)	1	2	yes	—
741	C₂²	C₂₉×#585	1	4	yes	—
742	C₂²	C₂⁶×C₂₉	1	1	yes	characteristic
743	C₄	—	2	4	no	—
744	C₄	—	2	2	no	—
745	C₄	—	2	2	no	—
746	C₄	—	2	4	no	—
747	C₄	—	2	8	no	—
748	C₄	—	2	4	no	—
749	C₄	—	2	8	no	—
750	C₄	—	2	4	no	—
751	C₄	—	2	8	no	—
752	C₂	—	2	4	no	—
753	C₂	—	4	4	no	—
754	C₂	—	4	8	no	—
755	C₂	—	4	4	no	—
756	C₂	C₂₉×#3545	1	4	yes	direct product factor
757	C₂	C₂²×C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
758	C₂	C₂×C₂₉×#585	1	2	yes	—

	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×#3545	C₂	direct (N × H)
2. C₂×C₂₉×#563	C₂	semidirect
3. C₂×C₂₉×#562	C₂	semidirect
4. C₂×C₂₉×H(3,𝔽₄)	C₂	semidirect
5. C₂×C₂₉×#555	C₂	semidirect
6. C₂×C₂₉×#551	C₂	semidirect
7. C₂×C₂₉×#551	C₂	semidirect
8. C₂×C₂₉×#546	C₂	semidirect
9. C₂×C₂₉×#542	C₂	semidirect
10. C₂×C₂₉×#538	C₂	semidirect
11. C₂×C₂₉×#536	C₂	semidirect
12. C₂×C₂₉×#534	C₂	semidirect
13. C₂×C₂₉×#529	C₂	semidirect
14. C₂²×C₂₉×#124	C₂	semidirect
16. C₂³×Q₈×C₂₉	C₂²	semidirect
18. C₂³×D₄×C₂₉	C₂²	semidirect
19. C₂₉×#563	C₂²	semidirect
20. C₂₉×#562	C₂²	semidirect
21. C₂₉×H(3,𝔽₄)	C₂²	semidirect
22. C₂₉×#555	C₂²	semidirect
23. C₂₉×#551	C₂²	semidirect
24. C₂₉×#551	C₂²	semidirect
25. C₂₉×#546	C₂²	semidirect
26. C₂₉×#542	C₂²	semidirect
27. C₂₉×#538	C₂²	semidirect
28. C₂₉×#536	C₂²	semidirect
29. C₂₉×#534	C₂²	semidirect
30. C₂×C₂₉×C₄⋊Q₈	C₂²	semidirect
31. C₂×C₂₉×C₄⋊Q₈	C₂²	semidirect
32. C₂₉×#529	C₂²	semidirect
33. C₂×C₂₉×#126	C₂²	semidirect
34. C₂×C₂₉×#126	C₂²	semidirect
35. C₂×C₂₉×#126	C₂²	semidirect
36. C₂×C₂₉×#125	C₂²	semidirect
39. C₂×C₂₉×#124	C₂²	semidirect
40. C₂×C₂₉×#124	C₂²	semidirect
41. C₂×C₂₉×#124	C₂²	semidirect
42. C₂×C₂₉×#124	C₂²	semidirect
43. C₂×C₂₉×#124	C₂²	semidirect
44. C₂×C₂₉×#124	C₂²	semidirect
45. C₂×C₂₉×#124	C₂²	semidirect
46. C₂×C₂₉×#124	C₂²	semidirect
47. C₂×C₂₉×#124	C₂²	semidirect
49. C₂×C₂₉×#123	C₂²	semidirect
50. C₂×C₂₉×#123	C₂²	semidirect
51. C₂×C₂₉×#123	C₂²	semidirect
52. C₂×C₂₉×#123	C₂²	semidirect
53. C₂×C₂₉×#123	C₂²	semidirect
54. C₂×C₂₉×#123	C₂²	semidirect
55. C₂×C₂₉×C₂²⋊Q₈	C₂²	semidirect
56. C₂×C₂₉×C₂²⋊Q₈	C₂²	semidirect
57. C₂×C₂₉×C₂²⋊Q₈	C₂²	semidirect
58. C₂×C₂₉×C₂²⋊Q₈	C₂²	semidirect
59. C₂×C₂₉×C₂²⋊Q₈	C₂²	semidirect
62. C₂×C₂₉×#121	C₂²	semidirect
63. C₂×C₂₉×#121	C₂²	semidirect
64. C₂×C₂₉×#121	C₂²	semidirect
67. C₂×C₂₉×#120	C₂²	semidirect
68. C₂×C₂₉×#120	C₂²	semidirect
69. C₂×C₄×Q₈×C₂₉	C₂²	semidirect
70. C₂×C₄×D₄×C₂₉	C₂²	semidirect
71. C₂×C₄×D₄×C₂₉	C₂²	semidirect
72. C₂×C₄×D₄×C₂₉	C₂²	semidirect
73. C₂×C₄×D₄×C₂₉	C₂²	semidirect
74. C₂×C₂₉×#117	C₂²	semidirect
75. C₂×C₂₉×#117	C₂²	semidirect
76. C₂×C₂₉×#117	C₂²	semidirect
77. C₂²×C₂²⋊C₄×C₂₉	C₂²	semidirect
78. C₂²×C₂²⋊C₄×C₂₉	C₂²	semidirect
79. C₂²×C₂²⋊C₄×C₂₉	C₂²	semidirect
80. C₂²×C₄²×C₂₉	C₂²	semidirect
91. C₂²×Q₈×C₂₉	C₂³	semidirect
104. C₂²×D₄×C₂₉	C₂³	semidirect
112. C₂₉×C₄⋊Q₈	C₂³	semidirect
113. C₂₉×C₄⋊Q₈	C₂³	semidirect
114. C₂₉×#126	C₂³	semidirect
115. C₂₉×#126	C₂³	semidirect
116. C₂₉×#126	C₂³	semidirect
117. C₂₉×#125	C₂³	semidirect
120. C₂₉×#124	C₂³	semidirect
121. C₂₉×#124	C₂³	semidirect
122. C₂₉×#124	C₂³	semidirect
123. C₂₉×#124	C₂³	semidirect
124. C₂₉×#124	C₂³	semidirect
125. C₂₉×#124	C₂³	semidirect
126. C₂₉×#124	C₂³	semidirect
127. C₂₉×#124	C₂³	semidirect
129. C₂₉×#123	C₂³	semidirect
130. C₂₉×#123	C₂³	semidirect
131. C₂₉×#123	C₂³	semidirect
132. C₂₉×#123	C₂³	semidirect
133. C₂₉×#123	C₂³	semidirect
134. C₂₉×#123	C₂³	semidirect
135. C₂₉×C₂²⋊Q₈	C₂³	semidirect
136. C₂₉×C₂²⋊Q₈	C₂³	semidirect
137. C₂₉×C₂²⋊Q₈	C₂³	semidirect
138. C₂₉×C₂²⋊Q₈	C₂³	semidirect
139. C₂₉×C₂²⋊Q₈	C₂³	semidirect
142. C₂₉×#121	C₂³	semidirect
143. C₂₉×#121	C₂³	semidirect
144. C₂₉×#121	C₂³	semidirect
147. C₂₉×#120	C₂³	semidirect
148. C₂₉×#120	C₂³	semidirect
149. C₄×Q₈×C₂₉	C₂³	semidirect
150. C₄×D₄×C₂₉	C₂³	semidirect
151. C₄×D₄×C₂₉	C₂³	semidirect
152. C₄×D₄×C₂₉	C₂³	semidirect
153. C₄×D₄×C₂₉	C₂³	semidirect
154. C₂₉×#117	C₂³	semidirect
155. C₂₉×#117	C₂³	semidirect
156. C₂₉×#117	C₂³	semidirect
181. C₂×C₂²⋊C₄×C₂₉	C₂³	semidirect
182. C₂×C₂²⋊C₄×C₂₉	C₂³	semidirect
183. C₂×C₂²⋊C₄×C₂₉	C₂³	semidirect
190. C₂×C₄²×C₂₉	C₂³	semidirect
286. C₂×#3545	C₂₉	direct (N × H)
346. #3545	C₂×C₂₉	direct (N × H)
347. C₂×#563	C₂×C₂₉	semidirect
348. C₂×#562	C₂×C₂₉	semidirect
349. C₂×H(3,𝔽₄)	C₂×C₂₉	semidirect
350. C₂×#555	C₂×C₂₉	semidirect
351. C₂×#551	C₂×C₂₉	semidirect
352. C₂×#551	C₂×C₂₉	semidirect
353. C₂×#546	C₂×C₂₉	semidirect
354. C₂×#542	C₂×C₂₉	semidirect
355. C₂×#538	C₂×C₂₉	semidirect
356. C₂×#536	C₂×C₂₉	semidirect
357. C₂×#534	C₂×C₂₉	semidirect
358. C₂×#529	C₂×C₂₉	semidirect
359. C₂²×#124	C₂×C₂₉	semidirect
388. C₂³×Q₈	C₂²×C₂₉	semidirect
390. C₂³×D₄	C₂²×C₂₉	semidirect
391. #563	C₂²×C₂₉	semidirect
392. #562	C₂²×C₂₉	semidirect
393. H(3,𝔽₄)	C₂²×C₂₉	semidirect
394. #555	C₂²×C₂₉	semidirect
395. #551	C₂²×C₂₉	semidirect
396. #551	C₂²×C₂₉	semidirect
397. #546	C₂²×C₂₉	semidirect
398. #542	C₂²×C₂₉	semidirect
399. #538	C₂²×C₂₉	semidirect
400. #536	C₂²×C₂₉	semidirect
401. #534	C₂²×C₂₉	semidirect
402. C₂×C₄⋊Q₈	C₂²×C₂₉	semidirect
403. C₂×C₄⋊Q₈	C₂²×C₂₉	semidirect
404. #529	C₂²×C₂₉	semidirect
405. C₂×#126	C₂²×C₂₉	semidirect
406. C₂×#126	C₂²×C₂₉	semidirect
407. C₂×#126	C₂²×C₂₉	semidirect
408. C₂×#125	C₂²×C₂₉	semidirect
411. C₂×#124	C₂²×C₂₉	semidirect
412. C₂×#124	C₂²×C₂₉	semidirect
413. C₂×#124	C₂²×C₂₉	semidirect
414. C₂×#124	C₂²×C₂₉	semidirect
415. C₂×#124	C₂²×C₂₉	semidirect
416. C₂×#124	C₂²×C₂₉	semidirect
417. C₂×#124	C₂²×C₂₉	semidirect
418. C₂×#124	C₂²×C₂₉	semidirect
419. C₂×#124	C₂²×C₂₉	semidirect
421. C₂×#123	C₂²×C₂₉	semidirect
422. C₂×#123	C₂²×C₂₉	semidirect
423. C₂×#123	C₂²×C₂₉	semidirect
424. C₂×#123	C₂²×C₂₉	semidirect
425. C₂×#123	C₂²×C₂₉	semidirect
426. C₂×#123	C₂²×C₂₉	semidirect
427. C₂×C₂²⋊Q₈	C₂²×C₂₉	semidirect
428. C₂×C₂²⋊Q₈	C₂²×C₂₉	semidirect
429. C₂×C₂²⋊Q₈	C₂²×C₂₉	semidirect
430. C₂×C₂²⋊Q₈	C₂²×C₂₉	semidirect
431. C₂×C₂²⋊Q₈	C₂²×C₂₉	semidirect
434. C₂×#121	C₂²×C₂₉	semidirect
435. C₂×#121	C₂²×C₂₉	semidirect
436. C₂×#121	C₂²×C₂₉	semidirect
439. C₂×#120	C₂²×C₂₉	semidirect
440. C₂×#120	C₂²×C₂₉	semidirect
441. C₂×C₄×Q₈	C₂²×C₂₉	semidirect
442. C₂×C₄×D₄	C₂²×C₂₉	semidirect
443. C₂×C₄×D₄	C₂²×C₂₉	semidirect
444. C₂×C₄×D₄	C₂²×C₂₉	semidirect
445. C₂×C₄×D₄	C₂²×C₂₉	semidirect
446. C₂×#117	C₂²×C₂₉	semidirect
447. C₂×#117	C₂²×C₂₉	semidirect
448. C₂×#117	C₂²×C₂₉	semidirect
449. C₂²×C₂²⋊C₄	C₂²×C₂₉	semidirect
450. C₂²×C₂²⋊C₄	C₂²×C₂₉	semidirect
451. C₂²×C₂²⋊C₄	C₂²×C₂₉	semidirect
452. C₂²×C₄²	C₂²×C₂₉	semidirect
457. C₂×C₂₉	#3545	direct (N × H)
470. C₂²×Q₈	C₂³×C₂₉	semidirect
483. C₂²×D₄	C₂³×C₂₉	semidirect
491. C₄⋊Q₈	C₂³×C₂₉	semidirect
492. C₄⋊Q₈	C₂³×C₂₉	semidirect
493. #126	C₂³×C₂₉	semidirect
494. #126	C₂³×C₂₉	semidirect
495. #126	C₂³×C₂₉	semidirect
496. #125	C₂³×C₂₉	semidirect
499. #124	C₂³×C₂₉	semidirect
500. #124	C₂³×C₂₉	semidirect
501. #124	C₂³×C₂₉	semidirect
502. #124	C₂³×C₂₉	semidirect
503. #124	C₂³×C₂₉	semidirect
504. #124	C₂³×C₂₉	semidirect
505. #124	C₂³×C₂₉	semidirect
506. #124	C₂³×C₂₉	semidirect
508. #123	C₂³×C₂₉	semidirect
509. #123	C₂³×C₂₉	semidirect
510. #123	C₂³×C₂₉	semidirect
511. #123	C₂³×C₂₉	semidirect
512. #123	C₂³×C₂₉	semidirect
513. #123	C₂³×C₂₉	semidirect
514. C₂²⋊Q₈	C₂³×C₂₉	semidirect
515. C₂²⋊Q₈	C₂³×C₂₉	semidirect
516. C₂²⋊Q₈	C₂³×C₂₉	semidirect
517. C₂²⋊Q₈	C₂³×C₂₉	semidirect
518. C₂²⋊Q₈	C₂³×C₂₉	semidirect
521. #121	C₂³×C₂₉	semidirect
522. #121	C₂³×C₂₉	semidirect
523. #121	C₂³×C₂₉	semidirect
526. #120	C₂³×C₂₉	semidirect
527. #120	C₂³×C₂₉	semidirect
528. C₄×Q₈	C₂³×C₂₉	semidirect
529. C₄×D₄	C₂³×C₂₉	semidirect
530. C₄×D₄	C₂³×C₂₉	semidirect
531. C₄×D₄	C₂³×C₂₉	semidirect
532. C₄×D₄	C₂³×C₂₉	semidirect
533. #117	C₂³×C₂₉	semidirect
534. #117	C₂³×C₂₉	semidirect
535. #117	C₂³×C₂₉	semidirect
560. C₂×C₂²⋊C₄	C₂³×C₂₉	semidirect
561. C₂×C₂²⋊C₄	C₂³×C₂₉	semidirect
562. C₂×C₂²⋊C₄	C₂³×C₂₉	semidirect
569. C₂×C₄²	C₂³×C₂₉	semidirect
570. C₂₉	C₂×#3545	direct (N × H)
756. C₂	C₂₉×#3545	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×#3545	2
C₂×C₂₉×#563	2
C₂×C₂₉×#562	2
C₂×C₂₉×H(3,𝔽₄)	2
C₂×C₂₉×#555	2
C₂×C₂₉×#551	2
C₂×C₂₉×#546	2
C₂×C₂₉×#542	2
C₂×C₂₉×#538	2
C₂×C₂₉×#536	2
C₂×C₂₉×#534	2
C₂×C₂₉×#529	2
C₂²×C₂₉×#124	2
C₂×#3545	29

Subgroups — C2×C29×#3545 #20357653

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₉×#3545 #20357653