Subgroups — #16833551

Order 3712.

1042 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14271880	C₂	1	1	yes	maximal, characteristic, complemented
2	#14271880	C₂	1	1	yes	maximal, characteristic, complemented
3	#14271868	C₂	1	1	yes	maximal, characteristic, complemented
4	#14271858	C₂	1	1	yes	maximal, characteristic, complemented
5	#14271856	C₂	1	1	yes	maximal, characteristic, complemented
6	#14271853	C₂	1	1	yes	maximal, characteristic, complemented
7	#14271846	C₂	1	1	yes	maximal, characteristic, complemented
8	#14271845	C₂	1	1	yes	maximal, characteristic, complemented
9	#14271842	C₂	1	1	yes	maximal, characteristic, complemented
10	#14271842	C₂	1	1	yes	maximal, characteristic, complemented
11	#14271842	C₂	1	1	yes	maximal, characteristic, complemented
12	#14271836	C₂	1	1	yes	maximal, characteristic, complemented
13	#14271813	C₂	1	1	yes	maximal, characteristic, complemented
14	#14271802	C₂	1	1	yes	maximal, characteristic, complemented
15	#14271802	C₂	1	1	yes	maximal, characteristic, complemented
16	#14271781	C₂	1	1	yes	maximal, characteristic, complemented
17	#14271772	C₂	1	1	yes	maximal, characteristic, complemented
18	#14271758	C₂	1	1	yes	maximal, characteristic, complemented
19	#14271754	C₂	1	1	yes	maximal, characteristic, complemented
20	#14271750	C₂	1	1	yes	maximal, characteristic, complemented
21	#14271745	C₂	1	1	yes	maximal, characteristic, complemented
22	#14271694	C₂	1	1	yes	maximal, characteristic, complemented
23	#14271693	C₂	1	1	yes	maximal, characteristic, complemented
24	#14271691	C₂	1	1	yes	maximal, characteristic, complemented
25	#14271690	C₂	1	1	yes	maximal, characteristic, complemented
26	C₂×#11745260	C₂	1	1	yes	maximal, characteristic, complemented
27	#126×D₂₉	C₂	1	1	yes	maximal, characteristic, complemented
28	#14271642	C₂	1	1	yes	maximal, characteristic, complemented
29	#14271635	C₂	1	1	yes	maximal, characteristic, complemented
30	C₄×#90807	C₂	1	1	yes	maximal, characteristic, complemented
31	C₂₉×#553	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#90807	C₂²	1	1	yes	characteristic
33	C₂×#90807	C₂²	1	1	yes	characteristic
34	C₂×D₄×D₂₉	C₂²	1	1	yes	characteristic
35	C₂₉×#126	C₂²	1	1	yes	characteristic, complemented
36	C₂₉×#126	C₂²	1	1	yes	characteristic, complemented
37	C₂₉×#125	C₂²	1	1	yes	characteristic, complemented
38	C₂₉×#123	C₂²	1	1	yes	characteristic, complemented
39	C₂₉×#123	C₂²	1	1	yes	characteristic, complemented
40	C₂₉×#121	C₂²	1	1	yes	characteristic
41	C₂₉×#121	C₂²	1	1	yes	characteristic
42	C₂₉×#121	C₂²	1	1	yes	characteristic, complemented
43	C₂₉×#121	C₂²	1	1	yes	characteristic, complemented
44	C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
45	C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic, complemented
46	C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic, complemented
47	C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic, complemented
48	C₂₉×#117	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic, complemented
50	#11745301	C₂²	1	1	yes	characteristic
51	#11745301	C₂²	1	1	yes	characteristic
52	#11745301	C₂²	1	1	yes	characteristic
53	#11745301	C₂²	1	1	yes	characteristic, complemented
54	#11745300	C₂²	1	1	yes	characteristic, complemented
55	#11745299	C₂²	1	1	yes	characteristic
56	#11745299	C₂²	1	1	yes	characteristic
57	#11745299	C₂²	1	1	yes	characteristic
58	#11745299	C₂²	1	1	yes	characteristic
59	#11745298	C₂²	1	1	yes	characteristic, complemented
60	#11745297	C₂²	1	1	yes	characteristic
61	#11745297	C₂²	1	1	yes	characteristic
62	#11745297	C₂²	1	1	yes	characteristic, complemented
63	#11745297	C₂²	1	1	yes	characteristic, complemented
64	#11745297	C₂²	1	1	yes	characteristic, complemented
65	#11745297	C₂²	1	1	yes	characteristic, complemented
66	D₄×Dic₂₉	C₂²	1	1	yes	characteristic
67	D₄×Dic₂₉	C₂²	1	1	yes	characteristic, complemented
68	D₄×Dic₂₉	C₂²	1	1	yes	characteristic, complemented
69	D₄×Dic₂₉	C₂²	1	1	yes	characteristic, complemented
70	D₄×Dic₂₉	C₂²	1	1	yes	characteristic, complemented
71	#11745291	C₂²	1	1	yes	characteristic
72	#11745291	C₂²	1	1	yes	characteristic
73	C₄×C₂²⋊D₂₉	C₂²	1	1	yes	characteristic
74	C₄×C₂²⋊D₂₉	C₂²	1	1	yes	characteristic
75	C₄×C₂²⋊D₂₉	C₂²	1	1	yes	characteristic
76	C₄×C₂²⋊D₂₉	C₂²	1	1	yes	characteristic
77	C₄×C₂²⋊D₂₉	C₂²	1	1	yes	characteristic, complemented
78	C₄×C₂²⋊D₂₉	C₂²	1	1	yes	characteristic, complemented
79	C₄×C₂²⋊D₂₉	C₂²	1	1	yes	characteristic, complemented
80	C₄×C₂²⋊D₂₉	C₂²	1	1	yes	characteristic, complemented
81	C₂×#90781	C₂²	1	1	yes	characteristic
82	C₂×#90781	C₂²	1	1	yes	characteristic
83	C₂×#90781	C₂²	1	1	yes	characteristic
84	C₂×#90781	C₂²	1	1	yes	characteristic
85	#11745288	C₂²	1	1	yes	characteristic, complemented
86	C₂×C₄⋊Dic₂₉	C₂²	1	1	yes	characteristic, complemented
87	#11745286	C₂²	1	1	yes	characteristic, complemented
88	#11745286	C₂²	1	1	yes	characteristic, complemented
89	#11745286	C₂²	1	1	yes	characteristic, complemented
90	#11745286	C₂²	1	1	yes	characteristic, complemented
91	C₂×#90779	C₂²	1	1	yes	characteristic, complemented
92	C₂×#90779	C₂²	1	1	yes	characteristic, complemented
93	C₂×C₄×Dic₂₉	C₂²	1	1	yes	characteristic, complemented
94	C₂×C₄×Dic₂₉	C₂²	1	1	yes	characteristic, complemented
95	#11745260	C₂²	1	1	yes	characteristic
96	#11745260	C₂²	1	1	yes	characteristic
97	#11745260	C₂²	1	1	yes	characteristic
98	#11745260	C₂²	1	1	yes	characteristic
99	#11745260	C₂²	1	1	yes	characteristic
100	#11745260	C₂²	1	1	yes	characteristic
101	#11745260	C₂²	1	1	yes	characteristic
102	#11745260	C₂²	1	1	yes	characteristic, complemented
103	#11745260	C₂²	1	1	yes	characteristic, complemented
104	#11745260	C₂²	1	1	yes	characteristic, complemented
105	#11745260	C₂²	1	1	yes	characteristic, complemented
106	#11745260	C₂²	1	1	yes	characteristic, complemented
107	#11745259	C₂²	1	1	yes	characteristic, complemented
108	#11745258	C₂²	1	1	yes	characteristic
109	#11745258	C₂²	1	1	yes	characteristic
110	#11745258	C₂²	1	1	yes	characteristic, complemented
111	#11745258	C₂²	1	1	yes	characteristic, complemented
112	#11745258	C₂²	1	1	yes	characteristic, complemented
113	#11745258	C₂²	1	1	yes	characteristic, complemented
114	#11745256	C₂²	1	1	yes	characteristic
115	#11745256	C₂²	1	1	yes	characteristic
116	#11745255	C₂²	1	1	yes	characteristic
117	#11745254	C₂²	1	1	yes	characteristic
118	#11745254	C₂²	1	1	yes	characteristic, complemented
119	C₄⋊C₄×D₂₉	C₂²	1	1	yes	characteristic, complemented
120	C₄⋊C₄×D₂₉	C₂²	1	1	yes	characteristic, complemented
121	C₄⋊C₄×D₂₉	C₂²	1	1	yes	characteristic, complemented
122	#11745252	C₂²	1	1	yes	characteristic, complemented
123	#11745251	C₂²	1	1	yes	characteristic, complemented
124	#11745251	C₂²	1	1	yes	characteristic, complemented
125	#11745251	C₂²	1	1	yes	characteristic, complemented
126	#11745251	C₂²	1	1	yes	characteristic, complemented
127	#11745251	C₂²	1	1	yes	characteristic, complemented
128	#11745251	C₂²	1	1	yes	characteristic, complemented
129	#11745250	C₂²	1	1	yes	characteristic, complemented
130	#11745250	C₂²	1	1	yes	characteristic, complemented
131	#11745249	C₂²	1	1	yes	characteristic, complemented
132	#11745249	C₂²	1	1	yes	characteristic, complemented
133	#11745249	C₂²	1	1	yes	characteristic, complemented
134	#11745249	C₂²	1	1	yes	characteristic, complemented
135	#11745248	C₂²	1	1	yes	characteristic
136	#11745248	C₂²	1	1	yes	characteristic, complemented
137	#11745247	C₂²	1	1	yes	characteristic
138	#11745247	C₂²	1	1	yes	characteristic
139	#11745247	C₂²	1	1	yes	characteristic
140	#11745247	C₂²	1	1	yes	characteristic
141	#11745247	C₂²	1	1	yes	characteristic
142	#11745247	C₂²	1	1	yes	characteristic, complemented
143	#11745246	C₂²	1	1	yes	characteristic
144	#11745246	C₂²	1	1	yes	characteristic
145	#11745245	C₂²	1	1	yes	characteristic, complemented
146	#11745245	C₂²	1	1	yes	characteristic, complemented
147	#11745245	C₂²	1	1	yes	characteristic, complemented
148	#11745245	C₂²	1	1	yes	characteristic, complemented
149	#11745243	C₂²	1	1	yes	characteristic
150	#11745243	C₂²	1	1	yes	characteristic
151	#11745243	C₂²	1	1	yes	characteristic
152	#11745243	C₂²	1	1	yes	characteristic
153	#11745243	C₂²	1	1	yes	characteristic, complemented
154	#11745243	C₂²	1	1	yes	characteristic, complemented
155	C₂²⋊C₄×D₂₉	C₂²	1	1	yes	characteristic
156	C₂²⋊C₄×D₂₉	C₂²	1	1	yes	characteristic
157	C₂²⋊C₄×D₂₉	C₂²	1	1	yes	characteristic
158	C₂²⋊C₄×D₂₉	C₂²	1	1	yes	characteristic
159	#11745241	C₂²	1	1	yes	characteristic, complemented
160	#11745241	C₂²	1	1	yes	characteristic, complemented
161	#11745241	C₂²	1	1	yes	characteristic, complemented
162	#11745241	C₂²	1	1	yes	characteristic, complemented
163	#11745241	C₂²	1	1	yes	characteristic, complemented
164	#11745241	C₂²	1	1	yes	characteristic, complemented
165	#11745240	C₂²	1	1	yes	characteristic, complemented
166	#11745240	C₂²	1	1	yes	characteristic, complemented
167	#11745240	C₂²	1	1	yes	characteristic, complemented
168	#11745240	C₂²	1	1	yes	characteristic, complemented
169	#11745239	C₂²	1	1	yes	characteristic, complemented
170	#11745239	C₂²	1	1	yes	characteristic, complemented
171	#11745239	C₂²	1	1	yes	characteristic, complemented
172	#11745239	C₂²	1	1	yes	characteristic, complemented
173	#11745239	C₂²	1	1	yes	characteristic, complemented
174	#11745239	C₂²	1	1	yes	characteristic, complemented
175	#11745238	C₂²	1	1	yes	characteristic
176	#11745238	C₂²	1	1	yes	characteristic
177	C₄×D₁₁₆	C₂²	1	1	yes	characteristic
178	#11745234	C₂²	1	1	yes	characteristic
179	#11745234	C₂²	1	1	yes	characteristic, complemented
180	#11745234	C₂²	1	1	yes	characteristic, complemented
181	#11745234	C₂²	1	1	yes	characteristic, complemented
182	C₄²×D₂₉	C₂²	1	1	yes	characteristic, complemented
183	#11745232	C₂²	1	1	yes	characteristic, complemented
184	C₄×Dic₅₈	C₂²	1	1	yes	characteristic, complemented
185	C₄×Dic₅₈	C₂²	1	1	yes	characteristic, complemented
186	C₄×Dic₅₈	C₂²	1	1	yes	characteristic, complemented
187	C₂³×D₂₉	C₂³	1	1	yes	characteristic
188	C₂³×D₂₉	C₂³	1	1	yes	characteristic
189	C₂×D₄×C₂₉	C₂³	1	1	yes	characteristic
190	C₂×D₄×C₂₉	C₂³	1	1	yes	characteristic
191	C₂×D₄×C₂₉	C₂³	1	1	yes	characteristic
192	C₂×D₄×C₂₉	C₂³	1	1	yes	characteristic
193	C₂×D₄×C₂₉	C₂³	1	1	yes	characteristic
194	C₂×D₄×C₂₉	C₂³	1	1	yes	characteristic
195	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
196	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
197	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
198	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
199	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
200	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
201	C₂×C₂²⋊D₂₉	C₂³	1	1	yes	characteristic
202	C₂×C₂²⋊D₂₉	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊D₂₉	C₂³	1	1	yes	characteristic
204	C₂×C₂²⋊D₂₉	C₂³	1	1	yes	characteristic
205	C₂×C₂²⋊D₂₉	C₂³	1	1	yes	characteristic
206	C₂×C₂²⋊D₂₉	C₂³	1	1	yes	characteristic
207	C₂×C₂²⋊D₂₉	C₂³	1	1	yes	characteristic
208	C₂×C₂²⋊D₂₉	C₂³	1	1	yes	characteristic
209	C₂²×Dic₂₉	C₂³	1	1	yes	characteristic
210	C₂²×Dic₂₉	C₂³	1	1	yes	characteristic
211	C₂²×Dic₂₉	C₂³	1	1	yes	characteristic
212	C₂²×Dic₂₉	C₂³	1	1	yes	characteristic
213	C₂²×Dic₂₉	C₂³	1	1	yes	characteristic
214	C₂²×Dic₂₉	C₂³	1	1	yes	characteristic
215	C₂²×Dic₂₉	C₂³	1	1	yes	characteristic
216	C₂²×Dic₂₉	C₂³	1	1	yes	characteristic
217	#90807	—	2	4	no	—
218	#90807	—	2	4	no	—
219	D₄×D₂₉	—	2	4	no	—
220	C₂×D₁₁₆	C₂³	1	1	yes	characteristic
221	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
222	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
223	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
224	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
225	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
226	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
227	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
228	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
229	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
230	C₂×Dic₅₈	C₂³	1	1	yes	characteristic
231	C₂×Dic₅₈	C₂³	1	1	yes	characteristic
232	C₂×Dic₅₈	C₂³	1	1	yes	characteristic
233	C₂×Dic₅₈	C₂³	1	1	yes	characteristic
234	C₂×Dic₅₈	C₂³	1	1	yes	characteristic
235	C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
236	C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
237	C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
238	C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
239	C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
240	C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
241	C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
242	C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
243	C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
244	C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
245	C₂²⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
246	C₂²⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
247	C₂²⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
248	C₂²⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
249	C₂²⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
250	C₂²⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
251	C₂²⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
252	C₂²⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
253	C₂²⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
254	C₂²⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
255	C₄²×C₂₉	C₂³	1	1	yes	characteristic
256	C₄²×C₂₉	C₂³	1	1	yes	characteristic
257	C₄²×C₂₉	C₂³	1	1	yes	characteristic
258	C₂²⋊Dic₂₉	C₂³	1	1	yes	characteristic
259	C₂²⋊Dic₂₉	C₂³	1	1	yes	characteristic
260	C₂²⋊Dic₂₉	C₂³	1	1	yes	characteristic
261	C₂²⋊Dic₂₉	C₂³	1	1	yes	characteristic
262	C₂²⋊Dic₂₉	C₂³	1	1	yes	characteristic
263	C₂²⋊Dic₂₉	C₂³	1	1	yes	characteristic
264	C₂²⋊Dic₂₉	C₂³	1	1	yes	characteristic
265	C₂²⋊Dic₂₉	C₂³	1	1	yes	characteristic
266	C₂²⋊Dic₂₉	C₂³	1	1	yes	characteristic
267	C₂²⋊Dic₂₉	C₂³	1	1	yes	characteristic
268	C₂²⋊Dic₂₉	C₂³	1	1	yes	characteristic
269	C₂²⋊Dic₂₉	C₂³	1	1	yes	characteristic
270	C₂²⋊Dic₂₉	C₂³	1	1	yes	characteristic
271	C₂²⋊Dic₂₉	C₂³	1	1	yes	characteristic
272	#90781	C₂³	1	1	yes	characteristic
273	#90781	C₂³	1	1	yes	characteristic
274	#90781	C₂³	1	1	yes	characteristic
275	#90781	C₂³	1	1	yes	characteristic
276	#90781	C₂³	1	1	yes	characteristic
277	#90781	C₂³	1	1	yes	characteristic
278	#90781	C₂³	1	1	yes	characteristic
279	#90781	C₂³	1	1	yes	characteristic
280	#90781	C₂³	1	1	yes	characteristic
281	#90781	C₂³	1	1	yes	characteristic
282	#90781	C₂³	1	1	yes	characteristic
283	#90781	C₂³	1	1	yes	characteristic
284	#90781	C₂³	1	1	yes	characteristic
285	#90781	C₂³	1	1	yes	characteristic
286	#90781	C₂³	1	1	yes	characteristic
287	#90781	C₂³	1	1	yes	characteristic
288	#90781	C₂³	1	1	yes	characteristic
289	#90781	C₂³	1	1	yes	characteristic
290	#90781	C₂³	1	1	yes	characteristic
291	#90781	C₂³	1	1	yes	characteristic
292	#90781	C₂³	1	1	yes	characteristic
293	#90781	C₂³	1	1	yes	characteristic
294	C₄⋊Dic₂₉	C₂³	1	1	yes	characteristic
295	C₄⋊Dic₂₉	C₂³	1	1	yes	characteristic
296	C₄⋊Dic₂₉	C₂³	1	1	yes	characteristic
297	C₄⋊Dic₂₉	C₂³	1	1	yes	characteristic
298	C₄⋊Dic₂₉	C₂³	1	1	yes	characteristic
299	C₄⋊Dic₂₉	C₂³	1	1	yes	characteristic
300	C₄⋊Dic₂₉	C₂³	1	1	yes	characteristic
301	C₄⋊Dic₂₉	C₂³	1	1	yes	characteristic
302	C₄⋊Dic₂₉	C₂³	1	1	yes	characteristic
303	C₄⋊Dic₂₉	C₂³	1	1	yes	characteristic
304	#90779	C₂³	1	1	yes	characteristic
305	#90779	C₂³	1	1	yes	characteristic
306	#90779	C₂³	1	1	yes	characteristic
307	#90779	C₂³	1	1	yes	characteristic
308	#90779	C₂³	1	1	yes	characteristic
309	#90779	C₂³	1	1	yes	characteristic
310	#90779	C₂³	1	1	yes	characteristic
311	#90779	C₂³	1	1	yes	characteristic
312	#90779	C₂³	1	1	yes	characteristic
313	#90779	C₂³	1	1	yes	characteristic
314	#90779	C₂³	1	1	yes	characteristic
315	#90779	C₂³	1	1	yes	characteristic
316	#90779	C₂³	1	1	yes	characteristic
317	#90779	C₂³	1	1	yes	characteristic
318	#90779	C₂³	1	1	yes	characteristic
319	#90779	C₂³	1	1	yes	characteristic
320	#90779	C₂³	1	1	yes	characteristic
321	#90779	C₂³	1	1	yes	characteristic
322	#90779	C₂³	1	1	yes	characteristic
323	#90779	C₂³	1	1	yes	characteristic
324	#90779	C₂³	1	1	yes	characteristic
325	#90779	C₂³	1	1	yes	characteristic
326	#90779	C₂³	1	1	yes	characteristic
327	#90779	C₂³	1	1	yes	characteristic
328	#90779	C₂³	1	1	yes	characteristic
329	#90779	C₂³	1	1	yes	characteristic
330	C₄×Dic₂₉	C₂³	1	1	yes	characteristic
331	C₄×Dic₂₉	C₂³	1	1	yes	characteristic
332	C₄×Dic₂₉	C₂³	1	1	yes	characteristic
333	C₄×Dic₂₉	C₂³	1	1	yes	characteristic
334	C₄×Dic₂₉	C₂³	1	1	yes	characteristic
335	C₄×Dic₂₉	C₂³	1	1	yes	characteristic
336	C₄×Dic₂₉	C₂³	1	1	yes	characteristic
337	C₄×Dic₂₉	C₂³	1	1	yes	characteristic
338	C₄×Dic₂₉	C₂³	1	1	yes	characteristic
339	C₄×Dic₂₉	C₂³	1	1	yes	characteristic
340	C₄×Dic₂₉	C₂³	1	1	yes	characteristic
341	C₄×Dic₂₉	C₂³	1	1	yes	characteristic
342	C₄×Dic₂₉	C₂³	1	1	yes	characteristic
343	C₄×Dic₂₉	C₂³	1	1	yes	characteristic
344	C₄×Dic₂₉	C₂³	1	1	yes	characteristic
345	C₂³×C₂₉	C₂⁴	1	1	yes	characteristic
346	C₂³×C₂₉	C₂⁴	1	1	yes	characteristic
347	C₂³×C₂₉	C₂⁴	1	1	yes	characteristic
348	C₂³×C₂₉	C₂⁴	1	1	yes	characteristic
349	C₂²×D₂₉	—	2	2	no	—
350	C₂²×D₂₉	—	2	2	no	—
351	C₂²×D₂₉	—	4	1	no	—
352	C₂²×D₂₉	—	4	1	no	—
353	C₂²×D₂₉	—	4	1	no	—
354	C₂²×D₂₉	—	4	1	no	—
355	C₂²×D₂₉	C₂⁴	1	1	yes	characteristic
356	C₂²×D₂₉	C₂⁴	1	1	yes	characteristic
357	C₂²×D₂₉	C₂⁴	1	1	yes	characteristic
358	D₄×C₂₉	—	2	2	no	—
359	D₄×C₂₉	—	2	2	no	—
360	D₄×C₂₉	—	2	2	no	—
361	D₄×C₂₉	—	4	1	no	—
362	D₄×C₂₉	—	4	1	no	—
363	D₄×C₂₉	—	4	1	no	—
364	C₂×C₄×C₂₉	—	4	1	no	—
365	C₂×C₄×C₂₉	—	4	1	no	—
366	C₂×C₄×C₂₉	—	4	1	no	—
367	C₂×C₄×C₂₉	—	4	1	no	—
368	C₂×C₄×C₂₉	—	4	1	no	—
369	C₂×C₄×C₂₉	—	4	1	no	—
370	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
371	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
372	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
373	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
374	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
375	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
376	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
377	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
378	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
379	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
380	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
381	C₂²⋊D₂₉	—	2	2	no	—
382	C₂²⋊D₂₉	—	2	2	no	—
383	C₂²⋊D₂₉	—	2	2	no	—
384	C₂²⋊D₂₉	—	4	1	no	—
385	C₂²⋊D₂₉	—	4	1	no	—
386	C₂²⋊D₂₉	—	4	1	no	—
387	C₂²⋊D₂₉	—	4	1	no	—
388	C₂²⋊D₂₉	#41	1	4	yes	—
389	C₂×Dic₂₉	—	2	2	no	—
390	C₂×Dic₂₉	—	2	2	no	—
391	C₂×Dic₂₉	—	2	2	no	—
392	C₂×Dic₂₉	—	2	2	no	—
393	C₂×Dic₂₉	—	4	1	no	—
394	C₂×Dic₂₉	—	4	1	no	—
395	C₂×Dic₂₉	—	4	1	no	—
396	C₂×Dic₂₉	—	4	1	no	—
397	C₂×Dic₂₉	C₂⁴	1	1	yes	characteristic
398	C₂×Dic₂₉	C₂⁴	1	1	yes	characteristic
399	C₂×Dic₂₉	C₂⁴	1	1	yes	characteristic
400	C₂×Dic₂₉	C₂⁴	1	1	yes	characteristic
401	C₂×Dic₂₉	C₂⁴	1	1	yes	characteristic
402	C₂×Dic₂₉	C₂⁴	1	1	yes	characteristic
403	C₂×Dic₂₉	C₂⁴	1	1	yes	characteristic
404	C₂×Dic₂₉	C₂⁴	1	1	yes	characteristic
405	C₂×Dic₂₉	C₂⁴	1	1	yes	characteristic
406	C₂×Dic₂₉	C₂⁴	1	1	yes	characteristic
407	C₂×Dic₂₉	C₂⁴	1	1	yes	characteristic
408	C₂×Dic₂₉	C₂⁴	1	1	yes	characteristic
409	C₂×Dic₂₉	C₂⁴	1	1	yes	characteristic
410	D₁₁₆	—	2	2	no	—
411	C₄×D₂₉	—	2	2	no	—
412	C₄×D₂₉	—	2	2	no	—
413	C₄×D₂₉	—	2	2	no	—
414	C₄×D₂₉	—	4	1	no	—
415	C₄×D₂₉	—	4	1	no	—
416	C₄×D₂₉	—	4	1	no	—
417	C₄×D₂₉	—	4	1	no	—
418	C₄×D₂₉	—	4	1	no	—
419	C₄×D₂₉	—	4	1	no	—
420	Dic₅₈	—	2	2	no	—
421	Dic₅₈	—	2	2	no	—
422	Dic₅₈	—	4	1	no	—
423	Dic₅₈	—	4	1	no	—
424	Dic₅₈	—	4	1	no	—
425	#3521	—	29	1	no	maximal, Sylow
426	C₂²×C₂₉	—	2	1	no	—
427	C₂²×C₂₉	—	2	1	no	—
428	C₂²×C₂₉	—	2	1	no	—
429	C₂²×C₂₉	—	2	1	no	—
430	C₂²×C₂₉	—	2	1	no	—
431	C₂²×C₂₉	—	2	1	no	—
432	C₂²×C₂₉	—	2	1	no	—
433	C₂²×C₂₉	—	2	1	no	—
434	C₂²×C₂₉	—	2	1	no	—
435	C₂²×C₂₉	—	2	1	no	—
436	C₂²×C₂₉	—	2	1	no	—
437	C₂²×C₂₉	C₂×#41	1	2	yes	—
438	C₂²×C₂₉	C₂⁵	1	1	yes	characteristic
439	C₂×D₂₉	—	2	1	no	—
440	C₂×D₂₉	—	2	1	no	—
441	C₂×D₂₉	—	2	1	no	—
442	C₂×D₂₉	—	2	1	no	—
443	C₂×D₂₉	—	2	1	no	—
444	C₂×D₂₉	—	2	1	no	—
445	C₂×D₂₉	—	2	1	no	—
446	C₂×D₂₉	—	2	1	no	—
447	C₂×D₂₉	—	8	2	no	—
448	C₂×D₂₉	—	8	2	no	—
449	C₂×D₂₉	C₂×#41	1	2	yes	—
450	C₄×C₂₉	—	2	1	no	—
451	C₄×C₂₉	—	2	1	no	—
452	C₄×C₂₉	—	2	1	no	—
453	C₄×C₂₉	—	2	1	no	—
454	C₄×C₂₉	—	2	1	no	—
455	C₄×C₂₉	—	2	1	no	—
456	C₄×C₂₉	—	2	1	no	—
457	C₄×C₂₉	—	2	1	no	—
458	C₄×C₂₉	—	2	1	no	—
459	C₄×C₂₉	—	2	1	no	—
460	C₄×C₂₉	—	2	1	no	—
461	Dic₂₉	—	2	1	no	—
462	Dic₂₉	—	2	1	no	—
463	Dic₂₉	—	2	1	no	—
464	Dic₂₉	—	2	1	no	—
465	Dic₂₉	—	2	1	no	—
466	Dic₂₉	—	2	1	no	—
467	Dic₂₉	—	2	1	no	—
468	Dic₂₉	—	2	1	no	—
469	Dic₂₉	—	2	1	no	—
470	Dic₂₉	—	2	1	no	—
471	Dic₂₉	—	2	1	no	—
472	Dic₂₉	—	2	1	no	—
473	Dic₂₉	C₂×#41	1	2	yes	—
474	#556	—	29	1	no	—
475	#556	—	29	1	no	—
476	#554	—	29	1	no	—
477	#553	—	29	1	no	—
478	#553	—	29	1	no	—
479	#553	D₂₉	1	1	yes	characteristic, complemented
480	#552	—	29	1	no	—
481	#552	—	29	1	no	—
482	#552	—	29	1	no	—
483	#551	—	29	1	no	—
484	#551	—	29	1	no	—
485	#551	—	29	1	no	—
486	#551	—	29	1	no	—
487	#547	—	29	1	no	—
488	#546	—	29	1	no	—
489	#546	—	29	1	no	—
490	#542	—	29	1	no	—
491	#541	—	29	1	no	—
492	#539	—	29	1	no	—
493	#539	—	29	1	no	—
494	#538	—	29	1	no	—
495	#538	—	29	1	no	—
496	#529	—	29	1	no	—
497	#529	—	29	1	no	—
498	#529	—	29	1	no	—
499	#529	—	29	1	no	—
500	C₂×#126	—	29	1	no	—
501	C₂×#126	—	29	1	no	—
502	#520	—	29	1	no	—
503	#518	—	29	1	no	—
504	C₄×#41	—	29	1	no	—
505	C₂×C₂₉	—	2	2	no	—
506	C₂×C₂₉	—	4	1	no	—
507	C₂×C₂₉	—	4	1	no	—
508	C₂×C₂₉	—	4	1	no	—
509	C₂×C₂₉	C₂²×#41	1	1	yes	characteristic
510	C₂×C₂₉	#585	1	1	yes	characteristic
511	C₂×C₂₉	#585	1	1	yes	characteristic
512	D₂₉	—	2	2	no	—
513	D₂₉	—	4	1	no	—
514	D₂₉	—	4	1	no	—
515	C₂×#41	—	29	1	no	—
516	C₂×#41	—	29	1	no	—
517	C₂²×D₄	—	29	1	no	—
518	C₄⋊Q₈	—	29	1	no	—
519	C₄⋊Q₈	—	29	1	no	—
520	#126	—	29	1	no	—
521	#126	—	29	1	no	—
522	#126	—	29	1	no	—
523	#126	—	29	1	no	—
524	#126	—	29	1	no	—
525	#126	—	29	1	no	—
526	#126	—	29	1	no	—
527	#126	—	29	1	no	—
528	#126	—	29	1	no	—
529	#126	—	29	1	no	—
530	#126	—	29	1	no	—
531	#126	—	29	1	no	—
532	#126	—	29	1	no	—
533	#126	—	29	1	no	—
534	#126	—	29	1	no	—
535	#126	—	29	1	no	—
536	#126	—	29	1	no	—
537	#126	—	29	1	no	—
538	#126	—	29	1	no	—
539	#126	—	29	1	no	—
540	#126	C₂×D₂₉	1	1	yes	characteristic, complemented
541	#126	C₂×D₂₉	1	1	yes	characteristic, complemented
542	#125	—	29	1	no	—
543	#125	—	29	1	no	—
544	#125	—	29	1	no	—
545	#125	—	29	1	no	—
546	#125	—	29	1	no	—
547	#125	—	29	1	no	—
548	#125	—	29	1	no	—
549	#125	—	29	1	no	—
550	#125	C₂×D₂₉	1	1	yes	characteristic, complemented
551	#124	—	29	1	no	—
552	#124	—	29	1	no	—
553	#124	—	29	1	no	—
554	#124	—	29	1	no	—
555	#124	—	29	1	no	—
556	#124	—	29	1	no	—
557	#124	—	29	1	no	—
558	#123	—	29	1	no	—
559	#123	—	29	1	no	—
560	#123	—	29	1	no	—
561	#123	—	29	1	no	—
562	#123	—	29	1	no	—
563	#123	—	29	1	no	—
564	#123	—	29	1	no	—
565	#123	—	29	1	no	—
566	#123	—	29	1	no	—
567	#123	—	29	1	no	—
568	#123	—	29	1	no	—
569	#123	—	29	1	no	—
570	#123	—	29	1	no	—
571	#123	—	29	1	no	—
572	#123	—	29	1	no	—
573	#123	—	29	1	no	—
574	#123	C₂×D₂₉	1	1	yes	characteristic, complemented
575	#123	C₂×D₂₉	1	1	yes	characteristic, complemented
576	C₂²⋊Q₈	—	29	1	no	—
577	C₂²⋊Q₈	—	29	1	no	—
578	C₂²⋊Q₈	—	29	1	no	—
579	C₂²⋊Q₈	—	29	1	no	—
580	C₂²⋊Q₈	—	29	1	no	—
581	C₂²⋊Q₈	—	29	1	no	—
582	C₂²⋊Q₈	—	29	1	no	—
583	C₂²⋊Q₈	—	29	1	no	—
584	C₂²⋊Q₈	—	29	1	no	—
585	C₂²⋊Q₈	—	29	1	no	—
586	C₂²⋊Q₈	—	29	1	no	—
587	C₂²⋊Q₈	—	29	1	no	—
588	C₂²⋊Q₈	—	29	1	no	—
589	C₂²⋊Q₈	—	29	1	no	—
590	C₂²⋊Q₈	—	29	1	no	—
591	#121	—	29	1	no	—
592	#121	—	29	1	no	—
593	#121	—	29	1	no	—
594	#121	—	29	1	no	—
595	#121	—	29	1	no	—
596	#121	—	29	1	no	—
597	#121	—	29	1	no	—
598	#121	C₂×D₂₉	1	1	yes	characteristic
599	#121	C₂×D₂₉	1	1	yes	characteristic
600	#121	C₂×D₂₉	1	1	yes	characteristic, complemented
601	#121	C₂×D₂₉	1	1	yes	characteristic, complemented
602	#120	—	29	1	no	—
603	#120	—	29	1	no	—
604	#120	—	29	1	no	—
605	#120	—	29	1	no	—
606	C₄×Q₈	—	29	1	no	—
607	C₄×Q₈	—	29	1	no	—
608	C₄×Q₈	—	29	1	no	—
609	C₄×Q₈	—	29	1	no	—
610	C₄×Q₈	—	29	1	no	—
611	C₄×Q₈	—	29	1	no	—
612	C₄×Q₈	—	29	1	no	—
613	C₄×D₄	—	29	1	no	—
614	C₄×D₄	—	29	1	no	—
615	C₄×D₄	—	29	1	no	—
616	C₄×D₄	—	29	1	no	—
617	C₄×D₄	—	29	1	no	—
618	C₄×D₄	—	29	1	no	—
619	C₄×D₄	—	29	1	no	—
620	C₄×D₄	—	29	1	no	—
621	C₄×D₄	—	29	1	no	—
622	C₄×D₄	—	29	1	no	—
623	C₄×D₄	—	29	1	no	—
624	C₄×D₄	—	29	1	no	—
625	C₄×D₄	—	29	1	no	—
626	C₄×D₄	—	29	1	no	—
627	C₄×D₄	—	29	1	no	—
628	C₄×D₄	—	29	1	no	—
629	C₄×D₄	—	29	1	no	—
630	C₄×D₄	—	29	1	no	—
631	C₄×D₄	—	29	1	no	—
632	C₄×D₄	—	29	1	no	—
633	C₄×D₄	—	29	1	no	—
634	C₄×D₄	C₂×D₂₉	1	1	yes	characteristic
635	C₄×D₄	C₂×D₂₉	1	1	yes	characteristic, complemented
636	C₄×D₄	C₂×D₂₉	1	1	yes	characteristic, complemented
637	C₄×D₄	C₂×D₂₉	1	1	yes	characteristic, complemented
638	#117	—	29	1	no	—
639	#117	—	29	1	no	—
640	#117	—	29	1	no	—
641	#117	—	29	1	no	—
642	#117	—	29	1	no	—
643	#117	—	29	1	no	—
644	#117	—	29	1	no	—
645	#117	—	29	1	no	—
646	#117	—	29	1	no	—
647	#117	—	29	1	no	—
648	#117	—	29	1	no	—
649	#117	—	29	1	no	—
650	#117	—	29	1	no	—
651	#117	C₂×D₂₉	1	1	yes	characteristic, complemented
652	C₂×C₄⋊C₄	—	29	1	no	—
653	C₂×C₄⋊C₄	—	29	1	no	—
654	C₂×C₄⋊C₄	—	29	1	no	—
655	C₂×C₄⋊C₄	—	29	1	no	—
656	C₂×C₄⋊C₄	—	29	1	no	—
657	C₂×C₄⋊C₄	—	29	1	no	—
658	C₂×C₄⋊C₄	C₂×D₂₉	1	1	yes	characteristic, complemented
659	C₂×C₂²⋊C₄	—	29	1	no	—
660	C₂×C₂²⋊C₄	—	29	1	no	—
661	C₂×C₂²⋊C₄	—	29	1	no	—
662	C₂×C₂²⋊C₄	—	29	1	no	—
663	C₂×C₂²⋊C₄	—	29	1	no	—
664	C₂×C₂²⋊C₄	—	29	1	no	—
665	C₂×C₂²⋊C₄	—	29	1	no	—
666	C₂×C₂²⋊C₄	—	29	1	no	—
667	C₂×C₄²	—	29	1	no	—
668	C₂×C₄²	—	29	1	no	—
669	C₂×C₄²	—	29	1	no	—
670	C₂₉	#3521	1	1	yes	characteristic, complemented, Sylow
671	C₂⁴	—	29	1	no	—
672	C₂⁴	—	29	1	no	—
673	#41	—	58	4	no	—
674	#41	—	58	4	no	—
675	C₂×Q₈	—	29	1	no	—
676	C₂×Q₈	—	29	1	no	—
677	C₂×Q₈	—	29	1	no	—
678	C₂×Q₈	—	29	1	no	—
679	C₂×Q₈	—	29	1	no	—
680	C₂×D₄	—	29	1	no	—
681	C₂×D₄	—	29	1	no	—
682	C₂×D₄	—	29	1	no	—
683	C₂×D₄	—	29	1	no	—
684	C₂×D₄	—	29	1	no	—
685	C₂×D₄	—	29	1	no	—
686	C₂×D₄	—	29	1	no	—
687	C₂×D₄	—	29	1	no	—
688	C₂×D₄	—	29	1	no	—
689	C₂×D₄	—	58	4	no	—
690	C₂×D₄	C₂²×D₂₉	1	1	yes	characteristic
691	C₂×D₄	C₂²×D₂₉	1	1	yes	characteristic
692	C₂×D₄	C₂²×D₂₉	1	1	yes	characteristic
693	C₂×D₄	C₂²×D₂₉	1	1	yes	characteristic
694	C₂×D₄	C₂²×D₂₉	1	1	yes	characteristic
695	C₂×D₄	C₂²×D₂₉	1	1	yes	characteristic
696	C₂²×C₄	—	29	1	no	—
697	C₂²×C₄	—	29	1	no	—
698	C₂²×C₄	—	29	1	no	—
699	C₂²×C₄	—	29	1	no	—
700	C₂²×C₄	—	29	1	no	—
701	C₂²×C₄	—	29	1	no	—
702	C₂²×C₄	—	29	1	no	—
703	C₂²×C₄	—	29	1	no	—
704	C₂²×C₄	—	29	1	no	—
705	C₂²×C₄	—	29	1	no	—
706	C₂²×C₄	—	29	1	no	—
707	C₂²×C₄	—	29	1	no	—
708	C₂²×C₄	—	29	1	no	—
709	C₂²×C₄	—	29	1	no	—
710	C₂²×C₄	—	29	1	no	—
711	C₂²×C₄	—	29	1	no	—
712	C₂²×C₄	—	29	1	no	—
713	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
714	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
715	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
716	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
717	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
718	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
719	C₄⋊C₄	—	29	1	no	—
720	C₄⋊C₄	—	29	1	no	—
721	C₄⋊C₄	—	29	1	no	—
722	C₄⋊C₄	—	29	1	no	—
723	C₄⋊C₄	—	29	1	no	—
724	C₄⋊C₄	—	29	1	no	—
725	C₄⋊C₄	—	29	1	no	—
726	C₄⋊C₄	—	29	1	no	—
727	C₄⋊C₄	—	29	1	no	—
728	C₄⋊C₄	—	29	1	no	—
729	C₄⋊C₄	—	29	1	no	—
730	C₄⋊C₄	—	29	1	no	—
731	C₄⋊C₄	—	29	1	no	—
732	C₄⋊C₄	—	29	1	no	—
733	C₄⋊C₄	—	29	1	no	—
734	C₄⋊C₄	—	29	1	no	—
735	C₄⋊C₄	—	29	1	no	—
736	C₄⋊C₄	—	29	1	no	—
737	C₄⋊C₄	—	29	1	no	—
738	C₄⋊C₄	—	29	1	no	—
739	C₄⋊C₄	—	29	1	no	—
740	C₄⋊C₄	—	29	1	no	—
741	C₄⋊C₄	—	29	1	no	—
742	C₄⋊C₄	—	29	1	no	—
743	C₄⋊C₄	—	29	1	no	—
744	C₄⋊C₄	—	29	1	no	—
745	C₄⋊C₄	—	29	1	no	—
746	C₄⋊C₄	—	29	1	no	—
747	C₄⋊C₄	—	29	1	no	—
748	C₄⋊C₄	—	29	1	no	—
749	C₄⋊C₄	—	29	1	no	—
750	C₄⋊C₄	—	29	1	no	—
751	C₄⋊C₄	—	29	1	no	—
752	C₄⋊C₄	—	29	1	no	—
753	C₄⋊C₄	—	29	1	no	—
754	C₄⋊C₄	—	29	1	no	—
755	C₄⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
756	C₄⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
757	C₄⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
758	C₄⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
759	C₄⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
760	C₄⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
761	C₄⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
762	C₄⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
763	C₄⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
764	C₄⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
765	C₂²⋊C₄	—	29	1	no	—
766	C₂²⋊C₄	—	29	1	no	—
767	C₂²⋊C₄	—	29	1	no	—
768	C₂²⋊C₄	—	29	1	no	—
769	C₂²⋊C₄	—	29	1	no	—
770	C₂²⋊C₄	—	29	1	no	—
771	C₂²⋊C₄	—	29	1	no	—
772	C₂²⋊C₄	—	29	1	no	—
773	C₂²⋊C₄	—	29	1	no	—
774	C₂²⋊C₄	—	29	1	no	—
775	C₂²⋊C₄	—	29	1	no	—
776	C₂²⋊C₄	—	29	1	no	—
777	C₂²⋊C₄	—	29	1	no	—
778	C₂²⋊C₄	—	29	1	no	—
779	C₂²⋊C₄	—	29	1	no	—
780	C₂²⋊C₄	—	29	1	no	—
781	C₂²⋊C₄	—	29	1	no	—
782	C₂²⋊C₄	—	29	1	no	—
783	C₂²⋊C₄	—	29	1	no	—
784	C₂²⋊C₄	—	29	1	no	—
785	C₂²⋊C₄	—	29	1	no	—
786	C₂²⋊C₄	—	29	1	no	—
787	C₂²⋊C₄	—	29	1	no	—
788	C₂²⋊C₄	—	29	1	no	—
789	C₂²⋊C₄	—	29	1	no	—
790	C₂²⋊C₄	—	29	1	no	—
791	C₂²⋊C₄	—	29	1	no	—
792	C₂²⋊C₄	—	29	1	no	—
793	C₂²⋊C₄	—	29	1	no	—
794	C₂²⋊C₄	—	29	1	no	—
795	C₂²⋊C₄	—	29	1	no	—
796	C₂²⋊C₄	—	29	1	no	—
797	C₂²⋊C₄	—	29	1	no	—
798	C₂²⋊C₄	—	29	1	no	—
799	C₂²⋊C₄	—	29	1	no	—
800	C₂²⋊C₄	—	29	1	no	—
801	C₂²⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
802	C₂²⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
803	C₂²⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
804	C₂²⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
805	C₂²⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
806	C₂²⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
807	C₂²⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
808	C₂²⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
809	C₂²⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
810	C₂²⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
811	C₄²	—	29	1	no	—
812	C₄²	—	29	1	no	—
813	C₄²	—	29	1	no	—
814	C₄²	—	29	1	no	—
815	C₄²	—	29	1	no	—
816	C₄²	—	29	1	no	—
817	C₄²	—	29	1	no	—
818	C₄²	—	29	1	no	—
819	C₄²	—	29	1	no	—
820	C₄²	—	29	1	no	—
821	C₄²	—	29	1	no	—
822	C₄²	—	29	1	no	—
823	C₄²	—	29	1	no	—
824	C₄²	—	29	1	no	—
825	C₄²	—	29	1	no	—
826	C₄²	C₂²×D₂₉	1	1	yes	characteristic
827	C₄²	C₂²×D₂₉	1	1	yes	characteristic
828	C₄²	C₂²×D₂₉	1	1	yes	characteristic
829	C₂³	—	29	1	no	—
830	C₂³	—	29	1	no	—
831	C₂³	—	29	1	no	—
832	C₂³	—	58	2	no	—
833	C₂³	—	58	2	no	—
834	C₂³	—	116	1	no	—
835	C₂³	—	116	1	no	—
836	C₂³	—	116	1	no	—
837	C₂³	—	116	1	no	—
838	C₂³	C₂³×D₂₉	1	1	yes	characteristic
839	C₂³	C₂³×D₂₉	1	1	yes	characteristic
840	C₂³	C₂³×D₂₉	1	1	yes	characteristic
841	C₂³	C₂³×D₂₉	1	1	yes	characteristic
842	Q₈	—	58	2	no	—
843	Q₈	—	58	2	no	—
844	Q₈	—	116	1	no	—
845	Q₈	—	116	1	no	—
846	Q₈	—	116	1	no	—
847	D₄	—	2	2	no	—
848	D₄	—	2	2	no	—
849	D₄	—	2	2	no	—
850	D₄	—	4	1	no	—
851	D₄	—	4	1	no	—
852	D₄	—	4	1	no	—
853	D₄	—	29	4	no	—
854	D₄	—	58	2	no	—
855	D₄	—	58	2	no	—
856	D₄	—	58	2	no	—
857	D₄	—	58	2	no	—
858	D₄	—	116	1	no	—
859	D₄	—	116	1	no	—
860	D₄	—	116	1	no	—
861	D₄	—	116	1	no	—
862	C₂×C₄	—	4	1	no	—
863	C₂×C₄	—	4	1	no	—
864	C₂×C₄	—	4	1	no	—
865	C₂×C₄	—	4	1	no	—
866	C₂×C₄	—	4	1	no	—
867	C₂×C₄	—	4	1	no	—
868	C₂×C₄	—	29	1	no	—
869	C₂×C₄	—	29	1	no	—
870	C₂×C₄	—	29	1	no	—
871	C₂×C₄	—	29	1	no	—
872	C₂×C₄	—	29	1	no	—
873	C₂×C₄	—	29	1	no	—
874	C₂×C₄	—	29	1	no	—
875	C₂×C₄	—	29	1	no	—
876	C₂×C₄	—	29	1	no	—
877	C₂×C₄	—	29	1	no	—
878	C₂×C₄	—	29	1	no	—
879	C₂×C₄	—	29	1	no	—
880	C₂×C₄	—	29	1	no	—
881	C₂×C₄	—	58	2	no	—
882	C₂×C₄	—	58	2	no	—
883	C₂×C₄	—	58	2	no	—
884	C₂×C₄	—	58	2	no	—
885	C₂×C₄	—	58	2	no	—
886	C₂×C₄	—	58	2	no	—
887	C₂×C₄	—	58	2	no	—
888	C₂×C₄	—	116	1	no	—
889	C₂×C₄	—	116	1	no	—
890	C₂×C₄	—	116	1	no	—
891	C₂×C₄	—	116	1	no	—
892	C₂×C₄	—	116	1	no	—
893	C₂×C₄	—	116	1	no	—
894	C₂×C₄	—	116	1	no	—
895	C₂×C₄	—	116	1	no	—
896	C₂×C₄	—	116	1	no	—
897	C₂×C₄	—	116	1	no	—
898	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
899	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
900	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
901	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
902	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
903	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
904	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
905	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
906	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
907	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
908	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
909	C₂²	—	2	1	no	—
910	C₂²	—	2	1	no	—
911	C₂²	—	2	1	no	—
912	C₂²	—	2	1	no	—
913	C₂²	—	2	1	no	—
914	C₂²	—	2	1	no	—
915	C₂²	—	2	1	no	—
916	C₂²	—	2	1	no	—
917	C₂²	—	2	1	no	—
918	C₂²	—	2	1	no	—
919	C₂²	—	2	1	no	—
920	C₂²	—	29	2	no	—
921	C₂²	—	58	1	no	—
922	C₂²	—	58	1	no	—
923	C₂²	—	58	1	no	—
924	C₂²	—	58	1	no	—
925	C₂²	—	58	1	no	—
926	C₂²	—	58	1	no	—
927	C₂²	—	58	1	no	—
928	C₂²	—	58	1	no	—
929	C₂²	—	232	2	no	—
930	C₂²	—	232	2	no	—
931	C₂²	#41×D₂₉	1	2	yes	—
932	C₂²	C₂⁴×D₂₉	1	1	yes	characteristic
933	C₄	—	2	1	no	—
934	C₄	—	2	1	no	—
935	C₄	—	2	1	no	—
936	C₄	—	2	1	no	—
937	C₄	—	2	1	no	—
938	C₄	—	2	1	no	—
939	C₄	—	2	1	no	—
940	C₄	—	2	1	no	—
941	C₄	—	2	1	no	—
942	C₄	—	2	1	no	—
943	C₄	—	2	1	no	—
944	C₄	—	29	2	no	—
945	C₄	—	58	1	no	—
946	C₄	—	58	1	no	—
947	C₄	—	58	1	no	—
948	C₄	—	58	1	no	—
949	C₄	—	58	1	no	—
950	C₄	—	58	1	no	—
951	C₄	—	58	1	no	—
952	C₄	—	58	1	no	—
953	C₄	—	58	1	no	—
954	C₄	—	58	1	no	—
955	C₄	—	58	1	no	—
956	C₄	—	58	1	no	—
957	C₂	—	2	2	no	—
958	C₂	—	4	1	no	—
959	C₂	—	4	1	no	—
960	C₂	—	4	1	no	—
961	C₂	—	58	2	no	—
962	C₂	—	116	1	no	—
963	C₂	—	116	1	no	—
964	C₂	C₂×#41×D₂₉	1	1	yes	characteristic
965	C₂	#14271998	1	1	yes	characteristic
966	C₂	#14271999	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₉
commutator, socle, cosocle	C₂²×C₂₉	C₂⁵
Fitting	C₂₉×#553	C₂
hypercenter	#553	D₂₉
hypocenter	C₂₉	#3521
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ #553

Complements

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

N	H ≅ G/N	type
1. #14271880	C₂	semidirect
2. #14271880	C₂	semidirect
3. #14271868	C₂	semidirect
4. #14271858	C₂	semidirect
5. #14271856	C₂	semidirect
6. #14271853	C₂	semidirect
7. #14271846	C₂	semidirect
8. #14271845	C₂	semidirect
9. #14271842	C₂	semidirect
10. #14271842	C₂	semidirect
11. #14271842	C₂	semidirect
12. #14271836	C₂	semidirect
13. #14271813	C₂	semidirect
14. #14271802	C₂	semidirect
15. #14271802	C₂	semidirect
16. #14271781	C₂	semidirect
17. #14271772	C₂	semidirect
18. #14271758	C₂	semidirect
19. #14271754	C₂	semidirect
20. #14271750	C₂	semidirect
21. #14271745	C₂	semidirect
22. #14271694	C₂	semidirect
23. #14271693	C₂	semidirect
24. #14271691	C₂	semidirect
25. #14271690	C₂	semidirect
26. C₂×#11745260	C₂	semidirect
27. #126×D₂₉	C₂	semidirect
28. #14271642	C₂	semidirect
29. #14271635	C₂	semidirect
30. C₄×#90807	C₂	semidirect
31. C₂₉×#553	C₂	semidirect
35. C₂₉×#126	C₂²	semidirect
36. C₂₉×#126	C₂²	semidirect
37. C₂₉×#125	C₂²	semidirect
38. C₂₉×#123	C₂²	semidirect
39. C₂₉×#123	C₂²	semidirect
42. C₂₉×#121	C₂²	semidirect
43. C₂₉×#121	C₂²	semidirect
45. C₄×D₄×C₂₉	C₂²	semidirect
46. C₄×D₄×C₂₉	C₂²	semidirect
47. C₄×D₄×C₂₉	C₂²	semidirect
48. C₂₉×#117	C₂²	semidirect
49. C₂×C₄⋊C₄×C₂₉	C₂²	semidirect
53. #11745301	C₂²	semidirect
54. #11745300	C₂²	semidirect
59. #11745298	C₂²	semidirect
62. #11745297	C₂²	semidirect
63. #11745297	C₂²	semidirect
64. #11745297	C₂²	semidirect
65. #11745297	C₂²	semidirect
67. D₄×Dic₂₉	C₂²	semidirect
68. D₄×Dic₂₉	C₂²	semidirect
69. D₄×Dic₂₉	C₂²	semidirect
70. D₄×Dic₂₉	C₂²	semidirect
77. C₄×C₂²⋊D₂₉	C₂²	semidirect
78. C₄×C₂²⋊D₂₉	C₂²	semidirect
79. C₄×C₂²⋊D₂₉	C₂²	semidirect
80. C₄×C₂²⋊D₂₉	C₂²	semidirect
85. #11745288	C₂²	semidirect
86. C₂×C₄⋊Dic₂₉	C₂²	semidirect
87. #11745286	C₂²	semidirect
88. #11745286	C₂²	semidirect
89. #11745286	C₂²	semidirect
90. #11745286	C₂²	semidirect
91. C₂×#90779	C₂²	semidirect
92. C₂×#90779	C₂²	semidirect
93. C₂×C₄×Dic₂₉	C₂²	semidirect
94. C₂×C₄×Dic₂₉	C₂²	semidirect
102. #11745260	C₂²	semidirect
103. #11745260	C₂²	semidirect
104. #11745260	C₂²	semidirect
105. #11745260	C₂²	semidirect
106. #11745260	C₂²	semidirect
107. #11745259	C₂²	semidirect
110. #11745258	C₂²	semidirect
111. #11745258	C₂²	semidirect
112. #11745258	C₂²	semidirect
113. #11745258	C₂²	semidirect
118. #11745254	C₂²	semidirect
119. C₄⋊C₄×D₂₉	C₂²	semidirect
120. C₄⋊C₄×D₂₉	C₂²	semidirect
121. C₄⋊C₄×D₂₉	C₂²	semidirect
122. #11745252	C₂²	semidirect
123. #11745251	C₂²	semidirect
124. #11745251	C₂²	semidirect
125. #11745251	C₂²	semidirect
126. #11745251	C₂²	semidirect
127. #11745251	C₂²	semidirect
128. #11745251	C₂²	semidirect
129. #11745250	C₂²	semidirect
130. #11745250	C₂²	semidirect
131. #11745249	C₂²	semidirect
132. #11745249	C₂²	semidirect
133. #11745249	C₂²	semidirect
134. #11745249	C₂²	semidirect
136. #11745248	C₂²	semidirect
142. #11745247	C₂²	semidirect
145. #11745245	C₂²	semidirect
146. #11745245	C₂²	semidirect
147. #11745245	C₂²	semidirect
148. #11745245	C₂²	semidirect
153. #11745243	C₂²	semidirect
154. #11745243	C₂²	semidirect
159. #11745241	C₂²	semidirect
160. #11745241	C₂²	semidirect
161. #11745241	C₂²	semidirect
162. #11745241	C₂²	semidirect
163. #11745241	C₂²	semidirect
164. #11745241	C₂²	semidirect
165. #11745240	C₂²	semidirect
166. #11745240	C₂²	semidirect
167. #11745240	C₂²	semidirect
168. #11745240	C₂²	semidirect
169. #11745239	C₂²	semidirect
170. #11745239	C₂²	semidirect
171. #11745239	C₂²	semidirect
172. #11745239	C₂²	semidirect
173. #11745239	C₂²	semidirect
174. #11745239	C₂²	semidirect
179. #11745234	C₂²	semidirect
180. #11745234	C₂²	semidirect
181. #11745234	C₂²	semidirect
182. C₄²×D₂₉	C₂²	semidirect
183. #11745232	C₂²	semidirect
184. C₄×Dic₅₈	C₂²	semidirect
185. C₄×Dic₅₈	C₂²	semidirect
186. C₄×Dic₅₈	C₂²	semidirect
479. #553	D₂₉	semidirect
540. #126	C₂×D₂₉	semidirect
541. #126	C₂×D₂₉	semidirect
550. #125	C₂×D₂₉	semidirect
574. #123	C₂×D₂₉	semidirect
575. #123	C₂×D₂₉	semidirect
600. #121	C₂×D₂₉	semidirect
601. #121	C₂×D₂₉	semidirect
635. C₄×D₄	C₂×D₂₉	semidirect
636. C₄×D₄	C₂×D₂₉	semidirect
637. C₄×D₄	C₂×D₂₉	semidirect
651. #117	C₂×D₂₉	semidirect
658. C₂×C₄⋊C₄	C₂×D₂₉	semidirect
670. C₂₉	#3521	semidirect

Maximal subgroups

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

subgroup	index
#14271880	2
#14271868	2
#14271858	2
#14271856	2
#14271853	2
#14271846	2
#14271845	2
#14271842	2
#14271836	2
#14271813	2
#14271802	2
#14271781	2
#14271772	2
#14271758	2
#14271754	2
#14271750	2
#14271745	2
#14271694	2
#14271693	2
#14271691	2
#14271690	2
C₂×#11745260	2
#126×D₂₉	2
#14271642	2
#14271635	2
C₄×#90807	2
C₂₉×#553	2
#3521	29