Subgroups — C₆₇×#34997 #30714248

Order 17152.

2378 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#2849	C₂	1	2	yes	maximal, complemented
2	C₆₇×#2848	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2847	C₂	1	1	yes	maximal, characteristic
4	C₆₇×#2646	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#2643	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2639	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#2510	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2505	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2493	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2488	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2450	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2444	C₂	1	2	yes	maximal, complemented
13	C₆₇×#2425	C₂	1	2	yes	maximal, complemented
14	C₆₇×#2419	C₂	1	2	yes	maximal, complemented
15	C₆₇×#2329	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#2325	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#2318	C₂	1	2	yes	maximal, complemented
18	C₄×#120×C₆₇	C₂	1	2	yes	maximal, complemented
19	C₂²×#95×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
21	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
22	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
23	C₂×#123×C₆₇	C₂²	1	2	yes	—
24	C₂×#123×C₆₇	C₂²	1	2	yes	—
25	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
29	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×#120×C₆₇	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
35	#401×C₆₇	C₂²	1	2	yes	complemented
36	#400×C₆₇	C₂²	1	2	yes	complemented
37	#400×C₆₇	C₂²	1	2	yes	complemented
38	#400×C₆₇	C₂²	1	2	yes	complemented
39	#400×C₆₇	C₂²	1	2	yes	complemented
40	#400×C₆₇	C₂²	1	2	yes	complemented
41	#400×C₆₇	C₂²	1	2	yes	complemented
42	#398×C₆₇	C₂²	1	2	yes	complemented
43	#398×C₆₇	C₂²	1	2	yes	complemented
44	#397×C₆₇	C₂²	1	2	yes	complemented
45	#397×C₆₇	C₂²	1	2	yes	complemented
46	#397×C₆₇	C₂²	1	2	yes	complemented
47	#397×C₆₇	C₂²	1	2	yes	complemented
48	#396×C₆₇	C₂²	1	2	yes	complemented
49	#394×C₆₇	C₂²	1	2	yes	complemented
50	#393×C₆₇	C₂²	1	2	yes	complemented
51	#391×C₆₇	C₂²	1	2	yes	complemented
52	#389×C₆₇	C₂²	1	2	yes	complemented
53	#388×C₆₇	C₂²	1	2	yes	complemented
54	#388×C₆₇	C₂²	1	2	yes	complemented
55	#388×C₆₇	C₂²	1	2	yes	complemented
56	#387×C₆₇	C₂²	1	2	yes	complemented
57	#387×C₆₇	C₂²	1	2	yes	complemented
58	#387×C₆₇	C₂²	1	2	yes	complemented
59	#387×C₆₇	C₂²	1	2	yes	complemented
60	#387×C₆₇	C₂²	1	2	yes	complemented
61	#386×C₆₇	C₂²	1	2	yes	—
62	#386×C₆₇	C₂²	1	2	yes	—
63	#386×C₆₇	C₂²	1	2	yes	—
64	#386×C₆₇	C₂²	1	2	yes	—
65	#386×C₆₇	C₂²	1	2	yes	—
66	#386×C₆₇	C₂²	1	2	yes	—
67	#386×C₆₇	C₂²	1	2	yes	—
68	#386×C₆₇	C₂²	1	2	yes	—
69	#386×C₆₇	C₂²	1	2	yes	—
70	#386×C₆₇	C₂²	1	2	yes	—
71	#386×C₆₇	C₂²	1	2	yes	complemented
72	#385×C₆₇	C₂²	1	2	yes	—
73	#385×C₆₇	C₂²	1	2	yes	—
74	#385×C₆₇	C₂²	1	2	yes	—
75	#385×C₆₇	C₂²	1	2	yes	—
76	#385×C₆₇	C₂²	1	2	yes	—
77	#385×C₆₇	C₂²	1	2	yes	—
78	#385×C₆₇	C₂²	1	2	yes	—
79	#385×C₆₇	C₂²	1	2	yes	—
80	#385×C₆₇	C₂²	1	2	yes	—
81	#385×C₆₇	C₂²	1	2	yes	—
82	#385×C₆₇	C₂²	1	2	yes	complemented
83	#383×C₆₇	C₂²	1	2	yes	complemented
84	#382×C₆₇	C₂²	1	2	yes	complemented
85	#381×C₆₇	C₂²	1	2	yes	—
86	#381×C₆₇	C₂²	1	2	yes	—
87	#381×C₆₇	C₂²	1	2	yes	complemented
88	#380×C₆₇	C₂²	1	1	yes	characteristic
89	#380×C₆₇	C₂²	1	1	yes	characteristic
90	#380×C₆₇	C₂²	1	1	yes	characteristic
91	#380×C₆₇	C₂²	1	1	yes	characteristic
92	#380×C₆₇	C₂²	1	1	yes	characteristic
93	#380×C₆₇	C₂²	1	1	yes	characteristic
94	#380×C₆₇	C₂²	1	2	yes	complemented
95	#379×C₆₇	C₂²	1	2	yes	—
96	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
97	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
98	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
99	C₂×#95×C₆₇	C₂²	1	2	yes	—
100	C₂×#95×C₆₇	C₂²	1	2	yes	—
101	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic
102	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic
103	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic
104	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic
105	C₂×#95×C₆₇	C₂²	1	2	yes	—
106	C₂×#95×C₆₇	C₂²	1	2	yes	—
107	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
109	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
110	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
111	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
112	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₆₇	—	2	4	no	—
114	C₂³×C₄×C₆₇	—	2	4	no	—
115	C₂³×C₄×C₆₇	—	2	4	no	—
116	C₂³×C₄×C₆₇	—	4	2	no	—
117	C₂³×C₄×C₆₇	—	4	2	no	—
118	C₂³×C₄×C₆₇	—	4	2	no	—
119	C₂³×C₄×C₆₇	—	4	2	no	—
120	C₂³×C₄×C₆₇	—	4	2	no	—
121	C₂³×C₄×C₆₇	—	4	2	no	—
122	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
123	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
124	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
125	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
130	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
132	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
133	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
134	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
135	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
136	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
137	#123×C₆₇	—	4	4	no	—
138	#123×C₆₇	—	4	4	no	—
139	C₂²⋊Q₈×C₆₇	—	2	4	no	—
140	C₂²⋊Q₈×C₆₇	—	4	2	no	—
141	C₂²⋊Q₈×C₆₇	—	4	2	no	—
142	#121×C₆₇	—	2	4	no	—
143	#121×C₆₇	—	4	2	no	—
144	#121×C₆₇	—	4	2	no	—
145	#120×C₆₇	—	2	8	no	—
146	C₄×D₄×C₆₇	—	2	8	no	—
147	C₄×D₄×C₆₇	—	4	4	no	—
148	C₄×D₄×C₆₇	—	4	4	no	—
149	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
152	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
153	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
155	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
157	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
158	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
159	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
160	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
161	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
162	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
166	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
168	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
169	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
174	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
175	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
176	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
179	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
180	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
181	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
183	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
184	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
185	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
186	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
187	#95×C₆₇	C₂³	1	2	yes	—
188	#95×C₆₇	C₂³	1	2	yes	—
189	#95×C₆₇	C₂³	1	2	yes	—
190	#95×C₆₇	C₂³	1	2	yes	—
191	#95×C₆₇	C₂³	1	2	yes	—
192	#95×C₆₇	C₂³	1	2	yes	—
193	#95×C₆₇	C₂³	1	2	yes	—
194	#95×C₆₇	C₂³	1	2	yes	—
195	#95×C₆₇	C₂³	1	2	yes	—
196	#95×C₆₇	C₂³	1	2	yes	—
197	#95×C₆₇	C₂³	1	2	yes	—
198	#95×C₆₇	C₂³	1	2	yes	—
199	#95×C₆₇	C₂³	1	2	yes	—
200	#95×C₆₇	C₂³	1	2	yes	—
201	#95×C₆₇	C₂³	1	2	yes	—
202	#95×C₆₇	C₂³	1	2	yes	—
203	#95×C₆₇	C₂³	1	2	yes	—
204	#95×C₆₇	C₂³	1	2	yes	—
205	#95×C₆₇	C₂³	1	2	yes	—
206	#95×C₆₇	C₂³	1	2	yes	—
207	#95×C₆₇	C₂³	1	2	yes	—
208	#95×C₆₇	C₂³	1	2	yes	—
209	#95×C₆₇	C₂³	1	2	yes	—
210	#95×C₆₇	C₂³	1	2	yes	—
211	#95×C₆₇	C₂³	1	2	yes	—
212	#95×C₆₇	C₂³	1	2	yes	—
213	#95×C₆₇	C₂³	1	2	yes	—
214	#95×C₆₇	C₂³	1	2	yes	—
215	C₂⁴×C₆₇	—	2	2	no	—
216	C₂⁴×C₆₇	—	2	2	no	—
217	C₂⁴×C₆₇	—	2	2	no	—
218	C₂⁴×C₆₇	—	2	2	no	—
219	C₂⁴×C₆₇	—	2	2	no	—
220	C₂⁴×C₆₇	—	2	2	no	—
221	C₂⁴×C₆₇	#41	1	4	yes	—
222	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
223	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
224	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
225	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
226	C₂×Q₈×C₆₇	—	2	2	no	—
227	C₂×Q₈×C₆₇	—	4	1	no	—
228	C₂×Q₈×C₆₇	—	4	1	no	—
229	C₂×D₄×C₆₇	—	2	4	no	—
230	C₂×D₄×C₆₇	—	2	4	no	—
231	C₂×D₄×C₆₇	—	2	4	no	—
232	C₂×D₄×C₆₇	—	2	4	no	—
233	C₂×D₄×C₆₇	—	2	4	no	—
234	C₂×D₄×C₆₇	—	2	4	no	—
235	C₂×D₄×C₆₇	—	2	4	no	—
236	C₂×D₄×C₆₇	—	2	4	no	—
237	C₂×D₄×C₆₇	—	2	4	no	—
238	C₂×D₄×C₆₇	—	2	2	no	—
239	C₂×D₄×C₆₇	—	4	1	no	—
240	C₂×D₄×C₆₇	—	4	1	no	—
241	C₂²×C₄×C₆₇	—	2	2	no	—
242	C₂²×C₄×C₆₇	—	2	2	no	—
243	C₂²×C₄×C₆₇	—	2	2	no	—
244	C₂²×C₄×C₆₇	—	2	2	no	—
245	C₂²×C₄×C₆₇	—	2	4	no	—
246	C₂²×C₄×C₆₇	—	2	4	no	—
247	C₂²×C₄×C₆₇	—	2	4	no	—
248	C₂²×C₄×C₆₇	—	2	4	no	—
249	C₂²×C₄×C₆₇	—	2	2	no	—
250	C₂²×C₄×C₆₇	—	2	2	no	—
251	C₂²×C₄×C₆₇	—	2	2	no	—
252	C₂²×C₄×C₆₇	—	2	2	no	—
253	C₂²×C₄×C₆₇	—	2	4	no	—
254	C₂²×C₄×C₆₇	—	2	4	no	—
255	C₂²×C₄×C₆₇	—	2	4	no	—
256	C₂²×C₄×C₆₇	—	2	4	no	—
257	C₂²×C₄×C₆₇	—	2	2	no	—
258	C₂²×C₄×C₆₇	—	2	2	no	—
259	C₂²×C₄×C₆₇	—	2	2	no	—
260	C₂²×C₄×C₆₇	—	2	2	no	—
261	C₂²×C₄×C₆₇	—	2	4	no	—
262	C₂²×C₄×C₆₇	—	4	1	no	—
263	C₂²×C₄×C₆₇	—	4	1	no	—
264	C₂²×C₄×C₆₇	—	4	2	no	—
265	C₂²×C₄×C₆₇	—	4	2	no	—
266	C₂²×C₄×C₆₇	—	4	1	no	—
267	C₂²×C₄×C₆₇	—	4	1	no	—
268	C₂²×C₄×C₆₇	—	4	1	no	—
269	C₂²×C₄×C₆₇	—	4	1	no	—
270	C₂²×C₄×C₆₇	—	4	1	no	—
271	C₂²×C₄×C₆₇	—	4	1	no	—
272	C₂²×C₄×C₆₇	—	4	1	no	—
273	C₂²×C₄×C₆₇	—	4	1	no	—
274	C₂²×C₄×C₆₇	—	4	1	no	—
275	C₂²×C₄×C₆₇	—	4	1	no	—
276	C₂²×C₄×C₆₇	—	4	1	no	—
277	C₂²×C₄×C₆₇	—	4	1	no	—
278	C₂²×C₄×C₆₇	—	4	2	no	—
279	C₂²×C₄×C₆₇	—	4	2	no	—
280	C₂²×C₄×C₆₇	—	4	1	no	—
281	C₂²×C₄×C₆₇	—	4	1	no	—
282	C₂²×C₄×C₆₇	—	4	2	no	—
283	C₂²×C₄×C₆₇	—	4	2	no	—
284	C₂²×C₄×C₆₇	—	4	16	no	—
285	C₂²×C₄×C₆₇	—	4	16	no	—
286	C₂²×C₄×C₆₇	—	4	16	no	—
287	C₂²×C₄×C₆₇	#41	1	4	yes	—
288	C₂²×C₄×C₆₇	#41	1	4	yes	—
289	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
290	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
291	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
292	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
293	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
294	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
295	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
296	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
297	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
298	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
299	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
300	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
301	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
302	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
303	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
304	C₄⋊C₄×C₆₇	—	2	4	no	—
305	C₄⋊C₄×C₆₇	—	2	2	no	—
306	C₄⋊C₄×C₆₇	—	2	2	no	—
307	C₄⋊C₄×C₆₇	—	2	4	no	—
308	C₄⋊C₄×C₆₇	—	4	2	no	—
309	C₄⋊C₄×C₆₇	—	4	2	no	—
310	C₄⋊C₄×C₆₇	—	4	1	no	—
311	C₄⋊C₄×C₆₇	—	4	1	no	—
312	C₄⋊C₄×C₆₇	—	4	1	no	—
313	C₄⋊C₄×C₆₇	—	4	1	no	—
314	C₄⋊C₄×C₆₇	—	4	2	no	—
315	C₄⋊C₄×C₆₇	—	4	2	no	—
316	C₄⋊C₄×C₆₇	—	4	2	no	—
317	C₄⋊C₄×C₆₇	—	4	2	no	—
318	C₄⋊C₄×C₆₇	—	4	2	no	—
319	C₄⋊C₄×C₆₇	—	4	2	no	—
320	C₂²⋊C₄×C₆₇	—	2	4	no	—
321	C₂²⋊C₄×C₆₇	—	2	4	no	—
322	C₂²⋊C₄×C₆₇	—	2	4	no	—
323	C₂²⋊C₄×C₆₇	—	2	4	no	—
324	C₂²⋊C₄×C₆₇	—	2	4	no	—
325	C₂²⋊C₄×C₆₇	—	2	4	no	—
326	C₂²⋊C₄×C₆₇	—	2	4	no	—
327	C₂²⋊C₄×C₆₇	—	2	4	no	—
328	C₂²⋊C₄×C₆₇	—	2	4	no	—
329	C₂²⋊C₄×C₆₇	—	2	4	no	—
330	C₂²⋊C₄×C₆₇	—	2	4	no	—
331	C₂²⋊C₄×C₆₇	—	4	2	no	—
332	C₂²⋊C₄×C₆₇	—	4	2	no	—
333	C₂²⋊C₄×C₆₇	—	4	2	no	—
334	C₂²⋊C₄×C₆₇	—	4	2	no	—
335	C₂²⋊C₄×C₆₇	—	4	2	no	—
336	C₂²⋊C₄×C₆₇	—	4	2	no	—
337	C₂²⋊C₄×C₆₇	—	4	2	no	—
338	C₂²⋊C₄×C₆₇	—	4	2	no	—
339	C₄²×C₆₇	—	2	4	no	—
340	C₄²×C₆₇	—	4	2	no	—
341	C₄²×C₆₇	—	4	2	no	—
342	C₂³×C₆₇	—	2	8	no	—
343	C₂³×C₆₇	—	2	8	no	—
344	C₂³×C₆₇	—	2	8	no	—
345	C₂³×C₆₇	—	2	8	no	—
346	C₂³×C₆₇	—	2	8	no	—
347	C₂³×C₆₇	—	2	8	no	—
348	C₂³×C₆₇	—	2	8	no	—
349	C₂³×C₆₇	—	2	1	no	—
350	C₂³×C₆₇	—	2	1	no	—
351	C₂³×C₆₇	—	2	1	no	—
352	C₂³×C₆₇	—	2	1	no	—
353	C₂³×C₆₇	—	2	1	no	—
354	C₂³×C₆₇	—	2	1	no	—
355	C₂³×C₆₇	—	2	1	no	—
356	C₂³×C₆₇	—	2	1	no	—
357	C₂³×C₆₇	—	2	1	no	—
358	C₂³×C₆₇	—	2	1	no	—
359	C₂³×C₆₇	—	2	1	no	—
360	C₂³×C₆₇	—	2	1	no	—
361	C₂³×C₆₇	—	2	2	no	—
362	C₂³×C₆₇	—	2	2	no	—
363	C₂³×C₆₇	—	2	2	no	—
364	C₂³×C₆₇	—	2	2	no	—
365	C₂³×C₆₇	—	2	2	no	—
366	C₂³×C₆₇	—	2	2	no	—
367	C₂³×C₆₇	—	2	2	no	—
368	C₂³×C₆₇	C₂×#41	1	2	yes	—
369	C₂³×C₆₇	C₂×#41	1	2	yes	—
370	C₂³×C₆₇	C₂×#41	1	2	yes	—
371	C₂³×C₆₇	C₂×#41	1	2	yes	—
372	C₂³×C₆₇	C₂×#41	1	2	yes	—
373	C₂³×C₆₇	H(5,𝔽₂)	1	2	yes	—
374	C₂³×C₆₇	H(5,𝔽₂)	1	2	yes	—
375	C₂³×C₆₇	H(5,𝔽₂)	1	2	yes	—
376	C₂³×C₆₇	2₋¹⁺⁴	1	2	yes	—
377	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
378	Q₈×C₆₇	—	8	2	no	—
379	D₄×C₆₇	—	4	8	no	—
380	D₄×C₆₇	—	4	8	no	—
381	D₄×C₆₇	—	4	8	no	—
382	D₄×C₆₇	—	8	2	no	—
383	C₂×C₄×C₆₇	—	2	2	no	—
384	C₂×C₄×C₆₇	—	2	2	no	—
385	C₂×C₄×C₆₇	—	2	1	no	—
386	C₂×C₄×C₆₇	—	2	1	no	—
387	C₂×C₄×C₆₇	—	2	1	no	—
388	C₂×C₄×C₆₇	—	2	1	no	—
389	C₂×C₄×C₆₇	—	2	2	no	—
390	C₂×C₄×C₆₇	—	2	2	no	—
391	C₂×C₄×C₆₇	—	2	2	no	—
392	C₂×C₄×C₆₇	—	2	2	no	—
393	C₂×C₄×C₆₇	—	2	2	no	—
394	C₂×C₄×C₆₇	—	2	2	no	—
395	C₂×C₄×C₆₇	—	2	2	no	—
396	C₂×C₄×C₆₇	—	2	2	no	—
397	C₂×C₄×C₆₇	—	2	2	no	—
398	C₂×C₄×C₆₇	—	2	2	no	—
399	C₂×C₄×C₆₇	—	2	2	no	—
400	C₂×C₄×C₆₇	—	2	1	no	—
401	C₂×C₄×C₆₇	—	2	1	no	—
402	C₂×C₄×C₆₇	—	2	2	no	—
403	C₂×C₄×C₆₇	—	2	2	no	—
404	C₂×C₄×C₆₇	—	2	2	no	—
405	C₂×C₄×C₆₇	—	2	2	no	—
406	C₂×C₄×C₆₇	—	2	2	no	—
407	C₂×C₄×C₆₇	—	2	2	no	—
408	C₂×C₄×C₆₇	—	2	2	no	—
409	C₂×C₄×C₆₇	—	2	2	no	—
410	C₂×C₄×C₆₇	—	2	2	no	—
411	C₂×C₄×C₆₇	—	2	1	no	—
412	C₂×C₄×C₆₇	—	2	1	no	—
413	C₂×C₄×C₆₇	—	2	2	no	—
414	C₂×C₄×C₆₇	—	2	2	no	—
415	C₂×C₄×C₆₇	—	2	2	no	—
416	C₂×C₄×C₆₇	—	2	2	no	—
417	C₂×C₄×C₆₇	—	2	2	no	—
418	C₂×C₄×C₆₇	—	2	2	no	—
419	C₂×C₄×C₆₇	—	2	2	no	—
420	C₂×C₄×C₆₇	—	2	1	no	—
421	C₂×C₄×C₆₇	—	2	1	no	—
422	C₂×C₄×C₆₇	—	2	2	no	—
423	C₂×C₄×C₆₇	—	2	2	no	—
424	C₂×C₄×C₆₇	—	2	2	no	—
425	C₂×C₄×C₆₇	—	4	4	no	—
426	C₂×C₄×C₆₇	—	4	4	no	—
427	C₂×C₄×C₆₇	—	4	8	no	—
428	C₂×C₄×C₆₇	—	4	8	no	—
429	C₂×C₄×C₆₇	—	4	4	no	—
430	C₂×C₄×C₆₇	—	4	4	no	—
431	C₂×C₄×C₆₇	—	4	4	no	—
432	C₂×C₄×C₆₇	—	4	4	no	—
433	C₂×C₄×C₆₇	—	4	4	no	—
434	C₂×C₄×C₆₇	—	4	4	no	—
435	C₂×C₄×C₆₇	—	4	8	no	—
436	C₂×C₄×C₆₇	—	4	4	no	—
437	C₂×C₄×C₆₇	—	4	4	no	—
438	C₂×C₄×C₆₇	—	4	8	no	—
439	C₂×C₄×C₆₇	—	8	4	no	—
440	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
441	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
442	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
443	C₂²×C₆₇	—	2	32	no	—
444	C₂²×C₆₇	—	2	2	no	—
445	C₂²×C₆₇	—	2	2	no	—
446	C₂²×C₆₇	—	2	2	no	—
447	C₂²×C₆₇	—	2	2	no	—
448	C₂²×C₆₇	—	2	2	no	—
449	C₂²×C₆₇	—	2	2	no	—
450	C₂²×C₆₇	—	2	2	no	—
451	C₂²×C₆₇	—	2	2	no	—
452	C₂²×C₆₇	—	2	2	no	—
453	C₂²×C₆₇	—	2	2	no	—
454	C₂²×C₆₇	—	2	2	no	—
455	C₂²×C₆₇	—	2	2	no	—
456	C₂²×C₆₇	—	2	2	no	—
457	C₂²×C₆₇	—	2	2	no	—
458	C₂²×C₆₇	—	2	2	no	—
459	C₂²×C₆₇	—	2	2	no	—
460	C₂²×C₆₇	—	2	2	no	—
461	C₂²×C₆₇	—	2	2	no	—
462	C₂²×C₆₇	—	4	2	no	—
463	C₂²×C₆₇	—	4	2	no	—
464	C₂²×C₆₇	—	4	2	no	—
465	C₂²×C₆₇	—	4	2	no	—
466	C₂²×C₆₇	—	4	2	no	—
467	C₂²×C₆₇	—	4	2	no	—
468	C₂²×C₆₇	—	4	2	no	—
469	C₂²×C₆₇	#529	1	4	yes	—
470	C₂²×C₆₇	#538	1	4	yes	—
471	C₂²×C₆₇	#539	1	4	yes	—
472	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
473	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
474	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
475	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
476	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
477	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
478	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
479	C₄×C₆₇	—	2	4	no	—
480	C₄×C₆₇	—	2	2	no	—
481	C₄×C₆₇	—	2	2	no	—
482	C₄×C₆₇	—	4	2	no	—
483	C₄×C₆₇	—	4	2	no	—
484	C₄×C₆₇	—	4	2	no	—
485	C₄×C₆₇	—	4	2	no	—
486	C₄×C₆₇	—	4	2	no	—
487	C₄×C₆₇	—	4	1	no	—
488	C₄×C₆₇	—	4	1	no	—
489	C₄×C₆₇	—	4	2	no	—
490	C₄×C₆₇	—	4	2	no	—
491	C₄×C₆₇	—	4	2	no	—
492	C₄×C₆₇	—	4	2	no	—
493	C₄×C₆₇	—	4	2	no	—
494	#34997	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
495	C₂×C₆₇	—	2	4	no	—
496	C₂×C₆₇	—	2	4	no	—
497	C₂×C₆₇	—	2	4	no	—
498	C₂×C₆₇	—	8	2	no	—
499	C₂×C₆₇	C₂×#529	1	1	yes	characteristic
500	C₂×C₆₇	C₂×#538	1	1	yes	characteristic
501	C₂×C₆₇	C₂×#539	1	1	yes	characteristic
502	C₂×C₆₇	#3490	1	1	yes	characteristic
503	C₂×C₆₇	#3490	1	1	yes	characteristic
504	C₂×C₆₇	#3492	1	1	yes	characteristic
505	C₂×C₆₇	#3492	1	1	yes	characteristic
506	#2849	C₂×C₆₇	1	2	yes	complemented
507	#2848	C₂×C₆₇	1	1	yes	characteristic, complemented
508	#2847	C₂×C₆₇	1	1	yes	characteristic
509	#2646	C₂×C₆₇	1	1	yes	characteristic, complemented
510	#2643	C₂×C₆₇	1	2	yes	complemented
511	#2639	C₂×C₆₇	1	1	yes	characteristic, complemented
512	#2510	C₂×C₆₇	1	2	yes	complemented
513	#2505	C₂×C₆₇	1	2	yes	complemented
514	#2493	C₂×C₆₇	1	2	yes	complemented
515	#2488	C₂×C₆₇	1	2	yes	complemented
516	#2450	C₂×C₆₇	1	2	yes	complemented
517	#2444	C₂×C₆₇	1	2	yes	complemented
518	#2425	C₂×C₆₇	1	2	yes	complemented
519	#2419	C₂×C₆₇	1	2	yes	complemented
520	#2329	C₂×C₆₇	1	1	yes	characteristic, complemented
521	#2325	C₂×C₆₇	1	1	yes	characteristic, complemented
522	#2318	C₂×C₆₇	1	2	yes	complemented
523	C₄×#120	C₂×C₆₇	1	2	yes	complemented
524	C₂²×#95	C₂×C₆₇	1	1	yes	characteristic, complemented
525	C₆₇	#34997	1	1	yes	characteristic, direct product factor, Sylow
526	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
527	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
528	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
529	C₂×#123	C₂²×C₆₇	1	2	yes	—
530	C₂×#123	C₂²×C₆₇	1	2	yes	—
531	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
532	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
533	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
534	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
535	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
536	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
537	C₂×#120	C₂²×C₆₇	1	2	yes	—
538	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
539	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
540	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
541	#401	C₂²×C₆₇	1	2	yes	complemented
542	#400	C₂²×C₆₇	1	2	yes	complemented
543	#400	C₂²×C₆₇	1	2	yes	complemented
544	#400	C₂²×C₆₇	1	2	yes	complemented
545	#400	C₂²×C₆₇	1	2	yes	complemented
546	#400	C₂²×C₆₇	1	2	yes	complemented
547	#400	C₂²×C₆₇	1	2	yes	complemented
548	#398	C₂²×C₆₇	1	2	yes	complemented
549	#398	C₂²×C₆₇	1	2	yes	complemented
550	#397	C₂²×C₆₇	1	2	yes	complemented
551	#397	C₂²×C₆₇	1	2	yes	complemented
552	#397	C₂²×C₆₇	1	2	yes	complemented
553	#397	C₂²×C₆₇	1	2	yes	complemented
554	#396	C₂²×C₆₇	1	2	yes	complemented
555	#394	C₂²×C₆₇	1	2	yes	complemented
556	#393	C₂²×C₆₇	1	2	yes	complemented
557	#391	C₂²×C₆₇	1	2	yes	complemented
558	#389	C₂²×C₆₇	1	2	yes	complemented
559	#388	C₂²×C₆₇	1	2	yes	complemented
560	#388	C₂²×C₆₇	1	2	yes	complemented
561	#388	C₂²×C₆₇	1	2	yes	complemented
562	#387	C₂²×C₆₇	1	2	yes	complemented
563	#387	C₂²×C₆₇	1	2	yes	complemented
564	#387	C₂²×C₆₇	1	2	yes	complemented
565	#387	C₂²×C₆₇	1	2	yes	complemented
566	#387	C₂²×C₆₇	1	2	yes	complemented
567	#386	C₂²×C₆₇	1	2	yes	—
568	#386	C₂²×C₆₇	1	2	yes	—
569	#386	C₂²×C₆₇	1	2	yes	—
570	#386	C₂²×C₆₇	1	2	yes	—
571	#386	C₂²×C₆₇	1	2	yes	—
572	#386	C₂²×C₆₇	1	2	yes	—
573	#386	C₂²×C₆₇	1	2	yes	—
574	#386	C₂²×C₆₇	1	2	yes	—
575	#386	C₂²×C₆₇	1	2	yes	—
576	#386	C₂²×C₆₇	1	2	yes	—
577	#386	C₂²×C₆₇	1	2	yes	complemented
578	#385	C₂²×C₆₇	1	2	yes	—
579	#385	C₂²×C₆₇	1	2	yes	—
580	#385	C₂²×C₆₇	1	2	yes	—
581	#385	C₂²×C₆₇	1	2	yes	—
582	#385	C₂²×C₆₇	1	2	yes	—
583	#385	C₂²×C₆₇	1	2	yes	—
584	#385	C₂²×C₆₇	1	2	yes	—
585	#385	C₂²×C₆₇	1	2	yes	—
586	#385	C₂²×C₆₇	1	2	yes	—
587	#385	C₂²×C₆₇	1	2	yes	—
588	#385	C₂²×C₆₇	1	2	yes	complemented
589	#383	C₂²×C₆₇	1	2	yes	complemented
590	#382	C₂²×C₆₇	1	2	yes	complemented
591	#381	C₂²×C₆₇	1	2	yes	—
592	#381	C₂²×C₆₇	1	2	yes	—
593	#381	C₂²×C₆₇	1	2	yes	complemented
594	#380	C₂²×C₆₇	1	1	yes	characteristic
595	#380	C₂²×C₆₇	1	1	yes	characteristic
596	#380	C₂²×C₆₇	1	1	yes	characteristic
597	#380	C₂²×C₆₇	1	1	yes	characteristic
598	#380	C₂²×C₆₇	1	1	yes	characteristic
599	#380	C₂²×C₆₇	1	1	yes	characteristic
600	#380	C₂²×C₆₇	1	2	yes	complemented
601	#379	C₂²×C₆₇	1	2	yes	—
602	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
603	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
604	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
605	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
606	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
607	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
608	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
609	C₂×#95	C₂²×C₆₇	1	2	yes	—
610	C₂×#95	C₂²×C₆₇	1	2	yes	—
611	C₂×#95	C₂²×C₆₇	1	2	yes	—
612	C₂×#95	C₂²×C₆₇	1	2	yes	—
613	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
614	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
615	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
616	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
617	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
618	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
619	C₂³×C₄	—	2	4	no	—
620	C₂³×C₄	—	2	4	no	—
621	C₂³×C₄	—	2	4	no	—
622	C₂³×C₄	—	4	2	no	—
623	C₂³×C₄	—	4	2	no	—
624	C₂³×C₄	—	4	2	no	—
625	C₂³×C₄	—	4	2	no	—
626	C₂³×C₄	—	4	2	no	—
627	C₂³×C₄	—	4	2	no	—
628	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
629	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
630	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
631	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
632	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
633	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
634	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
635	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
636	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
637	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
638	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
639	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
640	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
641	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
642	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
643	#123	—	4	4	no	—
644	#123	—	4	4	no	—
645	C₂²⋊Q₈	—	2	4	no	—
646	C₂²⋊Q₈	—	4	2	no	—
647	C₂²⋊Q₈	—	4	2	no	—
648	#121	—	2	4	no	—
649	#121	—	4	2	no	—
650	#121	—	4	2	no	—
651	#120	—	2	8	no	—
652	C₄×D₄	—	2	8	no	—
653	C₄×D₄	—	4	4	no	—
654	C₄×D₄	—	4	4	no	—
655	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
656	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
657	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
658	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
659	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
660	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
661	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
662	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
663	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
664	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
665	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
666	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
667	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
668	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
669	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
670	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
671	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
672	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
673	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
674	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
675	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
676	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
677	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
678	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
679	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
680	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
681	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
682	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
683	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
684	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
685	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
686	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
687	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
688	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
689	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
690	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
691	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
692	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
693	#95	C₂³×C₆₇	1	2	yes	—
694	#95	C₂³×C₆₇	1	2	yes	—
695	#95	C₂³×C₆₇	1	2	yes	—
696	#95	C₂³×C₆₇	1	2	yes	—
697	#95	C₂³×C₆₇	1	2	yes	—
698	#95	C₂³×C₆₇	1	2	yes	—
699	#95	C₂³×C₆₇	1	2	yes	—
700	#95	C₂³×C₆₇	1	2	yes	—
701	#95	C₂³×C₆₇	1	2	yes	—
702	#95	C₂³×C₆₇	1	2	yes	—
703	#95	C₂³×C₆₇	1	2	yes	—
704	#95	C₂³×C₆₇	1	2	yes	—
705	#95	C₂³×C₆₇	1	2	yes	—
706	#95	C₂³×C₆₇	1	2	yes	—
707	#95	C₂³×C₆₇	1	2	yes	—
708	#95	C₂³×C₆₇	1	2	yes	—
709	#95	C₂³×C₆₇	1	2	yes	—
710	#95	C₂³×C₆₇	1	2	yes	—
711	#95	C₂³×C₆₇	1	2	yes	—
712	#95	C₂³×C₆₇	1	2	yes	—
713	#95	C₂³×C₆₇	1	2	yes	—
714	#95	C₂³×C₆₇	1	2	yes	—
715	#95	C₂³×C₆₇	1	2	yes	—
716	#95	C₂³×C₆₇	1	2	yes	—
717	#95	C₂³×C₆₇	1	2	yes	—
718	#95	C₂³×C₆₇	1	2	yes	—
719	#95	C₂³×C₆₇	1	2	yes	—
720	#95	C₂³×C₆₇	1	2	yes	—
721	C₂⁴	—	2	2	no	—
722	C₂⁴	—	2	2	no	—
723	C₂⁴	—	2	2	no	—
724	C₂⁴	—	2	2	no	—
725	C₂⁴	—	2	2	no	—
726	C₂⁴	—	2	2	no	—
727	C₂⁴	#41×C₆₇	1	4	yes	—
728	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
729	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
730	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
731	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
732	C₂×Q₈	—	2	2	no	—
733	C₂×Q₈	—	4	1	no	—
734	C₂×Q₈	—	4	1	no	—
735	C₂×D₄	—	2	4	no	—
736	C₂×D₄	—	2	4	no	—
737	C₂×D₄	—	2	4	no	—
738	C₂×D₄	—	2	4	no	—
739	C₂×D₄	—	2	4	no	—
740	C₂×D₄	—	2	4	no	—
741	C₂×D₄	—	2	4	no	—
742	C₂×D₄	—	2	4	no	—
743	C₂×D₄	—	2	4	no	—
744	C₂×D₄	—	2	2	no	—
745	C₂×D₄	—	4	1	no	—
746	C₂×D₄	—	4	1	no	—
747	C₂²×C₄	—	2	2	no	—
748	C₂²×C₄	—	2	2	no	—
749	C₂²×C₄	—	2	2	no	—
750	C₂²×C₄	—	2	2	no	—
751	C₂²×C₄	—	2	4	no	—
752	C₂²×C₄	—	2	4	no	—
753	C₂²×C₄	—	2	4	no	—
754	C₂²×C₄	—	2	4	no	—
755	C₂²×C₄	—	2	2	no	—
756	C₂²×C₄	—	2	2	no	—
757	C₂²×C₄	—	2	2	no	—
758	C₂²×C₄	—	2	2	no	—
759	C₂²×C₄	—	2	4	no	—
760	C₂²×C₄	—	2	4	no	—
761	C₂²×C₄	—	2	4	no	—
762	C₂²×C₄	—	2	4	no	—
763	C₂²×C₄	—	2	2	no	—
764	C₂²×C₄	—	2	2	no	—
765	C₂²×C₄	—	2	2	no	—
766	C₂²×C₄	—	2	2	no	—
767	C₂²×C₄	—	2	4	no	—
768	C₂²×C₄	—	4	1	no	—
769	C₂²×C₄	—	4	1	no	—
770	C₂²×C₄	—	4	2	no	—
771	C₂²×C₄	—	4	2	no	—
772	C₂²×C₄	—	4	1	no	—
773	C₂²×C₄	—	4	1	no	—
774	C₂²×C₄	—	4	1	no	—
775	C₂²×C₄	—	4	1	no	—
776	C₂²×C₄	—	4	1	no	—
777	C₂²×C₄	—	4	1	no	—
778	C₂²×C₄	—	4	1	no	—
779	C₂²×C₄	—	4	1	no	—
780	C₂²×C₄	—	4	1	no	—
781	C₂²×C₄	—	4	1	no	—
782	C₂²×C₄	—	4	1	no	—
783	C₂²×C₄	—	4	1	no	—
784	C₂²×C₄	—	4	2	no	—
785	C₂²×C₄	—	4	2	no	—
786	C₂²×C₄	—	4	1	no	—
787	C₂²×C₄	—	4	1	no	—
788	C₂²×C₄	—	4	2	no	—
789	C₂²×C₄	—	4	2	no	—
790	C₂²×C₄	—	4	16	no	—
791	C₂²×C₄	—	4	16	no	—
792	C₂²×C₄	—	4	16	no	—
793	C₂²×C₄	#41×C₆₇	1	4	yes	—
794	C₂²×C₄	#41×C₆₇	1	4	yes	—
795	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
796	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
797	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
798	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
799	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
800	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
801	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
802	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
803	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
804	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
805	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
806	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
807	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
808	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
809	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
810	C₄⋊C₄	—	2	4	no	—
811	C₄⋊C₄	—	2	2	no	—
812	C₄⋊C₄	—	2	2	no	—
813	C₄⋊C₄	—	2	4	no	—
814	C₄⋊C₄	—	4	2	no	—
815	C₄⋊C₄	—	4	2	no	—
816	C₄⋊C₄	—	4	1	no	—
817	C₄⋊C₄	—	4	1	no	—
818	C₄⋊C₄	—	4	1	no	—
819	C₄⋊C₄	—	4	1	no	—
820	C₄⋊C₄	—	4	2	no	—
821	C₄⋊C₄	—	4	2	no	—
822	C₄⋊C₄	—	4	2	no	—
823	C₄⋊C₄	—	4	2	no	—
824	C₄⋊C₄	—	4	2	no	—
825	C₄⋊C₄	—	4	2	no	—
826	C₂²⋊C₄	—	2	4	no	—
827	C₂²⋊C₄	—	2	4	no	—
828	C₂²⋊C₄	—	2	4	no	—
829	C₂²⋊C₄	—	2	4	no	—
830	C₂²⋊C₄	—	2	4	no	—
831	C₂²⋊C₄	—	2	4	no	—
832	C₂²⋊C₄	—	2	4	no	—
833	C₂²⋊C₄	—	2	4	no	—
834	C₂²⋊C₄	—	2	4	no	—
835	C₂²⋊C₄	—	2	4	no	—
836	C₂²⋊C₄	—	2	4	no	—
837	C₂²⋊C₄	—	4	2	no	—
838	C₂²⋊C₄	—	4	2	no	—
839	C₂²⋊C₄	—	4	2	no	—
840	C₂²⋊C₄	—	4	2	no	—
841	C₂²⋊C₄	—	4	2	no	—
842	C₂²⋊C₄	—	4	2	no	—
843	C₂²⋊C₄	—	4	2	no	—
844	C₂²⋊C₄	—	4	2	no	—
845	C₄²	—	2	4	no	—
846	C₄²	—	4	2	no	—
847	C₄²	—	4	2	no	—
848	C₂³	—	2	8	no	—
849	C₂³	—	2	8	no	—
850	C₂³	—	2	8	no	—
851	C₂³	—	2	8	no	—
852	C₂³	—	2	8	no	—
853	C₂³	—	2	8	no	—
854	C₂³	—	2	8	no	—
855	C₂³	—	2	1	no	—
856	C₂³	—	2	1	no	—
857	C₂³	—	2	1	no	—
858	C₂³	—	2	1	no	—
859	C₂³	—	2	1	no	—
860	C₂³	—	2	1	no	—
861	C₂³	—	2	1	no	—
862	C₂³	—	2	1	no	—
863	C₂³	—	2	1	no	—
864	C₂³	—	2	1	no	—
865	C₂³	—	2	1	no	—
866	C₂³	—	2	1	no	—
867	C₂³	—	2	2	no	—
868	C₂³	—	2	2	no	—
869	C₂³	—	2	2	no	—
870	C₂³	—	2	2	no	—
871	C₂³	—	2	2	no	—
872	C₂³	—	2	2	no	—
873	C₂³	—	2	2	no	—
874	C₂³	C₂×#41×C₆₇	1	2	yes	—
875	C₂³	C₂×#41×C₆₇	1	2	yes	—
876	C₂³	C₂×#41×C₆₇	1	2	yes	—
877	C₂³	C₂×#41×C₆₇	1	2	yes	—
878	C₂³	C₂×#41×C₆₇	1	2	yes	—
879	C₂³	H(5,𝔽₂)×C₆₇	1	2	yes	—
880	C₂³	H(5,𝔽₂)×C₆₇	1	2	yes	—
881	C₂³	H(5,𝔽₂)×C₆₇	1	2	yes	—
882	C₂³	2₋¹⁺⁴×C₆₇	1	2	yes	—
883	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
884	Q₈	—	8	2	no	—
885	D₄	—	4	8	no	—
886	D₄	—	4	8	no	—
887	D₄	—	4	8	no	—
888	D₄	—	8	2	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	2	1	no	—
892	C₂×C₄	—	2	1	no	—
893	C₂×C₄	—	2	1	no	—
894	C₂×C₄	—	2	1	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	2	1	no	—
907	C₂×C₄	—	2	1	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	2	2	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	1	no	—
918	C₂×C₄	—	2	1	no	—
919	C₂×C₄	—	2	2	no	—
920	C₂×C₄	—	2	2	no	—
921	C₂×C₄	—	2	2	no	—
922	C₂×C₄	—	2	2	no	—
923	C₂×C₄	—	2	2	no	—
924	C₂×C₄	—	2	2	no	—
925	C₂×C₄	—	2	2	no	—
926	C₂×C₄	—	2	1	no	—
927	C₂×C₄	—	2	1	no	—
928	C₂×C₄	—	2	2	no	—
929	C₂×C₄	—	2	2	no	—
930	C₂×C₄	—	2	2	no	—
931	C₂×C₄	—	4	4	no	—
932	C₂×C₄	—	4	4	no	—
933	C₂×C₄	—	4	8	no	—
934	C₂×C₄	—	4	8	no	—
935	C₂×C₄	—	4	4	no	—
936	C₂×C₄	—	4	4	no	—
937	C₂×C₄	—	4	4	no	—
938	C₂×C₄	—	4	4	no	—
939	C₂×C₄	—	4	4	no	—
940	C₂×C₄	—	4	4	no	—
941	C₂×C₄	—	4	8	no	—
942	C₂×C₄	—	4	4	no	—
943	C₂×C₄	—	4	4	no	—
944	C₂×C₄	—	4	8	no	—
945	C₂×C₄	—	8	4	no	—
946	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
947	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
948	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
949	C₂²	—	2	32	no	—
950	C₂²	—	2	2	no	—
951	C₂²	—	2	2	no	—
952	C₂²	—	2	2	no	—
953	C₂²	—	2	2	no	—
954	C₂²	—	2	2	no	—
955	C₂²	—	2	2	no	—
956	C₂²	—	2	2	no	—
957	C₂²	—	2	2	no	—
958	C₂²	—	2	2	no	—
959	C₂²	—	2	2	no	—
960	C₂²	—	2	2	no	—
961	C₂²	—	2	2	no	—
962	C₂²	—	2	2	no	—
963	C₂²	—	2	2	no	—
964	C₂²	—	2	2	no	—
965	C₂²	—	2	2	no	—
966	C₂²	—	2	2	no	—
967	C₂²	—	2	2	no	—
968	C₂²	—	4	2	no	—
969	C₂²	—	4	2	no	—
970	C₂²	—	4	2	no	—
971	C₂²	—	4	2	no	—
972	C₂²	—	4	2	no	—
973	C₂²	—	4	2	no	—
974	C₂²	—	4	2	no	—
975	C₂²	#529×C₆₇	1	4	yes	—
976	C₂²	#538×C₆₇	1	4	yes	—
977	C₂²	#539×C₆₇	1	4	yes	—
978	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
979	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
980	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
981	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
982	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
983	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
984	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
985	C₄	—	2	4	no	—
986	C₄	—	2	2	no	—
987	C₄	—	2	2	no	—
988	C₄	—	4	2	no	—
989	C₄	—	4	2	no	—
990	C₄	—	4	2	no	—
991	C₄	—	4	2	no	—
992	C₄	—	4	2	no	—
993	C₄	—	4	1	no	—
994	C₄	—	4	1	no	—
995	C₄	—	4	2	no	—
996	C₄	—	4	2	no	—
997	C₄	—	4	2	no	—
998	C₄	—	4	2	no	—
999	C₄	—	4	2	no	—
1000	C₂	—	2	4	no	—
1001	C₂	—	2	4	no	—
1002	C₂	—	2	4	no	—
1003	C₂	—	8	2	no	—
1004	C₂	C₂×#529×C₆₇	1	1	yes	characteristic
1005	C₂	C₂×#538×C₆₇	1	1	yes	characteristic
1006	C₂	C₂×#539×C₆₇	1	1	yes	characteristic
1007	C₂	C₆₇×#3490	1	1	yes	characteristic
1008	C₂	C₆₇×#3490	1	1	yes	characteristic
1009	C₂	C₆₇×#3492	1	1	yes	characteristic
1010	C₂	C₆₇×#3492	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₆₇×#2847	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#2849	C₂	semidirect
2. C₆₇×#2848	C₂	semidirect
4. C₆₇×#2646	C₂	semidirect
5. C₆₇×#2643	C₂	semidirect
6. C₆₇×#2639	C₂	semidirect
7. C₆₇×#2510	C₂	semidirect
8. C₆₇×#2505	C₂	semidirect
9. C₆₇×#2493	C₂	semidirect
10. C₆₇×#2488	C₂	semidirect
11. C₆₇×#2450	C₂	semidirect
12. C₆₇×#2444	C₂	semidirect
13. C₆₇×#2425	C₂	semidirect
14. C₆₇×#2419	C₂	semidirect
15. C₆₇×#2329	C₂	semidirect
16. C₆₇×#2325	C₂	semidirect
17. C₆₇×#2318	C₂	semidirect
18. C₄×#120×C₆₇	C₂	semidirect
19. C₂²×#95×C₆₇	C₂	semidirect
35. #401×C₆₇	C₂²	semidirect
36. #400×C₆₇	C₂²	semidirect
37. #400×C₆₇	C₂²	semidirect
38. #400×C₆₇	C₂²	semidirect
39. #400×C₆₇	C₂²	semidirect
40. #400×C₆₇	C₂²	semidirect
41. #400×C₆₇	C₂²	semidirect
42. #398×C₆₇	C₂²	semidirect
43. #398×C₆₇	C₂²	semidirect
44. #397×C₆₇	C₂²	semidirect
45. #397×C₆₇	C₂²	semidirect
46. #397×C₆₇	C₂²	semidirect
47. #397×C₆₇	C₂²	semidirect
48. #396×C₆₇	C₂²	semidirect
49. #394×C₆₇	C₂²	semidirect
50. #393×C₆₇	C₂²	semidirect
51. #391×C₆₇	C₂²	semidirect
52. #389×C₆₇	C₂²	semidirect
53. #388×C₆₇	C₂²	semidirect
54. #388×C₆₇	C₂²	semidirect
55. #388×C₆₇	C₂²	semidirect
56. #387×C₆₇	C₂²	semidirect
57. #387×C₆₇	C₂²	semidirect
58. #387×C₆₇	C₂²	semidirect
59. #387×C₆₇	C₂²	semidirect
60. #387×C₆₇	C₂²	semidirect
71. #386×C₆₇	C₂²	semidirect
82. #385×C₆₇	C₂²	semidirect
83. #383×C₆₇	C₂²	semidirect
84. #382×C₆₇	C₂²	semidirect
87. #381×C₆₇	C₂²	semidirect
94. #380×C₆₇	C₂²	semidirect
494. #34997	C₆₇	direct (N × H)
506. #2849	C₂×C₆₇	semidirect
507. #2848	C₂×C₆₇	semidirect
509. #2646	C₂×C₆₇	semidirect
510. #2643	C₂×C₆₇	semidirect
511. #2639	C₂×C₆₇	semidirect
512. #2510	C₂×C₆₇	semidirect
513. #2505	C₂×C₆₇	semidirect
514. #2493	C₂×C₆₇	semidirect
515. #2488	C₂×C₆₇	semidirect
516. #2450	C₂×C₆₇	semidirect
517. #2444	C₂×C₆₇	semidirect
518. #2425	C₂×C₆₇	semidirect
519. #2419	C₂×C₆₇	semidirect
520. #2329	C₂×C₆₇	semidirect
521. #2325	C₂×C₆₇	semidirect
522. #2318	C₂×C₆₇	semidirect
523. C₄×#120	C₂×C₆₇	semidirect
524. C₂²×#95	C₂×C₆₇	semidirect
525. C₆₇	#34997	direct (N × H)
541. #401	C₂²×C₆₇	semidirect
542. #400	C₂²×C₆₇	semidirect
543. #400	C₂²×C₆₇	semidirect
544. #400	C₂²×C₆₇	semidirect
545. #400	C₂²×C₆₇	semidirect
546. #400	C₂²×C₆₇	semidirect
547. #400	C₂²×C₆₇	semidirect
548. #398	C₂²×C₆₇	semidirect
549. #398	C₂²×C₆₇	semidirect
550. #397	C₂²×C₆₇	semidirect
551. #397	C₂²×C₆₇	semidirect
552. #397	C₂²×C₆₇	semidirect
553. #397	C₂²×C₆₇	semidirect
554. #396	C₂²×C₆₇	semidirect
555. #394	C₂²×C₆₇	semidirect
556. #393	C₂²×C₆₇	semidirect
557. #391	C₂²×C₆₇	semidirect
558. #389	C₂²×C₆₇	semidirect
559. #388	C₂²×C₆₇	semidirect
560. #388	C₂²×C₆₇	semidirect
561. #388	C₂²×C₆₇	semidirect
562. #387	C₂²×C₆₇	semidirect
563. #387	C₂²×C₆₇	semidirect
564. #387	C₂²×C₆₇	semidirect
565. #387	C₂²×C₆₇	semidirect
566. #387	C₂²×C₆₇	semidirect
577. #386	C₂²×C₆₇	semidirect
588. #385	C₂²×C₆₇	semidirect
589. #383	C₂²×C₆₇	semidirect
590. #382	C₂²×C₆₇	semidirect
593. #381	C₂²×C₆₇	semidirect
600. #380	C₂²×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#2849	2
C₆₇×#2848	2
C₆₇×#2847	2
C₆₇×#2646	2
C₆₇×#2643	2
C₆₇×#2639	2
C₆₇×#2510	2
C₆₇×#2505	2
C₆₇×#2493	2
C₆₇×#2488	2
C₆₇×#2450	2
C₆₇×#2444	2
C₆₇×#2425	2
C₆₇×#2419	2
C₆₇×#2329	2
C₆₇×#2325	2
C₆₇×#2318	2
C₄×#120×C₆₇	2
C₂²×#95×C₆₇	2
#34997	67

Subgroups — C67×#34997 #30714248

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#34997 #30714248