Subgroups — C₆₇×#59947 #30739198

Order 17152.

2334 conjugacy classes of subgroups.

The subgroup lattice has 976 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#2803	C₂	1	2	yes	maximal, complemented
2	C₆₇×#2784	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2699	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#2610	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2593	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#2591	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#2583	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#2555	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#2526	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2476	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2472	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2424	C₂	1	2	yes	maximal, complemented
13	C₆₇×#2414	C₂	1	2	yes	maximal, complemented
14	C₆₇×#2410	C₂	1	2	yes	maximal, complemented
15	C₆₇×#2363	C₂	1	2	yes	maximal, complemented
16	C₆₇×#2358	C₂	1	2	yes	maximal, complemented
17	C₆₇×#2342	C₂	1	2	yes	maximal, complemented
18	C₂×#390×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#2290	C₂	1	2	yes	maximal, complemented
20	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
21	C₂×#124×C₆₇	C₂²	1	2	yes	complemented
22	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
23	C₂×#121×C₆₇	C₂²	1	2	yes	—
24	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×#121×C₆₇	C₂²	1	2	yes	—
26	C₂×#121×C₆₇	C₂²	1	2	yes	complemented
27	C₂×#120×C₆₇	C₂²	1	2	yes	—
28	C₂×#120×C₆₇	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
31	C₂×#117×C₆₇	C₂²	1	2	yes	complemented
32	C₂×#117×C₆₇	C₂²	1	2	yes	complemented
33	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
34	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
35	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
36	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
37	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
38	#400×C₆₇	C₂²	1	1	yes	characteristic, complemented
39	#400×C₆₇	C₂²	1	1	yes	characteristic, complemented
40	#398×C₆₇	C₂²	1	1	yes	characteristic, complemented
41	#398×C₆₇	C₂²	1	1	yes	characteristic, complemented
42	#397×C₆₇	C₂²	1	2	yes	complemented
43	#396×C₆₇	C₂²	1	2	yes	complemented
44	#395×C₆₇	C₂²	1	1	yes	characteristic, complemented
45	#395×C₆₇	C₂²	1	1	yes	characteristic, complemented
46	#394×C₆₇	C₂²	1	2	yes	—
47	#394×C₆₇	C₂²	1	2	yes	—
48	#394×C₆₇	C₂²	1	2	yes	complemented
49	#394×C₆₇	C₂²	1	2	yes	complemented
50	#394×C₆₇	C₂²	1	2	yes	complemented
51	#394×C₆₇	C₂²	1	1	yes	characteristic, complemented
52	#394×C₆₇	C₂²	1	1	yes	characteristic, complemented
53	#394×C₆₇	C₂²	1	2	yes	complemented
54	#393×C₆₇	C₂²	1	2	yes	complemented
55	#392×C₆₇	C₂²	1	2	yes	—
56	#392×C₆₇	C₂²	1	2	yes	—
57	#392×C₆₇	C₂²	1	2	yes	complemented
58	#390×C₆₇	C₂²	1	2	yes	—
59	#390×C₆₇	C₂²	1	1	yes	characteristic
60	#390×C₆₇	C₂²	1	1	yes	characteristic
61	#390×C₆₇	C₂²	1	1	yes	characteristic
62	#390×C₆₇	C₂²	1	2	yes	—
63	#390×C₆₇	C₂²	1	1	yes	characteristic
64	#390×C₆₇	C₂²	1	2	yes	complemented
65	#390×C₆₇	C₂²	1	2	yes	complemented
66	#390×C₆₇	C₂²	1	2	yes	complemented
67	#389×C₆₇	C₂²	1	2	yes	complemented
68	#389×C₆₇	C₂²	1	2	yes	complemented
69	#388×C₆₇	C₂²	1	2	yes	complemented
70	#388×C₆₇	C₂²	1	2	yes	complemented
71	#388×C₆₇	C₂²	1	2	yes	complemented
72	#388×C₆₇	C₂²	1	2	yes	complemented
73	#388×C₆₇	C₂²	1	2	yes	complemented
74	#388×C₆₇	C₂²	1	2	yes	complemented
75	#388×C₆₇	C₂²	1	2	yes	complemented
76	#388×C₆₇	C₂²	1	2	yes	complemented
77	#388×C₆₇	C₂²	1	2	yes	complemented
78	#388×C₆₇	C₂²	1	2	yes	complemented
79	#388×C₆₇	C₂²	1	2	yes	complemented
80	#388×C₆₇	C₂²	1	2	yes	complemented
81	#388×C₆₇	C₂²	1	2	yes	complemented
82	#387×C₆₇	C₂²	1	2	yes	complemented
83	#387×C₆₇	C₂²	1	2	yes	complemented
84	#386×C₆₇	C₂²	1	2	yes	—
85	#386×C₆₇	C₂²	1	2	yes	—
86	#386×C₆₇	C₂²	1	2	yes	—
87	#386×C₆₇	C₂²	1	2	yes	—
88	#386×C₆₇	C₂²	1	2	yes	—
89	#386×C₆₇	C₂²	1	2	yes	complemented
90	#386×C₆₇	C₂²	1	2	yes	complemented
91	#386×C₆₇	C₂²	1	2	yes	complemented
92	#385×C₆₇	C₂²	1	2	yes	—
93	#385×C₆₇	C₂²	1	2	yes	—
94	#385×C₆₇	C₂²	1	2	yes	—
95	#385×C₆₇	C₂²	1	2	yes	complemented
96	#381×C₆₇	C₂²	1	2	yes	complemented
97	#380×C₆₇	C₂²	1	2	yes	complemented
98	#379×C₆₇	C₂²	1	2	yes	—
99	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
100	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
101	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
102	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
103	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
104	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
105	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
106	#376×C₆₇	C₂²	1	2	yes	complemented
107	C₂⁵×C₆₇	C₂³	1	2	yes	—
108	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
109	C₂²×D₄×C₆₇	—	2	4	no	—
110	C₂²×D₄×C₆₇	—	4	2	no	—
111	C₂²×D₄×C₆₇	—	4	2	no	—
112	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
113	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
114	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
115	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
116	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
117	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
118	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
119	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
120	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
121	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
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	2	yes	—
128	#124×C₆₇	—	4	4	no	—
129	C₂²⋊Q₈×C₆₇	—	4	2	no	—
130	#121×C₆₇	—	2	8	no	—
131	#121×C₆₇	—	4	4	no	—
132	#121×C₆₇	—	4	4	no	—
133	#121×C₆₇	—	4	2	no	—
134	#120×C₆₇	—	2	8	no	—
135	#120×C₆₇	—	4	4	no	—
136	C₄×D₄×C₆₇	—	2	8	no	—
137	C₄×D₄×C₆₇	—	4	4	no	—
138	#117×C₆₇	—	4	4	no	—
139	#117×C₆₇	—	4	4	no	—
140	C₂×C₄⋊C₄×C₆₇	—	4	2	no	—
141	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
147	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
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	1	yes	characteristic
154	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
156	C₂×C₂²⋊C₄×C₆₇	—	4	4	no	—
157	C₂×C₂²⋊C₄×C₆₇	—	4	4	no	—
158	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
162	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
164	C₂×C₂²⋊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×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
185	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
186	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
187	C₂×C₄²×C₆₇	—	4	2	no	—
188	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
189	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
190	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
191	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
194	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
195	C₂×C₄²×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	1	yes	characteristic
201	#95×C₆₇	C₂³	1	2	yes	—
202	#95×C₆₇	C₂³	1	1	yes	characteristic
203	#95×C₆₇	C₂³	1	2	yes	—
204	#95×C₆₇	C₂³	1	1	yes	characteristic
205	#95×C₆₇	C₂³	1	1	yes	characteristic
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	C₂⁴×C₆₇	—	2	4	no	—
215	C₂⁴×C₆₇	—	2	4	no	—
216	C₂⁴×C₆₇	—	2	4	no	—
217	C₂⁴×C₆₇	—	2	4	no	—
218	C₂⁴×C₆₇	—	4	2	no	—
219	C₂⁴×C₆₇	—	4	2	no	—
220	C₂⁴×C₆₇	—	4	2	no	—
221	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
222	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
223	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
224	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
225	C₂×Q₈×C₆₇	—	4	1	no	—
226	C₂×Q₈×C₆₇	—	4	2	no	—
227	C₂×D₄×C₆₇	—	2	4	no	—
228	C₂×D₄×C₆₇	—	2	4	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	2	no	—
235	C₂×D₄×C₆₇	—	2	4	no	—
236	C₂×D₄×C₆₇	—	2	4	no	—
237	C₂×D₄×C₆₇	—	4	2	no	—
238	C₂×D₄×C₆₇	—	4	1	no	—
239	C₂×D₄×C₆₇	—	4	1	no	—
240	C₂×D₄×C₆₇	—	4	1	no	—
241	C₂×D₄×C₆₇	—	4	2	no	—
242	C₂×D₄×C₆₇	—	4	1	no	—
243	C₂×D₄×C₆₇	—	4	16	no	—
244	C₂×D₄×C₆₇	—	4	2	no	—
245	C₂×D₄×C₆₇	—	4	2	no	—
246	C₂×D₄×C₆₇	—	4	2	no	—
247	C₂×D₄×C₆₇	—	4	2	no	—
248	C₂×D₄×C₆₇	—	4	2	no	—
249	C₂×D₄×C₆₇	—	4	2	no	—
250	C₂×D₄×C₆₇	—	4	2	no	—
251	C₂×D₄×C₆₇	—	4	1	no	—
252	C₂×D₄×C₆₇	—	4	2	no	—
253	C₂×D₄×C₆₇	#41	1	4	yes	—
254	C₂²×C₄×C₆₇	—	2	2	no	—
255	C₂²×C₄×C₆₇	—	2	2	no	—
256	C₂²×C₄×C₆₇	—	2	2	no	—
257	C₂²×C₄×C₆₇	—	2	4	no	—
258	C₂²×C₄×C₆₇	—	2	4	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	—	2	4	no	—
263	C₂²×C₄×C₆₇	—	2	4	no	—
264	C₂²×C₄×C₆₇	—	2	4	no	—
265	C₂²×C₄×C₆₇	—	2	4	no	—
266	C₂²×C₄×C₆₇	—	4	2	no	—
267	C₂²×C₄×C₆₇	—	4	2	no	—
268	C₂²×C₄×C₆₇	—	4	2	no	—
269	C₂²×C₄×C₆₇	—	4	2	no	—
270	C₂²×C₄×C₆₇	—	4	2	no	—
271	C₂²×C₄×C₆₇	—	4	2	no	—
272	C₂²×C₄×C₆₇	—	4	2	no	—
273	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
274	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
275	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
276	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
277	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
278	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
279	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
280	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
281	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
282	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
284	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
285	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
286	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
287	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
288	C₄⋊C₄×C₆₇	—	2	4	no	—
289	C₄⋊C₄×C₆₇	—	2	4	no	—
290	C₄⋊C₄×C₆₇	—	2	4	no	—
291	C₄⋊C₄×C₆₇	—	2	4	no	—
292	C₄⋊C₄×C₆₇	—	4	1	no	—
293	C₄⋊C₄×C₆₇	—	4	1	no	—
294	C₄⋊C₄×C₆₇	—	4	1	no	—
295	C₄⋊C₄×C₆₇	—	4	1	no	—
296	C₄⋊C₄×C₆₇	—	4	2	no	—
297	C₄⋊C₄×C₆₇	—	4	2	no	—
298	C₄⋊C₄×C₆₇	—	4	2	no	—
299	C₄⋊C₄×C₆₇	—	4	1	no	—
300	C₄⋊C₄×C₆₇	—	4	1	no	—
301	C₄⋊C₄×C₆₇	—	4	2	no	—
302	C₂²⋊C₄×C₆₇	—	2	4	no	—
303	C₂²⋊C₄×C₆₇	—	2	4	no	—
304	C₂²⋊C₄×C₆₇	—	2	4	no	—
305	C₂²⋊C₄×C₆₇	—	2	4	no	—
306	C₂²⋊C₄×C₆₇	—	2	4	no	—
307	C₂²⋊C₄×C₆₇	—	2	4	no	—
308	C₂²⋊C₄×C₆₇	—	2	4	no	—
309	C₂²⋊C₄×C₆₇	—	2	4	no	—
310	C₂²⋊C₄×C₆₇	—	2	4	no	—
311	C₂²⋊C₄×C₆₇	—	2	4	no	—
312	C₂²⋊C₄×C₆₇	—	2	4	no	—
313	C₂²⋊C₄×C₆₇	—	2	4	no	—
314	C₂²⋊C₄×C₆₇	—	2	4	no	—
315	C₂²⋊C₄×C₆₇	—	2	4	no	—
316	C₂²⋊C₄×C₆₇	—	2	4	no	—
317	C₂²⋊C₄×C₆₇	—	4	2	no	—
318	C₂²⋊C₄×C₆₇	—	4	2	no	—
319	C₂²⋊C₄×C₆₇	—	4	2	no	—
320	C₂²⋊C₄×C₆₇	—	4	2	no	—
321	C₂²⋊C₄×C₆₇	—	4	2	no	—
322	C₂²⋊C₄×C₆₇	—	4	2	no	—
323	C₂²⋊C₄×C₆₇	—	4	2	no	—
324	C₂²⋊C₄×C₆₇	—	4	2	no	—
325	C₂²⋊C₄×C₆₇	—	4	2	no	—
326	C₂²⋊C₄×C₆₇	—	4	2	no	—
327	C₂²⋊C₄×C₆₇	—	4	2	no	—
328	C₂²⋊C₄×C₆₇	—	4	2	no	—
329	C₂²⋊C₄×C₆₇	—	4	2	no	—
330	C₂²⋊C₄×C₆₇	#41	1	8	yes	—
331	C₄²×C₆₇	—	2	4	no	—
332	C₄²×C₆₇	—	2	4	no	—
333	C₄²×C₆₇	—	2	4	no	—
334	C₄²×C₆₇	—	4	1	no	—
335	C₄²×C₆₇	—	4	1	no	—
336	C₄²×C₆₇	—	4	2	no	—
337	C₄²×C₆₇	—	4	2	no	—
338	C₄²×C₆₇	—	4	2	no	—
339	C₂³×C₆₇	—	2	1	no	—
340	C₂³×C₆₇	—	2	2	no	—
341	C₂³×C₆₇	—	2	1	no	—
342	C₂³×C₆₇	—	2	2	no	—
343	C₂³×C₆₇	—	2	2	no	—
344	C₂³×C₆₇	—	2	2	no	—
345	C₂³×C₆₇	—	2	2	no	—
346	C₂³×C₆₇	—	2	2	no	—
347	C₂³×C₆₇	—	2	2	no	—
348	C₂³×C₆₇	—	2	2	no	—
349	C₂³×C₆₇	—	2	2	no	—
350	C₂³×C₆₇	—	2	2	no	—
351	C₂³×C₆₇	—	2	2	no	—
352	C₂³×C₆₇	—	2	2	no	—
353	C₂³×C₆₇	—	2	2	no	—
354	C₂³×C₆₇	—	2	2	no	—
355	C₂³×C₆₇	—	2	2	no	—
356	C₂³×C₆₇	—	2	2	no	—
357	C₂³×C₆₇	—	2	2	no	—
358	C₂³×C₆₇	—	2	2	no	—
359	C₂³×C₆₇	—	2	2	no	—
360	C₂³×C₆₇	—	2	2	no	—
361	C₂³×C₆₇	—	2	2	no	—
362	C₂³×C₆₇	—	4	8	no	—
363	C₂³×C₆₇	—	4	8	no	—
364	C₂³×C₆₇	—	4	8	no	—
365	C₂³×C₆₇	—	4	8	no	—
366	C₂³×C₆₇	—	8	4	no	—
367	C₂³×C₆₇	—	8	4	no	—
368	C₂³×C₆₇	—	8	4	no	—
369	C₂³×C₆₇	C₂×#41	1	4	yes	—
370	C₂³×C₆₇	C₂×#41	1	4	yes	—
371	C₂³×C₆₇	H(5,𝔽₂)	1	2	yes	—
372	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
373	Q₈×C₆₇	—	8	2	no	—
374	D₄×C₆₇	—	4	4	no	—
375	D₄×C₆₇	—	4	8	no	—
376	D₄×C₆₇	—	4	8	no	—
377	D₄×C₆₇	—	4	4	no	—
378	D₄×C₆₇	—	4	8	no	—
379	D₄×C₆₇	—	8	4	no	—
380	D₄×C₆₇	—	8	4	no	—
381	D₄×C₆₇	—	8	2	no	—
382	D₄×C₆₇	—	8	4	no	—
383	C₂×C₄×C₆₇	—	2	8	no	—
384	C₂×C₄×C₆₇	—	2	2	no	—
385	C₂×C₄×C₆₇	—	2	2	no	—
386	C₂×C₄×C₆₇	—	2	1	no	—
387	C₂×C₄×C₆₇	—	2	2	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	1	no	—
393	C₂×C₄×C₆₇	—	2	1	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	2	no	—
401	C₂×C₄×C₆₇	—	2	2	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	2	no	—
412	C₂×C₄×C₆₇	—	2	2	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	1	no	—
417	C₂×C₄×C₆₇	—	2	1	no	—
418	C₂×C₄×C₆₇	—	2	1	no	—
419	C₂×C₄×C₆₇	—	2	1	no	—
420	C₂×C₄×C₆₇	—	4	8	no	—
421	C₂×C₄×C₆₇	—	4	8	no	—
422	C₂×C₄×C₆₇	—	4	8	no	—
423	C₂×C₄×C₆₇	—	8	4	no	—
424	C₂×C₄×C₆₇	—	8	2	no	—
425	C₂×C₄×C₆₇	—	8	2	no	—
426	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
427	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
428	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
429	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
430	C₂×C₄×C₆₇	H(5,𝔽₂)	1	4	yes	—
431	C₂²×C₆₇	—	2	4	no	—
432	C₂²×C₆₇	—	2	2	no	—
433	C₂²×C₆₇	—	2	4	no	—
434	C₂²×C₆₇	—	2	2	no	—
435	C₂²×C₆₇	—	2	4	no	—
436	C₂²×C₆₇	—	2	4	no	—
437	C₂²×C₆₇	—	2	4	no	—
438	C₂²×C₆₇	—	4	2	no	—
439	C₂²×C₆₇	—	4	2	no	—
440	C₂²×C₆₇	—	4	2	no	—
441	C₂²×C₆₇	—	4	2	no	—
442	C₂²×C₆₇	—	4	2	no	—
443	C₂²×C₆₇	—	4	2	no	—
444	C₂²×C₆₇	—	4	2	no	—
445	C₂²×C₆₇	—	4	2	no	—
446	C₂²×C₆₇	—	4	2	no	—
447	C₂²×C₆₇	—	4	2	no	—
448	C₂²×C₆₇	—	4	2	no	—
449	C₂²×C₆₇	—	4	2	no	—
450	C₂²×C₆₇	—	4	2	no	—
451	C₂²×C₆₇	—	4	2	no	—
452	C₂²×C₆₇	—	4	2	no	—
453	C₂²×C₆₇	—	4	2	no	—
454	C₂²×C₆₇	—	4	2	no	—
455	C₂²×C₆₇	—	4	2	no	—
456	C₂²×C₆₇	—	8	16	no	—
457	C₂²×C₆₇	#555	1	4	yes	—
458	C₂²×C₆₇	C₂²×#41	1	2	yes	—
459	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
460	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
461	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
462	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
463	C₄×C₆₇	—	2	4	no	—
464	C₄×C₆₇	—	2	2	no	—
465	C₄×C₆₇	—	2	2	no	—
466	C₄×C₆₇	—	2	4	no	—
467	C₄×C₆₇	—	2	4	no	—
468	C₄×C₆₇	—	4	2	no	—
469	C₄×C₆₇	—	4	2	no	—
470	C₄×C₆₇	—	4	2	no	—
471	C₄×C₆₇	—	4	2	no	—
472	C₄×C₆₇	—	4	2	no	—
473	C₄×C₆₇	—	4	1	no	—
474	C₄×C₆₇	—	4	1	no	—
475	C₄×C₆₇	—	4	1	no	—
476	C₄×C₆₇	—	4	1	no	—
477	C₄×C₆₇	—	4	2	no	—
478	#59947	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
479	C₂×C₆₇	—	2	4	no	—
480	C₂×C₆₇	—	4	4	no	—
481	C₂×C₆₇	—	8	2	no	—
482	C₂×C₆₇	—	8	2	no	—
483	C₂×C₆₇	C₂×#555	1	1	yes	characteristic
484	C₂×C₆₇	#3481	1	2	yes	—
485	C₂×C₆₇	#3490	1	1	yes	characteristic
486	C₂×C₆₇	#3519	1	2	yes	—
487	C₂×C₆₇	#3543	1	1	yes	characteristic
488	#2803	C₂×C₆₇	1	2	yes	complemented
489	#2784	C₂×C₆₇	1	1	yes	characteristic, complemented
490	#2699	C₂×C₆₇	1	1	yes	characteristic, complemented
491	#2610	C₂×C₆₇	1	2	yes	complemented
492	#2593	C₂×C₆₇	1	1	yes	characteristic, complemented
493	#2591	C₂×C₆₇	1	1	yes	characteristic, complemented
494	#2583	C₂×C₆₇	1	1	yes	characteristic, complemented
495	#2555	C₂×C₆₇	1	1	yes	characteristic, complemented
496	#2526	C₂×C₆₇	1	2	yes	complemented
497	#2476	C₂×C₆₇	1	2	yes	complemented
498	#2472	C₂×C₆₇	1	2	yes	complemented
499	#2424	C₂×C₆₇	1	2	yes	complemented
500	#2414	C₂×C₆₇	1	2	yes	complemented
501	#2410	C₂×C₆₇	1	2	yes	complemented
502	#2363	C₂×C₆₇	1	2	yes	complemented
503	#2358	C₂×C₆₇	1	2	yes	complemented
504	#2342	C₂×C₆₇	1	2	yes	complemented
505	C₂×#390	C₂×C₆₇	1	1	yes	characteristic, complemented
506	#2290	C₂×C₆₇	1	2	yes	complemented
507	C₆₇	#59947	1	1	yes	characteristic, direct product factor, Sylow
508	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
509	C₂×#124	C₂²×C₆₇	1	2	yes	complemented
510	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
511	C₂×#121	C₂²×C₆₇	1	2	yes	—
512	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
513	C₂×#121	C₂²×C₆₇	1	2	yes	—
514	C₂×#121	C₂²×C₆₇	1	2	yes	complemented
515	C₂×#120	C₂²×C₆₇	1	2	yes	—
516	C₂×#120	C₂²×C₆₇	1	2	yes	—
517	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
518	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
519	C₂×#117	C₂²×C₆₇	1	2	yes	complemented
520	C₂×#117	C₂²×C₆₇	1	2	yes	complemented
521	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
522	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
523	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
524	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
525	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
526	#400	C₂²×C₆₇	1	1	yes	characteristic, complemented
527	#400	C₂²×C₆₇	1	1	yes	characteristic, complemented
528	#398	C₂²×C₆₇	1	1	yes	characteristic, complemented
529	#398	C₂²×C₆₇	1	1	yes	characteristic, complemented
530	#397	C₂²×C₆₇	1	2	yes	complemented
531	#396	C₂²×C₆₇	1	2	yes	complemented
532	#395	C₂²×C₆₇	1	1	yes	characteristic, complemented
533	#395	C₂²×C₆₇	1	1	yes	characteristic, complemented
534	#394	C₂²×C₆₇	1	2	yes	—
535	#394	C₂²×C₆₇	1	2	yes	—
536	#394	C₂²×C₆₇	1	1	yes	characteristic, complemented
537	#394	C₂²×C₆₇	1	1	yes	characteristic, complemented
538	#394	C₂²×C₆₇	1	2	yes	complemented
539	#394	C₂²×C₆₇	1	2	yes	complemented
540	#394	C₂²×C₆₇	1	2	yes	complemented
541	#394	C₂²×C₆₇	1	2	yes	complemented
542	#393	C₂²×C₆₇	1	2	yes	complemented
543	#392	C₂²×C₆₇	1	2	yes	—
544	#392	C₂²×C₆₇	1	2	yes	—
545	#392	C₂²×C₆₇	1	2	yes	complemented
546	#390	C₂²×C₆₇	1	1	yes	characteristic
547	#390	C₂²×C₆₇	1	2	yes	—
548	#390	C₂²×C₆₇	1	1	yes	characteristic
549	#390	C₂²×C₆₇	1	2	yes	—
550	#390	C₂²×C₆₇	1	1	yes	characteristic
551	#390	C₂²×C₆₇	1	1	yes	characteristic
552	#390	C₂²×C₆₇	1	2	yes	complemented
553	#390	C₂²×C₆₇	1	2	yes	complemented
554	#390	C₂²×C₆₇	1	2	yes	complemented
555	#389	C₂²×C₆₇	1	2	yes	complemented
556	#389	C₂²×C₆₇	1	2	yes	complemented
557	#388	C₂²×C₆₇	1	2	yes	complemented
558	#388	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	#388	C₂²×C₆₇	1	2	yes	complemented
563	#388	C₂²×C₆₇	1	2	yes	complemented
564	#388	C₂²×C₆₇	1	2	yes	complemented
565	#388	C₂²×C₆₇	1	2	yes	complemented
566	#388	C₂²×C₆₇	1	2	yes	complemented
567	#388	C₂²×C₆₇	1	2	yes	complemented
568	#388	C₂²×C₆₇	1	2	yes	complemented
569	#388	C₂²×C₆₇	1	2	yes	complemented
570	#387	C₂²×C₆₇	1	2	yes	complemented
571	#387	C₂²×C₆₇	1	2	yes	complemented
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	#386	C₂²×C₆₇	1	2	yes	complemented
579	#386	C₂²×C₆₇	1	2	yes	complemented
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	complemented
584	#381	C₂²×C₆₇	1	2	yes	complemented
585	#380	C₂²×C₆₇	1	2	yes	complemented
586	#379	C₂²×C₆₇	1	2	yes	—
587	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
588	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
589	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
590	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
591	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
592	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
593	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
594	#376	C₂²×C₆₇	1	2	yes	complemented
595	C₂⁵	C₂³×C₆₇	1	2	yes	—
596	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
597	C₂²×D₄	—	2	4	no	—
598	C₂²×D₄	—	4	2	no	—
599	C₂²×D₄	—	4	2	no	—
600	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
601	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
602	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
603	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
604	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
605	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
606	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
607	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
608	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
609	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
610	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
611	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
612	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
613	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
614	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
615	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
616	#124	—	4	4	no	—
617	C₂²⋊Q₈	—	4	2	no	—
618	#121	—	2	8	no	—
619	#121	—	4	4	no	—
620	#121	—	4	4	no	—
621	#121	—	4	2	no	—
622	#120	—	2	8	no	—
623	#120	—	4	4	no	—
624	C₄×D₄	—	2	8	no	—
625	C₄×D₄	—	4	4	no	—
626	#117	—	4	4	no	—
627	#117	—	4	4	no	—
628	C₂×C₄⋊C₄	—	4	2	no	—
629	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
630	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
631	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
632	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
633	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
634	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
635	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
636	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
637	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
638	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
639	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
640	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
641	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
642	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
643	C₂×C₂²⋊C₄	—	2	8	no	—
644	C₂×C₂²⋊C₄	—	4	4	no	—
645	C₂×C₂²⋊C₄	—	4	4	no	—
646	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
647	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
648	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
649	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
650	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
651	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
652	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
653	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
654	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
655	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
656	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
657	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
658	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
659	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
660	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
661	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
662	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
663	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
664	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
665	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
666	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
667	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
668	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
669	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
670	C₂×C₂²⋊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×C₄²	—	4	2	no	—
676	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
677	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
678	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
679	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
680	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
681	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
682	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
683	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
684	#95	C₂³×C₆₇	1	2	yes	—
685	#95	C₂³×C₆₇	1	2	yes	—
686	#95	C₂³×C₆₇	1	2	yes	—
687	#95	C₂³×C₆₇	1	2	yes	—
688	#95	C₂³×C₆₇	1	1	yes	characteristic
689	#95	C₂³×C₆₇	1	2	yes	—
690	#95	C₂³×C₆₇	1	1	yes	characteristic
691	#95	C₂³×C₆₇	1	2	yes	—
692	#95	C₂³×C₆₇	1	1	yes	characteristic
693	#95	C₂³×C₆₇	1	1	yes	characteristic
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	C₂⁴	—	2	4	no	—
703	C₂⁴	—	2	4	no	—
704	C₂⁴	—	2	4	no	—
705	C₂⁴	—	2	4	no	—
706	C₂⁴	—	4	2	no	—
707	C₂⁴	—	4	2	no	—
708	C₂⁴	—	4	2	no	—
709	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
710	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
711	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
712	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
713	C₂×Q₈	—	4	1	no	—
714	C₂×Q₈	—	4	2	no	—
715	C₂×D₄	—	2	4	no	—
716	C₂×D₄	—	2	4	no	—
717	C₂×D₄	—	2	4	no	—
718	C₂×D₄	—	2	4	no	—
719	C₂×D₄	—	2	4	no	—
720	C₂×D₄	—	2	4	no	—
721	C₂×D₄	—	2	4	no	—
722	C₂×D₄	—	2	2	no	—
723	C₂×D₄	—	2	4	no	—
724	C₂×D₄	—	2	4	no	—
725	C₂×D₄	—	4	2	no	—
726	C₂×D₄	—	4	1	no	—
727	C₂×D₄	—	4	1	no	—
728	C₂×D₄	—	4	1	no	—
729	C₂×D₄	—	4	2	no	—
730	C₂×D₄	—	4	1	no	—
731	C₂×D₄	—	4	16	no	—
732	C₂×D₄	—	4	2	no	—
733	C₂×D₄	—	4	2	no	—
734	C₂×D₄	—	4	2	no	—
735	C₂×D₄	—	4	2	no	—
736	C₂×D₄	—	4	2	no	—
737	C₂×D₄	—	4	2	no	—
738	C₂×D₄	—	4	2	no	—
739	C₂×D₄	—	4	1	no	—
740	C₂×D₄	—	4	2	no	—
741	C₂×D₄	#41×C₆₇	1	4	yes	—
742	C₂²×C₄	—	2	2	no	—
743	C₂²×C₄	—	2	2	no	—
744	C₂²×C₄	—	2	2	no	—
745	C₂²×C₄	—	2	4	no	—
746	C₂²×C₄	—	2	4	no	—
747	C₂²×C₄	—	2	2	no	—
748	C₂²×C₄	—	2	2	no	—
749	C₂²×C₄	—	2	4	no	—
750	C₂²×C₄	—	2	4	no	—
751	C₂²×C₄	—	2	4	no	—
752	C₂²×C₄	—	2	4	no	—
753	C₂²×C₄	—	2	4	no	—
754	C₂²×C₄	—	4	2	no	—
755	C₂²×C₄	—	4	2	no	—
756	C₂²×C₄	—	4	2	no	—
757	C₂²×C₄	—	4	2	no	—
758	C₂²×C₄	—	4	2	no	—
759	C₂²×C₄	—	4	2	no	—
760	C₂²×C₄	—	4	2	no	—
761	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
762	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
763	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
764	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
765	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
766	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
767	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
768	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
769	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
770	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
771	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
772	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
773	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
774	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
775	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
776	C₄⋊C₄	—	2	4	no	—
777	C₄⋊C₄	—	2	4	no	—
778	C₄⋊C₄	—	2	4	no	—
779	C₄⋊C₄	—	2	4	no	—
780	C₄⋊C₄	—	4	1	no	—
781	C₄⋊C₄	—	4	1	no	—
782	C₄⋊C₄	—	4	1	no	—
783	C₄⋊C₄	—	4	1	no	—
784	C₄⋊C₄	—	4	2	no	—
785	C₄⋊C₄	—	4	2	no	—
786	C₄⋊C₄	—	4	2	no	—
787	C₄⋊C₄	—	4	1	no	—
788	C₄⋊C₄	—	4	1	no	—
789	C₄⋊C₄	—	4	2	no	—
790	C₂²⋊C₄	—	2	4	no	—
791	C₂²⋊C₄	—	2	4	no	—
792	C₂²⋊C₄	—	2	4	no	—
793	C₂²⋊C₄	—	2	4	no	—
794	C₂²⋊C₄	—	2	4	no	—
795	C₂²⋊C₄	—	2	4	no	—
796	C₂²⋊C₄	—	2	4	no	—
797	C₂²⋊C₄	—	2	4	no	—
798	C₂²⋊C₄	—	2	4	no	—
799	C₂²⋊C₄	—	2	4	no	—
800	C₂²⋊C₄	—	2	4	no	—
801	C₂²⋊C₄	—	2	4	no	—
802	C₂²⋊C₄	—	2	4	no	—
803	C₂²⋊C₄	—	2	4	no	—
804	C₂²⋊C₄	—	2	4	no	—
805	C₂²⋊C₄	—	4	2	no	—
806	C₂²⋊C₄	—	4	2	no	—
807	C₂²⋊C₄	—	4	2	no	—
808	C₂²⋊C₄	—	4	2	no	—
809	C₂²⋊C₄	—	4	2	no	—
810	C₂²⋊C₄	—	4	2	no	—
811	C₂²⋊C₄	—	4	2	no	—
812	C₂²⋊C₄	—	4	2	no	—
813	C₂²⋊C₄	—	4	2	no	—
814	C₂²⋊C₄	—	4	2	no	—
815	C₂²⋊C₄	—	4	2	no	—
816	C₂²⋊C₄	—	4	2	no	—
817	C₂²⋊C₄	—	4	2	no	—
818	C₂²⋊C₄	#41×C₆₇	1	8	yes	—
819	C₄²	—	2	4	no	—
820	C₄²	—	2	4	no	—
821	C₄²	—	2	4	no	—
822	C₄²	—	4	1	no	—
823	C₄²	—	4	1	no	—
824	C₄²	—	4	2	no	—
825	C₄²	—	4	2	no	—
826	C₄²	—	4	2	no	—
827	C₂³	—	2	1	no	—
828	C₂³	—	2	2	no	—
829	C₂³	—	2	1	no	—
830	C₂³	—	2	2	no	—
831	C₂³	—	2	2	no	—
832	C₂³	—	2	2	no	—
833	C₂³	—	2	2	no	—
834	C₂³	—	2	2	no	—
835	C₂³	—	2	2	no	—
836	C₂³	—	2	2	no	—
837	C₂³	—	2	2	no	—
838	C₂³	—	2	2	no	—
839	C₂³	—	2	2	no	—
840	C₂³	—	2	2	no	—
841	C₂³	—	2	2	no	—
842	C₂³	—	2	2	no	—
843	C₂³	—	2	2	no	—
844	C₂³	—	2	2	no	—
845	C₂³	—	2	2	no	—
846	C₂³	—	2	2	no	—
847	C₂³	—	2	2	no	—
848	C₂³	—	2	2	no	—
849	C₂³	—	2	2	no	—
850	C₂³	—	4	8	no	—
851	C₂³	—	4	8	no	—
852	C₂³	—	4	8	no	—
853	C₂³	—	4	8	no	—
854	C₂³	—	8	4	no	—
855	C₂³	—	8	4	no	—
856	C₂³	—	8	4	no	—
857	C₂³	C₂×#41×C₆₇	1	4	yes	—
858	C₂³	C₂×#41×C₆₇	1	4	yes	—
859	C₂³	H(5,𝔽₂)×C₆₇	1	2	yes	—
860	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
861	Q₈	—	8	2	no	—
862	D₄	—	4	4	no	—
863	D₄	—	4	8	no	—
864	D₄	—	4	8	no	—
865	D₄	—	4	4	no	—
866	D₄	—	4	8	no	—
867	D₄	—	8	4	no	—
868	D₄	—	8	4	no	—
869	D₄	—	8	2	no	—
870	D₄	—	8	4	no	—
871	C₂×C₄	—	2	8	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	1	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	1	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	2	1	no	—
881	C₂×C₄	—	2	1	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	2	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	1	no	—
905	C₂×C₄	—	2	1	no	—
906	C₂×C₄	—	2	1	no	—
907	C₂×C₄	—	2	1	no	—
908	C₂×C₄	—	4	8	no	—
909	C₂×C₄	—	4	8	no	—
910	C₂×C₄	—	4	8	no	—
911	C₂×C₄	—	8	4	no	—
912	C₂×C₄	—	8	2	no	—
913	C₂×C₄	—	8	2	no	—
914	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
915	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
916	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
917	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
918	C₂×C₄	H(5,𝔽₂)×C₆₇	1	4	yes	—
919	C₂²	—	2	2	no	—
920	C₂²	—	2	4	no	—
921	C₂²	—	2	2	no	—
922	C₂²	—	2	4	no	—
923	C₂²	—	2	4	no	—
924	C₂²	—	2	4	no	—
925	C₂²	—	2	4	no	—
926	C₂²	—	4	2	no	—
927	C₂²	—	4	2	no	—
928	C₂²	—	4	2	no	—
929	C₂²	—	4	2	no	—
930	C₂²	—	4	2	no	—
931	C₂²	—	4	2	no	—
932	C₂²	—	4	2	no	—
933	C₂²	—	4	2	no	—
934	C₂²	—	4	2	no	—
935	C₂²	—	4	2	no	—
936	C₂²	—	4	2	no	—
937	C₂²	—	4	2	no	—
938	C₂²	—	4	2	no	—
939	C₂²	—	4	2	no	—
940	C₂²	—	4	2	no	—
941	C₂²	—	4	2	no	—
942	C₂²	—	4	2	no	—
943	C₂²	—	4	2	no	—
944	C₂²	—	8	16	no	—
945	C₂²	#555×C₆₇	1	4	yes	—
946	C₂²	C₂²×#41×C₆₇	1	2	yes	—
947	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
948	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
949	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
950	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
951	C₄	—	2	4	no	—
952	C₄	—	2	2	no	—
953	C₄	—	2	2	no	—
954	C₄	—	2	4	no	—
955	C₄	—	2	4	no	—
956	C₄	—	4	1	no	—
957	C₄	—	4	1	no	—
958	C₄	—	4	1	no	—
959	C₄	—	4	1	no	—
960	C₄	—	4	2	no	—
961	C₄	—	4	2	no	—
962	C₄	—	4	2	no	—
963	C₄	—	4	2	no	—
964	C₄	—	4	2	no	—
965	C₄	—	4	2	no	—
966	C₂	—	2	4	no	—
967	C₂	—	4	4	no	—
968	C₂	—	8	2	no	—
969	C₂	—	8	2	no	—
970	C₂	C₂×#555×C₆₇	1	1	yes	characteristic
971	C₂	C₆₇×#3481	1	2	yes	—
972	C₂	C₆₇×#3490	1	1	yes	characteristic
973	C₂	C₆₇×#3519	1	2	yes	—
974	C₂	C₆₇×#3543	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
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×#2803	C₂	semidirect
2. C₆₇×#2784	C₂	semidirect
3. C₆₇×#2699	C₂	semidirect
4. C₆₇×#2610	C₂	semidirect
5. C₆₇×#2593	C₂	semidirect
6. C₆₇×#2591	C₂	semidirect
7. C₆₇×#2583	C₂	semidirect
8. C₆₇×#2555	C₂	semidirect
9. C₆₇×#2526	C₂	semidirect
10. C₆₇×#2476	C₂	semidirect
11. C₆₇×#2472	C₂	semidirect
12. C₆₇×#2424	C₂	semidirect
13. C₆₇×#2414	C₂	semidirect
14. C₆₇×#2410	C₂	semidirect
15. C₆₇×#2363	C₂	semidirect
16. C₆₇×#2358	C₂	semidirect
17. C₆₇×#2342	C₂	semidirect
18. C₂×#390×C₆₇	C₂	semidirect
19. C₆₇×#2290	C₂	semidirect
21. C₂×#124×C₆₇	C₂²	semidirect
26. C₂×#121×C₆₇	C₂²	semidirect
30. C₂×C₄×D₄×C₆₇	C₂²	semidirect
31. C₂×#117×C₆₇	C₂²	semidirect
32. C₂×#117×C₆₇	C₂²	semidirect
38. #400×C₆₇	C₂²	semidirect
39. #400×C₆₇	C₂²	semidirect
40. #398×C₆₇	C₂²	semidirect
41. #398×C₆₇	C₂²	semidirect
42. #397×C₆₇	C₂²	semidirect
43. #396×C₆₇	C₂²	semidirect
44. #395×C₆₇	C₂²	semidirect
45. #395×C₆₇	C₂²	semidirect
48. #394×C₆₇	C₂²	semidirect
49. #394×C₆₇	C₂²	semidirect
50. #394×C₆₇	C₂²	semidirect
51. #394×C₆₇	C₂²	semidirect
52. #394×C₆₇	C₂²	semidirect
53. #394×C₆₇	C₂²	semidirect
54. #393×C₆₇	C₂²	semidirect
57. #392×C₆₇	C₂²	semidirect
64. #390×C₆₇	C₂²	semidirect
65. #390×C₆₇	C₂²	semidirect
66. #390×C₆₇	C₂²	semidirect
67. #389×C₆₇	C₂²	semidirect
68. #389×C₆₇	C₂²	semidirect
69. #388×C₆₇	C₂²	semidirect
70. #388×C₆₇	C₂²	semidirect
71. #388×C₆₇	C₂²	semidirect
72. #388×C₆₇	C₂²	semidirect
73. #388×C₆₇	C₂²	semidirect
74. #388×C₆₇	C₂²	semidirect
75. #388×C₆₇	C₂²	semidirect
76. #388×C₆₇	C₂²	semidirect
77. #388×C₆₇	C₂²	semidirect
78. #388×C₆₇	C₂²	semidirect
79. #388×C₆₇	C₂²	semidirect
80. #388×C₆₇	C₂²	semidirect
81. #388×C₆₇	C₂²	semidirect
82. #387×C₆₇	C₂²	semidirect
83. #387×C₆₇	C₂²	semidirect
89. #386×C₆₇	C₂²	semidirect
90. #386×C₆₇	C₂²	semidirect
91. #386×C₆₇	C₂²	semidirect
95. #385×C₆₇	C₂²	semidirect
96. #381×C₆₇	C₂²	semidirect
97. #380×C₆₇	C₂²	semidirect
99. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
103. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
104. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
105. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
106. #376×C₆₇	C₂²	semidirect
478. #59947	C₆₇	direct (N × H)
488. #2803	C₂×C₆₇	semidirect
489. #2784	C₂×C₆₇	semidirect
490. #2699	C₂×C₆₇	semidirect
491. #2610	C₂×C₆₇	semidirect
492. #2593	C₂×C₆₇	semidirect
493. #2591	C₂×C₆₇	semidirect
494. #2583	C₂×C₆₇	semidirect
495. #2555	C₂×C₆₇	semidirect
496. #2526	C₂×C₆₇	semidirect
497. #2476	C₂×C₆₇	semidirect
498. #2472	C₂×C₆₇	semidirect
499. #2424	C₂×C₆₇	semidirect
500. #2414	C₂×C₆₇	semidirect
501. #2410	C₂×C₆₇	semidirect
502. #2363	C₂×C₆₇	semidirect
503. #2358	C₂×C₆₇	semidirect
504. #2342	C₂×C₆₇	semidirect
505. C₂×#390	C₂×C₆₇	semidirect
506. #2290	C₂×C₆₇	semidirect
507. C₆₇	#59947	direct (N × H)
509. C₂×#124	C₂²×C₆₇	semidirect
514. C₂×#121	C₂²×C₆₇	semidirect
518. C₂×C₄×D₄	C₂²×C₆₇	semidirect
519. C₂×#117	C₂²×C₆₇	semidirect
520. C₂×#117	C₂²×C₆₇	semidirect
526. #400	C₂²×C₆₇	semidirect
527. #400	C₂²×C₆₇	semidirect
528. #398	C₂²×C₆₇	semidirect
529. #398	C₂²×C₆₇	semidirect
530. #397	C₂²×C₆₇	semidirect
531. #396	C₂²×C₆₇	semidirect
532. #395	C₂²×C₆₇	semidirect
533. #395	C₂²×C₆₇	semidirect
536. #394	C₂²×C₆₇	semidirect
537. #394	C₂²×C₆₇	semidirect
538. #394	C₂²×C₆₇	semidirect
539. #394	C₂²×C₆₇	semidirect
540. #394	C₂²×C₆₇	semidirect
541. #394	C₂²×C₆₇	semidirect
542. #393	C₂²×C₆₇	semidirect
545. #392	C₂²×C₆₇	semidirect
552. #390	C₂²×C₆₇	semidirect
553. #390	C₂²×C₆₇	semidirect
554. #390	C₂²×C₆₇	semidirect
555. #389	C₂²×C₆₇	semidirect
556. #389	C₂²×C₆₇	semidirect
557. #388	C₂²×C₆₇	semidirect
558. #388	C₂²×C₆₇	semidirect
559. #388	C₂²×C₆₇	semidirect
560. #388	C₂²×C₆₇	semidirect
561. #388	C₂²×C₆₇	semidirect
562. #388	C₂²×C₆₇	semidirect
563. #388	C₂²×C₆₇	semidirect
564. #388	C₂²×C₆₇	semidirect
565. #388	C₂²×C₆₇	semidirect
566. #388	C₂²×C₆₇	semidirect
567. #388	C₂²×C₆₇	semidirect
568. #388	C₂²×C₆₇	semidirect
569. #388	C₂²×C₆₇	semidirect
570. #387	C₂²×C₆₇	semidirect
571. #387	C₂²×C₆₇	semidirect
577. #386	C₂²×C₆₇	semidirect
578. #386	C₂²×C₆₇	semidirect
579. #386	C₂²×C₆₇	semidirect
583. #385	C₂²×C₆₇	semidirect
584. #381	C₂²×C₆₇	semidirect
585. #380	C₂²×C₆₇	semidirect
587. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
591. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
592. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
593. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
594. #376	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×#2803	2
C₆₇×#2784	2
C₆₇×#2699	2
C₆₇×#2610	2
C₆₇×#2593	2
C₆₇×#2591	2
C₆₇×#2583	2
C₆₇×#2555	2
C₆₇×#2526	2
C₆₇×#2476	2
C₆₇×#2472	2
C₆₇×#2424	2
C₆₇×#2414	2
C₆₇×#2410	2
C₆₇×#2363	2
C₆₇×#2358	2
C₆₇×#2342	2
C₂×#390×C₆₇	2
C₆₇×#2290	2
#59947	67

Subgroups — C67×#59947 #30739198

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#59947 #30739198