Subgroups — C₆₇×#59810 #30739061

Order 17152.

2630 conjugacy classes of subgroups.

The subgroup lattice has 1198 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#555×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#550×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2686	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2673	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2555	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2544	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2543	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2491	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#2485	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#2476	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2459	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2451	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#2445	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#2428	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#2414	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#2407	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#2407	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#2362	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#2359	C₂	1	2	yes	maximal, complemented
20	C₆₇×#2339	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#121×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#121×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₇×#2297	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
25	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
26	#555×C₆₇	—	2	8	no	—
27	#550×C₆₇	—	2	8	no	—
28	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
29	C₂×#127×C₆₇	C₂²	1	2	yes	—
30	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×#124×C₆₇	C₂²	1	2	yes	—
32	C₂×#124×C₆₇	C₂²	1	2	yes	—
33	C₂×#124×C₆₇	C₂²	1	2	yes	—
34	C₂×#123×C₆₇	C₂²	1	2	yes	—
35	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
36	C₂×#121×C₆₇	C₂²	1	2	yes	—
37	C₂×#121×C₆₇	C₂²	1	2	yes	—
38	C₂×#121×C₆₇	C₂²	1	2	yes	—
39	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
40	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
41	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
42	C₂×#121×C₆₇	C₂²	1	2	yes	—
43	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
44	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
45	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
47	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
49	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
50	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
51	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
52	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
53	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
54	C₂×#117×C₆₇	C₂²	1	2	yes	—
55	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
56	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
57	#398×C₆₇	C₂²	1	2	yes	—
58	#397×C₆₇	C₂²	1	2	yes	—
59	#395×C₆₇	C₂²	1	2	yes	—
60	#394×C₆₇	C₂²	1	2	yes	—
61	#394×C₆₇	C₂²	1	2	yes	—
62	#394×C₆₇	C₂²	1	2	yes	—
63	#394×C₆₇	C₂²	1	2	yes	—
64	#394×C₆₇	C₂²	1	2	yes	—
65	#394×C₆₇	C₂²	1	2	yes	—
66	#394×C₆₇	C₂²	1	2	yes	—
67	#394×C₆₇	C₂²	1	2	yes	—
68	#393×C₆₇	C₂²	1	2	yes	—
69	#392×C₆₇	C₂²	1	2	yes	—
70	#392×C₆₇	C₂²	1	2	yes	—
71	#392×C₆₇	C₂²	1	2	yes	—
72	#392×C₆₇	C₂²	1	2	yes	—
73	#391×C₆₇	C₂²	1	2	yes	—
74	#391×C₆₇	C₂²	1	1	yes	characteristic
75	#391×C₆₇	C₂²	1	1	yes	characteristic
76	#391×C₆₇	C₂²	1	1	yes	characteristic
77	#390×C₆₇	C₂²	1	2	yes	—
78	#390×C₆₇	C₂²	1	1	yes	characteristic
79	#390×C₆₇	C₂²	1	1	yes	characteristic
80	#390×C₆₇	C₂²	1	1	yes	characteristic
81	#390×C₆₇	C₂²	1	1	yes	characteristic
82	#390×C₆₇	C₂²	1	1	yes	characteristic
83	#389×C₆₇	C₂²	1	1	yes	characteristic
84	#389×C₆₇	C₂²	1	1	yes	characteristic
85	#389×C₆₇	C₂²	1	1	yes	characteristic
86	#389×C₆₇	C₂²	1	1	yes	characteristic
87	#388×C₆₇	C₂²	1	2	yes	—
88	#388×C₆₇	C₂²	1	2	yes	—
89	#388×C₆₇	C₂²	1	2	yes	—
90	#388×C₆₇	C₂²	1	1	yes	characteristic
91	#388×C₆₇	C₂²	1	2	yes	—
92	#388×C₆₇	C₂²	1	1	yes	characteristic
93	#388×C₆₇	C₂²	1	2	yes	—
94	#388×C₆₇	C₂²	1	2	yes	—
95	#387×C₆₇	C₂²	1	2	yes	—
96	#387×C₆₇	C₂²	1	2	yes	—
97	#387×C₆₇	C₂²	1	2	yes	—
98	#386×C₆₇	C₂²	1	1	yes	characteristic
99	#386×C₆₇	C₂²	1	2	yes	—
100	#386×C₆₇	C₂²	1	2	yes	—
101	#386×C₆₇	C₂²	1	2	yes	—
102	#386×C₆₇	C₂²	1	1	yes	characteristic
103	#386×C₆₇	C₂²	1	2	yes	—
104	#386×C₆₇	C₂²	1	2	yes	—
105	#386×C₆₇	C₂²	1	2	yes	—
106	#386×C₆₇	C₂²	1	2	yes	—
107	#386×C₆₇	C₂²	1	2	yes	—
108	#386×C₆₇	C₂²	1	2	yes	—
109	#385×C₆₇	C₂²	1	2	yes	—
110	#385×C₆₇	C₂²	1	2	yes	—
111	#381×C₆₇	C₂²	1	2	yes	—
112	#380×C₆₇	C₂²	1	1	yes	characteristic
113	#380×C₆₇	C₂²	1	1	yes	characteristic
114	#380×C₆₇	C₂²	1	1	yes	characteristic
115	#380×C₆₇	C₂²	1	1	yes	characteristic
116	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
117	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
118	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
119	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
120	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
121	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
122	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
123	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
124	C₂×#95×C₆₇	C₂²	1	2	yes	—
125	C₂×#41×C₆₇	—	2	4	no	—
126	C₂×#41×C₆₇	—	2	4	no	—
127	C₂×#41×C₆₇	—	2	4	no	—
128	C₂×#41×C₆₇	—	2	4	no	—
129	C₂×#41×C₆₇	—	4	2	no	—
130	C₂×#41×C₆₇	—	4	2	no	—
131	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
132	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
133	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
134	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
135	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
136	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
137	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
138	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
139	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
140	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
141	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
142	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
143	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
144	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
145	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
146	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
147	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
148	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
149	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
150	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
151	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
152	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
153	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
154	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
155	C₄⋊Q₈×C₆₇	—	2	4	no	—
156	#127×C₆₇	—	2	8	no	—
157	#127×C₆₇	—	2	4	no	—
158	#124×C₆₇	—	2	8	no	—
159	#124×C₆₇	—	2	8	no	—
160	#124×C₆₇	—	4	4	no	—
161	#123×C₆₇	—	2	8	no	—
162	C₂²⋊Q₈×C₆₇	—	2	4	no	—
163	#121×C₆₇	—	2	8	no	—
164	#121×C₆₇	—	2	4	no	—
165	#121×C₆₇	—	2	8	no	—
166	#121×C₆₇	—	2	4	no	—
167	#121×C₆₇	—	2	4	no	—
168	#121×C₆₇	—	2	8	no	—
169	#121×C₆₇	—	4	4	no	—
170	#121×C₆₇	—	4	2	no	—
171	#121×C₆₇	D₄	1	8	yes	complemented
172	C₄×Q₈×C₆₇	—	2	4	no	—
173	C₄×D₄×C₆₇	—	2	4	no	—
174	C₄×D₄×C₆₇	—	2	4	no	—
175	C₄×D₄×C₆₇	—	2	4	no	—
176	C₄×D₄×C₆₇	—	2	8	no	—
177	C₄×D₄×C₆₇	—	4	2	no	—
178	C₄×D₄×C₆₇	—	4	2	no	—
179	C₄×D₄×C₆₇	—	4	4	no	—
180	#117×C₆₇	—	2	4	no	—
181	#117×C₆₇	—	2	4	no	—
182	#117×C₆₇	—	2	8	no	—
183	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
184	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
185	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
186	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
187	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
188	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
189	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
190	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
191	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
192	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
193	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
194	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
195	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
196	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
197	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
198	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
199	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
201	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
202	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
204	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
205	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
206	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
207	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
208	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
209	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
210	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
211	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
212	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
213	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
214	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
215	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
216	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
217	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
218	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
219	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
220	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
221	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
222	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
223	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
224	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
225	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
226	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
227	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
228	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
229	C₂×C₄²×C₆₇	—	4	2	no	—
230	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
231	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
232	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
233	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
234	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
235	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
236	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
237	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
238	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
239	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
240	#95×C₆₇	C₂³	1	1	yes	characteristic
241	#95×C₆₇	C₂³	1	2	yes	—
242	#95×C₆₇	C₂³	1	2	yes	—
243	#95×C₆₇	C₂³	1	2	yes	—
244	#95×C₆₇	C₂³	1	1	yes	characteristic
245	#95×C₆₇	C₂³	1	1	yes	characteristic
246	#95×C₆₇	C₂³	1	2	yes	—
247	#95×C₆₇	C₂³	1	1	yes	characteristic
248	#95×C₆₇	C₂³	1	2	yes	—
249	#95×C₆₇	C₂³	1	2	yes	—
250	#95×C₆₇	C₂³	1	2	yes	—
251	#95×C₆₇	C₂³	1	2	yes	—
252	#95×C₆₇	C₂³	1	1	yes	characteristic
253	#95×C₆₇	C₂³	1	2	yes	—
254	#95×C₆₇	C₂³	1	1	yes	characteristic
255	#95×C₆₇	C₂³	1	2	yes	—
256	#95×C₆₇	C₂³	1	2	yes	—
257	#95×C₆₇	C₂³	1	2	yes	—
258	#95×C₆₇	C₂³	1	2	yes	—
259	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
260	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
261	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
262	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
263	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
264	#41×C₆₇	—	4	16	no	—
265	#41×C₆₇	—	4	16	no	—
266	C₂×Q₈×C₆₇	—	2	2	no	—
267	C₂×Q₈×C₆₇	—	2	4	no	—
268	C₂×Q₈×C₆₇	—	2	2	no	—
269	C₂×Q₈×C₆₇	—	4	2	no	—
270	C₂×Q₈×C₆₇	—	4	2	no	—
271	C₂×Q₈×C₆₇	#41	1	4	yes	—
272	C₂×D₄×C₆₇	—	2	2	no	—
273	C₂×D₄×C₆₇	—	2	2	no	—
274	C₂×D₄×C₆₇	—	2	4	no	—
275	C₂×D₄×C₆₇	—	2	4	no	—
276	C₂×D₄×C₆₇	—	2	4	no	—
277	C₂×D₄×C₆₇	—	2	4	no	—
278	C₂×D₄×C₆₇	—	2	4	no	—
279	C₂×D₄×C₆₇	—	2	2	no	—
280	C₂×D₄×C₆₇	—	2	4	no	—
281	C₂×D₄×C₆₇	—	2	2	no	—
282	C₂×D₄×C₆₇	—	2	2	no	—
283	C₂×D₄×C₆₇	—	2	2	no	—
284	C₂×D₄×C₆₇	—	2	2	no	—
285	C₂×D₄×C₆₇	—	2	4	no	—
286	C₂×D₄×C₆₇	—	2	4	no	—
287	C₂×D₄×C₆₇	—	2	4	no	—
288	C₂×D₄×C₆₇	—	2	2	no	—
289	C₂×D₄×C₆₇	—	2	2	no	—
290	C₂×D₄×C₆₇	—	2	2	no	—
291	C₂×D₄×C₆₇	—	4	1	no	—
292	C₂×D₄×C₆₇	—	4	2	no	—
293	C₂×D₄×C₆₇	—	4	1	no	—
294	C₂×D₄×C₆₇	—	4	1	no	—
295	C₂×D₄×C₆₇	—	4	2	no	—
296	C₂×D₄×C₆₇	—	4	1	no	—
297	C₂×D₄×C₆₇	—	4	2	no	—
298	C₂×D₄×C₆₇	—	4	2	no	—
299	C₂×D₄×C₆₇	—	4	2	no	—
300	C₂×D₄×C₆₇	—	4	2	no	—
301	C₂×D₄×C₆₇	—	4	2	no	—
302	C₂×D₄×C₆₇	—	4	2	no	—
303	C₂×D₄×C₆₇	—	4	2	no	—
304	C₂×D₄×C₆₇	—	4	2	no	—
305	C₂×D₄×C₆₇	—	4	2	no	—
306	C₂×D₄×C₆₇	—	4	2	no	—
307	C₂×D₄×C₆₇	—	4	2	no	—
308	C₂×D₄×C₆₇	—	4	2	no	—
309	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
310	C₂×D₄×C₆₇	C₂×D₄	1	8	yes	—
311	C₂²×C₄×C₆₇	—	2	2	no	—
312	C₂²×C₄×C₆₇	—	2	2	no	—
313	C₂²×C₄×C₆₇	—	2	4	no	—
314	C₂²×C₄×C₆₇	—	2	4	no	—
315	C₂²×C₄×C₆₇	—	2	2	no	—
316	C₂²×C₄×C₆₇	—	2	4	no	—
317	C₂²×C₄×C₆₇	—	2	2	no	—
318	C₂²×C₄×C₆₇	—	2	2	no	—
319	C₂²×C₄×C₆₇	—	2	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	2	no	—
324	C₂²×C₄×C₆₇	—	2	2	no	—
325	C₂²×C₄×C₆₇	—	2	2	no	—
326	C₂²×C₄×C₆₇	—	2	2	no	—
327	C₂²×C₄×C₆₇	—	2	4	no	—
328	C₂²×C₄×C₆₇	—	4	1	no	—
329	C₂²×C₄×C₆₇	—	4	1	no	—
330	C₂²×C₄×C₆₇	—	4	1	no	—
331	C₂²×C₄×C₆₇	—	4	1	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	C₂×D₄	1	4	yes	—
338	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
339	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
340	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
341	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
342	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
343	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
344	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
345	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
346	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
347	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
348	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
349	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
350	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
351	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
352	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
353	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
354	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
355	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
356	C₄⋊C₄×C₆₇	—	2	2	no	—
357	C₄⋊C₄×C₆₇	—	2	2	no	—
358	C₄⋊C₄×C₆₇	—	2	4	no	—
359	C₄⋊C₄×C₆₇	—	2	2	no	—
360	C₄⋊C₄×C₆₇	—	2	2	no	—
361	C₄⋊C₄×C₆₇	—	2	4	no	—
362	C₄⋊C₄×C₆₇	—	2	2	no	—
363	C₄⋊C₄×C₆₇	—	2	4	no	—
364	C₄⋊C₄×C₆₇	—	2	4	no	—
365	C₄⋊C₄×C₆₇	—	2	2	no	—
366	C₄⋊C₄×C₆₇	—	4	1	no	—
367	C₄⋊C₄×C₆₇	—	4	1	no	—
368	C₄⋊C₄×C₆₇	—	4	2	no	—
369	C₄⋊C₄×C₆₇	—	4	2	no	—
370	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
371	C₄⋊C₄×C₆₇	#41	1	4	yes	complemented
372	C₂²⋊C₄×C₆₇	—	2	4	no	—
373	C₂²⋊C₄×C₆₇	—	2	4	no	—
374	C₂²⋊C₄×C₆₇	—	2	2	no	—
375	C₂²⋊C₄×C₆₇	—	2	2	no	—
376	C₂²⋊C₄×C₆₇	—	2	4	no	—
377	C₂²⋊C₄×C₆₇	—	2	4	no	—
378	C₂²⋊C₄×C₆₇	—	2	2	no	—
379	C₂²⋊C₄×C₆₇	—	2	4	no	—
380	C₂²⋊C₄×C₆₇	—	2	2	no	—
381	C₂²⋊C₄×C₆₇	—	2	2	no	—
382	C₂²⋊C₄×C₆₇	—	2	2	no	—
383	C₂²⋊C₄×C₆₇	—	2	4	no	—
384	C₂²⋊C₄×C₆₇	—	2	4	no	—
385	C₂²⋊C₄×C₆₇	—	2	4	no	—
386	C₂²⋊C₄×C₆₇	—	2	4	no	—
387	C₂²⋊C₄×C₆₇	—	2	2	no	—
388	C₂²⋊C₄×C₆₇	—	2	4	no	—
389	C₂²⋊C₄×C₆₇	—	2	2	no	—
390	C₂²⋊C₄×C₆₇	—	4	2	no	—
391	C₂²⋊C₄×C₆₇	—	4	2	no	—
392	C₂²⋊C₄×C₆₇	—	4	2	no	—
393	C₂²⋊C₄×C₆₇	—	4	1	no	—
394	C₂²⋊C₄×C₆₇	—	4	2	no	—
395	C₂²⋊C₄×C₆₇	—	4	1	no	—
396	C₂²⋊C₄×C₆₇	—	4	2	no	—
397	C₂²⋊C₄×C₆₇	—	4	2	no	—
398	C₂²⋊C₄×C₆₇	—	4	2	no	—
399	C₂²⋊C₄×C₆₇	—	4	2	no	—
400	C₂²⋊C₄×C₆₇	—	4	2	no	—
401	C₂²⋊C₄×C₆₇	C₂×D₄	1	8	yes	—
402	C₄²×C₆₇	—	2	4	no	—
403	C₄²×C₆₇	—	2	4	no	—
404	C₄²×C₆₇	—	2	2	no	—
405	C₄²×C₆₇	—	2	4	no	—
406	C₄²×C₆₇	—	2	2	no	—
407	C₄²×C₆₇	—	2	2	no	—
408	C₄²×C₆₇	—	2	2	no	—
409	C₄²×C₆₇	—	2	4	no	—
410	C₄²×C₆₇	—	4	1	no	—
411	C₄²×C₆₇	—	4	1	no	—
412	C₂³×C₆₇	—	2	2	no	—
413	C₂³×C₆₇	—	2	1	no	—
414	C₂³×C₆₇	—	2	2	no	—
415	C₂³×C₆₇	—	2	1	no	—
416	C₂³×C₆₇	—	2	1	no	—
417	C₂³×C₆₇	—	2	2	no	—
418	C₂³×C₆₇	—	2	2	no	—
419	C₂³×C₆₇	—	2	1	no	—
420	C₂³×C₆₇	—	2	2	no	—
421	C₂³×C₆₇	—	2	1	no	—
422	C₂³×C₆₇	—	2	1	no	—
423	C₂³×C₆₇	—	2	2	no	—
424	C₂³×C₆₇	—	2	1	no	—
425	C₂³×C₆₇	—	2	1	no	—
426	C₂³×C₆₇	—	2	2	no	—
427	C₂³×C₆₇	—	2	1	no	—
428	C₂³×C₆₇	—	2	2	no	—
429	C₂³×C₆₇	—	2	1	no	—
430	C₂³×C₆₇	—	2	1	no	—
431	C₂³×C₆₇	—	2	2	no	—
432	C₂³×C₆₇	—	2	1	no	—
433	C₂³×C₆₇	—	2	1	no	—
434	C₂³×C₆₇	—	2	2	no	—
435	C₂³×C₆₇	—	2	1	no	—
436	C₂³×C₆₇	—	2	1	no	—
437	C₂³×C₆₇	—	2	1	no	—
438	C₂³×C₆₇	—	2	2	no	—
439	C₂³×C₆₇	—	2	1	no	—
440	C₂³×C₆₇	—	2	2	no	—
441	C₂³×C₆₇	—	2	2	no	—
442	C₂³×C₆₇	—	2	1	no	—
443	C₂³×C₆₇	—	2	1	no	—
444	C₂³×C₆₇	—	2	1	no	—
445	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
446	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
447	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
448	Q₈×C₆₇	—	2	8	no	—
449	Q₈×C₆₇	—	8	4	no	—
450	D₄×C₆₇	—	2	8	no	—
451	D₄×C₆₇	—	4	8	no	—
452	D₄×C₆₇	—	4	4	no	—
453	D₄×C₆₇	—	4	8	no	—
454	D₄×C₆₇	—	4	4	no	—
455	D₄×C₆₇	—	4	8	no	—
456	D₄×C₆₇	—	4	8	no	—
457	D₄×C₆₇	—	4	4	no	—
458	D₄×C₆₇	—	4	4	no	—
459	D₄×C₆₇	—	8	4	no	—
460	D₄×C₆₇	—	8	4	no	—
461	D₄×C₆₇	—	8	4	no	—
462	D₄×C₆₇	—	8	4	no	—
463	C₂×C₄×C₆₇	—	2	1	no	—
464	C₂×C₄×C₆₇	—	2	1	no	—
465	C₂×C₄×C₆₇	—	2	2	no	—
466	C₂×C₄×C₆₇	—	2	1	no	—
467	C₂×C₄×C₆₇	—	2	1	no	—
468	C₂×C₄×C₆₇	—	2	1	no	—
469	C₂×C₄×C₆₇	—	2	2	no	—
470	C₂×C₄×C₆₇	—	2	1	no	—
471	C₂×C₄×C₆₇	—	2	2	no	—
472	C₂×C₄×C₆₇	—	2	1	no	—
473	C₂×C₄×C₆₇	—	2	1	no	—
474	C₂×C₄×C₆₇	—	2	1	no	—
475	C₂×C₄×C₆₇	—	2	1	no	—
476	C₂×C₄×C₆₇	—	2	2	no	—
477	C₂×C₄×C₆₇	—	2	8	no	—
478	C₂×C₄×C₆₇	—	2	1	no	—
479	C₂×C₄×C₆₇	—	2	2	no	—
480	C₂×C₄×C₆₇	—	2	1	no	—
481	C₂×C₄×C₆₇	—	2	1	no	—
482	C₂×C₄×C₆₇	—	2	2	no	—
483	C₂×C₄×C₆₇	—	2	1	no	—
484	C₂×C₄×C₆₇	—	2	2	no	—
485	C₂×C₄×C₆₇	—	2	1	no	—
486	C₂×C₄×C₆₇	—	2	2	no	—
487	C₂×C₄×C₆₇	—	2	2	no	—
488	C₂×C₄×C₆₇	—	2	1	no	—
489	C₂×C₄×C₆₇	—	2	1	no	—
490	C₂×C₄×C₆₇	—	2	1	no	—
491	C₂×C₄×C₆₇	—	2	1	no	—
492	C₂×C₄×C₆₇	—	2	2	no	—
493	C₂×C₄×C₆₇	—	2	1	no	—
494	C₂×C₄×C₆₇	—	2	2	no	—
495	C₂×C₄×C₆₇	—	2	1	no	—
496	C₂×C₄×C₆₇	—	2	1	no	—
497	C₂×C₄×C₆₇	—	2	2	no	—
498	C₂×C₄×C₆₇	—	2	1	no	—
499	C₂×C₄×C₆₇	—	2	2	no	—
500	C₂×C₄×C₆₇	—	2	1	no	—
501	C₂×C₄×C₆₇	—	2	2	no	—
502	C₂×C₄×C₆₇	—	2	1	no	—
503	C₂×C₄×C₆₇	—	2	1	no	—
504	C₂×C₄×C₆₇	—	2	2	no	—
505	C₂×C₄×C₆₇	—	2	2	no	—
506	C₂×C₄×C₆₇	—	2	1	no	—
507	C₂×C₄×C₆₇	—	2	1	no	—
508	C₂×C₄×C₆₇	—	4	8	no	—
509	C₂×C₄×C₆₇	—	4	8	no	—
510	C₂×C₄×C₆₇	—	4	8	no	—
511	C₂×C₄×C₆₇	—	4	4	no	—
512	C₂×C₄×C₆₇	—	4	4	no	—
513	C₂×C₄×C₆₇	—	4	4	no	—
514	C₂×C₄×C₆₇	—	4	4	no	—
515	C₂×C₄×C₆₇	—	8	4	no	—
516	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
517	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
518	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
519	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
520	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
521	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
522	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
523	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
524	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
525	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
526	C₂²×C₆₇	—	2	2	no	—
527	C₂²×C₆₇	—	2	4	no	—
528	C₂²×C₆₇	—	2	4	no	—
529	C₂²×C₆₇	—	2	2	no	—
530	C₂²×C₆₇	—	2	2	no	—
531	C₂²×C₆₇	—	2	4	no	—
532	C₂²×C₆₇	—	4	2	no	—
533	C₂²×C₆₇	—	4	1	no	—
534	C₂²×C₆₇	—	4	1	no	—
535	C₂²×C₆₇	—	4	2	no	—
536	C₂²×C₆₇	—	4	2	no	—
537	C₂²×C₆₇	—	4	1	no	—
538	C₂²×C₆₇	—	4	1	no	—
539	C₂²×C₆₇	—	4	2	no	—
540	C₂²×C₆₇	—	4	2	no	—
541	C₂²×C₆₇	—	4	1	no	—
542	C₂²×C₆₇	—	4	1	no	—
543	C₂²×C₆₇	—	4	1	no	—
544	C₂²×C₆₇	—	4	2	no	—
545	C₂²×C₆₇	—	4	1	no	—
546	C₂²×C₆₇	—	4	1	no	—
547	C₂²×C₆₇	—	4	2	no	—
548	C₂²×C₆₇	—	4	1	no	—
549	C₂²×C₆₇	—	4	1	no	—
550	C₂²×C₆₇	—	4	2	no	—
551	C₂²×C₆₇	—	4	1	no	—
552	C₂²×C₆₇	—	4	1	no	—
553	C₂²×C₆₇	—	4	1	no	—
554	C₂²×C₆₇	—	4	2	no	—
555	C₂²×C₆₇	—	4	1	no	—
556	C₂²×C₆₇	—	4	1	no	—
557	C₂²×C₆₇	—	4	2	no	—
558	C₂²×C₆₇	—	4	1	no	—
559	C₂²×C₆₇	—	4	2	no	—
560	C₂²×C₆₇	—	4	1	no	—
561	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
562	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
563	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
564	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
565	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
566	C₂²×C₆₇	#585	1	1	yes	characteristic
567	C₂²×C₆₇	#585	1	1	yes	characteristic
568	C₄×C₆₇	—	2	2	no	—
569	C₄×C₆₇	—	2	4	no	—
570	C₄×C₆₇	—	2	2	no	—
571	C₄×C₆₇	—	2	2	no	—
572	C₄×C₆₇	—	2	4	no	—
573	C₄×C₆₇	—	2	2	no	—
574	C₄×C₆₇	—	2	2	no	—
575	C₄×C₆₇	—	4	1	no	—
576	C₄×C₆₇	—	4	1	no	—
577	C₄×C₆₇	—	4	2	no	—
578	C₄×C₆₇	—	4	2	no	—
579	C₄×C₆₇	—	4	1	no	—
580	C₄×C₆₇	—	4	2	no	—
581	C₄×C₆₇	—	4	1	no	—
582	C₄×C₆₇	—	4	1	no	—
583	C₄×C₆₇	—	4	1	no	—
584	C₄×C₆₇	—	4	2	no	—
585	C₄×C₆₇	#546	1	4	yes	—
586	#59810	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
587	C₂×C₆₇	—	4	2	no	—
588	C₂×C₆₇	—	4	4	no	—
589	C₂×C₆₇	—	8	1	no	—
590	C₂×C₆₇	—	8	2	no	—
591	C₂×C₆₇	—	8	1	no	—
592	C₂×C₆₇	C₂×#546	1	1	yes	characteristic
593	C₂×C₆₇	D₄×#41	1	1	yes	characteristic
594	C₂×C₆₇	#3483	1	1	yes	characteristic
595	C₂×C₆₇	#3496	1	1	yes	characteristic
596	C₂×C₆₇	#3506	1	1	yes	characteristic
597	C₂×C₆₇	#3524	1	1	yes	characteristic
598	C₂×C₆₇	#3542	1	1	yes	characteristic
599	C₂×#555	C₂×C₆₇	1	1	yes	characteristic, complemented
600	C₂×#550	C₂×C₆₇	1	1	yes	characteristic, complemented
601	#2686	C₂×C₆₇	1	2	yes	complemented
602	#2673	C₂×C₆₇	1	2	yes	complemented
603	#2555	C₂×C₆₇	1	2	yes	complemented
604	#2544	C₂×C₆₇	1	2	yes	complemented
605	#2543	C₂×C₆₇	1	2	yes	complemented
606	#2491	C₂×C₆₇	1	1	yes	characteristic, complemented
607	#2485	C₂×C₆₇	1	1	yes	characteristic, complemented
608	#2476	C₂×C₆₇	1	2	yes	complemented
609	#2459	C₂×C₆₇	1	2	yes	complemented
610	#2451	C₂×C₆₇	1	1	yes	characteristic, complemented
611	#2445	C₂×C₆₇	1	1	yes	characteristic, complemented
612	#2428	C₂×C₆₇	1	1	yes	characteristic, complemented
613	#2414	C₂×C₆₇	1	1	yes	characteristic, complemented
614	#2407	C₂×C₆₇	1	1	yes	characteristic, complemented
615	#2407	C₂×C₆₇	1	1	yes	characteristic, complemented
616	#2362	C₂×C₆₇	1	1	yes	characteristic, complemented
617	#2359	C₂×C₆₇	1	2	yes	complemented
618	#2339	C₂×C₆₇	1	1	yes	characteristic, complemented
619	C₄×#121	C₂×C₆₇	1	1	yes	characteristic, complemented
620	C₄×#121	C₂×C₆₇	1	1	yes	characteristic, complemented
621	#2297	C₂×C₆₇	1	1	yes	characteristic, complemented
622	C₆₇	#59810	1	1	yes	characteristic, direct product factor, Sylow
623	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
624	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
625	#555	—	2	8	no	—
626	#550	—	2	8	no	—
627	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
628	C₂×#127	C₂²×C₆₇	1	2	yes	—
629	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic
630	C₂×#124	C₂²×C₆₇	1	2	yes	—
631	C₂×#124	C₂²×C₆₇	1	2	yes	—
632	C₂×#124	C₂²×C₆₇	1	2	yes	—
633	C₂×#123	C₂²×C₆₇	1	2	yes	—
634	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
635	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
636	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
637	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
638	C₂×#121	C₂²×C₆₇	1	2	yes	—
639	C₂×#121	C₂²×C₆₇	1	2	yes	—
640	C₂×#121	C₂²×C₆₇	1	2	yes	—
641	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
642	C₂×#121	C₂²×C₆₇	1	2	yes	—
643	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
644	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
645	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
646	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
647	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
648	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
649	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
650	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
651	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
652	C₂×#117	C₂²×C₆₇	1	2	yes	—
653	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
654	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
655	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
656	#398	C₂²×C₆₇	1	2	yes	—
657	#397	C₂²×C₆₇	1	2	yes	—
658	#395	C₂²×C₆₇	1	2	yes	—
659	#394	C₂²×C₆₇	1	2	yes	—
660	#394	C₂²×C₆₇	1	2	yes	—
661	#394	C₂²×C₆₇	1	2	yes	—
662	#394	C₂²×C₆₇	1	2	yes	—
663	#394	C₂²×C₆₇	1	2	yes	—
664	#394	C₂²×C₆₇	1	2	yes	—
665	#394	C₂²×C₆₇	1	2	yes	—
666	#394	C₂²×C₆₇	1	2	yes	—
667	#393	C₂²×C₆₇	1	2	yes	—
668	#392	C₂²×C₆₇	1	2	yes	—
669	#392	C₂²×C₆₇	1	2	yes	—
670	#392	C₂²×C₆₇	1	2	yes	—
671	#392	C₂²×C₆₇	1	2	yes	—
672	#391	C₂²×C₆₇	1	1	yes	characteristic
673	#391	C₂²×C₆₇	1	1	yes	characteristic
674	#391	C₂²×C₆₇	1	1	yes	characteristic
675	#391	C₂²×C₆₇	1	2	yes	—
676	#390	C₂²×C₆₇	1	1	yes	characteristic
677	#390	C₂²×C₆₇	1	1	yes	characteristic
678	#390	C₂²×C₆₇	1	1	yes	characteristic
679	#390	C₂²×C₆₇	1	2	yes	—
680	#390	C₂²×C₆₇	1	1	yes	characteristic
681	#390	C₂²×C₆₇	1	1	yes	characteristic
682	#389	C₂²×C₆₇	1	1	yes	characteristic
683	#389	C₂²×C₆₇	1	1	yes	characteristic
684	#389	C₂²×C₆₇	1	1	yes	characteristic
685	#389	C₂²×C₆₇	1	1	yes	characteristic
686	#388	C₂²×C₆₇	1	2	yes	—
687	#388	C₂²×C₆₇	1	2	yes	—
688	#388	C₂²×C₆₇	1	2	yes	—
689	#388	C₂²×C₆₇	1	2	yes	—
690	#388	C₂²×C₆₇	1	1	yes	characteristic
691	#388	C₂²×C₆₇	1	2	yes	—
692	#388	C₂²×C₆₇	1	1	yes	characteristic
693	#388	C₂²×C₆₇	1	2	yes	—
694	#387	C₂²×C₆₇	1	2	yes	—
695	#387	C₂²×C₆₇	1	2	yes	—
696	#387	C₂²×C₆₇	1	2	yes	—
697	#386	C₂²×C₆₇	1	2	yes	—
698	#386	C₂²×C₆₇	1	2	yes	—
699	#386	C₂²×C₆₇	1	2	yes	—
700	#386	C₂²×C₆₇	1	2	yes	—
701	#386	C₂²×C₆₇	1	2	yes	—
702	#386	C₂²×C₆₇	1	2	yes	—
703	#386	C₂²×C₆₇	1	2	yes	—
704	#386	C₂²×C₆₇	1	2	yes	—
705	#386	C₂²×C₆₇	1	1	yes	characteristic
706	#386	C₂²×C₆₇	1	2	yes	—
707	#386	C₂²×C₆₇	1	1	yes	characteristic
708	#385	C₂²×C₆₇	1	2	yes	—
709	#385	C₂²×C₆₇	1	2	yes	—
710	#381	C₂²×C₆₇	1	2	yes	—
711	#380	C₂²×C₆₇	1	1	yes	characteristic
712	#380	C₂²×C₆₇	1	1	yes	characteristic
713	#380	C₂²×C₆₇	1	1	yes	characteristic
714	#380	C₂²×C₆₇	1	1	yes	characteristic
715	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
716	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
717	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
718	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
719	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
720	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
721	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
722	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
723	C₂×#95	C₂²×C₆₇	1	2	yes	—
724	C₂×#41	—	2	4	no	—
725	C₂×#41	—	2	4	no	—
726	C₂×#41	—	2	4	no	—
727	C₂×#41	—	2	4	no	—
728	C₂×#41	—	4	2	no	—
729	C₂×#41	—	4	2	no	—
730	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
731	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
732	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
733	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
734	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
735	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
736	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
737	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
738	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
739	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
740	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
741	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
742	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
743	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
744	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
745	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
746	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
747	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
748	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
749	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
750	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
751	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
752	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
753	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
754	C₄⋊Q₈	—	2	4	no	—
755	#127	—	2	8	no	—
756	#127	—	2	4	no	—
757	#124	—	2	8	no	—
758	#124	—	2	8	no	—
759	#124	—	4	4	no	—
760	#123	—	2	8	no	—
761	C₂²⋊Q₈	—	2	4	no	—
762	#121	—	2	8	no	—
763	#121	—	2	4	no	—
764	#121	—	2	8	no	—
765	#121	—	2	4	no	—
766	#121	—	2	4	no	—
767	#121	—	2	8	no	—
768	#121	—	4	4	no	—
769	#121	—	4	2	no	—
770	#121	D₄×C₆₇	1	8	yes	complemented
771	C₄×Q₈	—	2	4	no	—
772	C₄×D₄	—	2	4	no	—
773	C₄×D₄	—	2	4	no	—
774	C₄×D₄	—	2	4	no	—
775	C₄×D₄	—	2	8	no	—
776	C₄×D₄	—	4	2	no	—
777	C₄×D₄	—	4	2	no	—
778	C₄×D₄	—	4	4	no	—
779	#117	—	2	4	no	—
780	#117	—	2	4	no	—
781	#117	—	2	8	no	—
782	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
783	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
784	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
785	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
786	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
787	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
788	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
789	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
790	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
791	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
792	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
793	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
794	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
795	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
796	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
797	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
798	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
799	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
800	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
801	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
802	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
803	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
804	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
805	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
806	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
807	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
808	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
809	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
810	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
811	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
812	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
813	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
814	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
815	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
816	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
817	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
818	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
819	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
820	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
821	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
822	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
823	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
824	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
825	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
826	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
827	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
828	C₂×C₄²	—	4	2	no	—
829	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
830	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
831	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
832	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
833	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
834	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
835	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
836	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
837	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
838	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
839	#95	C₂³×C₆₇	1	1	yes	characteristic
840	#95	C₂³×C₆₇	1	2	yes	—
841	#95	C₂³×C₆₇	1	2	yes	—
842	#95	C₂³×C₆₇	1	2	yes	—
843	#95	C₂³×C₆₇	1	1	yes	characteristic
844	#95	C₂³×C₆₇	1	1	yes	characteristic
845	#95	C₂³×C₆₇	1	2	yes	—
846	#95	C₂³×C₆₇	1	1	yes	characteristic
847	#95	C₂³×C₆₇	1	2	yes	—
848	#95	C₂³×C₆₇	1	2	yes	—
849	#95	C₂³×C₆₇	1	2	yes	—
850	#95	C₂³×C₆₇	1	2	yes	—
851	#95	C₂³×C₆₇	1	1	yes	characteristic
852	#95	C₂³×C₆₇	1	2	yes	—
853	#95	C₂³×C₆₇	1	1	yes	characteristic
854	#95	C₂³×C₆₇	1	2	yes	—
855	#95	C₂³×C₆₇	1	2	yes	—
856	#95	C₂³×C₆₇	1	2	yes	—
857	#95	C₂³×C₆₇	1	2	yes	—
858	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
859	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
860	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
861	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
862	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
863	#41	—	4	16	no	—
864	#41	—	4	16	no	—
865	C₂×Q₈	—	2	2	no	—
866	C₂×Q₈	—	2	4	no	—
867	C₂×Q₈	—	2	2	no	—
868	C₂×Q₈	—	4	2	no	—
869	C₂×Q₈	—	4	2	no	—
870	C₂×Q₈	#41×C₆₇	1	4	yes	—
871	C₂×D₄	—	2	2	no	—
872	C₂×D₄	—	2	2	no	—
873	C₂×D₄	—	2	4	no	—
874	C₂×D₄	—	2	4	no	—
875	C₂×D₄	—	2	4	no	—
876	C₂×D₄	—	2	4	no	—
877	C₂×D₄	—	2	4	no	—
878	C₂×D₄	—	2	2	no	—
879	C₂×D₄	—	2	4	no	—
880	C₂×D₄	—	2	2	no	—
881	C₂×D₄	—	2	2	no	—
882	C₂×D₄	—	2	2	no	—
883	C₂×D₄	—	2	2	no	—
884	C₂×D₄	—	2	4	no	—
885	C₂×D₄	—	2	4	no	—
886	C₂×D₄	—	2	4	no	—
887	C₂×D₄	—	2	2	no	—
888	C₂×D₄	—	2	2	no	—
889	C₂×D₄	—	2	2	no	—
890	C₂×D₄	—	4	1	no	—
891	C₂×D₄	—	4	2	no	—
892	C₂×D₄	—	4	2	no	—
893	C₂×D₄	—	4	2	no	—
894	C₂×D₄	—	4	1	no	—
895	C₂×D₄	—	4	1	no	—
896	C₂×D₄	—	4	2	no	—
897	C₂×D₄	—	4	1	no	—
898	C₂×D₄	—	4	2	no	—
899	C₂×D₄	—	4	2	no	—
900	C₂×D₄	—	4	2	no	—
901	C₂×D₄	—	4	2	no	—
902	C₂×D₄	—	4	2	no	—
903	C₂×D₄	—	4	2	no	—
904	C₂×D₄	—	4	2	no	—
905	C₂×D₄	—	4	2	no	—
906	C₂×D₄	—	4	2	no	—
907	C₂×D₄	—	4	2	no	—
908	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
909	C₂×D₄	C₂×D₄×C₆₇	1	8	yes	—
910	C₂²×C₄	—	2	2	no	—
911	C₂²×C₄	—	2	2	no	—
912	C₂²×C₄	—	2	4	no	—
913	C₂²×C₄	—	2	4	no	—
914	C₂²×C₄	—	2	2	no	—
915	C₂²×C₄	—	2	4	no	—
916	C₂²×C₄	—	2	2	no	—
917	C₂²×C₄	—	2	2	no	—
918	C₂²×C₄	—	2	2	no	—
919	C₂²×C₄	—	2	4	no	—
920	C₂²×C₄	—	2	4	no	—
921	C₂²×C₄	—	2	4	no	—
922	C₂²×C₄	—	2	2	no	—
923	C₂²×C₄	—	2	2	no	—
924	C₂²×C₄	—	2	2	no	—
925	C₂²×C₄	—	2	2	no	—
926	C₂²×C₄	—	2	4	no	—
927	C₂²×C₄	—	4	1	no	—
928	C₂²×C₄	—	4	1	no	—
929	C₂²×C₄	—	4	2	no	—
930	C₂²×C₄	—	4	2	no	—
931	C₂²×C₄	—	4	1	no	—
932	C₂²×C₄	—	4	1	no	—
933	C₂²×C₄	—	4	2	no	—
934	C₂²×C₄	—	4	2	no	—
935	C₂²×C₄	—	4	2	no	—
936	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
937	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
938	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
939	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
940	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
941	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
942	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
943	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
944	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
945	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
946	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
947	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
948	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
949	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
950	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
951	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
952	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
953	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
954	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
955	C₄⋊C₄	—	2	2	no	—
956	C₄⋊C₄	—	2	2	no	—
957	C₄⋊C₄	—	2	4	no	—
958	C₄⋊C₄	—	2	2	no	—
959	C₄⋊C₄	—	2	2	no	—
960	C₄⋊C₄	—	2	4	no	—
961	C₄⋊C₄	—	2	2	no	—
962	C₄⋊C₄	—	2	4	no	—
963	C₄⋊C₄	—	2	4	no	—
964	C₄⋊C₄	—	2	2	no	—
965	C₄⋊C₄	—	4	1	no	—
966	C₄⋊C₄	—	4	2	no	—
967	C₄⋊C₄	—	4	2	no	—
968	C₄⋊C₄	—	4	1	no	—
969	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
970	C₄⋊C₄	#41×C₆₇	1	4	yes	complemented
971	C₂²⋊C₄	—	2	4	no	—
972	C₂²⋊C₄	—	2	4	no	—
973	C₂²⋊C₄	—	2	2	no	—
974	C₂²⋊C₄	—	2	2	no	—
975	C₂²⋊C₄	—	2	4	no	—
976	C₂²⋊C₄	—	2	4	no	—
977	C₂²⋊C₄	—	2	2	no	—
978	C₂²⋊C₄	—	2	4	no	—
979	C₂²⋊C₄	—	2	2	no	—
980	C₂²⋊C₄	—	2	2	no	—
981	C₂²⋊C₄	—	2	2	no	—
982	C₂²⋊C₄	—	2	4	no	—
983	C₂²⋊C₄	—	2	4	no	—
984	C₂²⋊C₄	—	2	4	no	—
985	C₂²⋊C₄	—	2	4	no	—
986	C₂²⋊C₄	—	2	2	no	—
987	C₂²⋊C₄	—	2	4	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	—	4	1	no	—
990	C₂²⋊C₄	—	4	2	no	—
991	C₂²⋊C₄	—	4	1	no	—
992	C₂²⋊C₄	—	4	2	no	—
993	C₂²⋊C₄	—	4	2	no	—
994	C₂²⋊C₄	—	4	2	no	—
995	C₂²⋊C₄	—	4	2	no	—
996	C₂²⋊C₄	—	4	2	no	—
997	C₂²⋊C₄	—	4	2	no	—
998	C₂²⋊C₄	—	4	2	no	—
999	C₂²⋊C₄	—	4	2	no	—
1000	C₂²⋊C₄	C₂×D₄×C₆₇	1	8	yes	—
1001	C₄²	—	2	4	no	—
1002	C₄²	—	2	4	no	—
1003	C₄²	—	2	2	no	—
1004	C₄²	—	2	4	no	—
1005	C₄²	—	2	2	no	—
1006	C₄²	—	2	2	no	—
1007	C₄²	—	2	2	no	—
1008	C₄²	—	2	4	no	—
1009	C₄²	—	4	1	no	—
1010	C₄²	—	4	1	no	—
1011	C₂³	—	2	2	no	—
1012	C₂³	—	2	1	no	—
1013	C₂³	—	2	2	no	—
1014	C₂³	—	2	1	no	—
1015	C₂³	—	2	1	no	—
1016	C₂³	—	2	2	no	—
1017	C₂³	—	2	2	no	—
1018	C₂³	—	2	1	no	—
1019	C₂³	—	2	2	no	—
1020	C₂³	—	2	1	no	—
1021	C₂³	—	2	1	no	—
1022	C₂³	—	2	2	no	—
1023	C₂³	—	2	1	no	—
1024	C₂³	—	2	1	no	—
1025	C₂³	—	2	2	no	—
1026	C₂³	—	2	1	no	—
1027	C₂³	—	2	2	no	—
1028	C₂³	—	2	1	no	—
1029	C₂³	—	2	1	no	—
1030	C₂³	—	2	1	no	—
1031	C₂³	—	2	2	no	—
1032	C₂³	—	2	1	no	—
1033	C₂³	—	2	2	no	—
1034	C₂³	—	2	1	no	—
1035	C₂³	—	2	1	no	—
1036	C₂³	—	2	1	no	—
1037	C₂³	—	2	2	no	—
1038	C₂³	—	2	1	no	—
1039	C₂³	—	2	2	no	—
1040	C₂³	—	2	2	no	—
1041	C₂³	—	2	1	no	—
1042	C₂³	—	2	1	no	—
1043	C₂³	—	2	1	no	—
1044	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1045	C₂³	C₂²×D₄×C₆₇	1	4	yes	—
1046	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
1047	Q₈	—	2	8	no	—
1048	Q₈	—	8	4	no	—
1049	D₄	—	2	8	no	—
1050	D₄	—	4	8	no	—
1051	D₄	—	4	8	no	—
1052	D₄	—	4	8	no	—
1053	D₄	—	4	4	no	—
1054	D₄	—	4	8	no	—
1055	D₄	—	4	4	no	—
1056	D₄	—	4	4	no	—
1057	D₄	—	4	4	no	—
1058	D₄	—	8	4	no	—
1059	D₄	—	8	4	no	—
1060	D₄	—	8	4	no	—
1061	D₄	—	8	4	no	—
1062	C₂×C₄	—	2	1	no	—
1063	C₂×C₄	—	2	1	no	—
1064	C₂×C₄	—	2	2	no	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	2	1	no	—
1067	C₂×C₄	—	2	1	no	—
1068	C₂×C₄	—	2	2	no	—
1069	C₂×C₄	—	2	1	no	—
1070	C₂×C₄	—	2	2	no	—
1071	C₂×C₄	—	2	1	no	—
1072	C₂×C₄	—	2	1	no	—
1073	C₂×C₄	—	2	1	no	—
1074	C₂×C₄	—	2	1	no	—
1075	C₂×C₄	—	2	2	no	—
1076	C₂×C₄	—	2	8	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	2	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	2	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	2	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	2	no	—
1086	C₂×C₄	—	2	2	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	1	no	—
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	2	2	no	—
1092	C₂×C₄	—	2	1	no	—
1093	C₂×C₄	—	2	2	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	2	1	no	—
1096	C₂×C₄	—	2	2	no	—
1097	C₂×C₄	—	2	1	no	—
1098	C₂×C₄	—	2	2	no	—
1099	C₂×C₄	—	2	1	no	—
1100	C₂×C₄	—	2	1	no	—
1101	C₂×C₄	—	2	2	no	—
1102	C₂×C₄	—	2	1	no	—
1103	C₂×C₄	—	2	2	no	—
1104	C₂×C₄	—	2	2	no	—
1105	C₂×C₄	—	2	1	no	—
1106	C₂×C₄	—	2	1	no	—
1107	C₂×C₄	—	4	8	no	—
1108	C₂×C₄	—	4	8	no	—
1109	C₂×C₄	—	4	8	no	—
1110	C₂×C₄	—	4	4	no	—
1111	C₂×C₄	—	4	4	no	—
1112	C₂×C₄	—	4	4	no	—
1113	C₂×C₄	—	4	4	no	—
1114	C₂×C₄	—	8	4	no	—
1115	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1116	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
1117	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1118	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1119	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1120	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1121	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
1122	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1123	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
1124	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
1125	C₂²	—	2	2	no	—
1126	C₂²	—	2	4	no	—
1127	C₂²	—	2	4	no	—
1128	C₂²	—	2	2	no	—
1129	C₂²	—	2	2	no	—
1130	C₂²	—	2	4	no	—
1131	C₂²	—	4	2	no	—
1132	C₂²	—	4	1	no	—
1133	C₂²	—	4	1	no	—
1134	C₂²	—	4	2	no	—
1135	C₂²	—	4	2	no	—
1136	C₂²	—	4	1	no	—
1137	C₂²	—	4	1	no	—
1138	C₂²	—	4	2	no	—
1139	C₂²	—	4	1	no	—
1140	C₂²	—	4	1	no	—
1141	C₂²	—	4	2	no	—
1142	C₂²	—	4	1	no	—
1143	C₂²	—	4	2	no	—
1144	C₂²	—	4	1	no	—
1145	C₂²	—	4	2	no	—
1146	C₂²	—	4	1	no	—
1147	C₂²	—	4	1	no	—
1148	C₂²	—	4	1	no	—
1149	C₂²	—	4	2	no	—
1150	C₂²	—	4	1	no	—
1151	C₂²	—	4	1	no	—
1152	C₂²	—	4	2	no	—
1153	C₂²	—	4	1	no	—
1154	C₂²	—	4	1	no	—
1155	C₂²	—	4	2	no	—
1156	C₂²	—	4	1	no	—
1157	C₂²	—	4	1	no	—
1158	C₂²	—	4	1	no	—
1159	C₂²	—	4	2	no	—
1160	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1161	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
1162	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
1163	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1164	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1165	C₂²	#585×C₆₇	1	1	yes	characteristic
1166	C₂²	#585×C₆₇	1	1	yes	characteristic
1167	C₄	—	2	2	no	—
1168	C₄	—	2	2	no	—
1169	C₄	—	2	4	no	—
1170	C₄	—	2	2	no	—
1171	C₄	—	2	2	no	—
1172	C₄	—	2	4	no	—
1173	C₄	—	2	2	no	—
1174	C₄	—	4	1	no	—
1175	C₄	—	4	2	no	—
1176	C₄	—	4	1	no	—
1177	C₄	—	4	1	no	—
1178	C₄	—	4	2	no	—
1179	C₄	—	4	2	no	—
1180	C₄	—	4	1	no	—
1181	C₄	—	4	2	no	—
1182	C₄	—	4	1	no	—
1183	C₄	—	4	1	no	—
1184	C₄	#546×C₆₇	1	4	yes	—
1185	C₂	—	4	2	no	—
1186	C₂	—	4	4	no	—
1187	C₂	—	8	1	no	—
1188	C₂	—	8	2	no	—
1189	C₂	—	8	1	no	—
1190	C₂	C₂×#546×C₆₇	1	1	yes	characteristic
1191	C₂	D₄×#41×C₆₇	1	1	yes	characteristic
1192	C₂	C₆₇×#3483	1	1	yes	characteristic
1193	C₂	C₆₇×#3496	1	1	yes	characteristic
1194	C₂	C₆₇×#3506	1	1	yes	characteristic
1195	C₂	C₆₇×#3524	1	1	yes	characteristic
1196	C₂	C₆₇×#3542	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. C₂×#555×C₆₇	C₂	semidirect
2. C₂×#550×C₆₇	C₂	semidirect
3. C₆₇×#2686	C₂	semidirect
4. C₆₇×#2673	C₂	semidirect
5. C₆₇×#2555	C₂	semidirect
6. C₆₇×#2544	C₂	semidirect
7. C₆₇×#2543	C₂	semidirect
8. C₆₇×#2491	C₂	semidirect
9. C₆₇×#2485	C₂	semidirect
10. C₆₇×#2476	C₂	semidirect
11. C₆₇×#2459	C₂	semidirect
12. C₆₇×#2451	C₂	semidirect
13. C₆₇×#2445	C₂	semidirect
14. C₆₇×#2428	C₂	semidirect
15. C₆₇×#2414	C₂	semidirect
16. C₆₇×#2407	C₂	semidirect
17. C₆₇×#2407	C₂	semidirect
18. C₆₇×#2362	C₂	semidirect
19. C₆₇×#2359	C₂	semidirect
20. C₆₇×#2339	C₂	semidirect
21. C₄×#121×C₆₇	C₂	semidirect
22. C₄×#121×C₆₇	C₂	semidirect
23. C₆₇×#2297	C₂	semidirect
171. #121×C₆₇	D₄	semidirect
371. C₄⋊C₄×C₆₇	#41	semidirect
586. #59810	C₆₇	direct (N × H)
599. C₂×#555	C₂×C₆₇	semidirect
600. C₂×#550	C₂×C₆₇	semidirect
601. #2686	C₂×C₆₇	semidirect
602. #2673	C₂×C₆₇	semidirect
603. #2555	C₂×C₆₇	semidirect
604. #2544	C₂×C₆₇	semidirect
605. #2543	C₂×C₆₇	semidirect
606. #2491	C₂×C₆₇	semidirect
607. #2485	C₂×C₆₇	semidirect
608. #2476	C₂×C₆₇	semidirect
609. #2459	C₂×C₆₇	semidirect
610. #2451	C₂×C₆₇	semidirect
611. #2445	C₂×C₆₇	semidirect
612. #2428	C₂×C₆₇	semidirect
613. #2414	C₂×C₆₇	semidirect
614. #2407	C₂×C₆₇	semidirect
615. #2407	C₂×C₆₇	semidirect
616. #2362	C₂×C₆₇	semidirect
617. #2359	C₂×C₆₇	semidirect
618. #2339	C₂×C₆₇	semidirect
619. C₄×#121	C₂×C₆₇	semidirect
620. C₄×#121	C₂×C₆₇	semidirect
621. #2297	C₂×C₆₇	semidirect
622. C₆₇	#59810	direct (N × H)
770. #121	D₄×C₆₇	semidirect
970. C₄⋊C₄	#41×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#555×C₆₇	2
C₂×#550×C₆₇	2
C₆₇×#2686	2
C₆₇×#2673	2
C₆₇×#2555	2
C₆₇×#2544	2
C₆₇×#2543	2
C₆₇×#2491	2
C₆₇×#2485	2
C₆₇×#2476	2
C₆₇×#2459	2
C₆₇×#2451	2
C₆₇×#2445	2
C₆₇×#2428	2
C₆₇×#2414	2
C₆₇×#2407	2
C₆₇×#2362	2
C₆₇×#2359	2
C₆₇×#2339	2
C₄×#121×C₆₇	2
C₆₇×#2297	2
#59810	67

Subgroups — C67×#59810 #30739061

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#59810 #30739061